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ROCK MASS SLOPE STABILITY ANALYSIS BASED ON

3D TERRESTRIAL LASER SCANNING AND GROUND PENETRATING RADAR

Mark Anthony E. Pernito

February, 2008

ROCK MASS SLOPE STABILITY ANALYSIS BASED ON 3D TERRESTRIAL LASER SCANNING AND GROUND PENETRATING RADAR

Rock mass Slope Stability Analysis based on 3D Terrestrial Laser Scanning and

Ground Penetrating Radar

by

Mark Anthony E. Pernito

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: ( Applied Earth Sciences- Geo-engineering )

Thesis Assessment Board

Prof. Dr. FD van der Meer (Chair)

Dr.ir. E.C. Slob (External Examiner)

Dr. H.R.G.K. Hack (1st Supervisor)

Dr. Mark van der Meijde( 2nd Supervisor)

Observer

Drs. T.M. Loran, (Course Director AES)

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

A critical step in rock slope stability analysis is an accurate and detailed determination of the rock

mass discontinuity properties. However, traditional discontinuity measurements are time consuming,

subjective, prone to errors and based mainly on the surface measurements of the exposed

discontinuities. Alternatively, 3D terrestrial laser scanning (3D TLS) can provide a very accurate

point cloud data of the scanned slope within a few minutes, in which rock discontinuities can be

extracted in an automated and objective way. Further, Ground Penetrating Radar (GPR) can be used

to detect subsurface discontinuities that are not detected by the 3D TLS. This study investigates the

applicability and the reliability of discontinuity plane models, derived from the two survey methods,

in assessing the stability of a volcanic rock slope in Montemerlo, Italy.

The point cloud data from 3D TLS survey was processed using 3D Hough transform segmentation

algorithm to derive a discontinuity plane model of the scanned rock slope. The segmented

discontinuities were classified into various discontinuity sets using fuzzy K-mean clustering. The

results revealed that some of the discontinuities are not detected due to occlusion and orientation bias.

Most of the trace discontinuities are not detected. Subjectivity in numbering the clusters and error in

outlier removal is found to have a significant effect in the resulting discontinuity statistical

parameters. Comparison of 3D TLS discontinuity model against scanline discontinuity measurements

shows both weak and strong correlations of various discontinuity sets. The weak correlation with

scanline measurements, is mainly due to the low dipping discontinuities at the upper part of the slope

that are detected by 3D TLS, but out of reach of scanline measurements.

To objectively delineate the discontinuities in the GPR image, a semi-quantitative approach based on

automatic delineation of linear coherent events with high and extreme change in intensity values was

carried out. This was integrated with the GPR 3D modelling, which gives significant improvement in

the determination and correlation of several reflection events. However, the three-dimensional

spherical propagation effect of electromagnetic waves gives a reflection events coming from different

directions, which introduce uncertainties in the interpretation of the actual orientation and spacing of

the rock mass discontinuities.

Considering the uncertainties in 3D TLS and GPR model, a probabilistic slope stability analysis gives

a more realistic assessment of the stability of the slope as compared to the deterministic analysis.

However, the adopted probabilistic analysis considers only the orientation-dependent stability of the

slope. Slope Stability Probability Classification (SSPC) system consider both the orientation-

dependent and orientation-independent stability of the slope, thus, gives a better assessment of the

slope stability. 3D TLS and GPR measurements can be applied in slope stability analysis with due

consideration to the limitations and uncertainties involved.

.

Key words: 3D terrestrial laser scanning, Ground Penetrating Radar, slope stability, Hough

Transform, Probabilistic Analysis, SSPC.


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Acknowledgements

I would like to thank the Netherlands fellowship programme (NFP) and my employing organization,

the Bureau of Research and Standards for giving me this opportunity to study at ITC.

My deepest gratitude to my supervisors, Dr. H.R.G.K Hack and Mark van der Meijde. Thank you for

your advice, guidance, patience and for all the valuable comments that you have given me while

writing this thesis. I would like to thank Ir. Siefko Slob for all the knowledge you have shared.

I would also like to express my sincere gratitude to Dr. Antonio Galgaro and Dr. Giordano Teza of

Padova University, Italy for all the support during the research fieldwork it is an honor to work with

you!

To all my international friends Han, Agi, my geo-engineering and AES collegues, my ate’s and

kuya’s in ITC, I wish you all the best, thank you for everything. Especial thanks to Dr. John Carranza

for all his support and inspirational jokes! To Tam and Mrs. Phuong, thank you for all the wonderful

moments we’ve shared.

