Procedia Engineering 91 ( 2014 ) 328 – 333

1877-7058 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP)doi: 10.1016/j.proeng.2014.12.069

ScienceDirectAvailable online at www.sciencedirect.com

XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP) (TFoCE 2014)

The Comparison of the Calculation of the Volume of the Foundation Pit

Jaroslav Šímaa, Anna Seidlováa *

a Department of Geodesy, University of Zilina, FCE, Univerzitná 1, 01026 Žilina

Abstract

The realization of the earthwork represents a large part of the cost of construction works. Therefore, it is very important to determine the volume of the earthwork as accurately as possible. There are many ways how to determine its value. However, comparing the reasons of different methods we have discovered that results of quantification are often varying. In this paper, we will discuss the results of calculation of the volume by different methods. We will compare the conventional methods of the calculation with the differential exact calculation of using the digital terrain model derived by geodetic and photogrammetric methods. © 2014 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP).

Keywords: Geodesy; engineering geodesy; digital photogrammetry; digital terrain model;

1. Introduction

In the construction, there are cases which require determining the cubic content of the earthworks as precisely as possible. There are many ways in which we can determine the volume of earthworks. However, comparing the reasons of different methods we have discovered that results of quantification are often varying. The cubic content is exactly calculated from a differential digital models obtained by geodetic and photogrammetric methods. This is the case, when we are using a digital model of the flat or slope terrain.

There is often a situation in practice [1,2] that one of the models is formed by construction pit with vertical walls and in that case, the automatic calculation of volumes generally fails. In principle, following methods are currently used to obtain the cubic capacity:

calculation of the volume from profiles, calculation of the volume using DTM.

These methods differ mainly in elaborateness and processing time. Results obtained from graphical documents are often disputed by suppliers.

* Corresponding author. Tel.: +421 41 5135569; fax: +421 41 513 5510 E-mail address: anna.seidlova@fstav.uniza.sk

© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP)

329 Jaroslav Šíma and Anna Seidlová / Procedia Engineering 91 ( 2014 ) 328 – 333

2. Object of the experiment

The foundation pit was excavated during 2012 – 2013 with continual removal using individual trays of soil and slope ensuring with soil nails and shotcrete. After finalization, the vertical walls can allow for other construction activity at foundation pit, Fig.1.

Fig. 1 View of the wall excavation.

The main problem of calculations of the volume of the earthwork is often the lack of information concerning the

original terrain. In this case, the quality base map of y. 2010 was available, which we prepared for the transhipment utilities (in graphical and numerical version).

For mapping and staking out works was stabilized control minor. We used method combination of GNSS (static method) and terrestrial measurements, with the Leica Viva GNSS apparatus and ET LEICA TC 06. Using the results of measurements we prepared two specific maps of the area, together with a list of coordinates and heights of the original and modified terrain. For mapping of places very difficult to access, we used a prism system of electronic tachymeter.

3. Digital Terrain Model

Under the definition of digital terrain model (DTM) we understand the representation of the terrain or the model with coordinates of points. The coordinates are transmitting the quantities for digital terrain model. DTM is arranged set of numerical information (coordinates y, x, H) of the terrain relief stored in computer memory, by the relevant software for its use, [3]. The relief is the Earth's surface created by natural forces or artificially, without objects and features that are situated on it. Landscape area cannot be directly defined mathematically, it must be generalized. We eliminate the unimportant details and we neglect its roughness. The substitution of the terrain, which arose after generalization, is called the topographic surface, this area can be mathematically expressed as a function of two variables in the form H = z = f(y,x). Each point is recorded in the form of {i, y, x, z, k}, where i is the number of points, y, x, z are the coordinates of the point and k is code, [4].

3.1 Calculation of the cubic content of the earthworks from DTM

Program of the input data, which are the coordinates Y, X and Z, creates a digital surface which is defined by a TIN network. It is a triangular network containing all points of entry. Area created this way serves as the representation of the actual terrain.

The place where the slope of the terrain is changing rapidly, for example a pit or an excavation, it is necessary to

330 Jaroslav Šíma and Anna Seidlová / Procedia Engineering 91 ( 2014 ) 328 – 333

define them by using slope crests. Most of software’s use following kinds of slope crests: required, broken and direct. Using the correct type of slope crests depends on the user, and can modify the formation of DTM. Thus, created model can be used not only to generate and display contours, but also the calculations of volume. The difference of results obtained by final DMR without edges is shown in Fig. 3 and by using slope crests in Fig. 4. Generating the model at the vertical construction of pits can cause a problem to occur in which the wall is not ideally vertical and therefore creates a situation of the projection of the "cross" of the contour lines. This problem has been solved using the edge only partially, because the wall is not a perfect straight line and thus overlaps the lower and upper edge of the excavation. The most appropriate solution for the complete elimination of DTM is complete elimination of points on the pit wall in addition to the lower and upper edges. For this, we have used the procedure of tilt elevation in the floor plan followed by deleting unnecessary points (Figure 2 are highlighted in blue square).

