COMPARING DISCOUNTINUITY SURFACE ROUGHNESS DERIVED … · interpolated as a 3D virtual surface...

COMPARING DISCOUNTINUITY SURFACE ROUGHNESS DERIVED FROM 3D TERRESTRIAL LASER SCAN DATA

WITH TRADITIONAL FIELD-BASED METHODS

Ephrem Kinfe Tesfamariam February, 2007

Comparing discontinuity surface roughness derived from 3D terrestrial laser scan data with traditional field-based

methods

by

Ephrem Kinfe Tesfamariam Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation, Specialisation: Geological engineering Thesis Assessment Board Prof. Dr. F.D. van der Meer (Chairman) Prof. Dr. S.B. Kroonenberg (External Examiner) Ir. Siefko Slob (1st Supervisor) Dr. H.R.G.K. Hack (2nd Supervisor) Observer: Drs. J.D. de Smeth (Programme director)

INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION ENSCHEDE, THE NETHERLANDS

Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute.

��

��

��

��

��

��

��

��

��

i

Abstract

Discontinuity surface roughness estimation is very important in determining the Hydro-mechanical properties of rock masses. The normal ways of roughness estimation have been made traditionally by visual and simple instrumental field observations. These methods may require physical access to the exposed rock faces. This may expose field personnel to hazardous situations because the measurements have to be carried out below steep rock face, in a quarry or tunnel. The higher parts of a steep exposed rock face are also often difficult to reach. These traditional methods are also time consuming and subjective. This presentation describes a new method by which 3D point cloud data obtained by laser scanning can be used to model and determine discontinuity surface roughness in an automated way with high detail, high accuracy, and no human bias. The laser scan technique is also much faster and safer than the traditional field-based methods, since no direct physical access is needed to the rock face. In order to determine the surface roughness from the 3D laser scan point cloud data, two point cloud data sets with an average spatial resolution of 1cm and 6cm are used. These point data sets are interpolated as a 3D virtual surface model using a scattered data interpolation technique. To extract the 3D surface roughness from the 3D virtual surface model the mean orientation of circular windows with diameter of 5, 10, 20 and 40 cm was computed. The large-scale directional roughness also extracted by cropping and fitting narrow strips using curve fitting techniques. The results revealed that laser scan data can be used to model and estimate rock surface roughness. The extracted directional large-scale roughness profiles are comparable and can be used in rock mass index classification system. These can be used also to estimate roughness using the standard reference roughness determination profiles. However it is difficult to compare the field-based discs orientation with the circular windows mean orientation of the laser scan data. This is due to the low resolution point cloud data set and possible shifting of the exact location of the sample grid. The field-base instrument error and the dead zone due to inclination of undulations with respect to the scanner position have also appreciable influence in the possible relation of these methods. Key words: Laser scanning, Rock mass, 3D modelling, Roughness quantification

ii

Acknowledgements

My heart felt gratitude is due, to ITC (International Institute for Geo-information Science and Earth Observation) for enabling me to pursue my Master Program study by providing academic and financial supports. I would like to thank also my employing organization WRDB (Water Resources Development Bureau) for giving me this opportunity to study at ITC. Above all I am Indebted to my first supervisor, Ir. S. Slob, for his unceasing support and care during the whole study and thesis time. I benefited a lot from discussions I had with him owing to which I gained a deeper insight into and understanding of noisy point cloud data approximation theory and other areas of geo-engineering principles. I was never hesitant to discus with him openly mainly because of his very ‘accommodating’ and ‘cheerful’ outlook. I would like to thank Dr. H.R.G.K Hack., My second supervisor who taught me many of the aspects of this research, for his scientific comments and critically editing part of this thesis. Conversation with Ir. Dr. N. Rengers helped me to motivate development of the methodology in choosing the traditional way of roughness measurement, especially in compass and disc-clinometer method of roughness analysis of this study and is greatly appreciated. I would like to thank Dr. Paul Van Dijk for this continuous support during my studies at ITC. Drs. Boudewijn de Smeth the programme director of AES is also thanked for his critical comments and encouragement for the MSc day of ITC. I am indebted to you de Smeth. Thanks to all lecturers in AES programme, and to all my lovely international friends; Mam, Waw, Pook, Maria, Martin, Andrea, Sujan, Alidu, Data, Shreekamal, and Shahjahan. Not forgotten to Ethiopian students in ITC thanks for your support. Finally special gratitude to all my Ethiopian friends, especially Mr. Kulata, Hailu, Mulugeta, Sahlessilassie, Sisay; and family, Alemnesh, Mulugeta, Afework, Mearg and Almaz. My highest honour goes to Almighty God for being caring and loving father to me.

iii

Table of contents

1. INTRODUCTION......................................................................................................................................... 1

1.1. RESEARCH BACKGROUND...................................................................................................................... 1 1.2. RESEARCH PROBLEM ............................................................................................................................. 3 1.3. RESEARCH OBJECTIVE........................................................................................................................... 3

1.3.1. Specific objectives............................................................................................................................ 3 1.4. RESEARCH QUESTIONS .......................................................................................................................... 4 1.5. RESEARCH HYPOTHESIS......................................................................................................................... 4 1.6. LIMITATION OF THE RESEARCH .............................................................................................................. 5 1.7. STRUCTURE OF THE THESIS.................................................................................................................... 5

2. REVIEW OF ROUGHNESS MEASUREMENT METHODS ................................................................. 7

2.1. DISCONTINUITY SURFACE ROUGHNESS DATA ACQUISITION METHODS.................................................... 8 2.1.1. Contact methods .............................................................................................................................. 8 2.1.2. Non contact (remote sensing) methods .......................................................................................... 11

2.2. DISCONTINUITY SURFACE ROUGHNESS DETERMINATION METHODS..................................................... 13 2.2.1. Observational or Qualitative method ............................................................................................ 13 2.2.2. Quantitative methods ..................................................................................................................... 17

3. FIELD PROCEDURES AND EQUIPMENT USED IN ROUGHNESS MEASUREMENTS ............. 27

3.1. INTRODUCTION .................................................................................................................................... 27 3.2. DESCRIPTION OF THE SCAN DISCONTINUITY SURFACE AND SAMPLE AREA LOCATION........................... 27 3.3. COMPASS AND DISC-CLINOMETER ....................................................................................................... 28

3.3.1. Roughness acquisition procedure.................................................................................................. 29 3.4. STRAIGHT EDGE................................................................................................................................... 29

3.4.1. Roughness acquisition procedure.................................................................................................. 30 3.5. RIEGL 3D IMAGING SENSOR-LMS-Z420I ............................................................................................. 30

3.5.1. Scanning procedure ....................................................................................................................... 31

4. METHODOLOGY ..................................................................................................................................... 33

4.1. DETERMINATION OF DESIRE DIRECTION ............................................................................................... 34 4.2. COORDINATE ROTATION ...................................................................................................................... 36 4.3. DISCONTINUITY SURFACE RECONSTRUCTION (INTERPOLATION) .......................................................... 37

4.3.1. FastRBF scattered data interpolation technique ........................................................................... 37 4.3.2. Low pass filtering approach to smoothing..................................................................................... 39

4.4. DETERMINATION OF MEAN ORIENTATION OF A GIVEN CIRCULAR WINDOW DIAMETER.......................... 40 4.5. DIRECTIONAL ROCK SURFACE ROUGHNESS DETERMINATION ............................................................... 41 4.6. RANGE MEASUREMENT ERROR ESTIMATION ........................................................................................ 42 4.7. VISUALIZATION ................................................................................................................................... 42

5. DATA ANALYSIS AND RESULTS.......................................................................................................... 45

5.1. DATA PREPARATION ............................................................................................................................ 45 5.2. DATA PROCESSING AND VISUALIZATION.............................................................................................. 46

5.2.1. Geometric correction..................................................................................................................... 46 5.2.2. Surface reconstruction................................................................................................................... 47 5.2.3. Directional roughness profile reconstruction................................................................................ 51

5.3. ROUGHNESS QUANTIFICATION ............................................................................................................. 55

iv

5.3.1. Reconstructed surface roughness quantification ........................................................................... 55 5.3.2. Directional roughness quantification ............................................................................................ 64

5.4. RANGE MEASUREMENT ERROR ESTIMATION ........................................................................................ 68 5.5. ESTIMATION OF SMALL SCALE ROUGHNESS USING INTENSITY.............................................................. 72

6. COMPARISION WITH THE TRADITIONAL METHODS ................................................................. 73

6.1. COMPARISON WITH THE COMPASS AND DISC-CLINOMETER METHOD.................................................... 73 6.2. COMPARISON WITH THE FIELD OBSERVATIONAL RESULTS ................................................................... 81 6.3. COMPARISON WITH THE STRAIGHT EDGE METHOD ............................................................................... 81

7. CONCLUSIONS AND RECOMMENDATIONS .................................................................................... 83

7.1. SURFACE MODEL INTERPOLATION AND QUANTIFICATION..................................................................... 83 7.2. DIRECTIONAL ROUGHNESS MODEL CONSTRUCTION AND QUANTIFICATION .......................................... 84 7.3. LIMITATIONS AND RECOMMENDATIONS FOR THIS STUDY ..................................................................... 85 7.4. RECOMMENDATIONS FOR THE FUTURE STUDY DIRECTIONS: ................................................................ 86

REFERENCES USED......................................................................................................................................... 89

APPENDICES........................................................................................................................................................ I

APPENDIX 1 DATA SET OF TEILFER QUARRY, LUSTIN, BELGIUM........................................................................... I APPENDIX 2 DESCRIPTION OF FASTRBF FUNCTIONS AND MATLAB CURVE FITTING TOOL BOX ..........................VII APPENDIX 3 SCRIPTS OF MATLAB CODES & COMMAND LINES FOR THE IMPLEMENTATION OF METHODOLOGY.XIX APPENDIX 4 RECONSTRUCTED SURFACES WITH DIFFERENT FILTER WIDTH ................................................... XXVII APPENDIX 5 SENSITIVITY ANALYSIS RESULTS ................................................................................................ XXIX APPENDIX 6 COMPARISON OF MEASURED WITH LASER DERIVED DATA AND STEREOPLOTS ............................XXXV APPENDIX 7 RECONSTRUCTED NARROW STRIP PROFILES ........................................................................... XXXVIII

v

List of figures

Figure 1- 1 Simplified bilinear shear criterion for a discontinuty asperities ..........................................1 Figure 2- 1 A method of recording roughness in 3D using circular discs ...............................................9 Figure 2- 2 Practical measurement of joint wall waviness or undulation..............................................10 Figure 2- 3 Alternative method for estimating JRC from measurement of roughness amplitude .........11 Figure 2- 4 Typical roughness profiles for a range of JRC....................................................................15 Figure 2- 5 Typical ISRM profiles and Suggested nomenclatures ........................................................15 Figure 2- 6 Laubscher’s roughness profiles ..........................................................................................15 Figure 2- 7 Large and small scale roughness profiles for SSPC............................................................16 Figure 2- 8 Tilt test for measuring JRC .................................................................................................18 Figure 2- 9 Illustration of self-similar and self-affine fractals...............................................................22 Figure 2- 10 Double log graph of S(w) versus w....................................................................................23 Figure 2- 11 Correlations between Z2 and JRC; SF and JRC ................................................................24 Figure 3- 1 Schematic geological map of southern Belgium with location of the scan outcrop ...........28 Figure 3- 2 Location map of the scan discontinuity rock surface and selected sample area .................28 Figure 3- 3 The smallest and the largest base plates for measuring roughness .....................................29 Figure 3- 4 Straight edges for measurement of waviness ......................................................................30 Figure 3- 5 3D RIEGL LMS-Z420i scanner and its major components of the laser system .................31 Figure 4- 1 Summarized overall research design ...................................................................................33 Figure 4- 2 The relationship between an inclined and horizontal plane ................................................35 Figure 4- 3 Vector rotation around the Z-axis by angle � and its matrix representation .......................36 Figure 4- 4 Simulation of rotation around the Z-axis and X-axis ..........................................................37 Figure 4- 5 Fitting accuracy and evaluation accuracy............................................................................39 Figure 4- 6 Determination of the mean orientation of a given circular window size. ...........................40 Figure 4- 7 Methodology for determination of the maximum amplitude and i-angle............................41 Figure 4- 8 Overall research methodology.............................................................................................43 Figure 5- 1 Overview laserscan of a large bedding surface taken by Riegl 3D -LMS-Z420i................46 Figure 5- 2 Rotated and cropped raw laser scan data.set of crop01 and crop02....................................49 Figure 5- 3 Example of unfiltered reconstructed surface data of Crop02..............................................50 Figure 5- 4 Example of filtered with 1cm filter width reconstructed surface data of Crop02...............50 Figure 5- 5 Evaluation of 5mm and 10mm width narrow strip profile of crop02 raw data. ..................51 Figure 5- 6 The difference between the Delaunay, spline and shape-preserving interpolant ................53 Figure 5- 7 Example of the smoothed raw data and interpolated profiles of crop02.............................53 Figure 5- 8 Similarity between cubic spline and shape-preserving interpolant .....................................54 Figure 5- 9 Example of the narrow strip of reconstructed surface of crop02 ........................................55 Figure 5- 10 Example of the narrow strip of reconstructed surface of crop01 ......................................55 Figure 5- 11 Polar equal area plots of poles from crop02 laser scan data . ...........................................58 Figure 5- 12 Comparison of effective i-angle of raw, 1cm filtered, and 3cm filtered data of crop02...59 Figure 5- 13 The power law relations between S(w) and w of crop01 and crop02 data set...................60 Figure 5- 14 The delta angle of standard deviation of normal vector orientation deviation due to RBF

srface fitting before and after the raw data has been rotated into a horizontal position. ..61 Figure 5- 15 3D scatter plot of normal vector orientation deviation due to RBF surface fitting before

and after the raw data has been rotated into a horizontal position ....................................62

vi

Figure 5- 16 Example of 3D scatter plot of normal vector orientation deviation due to up-shifting.... 63 Figure 5- 17 Estimating JRC and waviness factor (jw) from measurement of roughness amplitude

(amax) for narrow raw data strip profile and sommthed raw data. ..................................... 66 Figure 5- 18 Estimating JRC and waviness factor (jw) from measurement of roughness amplitude

(amax) for narrow strip profiles of reconstructed surface of crop01 and crop02 ............. 67 Figure 5- 19 Power law relations between S(w) and w for crop02........................................................ 69 Figure 5- 20 Estimated JRC difference from measurement of roughness amplitude (amax) for raw data

strip profile and reconstructed surface strip profiles of crop02 ....................................... 71 Figure 6- 1 Polar equal area plots of poles from discs and laser scan derived from crop01................. 75 Figure 6- 2 2D scatter plot of laser scan derived versus measured dip amount .................................... 76 Figure 6- 3 3D scatter plot of the delta angle of deviation of measured normal vector orientation from

laser derived.in magnitude................................................................................................ 77 Figure 6- 4 Histograms of delta angle of standard deviation between measured and derived.............. 78 Figure 6- 5 Plot of i-angle versus window diameter of crop01, crop02 and measured......................... 80 Figure 6- 6 Estimating JRC and waviness factor (jw) from measurement of roughness amplitude (amax)

from 1m straight edge and narrow strip profiles of reconstructed surface of crop01 . .... 82

vii

List of tables

Table 2- 1 Summary of surface roughness data acquisition and determination methods........................7 Table 2- 2 Characterization of the joint planarity as suggested by Palmström (1995) ..........................10 Table 2- 3 ISRM roughness categories .................................................................................................14 Table 2- 4 Discontinuity characterization for sliding criterion in SSPC ...............................................17 Table 3- 1 Scanner settings and configurations during scanning...........................................................31 Table 5- 1 List of data sets used.............................................................................................................45 Table 5- 2 List of the two cropped data sets with their dimensions used for the analysis.....................46 Table 5- 3 The goodness of fit statistics for different fit models of Curve Fitting techniques..............53 Table 5- 4 The goodness of fit statistics for different fit models of Curve Fitting techniques..............54 Table 5- 5 Procedure of dividing the 2m2 square sub-sample into 4 inscribed circular windows.........57 Table 5- 6 Positive and negative i-angle of crop01 along the dip direction ..........................................59 Table 5- 7 Descriptive Statistics of normal vector deviation due to RBF surface fitting before and fter

the raw data has been rotated into a horizontal position for crop02 ....................................61 Table 5- 8 List of the four shifted data sets used for sensitivity analysis of possible shifting ..............63 Table 5- 9 The maximum amplitude form the residuals of crop02 raw data strip.................................65 Table 5- 10 The maximum amplitude form the residuals of crop02 smoothed raw data strip ..............65 Table 5- 11 The maximum amplitude form the residuals of crop02 and crop01 reconstructed surface

data strip ...............................................................................................................................67 Table 5- 12 Average Standard deviation of S(w) per window w of raw, unfiltered and filtered data set

of crop02 ..............................................................................................................................69 Table 5- 13 Fractal dimension and roughness amplitude of crop02 data set .........................................70 Table 5- 14 Estimation of the influence of the range measurement error using the chart developed by

Barton (1982).for crop02 .....................................................................................................71 Table 6- 1 Positive and negative i-angle for each window sizes of crop01, crop02 and field measured................................................................................................................................................................79

viii

List of symbols and abbreviations

A = Amplitude parameter D = Fractal dimension H = Hurst exponent C = Cohesion Sm = Discontinuous rock material cohesion i = Dilation angle; roughness angle I = Micro roughness angle L = Length �v = Normal displacement �m = Friction angle �disc.wall = Angel of internal friction of discontinuity wall � = Normal stress �m = Shear strength S(w) = Root mean square value of the profile height residuals on a linear trend fitted to the

sample points in a window of length w CNL = Constant Normal Load 3D = Three dimensional FsatRBF = Fast radial basis function PCA = Principal Component analysis JRC = Joint roughness coefficient ISRM = International society for rock mechanics SSPC = Slope stability classification probability �h = Horizontal displacement DSM = Digital surface measurement DTM = Digital terrain mode ACF = Auto correlation function SR = Structure function RMS = Root mean square Eq. = Equation ξ = Predefine direction

R = Schmidt hammer rebound on dry unweathered surface r = Schmidt hammer rebound on wet joint surface K = Absolute roughness CLA = Central line average Rl = Roughness profile index for 2D RA = Roughness area index for 3D α = Rengers’ roughness parameter RMi = Rock Mass index (rock mss classification) RMR = Rock Mass Rating (rock mss classification) Q’ = A modified Q-system, which is stress reduction free and where the rating given for joint

orientation are ignored Jw = Waviness of planarity (parameter in RMi)

ix

Matlab = MATrix LABoratory (a programming language for technical computing) Csaps = Cubic smoothing spline Pchip = Piecewise Cubic Hermite Interpolating Polynomial Spaps = Smoothing spline n = Normal vector npoj. = Projected normal vector (dip direction)

X = Arithmetic mean of X-coordinate

Y = Arithmetic mean of Y-coordinate

Z = Arithmetic mean of Z-coordinate θ = Azimuth angle theta

φ = Dip angle

RMS = Root mean squared PCA = Principal component analysis LPF = Low pass filtering Φ = The basic function S = Radial basis function P = Low degree polynomial, typically linear or quadratic

iλ = The radial basis function coefficient

ix = The radial basis function centres

STD = Standard deviation of the residuals VAR = Variance Ladar = Laser detection and ranging Lidar = Light detection and ranging

COMPARING DISCOUNTINUITY SURFACE ROGUHNESS DERIVED FROM 3D TERRESTRIAL LASER SCAN DATA WITH TRADITIONAL FIELD-BASED METHODS

1 1

1. Introduction

1.1. Research background

One of the most challenging tasks in engineering rock mechanics is in-situ characterization of jointed rock mass properties (Fardin et al., 2004). ‘Rock mass’ or ‘discontinuous rock mass’ are inhomogeneous and discontinuous media consisting of blocks or layers bounded by discontinuities with or with out cementation as a consequence of some certain phenomena such as genetic conditions, tectonic actions, and chemical, thermal and hydraulic changes (Ayadan and Kawamoto, 1990; Cunha, 1990; Cunha, 1992). These discontinuities in the discontinuous rock mass should be recorded in all engineering site investigations including orientation, persistence, spacing, aperture and shear strength characteristics (ISRM, 1978) because of their major influence on the hydro-mechanical properties of rock mass. The spatial variation of discontinuity surface roughness is another quantity that should be noted to quantify the likely hydro-mechanical response of the rock mass to stress and strain. The shear strength, deformation behaviour, and flow properties of the discontinuities are very much dependent on the surface roughness of the rock mass discontinuities (Kulatilake et al., 1995) and needs to be characterized in-situ accurately.

The roughness of the rock mass discontinuity is the surface irregularities or projections on a rough discontinuity surface. Patton, 1966 recognized that the asperity of a rough rock mass discontinuity surface occurs as first-order (waviness) and second-order (unevenness) categories based on their relative magnitudes. During small displacements the shear behaviour of a discontinuous rock surface is controlled primarily by the second-order asperity and then the first-order asperity governs the shearing behaviour for large displacements. The contribution of discontinuity surface roughness to the shear strength of a discontinuity can be directly measured with, for example, the shear box test usually in laboratory. Where as for large scale surfaces, theoretically the role of roughness to the shear strength can be determined using the friction angle of the material and the measurement of the discontinuity profile (Patton, 1966) as shown in the ‘bi-linear shear criterion’ below.

Figure 1- 1 Simplified bilinear shear criterion for a discontinuity with a regular set of triangular shaped asperities

(Patton, 1966 modified by Hack, 2003)

CHAPTER ONE

2 2

The terminology of shear strength along a discontinuity plane is explained in Figure 1-1 using the ‘bi-linear shear criterion’ (Patton, 1966) for a discontinuity with a regular set of triangular shaped asperities. The angle of friction (�disc.wall) along the discontinuity is a material constant depending on the texture, type of material, structure, micro roughness and degree of interlocking of the discontinuity surface at micro scale. The roughness that contributes dilatancy (opening in the direction perpendicular to the shear plane) of the discontinuity (i.e. �v) is not included in �disc.wall. The roughness that contributes dilatancy of the discontinuity is described by the angle of roughness (i-angle). The steepness of the roughness which is represented by triangular asperities in this example and the normal stress (�) across the discontinuity determine whether the asperities will break or they will be overridden. After the asperities are sheared off (break) or non fitting, the shear strength (�m) of the discontinuity wall is described by the discontinuous rock material parameters such as cohesion (Sm) and friction (�m). If there is no gluing or bounding agent between the walls of the discontinuity wall, the cohesion is described as ‘apparent cohesion’. If there any bonding agent is present, the cohesion or part of it may be ‘real cohesion’. The parameters (Sm, and �m) are normally not the same as the cohesion and angle of (internal) friction (�) of the intact rock material as described by the ‘Mohr-Coulomb failure criterion’ due to for example weathering. Generally, the material properties in the discontinuity wall are not the same as that of the intact rock. There are several and more complicated other theories about relations between roughness profiles and shear strength (Fecker and Rengers, 1971; ISRM, 1975; Barton and Choubey, 1977; Bandis et al., 1981; ISRM, 1981; Barton and Bandis, 1990; Grasselli and Egger, 2003). Many methods have been used also to measure and determine rock discontinuity surface roughness from simple to more sophisticated way (Fecker and Rengers, 1971; Weissbach, 1978; ISRM, 1981; Galante et al., 1991; Develi and Babadagli, 1998; Hack et al., 1998; Kulatilake and Um, 1999; Yilbas and Hasmi, 1999; Belem et al., 2000; Lanaro, 2000; Harrison and Rasouli, 2001; Maerz et al., 2001; Xie et al., 2001; Feng et al., 2003; Chae et al., 2004; Rahman et al., 2006). However, most of these relations between roughness and shear strength and estimation of rock discontinuity surface roughness are hampered by the scale effect (Cunha, 1990; Fadeev, 1991; Pistone, 1991; Cunha, 1992; Pinto Da Cunha, 1993; Exadaktylos, 1994; Grima, 1994; Mario Alvarez, 1994; Moon, 1994; Silberschmidt, 1994; Kulatilake, 1995; Castaing et al., 1997; Fardin et al., 2001; Rahman et al., 2006) or do not consider all the important discontinuity properties. Determination of the contribution of roughness to the shear strength is very complicated due to variations of roughness properties for discontinuity surfaces that are not exposed. Hence it is mostly impossible to obtain the roughness properties in the required detail to make it worth–while to apply sophisticated methodology (Hack, 2006).

3D laser scanning is a sophisticated active remote sensing techniques that has been used recently to derive more accurate discontinuity surface roughness (Chae et al., 2004; Fardin et al., 2004; Hong et al., 2006; Rahman et al., 2006). It is a promising tool in rock mechanics, geotechnical and geological engineering. However, practical measurements of rock surface roughness have traditionally been done by using standard reference roughness profiles and field-based analogue methods (Fecker and Rengers, 1971; ISRM, 1981; Barton and Bandis, 1990; Milne et al., 1991; Hack et al., 1998; Palmström, 2001). These traditional methods require direct contact with rock surface which may expose field personnel to hazardous conditions. The highest parts of a steep exposed rock face are also often difficult to reach. They are also time consuming and subjective. Although the traditional field-based methods have some limitations they are being used in Civil engineering works. Thus, this

INTRODUCTION

3 3

study tries to develop a new method by which 3D point cloud data obtained by terrestrial laser scanning can be used to model and quantify discontinuity surface roughness in a more objective , fast, precise and accurate manner. It is also tried to compare the roughness estimated using traditional field-based manual and visual methods with roughness derived from the laser scan data.

1.2. Research problem

Rock mass discontinuity surface roughness estimation is very important in, for example, slope stability, tunnelling, shear strength analysis, deformation behaviour, and flow properties of discontinuities. Discontinuity surface roughness determines the shear resistance of rock blocks and plays an essential role in the design of civil engineering works. Using 3D terrestrial laser scanning, it is possible to derive detailed 3D virtual models of exposed discontinuity surfaces. With these 3D surface models it is theoretically possible to characterize and quantify the large scale roughness of a discontinuity surface. This large scale roughness is often more relevant than the small scale roughness especially in slope stability design and can not be tested in laboratories and is very time consuming and expensive in in-situ tests (Stimpson, 1982; Johnson and Degraff, 1988).

The 3D terrestrial laser scanning has several advantages, for example, it is more objective, precise & accurate, cheaper (less labour intensive), faster and with out having any physical contact a high detailed surface roughness can be analyzed (Slob et al., 2004). However the traditional methods, which consist of visual and simple analogue instrumental field observations, are still commonly used for rock mass discontinuity roughness estimation. Hence, deriving large scale roughness from the 3D virtual models of discontinuity surfaces and compare it with the traditional field-based methods is a great challenge to achieve the benefits of 3D terrestrial laser scanning and accustom this new technology to the society.

1.3. Research Objective

The research will try to address the following main objective: The main objective of this study is to derive discontinuity surface roughness from the 3D terrestrial laser scan point cloud data and compare the results with the traditional field-based manual analogue methods of roughness quantification such as compass and disc-clinometer, and straight edge and qualitative standard reference profiles such as JRC, ISRM and SSPC.

1.3.1. Specific objectives

• To derive and quantify large scale rock mass discontinuity surface roughness from the 3D

virtual models of exposed discontinuity surface and compare the results with the traditional visual and field-based manual methods.

• To determine the influence of range measurement error of laser scan data on the roughness

quantification and its effect on the possible relationships with the traditional methods for roughness determination.

CHAPTER ONE

4 4

• If time permits to determine small-scale discontinuity surface roughness using the reflection intensity values of the laser scan data.

1.4. Research questions

The following research questions are proposed to achieve the objective of this study:

• Is it possible to model and quantify large scale discontinuity surface roughness from the geometry of 3D terrestrial laserscan data?

• Is it possible to establish a comparative relationship between roughnesses estimated visually

and manually measured using traditional methods and roughness derived from the 3D terrestrial laserscan data?

• Which interpolation method should be used for 3D virtual model reconstruction from noisy

3D terrestrial laserscan data?

• What are the influences of range measurement error of laserscan data on roughness quantification and how does this affect the possible relationship with the traditional method?

• Can reflection intensity aid in finding relationships between traditionally estimated roughness

and roughness derived from the 3D laserscan data?

• (Can small-scale discontinuity surface roughness be determine from the reflection intensity of laserscan data and could be related to the traditional field-based methods?)

1.5. Research hypothesis

3D object can be represented by the vertices or point cloud with X,Y,Z coordinates. From these points using mathematical analysis such as least square regression analysis can be computed to determine the mean orientation of a given window diameters corresponding the traditional discs.

• Based on differences in window diameter and orientation, it is possible to quantify large scale roughness from the 3D virtual models and compare the results with the traditional compass and disc-clinometer method.

“The rougher the surface is, the more diffusely the laser beam will be reflected (Slob et al., 2005)”. However, the relationship between roughness and intensity may be very complex, since parameters such as mineralogical composition, angle of inclination, moisture, etc also influence the intensity level (Slob et al., 2005)

• It is possible to estimate the small-scale discontinuity surface roughness form the intensity value of the laserscan data and establish relationship with the traditional field observations.

INTRODUCTION

5 5

1.6. Limitation of the research

This study contains several limitations that in general related to measuring instrument and data availability, computer hardware and etc. This is one of the major challenges working under no suitable field based-manual measuring instrument for roughness estimation and data with large range measurement error environment. It requires detailed investigation on the available instruments, data, and the proper techniques to produce the required information. The efficient technique in deriving detailed surface roughness is through the latest 3d Laserscan data with high resolution ‘Ladar’ (laser detection and ranging) techniques most suitable for short range only. However in this study the surface roughness should be derived from the terrestrial lidar (light detection and ranging) data through Riegl 3D-Z420i colour scanner with a resolution of 1 point per 1cm and 6cm. It is less precise than ‘Ladar’ and suitable for long range. Further more, the average resolution of the scan data set used for comparison with the compass and disc-clinometer method is 6 cm due to the inaccessibility of the relatively higher resolution data set. Roughness features less than the 6cm are not captured. It is also difficult to exactly locate the sample grid on the point cloud data due to loss of details in the coloured point cloud data. These and other assumptions such as there is no much more considerable change in rock surface asperities due to human interface and weathering since the date of laser scanning (06/05/2004) and the date of manual surface roughness measurement (19-20/09/2006) and the presence of vegetations on the rock face makes the comparison of laser derived roughness with the traditional field-based manual method hard. The intensity of the reflected laser beam is low and has a very small variation with in the sample grid and also may depend on other parameters such as weathering, mineralogical composition, target albedo, position of the scanner relative the rock face, angle of inclination, moisture, etc also influence the intensity level. Hence is not used in any of the analysis which has not been used in any of the analysis. The other constraint is regarding on the computer that used for the roughness derivation. High resolution 3D laser scan data and large window size analysis need good performance computer for the computation. Low computer performance had increased the computation time, for instance, window size of greater than 2m2 computation required about more time. The computation time increases for higher window size magnitude. On the other hand, the profile storage of the workspace exceeds after some time. Hence you have to remove some of them from your profile to local storage. These problems had caused long processing time in discontinuity surface roughness derivation.

1.7. Structure of the thesis

This thesis contains seven chapters: The first chapter touches the overview of the importance of roughness quantification and introduction of the research, which accommodates explanations on research background, research problem statement, research objectives, research questions and overall limitations of the research.

CHAPTER ONE

6 6

Chapter two covers literature reviews focussing on topics and fields that are crucial for this study. In general, this chapter is divided into two main subtopics; Discontinuity surface roughness data acquisition methods and Discontinuity surface roughness determination (quantification) methods. The first subtopic contains detailed explanation on the existing different surface roughness data acquisition methods. Apart from that, detailed discussion is also put on compass and disc-clinometer, straight edge and laser scanning which are more specifically focused on surface roughness data acquisition methods used in this research. The second subtopic accommodates explanations on the existing different surface roughness quantification methods. In general, this sub topic will discuss on the importance of roughness quantification and the attempts that has been done for quantification of surface roughness by different researchers. Further more it tries to address the limitation and challenges in different roughness quantification methods. Finally, the fractal method is reviewed back in detail in this sub topic. Chapter three deals with description of field procedures and equipments used in roughness measurements especially on the most commonly used and relatively simple traditional methods such as straight edge and compass and disc-clinometer methods. It is also discs the scanner setting and configuration procedures used during scanning. Chapter four devoted to the over all methodology implemented in this research. This topic deals with detailed explanation on determination of desire direction for rotation of point cloud data into a horizontal position and algorithm development in Matlab codes and script for surface reconstruction using scatter data interpolation technique and roughness quantification. Chapter five deals with data analysis and results of the terrestrial laser scan data using the proposed methodology and it also deals with results and discussion to find out the answers for the research questions. Chapter six discusses about the comparative results of the new proposed method with the results of traditional field based methods to check the applicability and accustom the new sophisticated technology to the society Recommendations and conclusions on the field equipment, 3D surface model reconstruction and quantification, directional roughness model interpolation and quantification and directions for future studies are discussed in the final chapter.

Thus, the following chapter of this study tries to assess the existing rock surface roughness measurement and determination methods to select the most commonly used traditional methods in rock surface determination. The selected methods will be compared with the new technology to find a way if there is any possible relation to accustom the new technology and quantify the qualitative way of discontinuity surface roughness estimation methods in a more objective, fast, precise and accurate manner.


7 7

2. Review of roughness measurement methods

It is important to estimate the discontinuity surface roughness accurately using standard data acquisition and quantification methods for appropriate application in shear strength, deformability, and hydraulic conductivity analysis of a discontinuous rock mass. Given its major effect on the hydro-mechanical behaviour of rock masses, a number of methods have been proposed and developed in different literature to quantitatively characterize the surface roughness (Fecker and Rengers, 1971; Barton, 1973; Barton and Choubey, 1977; ISRM, 1978; Weissbach, 1978; Tse and Cruden, 1979; ISRM, 1981; Bandis et al., 1983; Barton et al., 1985; Barton and Bandis, 1990; Cunha, 1990; Maerz et al., 1990; Odling, 1994; Develi and Babadagli, 1998; Hack et al., 1998; Kerstiens, 1999; Kulatilake and Um, 1999; Grasselli and Egger, 2000; Maerz et al., 2001; Feng et al., 2003; Fardin et al., 2004; Jing and Hudson, 2004; Hong et al., 2006; Rahman et al., 2006). The findings have been reported to characterize discontinuity surface roughness using standard profiles (JRC, ISRM suggested method, SSPC, ASTM and Laubscher’s), conventional statistical parameters, and fractal dimension etc. The most prominent approaches are discussed in this chapter. However the applicability and reliability of surface roughness characterization (analysis) is highly dependent on the accuracy of the data acquisition method. The existing Surface roughness data acquisition and determination methods are summarized in Table 2-1 below. Table 2- 1 Summary of discontinuity surface roughness data acquisition and determination methods

These studies have revealed the two main important properties of roughness i.e. it is scale dependent and anisotropic (Cunha, 1990; Huang and Doong, 1990). Only a few investigations have been made also in 3D analysis of roughness (Belem, et al., 2000; Fardin et al., 2004; Hong et al., 2006; Rahman

Roughness Information Methods Techniques

Mechanical profiling Compass and disc-clinometer Shadow profilometer

Contact

Tangent plane and connected pin sampling Photogrammetry Electro-fiber optic system Image processing Interferometry

Data acquisition

Non-contact

Laser scanning JRC ISRM SPPC

Qualitative

Laubscher’s Mechanical testing Statistical methods Spectral analysis

Data determination

Quantitative

Fractal method

CHAPTER TWO

8 8

et al., 2006). However nothing has been done about the possible relationship between the traditional ways of roughness determination methods with the roughness derived from the 3D laser scan data. In this study straight edge and Compass and disc-clinometer among the contact traditional data acquisition techniques, and Terrestrial laser scanner from the non contact techniques has been used for roughness data acquisition. For roughness analysis the standard profiles such as JRC, ISRM and SSPC has been used as a first estimation of roughness; and Statistical parameter method for the analysis and comparing laser scan data with the traditional field-based way of determination.

2.1. Discontinuity surface roughness data acquisition methods

There are several attempt techniques developed for accurate surface roughness data acquisition. These can be categorized in to two as contact and non contact techniques (Maerz et al., 1990). These are discussed in order of increasing technology complexity and automation ranging from simple manual methods to mechanical and electronic stylus profilometers (Contact techniques) and from photogrammetry to highly sophisticated optical methods (non contact techniques). The more advanced technique provides the benefit of acquiring large volume of test data in short time periods.

2.1.1. Contact methods

There are several ways of obtaining surface roughness using this technique, for example,

� Mechanical profiling (Fecker and Rengers, 1971; ISRM, 1978; Weissbach, 1978) � Compass and disc-clinometer (Fecker and Rengers, 1971) � Straight edge (Milne et al., 1991) � Shadow profilometry (Maerz et al., 1990) � Tangent plane and connected pin sampling (Harrison and Rasouli, 2001)

This study has been focused among the contact mechanical profiling methods on a straight edge because it is quick, cheap, easy and suitable to obtain large scale roughness profiles across rock plane applied in the field (Kerstiens, 1999). These will help us in minimizing the human bias in estimating the roughness visually. Further more Compass and disc-clinometer has been used to sample roughness in three dimensions. The rest, even they are relatively more accurate, they are applicable for the small scale roughness in the laboratory level.

2.1.1.1. Mechanical Profiling

Many researchers have developed several way of obtaining one directional profiles to characterize the discontinuity surface. The contacting (mechanical) means comprises a simple contour gauge and pattern maker (Stimpson, 1982), profilogragh (Fecker and Rengers, 1971), and more advanced equipment used for mechanical profiling, in general called profilometers. For the profilometers, a stylus measures the distance between a reference line and the discontinuity surface. The deflection of the stylus is measured by a displacement transducer and recorded as a function of the position (Maerz, et al., 1990). For this method the accuracy of the measurement can be influenced by the diameter of the stylus and stick slip motion of the needle on the surface.