I am greatly indebted to Dir. Antonio V. Molano Jr. for all the advice and word of encouragements.

Special thanks to my Research and Development Division family, especially to Juliet Clarion.

To Jimmy Matienzo Jr. and Richard Decellis thank you for the true friendship

My special thanks to my lovely sisters and brother Mae, Inday, Gang, Mahal and Val. I love you all.

To my mama I miss playing guitar to you in the morning! To papa I hope we could still play

basketball and have a long jogging in the morning. Thank you for all the love and sacrifices!


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Table of contents

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

1.1. Research Background ...........................................................................................................................1 1.2. Problem Statement................................................................................................................................1 1.3. Objective...............................................................................................................................................2 1.4. Research Questions...............................................................................................................................2 1.5. Research Hypothesis.............................................................................................................................2 1.6. Methodology and Thesis Structure .......................................................................................................3

2. LITERATURE REVIEW ............................................................................................................................5 2.1. Introduction ..........................................................................................................................................5 2.2. Traditional Rock Mass Discontinuity Measurements ...........................................................................5 2.3. 3D Terrestrial Laser Scanning Discontinuity Measurements................................................................7

2.3.1. Theory and Applications .............................................................................................................7 2.3.2. 3D TLS Limitations in Discontinuity Measurements ..................................................................9 2.3.3. 3D TLS Data Processing Errors................................................................................................10

2.4. Ground Penetrating Radar ..................................................................................................................10 2.4.1. Theory.......................................................................................................................................11 2.4.2. GPR Sensitivity and Resolution ..............................................................................................12 2.4.3. GPR Applications in Discontinuity Detection...........................................................................12 2.4.4. Limitations of GPR methods in discontinuity detection............................................................14

2.5. Discussion...........................................................................................................................................15 3. DESCRIPTION OF THE STUDY AREA AND FIELD PROCEDURES .............................................16

3.1. Location of the Study Area .................................................................................................................16 3.2. Geology ..............................................................................................................................................16 3.3. Field Survey........................................................................................................................................18

3.3.1. Scanline Measurements.............................................................................................................18 3.3.2. SSPC Measurements ...............................................................................................................18 3.3.3. 3D Terrestrial Laser Scanning Discontinuity Measurements ....................................................20 3.3.4. GPR Survey: Montemerlo Slope Subsurface Discontinuity Extraction.....................................21

4. 3D TERRESTRIAL LASER SCAN DATA PROCESSING AND ANALY SIS....................................23 4.1. Extraction of discontinuity plane from point cloud data.....................................................................23

4.1.1. Discontinuity Plane Segmentation via Hough Transform .........................................................23 4.1.2. Calculation of planar orientations of segmented point cloud ....................................................24 4.1.3. Discontinuity Set Classification via Fuzzy K-mean clustering..................................................25 4.1.4. Discontinuity Spacing Calculation ............................................................................................27

4.2. Result Analysis and Discussion .........................................................................................................27 4.3. Validation of 3D TLS with Scanline Measurements...........................................................................36 4.4. Conclusion..........................................................................................................................................39

5. GROUND PENETRATING RADAR DATA PROCESSING AND ANALYS IS .................................40 5.1. Methodology.......................................................................................................................................40

5.1.1. Standard GPR Data Processing.................................................................................................41 5.1.2. GPR object-oriented analysis based on Extreme Intensity Change........................................44

5.2. Discontinuity Delineation via GPR 3D Modeling.............................................................................45 5.3. Integration of intensity segmentation with 3D Modelling.................................................................46

5.3.1. 3D Model of V 24- 28 and H15 at slope face 4........................................................................46 5.3.2. Validation of Model V24, H15 with scanline S3 ......................................................................50 5.3.3. 3D Model of V22, V23, H15, H16 in Slope Face 3................................................................51 5.3.4. Validation of V23 with Scanline 4 ............................................................................................52 5.3.5. 3D Model H15-16 and V20-V21 in slope face 2 ......................................................................53 5.3.6. Validation GPR V20-21 and H15 with field observations ........................................................54 5.3.7. Summary of the Validation .......................................................................................................57 5.3.8. Conclusion ................................................................................................................................59

6. SLOPE STABILITY ANALYSIS BASED ON 3D TERRESTRIAL LA SER SCANNING AND GROUND PENETRATING RADAR ................................................................................................................61

6.1. Introduction ........................................................................................................................................61


