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8The CollectionandAnalysisofDiscontinuity Orientation DataforEngineering Design with ExamplesSTEPHEND PRIESTUniversityo South Australia Pooraka Australia; Formerly UniversityoAdelaide South Australia Australiat I N T R O D U C T I O N~ D A T A C O L L E C T I O N

83 1 The Scanline Technique822 PreliminaryData Processing

t_3 G R A P H I C A L R E P R E S E N T A T I O N OFO R I E N T A T I O N D A T AExample 1

14 V E C T O R I A L R E P R E S E N T A T I ON OFO R I E N T A T I O N D A T AExample 2

O R I E N T A T I O N S A M P L I N G BI ASDUE TO A L I N E A R S U R V E YExample 3Example 4

t I D E N T I F Y I N G AND D E L I M I T I N G S E T SExample 5

S. R E P R E S E N T A T I V E O R I E N T A T I O N FOR A SETExample 6

| T H E F I S H E R D I S T R I B U T I O NExample 7

19' S U M M A R YAND C O N C L U S I O N S0 R E F E R E N C E S

161691721731741761.77177178180181182184185187189190191

1 I N T R O D U C T I O NRockmassesusually contain such featuresas fractures faults joints beddingplanes cleavageand

rmechanicaldefectswhichareherecollectivelyreferred to as discontinuities.Thesediscontinuitieshavea major influence on the deformability strength stability and permeability of the rockmassthereby play a major part in dictating the design of foundations slopes tunnels and other

ctures associated w i t hdiscontinuous rockmasses.One of the aims of thischapteris topresenta listlilyaccessible references [1-62]which provide supplementary reading and further material forconcerned w i t h the collection and analysis of discontinuity orientation data. The greaterr t i on ofthesereferencescome rom the most active period ofresearchin thisarea: 19701985.

167

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17 Discontinuitiesa borehole but which does not suffer f rom the small sample w i d t h The location,orientation andconditionof the rock face are recorded on the first pageof theloggingsheettogether w i t h the treadand plunge of each scanline.Colorphotographs of the face,includinga scale and appropriate iabeLm ay also be taken before commencing the samplingprocess [27]. Each scanline tape is scanned,starting f rom the zero end.u n t i ladiscontinuitytrace is intersected. Thef o l l o w i n gproperties of ooKthosediscontinuitiesintersected by the tape are measured and recorded in a systematic tabular foraton alogging sheet such as the one illustrated in Figure 1.

i Intersection distance d This is the distance along the scanline to the intersectionpoint nskthediscontinuity.I f the face is not perfectly planar it may benecessary to extrapolate some of Ikediscontinuitiesto obtain thispoint.The intersection distance on agivenscanline provides asircrieand unambiguous method foridentifyingany particulardiscontinuityi n the sample. Kscontic i awspacings can be obtained by subtracting consecutive intersection distances for a specified group ofdiscontinuities [24, 28], Scanlinediscontinuity frequency, which is the average number of interjec-tions per unit length of scanline, is usually calculated separately for each identifiable set and the*processed to obtain the expected frequency along the normal to each set [16. 18. 26, 29].

ii j Orientation This is the f ive digitdipdirection/dipangle of thediscontinuity measured a: taepointof intersection w i t h the scanline. I fthediscontinuity ispoorly exposed at thispointit may benecessarytomeasurethe orientation at an exposed surface on thediscontinuitysome distance freethe scanline. The orientation is usually measured bymeansof a magnetic compass and clinomeasrdevice fitted with a spirit level [16, 30]. Ewan and West [31] concluded that different operauxsmeasuring the orientation of thesame feature have amaximum error 10for dipdirection and 5C for dip angle. Care must be taken to correct the readings of geographical azimuth for k n idifferences between true and magnetic north. This correction can often be achieved during A cmeasurement process itselfbymeansof aminoradjustment to the compass. I fthis adjustment is aetpossible it w i l l be necessary to correct the azimuth readings during data processing and plorcaaj.Compass needlesbalanced for magnetic inclinationin the northern hemisphere w i l lbe severely oarof balance in the southern hemisphere. It should be noted that the scanline wi l l tend to intersect