REVIEW OF ROUGHNESS MEASUREMENT METHODS

9 9

2.1.1.2. Compass and disc-clinometer

If the direction of potential sliding is not known, roughness should be sampled in three dimension using compass and disc-clinometer method (Fecker and Rengers, 1971; ISRM, 1978). It is developed to measure the roughness i-angle at different scales on a three dimensional surface. Circular base plates with a diameter of 5, 10, 20, and 40 cm are positioned on an exposed discontinuity surface. By varying the size of base plate it will be possible to assess the roughness in an area as large as or larger than the base plate. For each plate, the field measurements of dip and dip direction obtained with the different diameters of discs will be plotted as poles on an equal area net (Figure 2-1 b and c).

Alloy discClar compassDip readingLevel

bubble

Plate diameter cm

Direction of potential sliding

40cm diam. 20cm diam.

10cm diam. 5cm diam.

i2

i1

i

Figure 2- 1 A method of recording discontinuity roughness in three dimensions using circular discs of different diameters (e.g. 5, 10, 20 & 40cm) fixed in to a Clar compass and clinometer. (after Fecker and Rengers, 1971). The smaller roughness angles (i) are measured by placing the largest circular palate (i.e. 40 cm diam.) against the surface of the discontinuity in at least 25 different positions i.e. a surface area at least ten times as large as the area of the largest plate (ISRM, 1981).This procedure should be repeated for the other plate diameters. The smaller base plate gives the greater scatter of reading & largest roughness i-angle and vice versa. The maximum roughness angles for the given disc size can be plotted for any given direction of potential sliding (Figure 2-1 c). The vertical displacement (dilation) that will occur perpendicular to the discontinuity surface can be calculated by multiplying the appropriate base length and the tangent of maximum roughness angle. If several base lengths are analysed, the dilation curve can be obtained as in Figure 2-1 c. Here asperities smaller than the smallest plate diameter are assumed to not to influence the process of dilation (Fecker and rengers, 1971). In addition to this photographs representing surfaces of minimum, modal and maximum roughness should be taken, with a 1m ruler placed against the surface in question clearly visible. This study tries to apply this method to estimate the large scale (waviness) roughness of the Lustin and the “roche de Tailfer” quarry area out crop and compare the measured base plate (disc) size orientation (i-angle) with its corresponding mean circular window orientation calculated from the 3D laser scan data.

CHAPTER TWO

10 10

2.1.1.3. Straight edge

It is one of the linear profiling methods which can be used to measure large scale roughness (waviness) of discontinuity surface. Waviness (large scale) of the discontinuity wall appears as undulations from planarity. It is defined by the maximum amplitude or offset (amax) which can be found using a straight edge which is placed on the exposed discontinuity surface. The length of the edge should be of the same size as the joint, provided that this is practically possible (Palmström, 2001). As the length of the joint seldom can be observed or measured, simplifications in the determination of (U) are often done. A procedure described by Piteau (1970) was applied in this study with 1.0m long edge as shown in Figure 2-2. Palmström (2001) explained that, it is possible to apply this methodology even for the smallest joints by using shorter lengths. The orientation of the edge, together with the maximum amplitude should be recorded. The simplified waviness or undulation can be calculated as:

(L)joint alonglength Measured

(a) amplitude max. Measured=U Eq. [2-1]

After some training with measurements as shown in Figure 2-2, the joint waviness can roughly be assessed from simple observations. Where many joint observations are needed, the waviness is often determined by visual observation, because the measurement in Figure 2-2 is time consuming. Palmström (1995) suggested Characterization of the joint planarity expressed as the waviness factor (jw) (Table 2-2). Table 2- 2 Characterization of the joint planarity expressed as the waviness factor (jw) as suggested by Palmström (1995)

Term undulation waviness factor (U=a/L) (jw) Interlocking 3 Stepped 2.5 Large undulation U>3% 2 Small undulation U=0.3-3% 1.5 Planar U<0.3% 1

As explained above, the length of the surface of interest in the study area is several meters; JRC value can be estimated for the full scale using straight edge with help of Figure 2-3a (Barton, 1982). This method is also quick and applicable for large scale roughness.

Figure 2- 2 Practical measurement of joint wall waviness or undulation

(after Milne et al., 1991)


11 11

Figure 2- 3 Alternative method for estimating JRC from measurement of roughness amplitude for various measuring lengths (a) (after Barton, 1982) and the joint waviness and smoothness characterization using U value (b) (Palmström A., 1995)

2.1.2. Non contact (remote sensing) methods

There are several ways of obtaining surface roughness using this technique, for example:

� Photogrammetry (Wickens and Barton, 1971; ISRM, 1978) � Image processing (Galante et al., 1991) � Fiber optic probe, and He-Ne laser beam (Yilbas and Hasmi, 1999) � Interferometry topometric sensor (Grasselli and Egger, 2000), and � Laser scanning (Fardin et al., 2004; Hong et al., 2006; Rahman et al., 2006) � Electronic stylus profilometers (Grima, 1994; Kerstiens, 1999)

Optical means of profiling uses light beams to measure roughness with out damaging the asperities. This method includes interferometry, speckle metrology and laser profilometry.

2.1.2.1. Laser scanning

Laser scanning, which has been focused is a relatively new active remote sensing with a very high resolution, precision and accuracy method of capturing data in three dimensions. It can provide richer data which allows two or three dimension drawings, ortho-images faster than any other alternative techniques without coming into contact with the surveyed object or scene. Laser is an acronym of ‘Light amplification by stimulated emission of radiation’. The mirror of the scanner direct a pulsed narrow laser beam of lights across the object and the returns are captured and recorded by the scanner as ‘point clouds‘ with ‘X’, ‘Y’, ‘Z’ and ‘i’ values, which represents the location of points within a 3D Cartesian coordinate system (X,Y,Z) and intensity of the returned beam (i). The systems utilize the

(a) (b)

CHAPTER TWO

12 12

speed of light and very precise timing devices to calculate the distance between a laser emitter/receiver device and an object reflecting the beam. There are two ways of existing laser scanning.

� Ladar, often called ‘laser radar’, which uses phase differences of narrow laser beams of light

to determine distance. It is rather more accurate and precise than ‘Lidar’ and more suitable for short ranges only.

� Lidar, which uses differences in ‘time of flight of emitted narrow laser beams of light instead of phase difference to determined distance. It is less accurate and precise than ‘Ladar’ but more suitable for long ranges.

Both airborne and terrestrial laser scanning (ground-based) are now well established for the acquisition of accurate, precise and reliable 3D geo-information data with high resolution. Beyond the primary tasks in digital terrain model generation (DTM) (Axelsson, 1999; Wack and Stelzl, 2005), airborne laser scanning has also proven to be a Very suitable tool for Change detection (Girardeau-Montaut et al., 2005), Vegetation analysis (Yu et al., 2005) Waveform analysis (Jutzi et al., 2005), Building reconstruction (Schwalbe et al., 2005), Segmentation (Filin and Pfeifer, 2006), Virtual city modeling and so on.

“Rapid developments in sensor technology and supporting software tools have made terrestrial laser scanning an important, ubiquitous technology for spatial data capture in engineering and heritage recording applications and new areas such as forestry and forensics”(Lichti et al., 2006). In addition to time-of-flight scanners, active triangulation and especially range cameras are finding increasing use. Accompanying the opportunities terrestrial laser scanning has created are many significant research challenges in the areas of sensor modelling, feature extraction, point cloud registration, data fusion and others, e.g. multispectral scanning and sub-shot resolution. Terrestrial laser scanning is usefully emerging in many applications such as:

� Architecture and Facade measurement (Balzani et al., 2001; Runne et al., 2001 ) � Geomorphology � Geological engineering (Rowlands et al., 2003) � Monitoring and Civil Engineering (Lichti et al., 2000; Gordon et al., 2003 ) � Rock mechanics for example,

o Rock mass discontinuity set identification and characterization (Slob et al., 2002; Lemy and J., 2004; Slob et al., 2004; Slob and van Knapen, 2005; van Knapen and Slob, 2006).

o Roughness of rock mass discontinuity (Fardin et al., 2004; Hong et al., 2006; Rahman et al., 2006).

o Evaluation, and management of unstable rock slopes (Turner et al., 2006).

The main advantage of the laser scanning method is that a very high point density can be achieved, up to 5 mm resolution or larger. Therefore, the shape of the surveyed object or scene can be modelled with a very high resolution, precision and accuracy, in three dimensions (Slob et al., 2004). In the present study, two terrestrial lidar data sets collected using Riegl LMS-Z420i scanner are used to derive roughness characteristics of discontinuity surface and relate them with the traditional field-based methods of roughness determination.


13 13

2.2. Discontinuity Surface roughness determination methods

A wide range of techniques have been applied to determine the surface topography of a discontinuity. The topography of discontinuity is defined by the geometry of asperities. Here the two relevant (qualitative and quantitative) surface roughness characterization (determination) methods are discussed.

2.2.1. Observational or Qualitative method

The simplest roughness determination technique is inspection; where by the appearance of natural discontinuity fracture surfaces are compared visually with the standard profiles and Value corresponding to the profile which most closely matches that of discontinuity surface is chosen. For preliminary discontinuity surface roughness surveys a qualitative assessment using simple descriptive terms should be employed. Even though this approach is very subjective relying on visual or tactile assessment of the degree of roughness, it is still commonly used for rock mass discontinuity roughness estimation. The most commonly used standard profiles are:

� JRC (Join Roughness Coefficient) Method � ISRM (International Society for Rock Mechanics) suggested Methods � Laubscher’s Roughness Curves � Method used in SSPC (Slope Stability Probability Classification) System

2.2.1.1. JRC (Join Roughness Coefficient) Method

Barton and Choubey (1977) have developed standard roughness profiles (Figure 2-4) and an empirical relation that relates the profiles to the shear strength of more than 200 artificial tension fractures. These were developed with a guillotine in various weak model materials with low unconfined compression strength (0.05 Mpa). It is suggested as a means to determine the JRC value in two dimension, which is also related to shear strength as in Eq. [2-2].This method is surprisingly cheap

and relatively accurate method of estimating peak friction angle ( peakφ ).

��

��

� +��

�

�= rnn

peak JCSJRC ϕ

σστ

'10' log*tan Eq. [2-2]

Where, peakτ =Peak shear strength

n'σ = Effective normal stress on discontinuity surface

JRC = Joint roughness coefficient JCS = Discontinuity surface compression strength

rϕ = Residual friction angle The joint roughness is visually compared with the 10 standard profiles here refer to us as B-C profiles and Value corresponding to the profile which most closely matches that of discontinuity surface is chosen. The JRC values were assigned from 0 to 20 in steps of two starting from smoothest to the roughest joint (Figure 1-1). JRC is very simple and quick to use, but it is often very difficult to

CHAPTER TWO

14 14

establish the proper roughness value visually. A review of literature, Barton and Bandis, (1990) proposed a relationship that accounted for the scale effect between the JRC standard profiles (JRCo) for a100mm sample length and the equivalent roughness of a profile length Ln according to Eq. [2-3]. Even though it is condemn as inappropriate roughness measurement (Maerz et al, 1990; Rausouli and Hrrison 2001), it is still commonly used.

oJRC

o

non L

LJRCJRC

02.0−

��

��

�≈ Eq. [2-3]

Where subscripts (o) and (n) refer to lab scale and in-situ block sizes respectively.

2.2.1.2. ISRM Suggested Methods

International Society for Rock Mechanics (ISRM) in 1978 has developed standard profiles to universally determine discontinuity surface roughness. The descriptions of roughness are limited to descriptive terms which are based on two scale of observation; Intermediate scale (several meters) which, if interlocked and in contact, cause dilation during shear displacement sine they are too large to be sheared off and Small scale (several centimetres) which tend to be damaged during shear displacement unless the discontinuity surface is high strength and (or) the stress level is low, as the result dilation can also occur on these small scale asperities. The intermediate scale of roughness is divided in to three degrees; Stepped, undulating and planar where as the small scale which are superimposed on the intermediate are also divided in to three degrees, rough (irregular), smooth and slickenside. The term “slickenside” should be used only if there is a clear evidence of previous shear displacement along the discontinuity. The typical roughness profiles of ISRM, 1978 with nine classes are illustrated in Figure 2-5 and Table 2-3. Table 2- 3 ISRM roughness categories

Category Small scale Intermediate scale

I Rough (or irregular) II Smooth Stepped III Slickensided

IV Rough (or irregular) V Smooth Undulating VI Slickensided

VII Rough (or irregular) VIII Smooth Planar IX Slickensided

In terms of shear strength, the effective roughness angle (i) displayed by the nine categories of ISRM profiles, I > II > II, IV > V > VI > and VII > VII > IX taking in to consideration the mineral coatings are entirely absent, or present in equal amount. It should be pointed out that the direction of irregularities in the surface is in the least favourable direction to resist sliding.


15 15

2.2.1.3. Laubscher’s Roughness Curves

Laubscher (1990) in Geomechanics classification system for rating of rock mass in mine design has developed a set of descriptive terms for discontinuity surface roughness determination with factors rating the influence on the stability of underground excavations. The description of the profiles is partly based on the profiles of ISRM (1978) and (1981). The roughness is categorized in to two roughnesses that can be seen at different scales and can not be seen, but can be felt by using fingers (so called tactile roughness). See Figure 2-6. This is developed and applicable for underground excavations, hence it is not applied in this study.

2.2.1.4. Method used in SSPC System

Hack et al. (1998) have developed an empirical relation between tactile and visible roughness based on the (ISRM, 1978, 1981; Laubscher, 1990) profiles and the friction along discontinuity plane resulting from roughness for his slope stability probability classification (SSPC) system for the slopes. Hack et al. (1998), categorized the roughness in to two (large scale and small scale) roughness. The

Figure 2-5 Typical ISRM profiles and Suggested nomenclatures. The length of each profile is in the range of 1 to 10m. (ISRM, 1978).

Figure 2- 6 Laubscher’s roughness profiles (after Laubscher, 1990)

Figure 2- 4 Typical roughness profiles for a range of JRC. (after Barton and Choubey, 1977)

CHAPTER TWO

16 16

large scale roughness determined on sample area of larger than 20x20 cm but smaller than 1x1 m, is described in five classes as wavy, slightly wavy, curved, slightly curved, and straight in Figure 2-7a. Where as the small scale roughness determined on an area of 20x20 cm is a combination of visible and tactile roughness. The tactile roughness is to be distinguished by feeling with fingers and described in three classes as rough, smooth and polished as in Figure 2-7b. The visible small scale roughness is described in three classes as stepped, undulating and planar as in Figure 2-7c. The descriptive terms and their corresponding values for each term to estimate condition of discontinuity surface is shown in Table 2-4 below.

(a)

(b) (c)

Figure 2- 7 Large scale (a) and small scale (b) roughness profiles for SSPC and interpretation of regular forms of

roughness as a function of scale and angle(c) (after Hack et al., 1998)

The advantage of SSPC is that the infill material in discontinuities and the presence of karst along discontinuities are characterized following Table 2-4. This table also shows how the characteristics of the discontinuity are translated into values for four factors: large-scale (Rl) and small-scale (Rs) roughness, infill material (Im) and karst (Ka) (Table 2-4). The condition factor for a discontinuity (TC) is calculated by a simple multiplication of these four factors:

TC= Rl* Rs* Im* Ka Eq. [2-4]

From condition of discontinuity (TC) value a sliding criterion has been developed to estimate easily the shear strength of a discontinuity plane on slopes between 2 and 25m size (Hack and Price, 1995; Hack et al., 1998). From the sliding criterion, the sliding angle can be estimated using Eq. [2-5].The sliding angle gives the maximum angle under which a block on a slope is stable. It can be compared to tilt test idea.

0113.0/)Im***( KaRsRIanglesliding =−φ Eq. [2-5]


17 17

Table 2- 4 Discontinuity characterization for sliding criterion (after, Hack, et al., 1998)

Roughness Value 1.00 0.95

0.85 0.8

Large scale (RI)

Wavy Slightly wavy Curved Slightly curved Straight 0.8

0.95 0.9

0.85 0.80 0.75 0.7 0.65 0.6

Small scale (SI)

Rough stepped

Smooth stepped

Polish stepped

Rough undulating Smooth undulating

Polish undulating Rough Planar smooth planar Polish planar 0.55

1.07 Cement or cemented in fill No-in-fill (surface staining) 1.0

Coarse 0.95

Medium 0.9 Non-softening and sheared material (e.g. free of clay talc, etc.)

Fine 0.85

Coarse 0.75

Medium 0.65 Soft shear material (e.g. clay, talc etc.)

Fine 0.55

0.42

0.17

In-fill mat. (Im)

Gouge < irregularities

Gouge > irregularities

Flowing material 0.05 1.0

Karst (Ka) None

Karst 0.92

Notes: 1. For in-fill “Gourge >

irregularities” and “flowing material” small-scale roughness is 0.55.

2. If the roughness is anisotropic (e.g. ripple marks striation, etc.), roughness should be assigned perpendicular and parallel to the roughness and direction should be noted.

3. Non-fitting of discontinuity should be marked in the roughness column

Even though it is subjective way of roughness determination, it tries to solve the limitations of other visual roughness determination methods. Further more it tries to incorporate most of the factors that influence the discontinuity roughness.

2.2.2. Quantitative methods

Quantification of a discontinuity surface roughness can be done by measuring parameters of the height and steepness of the slopes of the topography surface with its spatial distribution. A number of quantitative techniques for the quantification of the discontinuity surface roughness are described in detail by ISRM (1978). Since the amount of parameters and method of quantification is impressive, the following methods are discussed covering a range of complexity.

� Tilt meter � Statistical methods � Spectral method � Fractal method

CHAPTER TWO

18 18

2.2.2.1. Mechanical testing

Barton and Choubey (1977) have proposed a scientific assessment of method called tiltmeter to account for the macroscopic impact of surface roughness. The meter allows the controlled and progressive inclination of an axially fractured core specimen. The methodology requires both complimentary parts of a fractured sample so that the specimen could be gradually tilted until the upper sample fragment slid over the lower fragment. The tests apply the principle of constant Normal Load (CNL) and the results used to back calculate JRC according to the following empirical formula.

��

��

�

−=

n

r

JCSJRC

σ

φα

log Eq. [2-6]

Where, α =The tilt angle (in degrees)

rφ =Residual friction angle (in degrees)

nσ =Normal stress on the joint at tilt failure (Mpa)

JCS=Joint wall compressive strength (from Schmidt hammer in Mpa), scaled for joint lengths greater than 100mm, according to Barton et al. (1985).

This method requires additional assessment of JCS and rφ ,

and can introduce errors if the Schmidt hammer is not used carefully in weathered discontinuity surface. The residual

fricton angel rφ is given by Eq. [2-7] below:

rφ = ( bφ - 20) + 20 (r/R) Eq. [2-7]

Where, bφ = basic friction angle

R = Schmidt hammer rebound on dry unweathered surface r = Schmidt hammer rebound on wet joint surface By substituting Eq. [2-7] on Eq. [2-6] it is possible to back calculate the JRC value.

2.2.2.2. Statistical methods

Roughness profiles are waveforms which could be analyse using similar methods for processing electrical signals. This leads to the development of several statistical roughness parameters by several researchers for analysis of two dimensional profiles and three dimensional surfaces, starting from simple measurement of amplitude, wavelength and slope to a more complex stochastic and frequency domain analysis and fractal dimension methods.

Figure 2-8 Tilt test for measuring JRC

(after Barton and Bandis, 1990)


19 19

In general these statistical roughness parameters can be subdivided as follows (Maerz et al., 1990).

� Amplitude parameters � Wave length parameters � Slope parameters � Stochastic methods � Power spectra parameters � Fractal dimension � Other methods

I) Amplitude parameters This category which belongs to the absolute roughness (k), comprises the central line average (CLA), the root men square (RMS) and the mean square value (MSV). These indexes can be determine in terms of a continuous function z(x,y) or as a collection of discrete points zij. Here indexes determined by a continuous function are presented. The absolute roughness (k), which represents the difference between the highest peak and the lowest valley of the asperities, can be computed by Eq. [2-8].

K= max [z(x,y)]-min [z(x,y)] Eq. [2-8] The central line average (CLA) represents the deviation of the asperity heights with respect to the regression plane or line in the case of profile. The parameter A is the area of the regression plane where as z values are values determined relative to this plane.

dAzA

CLAA = 1

Eq. [2-9]

The root mean square (RMS), which is also called z1, is the square root of the arithmetic mean of the squares of the asperity heights.

5.0

21��

��

�=

A

dAzA

RMS Eq. [2-10]

And the mean square value is (MSV) (Bendat and pierson, 1985) is:

=A

dAzA

MSV 21 Eq. [2-11]

There are two more slightly sophisticated statistical amplitude measurements like, Skewness (measures the symmetry of the profile line about the centreline) and kurtosis (measures the concentration of distribution of heights from the centreline) (Muralha, 1995; Silvester, 1996).

CHAPTER TWO

20 20

II) Slope parameters This category contains indexes, for example, the root men square of the first derivative of the asperity heights (z2), the root men square of the second derivative of the asperity heights (z3), a measure of the directionality of the roughness (z4), and another indexes like roughness profile index (Rp) and Micro average i-angle (i) (Maerz et al., 1990). They are originally developed in the metallurgy industry and are now also applied in roughness study of discontinuities (Kerstiens, 1999).

The root mean square of the first derivative of the asperities heights (z2) (Myers, 1962) is a single parameter measure that characterizes asperity height based on its average slope along a predefined directionξ , but it were recently transformed to characterize a surface by Muralha (1995) as in Eq. [2-

12]. It is unitless, scale dependent and more appropriate for stationary roughness.

5.02

2

1

��

�

��

�

��

�

�=

A ddz

Az

ξ Eq. [2-12]

The root mean square of the second derivative of the asperity heights (z3), along a prediction directionξ , gives the degree of curvature or rounding of asperities:

5.02

2

2

3

1

��

�

�

��

�

�

��

�

�=

A

dAd

zdA

zξ

Eq. [2-13]

The z4 parameter is the measure of the proportion of the area of a surface with positive slope (Ai, positive) minus the area with negative slope (Ai, negative) in the predefined directionξ , with respect to the true

total area (At) of the digitized surface.

t

negativeipositivei

A

AAz � �−

= ,,4 Eq. [2-14]

The ratio between the true digitized surface area to the projected area on the reference plane A is defined by RA (roughness area index) in Eq. [2-15]. In case of two dimensional profile data is available, the index RL (roughness profile index) is defined by the ratio of the true length of the profile to the length of the same profile projected on its regression line (El-Soudani, 1978).

AA

R tA = Eq. [2-15]

The presented formulas consider characterization of a surface along a predefined direction. They can be easily transformed to characterize profiles by substituting area A by length L.


21 21

III) Stochastic methods The Stochastic methods, in general, incorporate probability density functions as an input for analytical models. These are based on the assumption that a profile is a random, stationary process. Thus roughness measured in a small domain is valid for the entire surface (Reeves, 1985). The following functions are such parameters to relate equally spaced asperity heights. The auto-correlation function (ACF) represents the dependence of the amplitude of one point to the amplitude at another point separated by a constant lag. The structure function (SF) determines the arithmetic mean of the independent of the chosen reference system (Sayles and Thomas, 1977). The SF has an advantage over the ACF in that it is independent of the mean plane and can be computed over only a portion of the profile with out the loss of statistical significance (Sayles and Thomas, 1977). Further more, Iwano and Einstein (1993) characterized roughness stochastically as an isotropic random feature and refer to this method as a relatively easy and sufficiently accurate. However, it is noted that problems arise when modelling anisotropic using such process. IV) Power spectra parameters Discontinuity surface roughness can be characterized by spectral density functions, where a profile is approached as a complex intersection of sinusoidal waves with many harmonics of different wave lengths, amplitudes and phase angles. Two sets of two dimensional waves describe a surface where as only one set wave describe a profile. The waves can be represented by Fourier transforms of the original profile data (discretised data set of profile measurement), by Fourier transforms of a previously calculated correlation function, or by bandpass filtering, squaring and averaging of the signal (Myers, 1962). It is based on Harmonics which allows evaluation of the variance of sampled points relative to the mean of value as a function of harmonic number or sampling interval, also called power (Sylvester, 1996). This method describes both roughness and spatial correlation of discontinuity surface topography (Piggott and Elsworth, 1993). The power of harmonics can be calculated and plotted in a power spectrum to detect the strong interaction of the dominant wave sets. The number of harmonics calculated needs to be very large in order to obtain a reliable power spectrum. The sampling should be done very carefully due to the strong influence of aliasing (i.e. if the frequencies in the frequency spectra are higher than the critical frequency spectra) on the process of calculation. In addition, if the number of calculations are not abundant, very large errors can result (Sylvestre, 1996). V) Fractal dimension The concept of fractal dimension method is to resolve the mystery in measurement of the length of irregular objects such as coast lines (Mandelbrot, 1983). It is a new branch of Mathematics compared to Euclidean geometry, Algebra and Calculus. Smooth, regular geometric shapes such as cube, sphere cylinder or their derivatives can be described by Euclidean geometry. However, irregular and rough natural objects such as mountains, coastlines, trees etc are not sooth and can not be described by Euclidean geometry. These can be described by fractal geometry. For example, the length of an undulating coast line is not constant; it depends on the length of measuring yardstick. The longer the measuring yardstick (r) is the shorter the coast line length will be and vice versa. This shows the length of the coast line is not constant. That means fractal is any pattern that shows greater complexity as it is magnified. Fractal objects can be described as Mathematical functions that are continuous but

CHAPTER TWO

22 22

not differentiable. Hence fractal objects and processors are said to exhibit self-invariant (self-similar or self-affine) properties (Hastings and Sugihara, 1993). A self-similar fractal shows same statistical properties through various magnification of viewing; where as self-affine shows same statistical similar properties only when it is scaled differently in different directions (Figure 2-9a and 2-9b) below.

Figure 2-9 Illustration of self-similar (a) and self-affine (b) fractals (after Kulatilake et al., 1998) and double log

plot of (n x r) versus r (c).

Fractal dimension which is denoted by D like many summery statistics is obtained by averaging variations in data structure (Normat and Tricot, 1993). The fractal dimension (D) is most commonly estimated by counting the number of yardsticks of length r needed to cover the profile. This measurement is repeated for various lengths of r. Fractal dimension (D) of a linear profile across surface may have a value between 1 (topological dimension of a line) and 2 (dimension of a Euclidean plane). A rough surface may have fractal dimension between 2 and 3. A number of methods have been proposed to measure the fractal parameters for roughness of rock mass (for example, The divider (Mandelbrot, 1983); Box counting (Feder, 1988); Variogram (Orey, 1970); Spectral (Berry and Lewis, 1980); Roughness-length (Malinverno, 1990) and The line scaling (Matsushita and Ouchi, 1989). Rock surface roughness has been characterized using roughness length method to estimate the fractal dimension of 2D profiles (Malinverno, 1990; Kulatilake and Um, 1999) and for 3D surfaces (Fardin et al., 2001and 2004) from the scan rock surface. It is known that surface roughness of rock fractures can be adequately described using self-affine fractal models. Therefore, a self affine fractal object needs to be characterized by at least two parameters defined as fractal dimension (D) and amplitude parameter A, which specifies the variance or surface slope at a reference scale (Kulatilake and Um, 1999, Fardin et al., 2004). For 3D self-affine discontinuity surface, there is a power low relation between the standard deviation of the residual surface heights, S(w), and sampling window size, w, as follows:

HAwwS =)( Eq. [2-16]

w

eHA

ewS loglog))(log( +=

Eq. [2-17]

Where, S(w)= the residuals of the asperities height from the local fitting plane

(a) (b) (c)


23 23

w = the spanning or window length of the profile H = the Hurst exponent and H=E-D (where E is the Euclidean dimension,

i.e. E=2 for a profile and E=3 for a surface) A = a proportionality constant which is defined as a measure of the amplitude of the profile

w, mm

S(w

), m

m

Figure 2-10 Double log graph of standard deviation of reduced asperity height, S(w) versus profile length w

(after Fardin et al., 2001)

From Figure 2-10 it can be observed that different roughness profiles may have the same fractal dimension (D). For example, if in case same D but different A is calculated, the roughness of the profiles is not the same. .This means it is not possible to estimate surface roughness using only fractal dimension (D). For 2D profiles S(w) can be calculated as the root mean squared (RMS) value of the profile height residuals on a linear trend fitted to the sample points in a window of w according to equation Eq. [2-18] below.

�=

� −−

==wn

i wijzjz

imwnwRMSwS

12)(

2

11)()(

ε Eq. [2-18]

Where,

=wn The total number of windows per length w.

=im The number of points in window iw

=jz The residuals on the linear fitted trend

=z The mean residual in window iw

For 3D surface roughness the residuals of asperities heights S(w), defined as the normal distance between the surface asperity heights and their local fitting plane are calculated for each square window by least square regression analysis. The parameters used in Eq. [2-18] above are now re-defined as: nw, the total number of square windows of side length w; mi, the number of points in square window wi; zj, the residuals of the asperity height on the trend and the mean residual asperity height in square window wi, respectively. The non-stationarity resulting from a local trend is automatically removed by this method.

CHAPTER TWO

24 24

Kulatilake and Um (1999) in their roughness-length method proposed the following prerequisites for accurate quantification of roughness of natural rock joint profiles using roughness-length method:

� Data density (the number of data points per unit length) between 5.1 and 51.23; � Fractal dimension, D between 1.2 and 1.7; � Window sizes between 2% and 10% of the total sample length; � At least seven windows need to be selected with in the suitable minimum and maximum range

of window sizes. VI) Other methods Geostatistical analysis of roughness, which is based on the concept of regionalised variables, uses parameters that have characteristics between a random variable and a deterministic one. This variable is theoretically a continuous, but in practice due to sampling is discrete. According to Miller et al. (1995) and Roko, et al. (1997) the semi-variogram and the variance can be used to characterise the directional surface roughness along a specified direction in geostatistical description. Some researchers investigate the relationship between different statistical parameters and the JRC values given by Barton and Choubey (1977). For example, Tse and Cruden (1979) suggested that the values of Z2 and SF are strongly correlated with the 10 JRC standard roughness profiles. Figure 2-10 shows both linear relation between JRC and SF (Tse and Cruden, 1979), and the logarithmic relation between the same data variables that Rasouli and Harrison (2001) obtained reanalysing the data. This figure shows the logarithmic curve fits the data better than the linear curve. Tse and Cruden (1979) also developed a linear relation between the JRC and Z2 as:

210log*47.322.32 ZJRC += Eq. [2-19]

Eq. [2-19] implies that the JRC value will be greater than 20 if the value of Z2 is greater than 0.42, and smaller than 0 if the value of Z2 is smaller than 0.1. This shows it is difficult to correlate statistical parameter to the empirical parameter like JRC.

JRC=241.59SF + 2.7478

R2=0.8447

JRC=7.1496ln(SF) + 37.014

R2=0.9675

(a) (b)

JRC=32.2+32.47log10(z2)

R2=0.9860

JRC

Z2

JRC

SF

Figure 2-11 Correlation between Z2 and JRC (a) SF and JRC (b) for 10 standard B_C roughness profiles (After Tse and Cruden, 1979). The logarithmic relationship (b) was obtained by Harrison and Rasouli (2001).


25 25

Maerz et al. (1990) have achieved a correlation between JRC and roughness profile index (Rp) by substituting photo-analysis for manual digitization of Tse and Gruden (1979) and the closest correlation (R2=0.984) was obtained. Kulatilake et al. (1995) have investigated the conventional statistical parameters mentioned above to select the best parameters to quantify rock roughness using digitized data from Barton and Coubey (1977). Out of the statistical parameters, they found that parameters associated with the slope of the profile (Z2, i-angle, Rp) and structural function (SF) have strong correlation with the JRC. Among the slope parameters, Z2, which is unitless and scale dependent was found to be the best parameter. It is important to note that only a single statistical parameter is not sufficient to quantify discontinuity surface roughness arising from the stationary and non stationary part of the profile. If the discontinuity surface is inclined with respect to the large scale roughness (waviness), the shear strength of the discontinuity surface in the upward direction is different from that in the opposite direction. However, Z2 will be the same in both directions. Therefore, z2 alone is not sufficient to quantify surface roughness (Kulatilake et al., 1995). The non stationarity can be presented by linear function with a positive and negative slope as it is suggested by Kulatilake et al. (19995). According to their suggestion, the linear function is enough to model the non-stationary part of the discontinuity surface profile. The slope which is denoted by I can be estimated by regression analysis. In their investigation the parameter, I (slope) was selected to model the non-stationary (large-scale undulations) part of surface profile, where as the statistical parameter Z2 is elected for the stationary (small-scale) roughness. The next chapter will discuss about the field procedures used for roughness estimation during the filed work for the selected methods including the procedures applied during laser scanning of the rock surface


27 27

3. Field procedures and equipment used in roughness measurements

3.1. introduction

The most commonly used and relatively simple methods such as Straight edge, compass and disc-clinometer, and Visual inspection using standard reference profiles are used to gather information about discontinuity surface roughness in the field. A data set of JRC, ISRM and SSPC by visual inspection and maximum amplitude for the given length of straight edge of the selected surface topography is obtained with a regular sampling interval along the horizontal and vertical grid for 2D roughness estimation. A few standard profile ranges and maximum amplitude measurements for the given length of straight edge are often considered appropriate for characterization of the whole surface (Palmström, 2001). This might be due to the three dimensional irregular and anisotropic character of a discontinuity surface. In order to obtain the three dimensional characterization of the discontinuity surface roughness, it was decided to use compass and disc-clinometer method (Fecker and Rengers, 1971) which provides i-angle as a means to obtain three dimensional data of the surface topography. As it is explained in ISRM (1981) different disc size was used.

To compare the roughness derived from terrestrial laser scanning data with the commonly used traditional field-based methods, a total of 24 straight edge and 250 disc and compass-clinometer measurements was done in the selected accessible rock face (Figure 3-2). In addition to these some visual inspections using the standard profiles of JRC, ISRM and SSPC also carried out to compare visually with the large scale 2D roughness profiles derived from the 3D laser scan data.

3.2. Description of the scan discontinuity surface and sample area location

The southern part of Belgium is known for its frasnian carbonate moulds. A number of carbonate mounds are known and the majorities were actively quarried for marble. In the Dinant Synclinorium (Figure 3-1 left), three stratigraphic levels, in stratigraphic order, the Arche, the Lion and the Petit-Mont Members bear Frasnian carbonate mounds are found (Figure3-1 right). At the northern border of the Dinant Synclinorium and in the Namur Syncline, the entire Frasnian consists of bedded limestone and argillaceous strata (Figure 3-1 right). The rock type of the scanned discontinuity surface is one of the abandoned quarries and composed of laminated stromatopores bedded, slightly metamorphosed lime stone (Appendix 1-2). It is part of the Lustin Formation of carbonate moulds, which consists of shallow water calcareous deposits of middle- upper Devonian age (Da Silva and Boulvain, 2004).

CHAPTER THREE

28 28

Figure 3- 1 Schematic geological map of southern Belgium with location of the scan outcrop, (left) and N-S section in the Dinant Synclinorium before Variscan tectonism (Da Silva and Boulvain, 2004)

The southern part of Belgium, Lustin-Namur, where the discontinuous surface of the out crop has been scanned, is located at about 20km south of Namur city on the right side of mass river (Figure 3-2 left). The sample area for roughness measurement using the traditional field-based method was chosen at the lower right side of the out crop where it can be accessed using 3m long folding ladder (Figure3-2 right). The detail descriptions of roughness data accusation procedure using the selected methods are discussed below.

Figure 3- 2 Location map of the scan discontinuity rock surface (left) and selected sample area for roughness measurements using traditional methods (right).

3.3. Compass and disc-clinometer

For the three dimensional sampling of roughness, Disc and compass-clinometer was used. It is made of circular light alloy of various diameters (5cm, 10cm 20cm and 40cm) by the author in the ITC workshop according to the specification of Fecker and Rengers, 1971 (Figure 3-3). The smallest diameter is fixed to the circular light alloy on top by a tube of 2cm diameter to lay down the compass for measurement as in Figure 3-3a.

Location of The scan out crop

Key The outcrop Lustin city

Sample area 2*2m

FIELD PROCEDURES AND EQUIPMENT USED IN ROUGHNESS MEASUREMENTS

29 29

Figure 3- 3 The smallest (a) and the largest (b) base plates for measuring roughness (after Fecker and Rengers, 1971)

3.3.1. Roughness acquisition procedure

Before the actual measurement starts a rock face that can be accessed by 3m long ladder and having a size of 2m x 2m dimension was selected from the exposed surface (Figure 3-2 right). Then a local reference (coordinate) system of the selected sample discontinuity surface area was defined manually by taking horizontal and vertical grids parallel to the strike and dip direction respectively. It is divided in to different grid sizes according to the disc diameters. This local grid system was captured by six mega pixel digital camera for later georeferencing and approximate locating on the colour laser scan data by image to image rectification using special features like humps and holes found on both images. Then the roughness angle (i) and dip direction are measured for each disc size by placing the disc against the surface of the discontinuity with in the sample grid. To minimize the effect of wobbling due to highest asperities, the centre of the disc was held index finger. According to ISRM (1981), the number of measurements at different positions required for the largest disc should fulfil a surface area at least ten times as large as the area of the largest disc. Hence 25 measurements of largest disc at different positions with in the 40cm square grid of the 2m2 sample grid were carried out. This procedure was repeated in turn for all other plate diameters. The over all sensitivity of the measurements was improved by recording a large measurement of the smaller plate size, for example 185 positions with a 5cm disc, 175 positions with a 10cm disc and 120 positions with a 20cm disc (Appendix 1-2). For each plate, the field measurements of dip amount and dip direction obtained with the different diameters of discs are plotted as poles on an equal area net to show the range of roughness (waviness) (Appendix 6-2). In addition to this a photographs representing a close view of surfaces roughness was taken, with a 40cm ruler placed against the surface in question (Appendix 1-2).

3.4. Straight edge

Large scale (waviness) of the discontinuous surface can be numerically characterized by using straight edge as explained in chapter2, section 2.1.1.3. In this study a wooden straight edge having a width of 10mm and a thick of 30mm with length of 1m was used. The edge is graduated in mm as Figure 3-4 below. A 0.7mm diameter stylus graduated in mm also used to measure the perpendicular distances (Z) or (amax) from the straight edge to the discontinuity surface to the nearest mm for a given tangential distance. It is a quick way of roughness determination method and more applicable for large scale roughness in which we are interested to relate with the large scale roughness derived from the terrestrial laser scan data.