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6.2. Kinematic and Kinetic Stability of the slope ..................................................................................... 61 6.3. Deterministic approach in Rock Slope Stability Analysis ............................................................... 63 6.4. Probabilistic approach in Rock Slope Stability Analysis................................................................... 63

6.4.1. Probabilistic Rock Slope stability assessment via Monte Carlo Simulation.............................. 64 6.5. Implemenation of Monte Carlo Simulation in Montemerlo Slope Stability ....................................... 65 6.6. RESULTS........................................................................................................................................... 69

6.6.1. Stability analysis of Slope 4 (202/85) ....................................................................................... 69 6.6.2. Stability analysis of Slope 1 (229/80) ....................................................................................... 69

6.7. SSPC Slope Stability Analysis............................................................................................................ 73 6.8. Discussion and Conclusion................................................................................................................. 76

7. CONCLUSION AND RECOMMENDATION ........................................................................................ 77 7.1. Conclusion..........................................................................................................................................77

7.1.1. 3D Terrestrial Laser Scanning Reliability analysis ................................................................... 77 7.1.2. Ground penetrating radar discontinuity measurements ............................................................. 78 7.1.3. Stability Analysis of Montemerlo SLope .................................................................................. 78

7.2. Limitation and Recommendation........................................................................................................ 79 8. REFERENCES............................................................................................................................................. 80 9. APPENDICES ............................................................................................................................................. 87


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List of figures

Figure 1-1 Illustration of the general research methodology ................................................................................4

Figure 2-1 Rock mass geometrical properties of discontinuities .........................................................................5

Figure 2-2 Discontinuity orientation measurement using a geological compass ....................................................6

Figure 2-3 Principle of 3D terrestrial laser scanning data acquisition . ..............................................................8

Figure 2-4 Illustration of 3D TLS orientation bias ................................................................................................9

Figure 2-5 Illustration of the 3D TLS elevation bias. . .......................................................................................10

Figure 2-6 Principle of GPR constant-offset survey for........................................................................................13

Figure 3-1 Geology of Montemerlo Quarry Area and aerial photo of Montemerlo Quarry. ........................17

Figure 3-2 Graphical presentation of roughness parameter used as guide in SSPC field work.............................19

Figure 3-3 Illustration of GPR and Scanline survey. .........................................................................................21

Figure 3-4 Schematic diagram and detail description of GPR measurements.......................................................22

Figure 4-1 Illustration of the vector normal of the plane defined by points..........................................................25

Figure 4-2 Raw ILRIS Optech Point cloud data derived from from 3D ...............................................................28

Figure 4-3 Discontinuity plane extracted via Hough Transform Segmentation. ..................................................29

Figure 4-4 Illustration of the cause of occlusion of various rock faces. ...............................................................31

Figure 4-5 Stereoplot of discontinuity planes with outlier-like in Lambert equa-area stereonet. ........................32

Figure 4-6 Label of outlier-like poles from figure 16 which were further investigated. .......................................33

Figure 4-7 Stereoplot of the same segmented plane after removal of the presumed outliers. ..............................34

Figure 4-8 Stereoplot of segmented plane after fuzzzy K-mean clustering with 3 dcontinuity ets.........................34

Figure 4-9 Illustration of validity indices used to assess the optimum partitioning of pole planes ....................35

Figure 4-10 Comparison of discontinuity orientation derived from 3D TLS and Scanline ..................................39

Figure 5-1 Methodology for GPR Processing.....................................................................................................40

Figure 5-2. Horizontal GPR profile raw data and processed data in slope face 4 ................................................42

Figure 5-3 Raw data and processed vertical GPR profile data acquired along slope face 4 .............................43

Figure 5-4 Binary intensity image of segmented linear-coherent event w/ extreme intensity change ................44

Figure 5-5 Linear coherent features with extreme change in intensity of GPR image ........................................45

Figure 5-6 3D Model of GPR profile image V24-28 and H15 along scanline 4. ................................................47

Figure 5-7 Correlation of vertical GPR measurements, V24-28. .......................................................................49

Figure 5-8 Validation of GPR V24 at scanline 3. ..............................................................................................50

Figure 5-9 3D Model of GPR V22-23 along slope face 3. ................................................................................51

Figure 5-10GPR 3D Model of V23, H15 and H16 . ..............................................................................................52

Figure 5-113D Model of V20,V21, H15 & H16 along scanline 2. ......................................................................53

Figure 5-12 Photo of failing rock block in between slope face 1 and 2. . ...........................................................54