Un i ve rs i t yctAdelaide sconline logging form

PageDate Face locat ion Rock t ype

Scanl ine label Foce d ip d i rec t ion /dip ongie / Excavat ion m et nod

Measurementsby Non -overhang ing /overha ng ing Cond it ion o f exposure

Scan l i ne t r end / p l unge / Face height Comm ents

S e m i - t r a c e s l e f t / r i g h t / a b o v e /below

Figure1 Exampleof a scanline survey logging form

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The Collection and Analysis of Discontinuity Orientation Data for Engineering Design 171preferentially those discontinuity traces that make a large angle w i t h it , and in the l i m i t the scanlinewi l l fa i l to intersect tracesthat lie paral lel to it .This effect,whichis discussed in detail in Section 8.5,can be allowed for by applying simpletrigonometrical correction factors to the data before plottingand analysis.

H i) Semi-trace length I. This is the distance f r om the intersection point on the scanline to the endof the discontinuity trace. This distance can cither be measured directly i f the face is accessible,estimated by eye or scaled f r om the photograph of the rock face. There w i l l be two semi-trace lengthsassociated w i t h each discontinuity: one above and one below a horizontal scanline; one to the leftand one to the right of avertical scanline. In many cases the scanline w i l l have been set up close totheedge of the exposure so it w i l l onlybe possible tomeasure semi-trace lengths on one side of it .Thissamplingsystem presents no problem because the intersection point w i l l be at a random locationalong each discont inu ity trace, permitting the use of simple statistical techniques 1 estimate theproperties of the complete trace length distribution [20,32-37], Some operators choose to ignoresemitraces that are smaller than a given threshold value lt. If no record is kept of the number oftraces that are ignored, this practice has the effect of truncating the semi-trace length sample forvaluesless than k-If, on the other hand, a record is kept of the number oftracesthat are ignored, thesemi-trace length sample is said to be censored for values less than lt [38-41]. The different effects oftruncation and censoring must be allowed for during statistical processing. During this statisticalanalysis allowance can also be made for the fact that the scanline w i l l tend to have intersectedpreferentially discontinuitiesw i t h longertraces[20,25]. Although it can be argued that these longertraces are more significant f r om an engineering point ofview and should, therefore, feature moreprominently i n the sample, it is not satisfactory to replace engineering judgement by this arbit rarysampling bias. In the author s opinion it is preferable to remove all sampling bias and then toexamine the true rock structure data, taking into account not only discont inuity size but otherproperties such as orientation, frequency and strength. A number of papers have been writtendescribing ways ofremovingsampling bias, and ways ofdetermining thedistributional form and thedistribution parameters of discont inuity size measurements taken at planar rock faces of l im i t edextent [20, 25, 32, 35, 37, 42-46]. Discussion of these techniques, which comprise a variety ofingenious algori thms for processing truncated and censored samples, is beyond the scope of thischapter.

iv ) Termination. It can be helpful to keep a record of the nature of the termination of eachsemi-trace. The fo l lowing recording scheme has proved to be adequate: A = discontinuity traceterminates at another discontinuity; I = terminates m intact rock material; and O termination isobscured. The larger the proportion of discontinuities that terminate at other discontinuities thegreater the tendency for the rock mass to be blocky, relatively weak, of low stiffness and highlypermeable. A trace can be obscured by scree, vegetation or by extending beyond the l im i t s of theexposure. Obscuring in this way has the effect of censoring the sample of semi-trace lengths for valueslarger than a variable length that depends upon the geometry of the rock face, the location of thediscontinuity w i t h i n the face and the orientation of the discont inuity. This complex censoringproblem has been examined by Baecher [32],Kulatilakeand Wu [37, 42, 47], Laslett [43], Pahl[ 4 4 ] Priest and Hudson [25] , and Warbur ton [45, 46 ] who present a number of techniques fordetermining the distribution f o rm and distribution parameters of the complete trace lengths. One oftheapproaches adopted by these authors has been to adopt an areal sampling system, rather thanthe traditional line sampling techniques.