(a) (b)

CHAPTER THREE

30 30

Figure 3- 4 One and two meters long straight edges used for measurement of waviness (Undulations)

3.4.1. Roughness acquisition procedure

For this study straight edge with a manual stylus of radius 0.7mm was used to measure the maximum amplitude in millimetres for the given length of straight edge by placing the straight edge on the selected exposed discontinuity surface. The straight edge should be in contact with the highest points of the rock face and should be as straight as possible. Twelve horizontal and Twelve vertical scan lines were done using the 1m long straight edge parallel to the strike and dip direction (Appendix 1-2). Further more the U value (Eq. [2-1]) is calculated to compared later with the characterization class of Palmström A., 1995 from the laser scan data.

3.5. Riegl 3D imaging sensor-LMS-Z420i

Two terrestrial laser scan data was taken from Tailfer stone quarry in carboniferous limestone near Lustin, Belgium (Figure 5-1). They were generated using a Riegl 3D imaging sensor-LMS-Z420i (Figure 3-5). The RIEGL LMS-Z420i is a rugged and fully portable sensor especially designed for the rapid acquisition of high-quality 3D images even under high demanding environmental conditions. The range measurement precision of Riegl 3D imaging sensor-LMS-Z420i is + 10mm (Riegl, 2006). The range finder electronics, code number 1 in figure 3-5 (right) of the 3D scanner RIEGL LMS-Z420i is optimized in order to meet the requirements of high speed scanning. This part controls the emitting, receiving and processing of the laser beam. To obtain the roughness of a rock surface, the rock surface must be digitized with 3D co-ordinates for each data point. The 3D co-ordinates of each data point, are computed from both the range data captured by the single point laser measurement system and the angular (horizontal and vertical) measurements created from the beam deflection system. The Scan data: range, angle, signal amplitude, and optional timestamp are transmitted to a laptop (code 6) via TCP/IP Ethernet Interface (code 5). Camera (code 7) data are fed into the same laptop via USB/firewire interface (code 8). The laser scanner is also associated with operating and processing RiSCAN PRO software (code 9) (which provides a variety of registration, post processing and export functions), and a calibrated and definitely orientated high-resolution digital camera. The system provides data which lend itself to automatic or semi-automatic processing of scan data and image data to generate products such as textured triangulated surfaces or orthophotos with depth information Source (Riegl, 2006).

FIELD PROCEDURES AND EQUIPMENT USED IN ROUGHNESS MEASUREMENTS

31 31

Figure 3-5 3D RIEGL LMS-Z420i Scanner (left) and its major components of the laser system (right) (Riegl, 2006)

3.5.1. Scanning procedure

The rock surface was scanned in 06/05/2004 by S. Slob and his Colleagues. The 3D scanner RIEGL LMS-Z420i was placed at about a distance of 30 m from the rock face foot. The scanner was set with triggered unidirectional scanning mode and inactive beam of widening lens. The detail scanner configuration and setting for the two data sets used in this study, crop01 of ScanPos01_Scan01 and crop02 of ScanPos01_Scan02, is given in Table 3-1 below. The fracture surface exposed is about 80m x 70m. The whole exposed fracture surface (i.e. ScanPos01_Scan01) was scanned with an average resolution of about 6cm per a point where as part of this fracture (ScanPos01_Scan02 about 15m x 25m) was scanned with an average resolution of about 1cm per a point (Figure 5-1). The scanning lasted about 12.72 and 4.95 minutes for ScanPos01_Scan01 and ScanPos01_Scan02 respectively. Table 3- 1 Scanner settings and configurations during scanning

Scanner setting /configuration ScanPos01_Scan01 ScanPos01_Scan02 Horizontal deflection 155.025 degrees 11.85 degrees Vertical deflection 46.26 degrees 14.76 degrees Measured points 3545934 1751722 Scanning rate 4647 Pts/sec. 5898. Pts/sec. Laser rate 24100.0 Hz 24100.0 Hz Laser wave length 15000 η m 15000 η m

Temperature 240c 240c Supplied voltage 134 V DC 134 V DC Scan mode Triggered unidirectional Triggered unidirectional Software version V56.2-0302104.080027 V56.2-0302104.080027

The laser scanning data is georefferenced to its own coordinate system, relative to the scanner position (often defined as the origin: [0, 0, 0]). If it is needed to integrate into the existing data base in CAD or GIS environment, hence it has to be refferenced to a regional or a local grid system. Further more in case the scanner was inclined in order to capture the top of a steep slope rock face, it has to

CHAPTER THREE

32 32

undergo a complex transformation. For this case at least three white plywood board of dimension 60 x 60cm and three horizontally aligned white cylinders using water levelling were used in the scan scene (See Appendix 1-1). The orientation of the boards can be measured with a regular geological field compass or geodetic measurements. This information can be used in posterior georeferencing of the point cloud data to a regional or a local grid system.


33 33

4. Methodology

This study is divided into four main phases, namely; 1) Data and instrument requirement assessment 2) Fieldwork for roughness data collection and determination 3) Roughness data processing and analysis 4) Descriptive statistics and Statistical regression analysis for comparison and relating. Data and instrument need assessment required detailed investigation on the available point cloud data preparation and the existing traditional methods of surface roughness data capturing for roughness measurement during fieldwork. Therefore data requirement list and data collection form was prepared before fieldwork (Appendix 1-2). Two days fieldwork duration was used to collect rock roughness data using Visual inspection, Straight edge (Figure 3-4) and Compass and disc-clinometer (Figure 3-3) traditional field-based methods. The visual inspections are determined using the standard profiles of JRC (Figure 2-4), ISRM (Figure 2-5), and SSPC (Figure 2-7). The Straight edge measurements are determined according to Barton (1982) to estimate JRC for various measuring lengths and Palmström (1995) for joint waviness estimation. Further more, information regarding the human interaction on the rock surface after scanning was collected to assess whether there is asperity damage or not because this can influence the possible relation between the laser scan derived roughness and the traditionally measured roughness.

The third phase of the research methodology concerns on script development in Matlab codes and commands for surface reconstruction using the FastRBF scattered data interpolation technique and analysis of the raw and reconstructed surface point cloud data (Appendix 3). It concerns also narrow strip profile construction from the raw point cloud data and reconstructed surfaces based on various 2D scattered data curve fitting and smoothing techniques. Using the graphical and numerical fit examination of the reconstructed strip profiles, the ones which looks better and reduces the noises mostly due to the range measurement error of the laser scanner was chosen for the profile construction (section 5.2.3). The final phase of this research emphasizes on comparison and simple linear statistical regression analysis to relate the most commonly used traditional way of surface roughness determination methods and surface roughness derived from the 3D terrestrial laser scan data.

Point Cloud data

Point Cloud data

Field Obs.data

Field Obs.data

DataPreparation

DataPreparation

Data processing& analysis

Data processing& analysis

3D terrestrialLaser scanner3D terrestrial

Laser scanner

MATLAB®MATLAB®

Roughnessanalysis

Roughnessanalysis

Statistical & Visual comparison

Statistical & Visual comparison

FastRBF,Csaps,pchip etc

FastRBF,Csaps,pchip etc

Conclusions &Recommendations

Conclusions &Recommendations

DataOrganization

DataOrganization

Standard Profiles& analogue Instr.

Standard Profiles& analogue Instr.

KdtreeKdtree

Figure 4- 1 Summarized overall research design

CHAPTER FOUR

34 34

4.1. Determination of desire direction

The point clouds are typically georeferenced to a local project grid that have no relationship to geological significant directions such as the strike or dip direction of the discontinuity rock surface. Hence the desire direction will often dependent on the problem at hand. For example, in rock slope analysis, the desire profiles direction is parallel to the dip direction of the discontinuity surface, where as in tectonic studies of exhumed fault surfaces, the desire direction may be parallel to the slickenside directions or other surface features. The desired direction can be measured in the field using a compass and clinometer or, if down dip and along strike profiles are desire; they can be determined by calculating the dip direction of a plane fitted to the point cloud data. In this study, the desire direction was determined along the dip direction, where along and across which field Straight edge measurements and visual inspections of roughness were taken. It was calculated from the dip direction of the plane fitted to the cropped point cloud data in to the nearest one degree. This was applied by defining the normal vector, n = [nx,ny,nz]T (which is pointing up ward to enable keeping track of the dip direction), to the best fit plane passing through the centroid of the point cloud for a given X,Y,Z coordinates of N point clouds which defined the rock surface of interest. This eigenvector corresponds to the smallest eigenvalue of the matrix (Fienen, 2005). Mathematically this can be represented as follows:

��

�

�

��

�

�

−−−−−

−−−−−

−−−−−

��

��

��

===

===

===

N

ii

N

iii

N

iii

N

iii

N

ii

N

iii

N

iii

N

iii

N

ii

zzzzyyzzxx

zzyyyyyyxx

zzxxyyxxxx

1

2

11

11

2

1

111

2

)())(())((

))(()())((

))(())(()(

Eq. [4-1]

Where, yx, , and z are the arithmetic mean values of each coordinate. When we took all the

arithmetic mean values together, it represents the centroid of the point cloud data. This way of determining the mean of the point cloud data is preferable to standard least square methods because it minimizes the normal deviations between the points and the best fit plane, where as the other standard method minimizes only the z-direction deviations.

For easy extracting and analysing of discontinuity surface profiles, it is assumed that the point cloud data is georeferenced such that the positive x-axis corresponds to strike direction (east), the positive y-axis corresponds to north and the positive z-axis corresponds to elevation. To do these, the dip direction (nproj) of the best fit plane should be determined according to:

� = arctan��

�

��

�

y

x

nn

Eq. [4-2]

In Eq. [4-2] above the x and y components are reversed from their normal positions to account for the fact that the azimuth is referenced to the positive y-axis (north) rather than the positive x-axis (east).

METHODOLOGY

35 35

The dip direction is related to the azimuthal angle theta (�) between the nproj and the y-axis (north), but in order to follow the azimuthal convention where the strike (dip direction) is measured clockwise from true north , accommodations must be made for the various quadrants in which nproj is located. Equation [4-2] must be interpreted using as follows. In the first quadrant (northeast), where both the x-and y-components of nproj are greater than zero, dip direction equals to �. In quadrants II (northwest) and III (southwest), where the x-component of nproj is less than zero, dip direction equals 360°-�. In quadrant IV (southeast), where the x-component of nproj is greater than zero but the y-component is less than zero, dip direction equals �. Figure 4-2 graphically shows these relationships for an example in quadrant IV. If there is a local coordinate system other than a geographic coordinate system, the difference between the north and the local coordinate system y-axis must be taken in to account.

The dip direction of the point cloud data is directed downward. Hence the dip angles should be considered to be positive to maintain the consistency with the traditional geologic notation of dip angles. The dip angle of the best fit plane can be calculated as 900 minus the angle between the n and nproj. Mathematically it can be written as follows:

� = 900 - arctan��

�

�

��

�

�

+ 22yx

z

nn

n Eq. [4-3]

In this study the azimuthal convention is advantageous because it requires only a single number to report the result and, after correcting for the quadrants as above, the angles can be calculated automatically. The geologic right hand rule convention, which is strike is always 900 anticlockwise from dip direction or vice versa, was applied to determine strike from dip direction.

Figure 4- 2 Shows the relationship between an inclined and horizontal plane. The vector dip dir. is the dip direction of the plane, n is the unit normal vector defining the plane, and nproj is the projection of n on to the horizontal plane. The dip angle is calculated by evaluating the angle between the n and nproj (φ ) and subtracting the resulting from 900. Note that n is perpendicular to vector dip dir. The strike direction of this example can be evaluated by finding the angle between the positive y-axis and the nproj and subtract from 3600.

CHAPTER FOUR

36 36

4.2. Coordinate rotation

Once the desire direction has been determined as in section 4.1 above, the point cloud data coordinates of the cropped area can be referenced to a coordinate system having axes parallel and perpendicular to the desire direction i.e. in this case the strike and dip direction. This is important because the rotation much simplifies the subsequent data processing and makes available a variety of analytical and visualization tools in which the surface height is given as a function of the two independent orthogonal coordinates. The point cloud data can be rotated in such a way that the dip direction can be corresponds to the negative Y-axis, which is actually shifted to the west about 60 from geographic south, and the surface roughness corresponds to variation in the Z-direction. Here below are discussed the two rotations, first around Z-axis about � (theta) degree and then around X-axis about φ (phi) degree. The general equation in vector transformation i.e. rotation of a given vector

V1 magnitude of r to V2 of the same magnitude about the Z axis (i.e. perpendicular to this page) by an angle � is shown in Figure 4-3 below. Vector V1 is found at an angle � from the X-axis.

Figure 4- 3 Shows a vector rotation around the Z-axis (perpendicular to this page) by angle � and its matrix

representation The next step is applying the same procedure; rotation of the output vector again about the x-axis by an angle φ will be performed to align the best fit plane in the X-Y coordinate plane (Figure 4-4).

These two separate rotations can be composed in to a single matrix from the three dimensional rotation matrix as follows:

��

��

�

��

��

�

×��

�

�

��

�

�

−−

=��

��

�

��

��

�

��

�

�

�

��

��

�

��

��

�

×��

�

�

��

�

� −×��

�

�

��

�

�

−=��

��

�

��

��

�

z

y

x

z

y

x

z

y

x

z

y

x

φφθφθφφθφθ

θθ

θθθθ

φφφφ

cossincossinsinsincoscoscossin0sincos

'''

100

0cossin0sincos

cossin0

sincos0001

'

''

Eq. [4-4]

If the rotations are performed in the order discussed above, there is no need to specify the third Euler angle that is required for more general three dimensional rotations.

METHODOLOGY

37 37

Figure 4- 4 Shows the first rotation around the z-axis such that the desire direction has an azimuth of 00 (a), the second rotation around the X-axis such that the rotated best fit plane lies X-Y plane (b) and finally the two rotations gives the simulation of the frame orientation to align the dip direction with the y-axis and the roughness with the Z-axis (c).

4.3. Discontinuity surface reconstruction (Interpolation)

Once the dense point cloud coordinates have been recast in terms of a coordinate system parallel and perpendicular to the desired direction, they need to be interpolated to construct roughness surface of the discontinuity. There are several surface reconstruction techniques, for example, 2D Grid (topographic analysis) method, 3D Delaunay triangulation method (Dey et al., 2001; Cocone, 2004), FastRBF (RBF for Radial basis Function) (Carr, J.C. et al., 2001; Rahman et al., 2006) and so on. In this study FatRBF technique has been applied to construct the discontinuity surface. Even though the Delaunay triangulation method has the ability to describe the surface at different level of resolution, it was not applied in this study because in this technique every point needs to be connected to reconstruct discontinuity surface, which resulted in rougher surface than the actual one. The Delaunay triangulation technique works well on laser scan data set where the spatial resolution is relatively smaller than the laser’s range error (Slob et al., 2005). The FatRBF technique overcomes this problem without having to under-sampling or use a low scanning resolution. The detail description of the selected technique is discussed below.

4.3.1. FastRBF scattered data interpolation technique

FastRBF scattered data interpolation technique creates a smooth surface from the scattered data using a mathematical function (radial basis function) that is close to the actual surface of the discontinuity (Figure 5-4 and Appendix 4). ‘The resulting function and its gradient can be evaluated any where, for example, on a grid or on a surface. The ability to fit an RBF to large data sets has previously been considered impractical for data sets consisting of more than a few thousand points. FastRBF overcomes these computational limitations and allows millions of measurements to be modelled by a single RBF on a desktop PC. In addition to the exact interpolation of data, the FastRBF toolbox offers several techniques for fitting RBFs (smoothing) to noisy data including error-bar fitting, spline smoothing and linear filtering. FastRBF’s optimised surface-following isosurfacer and implicit surface modelling tools mean that FastRBF is particularly useful for reconstructing surfaces from incomplete meshes and from point cloud range data (FastRBF, 2004)’.

CHAPTER FOUR

38 38

4.3.1.1. Radial Basis Functions (RBFs)

Radial basis Functions (RBFs) are interpolation techniques to interpolate scattered data particularly when the data samples do not lie on a regular grid and when the sampling density varies. Franke (1982) identified RBF as “often giving the most accurate results of all tested methods” and producing surfaces that are “usually pleasing and very smooth”, in large scale comparison of methods for interpolating scattered data in two dimensions. Further more, Hardy (1990) listed a large number of areas where RBFs have been employed, usually with better results than competing techniques. Some of the applications are hydrology, geophysics, geodesy, signal processing and so on. A Radial basis function (FastRBF) as described in FastRBF, 2004 is a function of the form

�=

−Φ+=N

iii xxxpxS

1

)()()( λ Eq. [4-5]

Where:

S is the radial basis function (RBF for short), P is a low degree polynomial, typically linear or quadratic,

The iλ ’s are The RBF coefficients,

Φ is a real valued function called the basic function,

The ix ’s are the RBF centres.

The RBF consists of a weighted sum of a radially symmetric basic function Φ located at the centres

ix and a low degree polynomial P. Given a set of N points ix and values fi, the process of finding an

interpolating RBF, S, such that, S(xi) = fi , i = 1, 2, . . . , N Eq. [4-6]

is called fitting. The fitted RBF is defined by the iλ , the coefficients of the basic function in the

summation, together with the coefficients of the polynomial term p(x). If we let {P1, . . . , P�} be a monomial basis for polynomials of the degree of P, and C = (C1, . . . , C� )̀ be the coefficients that give P(x) in terms of this basis, then the interpolation conditions (Eq. [4-6]), that S(xi) = fi, can be rewritten in matrix form as a linear system,

��

�

�=��

�

�

��

�

�

00f

CP

PAT

λ Eq. [4-7]

Where:

( )jiji xxA −Φ=, i,j= 1,…,N,

( )ijji xpp =, i= 1,…,N, j= 1,…, ��

Solving the linear system (Eq. [4-7]) determines λ and C, and hence S(x).

METHODOLOGY

39 39

4.3.1.2. Fast RBF technique

According to FastRBF, 2004; ‘solving Eq. [4-7] by ordinary or direct methods is computationally expensive and rapidly becomes impossible as N, the number of points to be interpolated, becomes larger than a few thousand. This is particularly true for non-compactly supported basic functions such as the polyharmonic splines which have attractive energy minimisation properties and are consequently known as smoothest interpolators’. But the FastRBF library makes the solution and evaluation of very large systems (above 10,000 points) possible on ordinary hardware. In addition to this core ability, FastRBF also offers various ways of filtering (smoothing) noisy data and special functions for fitting surfaces to point cloud data and incomplete mesh data. The FastRBF library uses fast approximation methods to fit RBFs and to evaluate RBFs. This means that true equality at the interpolation nodes is never achieved. The maximum difference between the fitted RBF value and the given values,

iiNi

fxS −=

)(max,...,1

Eq. [4-8]

is called the fitting accuracy. For a given point x, calculating the value S(x) is called evaluating the RBF. Since the fast approximation methods are used, the true RBF value is not usually achieved. If ai’s are the approximate values of the RBF S at the points xi, then the evaluation accuracy is the value

iiNi

axS −=

)(max,...,1

Eq. [4-9]

Generally, the evaluation accuracy should be much higher (that is, a smaller number) than the fitting accuracy. Figure 4.5 illustrates an exaggerated case of ‘interpolating’ 1D data with FastRBF. The data are shown with fitting accuracy bars. The RBF approximation, the associated evaluation accuracy envelope and the points evaluated within this tolerance are also shown. The details of the FastRBF functions are discussed in Appendix 2-1.

4.3.2. Low pass filtering approach to smoothing

The well known Low pass filtering (LPF) approach is applied in this study rather than the spline-smoothing technique when fitting RBFs to noisy data. The spline-smoothing technique needs high computational time requirement and lacks an intuitive control parameter, where as LPF not. Further more the LPF technique allows a posteriori smoothing of the RBF to suit the desired level of detail required when generating a mesh from the RBF (Carr et al., 2003).

Figure 4- 5 Fitting accuracy and evaluation accuracy (FastRBF, 2004)

CHAPTER FOUR

40 40

4.4. Determination of mean orientation of a given circular window diameter

The determination of the mean orientation of a circular window size 5, 10, 20 and 40 cm diameter which correspond to the discs diameter used in the field actual measurement was carried out in an automated way using the Matlab codes and script (Appendix 3-1) as follows. The sample area of 2m2 from the point cloud data was girded and tilled in to four different square window sizes step by step starting from the smallest window to the largest one. With in each square window, an inscribed circle with a radius of half of the dimension of the square window and centre at C(h,v), where h and v are the centre of the square grid window, was determined using the standard equation of circle (Eq. [4-10]) below.

rvyhx =−+− 22 )()( Eq. [4-10]

Hence, the distance from the centre C(h,v) of a circle to any given point P(A,B) is:

dvBhA =−+− 22 )()( Eq. [4-11]

If point P is inside the circle then the distance d is less than the radius of the circle (r) otherwise it is out side of the circle. By translating this mathematical equation into Matlab codes and script it is possible to define a window of the same size and shape as the circular discs used in the field and defined any points which lay with in the defined circle (Figure 4-6). The defined point cloud data with in the circular window are sub-clustered and their mean orientation is calculated using PCA of Matlab. The third principal component, which is orthogonal to the first two principal components, defines the normal vector of the plane. By projecting this vector onto the X-Y plane, the dip and dip direction of its corresponding sub-clustered point cloud data was defined (see Appendix 3-1).

Figure 4- 6 Procedure showing determination of the mean orientation of a given circular window diameter using PCA in Matlab for the 40 cm window size and triangulation of local surface of sampling (adapted from Fardin et al., 2001).

2m2 main fitting plane

Local fitting to circular window

n

nproj x

y

Square sampling windows of size w

METHODOLOGY

41 41

The manually measured orientations were organized and prepared in Excel data sheet with dip and dip direction of each field data. The dip and dip direction measurements of the different disc sizes are rotated in to a horizontal reference plane position around a specified axis. The derived and manually measured dip and dip direction measurements are plotted as poles on an equal area stereonet in RockWare 2002 Utilities program for roughness quantification using the Fecker and Rengers (1971) method. A lower hemisphere projection was used in this study.

4.5. Directional rock surface roughness determination

From the rotated (recasted) point cloud coordinates into a coordinate system parallel and perpendicular to the desired direction, narrow strips are cropped for directional profile construction and further analysis from the raw and reconstructed point cloud data. The maximum length of profile in SSPC is 1m, and a standard stick of 1m long was used in Milne et al. (1991) in his joint roughness number (Jr) determination. Palmström (1995) also used a 0.9m long stick in his Joint waviness (undulations) estimation using the chart of Barton (1982) to estimate JRC for various measuring lengths. Hence, 1m long strip profile is focused in this study to estimate surface roughness and compare it with traditionally determined directional surface roughness results. Further more, as the stick length is increased to 2m, the roughness asperities increases in small amount or not as the result of homogeneity (i.e. small or no change in grain size or random distribution of certain minerals through out the plane).

Local trend

Max. residual

Min. residual

i-angle

Profile length (1m) Figure 4- 7 Methodology showing calculating of the residuals from the local trend of a given profile for determination of the maximum amplitude to estimate JRC for various measuring lengths using the chart of Barton (1982) and to estimate the i-angle and amplitude of roughness according to SSPC method. As the procedure described by Piteau (1970), the maximum amplitude or offset (Eq. [2-1]) in straight edge measurement is determined by measuring the maximum deviation from the planarity to the rock surface using a 1.0m long straight edge placed on the rock surface. In the same way the maximum amplitude or offset of the laser scan derived strip profiles are determined by adding the magnitude of the maximum and minimum residuals (which is the same as the maximum deviation of two lines parallel to the best fit line and passes through the maximum and minimum values of the profile residuals) from the best fit linear line of a 1m long strip (Figure 4-7). The strips from the raw point cloud data set are first smoothed using the smooth pane and smoothing spline of the Curve Fitting Tool in Matlab. The smoothed raw data strips and strips from the reconstructed surfaces are fitted using various fits of Curve Fitting Tool in Matlab and examined graphically (goodness of fit using residuals) and numerical fit results(goodness of fit statistics and

CHAPTER FOUR

42 42

confidence intervals on the fitted coefficients) to determine the best fit. For more details about the Curve Fitting Tool please see Appendix 2-2.

4.6. Range measurement error estimation

To evaluate how much amplitude is removed for a given low pass filtering (LPF) width during RBF fitting and to indirectly estimate the range measurement error or noise; the fractal parameters are extracted from the power law relation between the standard deviation of the residuals of surface heights S(w) and sample window diameter (w) following Eq. [2-18]. The residuals of asperities heights S(w), defined as the normal distance between the surface asperity heights and their local fitting plane are calculated for each square window by least square regression analysis. This method has been used for calculating fractal parameter of 3D discontinuity rock surface roughness (Fardin et al., 2004; Rahman et al., 2006). The range measurement error or noise of the 3D surface roughness was tried to estimate by subtracting the fractal parameters of reconstructed surface data set from raw data set. The range measurement error or noise of the 2D narrow strip profiles was tried to estimate by subtracting the maximum amplitude of the smoothed strip profile from raw data set strip profile. It was tried also to estimate the influence of this range measurement or noise in roughness estimation using the chart of Barton (1982) to estimate JRC for various profile lengths (measuring lengths) and standard reference profiles.

4.7. Visualization

Both colour and gray scale terrestrial laser scan point cloud data with ‘*.xyz’ extension have been visualized using the RISCAN_PRO and Split Engineering Fx version 1.0 (Figure 5-1) soft wares respectively for selecting discontinuity surface and approximate location of the sample grid where practical measurements have been done(Figure 3-2). The X,Y,Z coordinates of the scan data sets to be cropped can be read off relative to the scanner position in the above mentioned softwares. The interpolated laser scan data stets has been visualized in various stages of interpolation (Appendix 4) using Deep exploration software. The out puts of scatter data interpolation method (functions) are evaluated and compared visually using Deep Exploration (Figure 5-3 and Appendix 4).

Finally a sensitivity analysis of RBF surface fitting before and after the global trend has been removed was carried out to determine whether to rotate the raw data or interpolated data. This was followed by a sensitivity analysis of possible shifting of locating the 2m square grid on the low resolution point cloud data was carried out to defined four directions (up, down, & back by 10cm; and diagonal in SE direction by 14.14cm). Then after, it was tried to compare the circular window mean orientation with its corresponding disc orientation on the cell by cell basis. The results are visualized using stereonet plot as an equal area, 3D scatter plot and Histograms for easy recognition and comparison. The large scale directional roughness of the laser scan derived 1m long narrow strip profiles (Appendix 7) are also compared with the visually estimated and traditionally measured roughness using the standard profiles and field-based analogue instruments.

METHODOLOGY

43 43

Pha

se o

neP

hase

two

Pha

se th

ree

Pha

se fo

ur

Figure 4- 8 Overall research methodology


45 45

5. Data analysis and results

5.1. Data preparation

Two laser scan data sets which were taken at one large discontinuous rock surface with different resolution have been analysed. These data sets were generated using Reigl 3D imaging sensor-LMS-Z420i (for details see Table 3-1) from part of Tailfer stone quarry in carboniferous limestone near Lustin, Belgium (Figure3-2). The relative location of the two data sets used in this study is shown in Figure 5-1 below. The range measurement precision of the instrument used in this study is + 10mm (Riegl, 2006).

Table 5- 1 List of data sets used with their corresponding scanner measurement accuracy, average resolution and type of scanner. Data set collected Crop no. Name of data set Type of Scanner Measurement Resolution from accuracy (mm) (cm/pt)

Lustin-Belgium 01 Lustin_ScanPos01_scan01 Riegl 3D-Z420i + 10 6 Lustin-Belgium 02 Lustin_ScanPos01_scan02 Riegl 3D-Z420i + 10 1

The selection and cropping of the raw (x,y,z,) data starts with visualizing the point cloud data in Fx, beta version 1.0 from Split Engineering and RiSCAN PRO softwares. Since the scanner has a digital camera attached that takes picture of the object that is scanned, the colour information from the digital imagery can be used to colour the point cloud generated by the laser survey. It is also possible to read off the X,Y,Z coordinates of each point of point cloud data relative to the scanner’s position during visualization. The interested part of the point cloud data from the raw laser scan data of ScanPos01_scan01 was cropped by approximately locating the corners of 2m x 2m grid where the practical measurements were done. The combination of the key components such as the scanner, the RiSCAN PRO software, and the 8.2 mega pixel CANON EOS colour camera, results in a good identification of details (Reigl, 2006). Hence, the corner of the grid were located by rotating the colour laser scan data in to an approximate angle of view as the digital photo which was taken during the practical measurement on the rock face and their corresponding X,Y,Z, coordinates were picked. These X,Y,Z coordinates of the four corners are used to crop the laser scan data in Matlab for further analysis. The raw laser scan data of ScanPos01_scan02 was cropped by selecting a place where there is no or few influence of mosses which are grown on the rock surface. Figure 5-1 below shows the dip slope of the limestone bedding planes from which the two test surfaces (crop01 and crop02) have been selected.

CHAPTER FIVE

46 46

Figure 5- 1 Overview of the laserscan of a large bedding surface taken by Riegl 3D -LMS-Z420i (Scanpos01_scan01) (left) and Part of it (Scanpos01_scan02) (right) with average resolution of 6cm/pt and 1cm/pt respectively. The approximate locations of cropped samples (crop01and crop02) are indicated. Note: it is not a picture, but the xyz data added with the return signal amplitude for each pulse (intensity), and with colour (red, green, blue) information extracted from digital imagery (left). Table 5- 2 List of the two cropped data sets with their dimensions used for the analysis.

Name of data set Sample name Coordinate Dimension Minimum (m) maximum (m) after rotation X Y Z X Y Z (m x m)

Lustin_ScanPos01_scan01 crop01 -52.70 8.00 3.11 -50.00 10.70 6.87 3.64x5.12 Lustin_ScanPos02_scan02 crop02 -50.00 -11.10 16.97 -47.00 -8.10 12.50 4.21x6.13

5.2. Data processing and Visualization

5.2.1. Geometric correction

The point cloud data is in principle georeferenced to its own coordinate system, relative to the scanner’s position. Often the scanner’s position is defined as the origin, [0,0,0]. More over, the direction in which the scan is being made (where the laser beam has angle 0 and azimuth 0) is considered the Y direction (or false North) and X and Z the (false) Easting and (false) elevation, respectively (Slob et al., 2005). If it is needed to integrate the data into existing databases in CAD or GIS for example, then the data has to be referenced to a regional or a local grid system. For a very accurate georeferencing to a global or local grid, additional geodetic measurements will still be needed. However, in this study, it is not strictly necessary to georeference the entire data set to a local or regional grid or coordinate system. For deriving the 3D and 2D roughness, it is only required to re-orient the data relative to the desire directions i.e. the strike and dip direction (see chapter 4 section 4.1and 4.2). In other words, the (X,Y,Z) coordinates should be referenced such that the negative Y-axis represents the dip direction and the positive X-axis represents strike direction and Z represents the actual elevation (roughness) (see chapter 4 section 4.2). Of course, it is a crude way of re-orienting, which depends entirely on the precision with which the bearing of the scanner can be measured and the accuracy with which the scanner can be levelled. However, the relative accuracy

��

��

��

��

Sample area (crop 01)

Crop 02

DATA ANALYSIS AND RESULTS

47 47

remains intact (Slob et al., 2005). “For a slope stability analysis for example, it is merely needed to know the relative orientation of joints and bedding planes compared to the actual slope orientation and geometry. The same applies to quarry and tunnel operations, where the block size and block stability is of key importance, which does not require an absolute georeferencing (Slob et al., 2005)”.

5.2.2. Surface reconstruction

The raw point cloud data sets are converted into ASCII format and then interpolated as a 3D surface model in order to analyze the surface of the object they represent. As explained in section 4.3 of chapter 4, FastRBF scatter data interpolation technique was applied to reconstruct the 3D surface model and to remove the range measurement error using LPF approach. The raw data of crop01 from Scanpos01_scan01 and crop02 from Scanpos01_scan02 are used for surface reconstruction and to remove the range measurement error. The description of the FastRBF function parameters that are used to reconstruct the surface and model visualization is discussed below:

5.2.2.1. Using the FastRBF interpolation technique

By assuming that the noise, artefact (spikes) and (range measurement error) in the data can be discriminated by its contribution to the higher frequencies (random variations) in the surface data that are attributed to noise or to fit a smooth surface within some distance of the actual surface measurements, an attempt was made to reduce it by applying a low pass filter (LPF) with a suitable cut-off frequency, during RBF evaluations (see the detailed description of RBF in chapter 4, section 4.3). The FastRBF parameters used in reconstructing the discontinuity surface from the raw laser scan data sets are discussed below.

The FastRBF technique can be fitted the point cloud data in three steps. The first step is constructing a signed–distance function. The second step is fitting a RBF to the resulting distance function followed by Iso-surfacing the fitted surface to extract the interpolating surface (Carr et al., 2003, FastRBF, 2004). To cerate distance-to-surface density data for RBF fitter, first we need some surface normals. It was estimated by fitting a plane to a horizontally rotated subset of points in the neighbourhood of each point. The ambiguity in the sign of the normal can be resolved by using the position of the scanner when that point was measured. Since the surface data are only available as a point cloud without any additional information, i.e., purely vertex data, then fastrbf_normalsfrompoints was applied to estimate the normals with default parameters (i.e. 1.0, which means for a given N surface points, no more than N off-surface points will be added).

The distance-to-surface density data is derived from the points and normals by: ‘fastrbf_densityfronnormal’ function. The distance-to-surface density is not defined everywhere. It is defined only within a band surrounding the surface. The width of this band is set by the maximum normal length. RBF values at points further than the maximum normal length from the surface will not necessarily be the distance to the surface. A value of several times larger than the average mesh resolution is usually sufficient and must certainly be greater than the accuracy specified in the RBF fitter. Since the range measurement error of the scanner used in this study is + 0.01m, the minimum normal length is set to 0.01m. The maximum normal length is set to 0.030m, which is several times larger than the average mesh size and is also greater than the accuracy specified in the RBF fitter (i.e.

CHAPTER FIVE

48 48

0.002m). The next step is to ensure that no identical points exist before fitting using the ‘fastrbf_unique’ function. This is because the RBF fitter is unable to handle input data in which any points are either identical or very nearly identical.

The second step is fitting a plane to the data set using ‘fastrbf_fit’ function. There are four fitting strategies in FastRBF. These are direct, reduce, errorbar and rho (�). ’direct’ uses fast direct fitting algorithms to solve the traditional RBF fitting problem where each interpolation point is used as an RBF centre. This is the best fit for true density data. ‘reduce’ uses a greedy algorithm that selects a subset of interpolation points as RBF centres until the desired accuracy is met at all the points. This is best for clean data with little noise. In both these algorithms, the returned RBF is ”within the fitting accuracy of the smoothest interpolant of the data”. ‘errorbar’ uses a restricted range interpolation approach and the returned RBF approximates the data values. It is the best for noisy data or when the fitting accuracy is quite loose. ‘rho’ also fits an approximating RBF determined by a parameter � which balances faithfulness to the data against smoothness. The higher value of rho will create a smoother fit but will interpolate less accurately. The accuracy specifies the fitting accuracy or tolerance. The RBF value will be within this amount of the original value at each input point. In this study, the direct fitting option was applied, since each interpolation point has to be used as RBF centers. The fitting accuracy was set 0.002m which is less than the mesh resolution (i.e. 0.01m). The fitting accuracy more than 0.002m takes more time to fit an RBF surface for the Scanpos01_scan02 data set. The ‘reduce’, ‘errorbar’ and ‘rho (�)’ options are not used in this study because these options reduce the RBF centers significantly and only a subset of the original data points are utilized as RBF centers. There fore the roughness details of the rock surface can be lost.

The third step is extracting an isosurface from a 3D RBF solution using the ‘fastrbf_isosurf’ function. The mesh resolution of 0.01m is set for these laser scan data sets, because the average resolution of the Scanpos01_scan02 data set is 0.01m. Even though the average resolution of the Scanpos01_scan01 is 0.06m per a point, it should be interpolated with a mesh size of less than its resolution in order to analyse roughness using the smallest window diameter. For this case the Scanpos01_scan01 data is also set with mesh resolution of 0.01m. By assuming that the noise, artefact (spikes) in figure 5-3 can be discriminated by its contribution to the higher frequencies, it was tried to reduce it by applying a low pass filter (LPF) with a suitable cut-off frequency during RBF evaluations. The LPF (cut-off frequency) filter width is set to be 0.01m, since the range measurement error of the RieglLMS-Z420i is + 0.01m. Different iso-surfaces were also extracted with out and with filter width of 0.02, 0.03, 0.04, and 0.05m (see Appendix 4) for visual comparison of the reconstructed surfaces with the digital photo of the rock face and to evaluate how much amplitude is removed due to an increase of LPF by a given amount. Data smoothing can be achieved by performing another fit using the errorbar option or � smoothing to the exact fit RBF computed, but they need more computational time than LPF. Finally the filtered and unfiltered reconstructed surfaces data have been exported using the ‘FastRBF_export’ function as wave front ‘OBJ’ for visualization in deep exploration and formatted text ‘TXT’ format for further surface roughness analysis in Matlab. The above discussed surface fitting technique can be applied before or after the raw point cloud data have been rotated into a horizontal position. A sensitivity analysis was carried out for fitting RBF


49 49

surface before and after rotation has been carried out into horizontal position of the raw point cloud for this application. The results are discussed in section 5.3.1.1 of this chapter below.

5.2.2.2. Surface model visualization

Both raw colour and gray scale terrestrial laser scan point cloud data with ‘*.xyz’ extension have been visualized using the RISCAN_PRO and Split Engineering Fx version 1.0 softwares left and right of Figure 5-1 respectively for approximately locating the interested part of discontinuity surface; where practical measurements have been done. The raw point cloud data sets used for surface reconstruction i.e. crop01 from Lustin_Scanpos01_scan02 and crop02 from Lustin_Scanpos01_scan02 are shown in Figure 5-2 below using the Split Engineering Fx version 1.0.