Figure 5-13 Validation of Profile V19 (b) with scanline 2 at slope face 2 (a). ....................................................56

Figure 6-1 Photo a show the current condition of Slope face 1 (229/80) ............................................................61

Figure 6-2. Schematic diagram of wedge..............................................................................................................62

Figure 6-3. Stereonet for deriving coefficients in limit equilibrium computation.................................................62

Figure 6-4 Histogram factor of safety derived from Probabilistic analysis of slope 202/85................................72

Figure 6-5 Histogram factor of safety derived from Probabilistic analysis of slope 229/80................................73


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List of tables

Table 1 Specification and accuracy of Optech Ilris 3D ....................................................................................... 20

Table 2 Statistics of discontinutiy plane model A classified by Fuzzy K-mean Clustering ................................. 32

Table 3 Statistics of discontinuity plane model B and model C classified by Fuzzy K-mean ............................. 32

Table 4 Scanline measurement S-4...................................................................................................................... 51

Table 5. Summary of validation of scanline 4 with GPR measurements .............................................................. 58

Table 6. Summary of validation of scanline 3 with GPR measurements .............................................................. 58

Table 7 Summary of validation of scanline 2 with GPR measurments ................................................................ 59

Table 8 Statistical parameter of discontinuity sets derived from 3D TLS .......................................................... 67

Table 9 Result of Deterministic wedge failure analysis ...................................................................................... 71

Table10 Result of Probabilistic wedge failure analysis ..................................................................................... 71

Table 11. Comparison of SSPC orientation-dependent slope stability analysis based manual field measurements

against SSPC orientation-dependent analysis based on 3D TLS measurements.................................................... 75


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LIST OF SYMBOLS

∇ = divergence operator

E = electric field strength vector oµ = magnetic permeability of free space

σ = conductivity ε = electric permittivity of the material

D = the electric displacement

P = electric polarization rε = dielectric constant

ε o = permittivity in free space.

rθ = dip direction,

β = plunge of poles from the mean normal vector

eχ = electrical susceptibility wγ = unit weight of water

hw = height of groundwater surface

P(θ) = Fisher frequency density function

θ = angular distance from the cluster mean

K = Fisher’s constant

Nw = total weighted size of N observations

Rw = magnitude of the resultant true (mean) vector

rn. = normal vector

Ru = uniform random variable (0-1)

ß1 = random variable dip angle

α1 = trend of pole vector

ßn = plunge of the mean normal vector

αn = trend of the mean normal vector

λ = angle randomly uniform distribution over the interval (0, 2 Π)

Rl, = large scale

Rs = small scale roughness

Im = infill materials,

Ka = karst

Ω = dip angle of the line of intersection between two discontinuities

Φ = dip angles of the upper ground surface

δ = dip of the slope face

ρi = dip directions of the lines of intersection

ρs = dip directions of the slope face

γ = unit weight of the rock

Ψ = unit weight of water

H = total height of the wedge

(τ3) = highest eigenvalue which minimizes the fuzzy objective function

N = the number of poles


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K = number of clusters

D = orthogonal distance of the plane to the origin

Vi = pole cluster centre in a unit sphere

Pj = pole

i = cluster poles

k = centroids of the clusters

Jm = objective function to be minimized in fuzzy K-mean clustering

v = velocity of the electromagnetic energy into the medium,

f = nominal frequency of the GPR used. c = electromagnetic wave propagation velocity in air ( c = 0.3 m/ns).

R = reflection strength of the interface of two medium

E = electric field

θA = angles of friction on planes A

t

E

∂∂

= partial derivative of electric field with respect to time


1

1. INTRODUCTION

1.1. Research Background

Rock mass slope stability analysis is vital in assessing the safe and effective design of an excavated

slope and/or to analyze the equilibrium conditions of a natural slope. This analysis requires the

detailed information on the geometry of the exposed rock face, and definition and analysis of

discontinuity properties of the rock mass because these determine, largely, the mechanical behavior

(Bieniawski 1989). Furthermore, pre-requisite in slope stability analyses is that the internal structure

and the mechanical properties of the soil or rock mass of the slope, are known or can be estimated

with a reasonable degree of certainty (Hack, 2000).