Fig. 2 Points for abutment wall.

For creating the DTM we used the software of the Czech ATLAS DMT. The results are the original digital terrain models (Fig. 5) and foundation pit (Fig. 6) for illustratively supplement by the hypsometry.

Fig. 3 Model without required edges. Fig. 4 Model with required edges.

4. Calculation of the volume of earthwork

Calculation of the volume of the earthwork using the software can be, in principle, in two ways, or by calculation through the comparative plane or comparative model. From our experiences, we can say that in most cases, it is optimal to use two models (which are not always available). The software ATLAS allows us to create model differences arising geometric penetration of both DMR and removing the marginal parts, [5, 6]. Differential model of building pit is shown in Fig. 7 and supplemented by the hypsometry. Considering that this is a 3D model, it is possible to perform all operations with 3D model in any kind of software.

4.1 Computation of the volume of the earthwork using AutoCad

System of solution of the volume of the earthwork in AutoCad differs from ATLAS. The base is created by imported points and creation of TIN model from these points.

After inserting the required edges, two digital models (in AutoCAD they are called surfaces) are created and the

331 Jaroslav Šíma and Anna Seidlová / Procedia Engineering 91 ( 2014 ) 328 – 333

volume of the earthwork is calculated from the reference planes or from two models and showed in the properties of the surface.

Fig. 5 Model of the original terrain with hypsometry. Fig. 6 Model of the foundation pit with hypsometry.

Fig. 7 Model of differences - without the surrounding terrain. Fig. 8 Profiles of the foundation pit.

4.2 Comparison of results

Sometimes the results obtained from 3D models are often disputed by suppliers, therefore we determined the cubic capacity by a traditional way of using cross sections, [7, 8]. We have used a density of sections 5 and 10 m. Profiles were generated from DMR of superstructure " EZY ", profiles were used identical-parallel to the east wall of the pit (Fig. 8). From the individual profiles, surfaces for comparative to the reference plane of 335.00 m were calculated, [6]. The resulting volumes were calculated from the profiles according to the equation (1) and using the Simpson formula (2) and (3). Results and comparisons are shown in Tab. 1, 2 and 3.

221 PPdV

(1)

21 46

PPsPdV (2)

PS is the area of the middle and is determined from the equation:

332 Jaroslav Šíma and Anna Seidlová / Procedia Engineering 91 ( 2014 ) 328 – 333

221

2PP

Ps (3)

Tab. 1. Difference in the volume according to density of cross sections. Density of sections V [m3] Difference [m3]

10 m 6120 17

5 m 6137

Tab. 2 Difference in the AutoCad.

AutoCad estimation V [m3] Difference [m3]

2 models 6336 4

Model with reference plane 6332

Tab. 3 Difference in the volume ATLAS.

ATLAS estimation V [m3] Difference [m3]

2 models 6358 2

Model with reference plane 6360

5. Utilization of digital photogrammetry

In the last 20 years, we have started to use digital photogrammetry for obtaining the digital images made by conventional photographic cameras. In our case we used digital images of vertical excavation walls and performed visualization in software Photomodeller [3] with the following procedure:

- calibration of the camera for field calibration points - to determine the components of interior orientation of the camera (focal length, coordinates of mine point, sensor size, parameters and radial and decentration distortion),

- orientation of images on identical points - obtain the elements of exterior orientation images, thus reconstruction to the camera positions of the object during imaging (coordinates x, y and z of projection centres and rotation angle of the camera in all three directions). The second point can now to go for fully automated so-called SmartPoints (Technology Structure from motion),

- creation of 3D model - can be performed either manually on the basis of evaluation the break points of the subject, or again using fully automated image scanning technology utilizing a correlation between a pair of image frames - the result is that if a cloud of points.

The result is a cloud of points in a grid of about 10 x 10 cm and its export to AutoCAD DXF format - in this case it is about 100 000 points (cut-out section shown in Fig. 9).

Fig. 9. 3D view of part of the wall in AutoCAD.

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6. Conclusion and analysis of the results

Analysis of the results clearly confirmed the suitability of the applied equipment and software used for processing of data. Differences of using individual methods and the software are insignificant and create about 0.3% of the total volume of the earthwork, which is a negligible value. The usual requirement for accuracy is in the range of 3-5%. Comparison of the software is really difficult, because both of them require some experience and practice, [9]. From this point of view, the evaluation is usually not very objective. Acknowledgment

This article is the result of the implementation of the project: "Innovation and internationalization of education – the means to increase the quality of the University of Zilina in the European educational space (ITMS: 26110230079) supported by the Research & Development Operational Programme funded by the ERDF.

This article is the result of the implementation of the project VEGA No. 1/0597/14 “Analysis of methods used to measure the unconventional railway track construction from the point of view of accuracy and reliability “supported by the Scientific Grant Agency of the Ministry of Education, science, research and sport of the Slovak Republic and the Slovak Academy of Sciences.

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