Figure 5- 2 Rotated and cropped raw laser scan data of crop 02 from Lustin_Scanpos01_scan02 (left) and crop01 from Lustin_Scanpos01_scan01 (right) with an average spatial resolution of 1cm and 6cm per a point respectively in Engineering Fx version 1.0 software. The green line indicates the positive x-axis; the blue line indicates the positive y-axis and perpendicular to this page is z-axis. Dimension: 2m x 2m. The reconstructed laser scan data stets have been visualized in various stages of interpolation using Deep exploration software (Appendix 4). The unfiltered reconstructed surface data are showing artifacts (unwanted spikes) due to noise or range measurement error of the scanner, for example, unfiltered reconstructed surface data of Crop02 from Scanpos01_scan02 (Figure 5-3). The filtered reconstructed surface data of the same data set are not showing much artefacts; this means that most of the noise contributed due to the range measurement error of the scanner have been removed (Figure 5-4). The reconstructed surface (synthetic shaded) relief images in Figure 5-3, 5-4 and Appendix 4 are illuminated from three different directions in space: from top in southwest inclined at 450, from side northeast and from bottom up ward.

x

y y

x

CHAPTER FIVE

50 50

Figure 5- 3 Example of unfiltered reconstructed surface data of Crop02 from Lustin_ScanPos01_Scan002, mesh resolution 1 cm, raw data resolution 1cm per point, showing unwanted spikes

Figure 5- 4 Example of filtered with 1cm filter width reconstructed surface data of Crop02 from Lustin_ScanPos01_Scan002, mesh resolution 1 cm, raw data resolution 1cm per point.


51 51

5.2.3. Directional roughness profile reconstruction

From the rotated into a horizontal position of raw and reconstructed data sets, three vertical and horizontal narrow strips of 1cm width and 1m length are cropped for directional profile reconstruction and further analysis as described in chapter four, section 4.5. The raw data narrow strips of crop02 from Scanpos01_scan02 are used for profile reconstruction and to remove the range measurement error. However, narrow strips of crop01 raw data set are not considered due to its low resolution, which is 6cm per a point. That means the number of points picked in the 1cm narrow strip are too low to reconstruct a profile. The number of points picked varies from minimum of 3 to 8 according to the position and roughness complexity of the surface for 1m length in crop01 raw data set. The vertical strips are cropped from the top left corner, middle and top right corner down ward, where as the horizontal are cropped from the bottom right corner, middle and top right corner of the sub-sample 2m2 grid. The cropped narrow strips are fitted using various fits of Curve Fitting technique in Matlab. The detailed description of the Curve Fitting techniques which are used to reconstruct (interpolate) the 2D directional roughness profile model is discussed below:

5.2.3.1. Raw data directional roughness profile

Two 1m long narrow strips with width of 5mm and 10mm of crop02 laser scan data are evaluated to determine the appropriate width of narrow strip for profile reconstruction. Among these, the profile with strip width of 10mm is chosen because the point information which were lost in the 5mm strip due to shadowing effect of out prodding asperities and complexity of roughness distribution are substituted (considered) in the 10mm strip width (Figure 5-5). Figure 5-5 shows how much the gaps are improved by having a narrow strip of 10mm width than 5mm width. The red points are the newly added point’s information by increasing the strip width to 10mm. Furthermore by taking a strip width of 10mm we will have consistency width with the straight edge width (10mm) which was used in the manual measurement to estimate JRC and waviness factor (jw) for various measuring length using the chart of Barton (1982). But we might have at the same location two heights, hence one of them should be remove otherwise the spline interplant will not work in the raw data set strip smoothing using the smooth pane in Matlab.

Figure 5- 5 Evaluation of 5mm and 10mm width narrow strip horizontal profile of Scanpos01-scan02 raw data set. It shows how much the gaps are improved by having a narrow strip of 10mm width than 5mm width. The red points are the newly added point’s information by increasing the strip width to 10mm.

Three vertical and horizontal narrow strips are taken from raw data of crop02 for two dimensional profile reconstruction. The raw data strips of crop02 data set are smoothed using the smooth pane and smoothing spline of the Curve Fitting Tool in Matlab. The smooth pane produces a new data set containing the smoothed response values using six smoothing method (Moving average, Lowess, Loess, Savitzky-Golay, robust-Lows and Robust-Loess). In this study among the six smooth panes, a Lowess (linear fit) is chosen to reduce the noise mostly due to the range measurement error because it

CHAPTER FIVE

52 52

locally weighted the scattered plot smooth using the linear least squares fitting and a first degree polynomial. However the others either do not consider the local weighted or are only outlier resistant. By increasing the span (the number of data points used to compute each smooth value), from 3 to 8 with one step increase, a higher smoothing effect can be achieved. Among these spans, a span of 6 is chosen for the analysis. Because it gives a more or less better look profile as compared to the higher and lower span number profiles. It looks also similar to the profiles from the representative surface model (Appendix 7) and field estimated standard profiles. Smoothing Spline, which is a piecewise polynomial that varies from linear to cubic by adjusting the level of smoothing with the smoothing parameter from zero to one also gives good results of profile. The default parameter value depends on the data and often produces the smoothest fit. But in this study the smoothing effect of smoothing spline in the raw strip data sets is not good as the Lowess in the smooth pane. With the Curve Fitting Tool in Matlab, the smoothed raw data strips are visually explored and fitted using various fits. The various fits such as using a library (Exponential, Fourier series, Gaussian, Polynomials, Power series etc) or custom equation, a smoothing spline, or an interpolant are examined graphically (using visual goodness of fit using residuals) (Figure 5-6 below) and numerical fit results (using goodness of fit statistics and confidence intervals on the fitted coefficients) (Table 5-3) to determine the best fit. The goodness of fit statistics determines how well the curve fits the data. The confidence intervals (which is set 95%) on the coefficients determine their accuracy. In this study, the sum of squares due to error (SSE), the residual degrees of freedom (DFE) and the adjusted R-square statistics are used to determine the best fit (Table 5-3). The SSE statistic is the least squares error of the fit, with a value closer to zero indicating a better fit. The adjusted R-square statistic is generally the best indicator of the fit quality when you add additional coefficients to your model. DFE is defined as the number of response values minus the number of coefficients estimated from the response values. For more details see Curve Fitting Toolbox in Appendix 2-2. In this study interpolant fit model with spline, delaunay and shape preserving interpolants gives a good numerical fit results (Table 5-3). The spline interpolant uses the spline function, while the shape-preserving interpolant uses the pchip function (See Appendix 2-2 for details). The cubic polynomial fit, which uses the polyfit function, gives a much smoother profile hence it is not considered in to account for comparison with the standard profiles. The graphical examination of the profiles from the delaunay and shape preserving fit models show more or less the same profile curves for 1m long strip profiles from the raw data in the 1 to 1 vertical to horizontal scale (Figure 5-6). The spline interpolant gives unrealistic big humps (profile heights) in the case of raw data strip profile construction and some limitations at the start and end of the profile, (Figure 5-6 and Appendix 7). The reason for these huge humps in case of spline interpolant is the abrupt change of consecutive points of closely spaced (dx) with the large relative elevation difference (dy) to small or no elevation difference but large relative horizontal distance difference (Figure 5-6). However it is not much observed in the case of smoothed raw data strip interpolation (Figure 5-7). Hence the shape preserving interpolant fit model is chosen to reconstruct directional roughness from the raw data to compare it with the standard profiles and straight edge results. All the reconstructed raw data narrow strip profiles are in Appendix 7.


53 53

Figure 5- 6 The difference between the Delaunay, spline and shape-preserving interpolant for the raw strip profile

reconstruction from crop02.

Table 5- 3 The goodness of fit statistics for different fit models of Curve Fitting techniques in Matlab Name of model

Type of fit model Data set SSE R2

Adjusted R2

DFE RMSE

Cubic spline interpolant Strip H1 raw 7.52E-35 1 0 0 NaN

Shape preserving interpolant Strip H1 raw 0 1 0 0 NaN

Cubic polynomials Polynomials Strip H1 raw 9.16E-04 0.7478 0.7455 59 3.94E-03

9th degree poly. Polynomials Strip H1 raw 8.73E-04 0.7691 0.7299 53 4.06E-03

Power series Power series Strip H1 raw 3.71E-03 1.88E-02 2.73E-03 61 7.80E-03

Exponential Exponential Strip H1 raw 3.14E-03 0.1706 0.157 61 7.17E-03

Fourier series Fourier series Strip H1 raw 3.47E-03 8.33E-02 3.67E-02 59 7.66E-03

Smoothing spline Smoothing spline Strip H1 raw 2.16E-04 9.43E-01 0.7546 14.41 3.87E-03

Figure 5- 7 Example of the smoothed raw data using the smooth pane (top) and interpolated profiles of crop02,

strip_H1 using Cubic spline (middle) and shape-preserving (bottom) interpolant techniques: Approximately vertical to horizontal scale is 1:1.

5.2.3.2. Reconstructed surface directional roughness profile

The mean of the reconstructed surface data is slightly changed by 2 or 3 mm from [0 0 0] as the result of converting the format from ‘*.xyz’ to ‘*.txt’ for surface reconstruction. Hence the mean of the reconstructed surface vertices are translated to mean [0 0 0] before narrow strip cropping. Three vertical and horizontal narrow strips with 1cm width and 1m length as the raw data strips are cropped from crop01 and crop02 reconstructed surfaces with 1cm filter width and mesh size. These cropped

CHAPTER FIVE

54 54

strips need to be interpolated (fitted) to reconstruct directional roughness profiles. The same procedure was applied as raw data strip profile reconstruction and evaluation (See section 5.2.3.1 above). The cubic spline and shape preserving interpolants gives much better looking profiles and good numerical fit results (Figure 5-9, Figure 5-10 and Table 5-4 below). The graphical examination of profiles from these two interpolant curve fitting models is more or less the same in the 1:1 vertical to horizontal scale (Figure 5-9). The unrealistic humps (profiles heights) in case of raw data strip profile construction (Figure 5-6), are mostly removed due to more point information with more or less equally spaced are taken into consideration as the result of interpolation during surface reconstruction. However; the problem of humps is not solved in some of the profile as discussed in raw data strip profile construction section 5.2.3.1 above. There fore, the shape-preserving interpolant fit model is chosen to reconstruct directional roughness from the reconstructed surface data strips to compare it with the standard profiles and straight edge results as discussed in section 5.2.3.1. All the reconstructed profiles from the narrow strip reconstructed surface data are in Appendix 7.

Figure 5- 8 Similarity between cubic spline and shape-preserving interpolant for the reconstructed surface narrow

strip profile interpolation of crop02. Table 5- 4 The goodness of fit statistics for different fit models of Curve Fitting techniques in Matlab

Name of model

Type of fit model Data set SSE R2

Adjusted R2

DFE RMSE

Cubic spline interpolant Strip H1r raw 0 1 NaN 0 NaN

Shape preserving interpolant Strip H1r raw 0 1 NaN 0 NaN

Cubic polynomials Polynomials Strip H1r raw 3.04E-04 0.9223 0.9194 80 1.95E-03

9th degree poly. Polynomials Strip H1r raw 2.28E-04 0.9417 0.9346 74 1.76E-03

Power series Power series Strip H1r raw 3.67E-03 0.0614 0.05 82 6.69E-03

Exponential Exponential Strip H1r raw 2.81E-03 0.2821 0.2734 82 5.85E-03

Fourier series Fourier series Strip H1r raw 3.87E-03 0.0112 -0.0259 80 6.95E-03

Smoothing spline Smoothing spline Strip H1r raw 7.81E-06 0.998 0.9946 30.75 5.04E-04


55 55

Figure 5- 9 Example of the narrow strip of reconstructed surface of crop02, strip_Hr1 (top) and reconstructed profiles using spline (middle) and shape-preserving (bottom) interpolant techniques: Approximately vertical to horizontal scale is 1:1.

Figure 5- 10 Example of the narrow strip of reconstructed surface of crop01, strip_Hr1 (top) and reconstructed profiles using spline (middle) and shape-preserving (bottom) interpolant techniques: Approximately vertical to horizontal scale is 1:1.

5.3. Roughness quantification

5.3.1. Reconstructed surface roughness quantification

The 1cm filtered rectangular samples of reconstructed surface models of crop01 from ScanPos01_scan01 and crop02 from ScanPos01_scan02 have been selected for analysis. The Matlab script used for this analysis is in Appendix 3-1. The filtered reconstructed surface data are loaded as ‘*.txt’ file separately in Matlab. The circular window diameters used for the analysis of roughness are defined according to the field-based compass and disc-clinometer method suggested by Fecker and Rengers (1971). The details of the procedures that have been applied to analyze the filtered reconstructed surface data sets (for example, Figure 5-4 and Appendix 4) are:

CHAPTER FIVE

56 56

� The raw point cloud data samples were not in a horizontal position. The RBF surface can be fit to these raw samples or after the raw samples have been rotated into a horizontal position. If RBF surface is fitted to the raw samples before they have been rotated into a horizontal position, it is necessary to remove the global trend of the discontinuity surface to have appropriate dimension window sizes in the X-Y plane rather than projected dimension for appropriate roughness quantification following the traditional Fecker and Rengers (1971) method. Therefore, in this study the raw samples need to be rotated into a horizontal position first and then fitted with RBF surface. The samples are rotated in such a way that the dip direction can be corresponds to the negative y-axis, and the surface roughness corresponds to variation in the z-direction (see chapter 4 section 4.2). From the sample rotated into the horizontal X-Y plane and fitted with RBF surface, a square sub sample size of 2m2 has been taken for analysis from each initial sample of crop01 and crop02. A detail description of this procedure is given in Matlab scrip in Appendix 3-1. This could help us also in carrying out the sensitivity of RBF fitting before and after the raw point could data samples have been rotated into a horizontal position for this application (see section 5.3.1.2 below).

� The square sub-sample (size: 2m2) has been divided into square grid or windows. The window

sizes are 2.5%, 5%, 10% and 20 % of the total sub-sample size (Table 5-5). With in the square grid an inscribed circle of diameter the same as the dimension of the square grid was defined. These circular windows correspond to the discs size of 5, 10, 20 and 40 cm diameter of Fecker and Rengers (1971).

� For each circular window, a local fitting plane is defined by a least square-regression analysis

using Matlab’s Principal Component Analysis (PCA) function (see Appendix 3-1). The dip and strike direction are calculated for each window from the normal vector of the best fitting plane using the least square regression analysis. Accommodations’ are done to maintain the consistency with the geologic right hand rule convention of notation dip angle and dip direction (see chapter 4 section 4.1). Further more, residuals of asperity height (S(w)), defined as the normal distance between the surface asperity heights and their local fitting plane and the total number of points considered in each window is also calculated for each circular window from the trend surface of the least square-regression.

� The unit normal vector orientation, the standard deviation of S(w) of all points, dip and dip

direction of each window are calculated in Matlab. The dip and dip direction results are subsequently exported to Excel format which is supported by rockware for importing the data to plot as poles on an equal area net (Figure 5- 11). The standard deviations of S(w)of all windows in each sub-sample are added together in Excel and the average standard deviation of S(w) per window is calculated (Table 5-12).

� The dip and dip direction data is plotted on polar equal area nets separately for each of the

four windows as shown in Figure 5-11 and Appendix 6. The effective positive and negative roughness angle have been estimated from contours of maximum scatter for different window diameters along the dip direction and are plotted as plot of effective i-angle versus circular window diameter s (Figure 5-12 and 6-5).


57 57

� Circular window sizes and their corresponding average S(w) of crop02 are plotted as double log graph in X and Y-axis respectively (Figure 5-19).

� A best fit line has been drawn using the power law equations in Excel to evaluate the fractal

parameter D and amplitude parameter A for the raw data and a given LPF width. The parameter D and A can be easily estimated from the constant coefficient of the power law equation (Figure 5-19) to estimate the range measurement error.

� Finally the laser scan derived circular windows orientation is compared with the measured

discs orientation using field-based disc and clinometer method. The delta angle of standard deviation of normal vector difference was calculated and visualize as 3D scatter plot in Matlab (Figure 5-1 and Appendix 6). Further more histograms which show the deviation from the measured dip amount and dip directions are plotted in Appendix 6.

Table 5- 5 Procedure of dividing the square sub-sample of 2m2 into four inscribed circular windows with in the four square grids.

Square window Grid cells Total number of Circular window size (%) Circular windows area (cm2)

2.5 40 x 40 1600 78.54 5 20 x 20 400 314.16 10 10 x 10 100 1256.64 20 5 x 5 25 5026.55

Once the point cloud coordinates of crop01 and crop02 have been recast in terms of a coordinate system parallel and perpendicular to the desired direction as in chapter 4 section 4.2 and reconstructed as in section 5.2.2, they need to be quantified their roughness according to the procedure discussed above. The unfiltered and filtered reconstructed surface data of crop01 and crop02 have been analyzed on the basis of compass and disc-clinometer method using Matlab script. The script is discussed in Appendix 3-1. Only raw data set of crop02 has been analyzed as the procedures used for the reconstructed surface data. The raw data is loaded as ‘*.xyz’ file in Matlab. The raw data set of crop01 is not analyzed because it doesn’t fulfil the minimum number of points (i.e. three points) for the 5 and 10 cm diameter windows to calculate the orientation of best fit plane as discussed above. This is due to its low resolution (i.e. 6cm per a point). Hence crop01 data is interpolated with a mesh size of 1cm i.e. smaller than the raw data point spacing. This can produce a smooth surface that is more easily visualized than the one based on the coarse mesh. It doesn’t add any information about roughness components with wave lengths shorter than the raw data point spacing. This could assist in fulfilling the minimum point data density requirement for mean plane orientation calculation for the smallest window. The derived dip and dip direction of raw, filtered and unfiltered data set from crop02 and crop01 (not raw data) are plotted on polar equal area nets separately for each of the four windows (Figure 5-11 and Appendix 6).

CHAPTER FIVE

58 58

Figure 5- 11 Polar equal area plots of poles from crop02 of Scanpos01_scan02 laser scan data for circular windows of diameters (5, 10, 20 and 40 cm) (1cm filtered). The arrow indicates dip direction.

The result of the polar plot shows that the scattering of pole increases from the largest window diameter to the smallest as it is discussed in compass and disc-clinometer method. It also shows the scale dependency clearly by the scattering. This means poles with the largest distance from the centre of polar net represent largest roughness angle (i-angle) between the mean orientation of the square 2m2 sub-sample window and the mean orientation of the circular windows. The mean orientation of circular windows is assumed to represent the roughness tangent as explained in the compass and disc-clinometer method (see chapter 2, section 2.1.1.2). These poles with the largest distance from the centre are connected to form a contour of maximum scatter (envelope) for each window size. From these envelopes the effective positive and negative maximum roughness angle (i-angle) has been estimated for each circular window size (Table 5-6) in the dip direction. The maximum roughness angle for a given window diameter can be plotted for any direction of potential sliding, for cases where the potential sliding is not known. Since the potential sliding is known in this case that is the dip direction, the maximum roughness angles are estimated along the dip direction These extreme values of maximum roughness angle (i-angle) are plotted versus the circular window diameters of


59 59

raw, 1cm filtered and 3cm filtered reconstructed surfaces of crop02 data set as in Figure5-12 below to see the effect of noise along the dip direction. Table 5- 6 Positive and negative i-angle estimated from the envelopes of effective i-angle for each window size from crop02 of ScanPos01_scqn02 data set along dip direction. Window diameter raw data 1cm filtered 3cm filtered (cm) +ve i (deg.) –ve i (deg.) +ve i (deg.) –ve i (deg +ve i (deg.) –ve i (deg.)

5 12.5 6 7.5 11 13 8 10 7.5 5 5 6 6 6 20 2.5 2 2 4 1.5 3 40 1.5 0.5 0.5 2.5 0.5 2.5

Effective roughness angle (i-angle) versus window diameter of crop02

-15

-10

-5

0

5

10

15

0 10 20 30 40Window diameter (cm)

i-ang

le (d

eg.)

Positive i-angle rawNegative i-angle rawPositive i-angle 1cm filteredNegative i-angle 1cm filteredpostive i-angle 3cm filterednegative i-angle 3cm filtered

Figure 5- 12 Comparison of the effective i-angle of raw, 1cm filtered, and 3cm filtered of crop02 of

ScanPos01_scan02 data set along dip direction.

The plot of the i-angle of the raw and filtered of crop02 (Figure 5-12) show that they do not show any consistent decrease or increase in i-angle for the corresponding windows from the raw data to the filtered data. This can tell us it is hard to determine the influence of the range measurement error in determining the extreme i-angle, since it is calculated from the mean orientation of circular windows. The range measurement error is also distributed randomly though out the scan discontinuity plane. Removing of the range measurement error could increase or decrease the mean orientation of the window; since the high frequency values are removed by a given LPF width (see section 5.2.2.1). Table 5-6 and Figure 5-12 also show the maximum values of the roughness angle for the raw and 3cm filtered reconstructed surface of crop02 is the positive i-angle while for the 1cm filtered is the negative i-angle. This means the highest roughness angle for the raw and 3cm filtered data set is in the opposite of dip direction, but for the 1cm filtered is along the dip direction. The tangent of these i-angles multiplied by the appropriate window diameter gives the displacement (dilation) that will occur perpendicular to the discontinuity plane. The value of i-angle can be used in shear strength parameter estimation. According to ISRM (1981), this method is most appropriate to shearing of rocks at low effective normal stress. Asperities smaller than the smallest window

CHAPTER FIVE

60 60

diameters are assumed not to influence the process of dilation as also discussed in ISRM (1981). According to technical note of Ojo (1989), i-angle should be determined according to the damage to the surface of discontinuity during shearing. If damage to the surface is substantial, then the higher value of i-angle should be used otherwise the lower value of i-angle should be used in shear strength estimation. A number of reconstructed surface models with different filter width from crop01 and crop02 data sets have been analyzed visually (removal of spikes) (Appendix 4) and the amplitude parameter from the double log graph for noise removal evaluation (see section 5.4). The best looking surface (i.e. with filtering width of 1cm) has been selected from the two data sets to compare their roughness by plotting their circular window diameters and corresponding average standard deviations of S(w) as double log graph in X and Y-axis respectively (Figure 5-13 below). The amplitude parameter A of crop01 and crop02 from figure 5-13 below are close but the fractal dimension D differ slightly. This means the roughness of discontinuity surface models of both cropped samples differ slightly.

S(w) versus window diameter w for 1cm filter width of crop01 and crop02 data sets

y = 0.1427x0.2066

R2 = 0.9518, crop02

y = 0.1386x0.319

R2 = 0.9706, crop01

0.1

1

1 10 100Circular window w diameter (cm)

Avg

. S(w

) in

cm

Crop02Cropo1Power (Crop02)Power (Cropo1)

Figure 5- 13 Power law relations between S(w) and window diameter for the 1cm filtered data set of crop01 and

crop02 with resolution 6cm and 1cm respectively ; Mesh size 1cm, Sub-sample size 2m2.

5.3.1.1. Sensitivity analysis of RBF surface fitting

RBF surface can be fitted to a raw point cloud data before it has been rotated into a horizontal position or after. A sensitivity analysis of RBF surface fitting has been carried out for these two cases to see its effect in roughness quantification especially for this application. It has been found that fitting RBF function to a raw point data before and after the global trend has been removed is very sensitive for the smallest window diameter than the largest diameter as it is observed from the 3D scatter plot of normal vector orientation deviation in magnitude (Figure 5-15). Figure 5-14 also shows the sensitivity of this analysis decrease logarithmically from the smaller to the larger window. This means it is very sensitive for the smallest window, but it has minimum effect for the largest window diameter. The delta angle of the standard deviation of normal vectors orientation deviation between the two corresponding window planes varies about 4, 3, 2, and 1 degrees for the 5, 10, 20, and 40 cm window diameters of crop02 from scanpos01_scan02 respectively (Table 5-7). However the


61 61

sensitivity of this analysis is relatively lower for the crop01 data set because of its low resolution (Figure 5-14). The mean and other descriptive statistics of normal vector orientation deviation in degrees are listed in Table 5-7 below Table 5- 7 Descriptive Statistics of normal vector deviation of each window by fitting a RBF surface before and after the raw data has been rotated into a horizontal position (in deg.). Crop02: mesh size 1cm, filter width 1cm. 5cm diameter 10cm diameter 20cm diameter 40cm diameter

No. Of windows 1600 400 100 25 Mean 4.51 3.01 2.49 1.14 Median 3.14 2.32 1.87 0.99 Std. Deviation 4.04 2.55 2.04 0.70 Variance 16.33 6.49 4.17 0.50 Skewness 1.54 1.97 1.85 1.72 Kurtosis 2.47 5.27 4.32 3.73 Range 24.68 16.52 11.34 3.15 Minimum 0.05 0.06 0.08 0.27

Maximum 24.73 16.58 11.42 3.42

Percentile 25 1.45 1.32 1.19 0.63 50 3.14 2.32 1.87 0.99 75 6.44 3.97 3.34 1.51

Trend of standard deviation of normal vectors due to RBF surface fitting before and after roatation of raw data into a horizontal position

y = -1.5171Ln(x) + 6.3521R2 = 0.9699____ crop02

y = -0.8594Ln(x) + 3.8835R2 = 0.9887

- - - - crop01

0

1

2

3

4

5

0 10 20 30 40 50

Circular window diameter (cm)

Stan

dard

dev

iatio

n of

nor

mal

vec

tor

devi

atio

n (d

eg.)

Figure 5- 14 Showing the trend of the delta angle of standard deviation of normal vector orientation deviation in degrees for a given window due Fitting RBF surface before and after the raw point cloud data has been rotated into a horizontal position. Crop02 of Scanpos01_scan02, resolution 1cm, and Crop01 of Scanpos01_scan01, resolution 1cm: mesh size of the two data sets is 1cm.

CHAPTER FIVE

62 62

Figure 5- 15 The 3D scatter plot of circular window normal vector orientation deviation in vector magnitude (m) for a given window due to Fitting RBF surface before and after the raw point cloud data has been rotated into a horizontal position. Crop02 of Scanpos01_scan02, resolution 1cm, mesh size 1cm. One of the reasons for this might be the sampling grid considered to fit the bounding box is not the same in both cases. The number of points consider for a given mesh size is higher for the inclined plane rather than for the rotated plane into a horizontal position. This is due to the projected points into the X-Y plane are considered in the case of inclined plane. Hence the RBF fitting is different for both cases. Further more the newly generated (approximated) vertices of the reconstructed surface of the inclined point cloud data are rotated as discussed in chapter 4, section 4.2, to quantify the surface roughness according to the procedures discussed in chapter 5, section 5.3.1. In this study rather than fitting the RBF surface first and then rotating the newly generated (approximated) reconstructed surface vertices, rotating the raw point cloud data and then fitting RBF surface is chosen for roughness quantification.

5.3.1.2. Sensitivity analysis of possible shifting

Exactly locating the 2m2 sub-sample square grid on the point cloud data is difficult due to its low resolution. The details of the colour point cloud data losses when zoom in, which was assumed to give a good identification of details. Hence a sensitivity analysis was carried out to see the effect of slightly shifting to a defined direction in comparing with the compass and disc-clinometer results. Assuming that there might be about a maximum of 10 to 15cm possible shifting in locating the 2m2 sub-sample grid on the point cloud data, a sensitivity analysis has been carried out in four defined directions (i.e. N, S & W by 10 cm and SW by 14.14 cm) even though it can vary in any given direction. To do so, a surface was constructed on a sample area slightly bigger than 2m2, which encompasses the possible location of the sub-sample grid on the point cloud data using the major features such as humps and depressions on the reconstructed surface and digital photo of the sub-ample area (Appendix 1-2). By shifting the 2m2 sub-sample grid with in this interpolated surface, the sensitivity analysis has been carried out for the four defined directions. The X,Y,Z minimum and maximum values of the shifted and the reference data sets are listed below in Table 5-8.


63 63

Table 5- 8 List of the four Shifted data sets used for the sensitivity analysis of possible shifting with their Coordinates relative to the mean of the reconstructed data set of crop01(i.e. Scanpos01_scan01_zx_r_xyz_rbf_r1cm_smooth5cm_v1.txt). Name of data set Shift name Coordinate Dimension Minimum (m) maximum (m) X Y Z X Y Z (mxm)

Crop01 ScanPos01_scan01 Reference -0.85 -1.00 NaN 1.15 1.00 NaN 2x2 Crop01 ScanPos01_scan01 up -0.85 -0.90 NaN 1.15 1.10 NaN 2x2 Crop01 ScanPos01_scan01 down -0.85 -1.10 NaN 1.15 0.90 NaN 2x2 Crop01 ScanPos01_scan01 back -0.95 -1.00 NaN 1.05 1.00 NaN 2x2 Crop01 ScanPos01_scan01 front -0.75 -1.00 NaN 1.25 1.00 NaN 2x2 Crop01 ScanPos01_scan01 diagonal -0.95 -1.10 NaN 1.05 0.90 NaN 2x2

The result shows that the sensitivity is higher for the smallest window diameter than the largest diameter for the normal vector orientation deviation. The magnitude of the difference vector of the two corresponding normal vectors shows the magnitude of the deviation between them and can be used to calculate the delta angle of deviation in degrees as explained in chapter 6, section 6.1. For example, the delta angle of standard deviation of normal vector orientation deviation of the reference grid due to up shifting by 10cm is 10, 6, 3 and 2 degrees respectively for 5, 10, 20 and 40cm window diameters of crop01 from scanpos01_scan01 reconstructed data set (Appendix 5-2). To visualize the scattering of normal vector deviation for the different window diameters, the difference vector magnitudes are plotted in 3D Cartesian coordinate system as shown in Figure 5-16. The 3D scatter plot, descriptive statistics and histogram of delta angle of standard deviation for the defined shifting directions is shown in Appendix 5-2. All the scatter plots show that the scattering of the smallest window is much more pronounced than the largest window. The same results have been also found by plotting scattering of dip amount variation from the measured along the dip direction (Figure 6-2).

Figure 5- 16 Example of the 3D scatter plot of circular window normal vector orientation deviation in magnitude (m) for a given window due to up-shifting of the reference sub-sample square grid by about 10cm. Crop01 of Scanpos01_scan01, resolution 6cm, mesh size 1cm.

CHAPTER FIVE

64 64

The main reason for this is because of the total shifting of the smallest window location to another new location. Fore example measuring of the two sides of ripple marks as the result of complete shifting of location. Hence in this study the influence of these shifting and other factors (discussed in chapter 6, section 6.1) in the possible relation with the compass and disc-clinometer method should be taken into consideration.

5.3.2. Directional roughness quantification

The directional surface roughness estimation from the raw and reconstructed surface profiles has been tried to estimate quantitatively using the chart developed by Barton (1982) to estimate JRC and waviness factor (jw) for various profile lengths, and visually by comparing the extracted profiles with the standard reference profiles. It is also possible to estimate the JRC value using several proposed empirical correlations, fore example Maerz et al. (1990), Tse and Cruden (1979), and spectral method (Kulatilake et al., 1995). However it is not the main objective of this study. The original point cloud data are separated by centimetres in order of 1 and 6cm. Hence, the scan rock surface has a potential of easily characterize the first order variations (large scale) in roughness that could occur over hundreds of centimetres. As the result only the large scale roughness estimation are discussed in this study. The finer scale (second order) roughness, often estimated over scales of 5 to 10cm, is not considered because the average spacing is not in order of millimetres. The details of raw and reconstructed surface narrow strip profiles data quantification are discussed below.

5.3.2.1. Raw data directional profile roughness quantification

The maximum amplitude (amax) or offset of raw data narrow strip profiles of crop02 data set are used to estimate roughness for 1m profile length. The maximum amplitude (amax) is calculated by adding the magnitude of maximum and minimum residuals from the best fit linear trend of 1m long strip profile as discussed in chapter 4 section 4.5. The plot of maximum amplitude versus the profile length (Figure 5-17) also used to determined the joint planarity expressed as the waviness factor (jw) as suggested by Palmström (1995) for rock mass rating (RMI) classification system(see chapter 2, section 2.1.1.3). The result of the plot shows, JRC values ranging from 4 to 7 (Table 5-9) and 2.5 to 6 (Table 5-10) can be obtained from the raw data and smoothed raw data strips respectively. Generally the amax and the JRC value of the smoothed raw data using the smooth pane are lower than the raw data. However Strip_crop02_H_raw2 has the same amax and JRC value with its corresponding smoothed strip raw data (i.e. Strip_crop02_ H_raw2). This shows the Lowess (linear fit) smooth pane, which reduces the noise by locally weighting the scattered plot using the linear least squares fitting and a first degree polynomial, doesn’t have much effect on points which are close to each other and have more of less the same elevation. The percentage of undulation (U), which is calculated by dividing amax by stick length, falls with in slightly to moderately undulating zone (i.e. with U value between 3 and 0.3%) of RMI classification system (Figure 5-17 below). Large scale rock surface roughness characterization in SSPC method is based on the i-angle and roughness amplitude estimation in an area of between 0.2m2 and 1m2. In this study only i-angle


65 65

estimation from the reconstructed profile is considered to determine the profile according to SSPC large scale profile characterization method. It is practically difficult to find a theoretical sinusoidal form of roughness, from which i-angle and the amplitude roughness can be estimated as the SSPC large scale profile curves. Hence the i-angle is estimated by estimating the maximum angle of profile for a given base length between 0.2 and 1m as shown in Figure 4-7. The i-angle estimation from the raw data strip profiles is difficult due to the erratic (noisy) nature of the point information along the profile (Figure 5-5). These results in more undulations with in wave length of less than the minimum base length required for the large scale i-angle estimation in SSPC that is 0.2m. It is tried to estimate the i-angle of raw data strip profiles from the angle between the mean orientation of the profile and base length of between 0.2 and 1m. The results show that the i-angle of the raw data strip profiles are either with in the same range of i-angle or greater than the strip profiles from the smoothed raw data and reconstructed surface (Table 5-9, 5-10 and 5-11). The increase in i-anlge of raw dat strip profiles can be explained due to the contribution of noise (mostly assumed to be the range measurement error). The visual estimation of the reconstructed profiles from the raw data strip profiles according to the ISRM large scale roughness profiles are mostly seems to be categorized under stepped roughness profiles, where as the smoothed raw data strip profiles are under undulating (Table 5-9 and 5-10). The advantage of determination of the extracted profiles using the standard reference profiles than the traditional way are, it is easy to compare profiles with profiles rather than rock surface with profiles visually and easy to estimate the roughness angle from profiles than from rock surface. It is also possible to estimate roughness along a give direction often the direction of potential sliding. Table 5- 9 The maximum amplitude amax (in mm) calculated form the residuals of crop02 raw data set strip and its corresponding estimated JRC value using the chart developed by Barton (1982) for 1m profile length. Estimated SSPC value using i-angle and visually inspected ISRM categories results. Strip name Estimated JRC Estimated SSPC Estimated ISRM amax (mm) JRC value i-angle SSPC value (Visually)

Strip_crop02_ H_raw1 26 6 4-8 0.85 Stepped Strip_crop02_ H_raw2 19 4 4-8 0.85 Stepped Strip_crop02_ H_raw3 29 6.5 4-8 0.85 Stepped Strip_crop02_ V_raw1 18 4 4-8 0.85 Stepped Strip_crop02_ V_raw2 24 5.5 4-8 0.85 Undulating Strip_crop02_ V_raw3 31 7 4-8 0.85 Stepped

Table 5- 10 The maximum amplitude amax (in mm) calculated form the residuals of crop02 smoothed raw data set strip and its corresponding estimated JRC value using the chart developed by Barton (1982) for 1m profile length. Estimated SSPC value using i-angle and visually inspected ISRM categories results. Strip name Estimated JRC Estimated SSPC Estimated ISRM amax (mm) JRC value i-angle SSPC value (Visually)

Strip_crop02_ H_raw_S1 21 5 4-8 0.85 Undulating Strip_crop02_ H_raw_S2 19 4 2-4 0.80 Undulating Strip_crop02_ H_raw_S3 25 6 4-8 0.85 Undulating Strip_crop02_ V_raw_S1 12 2.5 2-4 0.80 Undulating Strip_crop02_ V_raw_S2 18 4 2-4 0.80 Undulating Strip_crop02_ V_raw_S3 20 4.5 2-4 0.80 Undulating

CHAPTER FIVE

66 66

Rock surface characterization using straight edge

2016121086543

2

1

0.5

0.1

1

10

100

1000

0.1 1 10Straight edge (Strip profile ) length (m)

Max

imum

am

plitu

de o

f asp

eriti

es (m

m)

JRC 1.5 (U=0.3%)JRC 15 (U=3%)Strip_crop02_H_raw1Strip_crop02_H_raw2Strip_crop02_H_raw3Strip_crop02_V_raw1Strip_crop02_V_raw2Strip_crop02_V_raw3

Join

t rou

ghne

ss c

oeff

icie

nt (J

RC

)

Planar

Slightly to moderately undulating

Strongly undulating


201612108

6543

2

1

0.5

0.1

1

10

100

1000


Max

imum

am

plitu

de o

f asp

eriti

es (m

m)

JRC 1.5 (0.3%)JRC 15 (U=3%)Strip_crop02_H_rawS1Strip_crop02_H_rawS2Strip_crop02_H_rawS3Strip_crop02_V_rawS1Strip_crop02_V_rawS2Strip_crop02_V_rawS3

Join

t rou

ghne

ss c

oeff

icie

nt (J

RC

)

Planar


Strongly undulating

Figure 5- 17 Estimating JRC and waviness factor (jw) from measurement of roughness amplitude (amax) for 1m length of narrow raw data strip profile (left) and smoothed raw data using the smoothing pane (right) using the chart developed by Barton (1982). The red lines are the upper and lower limit of slightly to moderately undulating waviness class of Palmström (1995) in his joint waviness and smoothness characterization using U value.