v) Roughness. Surface irregulari ties w i t h a wavelengthless than about 100 mm are here referredto as roughness. Roughness can be measured by taking an impression of the surface, then digitizingand quantifying representative profiles. For most practical purposes, however, it is sufficient toassessroughness visuallyon a fivepoint scale ranging f rom 1 = smooth to 5 = very rough, based onexperience at a given site. The results can then be correlated w i t h shear strength parameters for eachdiscontinuitytype on the site, or alternatively analyzed f o l l ow i ng the methods recommended by theI S RM [16],

vi ) Curvature. Surface irregulari ties w i t h a wavelength greater than about 100 mm are herereferred to as curvature. Curvature can be determined by measuring offsets at 100 mm intervalsalonga straight base line then digitizing and quantifying the resultingprofile. As w i t h roughness,however, it is often sufficient to assess curvature visually on a five point scale ranging f r om1 = planar to 5 = very curved.m i) Comments. The comments column is used to provide additional qual itative informationabout each discontinuity in abbreviated f o rm . The fo l lowing information may be recorded.

a) Type of discontinuity i.e. whether it is a j o i n t bedding plane, fault or blasting crack [ 4 8 ] . Itmay be possible to recognize and ignore blasting cracks since they are usually small, rough, clean.

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The Collection and Analysis of Discontinuity Orientation Data for Engineering Design 173processorsystem as soon as the preliminary processing referred to above has been complefed. Theparticular program C A N D O has been designed to accept up to 3000 orientation values sampledalong up to 100separatescanlines.Thesedataare read f rom a file specified by the user at thestartofthe analysis session.

G R P H I C L R E P R E S E N T T I O N O F O R I E N T T I O N D TThe aim of collecting discontinuity orientation data is todelectconsistentpatterns(or theabsence

of them) and to predict their influence on the engineering performanceof the rock mass. A graphicalrepresentationof the orientation data can help in achieving this aim, not only by presenting the rawdata but also by displaying the results of any statistical analyses.

One of the simplest forms of graphical representation is the rosediagram [19, 49]. This approachis particularly suited tocaseswhere mostof the discontinuities have anglesof dip inexcessofabout60 .I nsuch cases the dip direction data are of primary significance and can be plotted on a simplecircular histogram. The 0 to 36 circle is divided into convenient class intervals, usually of 5, 10 or15depending upon the sample size, and the numberof dip direction values ineachclassinterval iscounted. The results are plotted as wedges which have a radial extent that is proportional to thefrequency in each class interval. This frequency can be expressed either as a raw number, asa proportion or as a percentage of the total samplesize. The rose diagram in Figure 2based upona sampleof 226 discontinuities obtained by Priest [22],shows how the orientation and the relativesignificance ofclusters of preferred dip direction are clearly visible. In theauthor s opinion there isl i t t le point in plottingrosediagramsbased upon strike direction sincethisproducesa duplication ofinformation across the rose diagram and an associated loss of dip direction data.

The disadvantageofrosediagrams is that they contain no information on dip angle. This can beovercometosomeextent by selecting data f rom themoresignificant class intervals and then plottinga histogram of dipangles. The histogram in Figure 3,based upon 52values f rom Figure 2 w i t h a dipdirection in the range320 to 0 2 0 showsthat 33 of the discontinui ties i n this rangehavean angleofdipgreater than 60; only one discontinui ty has an angleof dip less than 30. In this case, then, therosediagram provides a reasonable representation of discontinuity orientation.

The difficulties ofrepresentingthree-dimensional orientation datain twodimensionson asheetofpaper can be overcome by adopting the technique known as stereographic, or hemispherical,projection [4, 5,23, 50-52]. The basicprinciple of hemispherical projection is that the orientation ofa line in three-dimensional spaceis uniquely represented by the position of a point w i t h i n a circularprojection area of radius R The perimeter of this projection area is associated w i t h the circle ofgeographical azimuth directions so that the radius on which the point plots is given directly by thetrend direction, a, of the line that itrepresents. It isusual to mark the north (azimuth 0) directionwi th a small line labeled N to provide a reference direction on the projection. This convention wi l l

ieoFigure 2 Rose diagram for discontinuitydip direction, Chinnor, Location 2, 226values