However, traditional discontinuity measurements such as scanline, cell mapping and geologic

structure mapping have several major disadvantages (Priest and Hudson, 1981; Priest, 1993, Hack,

1998). Scanline technique, which is the commonly applied method, is time-consuming, prone to

errors, hazardous and mainly based on surface measurements of rock mass exposures. Orientation bias

in scanline survey as pointed out by Hack (1996), adds to the uncertainty of discontinuity

measurements. Typically, field measurements are performed at the base of the slopes, which exposed

the operator to a potential rock fall of blocks above the slopes or slope failure may occur during the

survey. Further, discontinuities on the upper part of the slope which are beyond the reach of scanline

technique are not measured.

The advent of ground-based remote sensing technology such as 3D Terrestrial Laser scanner (3D

TLS) pave the way for a more accurate, rapid and safe rock mass discontinuity measurements. 3D

TLS can extract very accurate Digital Elevation Model (DEM) of the scanned slope within a few

minutes without being in contact in the slope, thus, avoiding the hazard for the operator. The 3D TLS

raw data can then be process to extract discontinuities of the slope, which in turn can be an input for

slope stability analysis.

Ground penetrating radar (GPR) also plays an important role in discontinuity detection by

understanding the underground propagation of electromagnetic waves (Annan, 2001). GPR is a high

resolution and non-destructive geophysical technique that can provide vital subsurface information of

rock mass discontinuity properties that may not be readily apparent during field measurements or

totally not exposed on the surface of the rock slope.

1.2. Problem Statement

3D terrestrial Laser Scanner (3D TLS) and Ground Penetrating Radar (GPR) plays a significant role

for a more accurate and objective surface and subsurface discontinuity determination. However,

Sturzenegger et al., 2007 have demonstrated that 3D terrestrial laser scanning, though proven to be a

good tool for automatic rock mass discontinuity extraction, also have some limitations due to

occlusion, elevation, and orientation bias. On the other hand, GPR resolution and depth of penetration

Rock mass slope stability analysis based on 3d terrestrial laser scanning and ground penetrating radar

2

depend on the available frequency and electrical properties of subsurface propagation media.

Interpretation of GPR profile is also highly subjective and based primarily on interpreter’s experience

and ability to detect the discontinuity pattern in a radar image.

In view of the above, the combination of 3D Terrestrial Laser Scanning and GPR may be of great help

to compensate for each other’s limitations. GPR can be used to investigate the subsurface extension,

internal state and discontinuity pattern of exposed discontinuities extracted by 3D TLS, thus,

improved the certainty in rock mass characterization, and stability analysis of the rock slope.

1.3. Objective

The main objective of this research is to assess the stability of the volcanic rock slope based on the

discontinuity plane model derived from the 3D terrestrial laser scanning and Ground Penetrating

Radar.

The specific objectives are the following:

• to develop a rock mass discontinuity plane model from 3D terrestrial laser scanning (3D TLS) point cloud data

• to determine its subsurface extensions and orientation using Ground Penetrating Radar • to develop a subsurface discontinuity model based on semi-quantitative detection of

discontinuities from the GPR image. • to validate 3D TLS and GPR discontinuity plane models with scanline field measurements • to conduct deterministic and probabilistic slope stability analysis and compare the results with

the Slope Stability Probability Classification (SSPC) slope stability analysis.

1.4. Research Questions

• What are the factors that affect the reliability of discontinuity plane model derived from 3D TLS survey of the rock slope under investigation?

• Does 3D TLS measurement correlate with scanline measurements? • Is it possible to incorporate an object-oriented discontinuity detection in GPR 3D modelling.

If so, does it improve the interpretation as compared to 3D modelling of a normal GPR image?

• Can GPR detect subsurface discontinuities not detected by 3D TLS measurements • Does probabilistic slope stability analysis based on 3D TLS data gives a better slope stability

assessment as compared with deterministic analysis? • Does Probabilistic analysis give a better assessment of the stability of the slope as compared

with SSPC Analysis.

1.5. Research Hypothesis

1. Occlusion and orientation bias and other field procedural errors can occur during the 3D TLS

survey (Slob, 2005; Sturzenneger, 2007). These errors could have also occurred during the

3D TLS survey conducted on the slope under investigation. Thus, the reliability of 3D TLS

data and the uncertainty involved in its processing should be investigated prior to its

application in slope stability analysis.


3

2. The reflection strength of a rock discontinuity depends mainly on the aperture and the

presence of infill materials (Gregoire, 2001). This will give a distinctive linear, coherent

event, with a high and extreme increase in amplitude as compared to background reflections,

in the GPR image. Thus, this distinctive reflection signature can be used as criteria in

objectively delineating the rock mass discontinuities.