5.3.2.2. Reconstructed surface directional profile roughness quantification

The directional roughness profiles from the narrow strips of the reconstructed surfaces are quantified using the same procedures as for the raw data strip profiles above. The JRC value ranging from 3 to 6 are obtained from the reconstructed surface strip profiles of crop01 and crop02 (Table 5-11 below). The maximum amplitudes (amax) and estimated JRC values of narrow strip profiles from reconstructed surfaces of crop02 are lower than their corresponding raw data strip profiles (Table 5-9). This is due to the removal of noise (mostly due to the contribution of range measurement error) by RBF surface fitting and LPF (see section 5.2.2.1 of this chapter). The JRC values of the reconstructed surface strips of crop02 vary from its raw data strips profiles with mean 1.75 and standard deviation of 1.13. This could result in over estimation of the JRC value in shear strength estimation if the raw data with out removal of noise is used. The percentage of undulation (U), which are calculated by dividing amax by stick length, are characterized as small undulations (slightly to moderately undulating) class with the waviness factor (jw) of 1.5 according to Palmström (1995) in his Characterization of joint planarity (i.e. with U value between 3 and 0.3%) (Figure 5-18). This characterization class range is the same as the raw data strip profiles class range, because the range of slightly to moderately undulating is wide enough, that is it ranges from JRC value of 1.5 to 15 (Figure 5-18). Hence all the strips of raw data


67 67

and reconstructed surface are falls with in the same range of joint planarity characterization system. This shows the noise doesn’t have much influence in this classification system. Table 5- 11 The maximum amplitude amax (in mm) calculated form the residuals of crop02 and crop01 reconstructed surface strip data sets and their corresponding estimated JRC value using the chart developed by Barton (1982) for 1m profile length. Strip name Estimated JRC Estimated SSPC Estimated ISRM amax (mm) JRC value i-angle(deg.) SSPC value (visually)

Strip_crop02_H_rec1 18 4 4-8 0.85 Undulating Strip_crop02_H_rec2 14 3 4-8 0.85 Undulating Strip_crop02_H_rec3 26 6 4-8 0.85 Undulating Strip_crop02_V_rec1 13 3 2-4 0.80 Undulating Strip_crop02_V_rec2 13 3 4-8 0.85 Undulating Strip_crop02_V_rec3 15 3.5 2-4 0.80 Undulating Strip_crop01_H_rec1 24 5.5 4-8 0.85 Undulating Strip_crop01_H_rec2 20 4.5 4-8 0.85 Undulating Strip_crop01_H_rec3 20 4.5 4-8 0.85 Undulating Strip_crop01_V_rec1 16 3.5 4-8 0.85 Undulating Strip_crop01_V_rec2 15 3.5 2-4 0.80 Undulating Strip_crop01_V_rec3 13 3 4-8 0.85 Undulating


201612108

6543

2

1

0.5

0.1

1

10

100

1000


Max

imum

am

plitu

de o

f asp

eriti

es (m

m)

JRC 1.5 (U=0.3%)JRC 15 (U=3%)Strip_crop01_H_rec1Strip_crop01_H_rec2Strip_crop01_H_rec3Strip_crop01_V_rec1Strip_crop01_V_rec2Strip_crop01_V_rec3

Join

t rou

ghne

ss c

oeff

icie

nt (J

RC

)


Strongly undulating

Planar


2016121086543

2

1

0.5

0.1

1

10

100

1000


Max

imum

am

plitu

de o

f asp

eriti

es (m

m)


Join

t rou

ghne

ss c

oeff

icie

nt (J

RC

)


Strongly undulating

Planar

Figure 5- 18 Estimating JRC and waviness factor (jw) from measurement of roughness amplitude (amax) for 1m length of narrow strip profiles from the reconstructed surface of crop01 (left) and crop02 (right) using the chart developed by Barton (1982). The red lines are the upper and lower limit of slightly to moderately undulating waviness class of Palmström (1995) in his joint waviness and smoothness characterization using U value.

CHAPTER FIVE

68 68

In this study only i-angle estimation from the reconstructed profile is considered to determine the profile according to SSPC large scale profile characterization method as it is used for the raw data strip profiles. It is tried to estimate the i-angle of reconstructed surface strip profiles from the angle between the profile and base length of between 0.2 and 1m. The result shows that the i-angle range of the strip profiles are with in the same range of i-angle range of the raw data strip profiles (Table 5-9 and 5-11) except Strip_crop02_V_rec1, which is lower. This means they do have the same roughness curves according to SSPC method. The decrease in i-angle of Strip_crop02_V_ rec1 from its raw data strip profiles can be explained due to the removal of noise (mostly assumed to be the range measurement error). Even tough there is some removal of noise in the other strips which is clearly visible in the maximum amplitude amax, it is not seen in the i-angle range because of its wide range (fore example, the curved profile class of SSPC has 4-8 degrees i-angle range). The visual estimation of the profiles from the reconstructed surfaces of crop01 and crop02 strips according to the ISRM large scale roughness profiles are mostly likely to be characterized as undulating roughness profiles (Table 5-11 and Appendix 7).

5.4. Range measurement error estimation

It is difficult to estimate the range measurement error by comparing the laser derived roughness with the manually measured roughness. The possible relation of the laser scan derived and measured roughness is highly influenced by many factors as discussed in Chapter six section 6.1. Hence the range measurement error has been tried to evaluate and estimate by comparing the raw data roughness with the reconstructed surface roughness for the surface and directional roughness. The range measurement error of the surface roughness has been tried to estimate from the double log graph by subtracting the Amplitude (A) and fractal dimension (D) parameters of the interpolated surface with 1cm filtered from the raw data. To determined D and A, a series of circular windows, w of diameter 2.5%, 5%, 10% and 20% of the total sub-sample window length of 2m have been selected and the whole area of the sub-ample square window has been divided into small window. After determining the best fitting plane for each circular window as in section 5.3.1, the standard deviation of the reduced asperity height, S(w), has been calculated for the defined series of widow w in Matlab. To evaluate and estimate the fractal parameter D and A, S(w) versus w has been plotted on double log diagram for crop02. A best fit line has been drawn using the power law equations in Excel to evaluate the amplitude parameter A and fractal dimension D for the raw data and reconstructed surfaces without and with a given LPF width (Figure 5-19). The graph shows that a strong linear relation exists between the S(w) and w for the selected sub-sample window except for the raw data set. There fore the parameter A and Hurst exponent H can be easily estimated from the constant coefficient and slopes of the power law equation respectively (Figure 5-19). The fractal dimension D can be determine from the relation of D=3-H. The amplitude parameter could tell us indirectly how much noise (to some extent roughness) has been removed by subtracting the amplitude of the filtered from the raw. Crop01 is not considered in this analysis since it doesn’t fulfil minimum data requirement for plane fitting for window diameters of 2.5% and 5% because of it low resolution i.e. 6cm/pt. The raw, unfiltered and filtered reconstructed data sets of crop02 with five different filter width and 5, 10, 20 and 40 cm window diameters are considered to determined the fractal parameter D and amplitude parameter A.


69 69

Table 5- 12 Window diameter (w) and corresponding average Standard deviation S (w) per window w of raw, unfiltered and filtered data set of crop02 from Scanpos01_scan02. Window diam Raw data Unfiltered 1cm filtered 2cm filtered 3cm filtered 4cm filtered 5cm filtered w(cm) S(w) (cm) S(w) (cm) S(w) (cm) S(w) (cm) S(w) (cm) S(w) (cm) S(w) (cm) 5 0.4839 0.2818 0.2040 0.1574 0.1310 0.1121 0.1000 10 0.4530 0.2701 0.2274 0.1875 0.1574 0.1457 0.1381 20 0.5027 0.2951 0.2511 0.2180 0.2045 0.1631 0.1433 40 0.5249 0.3544 0.3182 0.2809 0.2539 0.2302 0.2255

S(w) per window diameter w for different filter width of crop02 from scanpos01_scan02 data set

y = 0.4293x0.0502

R2 = 0.518, raw

y = 0.222x0.1119

R2 = 0.7018, unfiltered

y = 0.1427x0.2066

R2 = 0.9518, 1cm filtered

y = 0.1002x0.2725


y = 0.0767x0.3241


y = 0.0661x0.3276


y = 0.0564x0.3573


0.1

1

1 10 100Circular window w diameter (cm)

Ave

rage

S(w

) in

cm

raw dataUnfiltered1cm filtered2cm filtered3cm filtered4cm filtered5cm filteredPower (raw data)Power (Unfiltered)Power (1cm filtered)Power (2cm filtered)Power (3cm filtered)Power (4cm filtered)Power (5cm filtered)

Figure 5- 19 Power law relations between S(w) and w for the raw, unfiltered and filtered data set of crop02 from

Scanpos01_scan02. Raw data resolution 1cm per a point, Mesh size 1cm, Sub-sample size 2m2.

The average resolution of cropo2 is 1cm. Therefore roughness features less than 1cm are not captured in the data set. It is necessary to choose a unit of measurement (scale) to calculate the fractal dimension D and amplitude parameter A of a natural rock profile. According to Kulatilake and Um (1999) a roughness measurement unit of less than 1mm is needed for data density (resolution) between 5.1 and 51.23 per mm for rock mass discontinuity profile. However Rahman et al. (2006) also suggested in their work 5cm measurement unit for 1cm resolution to calculate the fractal dimension and amplitude parameter with strong linear relation between S(w) and w for the same data set used in this study . There for the measurement unit need to be 5cm for crop02 to fulfil the data density requirement proposed by Kulatilate and UM (1999). In this study the window shape and size are fixed according to the discs diameter used in the compass and disc-cilinomer method. That is circular windows are used rather than square windows to have consistency with the discs. Due to these reasons it is impractical to fulfil the data density requirement proposed by Kulatilake and Um, (1999). How ever the result of double graph of the filtered data show a linear trend using a power law regression analysis with least square analysis value greater than 0.91 (Figure 5-19). The R2 (least square analysis) values are more than 0.81 can be acceptable as suggested by Kulatilake and Um, 1999. The R2 (least square analysis) values for the raw and unfiltered data set are 0.52 and 0.70 respectively for crop02.

CHAPTER FIVE

70 70

The slope (Hurst index H) of the power low equation shows the scale dependency of the roughness. In the raw data set this slope is almost flat. This shows the smallest and the largest windows have more or less the same roughness. It has been also found that the fractal dimension D and amplitude parameter A of raw data are higher than the unfiltered and filtered (Figure 5-19 and Table 5-13). This is due to the inherent noise of the raw data. This can to a large part be contributed by the range measurement error of the scanner. In this study an attempt was tried to remove the inherent noise from the raw laser scan data using a scattered data interpolation technique so called FastRBF ‘fitting plane and ‘3D iso-surface’ functions (See section 4.3.1 and section 5.2.2.1). As the result of this technique the fractal dimension and roughness amplitude of reconstructed surfaces data are less than that of the noisy raw data. After the surface is reconstructed in this manner the roughness of 1cm filtered surface model is assumed to be more representative to the actual roughness of the discontinuity surface. The measure of the change of amplitude parameter shows the amount of amplitudes (noise and or roughness in cm) removed due to a given LPF filtering width. The power low equation for different filter width also shows the more the filtering, the more the influence of the noise (error) and roughness as well are removed. Even though the amplitude parameter could not exactly determine the error unless you have a calibrated perfectly flat surface scanned, it can be used as an indirect method of evaluation range measurement error influence in filter width determination. There fore in this study it is tried to indirectly estimate the range measurement error by subtracting fractal dimension D and amplitude A of reconstructed surface data using 1cm filtered from the raw data (Table 5-14 below). The contribution of the range measurement error can be assumed to be 0.1564 and 0.2866 cm for fractal dimension D and amplitude parameter A of crop02 data set. Table 5- 13 Fractal dimension and roughness amplitude of raw data and 1cm filtered reconstructed surface of crop02 from Scanpos01_scan02. Data type Hurst exponent Fractal dimension Roughness Amplitude Least squared regression H D A (cm) value (R2) Raw data points 0.0502 2.9498 0.4293 0.5180 Interpolated data 0.2066 2.7934 0.1427 0.7018 (1cm filtered)

The fractal dimension of surface roughness of rock fractures ranges between 2 and 2.5 in 3D surface and 1 and 1.5 in 2D (Fradin et al., 2004). In this study the fractal dimension for the interpolated surface data has been found to be 2.7934, which is higher than the maximum fractal dimension for surface roughness. This means the rock surface has overhanging asperities which is not the case in Rahman et al. (2006) study using the same data set. The main reason for this is that the fractal dimension analysis was not carried out in accordance with requirements for accurate quantification using the roughness length method (Kulatilake and Um, 1999). It is also tried with square window size of the same dimension as the circular windows. It has been found a fractal dimension of 2.7849, which is also higher than the maximum fractal dimension for surface roughness (Appendix 3-2). As discussed above the range measurement for the profiles was also tried to estimate by subtracting the maximum amplitude of reconstructed profile from the raw data strip profiles (Table 5-14 below). It has been found that there is about an average increase of 3.2 JRC value with standard deviation of 1.8 from the reconstructed surface narrow strip profile (Figure 5-20 and Table 5-14). This increase in


71 71

JRC value is due to the noise, mostly the contribution of the range measurement error as discussed above. However, most of the raw data and the interpolated surface profile i-angles for a given base length are characterized under the same SSPC curve class. The same is true in the joint planarity characterization system class (Figure 5-17). This shows the range measurement error doesn’t have much influence in roughness determination using the joint planarity characterization system and SSPC method because of their wide class range (Table 5-10 and 5-11). Table 5- 14 Procedure of estimating JRC from the laser scan data and estimation of the influence of the range measurement error using the chart developed by Barton (1982). Data source Profile code Raw data amplitude Rec. data amplitude Estimated JRC value Difference in (mm) (mm) raw. Rec. (JRC estimated.)

Crop 02 H1 26 18 12 10 2 Crop 02 H2 19 14 8 6 2 Crop 02 H3 29 26 13.5 11.5 2 Crop 02 V1 18 13 8 5.5 2.5 Crop 02 V2 24 13 10 6 4 Crop 02 V3 31 14 13 6.5 6.5


201612108

6543

2

1

0.5

0.1

1

10

100

1000


Max

imum

am

plitu

de o

f asp

eriti

es (m

m)

JRC 1.5 (U=0.3%)JRC 15 (U=3%)Strip_crop02_V_rec3Strip_crop02_V_raw3

Join

t rou

ghne

ss c

oeff

icie

nt (J

RC

)

Strongly undulating


Planar


2016121086543

2

1

0.5

0.1

1

10

100

1000


Max

imum

am

plitu

de o

f asp

eriti

es (m

m)

JRC 1.5 (U=0.3%)JRC 15 (U=3%)Strip_crop02_H_rec3Strip_crop02_H_raw3

Join

t rou

ghne

ss c

oeff

icie

nt (J

RC

)

Strongly undulating


Planar

Figure 5- 20 Estimated JRC difference from measurement of roughness amplitude (amax) for 1m length of raw data strip profile (left) and reconstructed surface strip profiles of crop02 (right) using the chart developed by Barton (1982). The red lines are the upper and lower limit of slightly to moderately undulating waviness class of Palmström (1995) in his joint waviness and smoothness characterization using U value.

CHAPTER FIVE

72 72

5.5. Estimation of small scale roughness Using intensity

The return signal amplitude for each pulse (reflectance intensity) of the high resolution laser scan data was found to be ranges from 31 to 41value. So it was not possible to do some experiments due to the low variation in intensity value and some other reflection intensity influencing factors such as weathering, mineralogical composition, position of the scanner relative the rock face, distance form the rock face to the laser scanner, target albedo, mosses grown on the rock surface and etc. Further more; there was no enough time to consider this all factors. Hence the aid of reflectance intensity in relating these methods wasn’t considered in this study.


73 73

6. Comparision with the traditional methods

3D laser scanning is a newly merging sophisticated technology used for various functions including rock surface roughness capturing as discussed in chapter 2, section 2.1.2.1. However, the traditional field-based methods are commonly used in roughness estimation with their limitations. Hence to check the applicability of the roughness measurement by 3D terrestrial laser scanner, the roughness results are compared with the traditional methods such as compass and disc-clinometer, straight edge and visual inspections using standard reference profile results. This chapter will discussed about the assumptions drawn for comparison, the comparative results and the main challenges of this comparative study.

6.1. Comparison with the compass and disc-clinometer method

The outcrop rock surface is about 80m by 70m dimension and 470 steep. The high resolution laser scan data was taken at the middle part of the outcrop face (Figure 5-1), which is practically inaccessible. Then the following assumptions are taken in to consideration to compare the general roughness of the high resolution crop02 and low resolution crop01 laser scan data sets with the manually measured roughness using compass and disc-clinometer:

� There is no much more considerable change in rock surface asperities due to human interface and weathering since the date of laser scanning (06/05/2004) and the date of field surface roughness measurement (19-20/09/2006). The reason for the human interface is the quarry area is abandon since 1960th.

� The roughness of the selected accessible sample area for practical roughness measurement has

more or less similar roughness or can represent the whole plane. The reason for this is that the entire rock out crop, which is more or less compositionally homogeneous, thick, formed in the same marine environment, slightly metamorphosed, with out any discontinuity within the plane will have the same roughness. It is also visually inspected according to the ISRM standard profiles of roughness determination to have undulating large scale roughness in the field.

� The mosses (vegetations) which are found on the rock surface as in Appendix 1-2, are

considered as they were not there during the time of laser scanning. These assumptions let us to do some statistical analysis and comparison between the manually measured rock surface roughness using the traditional methods and the laser scan derived surface roughness. The dip amount, dip direction, and normal vector of circular windows of the laser scan data are compare with its corresponding measured disc orientation using the field-based compass and disc-clinometer method. To do so the field measured orientation has to be rotated into a horizontal position around a rotation axis for easier visualization and comparison. The rotation axis was

CHAPTER SIX

74 74

determined from the mean orientation of the largest discs orientation as they are more clustered near by the reference plane orientation compared with the smaller disc. The mean orientation of the reference plane from the measured discs orientation is calculated to be 46.450 dip and 187.360 dip direction. This is found to be consistent with the mean orientation of the sub-sample plane (2m2) that is 45.80 dip and 186.690 dip direction from the laser scan data. The one degree deviation in dip and dip direction can be explained by the error encounter in measuring orientation using the breithaupt compass to one degree precision or slightly shifting in locating the sub-sample gird (see chapter 5, section 5.3.1.2). The mean orientation of the reference plane used for rotation of the dip and dip direction of field measurements into a horizontal position is 460 dip and 1870 dip direction, which is rounded into one degree precision according to the following procedures. The field measured dip and dip direction of different disc sizes are rotated into a horizontal reference plane position using the RockWare2002 Utilities program around the specified axis above. The resulting dip direction and dip angle (or strike and dip) values are listed in two new columns of the data sheet. The input data can be entered using the right-hand rule (strike and dip) or as dip direction and dip angle. The parameters used for rotation of the data sets in this study are:

• 960 rotational Axis bearing which is the strike direction of the sample plane around which each data item will be rotated.

• 00 rotational Axis Plunge which is the plunge angle of the axis around which the data will be rotated, with horizontal = 0 and vertical (downward) = 90. Since the strike direction is horizontal, zero value is set.

• Negative 460 rotation amount which is the number of degrees around the rotational axis that the data is to be rotated. A positive value (0 to 360) will rotate the data clockwise and a negative value (0 to –360) will rotate the data counter-clockwise. Hence our data set is dipping at 460 and will be rotated 460 counter-clockwise to bring it into horizontal position.

After the field data has been rotated into a horizontal position, the resulting dip and dip directions and their corresponding laser scan derived orientations are organized in Excel and imported into RockWare 2002 program. RockWare 2002 Utilities program was used to read planar and linear data from the data sheet, and displays the orientation of these features on a stereonet diagram with contour using points and great circles (Figure 6-1). Planes from the laser scanning and field measured are specified with different colour for easy recognition and comparison in the stereonet plot in dip and dip direction.. All the data sets are projected on the stereonet plot, as an equal area or Schmidt projection. A lower hemisphere projection was used in this study. Optional gridding is also tried to set for the laser scan derived and manually measured planes to display point density with line contours of 5 degree. By contouring the poles (orientation data) on an equal area stereonet, it is possible to see data density pattern and subtle patterns which might be caused due to measuring of sampling error are often brought out by such treatment. The amount of spread is also a function of how well behaved the populations is (the natural variation) and the amount of measurement error, and this can also be very important information.

COMPARISON WITH THE TRADITIONAL METHODS

75 75

Figure 6- 1 Polar equal area plots of poles from measurements on a discontinuity rock surface using circular discs (back colour) and crop01 laser scan derived (red colour) of different circular window diameters (e.g. 5, 10, 20 and 40 cm ) (1cm filtered). The arrow indicates dip direction. It is tried to compare both the measured and laser scan derived dip and dip direction orientation on cell to cell basis by plotting them on steronet diagram (Figure 6-1 above). The results of the plot show that the dip amount of the plot is comparable for all diameters except for the 5cm which is slightly differ. The standard deviation of dip amount between the measured and laser derived is 50, 40, 20, and 10 for the 5, 10, 20 and 40cm diameters respectively. However the dip direction of the laser derived is scattered except for the 10cm diameter, where as the measured dip directions are elongated along the dip direction of the reference plane as if there is anisotropic due to ripple marks (Figure 6-1). The anisotropic of the measured dip directions can be explained by instrument error, and measuring error such as wobbling and uncomfortably in measuring being on ladder on steep slope rock face. The anisotropic of the laser scan (10cm diameter) can be explained due to sampling bias of the laser scan data because this anisotropic is mostly removed when all the laser derived data are plotted (Appendix 6-2). The 20cm and 40cm diameters location are scattered thorough out the reference plane where as the 5cm and 10cm diameters are located on the right top corner of the 2m2 reference plane for easy

CHAPTER SIX

76 76

referencing with the field data. The result of the scatter plot of the field measured and laser scan derive dip amount data shows that the scattering is higher for the smallest diameter than the largest diameter (Figure 6-2 below). This means the deviation of the best fit linear model of each diameter from the best fit theoretical model (i.e. with slope equals to one) becomes smaller from the smallest to the largest diameter (Appendix 6-2).

0 2 4 6 8 10 12 14 16 18 20

Dip amount field measured (deg.)

0

2

4

6

8

10

12

Dip

am

ount

Las

er s

can

deri

ved

(deg

.)

Legend10cm disc/window20cm disc/window40cm disc/window5cm disc/window

Scatter plot of Laser scan derived Vs field measured dip amount

Figure 6- 2 Two dimensional scatter plot of laser scan derived versus field measured dip amount. Crop01 of

Scanpos01_scan01, resolution 6cm, mesh size 1cm. The dip amount and dip direction are coupled and can’t be separately compared. Hence the delta angle of deviation was used to quantify the deviation between the measured and laser derived normal vectors. The angular difference is determined by taking the inner angle difference and the sign is assigned based on the direction of the vector defined by the difference of two vectors to plot it on 3D scatter plot as in Figure 6-3 below. To do so the field measured dip amount and dip direction data sets are first rotated 6 degree anticlockwise to aligned with the dip direction of the 2m2 sub-sample plane that is the negative y-axis or south direction. They need to be transferred into spherical coordinate system by taking a unit normal vector as the laser derived normal vector length. Accommodations are also done for the dip amount and dip direction angle measurements because they are measured with respect to the horizontal XY-plane down ward and the north axis (positive y-axis) in clock wise direction respectively. But the spherical coordinate system is measured with respect to the positive X-axis, anti-clock wise direction (theta) and XY-plane up ward (phi) in radiance respectively. Since the Laser scan derived normal vectors are in Cartesian coordinate system one of the coordinate system should be transferred to do simple vector arithmetic operation. In this study the field measured data are also transferred from the spherical to the Cartesian coordinate system in Matlab to determine the magnitude of the normal vector deviation length from the corresponding laser scan derived. The magnitude of the deviation of the two vectors shows the magnitude of the angle of deviation from one another because both are a normal unit vectors of length one. That means the smaller the magnitude is the smaller the deviation angle. To visualize the scattering of normal vector orientation deviation of


77 77

discs from windows, the magnitude of the difference vectors are plotted in 3D Cartesian coordinate system as shown in Figure 6-3. This shows the scattering of the smallest discs from windows is much more pronounced than the largest.

Figure 6- 3 Example of the 3D scatter plot of the delta angle of deviation of measured from the circular window normal vector orientation in magnitude (m) for Crop01 of Scanpos01_scan01, resolution 6cm, mesh size 1cm.

Since we have the three sides of a triangle in 3D space, it is possible to calculate the opposite angle of the base of an isosceles triangle formed by two unit normal vectors of field and laser scan data, and the difference vector magnitudes. Using the cosine law it is possible to determine the delta angle of deviation between the two normal vectors in degrees. All the out puts are export to Excel for descriptive statistical analysis. The result shows that the delta angle of standard deviation of normal vector deviation decreases from the smallest to the largest discs (Figure 6-4 below).

0 10 20 30 40

Angle difference between measured and Laser derived normal vectors of 5cm disc

(deg.)

0

3

6

9

12

15

Freq

uenc

y

Mean = 11.3662Std. Dev. = 7.25674N = 96

0 5 10 15 20 25


(deg.)

0

5

10

15

20

Freq

uenc

y

Mean = 8.8572Std. Dev. = 4.95701N = 72

CHAPTER SIX

78 78

0 2 4 6 8 10 12 14


(deg.)

0

5

10

15

20

Freq

uenc

y

Mean = 6.4233Std. Dev. = 2.98816N = 92

0.00 2.00 4.00 6.00 8.00 10.00


(deg.)

0

1

2

3

4

5

6

Freq

uenc

y

Mean = 4.2483Std. Dev. = 1.84683N = 25

Figure 6- 4 Histograms of the delta angle of standard deviation between the measured and laser scan derived

normal vectors orientation in degrees on the cell-to-cell basis. The scatter plots (Figure 6-2 and 6-3), stereonet diagrams (Figure 6-1), and Histograms (Figure 6-4) show that it is hard to relate the field measured orientations with the laser derived orientations. Some of the main reasons for this are:

� The possible shifting of the exact location (see chapter5, section 5.3.1.2) � The loss of the details of the scan rock surface due to the low resolution data set (i.e. 6cm per

a point). Interpolation with smaller grid size than the data spacing doesn’t add any information about roughness components with wave length shorter than the typical data point spacing.

� The dead zone due to the inclination of waviness with respect to the scanner position could

underestimate the actual roughness.

� The dip amount and dip direction of manually measured are determined by measuring the angle between the reference plane and the roughness tangents by compass. This is greatly affected by few highly out prodding asperities and wobbling. Where as the laser scan measurements are determined by calculating the angle between the sub-sample (2m2) mean orientation and the circular windows mean orientation using the least square regression analysis in Matlab’s principal component analysis (see details in Appendix 3-1).

� Inaccuracies in the Compass measurements (Windsor and Robertson, 1994).

� The mosses which were grown on the rock surface during the scanning time (06/05/2004) are

removed during the practical measurement time (19-20/09/2006) and


79 79

� The sampling biasness especially for the 5cm and 10cm window diameter. Most of the smaller disc and laser scan derived measurement are located at the upper right corner of the sub-sample grid location for easy referencing.

There fore the relation between these two methods can be improved if the following things are taken in to consideration:

� The rock surface should be scan with high fixed resolution (at least 1cm per a point) several times at different locations and angle (multi-view) to capture the details of the roughness and to remove the dead zone effect.

� The field measurements should be carried out with an electronic compass of one degree

accuracy of measurement instead of using Breithaupt compass with 50 accuracy.

� During scanning, the key markers of the sample grid (at least three points) should be captured by high resolution digital camera fixed on top the scanner for easy identification of the detials in locating the sample grid on the coloured point cloud data.

� The circular discs should be quiped with appropriate screw pins separated by 600 at each end

for accurate mean orientation mesurement and wobbling effect minimization.

It is also tried to compare the general roughness parameter (for example, i-angle) derived from the laser scan of crop01 and crop02 with the manually measured roughness rather than comparing discs with the circular windows on a cell-to-cell basis. The comparison of the largest roughness angle (i-angle) extracted from the stereonet plot of crop01 and crop02 (Appendix 6-2) with the manually measured largest roughness angle along the dip direction shows that, the positive and negative i-angle of the laser scan data are generally lower than the manually measured (Figure 6-5 below). The reason is that the i-angle of manually measured is determined by measuring the angle between the reference plane and the roughness tangents by compass. This is greatly affected by few highly out prodding asperities and wobbling. Where as the i-angle of the laser scan is determined by calculating the angle between the sub-sample (2m2) mean orientation and the circular windows mean orientation using the least square regression analysis in Matlab’s principal component analysis (See Appendix 3-1). In addition to these there is also a possible shifting and slightly surface roughness variation between crop02 and crop01 locations (Figure 5-13). It is also shown in Figure 6-5 below that the positive i-angle of the laser scan data of crop01 is the same for the 5 and 10cm windows. This means they do have the same roughness along the dip direction for these two windows. Table 6- 1 Positive and negative i-angle estimated from the envelopes of effective i-angle for each window size from crop01, crop02 and field measured data sets along dip direction. Window diameter Crop01 (1cm filtered) Crop02 (1cm filtered) Field measured (cm) +ve i (deg.) –ve i (deg.) +ve i (deg.) –ve i (deg +ve i (deg.) –ve i (deg.)

5 11 12 7.5 11 12 17 10 11 8.5 5 6 10 10 20 3 5 2 4 5 6 40 2 3.5 0.5 2.5 2 3

CHAPTER SIX

80 80

Effective roughness angle (i-angle) versus window diameter of crop01, crop02 and measured data sets

-20

-15

-10

-5

0

5

10

15

0 10 20 30 40Window diameter (cm)

i-ang

le (d

eg.)

Positive i-angle manually measuredNegative i-angle manually measuredPositive i-angle crop01_1cm filteredNegative i-angle crop01_1cm filteredpositive i-angle crop02_1cm filteredNegative i-angle crop02_1cm filtered

Figure 6- 5 Plot of effective roughness i-angle along dip direction of the rock surface data using the maximum

scattering of different window diameters from crop01 (blue), crop02 (green) laser scan data and field data (red).

The extreme roughness angle of laser scan derived decreases from the smallest to the largest as it is clearly also observed from the compass and disc-clinometer extreme roughness angles (Figure 6-5 above). Further more the maximum values of the roughness angle for laser scan and measured using the compass and disc-clinometer method is the negative i-angle. This means the highest roughness angle for both data sets is in the dip direction. From this it can be say that the laser scan data can be used to derive the three dimensional roughness using the same method as the traditional compass and disc-clinometer method. The laser scanning in combination with this new an automated roughness quantification method has more advantages than the traditional field-based method. For example:

� It is cheaper, more objective, precise and more accurate than the traditional (manual) techniques (Slob et al., 2005).

� It can be carried out with out any physical contact rapidly (in minutes) and at some distance

(from 4 up to 800 meters) away from the rock face in a controlled environment. Hence, safety risks are minimized. Some laser scanners can even be operated by remote control via an infrared or wireless Ethernet link (Knapen and Slob, 2006).

� Much more rock surface roughness covering large part (whole) fracture surface can be

extracted than specific locations using traditional (manual) technique (Knapen and Slob, 2006). This could allow in applying different statistical roughness quantification techniques.

� The dip and dip direction of a given circular window is determined by calculating its mean

orientation using the least square regression analysis (Appendix 3-1). Where as the dip amount and dip direction (the mean orientation) of a rock surface for a given disc diameter is determined by manually measuring the dip between the reference plane and the roughness tangents and strike by compass. This is greatly affected by instrument error, few highly out


81 81

prodding asperities and wobbling, which is almost removed of not the case in this new method.

� “Laser scanning can also assist other aspects of a geotechnical project. An important example is that an accurate survey of the geometry of a slope is realized, which can be integrated with other geometric elements, such as drainage ditches, road surface in a CAD or GIS system” (Slob et al., 2005).

6.2. Comparison with the field Observational results

Since The JRC standard profiles are developed for small scale roughness over scales of 5 to 10 cm, only the ISRM (1981) and SSPC large scale standard profiles are considered. The Visual inspection of large scale rock surface roughness using the ISRM and SSPC standard profiles in the field are found to be undulating and slightly wavy respectively. The Visual inspection of the laser scan profiles using the ISRM and SSPC standard profiles found to be undulating and slightly curved to curved respectively (Table 5-13 and Appendix 7). This shows there is consistency between the field and laser scan profile visual inspection using the ISRM but not in SSPC. This is due to difficulty in visually estimating the i-angle from rock surface area of greater than 0.2m2 for the SSPC and other factors discussed in section 6.1 of this chapter. Instead of visually estimating the rock surface with standard profiles it is better to construct the proper narrow strip profile and compare it with the standard profiles. This will minimize the subjectivity and it is rather easy to compare profile with profile rather than rock surface with profile.

6.3. Comparison with the straight edge method

With the assumption drawn in section 6.1 such as, the possible shifting and loss of details in the low resolution (crop01 of scanpos01_scan01) data set, it is tried to compare the general large scale roughness determined using the manual straight edge and narrow strip profiles derived from smooth raw data and reconstructed surface strips of crop02 and crop01. From Figure 6-6 it has been found that the maximum amplitude of manually measured are relatively higher than the laser scan derived. This is due to the loss of details of the data set, shadowing (dead zone) effect and possible shifting of the exact location of the narrow strip from the straight edge location. However, the profiles from the reconstructed surfaces and smoothed raw data strips constructed using the curve fitting tool box (as section 5.2.3) are characterized as small undulations (slightly to moderately undulating) class with the waviness factor (jw) of 1.5 as suggested by Palmström (1995) in his Characterization of the joint planarity as the manual measurements (Figure 6-6 below). These show the laser scan derived roughnesses are comparable with the manually measured roughness and can be used in the rock mass index (RMi) characterization system of Palmström (1995).

CHAPTER SIX

82 82


201612108

6543

2

1

0.5

0.1

1

10

100

1000


Max

imum

am

plitu

de o

f asp

eriti

es (m

m)

JRC 1.5 (U=0.3%)JRC 15 (U=3%)Field measured_H1Field measured_H2Field measured_H3Field measured_V1Field measured_V2Field measured_V2

Join

t rou

ghne

ss c

oeff

icie

nt (J

RC

)

Slightly to moderatley undulating

Strongly undulating

Planar


201612108

6543

2

1

0.5

0.1

1

10

100

1000


Max

imum

am

plitu

de o

f asp

eriti

es (m

m)


Join

t rou

ghne

ss c

oeff

icie

nt (J

RC

)


Strongly undulating

Planar

Figure 6- 6 Estimating JRC and waviness factor (jw) from measurement of roughness amplitude (amax) for 1m straight edge (manually measured) (left) and narrow strip profiles of reconstructed surface of crop01 (right) using the chart developed by Barton (1982). The red lines are the upper and lower limit of slightly to moderately undulating waviness class of Palmström A. (1995) in his joint waviness and smoothness characterization using U value.


83 83

7. Conclusions and recommendations

Rock surface roughness estimation is an important factor in determining the Hydro-mechanical properties of rock mass discontinuities (joints). The shear strength, deformation behaviour and flow properties of the discontinuities are very dependent on surface roughness of the rock mass discontinuities (Kulatilake et al., 1995). However practical estimation of rock surface roughness has been done traditionally using standard profiles and field-based manual methods. These methods are time consuming, subjective and need physical access to the rock faces which may expose field personnel to hazardous situations. The higher part of the rock face is also difficult to reach. Hence, the main objective of this study was to derive rock surface roughness from 3D point cloud data in an automated, objective and safer way and compare the results with the traditional field-based methods. The following main out comes of this comparative study can be summarized:

7.1. Surface model interpolation and quantification

Two terrestrial laser scan data with average spatial resolution of 1cm and 6cm per a point were used to reconstruct the 3D surface model and quantify the rock surface roughness. FastRBF scatter data interpolation and LPF smoothing technique was applied to reconstruct and remove the range measurement error of the scanner. Surface roughness was quantified using the mean orientation of circular window diameters of 5, 10, 20 and 40 cm which corresponds the traditional disc. The mean orientation is defined using least square regression analysis in Matlab’s Principal Component Analysis function (Appendix 3-1). The following main out comes are summarized as follows:

� In general the manually measured maximum roughness angles compared to the derived roughness angles along the dip direction are relatively higher (Figure 6-5).

� The standard deviation of the inner angle difference between the manually measured and laser derived normal vectors, decreases with increasing the diameter of the discs (windows). The main reasons for the above two points are: o The possible shifting of the exact location on the point cloud data. o The loss of details of the scan rock surface due to low resolution data set. o The dead zone due to the inclination of waviness. o Inaccuracies in the compass measurements and o The wobbling effect

� It was found difficult to determine the influence of the range measurement error by comparing the maximum roughness angles of raw with the interpolate data (Figure 5-12). Removing the range measurement error resulted in change of the mean orientation of window, since it is distributed randomly though out the scan discontinuity plane. Hence, the range measurement error was tried to evaluate and estimate using the fractal parameters. The fractal parameters of raw laser scan data are higher than that of interpolated data. By subtracting the fractal parameters of interpolated data from the raw data, the range measurement error was tried to estimate.

CHAPTER SEVEN

84 84

7.2. Directional roughness model reconstruction and quantification

Horizontal and vertical narrow strips of raw and interpolated surface data are cropped and fitted using curve fitting technique in Matlab to quantify the directional rock surface roughness. The raw data strips are also smoothed using smoothing technique to remove the range measurement error. The fitted roughness profiles are quantified using the maximum amplitude with the help of the chart developed by Barton (1982) and Palmström (1995). It is also tried to estimate roughness by visually compare the extracted profiles with the standard reference profiles of ISRM and SSPC. By estimating the i-angle of extracted profiles it was tried also to estimate the SSPC curves. The following main out comes are summarized as follows:

� The roughness amplitudes of raw data narrow strips are higher than the interpolated surface and smoothed strip profiles. The range measurement error in the interpolated surface data are mostly removed by LPF. Therefore by subtracting the maximum amplitude of the interpolated or smoothed strip profile from the raw data strip profile, the influence of the range measurement error in roughness quantification was tried to estimate.