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174 iscontinuities

Dip direction 32 -2 52 values

1 -

1 20 3 4 6 7 ec 9Dip angle i

Figure3 Histogram for discontinuity dip angle, Chinnoi. Location 2, dip direction 320-020t

be adopled here. The radial distance, r, of the point f rom the center of the projection circle uafunction of the plunge,/S, of thelinethat itrepresents, subject to the boundary conditions that r = Iwhen P =90 and r = R when fi= 0. The form of the functional relation between rand fidependsupon the projection method adopted. Two of the most common projection methods utilize asimaginary hemisphere of radius R positioned below the plane of projection so that its circular faceforms the projection circle. The first of these methods, termed the lower hemisphere equal arigkprojection, gives rise to the fo l lowing relation between r and ji

The second method, termed the lower hemisphere equal area projection, gives the fo l lowingrelation

A f u l l discussion of the properties and the relative merits ofthese two methods of projection sgiven by Priest [23].

Example 1 Figure 4)Plot on a lower hemisphere equal angle projection of 100 mm diameter, points repres-

enting the line of maximum dip and the normal to a plane of dip direct ion/dip angle

The trend and plunge of the lineof maximumdip a*, jd are givendirectlyby the dipdirection anddipangle of the plane. Hence ad = 146and /Jd = 57 .The trend and plunge of the normal a, fl, are,byequations (1) and (2), respectively 326and 33. The point D, representing the line of maximumdip, and the point N, representing the normal, plot along radii of azimuths 146 and 326*respectively on the 100 mm diameter projection circle in Figure 4. SettingR = 50 mm in equation in -puts the point D 14.8 mm f rom the center, and the point N 27.1 mm f rom the center of theprojection.

a large number ofdata points are to be plotted it is usually convenient to adopt computergraphics in preference to manual plottingmethods. Figure 5(a) shows a circular projectionarea ofradiusR related to anx, yCartesian coordinate system inwhich po sitive .x is horizontal to the north(trend 000 and positivey is horizontal to the east (trend 090 . The x,y Cartesian coordinates ofa point on the projection representing a lineof trend/plungea/Bare given in Table 1for equal angleand equal area projections. The x, y coordinates for the points D and N in Example 1, determinedf rom the top row of Table 1, are given in Figure 4. It is a relatively straightforward matter to winea computer program that utilizes the expressions in Table 1 to enableautomatic plotting of dau.

Large numbers of discontinuity orientation values can be plotted on a lower hemisphereprojectionto give a graphical representation of the orientation properties of the rock structure.Toe

146/157.

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The Collection and Analysis of Discontinuity Orientation Data for Engineering Design 175

// r S 2 . 5 m m \ . 2 7 . lmm/ y 15.2m m \

Figure4 Lower hemisphere equalangleprojection of the line of maximum dip, D, and the normal. N, of a plane of dipdirection/dipangle 146/57 Example 1)

yEos

x Horfrontal north

yHorizontal east

7 Vert ica l down

Figure5 a) Two-dimensional Cartesian coordinate system, b) Three-dimensional Cartesian coordinate system

Table1 Thex yCartesianCoordinates ofaPoint RepresentingaLineofTrend/Plungea//? on a Lower Hemisphere Projection of RadiusRxcoordinate {north000] ycoordinate{east 090

qual angle Rcos a tan

qual area R^/lcosac /90

/90 - fi\RsinatanI 1

T . fW + 0R J 2sinacosI

best approach is to plot only the points representing the normals toeachdiscontinuity plane. It isoften feasible to use symbols of different shapestorepresentdifferent types of discontinuities (joints.,beddingplanes,faults,etc. and to use symbols of differentsizestorepresent arangeof discontinuitysizes.An example of such a plot, rom Priest [23] is reproduced in Figure 6. Plots of this type permitthe identif ication of groups of subparallel discontinuities, or sets , that have been produced bya single geological process [48]. The orientation of these sets,and the degreeof clustering w i t h i neach set, can have a major influence on the engineering performance of the rock mass. It can bebeneficial, therefore, to apply quantitative methods in the analysis ofdiscontinuity orientationdata,to provide an objective assessment of any preferred orientation.