3. Combination of 3D TLS and GPR can provide a better rock mass characterisation as both the

surface and subsurface characteristics of the rock slope are considered. However, possible

uncertainties in the modelling the 3D TLS and GPR data, and variability inherent in

discontinuity properties exist. Thus, a probabilistic approach will give a better assessment of

the stability of the slope.

1.6. Methodology and Thesis Structure

The general methodology implemented in this research is shown in figure 1-1. 3D terrestrial laser

scanning was carried out to assess the stability of the volcanic rock cliff in Montemerlo, Italy. This

was followed by a subsurface investigation of the same rock slope using Ground Penetrating Radar

with 500 MHz monostatic antenna. For the purpose of comparison and validation, SSPC slope

stability analysis and scanline field measurements were also conducted.

The data derived from 3D TLS and GPR were processed separately to obtain a surface and subsurface

discontinuity plane models, respectively. The discontinuity orientation and spacing parameter derived

from the two models were both validated with scanline measurements. Then, the data were used as an

input in the deterministic and probabilistic slope stability analysis. 3D TLS and GPR data were also

applied in SSPC slope stability analysis, which was compared with the SSPC slope stability analysis

based on manual field measurements. The details of the methodology used in slope stability analysis

are discussed in chapter VI.

The thesis is divided into seven chapters. This chapter (Chapter I) provide the general introduction of

the this research. Chapter two deals with the relevant literature about various conventional method of

rock mass characterizations and its limitations. This is followed by a discussion on the fundamentals,

applications, and limitation of 3D TLS and GPR in rock mass discontinuity measurements. Chapter III

gives the description of the study area and the details on the field procedures that were carried out in

the study area as described above. Chapter IV presents the processing and analysis of point cloud data

derived from the 3D TLS laser scanning, which was validated with scanline measurements. Chapter V

deals with the processing of GPR data. This includes detailed explanation on the procedure of the

proposed semi-quantitative linear reflection event detection technique and GPR 3D modelling.

Chapter VI presents the application of discontinuity measurements derived from 3D TLS and GPR in

slope stability analysis. Finally, the conclusion and recommendation are summarized in chapter VII.


4

Figure 1-1 Illustration of the general methodology of this research


5

2. LITERATURE REVIEW

2.1. Introduction

Rock mass discontinuity measurement is a critical initial step in the analysis of the stability of the

slope. Thus, a review is presented on the conventional method of rock mass characterizations and its

limitations. This is followed by a discussion on the application of laser scanning and its limitations in

discontinuity detections. Fundamentals and application of GPR in discontinuity detection is also

presented.

2.2. Traditional Rock Mass Discontinuity Measurements

“Inadequacies in site characterisation of geological data probably present the major impediment

to the design, construction and operation of excavations in rock. Improvements in site

characterisation methodology and techniques, and in the interpretation of the data are of primary

research requirements, not only for large rock caverns, but for all forms of rock engineering."

Brown (1986)

The critical initial step in any rock slope stability analysis is a detailed evaluation of the rock mass

discontinuity properties (Fig 2-1). From this follows the necessity to determine if the orientation of

the existing discontinuity sets could lead to instability. It is therefore of paramount importance, in

both civil engineering and mining applications, to accurately collect and analyze data on the

discontinuities present in a rock mass.

Figure 2-1 Rock mass geometrical Properties of Discontinuities ( Hudson, 1989 )

Traditional method for rock slope assessment such as scanline measurements and cell mapping are

still widely used today. It is conducted using established techniques developed to provide consistent

results under a wide range of conditions (Priest and Hudson, 1981). However, these techniques are

time consuming and are susceptible to human errors. The quality of the data acquired during mapping

depends on a number of factors, in particular: the accuracy of the measurements and the sampling

associated with the measurements (Lanaro, 2001). In Scanline technique discontinuity orientation, dip

direction and dip angle are measured using geological compass and inclinometer (Fig. 2-2). The


6

measuring tape is used to measure spacing and persistence whereas roughness is measured using

roughness profile gauge.

Figure 2-2 Discontinuity orientation measurement using a geological compass with inclinometer for measuring (a) dip direction and (b) dip angle ( after Priest)

In the scanline survey, fracture information is collected along a line at a rock face. Dip and dip

direction are measured on site by a geological compass along scan lines, recording the location of the

measurement point on sketches or images. Scanline surveys provide detailed information on the

individual fractures in each set that can be subsequently statistically analysed. However Scanline

survey has major disadvantages:

• The measurements are subjective because the orientation of discontinuity is initially observed

and interpreted, then, measured in a way depending on the experience and geological

knowledge of personnel doing the measurements. According to Ewan and West (1981), error

in compass measurement due to an operator may be up to 5o for dip angle and 10o for dip

direction. Previous study by Herda (1999) has shown that deviation of strike measurement for

shallow dipping discontinuities can exceed 20o to 30o even if the compass is repeatedly

placed on the same spots that add more to uncertainty.