� The laser derived maximum amplitudes are smaller than the measured (Figure 6-6) due to the low resolution data set, shadowing effect and possible shifting of narrow strip location. However most of the measured and all the strip profiles from the interpolated surface and smoothed raw data strips are characterized as slightly to moderately undulating class (Figure 6-6) with waviness factor (jw) of 1.5 as suggested by Palmström (1995). Hence the laser derived profiles can be used in the rock mass index (RMi) characterization system of Palmström (1995).

� The visual inspection of profiles from the interpolated surface and smoothed raw data strips are characterized as undulating descriptive term of ISRM (1981), the same as field visual inspection results. It is also found easy to compare profile with profile rather than rock surface with profile.

� The visually estimated i-angle from the rock surface is higher than the interpolated surface profiles for a given base length between 0.2 and 1m. This is due to the difficulty in visually estimating the i-angle from the rock surface, subjectivity and loss of details of the scan data.

� Most of the raw and the interpolated surface profile data are characterized under the same joint waviness factor (jw) and SSPC curve class. This showed that the range measurement error doesn’t have much influence in roughness determination using the joint planarity characterization system and SSPC method because of their wide class range.

The comparative advantages of this new method described in this study are:

� The 3D point cloud data can be used to model and quantify rock surface roughness in combination with an automated analysis. The laser scan-based roughness acquisition and automated analysis can be considerably faster, less labour-intensive and there fore cheaper than the traditional field-based roughness acquisition methods.

� More roughness data can be gathered than using the traditional field-based manual methods. Even covering the higher parts of the steep slope which is often difficult to reach can now be analyzed using this new technique. This could allow proper application of statistical tools

CONCLUSIONS AND RECOMMENDATIONS

85 85

and remove sampling biasness. Higher accuracy of orientation measurement can be achieved. The average orientation of a given window diameter is measured with high precision rather than the specific location where the Compass and disc-clinometer is laid. The orientation measurement of the discs is greatly governed by the accuracy of compass and wobbling effect.

� Human bias in determining the roughness by visually inspecting the rock surface with the standard profiles is mostly removed. Moreover, it is easy and simple to compare derived roughness profiles with the standard reference profiles rather than rock surface with the standard profiles.

� “No physical access is needed to or near the rock face to measure roughness. This has obvious advantage in terms of safety (Slob, et al., 2005)”.

7.3. Limitations and recommendations for this study

Limitation of the study: � The data density (average resolution) is low (i.e. 1 and 6cm per a point) and are not only

randomly distributed but also their side interval is not the same and change from location to location. Therefore the data density requirement for accurate quantification of roughness of the discontinuity using the roughness length method could not be followed strictly for the evaluation of the scale dependency of the roughness to determine the optimal filtered width and range measurement error besides visual inspection. A new series of window diameters was selected following the traditional disc diameters.

� The average resolution of the scan data set used for comparison with the compass and disc-clinometer method is 6 cm. Roughness features less than the 6cm are not capture. There for the laser scan data resolution should be improved and the range measurement error should be decreased for good quantification of roughness and comparison. This could help also to investigate the secondary roughness of a discontinuity surface.

Recommendations: This study showed that it is possible to derive rock surface roughness from the 3D point cloud data in combination with an automated way. The roughness derived from the point cloud data compare to the manually measured are relatively lower. The comparison of mean orientation of circular windows with the discs on a cell-to-cell basis also showed deviation form each other. To get a good comparable results and in order to confirm that this method can really replace these traditional and accepted techniques, the following recommendations are drawn to improve this study.

� The roughness is distorted due to the dead zone as the result of inclination of waviness with respect to the scanner position. This can not be removed by increasing the resolution of the scanner. This, which may cause under estimation of maximum roughness amplitude, can be improved by multi-view scanning with high but fixed resolution.

� The quantity of the orientation measurements might be improved by the use of an electronic compass with one degree precision.

� The discs should be equipped with proper connected pins to minimize the wobbling effect and adjust more or less the mean orientation of plane.

CHAPTER SEVEN

86 86

� For easy and exact referencing of the sample grid on the point cloud data, at least three key marks should be captured by high resolution digital camera and scanner during scanning.

� Different discontinuities should be scanned with the same resolution and scanner to classify the roughness of different rock mass discontinuities. One discontinuity surface should be scanned with different resolutions of the scanner to see the effect of resolution differences on roughness quantification.

� The point-cloud data are available as purely vertex data. In general, without any additional information, estimating normals from purely vertex data is ambiguous and likely to be less robust than using normalsfrommesh, normalsfromsigns or normalsfromscan (FastRBF Toolbox, 2004). Hence scanner position information is need for estimating normals.

� The laser scan data should be simulated to estimate the error of the laser scan data to established better theoretical relationship between the error and resolution and plane geometry.

� The roughness angle of rock surface derived using circular windows of different diameter should be measured from the centre of the polar plot to the maximum envelop contour of pole plots in a direction towards the slope orientation.

� Critical examination of the damage caused to asperities during shearing tests at different normal stress levels will aid in deciding the values of roughness angle (i-angle) that will cause dilation of the plane during shearing.

7.4. Recommendations for the future study directions:

For the future studies, it is recommended to:

� The narrow strip profiles of the laser scan data can be used also to estimate the JRC value using any of several proposed empirical correlations such as the Tse and Cruden (1979) Z2 relationship and Maerz et al. (1990) Rp relationship between JRC and measurement increments.

� The intensity of the reflected laser beam, which has not been used in any of the analysis yet, may also be used in relating these methods as well as determination of the small scale roughness. The rougher the surface is, the more diffusely the laser beam will be reflected (slob et al., 2005). However, the relationship between roughness and intensity may be very complex, since parameters such as weathering, mineralogical composition, position of the scanner relative the rock face, target albedo, angle of inclination, moisture, etc also influence the intensity level.

� Compared with the photogrammetry the laser object resolution is generally little worse from geometric point of view and dramatically worse from radiometric viewpoint. It also became clear that a combination of both photogrametry (with its high geometric and radiometric resolution) and terrestrial laser scanning (allowing highly automated direct 3D measurement) would be promising. Hence it can be combined with image analysis as proposed by Kemeny et al. (2003) for smooth fracture surface trace which could not generate good result in this method.

� The development of the laser scanning is very rapid. If the range measurement error, beam divergence and resolution are improved, it is recommended to:

CONCLUSIONS AND RECOMMENDATIONS

87 87

o Apply two dimensional interpolation techniques and extract surface roughness profiles in an arbitrary directions referenced to structurally and mechanically significant vector. Once the profiles are extracted, the well known and widely used JRC value can be estimated using any of the several empirical correlations.

o Build 3D point cloud model estimation of the spacing between the fracture surfaces to estimate ground water flow properties. Once the spacing is estimated properly, it broadens the scope of the application of the 3D point cloud data in different geo-engineering factors in a spatial context.

� The effective positive and negative roughness angles of the laser scan data are estimated from the contours of maximum scatter (envelope) of the four window sizes along a given direction. It is recommended to have a higher number of window sizes to derive more detailed roughness and compare the results with the profile along the defined direction.


89 89

References used

Axelsson, P., 1999. Processing of laser scanner data-algorithms and applications. ISPRS Journal of Photogrammetry and Remote Sensing, 54(2-3): 138-147.

Ayadan, O. and Kawamoto, T., 1990. Discontinuities and their effect on rock mass In: N. Barton and O. Stephansson (Editors), Proc. International Symposium on Rock Joints. Publ Rotterdam: A A Balkema, Loen/Norway, pp. 149-156.

Balzani, M., Pellegrinelli, A., Perfetti, N. and Uccelli, F., 2001. A Terrestrial 3D Laser Scanner- Accuracy Tests. In: J. Albertz (Editor), Proceedings of the XVIII. International Symposium of CIPA 2001, Potsdam ,Germany pp. 445-453.

Bandis, S., Lumsden, A.C. and Barton, N.R., 1981. Experimental studies of scale effects on the shear behaviour of rock joints. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 18(1): 1-21.

Bandis, S.C., Lumsden, A.C. and Barton, N.R., 1983. Fundamentals of rock joint deformation. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 20(6): 249-268.

Barton, N., 1973. Review of a new shear-strength criterion for rock joints. Engineering Geology, 7(4): 287-332.

Barton, N., 1982. Modellimg rock joint behaviour from in situ block tests: Implications for nuclear waste respository design. ONWI-308, Columbus, OH, 96.

Barton, N. and Bandis, S., 1990. Review of predictive capabilities of JRC-JCS model in engineering practice In: N. Brton and O. Stephansson (Editors), Proc. International Symposium on Rock Joints. Publ Rotterdam: A A Balkema, Loen/Norway, pp. 603-610.

Barton, N., Bandis, S. and Bakhtar, K., 1985. Strength, deformation and conductivity coupling of rock joints. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 22(3): 121-140.

Barton, N. and Choubey, V., 1977. The shear strength of rock joints in theory and practice. Rock Mechanics and Rock Engineering, 10(1 - 2): 1-54.

Belem, T., Homand-Etienne, F. and Souley, M., 2000. Quantitative Parameters for Rock Joint Surface Roughness. Rock Mechanics and Rock Engineering, 33(4): 217-242.

Bendat, J.S. and pierson, A.G., 1985. Random data Analysis & Measurement Procedures. John Wiley & Sons, New York, 566 pp.

Berry, M.V. and Lewis, Z.V., 1980. On the Weierstrass-Mandelbrot fractl function, Proc. Ser. A. 370,

R. Soc. London, pp. 459-484.

REFERENCES USED

90 90

Carr, J. et al., 2003. Smooth surface reconstruction from noisy range data, International Conference on Computer Graphics and Interactive Techniques: in Austalasia and South East Asia (Graphite 2003).

Carr, J.C. et al., 2001. Reconstruction and Representation of 3D Objects with Radial Basis Functions.

ACM SIGGRAPH 2001, Los Angeles, CA, pp. 67-76, 12-17 August 2001.

Castaing, C., Genter, A., Chiles, J.P., Bourgine, B. and Ouillon, G., 1997. Scale effects in natural fracture networks. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 34(3-4): 389-389.

Chae, B.G., Ichikawa, Y., Jeong, G.C., Seo, Y.S. and Kim, B.C., 2004. Roughness measurement of rock discontinuities using a confocal laser scanning microscope and the Fourier spectral analysis. Engineering Geology, 72(3-4): 181-199.

Cocone, 2004. Cocone Softwares for surface reconstruction and medial axis. http://www.cse.ohio-state.edu/~tamaldey/cocone.html.

Cunha, A.P., 1990. Scale effects in rock masses : proceedings of the 1st international workshop on scale effects in rock masses, Loen Norway, 7-8 June 1990. Balkema A.A., Rotterdam 339 pp.

Cunha, A.P., 1992. Scale effects in the determination of mechanical properties of joints and rock masses : Proc 7th ISRM International Congress on Rock Mechanics, Aachen, 16-20 September 1991 V1, P311-318. Publ Rotterdam: A A Balkema, 1991. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 29(4): 214-214.

Da Silva, A.C. and Boulvain, F., 2004. From palaeosols to carbonate mounds: facies and environments of the Middle Frasnian platform in Belgium. Geological Quarterly, 48, 253-266

Develi, K. and Babadagli, T., 1998. Quantification of natural fracture surfaces using fractal geometry. Mathematical Geology, 30(8): 971-998.

Dey, T.K., Giesen, J. and Hudson, J.A., 2001. Delaunay Based Shape Reconstruction from Large Data, Proc. IEEE Symposium in Parallel and Large Data Visualisation and Graphics (PVG2001), pp. 19-27.

El-Soudani, S.M., 1978. Profilometric analysis of fractures. Metallograghy, 11: 247-336.

Exadaktylos, G.E.T., C E, 1994. Scale effect on rock mass strength and stability : Exadaktylos, G E; Tsoutrelis, C E Proc Second International Conference on Scale Effects in Rock Masses, Lisbon, 25 June 1993 P101-110. Publ Rotterdam: A A Balkema, 1993. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 31(2): A69-A69.

Fadeev, 1991. Scale effect of rock strength : Fadeev, A B Proc 1st International Workshop on Scale Effects in Rock Masses, Loen, 7-8 June 1990 P183-189. Publ Rotterdam: A A Balkema, 1990. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 28(2-3): A72-A72.

Fardin, N., Feng, Q. and Stephansson, O., 2004. Application of a new in situ 3D laser scanner to study the scale effect on the rock joint surface roughness. International Journal of Rock Mechanics and Mining Sciences, 41(2): 329-335.

REFERENCES USED

91 91

Fardin, N., Stephansson, O. and Jing, L., 2001. The scale dependence of rock joint surface roughness. International Journal of Rock Mechanics and Mining Sciences, 38(5): 659-669.

FastRBF, 2004. FastRBF Toolbox-Scattered Data Interpolation with Radial Basis Functions- MATLAB interface, version 1.4, FarField Technology Christchurch, new Zealand.

Fecker, E. and Rengers, N.F., 1971. Measurement of large -scale roughness of rock planes by means of profilogragh and geological compass, 1st Int. Symp. Rock Mech., Nancy, pp. 1-18.

Feder, J., 1988. Fractals, 283. Plenum Press, New York.

Feng, Q., Fardin, N., Jing, L. and Stephansson, O., 2003. A New Method for In-situ Non-contact Roughness Measurement of Large Rock Fracture Surfaces. Rock Mechanics and Rock Engineering, 36(1): 3-25.

Fienen, M.N., 2005. The three-point problem , vector analysis and extension to the N-point problem. jornal of geoscience education, 53(3): 257-262.

Filin, S. and Pfeifer, N., 2006. Segmentation of airborne laser scanning data using a slope adaptive neighborhood. ISPRS Journal of Photogrammetry and Remote Sensing, 60(2): 71-80.

Franke, R., 1982. Smooth interpolation of scattered data by local thin plate splines. Computers & Mathematics with Applications, 8(4): 273-281.

Fredrich, J.T. and Lindquist, W.B., 1997. Statistical characterization of the three-dimensional microgeometry of porous media and correlation with macroscopic transport properties. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 34(3-4): 368-368.

Galante, G., Piacentini, M. and Ruisi, V.F., 1991. Surface roughness detection by tool image processing. Wear, 148(2): 211-220.

Girardeau-Montaut, D., Roux, M., Marc, R. and Thibault, G., 2005. Change detection on point cloud data acquired with a ground laser scanner In: G. Vosselman and C. Brenner (Editors), Proceedings of the ISPRS Workshop Laser scanning 2005, Enschede, the Netherlands, .

Gordon, S.J., Lichti, D.D., Chandler, I., Stewart, M.P. and Franke, J., 2003 Precision Measurement of Structural Deformation using Terrestrial Laser Scanners, . Proceedings of Optical 3D Methods, Zurich, Switzerland, 22 - 25 September, pp. 322 - 329. .

Grasselli, G. and Egger, P., 2000. 3D surface characterisation for the prediction of the shear strength of rough joints. . In: A. Aachen (Editor), Symposium EUROCK 2000, Germany, pp. 281-286.

Grasselli, G. and Egger, P., 2003. Constitutive law for the shear strength of rock joints based on three-dimensional surface parameters. International Journal of Rock Mechanics and Mining Sciences, 40(1): 25-40.

Grima, M.A., 1994. Scale effect on shear strength behaviour of ISRM roughness profile. MSc Thesis, ITC Delft, Kanaalweg 3, 2628 EB Deft, The Netherlands, 200 pp.

Hack, H.R.G.K., 2006. Discontinuous rock mechanics. . lecture notes, version 5.0 (unpublished),. ITC The Nethelands, Hengelosestraat 99, 7514 AE Enschede,, 233 pp.

REFERENCES USED

92 92

Hack, H.R.G.K. and Price, D.G., 1995. Determination of discontinuity friction by rock mass classification. In: 8th International Congress on Rock Mechanics, Tokyo 1995 / ed. by T. Fujii. pp. 23-27.

Hack, H.R.G.K., Prince, S.D. and Rengers, N., 1998. Slope stability probability classification SSPC, ITC, Enschede, 258 p. pp.

Hardy, R.L., 1990. Theory and applications of the multiquadric biharminic method. Comput. Math. Applic., 19: 163-208.

Harrison, J.P. and Rasouli, V., 2001. In-plane analysis of fracture surface roughness: anisotropy and scale effect in anisotropy. In: H.K. Tinucci JP, Elsworth D (Editor), Proceedings of the 38th US rock mechanics symposium. Lisse, Netherlands, Swets & Zeitlinger Washington DC, USA, pp. 777 - 783.

Harrison, J.P.G., R J F 1994. Effect of scale on roughness anisotropy and magnitude : Harrison, J P; Goodfellow, R J F Proc Second International Conference on Scale Effects in Rock Masses, Lisbon, 25 June 1993 P111-117. Publ Rotterdam: A A Balkema, 1993. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 31(2): A73-A73.

Hastings, H.M. and Sugihara, G., 1993. Fractals: a user's guide for the natural sciences. Oxford university Press, Oxford, England.

Hong, E., Lee, I. and Lee, J., 2006. Measurement of Rock Joint Roughness by 3D Scanner Geotechnical Testing Journal, 29 (6): 8.

Huang, T.H. and Doong, Y.S., 1990. Anisotropic shear strength of rock joints. In: N. Barton and O. Stephansson (Editors), Proc. International Symposium on Rock Joints. Publ Rotterdam: A A Balkema, Loen/Norway, pp. 211-217.

ISRM, 1975. Suggested methods for determining shear strength : ISRM 9F, 1T ISRM Commission on Standard. Lab. Field Tests. Committee on Field Tests, Document, N1, FEB. 1974, 23P. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 12(3): A35-A35.

ISRM, 1978. Commission on standardization of laboratory and field tests:Suggested methods for the quantitative description of dioscountinuties in rock mases. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 15(6): 319-368.

ISRM, 1981. Suggested methods for the Quantitative Description of Discontinuities. Rock characterization, testing and monitoring - ISRM suggested methods. Pergamon press, Oxfrod, 3-52 pp.

Iwano, M. and Einstein, H.H., 1993. Stochastic analysis of surface roughness, aperture and flow in a single fracture Proc EUROCK'93. Publ Rotterdam: A A Balkema, Lisbon, pp. 134-141.

Jing, L. and Hudson, J.A., 2004. Fundamentals of the hydro-mechanical behaviour of rock fractures: roughness characterization and experimental aspects. International Journal of Rock Mechanics and Mining Sciences, 41(Supplement 1): 157-162.

Johnson, R.B. and Degraff, J.V., 1988. Principles of engineering geology. John wiley & sons, New York USA, 497 pp.

REFERENCES USED

93 93

Jutzi, B., Neulist, J. and U., S., 2005. Sub-pixel edge localization based on laser waveform analysis In: G. Vosselman and C. Brenner (Editors), Proceedings of the ISPRS Workshop Laser scanning 2005, Enschede, the Netherlands.

Kerstiens, C.M.D., 1999. A Generic UDEC model for rock joint shear tests, including roughness characterisation MSc Thesis, TU Delft, Kanaalweg 3, 2628 EB Deft, The Netherlands, 211 pp.

Knapen, B.V. and Slob, S., 2006. Identification and characterisation of rock mass discontinuity sets using 3D laser scanning In IAEG 2006 : Pre-proceedings 10th international congress International Association of Engineering Geology :Engineering geology for tomorrow's cities. Geological Society of London, 2006. paper 438, Nottingham, United Kingdom CD-ROM / London, pp. 11.

Kulatilake, P., Shou, G., Huang, T.H. and Morgan, R.M., 1995. New Peak Shear-Strength Criteria for Anisotropic Rock Joints. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 32(7): 673-697.

Kulatilake, P. and Um, J., 1999. Requirements for accurate quantification of self-affine roughness using the roughness-length method. International Journal of Rock Mechanics and Mining Sciences, 36(1): 5-18.

Kulatilake, P., Um, J. and Pan, G., 1998. Requirements for accurate quantification of self-affine roughness using the variogram method. International Journal of Solids and Structures, 35(31-32): 4167-4189.

Kulatilake, P.H.S.W., 1995. Scale effects on rock mass deformability : P. H. S. W. Kulatilake, in: Geomechanics 93. Proc. conference, Ostrava, 1993, ed Z. Rakowski, (Balkema), 1994, pp 151-158. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 32(2): A61-A61.

Lanaro, F., 2000. A random field model for surface roughness and aperture of rock fractures. International Journal of Rock Mechanics and Mining Sciences, 37(8): 1195-1210.

Laubscher, D.H., 1990. Geomechanics classification system for the rating of rock mass in mine design Journal of South African Inst. of Mining and metallurgy, 90(10): 257-273.

Lemy, F. and J., H., 2004. A field application of laser scanning technology to quantify rock fracture orientation, In: Proceedings of ‘EUROCK 2004 & 53rd Geomechanics Colloquium, Salzburg, pp. 435-438.

Lichti, D., Pfeifer, N. and Maas, H.-G., 2006. ISPRS Journal of Photogrammetry and Remote Sensing-- Theme issue "Terrestrial Laser Scanning". ISPRS Journal of Photogrammetry and Remote Sensing, 60(5): 359-359.

Lichti, D.D., Stewart, M.P., Tsakiri, M. and Snow, A.J., 2000. Benchmark Tests on a Three-dimensional Laser Scanning System geomatics research Australia, 72: 1-24.

Maerz, N.H., Chepur, P., Myers, J.J. and Linz, J., 2001. Concrete Roughness Characterization Using Laser Profilometry for Fiber-Reinforced Polymer Sheet Application. Transportation research record,, 1775 132.

Maerz, N.H., Franklin, J.A. and Bennett, C.P., 1990. Joint roughness measurement using shadow profilometry. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 27(5): 329-343.

REFERENCES USED

94 94

Malinverno, A., 1990. A simple method to estimate the fractal dimension of self-affine series. Goephys. Res. Lett., 17: 1953-1956.

Mandelbrot, B.B., 1983. The fractal goemetry of nature. W.Freeman, San Francisco, 468 pp.

Mario Alvarez, G., 1994. Scale effect on shear strength behaviour of ISRM roughness profile, ITC, Delft, 200 p. pp.

Matsushita, M. and Ouchi, S., 1989. On the self-affinity fo various curves. Physica. D., 38: 246-251.

Milne, D., Germain, P., Grant, D. and Noble, P., 1991. Field observation for the standardization of the NGI classification system for underground mine design. International Congress on Rock Mechanics, A.A. Balkema, Aachen, Germany.

Moon, H.K.K., C Y, 1994. Scale effects in the elastic moduli and strength of jointed rock masses : Moon, H K; Kim, C Y Proc Second International Conference on Scale Effects in Rock Masses, Lisbon, 25 June 1993 P39-48. Publ Rotterdam: A A Balkema, 1993. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 31(1): A10-A10.

Muralha, J.J.R.D., 1995. Mechanical behaviour of discountinuities of rock masses (in portuguese). Ph.D. Thesis, Technical University of Lisbon,, Lisbon.

Myers, N.O., 1962. Characterization of surface roughness. Wear, 5: 182-189.

Normat, F. and Tricot, C., 1993. Fractal simplificstion of lines using convex hulls. Goegr. Anal., 25: 118-129.

Odling, N.E., 1994. Natural fracture profiles, fractal dimension and joint roughness coefficients. Rock Mechanics and Rock Engineering, 27(3): 135-153.

Ojo, O., 1989. Application of measuring plates of different diameters in the measurement of surface roughness of discontinuties. International Journal of Mining and geological engineering, 7: 267-270.

Orey, S., 1970. Gaussian sample functions and Housdorff dimensions of level crossings. Wahrsheninkeits theorie verw, Gebierte, 15: 249-256.

Palmström, A., 1995. RMi - a rock mass characterization system for rock engineering purposes.Ph.D thesis Ph.D Thesis, University of Oslo, Oslo, Norway, 409p pp.

Palmström, A., 2001. Measurement and characterization of rock mass jointing. In: V.M. Sharma and K.R. Saxena (Editors), In In-situ characterization of rocks. A.A. Balkema publishers, N-0378 Oslo, Norway, pp. 49 - 97.

Patton, F.D., 1966. Multiple model of shear failure in rock, Porc. of the 1st Congress of ISRM, Libson, portugal, pp. 509-513.

Piggott, A.R. and Elsworth, D., 1993. Comparison of methods of characterizing fracture surface roughness : Proc Conference on Fractured and Jointed Rock Masses, Lake Tahoe, 3-5 June 1992 P490-496. Publ California: Lawrence Berkeley Laboratory, 1992.Abst. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 30(5): 282-282.

Pinto Da Cunha, A.M., J, 1993. Scale effects in the determination of mechanical properties of jointed rock masses : Pinto da Cunha, A; Muralha, J Proc Conference on Fractured and Jointed Rock

REFERENCES USED

95 95

Masses, Lake Tahoe, 3-5 June 1992 P497-504. Publ California: Lawrence Berkeley Laboratory, 1992. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 30(5): 276-276.

Pistone, S., 1991. Scale effect in the shear strength of rock joints: Sarra Pistone, R Proc 1st International Workshop on Scale Effects in Rock Masses, Loen, 7-8 June 1990 P201-206. Publ Rotterdam: A A Balkema, 1990. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 28(2-3): A138-A138.

Piteau, D.R., 1970. Geological factors significant to the stability of slopes cut in rock Proc. Symp. on Planning Open Pit Mines, Johannesburg, South Africa, pp. 33-53.

Rahman, Z., Slob, S. and Hack, H.R.G.K., 2006. Deriving roughness characteristics of rock mass discontinuities from terrestrial laser scan data. Proc. Engineering geology for tomorrow's cities. 10th IAEG Congress, Nottingham, United Kingdom, 6-10 September 2006 (article) (accepted for publication)

Reeves, M.J., 1985. Rock surface roughness and friction strength. International Journal of Rock

Mechanics and Mining Science and Geomechanics. Abstract, 22: 429-442.

Riegl, 2006. Riegl 3D-Ler Mirror Scanner LMS-Z420i, http://www.riegl.com/terrestrial_scanners/lms-z420i_/420i_all.htm, access date, 20/11/06.

Rowlands, K.A., Jones, L.D. and Whitworth, M., 2003. Landslide Laser Scanning: a new look at an old problem. . Quarterly Journal of Engineering Geology and Hydrogeology, 36: 155-157.

Runne, H., Niemeier, W., Kern, F. and Heribert, 2001 Application of Laser Scanners to Determine the Geometry of Buildings. Optical 3D Measurement Techniques, 1(4): 41-48.

Sayles, R.S. and Thomas, T.R., 1977. The spatial representation of surface roughness by means of the structure function: A practical alternative to correlation. Wear, 42(2): 263-276.

Schwalbe, E., Maas, H.-G. and Seidel, F., 2005. 3D building model generation from airborne laserscanner data using 2D GIS data and orthogonal point cloud projections In: G. Vosselman and C. Brenner (Editors), Proceedings of the ISPRS Workshop Laser scanning 2005, Enschede, the Netherlands.

Silberschmidt, V.V., 1994. Scale invariance in stochastic fracture of rocks: Silberschmidt, V V Proc Second International Conference on Scale Effects in Rock Masses, Lisbon, 25 June 1993 P49-54. Publ Rotterdam: A A Balkema, 1993. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 31(1): A13-A13.

Silvester, M.V., 1996. Geometrical and Hydro-Mechanical Characterisation of Discountinuities: An experimental study. MSc. Thesis, TU Delft, Delft, 227 pp.

Slob, S., Hack, H.R.G.K. and Turner, K., 2002. An approach to automate discontinuity measurements of rock faces using laser scanning techniques. In: C. Dinid da Gama and L. Riberia e Sousa (Editors), Proceedings of ISRM EUROCK 2002. Lisboa, Sociedade Portuguesa de Geotecnia, Funchal, Portugal, pp. 87-94.

Slob, S., Hack, H.R.G.K., van Knapen, B. and Kemey, J., 2004. Automated identification and characterisation of discontinuity sets in outcropping rock masses using 3D terrestrial laser scan survey techniques. In: Proceedings of the ISRM regional symposium EUROCK 2004 and

REFERENCES USED

96 96

53rd Geomechanics colloquy : Rock engineering and practice, October 7-9, 2004 Salzburg, Austria. / ed. by W. Schubert. Essen; Verlag GlÃ¼ckauf, 2004. pp. 439-443.

Slob, S., Hack, H.R.G.K., van Knapen, B., Turner, K. and Kemeny, J., 2005. A method for automated discontinuity analysis of rock slopes with three - dimensional laser scanning. Transportation research record : journal of the transportation research board(2005): 187-194.

Slob, S. and van Knapen, B., 2005. Rock mass characterization with 3D laser scanning: never again struggling with geologic compass and measuring tape? Ingeokring Newsletter,12(2005 1):4-9.

Stimpson, B., 1982. A rapid field method for recording joint roughness profiles. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 19(6): 345-346.

Tse, R. and Cruden, D.M., 1979. Estimating joint roughness coefficients. International Journal of Rock Mechanics and Mining Sciences. Abstr. , 15: 303-307.

Turner, A.K., Kemeny, J., Slob, S. and Hack, H.R.G.K., 2006. Evaluation, and management of unstable rock slopes by 3D laser scanning. In: IAEG 2006: Pre-proceedings 10th international congress International Association of Engineering Geology: Engineering geology for tomorrow's cities 6-10 September, Nottingham, United Kingdom CD-ROM / London : Geological Society of London, 2006. paper 404. 11 p.

van Knapen, B. and Slob, S., 2006. Identification and characterisation of rock mass discontinuity sets using 3D laser scanning In IAEG 2006: Pre-proceedings 10th international congress International Association of Engineering Geology:Engineering geology for tomorrow's cities. Geological Society of London, 2006. paper 438, Nottingham, United Kingdom CD-ROM / London, pp. 11.

Wack, R. and Stelzl, H., 2005. Laser DTM generation for South-Tyrol and 3D-visualization In: G. Vosselman and r.C. Brenne (Editors), Proceedings of the ISPRS Workshop Laser scanning 2005, Enschede, the Netherlands.

Walsh, S.J., Bian, L., McKnight, S., Brown, D.G. and Hammer, E.S., 2003. Solifluction steps and risers, Lee Ridge, Glacier National Park, Montana, USA: a scale and pattern analysis. Geomorphology, 55(1-4): 381-398.

Weissbach, G., 1978. A new method for the determination of the roughness of rock joints in the laboratory. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 15(3): 131-133.

Wickens, E.H. and Barton, N.R., 1971. Application of photogrammetry to the stability of excavated rock slopes Photogrammetric Record, 7(37): 46-54.

Windsor, C.R. and Robertson, W.V., 1994. Rock Reinforcement Practice. Rock Mass Formulation, 1.

Xie, H., Sun, H., Ju, Y. and Feng, Z., 2001. Study on generation of rock fracture surfaces by using fractal interpolation. International Journal of Solids and Structures, 38(32-33): 5765-5787.

Yilbas, Z. and Hasmi, M.S.J., 1999. Surface roughness measurement using an optical system. Journal of Materials Processing Technology, 88(1-3): 10-22.

Yu, X. et al., 2005. Applicability of first pulse derived digital terrain models for boreal forest zone In: G. Vosselman and C. Brenner (Editors), Proceedings of the ISPRS Workshop Laser scanning 2005, Enschede, the Netherlands, pp. 6.


i i

Appendices

Appendix 1 Data set of Teilfer quarry, Lustin, Belgium

Appendix 1.1 Terrestrial laser scan data collected by Siefko Slob, ITC, The Netherlands

Lustin_ScanPos01_scan01 with resolution of 1 point per 6cm (left) and Lustin_ScanPos01_scan02 with

resolution of 1 point per 1cm (right) gray colour laser scan data. Type pf scanner: Reigel3D-Z420i.

The scanner position and procedures for georeferencing the scan Lustin out crop. Two white plywood board of dimension 60x60cm were used in the scan scene to georefference the data set. In case the scanner was inclined for scanning at an angle three horizontally aligned white cylinders using water levelling were used in the scene.

APPENDICES

ii ii

Appendix 1.2 Measured rock surface roughness data using traditional methods

Photographs showing manufacturing field equipment (Discs & straight edge) for roughness measurement in the ITC workshop, the scene of scan discontinuity plane and sample area location with a local grids, Measurement of dip/dip direction, and a close view of the surface with a 40cm ruler placed on it

APPENDICES

iii iii

Collected by:

Ephrem K.

ROCK SURFACE CHARACTERISATION Using Compass and disc-clinometer Sheet No. 1 Date: 19/9/06

S.no. Disc size

Grid position

Dip amount

Dip direction

S.no. Disc size

Grid position

Dip amount

Dip direction

1 40cm 1 48 188.5 51 20cm 6-1 47 188 2 40cm 2 46 185 52 20cm 6-2 50 189 3 40cm 3 47 183 53 20cm 6-3 46 190 4 40cm 4 46 183 54 20cm 6-4 48 192 5 40cm 5 45 184 55 20cm 6-5 46 194 6 40cm 6 48 187 56 20cm 7-1 44 184 7 40cm 7 47 186 57 20cm 7-2 50 186 8 40cm 8 47 189 58 20cm 7-3 49 186 9 40cm 9 45 186 59 20cm 7-4 47 185

10 40cm 10 44 186 60 20cm 7-5 47 187 11 40cm 11 49 186 61 20cm 8-1 -- -- 12 40cm 12 47 193 62 20cm 8-2 -- -- 13 40cm 13 45 189 63 20cm 8-3 -- -- 14 40cm 14 44 192 64 20cm 8-4 -- -- 15 40cm 15 45 187 65 20cm 8-5 -- -- 16 40cm 16 49 186 66 20cm 9-1 46 191 17 40cm 17 44 192 67 20cm 9-2 45 187 18 40cm 18 45 189 68 20cm 9-3 46 192 19 40cm 19 46 187 69 20cm 9-4 44 187 20 40cm 20 47 187 70 20cm 9-5 45 185 21 40cm 21 48 192 71 20cm 10-1 44 188 22 40cm 22 48 189 72 20cm 10-2 45 183 23 40cm 23 49 192 73 20cm 10-3 41 185 24 40cm 24 48 182 74 20cm 10-4 43 182 25 40cm 25 49 183 75 20cm 10-5 44 184 26 20cm 1-1 44 182 76 20cm 11-1 52 192 27 20cm 1-2 48 196 77 20cm 11-2 50 182 28 20cm 1-3 47 190 78 20cm 11-3 48 189 29 20cm 1-4 50 185 79 20cm 11-4 41 179 30 20cm 1-5 48 189 80 20cm 11-5 39 184 31 20cm 2-1 49 188 81 20cm 12-1 47 188 32 20cm 2-2 49 181 82 20cm 12-2 47 187 33 20cm 2-3 51 189 83 20cm 12-3 51 190 34 20cm 2-4 48 185 84 20cm 12-4 45 185 35 20cm 2-5 48 182 85 20cm 12-5 48 188 36 20cm 3-1 -- -- 86 20cm 13-1 42 185 37 20cm 3-2 -- -- 87 20cm 13-2 45 192 38 20cm 3-3 -- -- 88 20cm 13-3 46 188 39 20cm 3-4 -- -- 89 20cm 13-4 45 192 40 20cm 3-5 -- -- 90 20cm 13-5 46 191 41 20cm 4-1 44 178 91 20cm 14-1 45 190 42 20cm 4-2 46 180 92 20cm 14-2 49 187 43 20cm 4-3 48 182 93 20cm 14-3 46 188 44 20cm 4-4 47 180 94 20cm 14-4 44 190 45 20cm 4-5 46 183 95 20cm 14-5 48 191 46 20cm 5-1 47 184 96 20cm 15-1 42 190 47 20cm 5-2 45 187 97 20cm 15-2 45 180 48 20cm 5-3 45 186 98 20cm 15-3 45 194 49 20cm 5-4 44 186 99 20cm 15-4 44 180 50 20cm 5-5 46 186 100 20cm 15-5 44 189

APPENDICES

iv iv

Collected by:

Ephrem K. ROCK SURFACE CHARACTERISATION

Using Compass and disc-clinometer Sheet No. 2 Date: 19/9/06 S.no. Disc

size Grid

position Dip

amount Dip

direction S.no. Disc

size Grid

position Dip amount Dip

direction 101 20cm 16-1 45 197 151 10cm 1-1 43 180 102 20cm 16-2 50 186 152 10cm 1-2 40 185 103 20cm 16-3 50 184 153 10cm 1-3 45 196 104 20cm 16-4 49 188 154 10cm 1-4 45 192 105 20cm 16-5 50 182 155 10cm 1-5 50 180 106 20cm 17-1 45 181 156 10cm 1-6 54 182 107 20cm 17-2 48 187 157 10cm 1-7 50 192 108 20cm 17-3 48 193 158 10cm 1-8 48 187 109 20cm 17-4 50 193 159 10cm 1-9 50 178 110 20cm 17-5 43 185 160 10cm 1-10 47 178 111 20cm 18-1 44 188 161 10cm 1-11 49 200 112 20cm 18-2 44 192 162 10cm 1-12 50 176 113 20cm 18-3 46 192 163 10cm 1-13 50 182 114 20cm 18-4 47 190 164 10cm 1-14 46 186 115 20cm 18-5 48 181 165 10cm 1-15 46 195 116 20cm 19-1 44 188 166 10cm 1-16 52 173 117 20cm 19-2 45 190 167 10cm 1-C 48 188 118 20cm 19-3 45 188 168 10cm 2-1 52 184 119 20cm 19-4 47 187 169 10cm 2-2 50 187 120 20cm 19-5 47 193 170 10cm 2-3 50 184 121 20cm 20-1 49 192 171 10cm 2-4 55 182 122 20cm 20-2 47 185 172 10cm 2-5 53 181 123 20cm 20-3 44 192 173 10cm 2-6 56 188 124 20cm 20-4 47 190 174 10cm 2-7 50 183 125 20cm 20-5 49 191 175 10cm 2-8 45 177 126 20cm 21-1 48 192 176 10cm 2-9 46 185 127 20cm 21-2 47 190 177 10cm 2-10 50 180 128 20cm 21-3 49 188 178 10cm 2-11 48 190 129 20cm 21-4 48 186 179 10cm 2-12 50 190 130 20cm 21-5 49 192 180 10cm 2-13 47 188 131 20cm 22-1 50 189 181 10cm 2-14 54 186 132 20cm 22-2 50 200 182 10cm 2-15 50 198 133 20cm 22-3 50 190 183 10cm 2-16 43 190 134 20cm 22-4 49 192 184 10cm 2-C 50 188 135 20cm 22-5 47 188 185 10cm 6-1 46 177 136 20cm 23-1 50 190 186 10cm 6-2 55 193 137 20cm 23-2 46 188 187 10cm 6-3 38 182 138 20cm 23-3 51 191 188 10cm 6-4 47 185 139 20cm 23-4 51 189 189 10cm 6-5 47 184 140 20cm 23-5 51 190 190 10cm 6-6 45 195 141 20cm 24-1 46 183 191 10cm 6-7 50 182 142 20cm 24-2 48 186 192 10cm 6-8 46 194 143 20cm 24-3 51 181 193 10cm 6-9 49 183 144 20cm 24-4 50 191 194 10cm 6-10 48 185 145 20cm 24-5 50 186 195 10cm 6-11 49 188 146 20cm 25-1 50 180 196 10cm 6-12 48 180 147 20cm 25-2 49 183 197 10cm 6-13 43 188 148 20cm 25-3 47 186 198 10cm 6-14 47 188 149 20cm 25-4 50 188 199 10cm 6-15 36 192 150 20cm 25-5 49 184 200 10cm 6-16 50 180

APPENDICES

v v

Collected by:

Ephrem K.