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176 Discontinuities

Trace length< nn 2 -4m > 4 m

jointbedding

OSampling lineI

O O Q O3 c Q o o o

Samplinglin

=

Figure6 Lowerhemisphere,equa angle plot ofdiscontinuitynormals (reproduced fromref. 23with permissionc4\Hyman)

8.4 VECTORIAL REPRESENTATION OF ORIENTATION DATAFigure5(b) shows a right-handed Cartesian coordinate system n which positivex ishorizontal at

thenorth (trend000),positivey is horizontal to theeast (trend090)and positivezisvertical ckmmThis coordinate system has been selected to maintain compatibility with the two-dimenssotaasystem in Figure 5(a)whileensuring that positivez isassociated with positiveanglesofplunge, h aworthnotingthat this coordinate system isslightly different from the left-handed systemadoptee*Priest [23] inwhich x iseast and y isnorth.Conversionfrom this left-handed system to thecurrc tright-handed system can be achieved simply by swopping x and y on the diagrams and m n cassociated equations. Any line or vector u in three-dimensional space can be represented m ikeCartesian system of Figure 5(b) by putting the start point of the line or vector at the origin of tarsystem and then noting the Cartesian coordinates u, uus of its end point.Thesecoordinates aaeusuallyreferred to as the Cartesian components of the vector. The length of the l i D e or magrmuoe ofthe vector, is given by

ll = Jul + 0, then a = 90while i ux = 0 and u 0 then B =9 0 while ifu.

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The Collection and Analysis of Discontinuity Orientation Data for Engineering DesignTable 2 The Quadrant ParameterQin

Equation(6)

Q20 20 0

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176 Discontinuities

Trace length4m

joint o o Obedding o D

N

ampling lineI

Sampling line 80t ?o c *

ampling me

Figure6 Lowerhemisphere, equal angle plot of discontinuity normais reproduced from ref. 23 with permission of Uc-s eHyman)3

8.4 V E C T O R I A L REPRESENTATION OF O R I E N T A T I O N D A T AFigure5(b) shows a right-handed Cartesian coordinate system inwhichpositivexishorizontal tothenorth(trend 0 0 0 ) ,positiveyis horizontal to theeast(trend090 and positive z isvertical down.

This coordinate system has been selected to maintain compatibility w i t h the two-dimensionalsystem in Figure 5(a)whileensuring that positive z isassociated w i t h positiveanglesofplunge.It isworthnotingthat this coordinate system isslightlydifferent f r o mthe left-handed system adopted byPriest [23] inwhichx iseastand yisnorth.Conversion fromthis left-handed system to the currentright-handed system can be achieved simply by swopping x and y on the diagrams and in theassociated equations. Anyline or vector uin three-dimensional space can be represented in theCartesian system of Figure 5(b) by puttingthe start pointof the line or vector at the o r i g i nof thesystem and then noting the Cartesian coordinates ux, uf, us of its end point.These coordinates areusuallyreferred to as the Cartesian components of the vector. The length of the l i D e or magnitude ofthe vector, is given by

= Jul + u, + u\)

Thetrend a and plunge 6of aline w i t hCartesian components ux u vanduzin the system ofaxesinFigure5(b) are given bya = arctan^J + Q {(

= arctan( , = _^ | f7lThe parameter Qis an angle, indegreesthatensuresthat a lies in the correct quadrant and in therange0 to 3 6 0 .This parameter, which depends upon the signs ofux and u,. aslisted in Table 2, is

required because the arc tangent function of most computers returns a value in the range - 90Lto + 9 0 .Care must be taken when the denominators in equations (6) and (7) are zero In equation(6), i ux = 0 and uy >0, then a = 90while i ux = 0 and u,.< 0 then a = 2 7 0 .I n equation (7),a zerodenominator means that ifu2 >0 then B= 90while if u. < 0 then /) = 9 0 .

The inverse forms of equations (6) and (7) areux = |u|cosacosft uy = | | s i n a c o s / , uz = |u|sin/3 (8)

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178 Discontinuitieswhere < is theacute angle between the discontinuity normal and the samplingline. So

cc 4cos

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