• Difficulty in gathering a large number of measurements in a short period of time due to its

intensive manual operation. For instance, (i) aligning and levelling the compass; (ii)

determining where the compass can be put in order to obtain the true orientation of the

discontinuities; (iii) taking notes in the field notebook to record measurements are time

consuming (Feng, 2001). Thus, it is difficult to derive enough data for a sound statistical

analysis. ISRM (1978) suggests a minimum of 150 measurements is needed for a sound

statistical analysis.

Cell mapping technique is carried out by selecting a square area on the rock face. All the

discontinuities that fall with in the selected are measured and recorded. According to Priest (1993),

the area should be large as possible so that sampling bias can be minimised. Further, selection of the

area to be measured should be done for at least two rock faces that are perpendicular to each other to


7

minimised or avoid the under sampling of discontinuities that are nearly parallel to the rock face.

However, cell mapping, as in scanline measurement, is also subject to various disadvantages such

measurement or sampling bias.

Measurement bias in cell mapping and scanline techniques for discontinuity characterization have

also been documented (Terzaghi 1965; Priest 1993; Hack 1998). Sources of bias include: (i)

orientation, where discontinuities nearly parallel to the scanline are under-sampled; (ii) censoring,

wherein discontinuities larger than the sampling window are not completely characterized; (iii)

truncation, where discontinuities smaller than a certain size are not included; (iv) length bias where

the probability of sampling persistent discontinuities is greater than the probability of sampling

smaller ones ( Sturzenegger , 2007).

Due to disadvantages in the traditional method for discontinuity measurements, various methods such

digital photogrametry and image processing (Post and Kemeny, 2001), total station (Bulut and

Tudes,1996) and 3D terrestrial Laser scanning (Slob et al., 2002; Turner, 2001; Feng,2001; Lanaro

2001) have emerged. These techniques allow for rock mass characterisation in a semi-automatic or

automatic way without physical contact with the slope. These methods minimised the errors

associated with human bias and increased the amount of information in rock mass characterisation due

to its wider coverage. Further, safety and accessibility related problems are minimised as it can be

done at a distance from the slope (Post et al., 2001). However, this research will investigate more on

the applicability of 3D Terrestrial Laser Scanner in rock mass slope stability analysis.

2.3. 3D Terrestrial Laser Scanning Discontinuity Measurements

2.3.1. Theory and Applications

3D terrestrial laser scanning represents an especially valuable new technology for providing detailed

information on exposed rock faces, which are vital in slope stability analysis (Slob et al., 2005, Hack

& Turner 2002). This new technology is getting more wide attention in geo-engineering community

due to various disadvantages encountered with conventional field survey methods, as discussed above

(Kemeny & Post, 2003).

The principle of 3D Terrestrial Laser scanning is depicted in figure 2-3. Inside the scanner, two

mirrors rapidly and systematically sweep narrow a laser beam pulse along a direction characterized by

lateral (φ) and vertical (α) angles relative to the scanned object. Then, the two-way travel time of the

reflected laser beam is measured to obtain the distance, d. The results are commonly known as “point

cloud,” which is a 3D representation of each reflecting point of the target object with respect to laser

scanner. In this way, the spherical coordinates (d, φ, α), or the Cartesian coordinates (x, y, z), of the

reflecting point are obtained.

Various researches have shown that 3D laser scanning is a promising remote sensing technique to

gather, from a safe distance, highly accurate discontinuity measurements ( Feng et al 2001; Lanaro,

2001; Kemeny & Post, 2003; Slob et al., 2004; Forlani et al., 2004; Monte et al., 2006; Voyat et al.,

2006; and Sturzenegger et al., 2007). Particularly, its wider area coverage, high precision (in


8

millimetre) independent of range or field of view, ease and faster data acquisition gives a significant

advantage as compared to conventional methods.

Figure 2-3 Principle of 3D terrestrial laser scanning data acquisition. 3D TLS generate a laser pulse in the direction defined by angular coordinates φ and α. The distance d of the reflected signal is computed from the two-way travel time . Then, the position (x,y,z,) of the reflector can be derived from the corresponding angular coordinates (d, φ, α.) (after, Galgaro et al., 2005).