S.no. Disc size

Grid position

Dip amount

Dip direction

S.no. Disc size

Grid position Dip amount

Dip direction

201 10cm 6-C 50 188 251 5cm 1-7-1 52 184 202 10cm 7-1 47 180 252 5cm 1-7-2 56 197 203 10cm 7-2 41 186 253 5cm 1-7-3 45 185 204 10cm 7-3 44 193 254 5cm 1-7-4 45 200 205 10cm 7-4 50 176 255 5cm 1-8-1 47 197 206 10cm 7-5 41 177 256 5cm 1-8-2 47 189 207 10cm 7-6 46 190 257 5cm 1-8-3 46 190 208 10cm 7-7 49 183 258 5cm 1-8-4 55 180 209 10cm 7-8 49 180 259 5cm 1-9-1 51 180 210 10cm 7-9 50 187 260 5cm 1-9-2 56 180 211 10cm 7-10 48 182 261 5cm 1-9-3 50 181 212 10cm 7-11 49 182 262 5cm 1-9-4 50 183 213 10cm 7-12 46 185 263 5cm 1-10-1 52 190 214 10cm 7-13 48 189 264 5cm 1-10-2 47 188 215 10cm 7-14 50 182 265 5cm 1-10-3 47 193 216 10cm 7-15 40 190 266 5cm 1-10-4 49 184 217 10cm 7-16 51 181 267 5cm 1-11-1 36 193 218 10cm 7-C 47 190 268 5cm 1-11-2 36 222 219 10cm 11-1 51 199 269 5cm 1-11-3 55 206 220 10cm 11-2 47 188 270 5cm 1-11-4 57 200 221 10cm 11-3 46 189 271 5cm 1-12-1 49 175 222 10cm 11-4 48 175 272 5cm 1-12-2 55 175 223 10cm 12-1 38 187 273 5cm 1-12-3 50 180 224 10cm 12-2 50 181 274 5cm 1-12-4 57 179 225 10cm 12-3 49 190 275 5cm 1-13-1 53 173 226 20cm 12-4 45 186 276 5cm 1-13-2 54 184 227 5cm 1-1-1 50 171 277 5cm 1-13-3 53 173 228 5cm 1-1-2 42 167 278 5cm 1-13-4 46 186 229 5cm 1-1-3 40 190 279 5cm 1-14-1 48 190 230 5cm 1-1-4 38 180 280 5cm 1-14-2 48 181 231 5cm 1-2-1 41 186 281 5cm 1-14-3 51 202 232 5cm 1-2-2 43 194 282 5cm 1-14-4 49 186 233 5cm 1-2-3 36 176 283 5cm 1-15-1 49 194 234 5cm 1-2-4 41 191 284 5cm 1-15-2 63 178 235 5cm 1-3-1 45 195 285 5cm 1-15-3 45 186 236 5cm 1-3-2 55 222 286 5cm 1-15-4 44 176 237 5cm 1-3-3 48 190 287 5cm 1-16-1 57 180 238 5cm 1-3-4 51 204 288 5cm 1-16-2 63 177 239 5cm 1-4-1 44 190 289 5cm 1-16-3 45 180 240 5cm 1-4-2 51 180 290 5cm 1-16-4 51 174 241 5cm 1-4-3 47 190 291 5cm 6-1-1 49 184 242 5cm 1-4-4 50 180 292 5cm 6-1-2 49 177 243 5cm 1-5-1 47 187 293 5cm 6-1-3 45 186 244 5cm 1-5-2 55 179 294 5cm 6-1-4 43 180 245 5cm 1-5-3 48 177 295 5cm 6-2-1 60 193 246 5cm 1-5-4 55 180 296 5cm 6-2-2 60 194 247 5cm 1-6-1 45 182 297 5cm 6-2-3 45 188 248 5cm 1-6-2 51 175 298 5cm 6-2-4 52 202 249 5cm 1-6-3 55 186 299 5cm 6-3-1 51 195 250 5cm 1-6-4 48 176 300 5cm 6-3-2 47 177

APPENDICES

vi vi

Collected by:

Ephrem K.


S.no. Disc size

Grid position

Dip amount

Dip direction

S.no. Disc size

Grid position Dip amount

Dip direction

301 5cm 6-3-3 50 202 312 5cm 6-6-2 42 195 302 5cm 6-3-4 51 180 313 5cm 6-6-3 46 192 303 5cm 6-4-1 49 186 314 5cm 6-6-4 49 192 304 5cm 6-4-2 45 180 315 5cm 6-7-1 47 190 305 5cm 6-4-3 48 190 316 5cm 6-7-2 53 184 306 5cm 6-4-4 44 185 317 5cm 6-7-3 46 183 307 5cm 6-5-1 47 186 318 5cm 6-7-4 53 185 308 5cm 6-5-2 48 180 319 5cm 6-8-1 47 196 309 5cm 6-5-3 46 186 320 5cm 6-8-2 46 185 310 5cm 6-5-4 50 180 321 5cm 6-8-3 50 191 311 5cm 6-6-1 45 184 322 5cm 6-8-4 46 193

Data sheet of field measured dip direction and dip amount for the four different disc sizes

Collected by:

Ephrem K. ROCK SURFACE CHARACTERISATION Using Straight edge method Sheet No. 1 Date: 19/9/06

Relative distance S.no. Length of straight edge

(m)

Position Name

(Relative)

Max. A

(mm)

JRC Estimated

U=a/L

(%)

Ref.1

(cm)

Ref.2

(cm)

Orientation

(Relative) 13 1.00 V11 19 4.2 9.5 00 NA Dip-Direction 14 1.00 V12 41 8.2 18 Below NA Dip-Direction 15 1.00 V21 25 6 12.5 40 NA Dip-Direction 16 1.00 V22 36 6.6 14 Below NA Dip-Direction 17 1.00 V31 23 5.4 11.5 80 NA Dip-Direction 18 1.00 V32 43 10.3 21.5 Below NA Dip-Direction 19 1.00 V41 17 4 8.5 120 NA Dip-Direction 20 1.00 V42 45 10 20.5 Below NA Dip-Direction 21 1.00 V51 20 4.6 10 160 NA Dip-Direction 22 1.00 V52 22 5 11 Below NA Dip-Direction 23 1.00 V61 19 4.4 9.5 200 NA Dip-Direction 24 1.00 V62 36 10.2 22.5 Below NA Dip-Direction 25 1.00 H11 25 6 12.5 NA 00 Strike-Dir. 26 1.00 H12 30 8.2 18 NA Right Strike-Dir. 27 1.00 H21 18 4.1 9 NA 40 Strike-Dir. 28 1.00 H22 13 3 6.5 NA Right Strike-Dir. 29 1.00 H31 19 4.2 9.5 NA 80 Strike-Dir. 30 1.00 H32 23 5.4 11.5 NA Right Strike-Dir. 31 1.00 H41 22 5.3 11 NA 120 Strike-Dir. 32 1.00 H42 20 4.6 10 NA Right Strike-Dir. 33 1.00 H51 21 5.2 10.5 NA 160 Strike-Dir. 34 1.00 H52 18 4.1 9 NA Right Strike-Dir. 35 1.00 H61 19 4.2 9.5 NA 200 Strike-Dir. 36 1.00 H62 26 6.1 13 NA Right Strike-Dir.

Data sheet of straight edge measurements, estimated JRC values using the Barton (1982) chart and

characterization of waviness (U=a/L) as suggested by Palmström (1995).

N.B. Ref.1 is the top horizontal grid of the grid system of 2x2m.

Ref.2 is the left vertical grid of the grid system of 2x2m

APPENDICES

vii vii

Appendix 2 Description of FastRBF functions and Matlab curve fitting tool box

Appendix 2-1 Description of FastRBF functions The FastRBF toolbox allows scattered 2D and 3D data sets to be described by a single mathematical function, a Radial Basis Function (FastRBF). The FastRBF toolbox works in Matlab interface. The Matlab scripts prepared for this study using the RBFs are given in appendix 3-2.the description of the FastRBF functions is from the FastRBF Toolbox (2004). The RBFs which have been used in the processing and analyzing of the laser scan data of the discontinuity rock surface are discussed below. Importing into FastRBF Since basic data type is a pointlist.in FastRBF and provides the facility to import and export formatted text files directly, the original ASCII (*.xyz) point cloud file of laser scan data has been transformed into formatted text (*.txt) files. Then the text formatted files are imported to Matlab using the following command: Data3d = fastrbf_import(’filename.txt’,’format’, ‘format’,’%x %y %z %(*s)\n’) The above command loads the external text formatted file into FAstRBF data type. The ‘filename’ argument means the name of the file to be loaded. The ‘txt’ sets the format string fro formatted text in put to FMT. The string specifies the format for each line in the input file. It is required with ‘txt’. The text input files are interpreted according to the scanf-like format string fmt. Three types of data field can be specified with n the format string: Required fields, optional attribute fields and Skip fields.

The format for the required field is: Filed format: % datatype Where ‘datatype’ is one of the following: X Location[0] Y Location[0] Z Location[0]

The fields %x and %y must occur in the formatting string. The dimension of the imported point list data, where the data are 2D or 3d, is determined by the presence or absence of the %z field in the format string. The format for optional fields is: Field format: %<attributename>.datatype Where ‘datatype is one of the following: v Value a Accuracy u Upper (error-bar) l Lower (error-bar) dx Gradient[0] yx Gradient[1] zx Gradient[2]

APPENDICES

viii viii

and ‘attribuitename’is the name of the attribute to which the data is assigned. If no attribute name is specified i.e., the format string is %data type, then the data are read as the default value at the data location. Normally a value field, %v, will be present in the format string, but it need not be when reading point cloud surface data which may consist of just of the required data-the location of the surface points. All the above points are read as doubles. Finally, the format for skipped field is: Skip field format: %*[width] type Where ‘type’ is scanf type, e.g., i, d, s, f, ...etc, and ‘width’ is optionally used to specify a fixed number of characters to skip. Some example format strings and corresponding data lines are given below: Data: 4.52e+04 3.63e+02 2.25e+04 23.0 Format: %x%y%zv\n Data: 4.52e+04 3.63e+02 2.25e+0423.0 255 255 23 Format: %x%y%z%v %< Red>v %< Green>v %< Blue>v\n Data: 4.52e+04 3.63e+02 2.25e+04 RBFsRus 23.0 0.5 0.5 0.707 Format: %x%y%z%v %*s%dx%dy%dz\n Care should be taken when specifying gradient fields (RBF data type dx, dy or dz) that all the components are assigned values, as this is not enforced. If multiple values are read to the same attribute, then the last entry read will overwrite the previous values FastRBF crop The required part of the scan has been captured giving the maximum and minimum x, y z coordinate values that are taken using Split Engineering, Fx.The command used to crop the data is as follows: Y=FastRBF_Crop(X, MJN, MAX) This command removes parts of a point list, X that are outside a specified cropping box. Individual elements in the MIN and MAX arguments can be omitted by putting NaN in the vector instead of a number .For example, passing [NaN NaN1] for the MIN argument sets the minimum z values to 1, but does not crop in the x and y directions. The X is the point list to crop. The MIN is the minimum corner of the crop box and the MAX is the maximum corner of the crop box. FastRBF normals from points If the surface data are only available as a point cloud without additional information, i.e., purely vertex data, then fastrbf _normalsfrompoints can be used to estimate the normals. The following command is used to estimate 3D surface normal: P=FastRBF_NormalsFromPoints (P)

APPENDICES

ix ix

NormalsFromPointsestimates normals by fitting a least squares plane through a neighborhood around each point. The P is the surface data for which the normals are estimated. FastRBF density from normals The normals are used to generate the distance-to-surface density data. The distance-to-surface is not defined everywhere, only with in a band surrounding the surface. The maximum normal length set the width of this band.RBF values at points further than the maximum normal length from the surface will not necessarily be the distance to the surface. A value of several times larger than the average mesh resolution is usually sufficient and certainly be greater than the accuracy specified in the RBF fitter. The following command is used to convert 3D surface points and normals to a density field. P = FastRBF_DensityFromNormals (Q MIN<MAX) This creates new points inside and outside the surface by following the point normal. The value field is filled with distance-to-surface data. The Q is the point list with surface normals. The MIN is the minimum projection distance. Distance is 0.The MAX is the maximum projection distance. FastRBF unique Fastrbf_unique command removes duplicate points from a point list, mesh or scan. Point is considered duplicate if they are closer than the specified minimum inf-norm distance. When two points are considered duplicate the point with the highest index is removed. When a point is removed, corresponding elements of all of the optional fields, including atrr-array fields, are removed as well. It can be noted that fastrbf_unique is order sensitive and removes duplicate’ points as it encounters them. If the input pointlist is re-ordered then the points removed and the number of points removed may change For example, if a point is close to two other points, but those points are sufficiently far apart then both will be preserved if the common point is encountered first and removed. Alternatively, two of the three points will be removed if the common point is not encountered first. The following command is used in the analysis: X = FastRBF_Unique (X) X is a point list, mesh or scan structure. FastRBF fit FastRBF supports 3 basic functions in 2D and 3D. These are the biharmonic spline, triharmonic spline and generalized multiquadratic.FastRBF uses fast algorisms to fit RBFs with all of the basic functions. The triharmonic spline in 2D however is significantly slower to solve for. The fitted RBF includes the polynomial term. The minimum degree of the polynomial depends on the basic function used.

APPENDICES

x x

There are four fitting strategies in fastRBF.The fitting options are direct, reduce, errorbar and rho.The direct uses fast algorism to solve the traditional RBF fitting problem where each interpolation point is used as an RBF centre. The reduce uses the greedy algorism that selects a number of interpolation points as RBF centers until the desired accuracy is met at all the points. In both these algorisms the returned algorism is “within ∈ of the smoothest interpolate of the data”, where ∈ the fitting accuracy. The errorbar uses a restricted range of interpolation approach and the returned RBF approximates the

data values. It is “the smoothest interpolate within∈ of the data values”. Hence when C is a

discemible then the errorbar algorism will give a smooth RBF. The rho also fits an approximating RBF determined by a parameter p which balances faithfulness to the data against smoothness. The rho can be used with reduce to produce an approximating RBF with fewer centers. The fitting accuracy can be a pre-point value taken from the Accuracy field of p (p.accuracy),if present ,or a global value determined by the ACCURACY argument. Similarly, pre-point values for upper and lower error bounds can be taken from the pointlist fields, P.Upper and P.Lower –if present. These fields are used with the error-bar fitting strategy to specify asymmetric error bounds. If only one of the upper or lower fields is specified, then the bound is applied symmetrically. If the pre-point accuracy field (P.accuracy) exists, but neither an upper nor lower field is available, then the errorbar fitter will apply the pre-point accuracy as a symmetric pre-point error bound. If the global ACCURACY argument is specified with an errorbar fit, the it will be interpreted as a symmetric bound applied to data values. The ACCURACY argument and the upper, lower and Accuracy pointlist fields are all positive quantities specifying the absolute difference between a bound and the given data value. For example, if a value was 13.6 and had an upper value of 14.3 and lower value 13,2 then the upper bound would be +0.7 and the lower bound would be +0.4.When a global fitting tolerance(ACCURACY argument)is specified along with a local per point bound, the greater of the two (i.e., the loosest constraint)is applied at each data point. This facilitates incremental fitting where the closeness of a fit to the data is progressively refined from coarse to fine using the initial option. To force per point fields to be used at all data points, specially an ACCURACY value of zero. By default, an RBF is fitted to the values in P.Value using the pre-point bounds P. Accuracy, P.Lower and P.Upper if present and appropriate to the fitting strategy. Use the ‘attr’ option with the NAME argument to fit to another attribute. The corresponding P.NAME value, P.NAME Accuracy, P.NAME.Lower and P.NAME.Upper fields will then be used. Incremental fitting, either to improve the accuracy of a fit or to add new points, is possible using the initial option. Ensure that the ordering of the point list is consistent with that used to compute the initial RBF. Ensure that the presence of any attributes is consistent between newly added points and previous points. The set-up overhead is proportional to the number of interpolation nodes. Therefore it can be inefficient to use initial for the addition of small number of points at a point. The following commands are used to fit an RBF to a list of 2D or 3D point locations and values. RBF = FastRBF_Fit (P.ACCURACY) FastRBF_Fit (…,’direct’|’reduce’|’errorbar’)

APPENDICES

xi xi

FastRBF_Fit (…,’biharm’|’triharm’|’multi’) FastRBF_Fit (…,’rho’, S) FastRBF_Fit (…,’c’, CONST) FastRBF_Fit (…,’k’EXP) FastRBF_Fit (…,’degree’, DEG) FastRBF_Fit (…,’confidence’, CONF) FastRBF_Fit (…,’memlimit’, M) FastRBF_Fit (…,’attr’, NAME) The P is the point list containing the data to fit. The ACCURACY specifies the fitting accuracy or tolerance. The RBF value will be within this amount of the original value at each input value. The ‘Direct’ specifies the direct fitting algorithm. This is the default. All input points are used as centers. This is the best for true density data. The ‘reduce’ specifies the center reduction fitting algorithm. This is the best for clean data with little or no discernible noise. The ‘rho’ sets the smoothing value to S (input RBF). Higher values will create a smoother fit, but will interpolate less accurately. The ‘errorbar’ uses error bar fitting algorithm. This is the best for noisy data or when the fitting accuracy is quite loose. The ‘biharm’ sets the basic function to the biharmonic spline. This is the default. The ‘triharm’ sets the basic function to the triharmonic spline. The ‘multi’ sets the basic function to the generalized multiquadric (r) = (r2+c2)k. The ‘c’ sets the multiquadric constant to CONST. The ‘k’ sets multiquadric exponent to EXP/2. K must be odd and less than 6. The default is 1. The ‘degree’ sets the degree of the RBF polynomial to DEG.-1 for the no polynomial, 0 for a constant, 1 for a linear, 2 for a quadratic. The ‘confidence’ sets the confidence that you have in the accuracy to CONF. CONF*length(P.Location) of the points must have the specified accuracy. The default is 1.0 (all points have the specified accuracy). The ‘memlimit’ sets a soft limit on the amount of RAM to use to M megabytes. It may be exceeded if the M is less than the core memory requirements. The default is half the available physical RAM. The ‘initial’ specifies an initial RBF solution. The benefit of using an RBF estimate depends how similar the estimate is to the final RBF. The ‘attr’ fits to the fields associated with the NAME attributed instead of the default fields in the point list. The specified attribute must exist. In present study, the direct fitting option has been used: because in this option, each interpolation point is used as RFB center. The fitting accuracy has been taken as 3mm which is less than the mesh resolution. Fitting accuracy more than 3mm takes more time to fit an RFB. But, reduce, errorbar and rho options reduce the RFB centers significantly and only a subset of the original data points is utilized as RFB centers. As a result, roughness details of rock masses can be lost. FASTRFB 3D isosurfacing The following commands extract an isosurface from a 3D RFB solution: M = FastRFB_Isosurf(S, RES)

FastRBF_Isosurf(S, RES, ISOVALUE)

FastRBF_Isosurf(S, RES, ISOVALUE, ACC)

FastRBF_Isosurf(…, ‘min’, MIN)

APPENDICES

xii xii

FastRBF_Isosurf(…, ‘max’, MAX)

FastRBF_Isosurf(…, ‘it’, FIT)

FastRBF_Isosurf(…, ‘normals’)

FastRBF_Isosurf(…, ‘invert’)

FastRBF_Isosurf(…, ‘open’| ‘closeminus’| ‘closeplus’)

FastRBF_Isosurf(…, ‘optimal’| ‘plane’| ‘grid’)

FastRBF_Isosurf(…, ‘tri’| ‘quad’| ‘triquad’’)

FastRBF_Isosurf(…, ‘orient’, T)

FastRBF_Isosurf(…, ‘up’, DIR)

FastRBF_Isosurf(…, ‘seeds’, P)

FastRBF_Isosurf(…, ‘seedlimit’, N) S is the fastRBF solution to isosurface. RES specifies the surface resolution. The default is 1 (one). ISOVALUE specifies the function of the isosurface. The default is zero.ACC specifies the RBF evaluation accuracy. The default value is S. DefaultEvalAcc. If this field is missing then ACC must be present. The ‘min’ sets the minimum corner of the evaluation box to MIN. the default is S. DataMax. The ‘fit’ tells the isosufacer to adjust the sampling grid to fit exactly to the bounding box. The characters ‘x’, ‘y’, ‘z’ in FIT specify which axes to adjust along. The default is ‘xyz’. The ‘normals’ enable evaluation of the RBF gradient at each point to create surface normal vectors. The ‘invert’ inverts the surface orientation. The ‘open’ means no boundary capping is performed. This is the default. The ‘closeminus’ but assumes points out side the evaluation box have values less than the isosuface value. The ‘closeplus’ same as ‘closeminus’ but assumes points outside the evaluation box have values greater than the isosurface value. The ‘orient’ sets the evaluation lattice transformation matrix to the 4-by-4 matrix T. This can be used with ‘plane’ to set the orientation of the parallel planes. The ‘up’ sets the evaluation lattice “up” direction to DIR. This can be used with ‘plane’ to set the orientation of the parallel planes. The ‘optimal’ optimizes the mesh faces. This is the default. The ‘plane’ optimizes the mesh faces, force vertices to lie on parallel planes. The orientation of plane defaults to the xy plane. This can be modified using the ‘orient’ or ‘up’ option. The ‘grid’ do not optimizes the mesh vertices. They will lie on the tetrahedral evaluation grid. This can be modified using the ‘orient’ or ‘up’ option. The ‘tri’ constructs the surface from triangular faces. This is the default. The ‘quad’ constructs the surface from quadrilateral faces. The ‘seedlimit’ uses at most N successful surface seeds. The default is 1(one). If the seedlimit is set to 0 then all available seeds are used. The ‘seeds’ uses the locations in P as surface seeds. The default is to use the centers from the RBF solution. P may be a point list or a 3 × N array. The ‘min’ and ‘max’ options default to the bounding box of the input RBF, S. Individual elements in the MIN and MAX argument can be omitted by putting NaN in the vector instead of a number. For example, passing [NaN NaN 1] for the MIN argument sets the minimum z value to 1, but uses the default values for x and y. passing [NaN NaN NaN] is equivalent to omitting the option completely. Passing a scaler s is equivalent to passing [s s s]. By default the isosurface increases the sampling resolution slightly to get an exact fit to the specified bounding box. The ‘fit’ parameter may be used to use the specified resolution in any direction. In this case the isosuface may extend slightly beyond the

APPENDICES

xiii xiii

specified bounding box, so that an integer number of sampling interval is achieved. The ‘fit’ parameter is a string consisting of any combination of ‘x’, ‘y’, or ‘z’. These signify exact clipping along the corresponding axes. For example, ‘x’ causes the resolution in the x direction to be increased so that an exact fit to the bounding box is achieved in the x direction, and the specified resolution is in the y and z directions. The orientation of the sampling lattice, by default, corresponds to the data coordinate system implicit in the RBF data structure, S. This can be altered by specifying the orientation matrix, T. The orientation matrix transforms a point in the RBF coordinate system into the lattice coordinate system. This 4x4 homogeneous transform may include an affine transform component and provides user with means of altering the relative sampling frequencies in the lattice directions as well as the lattice orientation. This will interact with the specified sampling resolution RES. A simpler way of specifying the orientation of the sampling lattice, if scaling is desired, is to use the ‘up’ option to specify the lattice “up” direction (normal of the plane). DIR need not have unit length. Note that valid seeds, for initializing surface-following, must lie within a sampling interval of the bounding box. The ‘min’ and ‘max’ are specified in the RBF coordinate system is chosen to just enclose that specified in the data coordinate system by min and max. FastRBF export The following commands are used to saves FastRBF data struct to third party file formats. If no export

type option is specified then the type will be determined from the file extension.

FastRBF_Export(X, FILENAME)

FastRBF_Export(X, RGB, RGBMAX, FILENAME)

FastRBF_Export(…, ‘dxf’| ‘obj’| ‘stl’ ‘txt’| ‘vrml’)

FastRBF_Export(…, ‘format’, FMT)

FastRBF_Export(…, ‘precision’, N)

FastRBF_Export(…, ‘ascii’)

X is the data to export. FILENAME is the name of the file to write to. RGB specifies the RGB colour

per vertex data, 3 × N. This argument is valid with VRML and wavefront OBJ formats only. The

wavefront colour-per vertex format is not standard. RGBMAX specifies the range of the RGB data.

This is usually 1 or 255. The ‘dxf’ (or ext. .txt) sets the output file type to AutoDESK DXF. It uses

the precision option to set the number of decimal places. The ‘obj’ (or ext. .obj) sets the export type to

Alias| Wavefront OBJ. The ‘stl’ (or ext. .stl) sets the export type Stereo-litholography. Defaults is to

binary format. It uses ‘ascii’ to write ascii format. The ‘vrml’ (or ext. .wrl) sets the export type to

VRML. The ‘txt’ (or ext. .txt) sets the export type to formatted text. The ‘ascii’ specifies the ascii data

format for STL type. The ‘precision’ sets the number of decimal places in the DXF format to N. The

default is to write full machine precision. The ‘format’ sets the format string for formatted text output

to FMT. The string specifies the format for each line in the output file.

APPENDICES

xiv xiv

Text export format specification

The format specification for exporting text files contains printf-like format fields with additional

syntax to specify the data to write to each line of the text file. The complete specification is:

Export format: %[([flag][width][.precision]type)][<attributename>]value

The ‘flag’ is for printf. The ‘width’ is for printf. The ‘precision’ is for printf. The ‘type’ is one of g, f,

E or e. The ‘attributename’ is the name of the attribute, if none is given then the default is used. The

‘value’ identifies the data that is to be formatted. One of:

x Location[i][0]

y Location[i][1]

z Location[i][2]

v Value[i]

a Accuracy[i]

a Upper[i]

a Lower[i]

dx Gradient[i][0]

dy Gradient[i][1]

dz Gradient[i][2]

An attribute name is not specified when formatting the location values x, y, and z. If a specific

attribute name is not given when formatting other values then the default value is used. The default

printf format is (.log). To write a value as an integer (.of) is used. Other parts of the format string are

simply echoed to the output. As the file is opened in binary mode the end of line should be specified

with \r\n for windows and \n for UNIX.

Some valid format strings are shown below:

Format: %(.2e)x %(2e)y %(.2e)z\n

Result: 4.52e+04 3.63e+02 2.25e+04

Format: rgb = %(.0f)<Red>v \t%(.0f)<Green>v \t%(.0f)<Blue>v)\n

Result: rgb = 2 120 34

Format: v %x %y %z \nvn %(.4f)dx %(.4f)dy %(.4f)dz\n

Result: v 1.2323456256 4446.5634454393 7.8934566432e-05

Vn 0.8256 0.2008 0.5273

Load FastRBF files

X = FastRBF_Load(FILENAME)

Above command loads an ARANZ format file containing a FastRBF data type. If successful X be a

point list, solution, grid, scan, or mesh.

FILENAME is the name of the file to load.

Save FastRBF files

APPENDICES

xv xv

FastRBF_Save(X, FILENAME)

FastRBF_Save(…, ‘ascii’)

These commands save a FastRBF data struct X to an ARANZ format file. X is the data to export.

FILENAME is the name of the file to write to. The ‘ascii’ specifies ascii format instead of binary.

Appendix 2-2 Description of Curve fitting tool box The Curve Fitting Toolbox is a collection of graphical user interfaces and M-file functions that allow you to explore and analyze data sets and fits. The description of the Curve Fitting functions is from the Matlab help (released 13 and 14). The toolbox provides the following main features:

� Data pre-processing such as sectioning and smoothing � Parametric data fitting using library or custom equations and non parametric data fitting using

splines or various interpolants. Library equations include polynomials, exponentials, rationals, sum of Gaussians, and so on, and nonparametric data fitting.

� Standard linear least squares, nonlinear least squares, weighted least squares, constrained least squares, and robust fitting procedures.

� Fit statistics to assist you in determining the goodness of fit. � Analysis capabilities such as extrapolation, differentiation, and integration. � Ability to save your work in various formats including M-files, binary files, and workspace

variables The following non parametric data fitting functions have been used in this study to fit the strip data points using the MATLAB Basic Fitting which is a graphical user interface (GUI) for 2-D plots. Cubic spline data interpolation Syntax pp = spline(x,Y) yy = spline(x,Y,xx) pp = spline(x,Y) returns the piecewise polynomial form of the cubic spline interpolant for later use with ppval and the spline utility unmkpp. x must be a vector. Y can be a scalar, a vector, or an array of any dimension, subject to the following conditions: If Y is a scalar or vector; it must have the same length as x. A scalar value for x or Y is expanded to have the same length as the other. See Exceptions (1) for an exception to this rule, in which the not-a-knot end conditions are used. If Y is an array that is not a vector, the size of Y must have the form [d1,d2,...,dk,n], where n is the length of x. The interpolation is performed for each d1-by-d2-by-...-dk value in Y. See Exceptions (2) for an exception to this rule. yy = spline(x,Y,xx) is the same as yy = ppval(spline(x,Y),xx), thus providing, in yy, the values of the interpolant at xx. xx can be a scalar, a vector, or a multidimensional array. The sizes of xx and yy are related as follows: If Y is a scalar or vector, yy has the same size as xx. If Y is an array that is not a vector, If xx is a scalar or vector, size (Yu et al.) equals [d1, d2, ..., dk, length(xx)]. If xx is an array of size [m1,m2,...,mj], size(Yu et al.) equals [d1,d2,...,dk,m1,m2,...,mj].

APPENDICES

xvi xvi

Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) for shape-preserving interpolant Syntax yi = pchip(x,y,xi) pp = pchip(x,y) yi = pchip(x,y,xi) returns vector yi containing elements corresponding to the elements of xi and determined by piecewise cubic interpolation within vectors x and y. The vector x specifies the points at which the data y is given. If y is a matrix, then the interpolation is performed for each column of y and yi is length (xi)-by-size(y,2). pp = pchip(x,y) returns a piecewise polynomial structure for use by ppval. x can be a row or column vector. y is a row or column vector of the same length as x, or a matrix with length(x) columns. pchip finds values of an underlying interpolating function p(x) at intermediate points, such that:

� On each subinterval xk<x<xk+1, p(x) is the cubic Hermite interpolant to the given values and certain slopes at the two endpoints.

� P(x) interpolates y, i.e. p(xj) = yj, , and the first derivative p’(x) is continuous. P”(x) is probably not continuous; there may be jumps at the xj.

� The slopes at the xj. are chosen in such a way that p(x) preserves the shape of the data and respects monotonicity. This means that, on intervals where the data are monotonic, so is p(x); at points where the data has a local extremum, so does p(x).

Note: If y is a matrix, p(x) satisfies the above for each column of y. Smoothing spline (spaps ) Syntax [SP,VALUES] = spaps(X,Y,TOL) returns the B-form and, if asked, the values at X , of a cubic smoothing spline f for the given data (X(i),Y(:,i)), i=1,2, ... The sequence X of data sites need not be increasing, but if it is not, then it is sorted, and the columns of Y are correspondingly reordered. After that, X must be strictly increasing. The smoothing spline f minimizes the roughness measure: F(D^M f) := integral ( D^M f(t) )^2 dt on X(1) < t < X(n) over all functions f for which the error measure E(f) := sum_j { W(j)*( Y(:,j) - f(X(j)) )^2 : j=1,...,n } is no bigger than the given TOL. Here, D^M f denotes the Mth derivative of f. The weights W are chosen so that E(f) is the Composite Trapezoid Rule approximation for F(y-f). The integer M is chosen to be 2, hence D^M f is the second derivative of f. For this choice of M, f is a CUBIC smoothing spline. This is so because f is constructed as the unique minimizer of

APPENDICES

xvii xvii

rho*E(f) + F(D^2 f) , with the smoothing parameter RHO so chosen that E(f) equals TOL . Hence, FN2FM(SP,'pp') should be (up to roundoff) the same as the output from CPAPS(X,Y,RHO/(1+RHO)). [SP,VALUES,RHO] = spaps(X,Y,...) also returns RHO. When TOL is 0, the variational interpolating cubic spline is obtained. If TOL is negative, then -TOL is taken as the value of RHO to be used. If Y is not a vector, then Y must have length(X) columns, and then the number d of rows of Y is taken to be the dimension of the target of the smoothing spline, i.e., SP describes a d-vector-valued function. In this case, the expression (D^M f(t))^2 in the roughness measure is meant as the square of the Euclidean length of the d-vector D^M f(t) (i.e., of the value at t of the Mth derivative of f ); and the expression (Y(:,j) - f(X(j))^2 in the error measure is correspondingly taken to be the square of the Euclidean length of the d-vector Y(:,j)-f(X(j)) (i.e., of the error at X(j) of f ). Cubic smoothing spline (Csaps) Syntax [CS,VALUES] = csaps(X,Y) returns the ppform of a cubic smoothing spline for the given data X,Y, with X and Y vectors of the same length. The sequence X of data sites need not be increasing, but if it is not, then it is sorted, and the sequence Y of data values is then correspondingly reordered. After that, X must be strictly increasing. This smoothing spline f minimizes P * sum_i W(i)( Y(i) - f(X(i)) )^2 + (1-P) * integral (D^2 f)^2 . Here, the sum is over i=1:length(X), the integral is taken over the interval [min(X),max(X)], D^2 f is the second derivative of the function f , W = ones(length(X),1) is the default value for W, and the default value for the smoothing parameter P is chosen, in an ad hoc fashion and in dependence on X, as indicated in the next paragraph. You can supply a specific value for P, by using csaps(X,Y,P) instead. When P is 0, the smoothing spline is the least-squares straight line fit to the data, while, at the other extreme, i.e., when P is 1, it is the natural' or variational cubic spline interpolant. The transition region between these two extremes is usually only a rather small range of values for P and its location strongly depends on the data sites. It is in this small range that P is chosen when it is not supplied, or when an empty P or a negative P is input. If P > 1 , the corresponding solution of the above minimization problem is returned, but this amounts to a roughening rather than a smoothing. [OUT,P] = csaps(X,Y,...) returns the value of P actually used, and this is particularly useful when no P or an empty P was specified. If you have difficulty choosing P but have some feeling for the size of the noise in Y, consider using instead spaps(X,Y,tol) which, in effect, chooses P in such a way that the roughness measure,

APPENDICES

xviii xviii

integral (D^2 f)^2 , is as small as possible subject to the condition that the error measure, sum_i W(i)(Y(i) - f(X(i)))^2 , does not exceed the specified tol . This usually means that the error measure equals the specified tol. csaps(X,Y,P,XX) returns the value(s) at XX of the cubic smoothing spline, unless XX is empty, in which case the ppform of the cubic smoothing spline is returned. This latter option is important when the user wants the smoothing spline (rather than its values) corresponding to a specific choice of error weights, as in the following: csaps(X,Y,P,XX,W) returns, depending on whether or not XX is empty, the ppform, or the values at XX, of the cubic smoothing spline for the pecified weights W. Any negative weight is replaced by 0, and that makes the resulting smoothing spline independent of the corresponding data point.

APPENDICES

xix xix

Appendix 3 Scripts of Matlab codes and command lines for the implementation of methodology.

Appendix 3-1 Sample script of Matlab codes and command lines for raw and reconstructed surface data analysis The methodology described in chapter four section 4.1 have been translated in to Matlab script using Matlab codes and Fast RBF tool box on the basis of conventional statistical parameters and mean orientation of a given circular window size to determined the rock surface roughness according to Fecker E. and rengers N., 1971 from the virtual model of the 3D terrestrial laser scanning data. The command lines and codes used for the preparation and processing of the point cloud data in Matlab script are indicated as numbered such as 1_, 2_, 3_ … and the its description by %. I) Data importing and cropping 1_ points_temp = load('Lustin_ScanPos01_Scan001_XYZ_I.xyz'); 2_ points = points_temp(:,1:3); % Loads all the variables from the file specified by 'Lustin_ScanPos01_Scan001_XYZ_I.xyz' and % assigns the first 3 columns with out the intensity value of the 'points_temp' array to 'points' array. 3_ tree = kdtree(Points); 4_ range = [ [-51.00 -48.00]; [-4.60 -1.60]; [min(x(:,3)) max(x(:,3))] ]; 5_ crop_scan01 = kdtree_range(tree,range); 6_ n = 1:size(crop_scan01,2); 7_ crop_scan01_xyz = points(crop_scan01(n),:); 8_ crop_scan01_I = points_temp(crop_scan01(n),:); % kdtree is both a directory and a function. It creates a KD Tree from the list of 'Points' and outputs % it in the abstract object "kdtree". Then, it can be used for range finding and nearest neighbour % searching. Find all the points within the cube defined by "Range". Returns the size of the second % dimension of 'crop_scan01' array. Take all the 3 columns from 'points' for the corresponding % values of 'crop_scan01' points. Take all the 4 columns from 'points_temp' for the corresponding % values of 'crop_scan01' points. 9_ fid = fopen('crop_scan01_I.xyz','wt'); % 'w' stands for Open file, or create new file, for writing; discard existing contents, if any. To open % in text mode, add "t" to the end of the mode string, for example 'wt+' and 'rt'. 10_ fprintf(fid,'crop scan01 with intensity\n\n'); % The syntax call to fprintf outputs a title called'cropp01 with intensity', followed by two carriage % returns. 11_ fprintf(fid,'%7.3f %7.3f %7.3f %3.0f\n', crop01_scan01_I'); 12_ fclose(fid); % fprintf converts the elements of array 'crop_scan01_I' in column order. The function uses the % format string repeatedly until it converts all the array elements for visualization purpose in Split % Engineering Fx program. I) Principal component analysis 13_ Clear all; 14_ points_temp = load('crop_scan01_I.xyz');

APPENDICES

xx xx

15_ X = points_temp(:,1:3); 16_ [coeff,score,latent,tsquare] = princomp(X); % Function that fits a plane to sub-clustered point cloud data using PCA (principal component % analysis) on the N-by-3 data matrix X,and returns 3-by-3 principal component coefficients. % The coefficients for the first two principal components define vectors that span the plane. The % third PC is orthogonal to the first two, and its coefficients define the normal vector of the plane. % The score holds the so-called Z-scores i.e., the representation of X in the principal component % space. Rows of SCORE correspond to observations, columns to components. The eigenvalues of % the covariance matrix of X are stored in LATENT (Girardeau-Montaut et al.), and TSQUARED returns Hotelling's % T- squared statistic for each data point in matrix X. 17_ normal = coeff(:,3); % In command line 17th, the normal is Normalised normal unit vector (length 1). The first two % coordinates of the principal component scores give the projection of each point onto the plane, in % the coordinate system defined by the first and second PC's. To get the fitted points in the original % coordinate system, multiply each PC % coefficient vector by the corresponding score, and add % back in the mean of the data. The residuals are simply the original data minus the fitted points. 18_ [n,p] = size(X); % to assigned the size of X variable 19_ Mean_X = mean(X,1); 20_ for i =1:n 21_ Xtr(i,1) = X(i,1) - Mean_X(1,1); 22_ Xtr(i,2) = X(i,2) - Mean_X(1,2); 23_ Xtr(i,3) = X(i,3) - Mean_X(1,3); 24_ end 25_ mean(Xtr,1); % the above commands translated all points with Mean_X as origin (0,0,0). 26_ [coeff_tr,score_tr,latent_tr,tsquare_tr] = princomp(Xtr); 27_ normal_tr = coeff_tr(:,3); 28_ meanX_tr = mean(Xtr,1); 29_ if normal(3,1) < 0 30_ normal_tr(1,1) = - normal(1,1); 31_ normal_tr(2,1) = - normal(2,1); 32_ normal_tr(3,1) = - normal(3,1); 33_ else normal_tr = normal; 34_ end % Reverse direction of normal in case normal of points "down", always assume normal is pointing % "upward" (i.e. z is positive). III) Rotation around Z-axis followed by rotation around X-axis 35_ ulength = sqrt(normal_tr(2,1)^2 + normal_tr(1,1)^2); % the above command Determined the length of projected normal vector in X-Y plane. 36_ arad = -((pi/2) + (atan(abs(normal_tr(2,1))/abs(normal_tr(1,1))))); 37_ adeg = (arad/pi) * 180;

APPENDICES

xxi xxi

% Line 36th and 37th Determined the angle between the projected normal vector (dip direction) and % the negative Y-axis over which the rotation has to be carried out to aligned the dip direction with % the negative Y-axis of scanner in radian and degrees respectively. 38_ brad = - ((pi/2)- atan(normal_tr(3,1)/ulength)); 39_ bdeg = (brad/pi) * 180; % Line 38th and 39th Determined the dip angle rotation around the X-axis along the dip direction to % aligned the Y-axis with the fit plane and Z-axis perpendicular to the fit plane in radian and degrees % respectively. 40_ for i =1:n 41_ Xrt(i,1) = Xtr(i,1) * cos(arad) - Xtr(i,2) * sin(arad); 42_ Xrt(i,2) = Xtr(i,1) * sin(arad) * cos(brad) + Xtr(i,2) * cos(arad) * cos(brad) - Xtr(i,3) * sin(brad); 43_ Xrt(i,3) = Xtr(i,1) * sin(arad) * sin(brad) + Xtr(i,2) * cos(arad) * sin(brad) + Xtr(i,3) * cos(brad); 44_ end % The above command first rotate around the Z-axis along the strike by ‘arad’ amount to aligned the % dip direction along the negative Y-axis and then followed by rotation around the X-axis by ‘brad’ % amount to aligned the the Y-axis with the fit plane and Z-axis perpendicular to the fit plane. 45_ [coeff_tr1,score_tr1,latent_tr1,tsquare_tr1] = princomp(Xrt); 46_ coeff_tr1(:,3); 47_ mean_Xrt = mean(Xrt,1); % The above commands are used to check the normal vector after both axis rotation is [0 0 1]. % If visualization of the rotated point cloud data is needed in Split Engineering Fx program, % The following commands can be used to add the intensity value and export as ‘*.xyz’ file format. % intensity = points_temp(:,4); % To assigned the 4th column (intensity) to array intensity. % crop01_scan02c_zx_xyz_I = cat(2,Xrt,intensity); % concatenate the arrays Xrt and intensity % along the dimension 2. % fid = fopen('crop01_scan02c_zx_xyz_I.xyz','wt'); % fprintf(fid,'%7.3f %7.3f %7.3f %3.0f\n',crop01_scan02c_zx_xyz_I'); % fclose(fid); 48_ hold on; % line 48th holds the current plot and all axis properties so that subsequent graphing commands add to % the existing graph. IV) Drawing grid defining rotated surface 49_ grid_n = 30; % It is arbitrary assigned to set no of grids per dimension (x and z). 50_ [xgrid,ygrid] = meshgrid(linspace(min(Xrt(:,1)),max(Xrt(:,1)),grid_n), ... linspace(min(Xrt(:,2)),max(Xrt(:,2)),grid_n)); 51_ zgrid = (1/normal_Xrt(3)) .* (mean_Xrt*normal_Xrt - (xgrid.*normal_Xrt(1) +

ygrid.*normal_Xrt(2))); 52_ h = mesh(xgrid,ygrid,zgrid,'EdgeColor',[0 0 1],'FaceAlpha',0); 53_ axis([min(Xrt(:,1)) max(Xrt(:,1)) min(Xrt(:,2)) max(Xrt(:,2)) min(Xrt(:,3)) max(Xrt(:,3))]); 54_ Xfit = repmat(mean_Xrt,n,1) + score_Xrt(:,1:2)*coeff_Xrt(:,1:2)'; 55_ residuals = Xrt - Xfit; % the above commands draw grids on a defined rotated plane and set the number of grids per defined % dimension of X and Y-axis. The equation of the fitted plane is (x,y,z)*normal - meanX*normal = 0.

APPENDICES

xxii xxii

% The plane passes through the point meanX, and its perpendicular distance to the origin is % meanX*normal.The perpendicular distance from each point to the plane, i.e., the norm of the % residuals, is the dot product of each centered point with the normal to the plane. The fitted plane % minimizes the sum of the squared errors. % To visualize the fit, using the following commands it is possible to plot the plane, the original data, % and their projection to the plane by defining grids on the rotated surface. above = (Xrt-repmat(mean_Xrt,n,1))*normal_Xrt > 0; below = ~above; nabove = sum(above); x_1 = [Xrt(above,1) Xfit(above,1) nan*ones(nabove,1)]; x_2 = [Xrt(above,2) Xfit(above,2) nan*ones(nabove,1)]; x_3 = [Xrt(above,3) Xfit(above,3) nan*ones(nabove,1)]; plot3(x_1',x_2',x_3','-', Xrt(above,1),Xrt(above,2),Xrt(above,3),'o', 'Color',[0 .7 0]); nbelow = sum(below); x_1 = [Xrt(below,1) Xfit(below,1) nan*ones(nbelow,1)]; x_2 = [Xrt(below,2) Xfit(below,2) nan*ones(nbelow,1)]; x_3 = [Xrt(below,3) Xfit(below,3) nan*ones(nbelow,1)]; plot3(x_1',x_2',x_3','-', Xrt(below,1),Xrt(below,2),Xrt(below,3),'o', 'Color',[1 0 0]); axis square view(-23.5,5); V) Defining sample size and window size of the discountinuty plane 56_ xdim = max(Xrt(:,1))- min(Xrt(:,1));% discontinuity plane size in x direction 57_ ydim = max(Xrt(:,2))- min(Xrt(:,2));% discontinuity plane size in y direction 58_ if xdim < ydim 59_ mindim = xdim; 60_ else 61_ mindim = ydim; 62_ end % The above commands defined sample size and window size of the discontinuity plane along % x and y direction. 63_ j = 0; % teller for the records of GRIDSTATS 64_ sample = 2; % initial sample size (in m) 65_ xsmax = (mean_Xrt(1) ) + sample/2; 66_ xsmin = (mean_Xrt(1) ) - sample/2; 67_ ysmax = (mean_Xrt(2) ) + sample/2; 68_ ysmin = (mean_Xrt(2) ) - sample/2; 69_ for w = [2.5,5,10,20] 70_ wsize = (w/100)*sample; 71_ xwmin = xsmin; 72_ ywmin = ysmin; % The above commands defined the maximum and minimum dimension in X and Y direction of the % 2m sample size and determined the percentage of window size (i.e. 2.5, 5, 10, and 20%) of the % sample size.

APPENDICES

xxiii xxiii

73_ tn = 0; 74_ samp = sample; % Command line 73rd is tile number start value. Where as command line 74th is just a trick, otherwise, % somehow GRIDSTATS does not accept sample, don’t know why, now it works. 75_ for tc=1:(100/w) 76_ tc; 77_ ywmin = ysmin; 78_ for tr=1:(100/w) 79_ tr; 80_ xwmax = xwmin+wsize; 81_ ywmax = ywmin+wsize; % Command line 75th and 76th tells the tile column number where as command line 78th and 79th tells % the tile row number in the GRIDSTATS. 82_ m = 1; 83_ for k=1:n 84_ if ((Xrt(k,1) < xwmax) & (Xrt(k,1) >=xwmin)) 85_ h=((xwmax+xwmin)./2); 86_ if ((Xrt(k,2) < ywmax) & (Xrt(k,2) >= ywmin)) 87_ v=((ywmax+ywmin)./2 88_ r=((ywmax-ywmin)./2 89_ if ((sqrt((h - Xrt(k,1)).^2 + (v - Xrt(k,2)).^2)) <= r); 90_ Xtile(m,1) = Xrt(k,1); 91_ Xtile(m,2) = Xrt(k,2); 92_ Xtile(m,3) = Xrt(k,3); 93_ m = m+1; 94_ end; 95_ end; 96_ end; 97_ end; % Command line 84th and 86th will be executed if a given point coordinate falls with in a defined X % and Y dimension respectively. Command line 85th and 87th determined the centre coordinate of X % and Y for the defined dimension respectively. Where as command line 88th determined the radius % of an inscribed circle by the square grid define by command line 84th and 86th. The rest command % lines determined those points which fall with in the inscribed circle and sub clusters for PCA % analysis. % If Xtile does contains more than or equal to three values, then carry out the following. 98_ if m>=3; 99_ [coeff,score,tau,tsquare] = princomp(Xtile); 100_ normal_tile = coeff(:,3); 101_ if normal_tile(3,1)<0; 102_ normal_tile_r(1,1) = - normal_tile(1,1); 103_ normal_tile_r(2,1) = - normal_tile(2,1); 104_ normal_tile_r(3,1) = - normal_tile(3,1); 105_ else normal_tile_r = normal_tile; 106_ end

APPENDICES

xxiv xxiv

% Reverse direction of normal in case normal of points "down", always assume normal is pointing % "upward" (i.e. z is positive). 107_ if ((normal_tile_r(1,1)>=0) & (normal_tile_r(2,1)>0)); 108_ atile = atan(abs(normal_tile_r(1,1))/abs(normal_tile_r(2,1))); 109_ strike_deg = 360 - ((atile/pi)*180); % Strike is dip direction 110_ elseif ((normal_tile_r(1,1)<0) & (normal_tile_r(2,1)>=0)); 111_ atile = 3*(pi/2) + atan(abs(normal_tile_r(2,1))/abs(normal_tile_r(1,1))); 112_ strike_deg = ((atile/pi)*180) - 90; 113_ elseif ((normal_tile_r(1,1)<=0) & (normal_tile_r(2,1)<0)); 114_ atile = (pi) + atan(abs(normal_tile_r(1,1))/abs(normal_tile_r(2,1))); 115_ strike_deg = ((atile/pi)*180) - 90; 116_ else 117_ atile = (pi/2) + atan(abs(normal_tile_r(2,1))/abs(normal_tile_r(1,1))); 118_ strike_deg = ((atile/pi)*180) - 90; 119_ end %((normal_tile_r(1,1)>0) & (normal_tile_r(2,1)>0)); % The above command lines from 107th to 119th determined the azimuthal convention where the % strike is measured clockwise from true north; accommodations must be made for the various % quadrants in which the projected normal vector (nproj) is located. 120_ atile_deg = (atile/pi)*180; 121_ diptile = (pi/2 - asin(normal_tile_r(3,1))); 122_ diptile_deg = ( diptile/pi)*180; % Dip direction in degrees (command line 120th). Dip angle in degrees (command line 122nd), since % the normal is a normalised vector (length 1), the Z index gives the dip. VI) Calculating the associated parameters 123_ [a,b] = size(Xtile); 124_ meanXtile = mean(Xtile,1); 125_ Xfit_tile = repmat(meanXtile,a,1) + score(:,1:2)*coeff(:,1:2)'; 126_ residuals = Xtile - Xfit_tile; 127_ error_tile = (Xtile-repmat(meanXtile,a,1))*normal_tile; 128_ tn = tn + 1; % tilenumber 129_ j = j + 1; % just a teller for the GRIDSTATS results matrix 130_ GRIDSTATS(j,1) = samp; % sample window size in meters (2m, etc) 131_ GRIDSTATS(j,2) = w; % window size in percentage of sample size 132_ GRIDSTATS(j,3) = tn; % tilenumber start value 133_ GRIDSTATS(j,4) = tc; % tilecolumn number 134_ GRIDSTATS(j,5) = tr; % tilerow number 135_ GRIDSTATS(j,6) = std(error_tile); % Standard deviation 136_ GRIDSTATS(j,7) = var(error_tile); % Variance 137_ GRIDSTATS(j,8) = a; % number of points 138_ GRIDSTATS(j,9) = atile_deg; % Dip direction in degrees 139_ GRIDSTATS(j,10) = strike_deg; % Strike direction 140_ GRIDSTATS(j,11) = diptile_deg; % Dip amount in degrees 150_ GRIDSTATS(j,12) = xwmin; %

APPENDICES

xxv xxv

160_ GRIDSTATS(j,13) = xwmax; % 161_ GRIDSTATS(j,14) = ywmin; % 162_ GRIDSTATS(j,15) = ywmax; % 163_ GRIDSTATS(j,16) = normal_tile_r(1,1); % 164_ GRIDSTATS(j,17) = normal_tile_r(2,1); % 165_ GRIDSTATS(j,18) = normal_tile_r(3,1); % 166_ ywmin = ywmax; 167_ end % if m>1 168_ ywmin = ywmax; 169_ end % tr=1:(100/w) 170_ xwmin = xwmax; 171_ end % tc=1:(100/w) 172_ end % w = 1:10 % To export the out put matrix GRIDSTATS to the Excel file format. 'GRIDSTATS_SCAN01.xls' % and as an array in ASCII format and uses space as a delimiter the following commands are used. !78_ xlswrite('5cm filtered_scan02', GRIDSTATS); 179_ dlmwrite('scanpos01_scan01.txt',Xrt,' ');

The out puts for the corresponding window size of the laser scan data (i.e. azimuth, dip of tile, number of points, standard deviation, window size etc see chapter4 page 40) have been exported to Excel format which is supported by rock ware 2002 for importing and plotting as poles on an equal area net. It is more convenient in rock ware 2002 to plot the poles on an equal area net with different colors (Figure 6-1) for the field measured and derived data than in Matlab which requires extensive script writing. Appendix 3-2 Sample script of Matlab codes and command lines for surface reconstruction Points = fastrbf_import('crop_scan01_zx_r_xyz.txt','format', '%x %y %z\n'); Points = fastrbf_crop(Points,[-1.0 -1.0 NaN],[1.0 1.0 NaN]); % Crops (removes) scan, mesh or point list data from 'Points' array that lie % outside the region specified by MIN and MAX. Fastrbf_export(Points,'crop_scan01_zx_r_xyz.obj'); % Export FastRBF data ('Points')to third-party file formats determined by the type of extension (.obj). Normals = fastrbf_normalsfrompoints(Points); % Estimates vertex normals for the point list 'Points'. Density = fastrbf_densityfromnormals(Normals, 0.01, 0.03); % Creates a density field 'Density' from an input point list 'Normals' % with normal vectors length between 1cm and 3cm. Density = fastrbf_unique(Density); % Removes duplicate points from the point list, mesh or scan 'Density'. Points are considered %identical when the distance between them is less than DIST*(longest side of bounding box of %points).

APPENDICES

xxvi xxvi

Rbf = fastrbf_fit(Density, 0.002);% can be increased for small data sets otherwise it will take more %time. Create an RBF solution that interpolates the 'Density'. Mesh1 = fastrbf_isosurf(Rbf, 0.01, 'smooth', 0.03); % Extracts an isosurface with isosurface resolution of 0.01m from the RBF solution 'Rbf'. % and filters the rbf values with a low pass filter of width 0.03m. fastrbf_export(Mesh1,'crop_scan01_zx_r_xyz_rbf_r1cm_smooth3cm_v1.obj'); fastrbf_export(Mesh1,'crop_scan01_zx_r_xyz_rbf_r1cm_smooth3cm_v1.txt','format','%x %y %z\n'); Mesh2 = fastrbf_isosurf(Rbf, 0.01, 'smooth', 0.02); fastrbf_export(Mesh2,'crop_scan01_zx_r_xyz_rbf_r1cm_smooth2cm_v1.obj'); fastrbf_export(Mesh2,'crop_scan01_zx_r_xyz_rbf_r1cm_smooth2cm_v1.txt','format','%x %y %z\n'); Mesh3 = fastrbf_isosurf(Rbf, 0.01, 'smooth', 0.01); fastrbf_export(Mesh3,'crop_scan01_zx_r_xyz_rbf_r1cm_smooth1cm_v1.obj'); fastrbf_export(Mesh3,'crop_scan01_zx_r_xyz_rbf_r1cm_smooth1cm_v1.txt','format','%x %y %z\n'); Mesh4 = fastrbf_isosurf(Rbf, 0.01); fastrbf_export(Mesh4,'crop_scan01_zx_r_xyz_rbf_r1cm_v1.obj'); fastrbf_export(Mesh4,'crop_scan01_zx_r_xyz_rbf_r1cm_v1.txt','format','%x %y %z\n'); Fastrbf_view(Mesh1); colormap summer; lighting g; camlight left; material shiny; Square window size (w) and corresponding average Standard deviation S (w) per window w of raw, unfiltered and filtered data set of crop02 Window diam Raw data Unfiltered 1cm filtered 2cm filtered 3cm filtered w(cm) S(w) (cm) S(w) (cm) S(w) (cm) S(w) (cm) S(w) (cm) 5 0.4517 0.2757 0.2101 0.1557 0.1370 10 0.4619 0.2741 0.2349 0.2173 0.1864 20 0.4960 0.3059 0.2633 0.2425 0.2252 40 0.5427 0.3700 0.3324 0.2959 0.2857

S(w) per window size w for different filter width of crop02 from scanpos01_scan02 data set

y = 0.3839x0.0897

R2 = 0.9421, raw

y = 0.2082x0.1431

R2 = 0.8352, unfiltered

y = 0.145x0.2151


y = 0.102x0.2936


y = 0.0806x0.3454


0.1

1

1 10 100 window size w (cm)

Ave

rage

S(w

) in

cm

raw dataUnfiltered1cm filtered2cm filtered3cm filteredPower (raw data)Power (Unfiltered)Power (1cm filtered)Power (2cm filtered)Power (3cm filtered)

Power law relations between S(w) and w for the raw, unfiltered and filtered data set of crop02. Raw data resolution 1cm per a point, Mesh

size 1cm, Sub-sample size 2m2 using square window

APPENDICES

xxvii xxvii

Appendix 4 Reconstructed surfaces with different filter width

Appendix 4-1 Reconstructed surfaces of Scanpos01_scan02 (high resolution) data set

Reconstructed surfaces from unfiltered (top left) to a filter width of 5cm (bottom right)

APPENDICES

xxviii xxviii

Appendix 4-2 Reconstructed surfaces of Scanpos01_scan01 (low resolution) data set

Reconstructed surfaces starting from unfiltered (top left) to a filtered surface with filter width of 5cm (bottom right)

APPENDICES

xxix xxix

Appendix 5 Sensitivity analysis results

Appendix 5-1 Sensitivity analysis of RBF surface fitting before and after rotating the raw data set of crop02 from Scanpos01_scan02 (high resolution)

Descriptive statistics of mean orientation (dip amount) variation of a given window size in degrees due to RBF surface fitting before and after rotation has been taken place into the horizontal position 5cm window 10cm window 20cm window 40cm window

N 1600 400 100 25 Mean -.588 .477 .193 .092 Std. Deviation 1.6749 1.2874 .7696 .3256 Variance 2.805 1.657 .592 .106 Skewness -.518 1.310 1.153 .056 Std. Error of Skewness .061 .122 .241 .464 Kurtosis 2.586 2.433 3.427 .333 Std. Error of Kurtosis .122 .243 .478 .902 Range 14.9 8.7 4.9 1.3 Minimum -8.2 -2.5 -1.3 -.6 Maximum 6.7 6.2 3.6 .8 Percentiles 25 -1.289 -.387 -.291 -.120 50 -.357 .183 .151 .046 75 .256 1.079 .547 .316

0.00 5.00 10.00 15.00 20.00 25.00

Normal vector deviation before and after RBF surface has been fitted in degrees for

the 5cm window size.

0

100

200

300

Freq

uenc

y

Mean = 4.5147Std. Dev. = 4.04061N = 1,600

0.00 5.00 10.00 15.00 20.00



0

10

20

30

40

50

60

70

Freq

uenc

y

Mean = 3.0144Std. Dev. = 2.54659N = 400

0.00 2.00 4.00 6.00 8.00 10.00 12.00



0

10

20

30

40

Freq

uenc

y

Mean = 2.4881Std. Dev. = 2.04099N = 100

0.00 1.00 2.00 3.00 4.00



0

2

4

6

8

10

Freq

uenc

y

Mean = 1.1395Std. Dev. = 0.70389N = 25

Histograms of normal vector deviation of a given window size diameter due to RBF surface fitting before and

after the raw data has been rotated into a horizontal position (in degrees)

APPENDICES

xxx xxx

Appendix 5-2 Sensitivity analysis of possible shifting of the sample grid location on the point cloud data of crop01 from Scanpos01_scan01 (low resolution) The following analyses are carried out relative to the reference one which was assumed to be as exact location

Descriptive statistics of normal vector orientation deviation due to up shifting of reference grid

5cm dia.

(deg.) 5cm diam.

(m) 10cm dia.

(deg.) 10cm (m)

20cm dia. (deg.)

20cm (m)

40cm dia. (deg.)

40cm dia. (deg.)

N 1600 1600 400 400 100 100 25 25

Mean 5.59 .047991 6.30 .054799 4.34 .037837 2.14 2.141695

Std. Deviation 9.755 .0773454 6.095 .0527579 3.026 .0263548 1.568 1.568308

Variance 95.162 .006 37.148 .003 9.154 .001 2.460 2.460

Skewness 6.733 4.756 1.957 1.922 1.228 1.223 1.331 1.331

Std. Error of Skewness .061 .061 .122 .122 .241 .241 .464 .464

Kurtosis 82.557 37.024 5.126 4.877 1.800 1.775 1.845 1.845

Std. Error of Kurtosis .122 .122 .243 .243 .478 .478 .902 .902

Range 180 1.0563 41 .3529 16 .1380 6 6.4729

Minimum 0 .0001 0 .0003 0 .0027 0 .2456

Maximum 180 1.0564 41 .3532 16 .1407 7 6.7185

Percentiles 25 .75 .006588 1.81 .015769 2.06 .018008 .99 .989195

50 2.25 .019631 4.55 .039666 3.70 .032244 1.56 1.558845

75 6.60 .057554 8.60 .074971 5.71 .049830 3.13 3.129530

0 50 100 150 200

Normal vector deviation due to up shifting of reference sub-sample for 5cm diam.

(deg.)

0

200

400

600

800

1,000

1,200

Freq

uenc

y

Mean = 5.59Std. Dev. = 9.755N = 1,600

0 10 20 30 40 50

Normal vector deviation due to up shifting of reference sub-sample grid for 10 cm diam.

(deg.)

0

20

40

60

80

100

Freq

uenc

y

Mean = 6.3Std. Dev. = 6.095N = 400

0 5 10 15 20

Normal vecotor deviation due to up shifting of reference sub-sample grid for the 20 cm

diam. (deg.)

0

5

10

15

20

Freq

uenc

y

Mean = 4.34Std. Dev. = 3.026N = 100

0 1 2 3 4 5 6 7

Normal vector deviation due to up shifting of reference grid for 40 cm diam. (deg.)

0

2

4

6

8

10

Freq

uenc

y

Mean = 2.14Std. Dev. = 1.568N = 25

Histogram of the delta angle of standard deviation of normal vectors in degrees due to up shifting of the reference

sub-sample grid by 10cm

APPENDICES

xxxi xxxi

Descriptive statistics of normal vector orientation deviation due to Down shifting of reference grid

5cm dia.

(deg.) 5cm diam.

(m) 10cm dia.

(deg.) 10cm (m)

20cm dia. (deg.)

20cm (m)

40cm dia. (deg.)

40cm dia. (deg.)

N 1600 1600 400 400 100 100 25 25 Mean 10.69 .091849 7.84 .068166 4.86 .042332 2.21 .019307 Std. Deviation 13.577 .1134045 7.313 .063076 3.446 .030000 .947 .008263 Variance 184.334 .013 53.482 .004 11.878 .001 .897 .000 Skewness 2.341 1.963 1.923 1.877 1.348 1.339 .306 .305 Std. Error of Skewness .061 .061 .122 .122 .241 .241 .464 .464 Kurtosis 9.548 5.258 4.773 4.503 2.381 2.333 -.631 -.631 Std. Error of Kurtosis .122 .122 .243 .243 .478 .478 .902 .902 Range 142 .9460 43 .3681 19 .1662 4 .0318 Minimum 0 .0001 0 .0003 0 .0027 1 .0059 Maximum 142 .9461 43 .3684 19 .1689 4 .0377 Percentiles 25 1.03 .009021 2.69 .023495 2.32 .020249 1.32 .011553 50 5.27 .045995 5.47 .047694 3.94 .034351 2.16 .018808 75 15.54 .135165 10.95 .095378 7.02 .061249 3.05 .026639

0 30 60 90 120 150

Normal vector deviation due to dawn shifting of the reference grid for the

5cmdiam. (deg.)

0

200

400

600

800

Freq

uenc

y

Mean = 10.69Std. Dev. = 13.577N = 1,600

0 10 20 30 40 50

Normal vector deviation due to dawn shifting of the reference grid for the 10cm diam.

(deg.)

0

10

20

30

40

50

60

70

Freq

uenc

y

Mean = 7.84Std. Dev. = 7.313N = 400

0 5 10 15 20

Normal vector deviation due to dawn shifting of the reference grid for the 20cm diam.

(deg.)

0

5

10

15

20

25

Freq

uenc

y

Mean = 4.86Std. Dev. = 3.446N = 100

0 1 2 3 4 5

Normal vector deviation due to dawn shifting of the reference grid for the 40cm diam. (deg.)

0

1

2

3

4

5

6

Freq

uenc

y

Mean = 2.21Std. Dev. = 0.947N = 25

Histogram of the delta angle of standard deviation of normal vectors in degrees due to Down shifting of the reference sub-sample grid by 10 cm

APPENDICES

xxxii xxxii

Descriptive statistics of normal vector orientation deviation due to Back shifting of reference grid

5cm dia.

(deg.) 5cm diam.

(m) 10cm dia.

(deg.) 10cm (m)

20cm dia. (deg.)

20cm (m)

40cm dia. (deg.)

40cm dia. (deg.)

N 1600 1600 400 400 100 100 25 25

Mean 8.28 .071019 9.38 .081418 5.80 .050549 2.03 .017750

Std. Deviation 11.413 .0898817 8.422 .0723632 4.050 .0352091 1.298 .0113252

Variance 130.265 .008 70.935 .005 16.403 .001 1.685 .000

Skewness 5.727 4.166 1.829 1.759 1.430 1.413 .951 .951


Kurtosis 56.697 28.482 4.663 4.194 3.416 3.318 .330 .327


Range 180 1.0743 57 .4739 24 .2051 5 .0435

Minimum 0 .0003 0 .0001 1 .0052 1 .0045

Maximum 180 1.0746 57 .4740 24 .2103 6 .0480

Percentiles 25 2.03 .017754 3.61 .031482 2.68 .023390 .93 .008157

50 4.74 .041335 6.25 .054526 4.91 .042836 1.64 .014296

75 11.38 .099173 13.69 .119215 7.95 .069309 3.06 .026742

0 50 100 150 200

Normal vector deviation due to back shifting of reference sub-sample grid for

the 5cm diam. (deg.)

0

200

400

600

800

1,000

Freq

uenc

y

Mean = 8.28Std. Dev. = 11.413N = 1,600

0 10 20 30 40 50 60

Normal vector deviation due to back shifting of reference sub-sample for the 10cm diam

grid (deg.)

0

20

40

60

80

100

Freq

uenc

y

Mean = 9.38Std. Dev. = 8.422N = 400

0 5 10 15 20 25

Normal vector deviation due to back shifting of reference sub-sample grid f0r the 20cm

diam. (deg.)

0

5

10

15

20

Freq

uenc

y

Mean = 5.8Std. Dev. = 4.05N = 100

0 1 2 3 4 5 6

Normal vector deviation due to back shifting of reference sub-sample grid for the 40cm

diam. (deg.)

0

2

4

6

8

Freq

uenc

y

Mean = 2.03Std. Dev. = 1.298N = 25

Histogram of the delta angle of standard deviation of normal vectors in degrees due to Back shifting of the reference sub-sample grid by 10 cm

APPENDICES

xxxiii xxxiii

Descriptive statistics of normal vector orientation deviation due to Diagonal shifting of reference grid

5cm dia.

(deg.) 5cm diam.

(m) 10cm dia.

(deg.) 10cm (m)

20cm dia. (deg.)

20cm (m)

40cm dia. (deg.)

40cm dia. (deg.)

N 1600 1600 400 400 100 100 25 25

Mean 11.84 .101489 9.66 .083929 6.34 .055253 2.57 .022416

Std. Deviation 14.093 .1142461 7.758 .0669244 4.293 .0373206 1.227 .0107013

Variance 198.607 .013 60.189 .004 18.428 .001 1.505 .000

Skewness 3.245 2.375 1.439 1.405 1.243 1.235 .579 .579


Kurtosis 20.773 8.935 2.205 2.043 1.360 1.331 .425 .423


Range 180 1.0509 44 .3752 20 .1729 5 .0461

Minimum 0 .0008 0 .0022 0 .0043 0 .0041

Maximum 180 1.0516 44 .3775 20 .1772 6 .0502

Percentiles 25 2.53 .022119 3.87 .033788 3.17 .027620 1.68 .014695

50 7.00 .061091 7.68 .066999 5.40 .047142 2.44 .021299

75 16.08 .139858 13.12 .114257 8.21 .071541 3.42 .029819

0 50 100 150 200

Normal vector deviation due to diagonal shifting of the reference grid for the 5cm

daim. (deg.)

0

200

400

600

800

Freq

uenc

y

Mean = 11.84Std. Dev. = 14.093N = 1,600

0 10 20 30 40 50

Normal vector deviation due to daigonal shifting of the reference grid for the 10cm

diam. (deg.)

0

10

20

30

40

50

60

Freq

uenc

yMean = 9.66Std. Dev. = 7.758N = 400

0 5 10 15 20 25


diam. (deg.)

0

5

10

15

20

Freq

uenc

y

Mean = 6.34Std. Dev. = 4.293N = 100

0 1 2 3 4 5 6


diam. (deg.)

0

2

4

6

8

10

Freq

uenc

y

Mean = 2.57Std. Dev. = 1.227N = 25

Histogram of the delta angle of standard deviation of normal vectors in degrees due to Diagonal in the SW direction shifting of the reference sub-sample grid by 14.14 cm

APPENDICES

xxxiv xxxiv

3D scatter plot of normal vector orientation deviation for a give window due to Down shifting (in magnitude m)

3D scatter plot of normal vector orientation deviation for a give window due to Back shifting (in magnitude m)

3D scatter plot of normal vector orientation deviation for a give window due to Diagonal shifting

(in magnitude m)

APPENDICES

xxxv xxxv

Appendix 6 Comparison of measured with laser derived data and stereoplots

Appendix 6-1 Descriptive Statistics of the difference vector in its length (m), angle (deg.) and hhistograms of normal vector deviations between the measured and laser scan derived data.

5cm (deg.)

5cm (m)

10cm (deg.)

10cm (m)

20cm (deg.)

20cm (m)

40cm (deg.)

40cm (m)

N 96 96 72 72 92 92 25 25

Mean 11.3662 .098788 8.8572 .077138 6.4233 .056004 4.2483 .037060

Median 10.1115 .088125 7.8481 .068434 6.3362 .055266 4.1231 .035973

Std. Deviation 7.25674 .0626595 4.9570 .043050 2.98816 .026021 1.84683 .016102

Variance 52.660 .004 24.572 .002 8.929 .001 3.411 .000

Skewness 1.031 1.007 .568 .558 .341 .337 .538 .537


Kurtosis .892 .815 .036 .022 -.182 -.186 -.472 -.473


Range 33.38 .2869 20.80 .1805 13.63 .1187 6.73 .0587

Minimum .87 .0076 .13 .0012 .17 .0015 1.44 .0126

Maximum 34.25 .2944 20.93 .1817 13.81 .1202 8.17 .0712

Percentiles 25 5.7152 .049854 5.5758 .048639 4.3393 .037858 2.8372 .024757

50 10.1115 .088125 7.8481 .068434 6.3362 .055266 4.1231 .035973

75 15.5581 .135353 11.482 .100029 8.0216 .069944 5.4514 .047555

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Difference vector magnitud between measured and Laser derived normal vectors

of 5cm disc (m).

0

5

10

15

20

Freq

uenc

y

Mean = 0.098788Std. Dev. = 0.0626595N = 96

0.00 0.05 0.10 0.15 0.20


of 10cm disc (m).

0

5

10

15

20

Freq

uenc

y

Mean = 0.077138Std. Dev. = 0.0430501N = 72

0.00 0.02 0.05 0.08 0.10 0.12


of 20cm disc (m).

0

2

4

6

8

10

12

14

Freq

uenc

y

Mean = 0.056004Std. Dev. = 0.0260213N = 92

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08


of 40cm disc (m).

0

2

4

6

8

10

Freq

uenc

y

Mean = 0.03706Std. Dev. = 0.0161016N = 25

Histogram of the delta angle of standard deviation of normal vector deviation from the measured normal vector

orientation in magnitude (m).

APPENDICES

xxxvi xxxvi

Appendix 6-2 Polar Stereoplots and scatter plot with best fit linear model

Polar equal area plots of poles from Scanpos01_scan01_sample area laser scan data derived using circular windows of different diameters (e.g. 5, 10, 20 and 40 cm) (1cm filtered)

APPENDICES

xxxvii xxxvii

Polar equal area plots of poles crop02 from Scanpos01_scan02 laser scan data derived using circular windows of

different diameters (e.g. 5, 10, 20 and 40 cm) (1cm filtered)

Scatter plot and the best fit linear models for laser derived and measured dip amount

APPENDICES

xxxviii xxxviii

Appendix 7 Reconstructed narrow strip profiles

Appendix 7-1 Raw data strip profiles of crop02 from Scanpos01_scan02 Strip_crop02_H_raw1

Strip_crop02_H_raw2

Strip_crop02_H_raw3

APPENDICES

xxxix xxxix

Strip_crop02_V_raw1

Strip_crop02_V_raw2

Strip_crop02_V_raw3

APPENDICES

xl xl

Appendix 7-2 Smoothed raw data strip profiles of crop02 from ScanPos01_scan02 Strip_crop02_H_rawS1

Strip_crop02_H_rawS2

Strip_crop02_H_rawS3

APPENDICES

xli xli

Strip_crop02_V_rawS1



APPENDICES

xlii xlii

Appendix 7-3 Reconstructed surface strip profiles of crop01 from Scanpos01_scan01 Strip_crop01_H_rec1

Strip_crop01_H_rec2

Strip_crop01_H_rec3

APPENDICES

xliii xliii

Strip_crop01_V_rec1

Strip_crop01_V_rec2

Strip_crop01_V_rec3

APPENDICES

xliv xliv

Appendix 7-3 Reconstructed surface strip profiles of crop02 from Scanpos01_scan02 Strip_crop02_H_rec1

Strip_crop02_H_rec2

Strip_crop02_H_rec3

APPENDICES

xlv xlv

Strip_crop02_V_rec1

Strip_crop02_V_rec2

Strip_crop02_V_rec3

COMPARING DISCOUNTINUITY SURFACE ROUGHNESS DERIVED … · interpolated as a 3D virtual surface...

Documents

Transcript of COMPARING DISCOUNTINUITY SURFACE ROUGHNESS DERIVED … · interpolated as a 3D virtual surface...