Slob et al., 2004 has demonstrated that an automated identification and characterization of rock mass

discontinuity sets can be done from 3D terrestrial laser scan data. The algorithm he developed is

based on point cloud surface reconstruction and Principal Component Analysis segmentation

approach. Vozzelman et al., 2005 have also developed a different segmentation approach via 3D

Hough Transform algorithm. This approach was originally intended for identifying and segmenting

urban structures derived from airborne laser scanning point cloud data. However, it was also found to

be effective in segmenting discontinuity plane derived from 3D terrestrial Laser Scan data and can be

further process and analyse to identify various discontinuity sets.

Rahman (2006) and Tesfamariam (2007) have shown that the discontinuity surface roughness can be

extracted from laser scan point cloud data. Combination of laser scanning and geophysics were also

used by Galgaro, (2006) in landslide detection. Galgaro et al., (2005) was also successful in detecting

landslide movement in Perarolo and Lamosano, Italy by using iterative closest point (ICP) algorithm

on various multi-temporal 3D TLS data. ICP is a mathematical algorithm used to registered multi-

temporal laser scanned images from a original or reference 3D TLS point cloud. Then, this gives a

deviations indicating movement or changes of an object being surveyed. 3D TLS survey using

iterative closest point algorithm and geostatiscal analysis was also applied by Peifer et al., 2005 to

detect the deformation of a lock in the sea entrance dam of the Amsterdam harbor, considering the

noise present in point cloud data.


9

2.3.2. 3D TLS Limitations in Discontinuity Measurements

3D TLS though, offer a great improvement in rock mass discontinuity characterization, also have

some limitations. These limitations are outlined by Sturzenegger et al., (2007) which include the

following: (i) occlusion bias (iii) censoring; (iv) truncation; (ii) orientation bias.

• Occlusion occurs when the part of the rock face is not sampled due to unfavourable positions

of the laser scanner during the survey or some other rock slope features cover the rock face.

The effect of occlusion is that parts of the rock slope are prevented from being imaged and

characterized where important information about the rock slope maybe missed.

• Censoring occur, because a surface appears only partly on a rock face with the part of the

surface hidden within the rock face which result to underestimation of the persistence of

discontinuities.

• Truncation occurs when the exposure of discontinuity is less than the available resolution of

the 3D TLS.

• Orientation bias occurs when the 3D TLS line of site is nearly parallel to the orientation of

the discontinuity, which can happen horizontally and vertically (Figure 2-4 and 2-5). This is

particularly important in cases, when the 3D TLS line of sight is oriented up dip, while the

discontinuities in the slope are dipping towards it (Figure 2-4). Usually, these dipping or

daylighting discontinuities have a great influence in the stability of the slope. Thus, very

important information may not be considered in slope stability analysis if this bias occurred.

Figure 2-4 Illustration of orientation bias where the dipping discontinuities are nearly parallel to 3D TLS line of sight. ( after Sturzenegger et al., 2007).


10

Figure 2-5 Illustration of the Laser Scan elevation bias. a) Rock face showing bedding joints, b) positions of the laser scanner at two different elevation with respect to the rock face, c) stereonet obtained from the upper position, on which bedding joints do not appear, d) stereonet obtained from the lower position showing poles representing the bedding joints (inside the black circle). ( after, Sturzenegger et al., 2007 ).

2.3.3. 3D TLS Data Processing Errors

During the processing and analysis of the raw laser scan data, several errors should be taken into

account. Since several processes and assumptions are involved, it is difficult to quantify the accuracy

of the defined discontinuity characteristics (Slob, 2006). According to Slob 2006, during 3D TLS

survey, the laser scan system will always be susceptible to small errors, which depend upon the 3D

TLS system characteristic parameters, such as the angular accuracy, beam divergence and range

accuracy. Furthermore, noise due to the presence of vegetation, animals or insects and other man

made or natural disturbances can significantly affect the quality of the acquired data. The clustering

algorithm adopted in classifying various discontinuities and the assumption of the distribution such as

Fisher distribution or Bingham distribution may influence the reliability of 3D TLS discontinuity

plane model (Slob, 2006). The data selected for analysis may also result in under-representation and

over-representation of discontinuity sets.

2.4. Ground Penetrating Radar

Rock mass stability is usually assessed based on surface observations, such as slope morphology,

mass fracturing, and/or deformation measurements (Hoek and Bray, 1981). Traditional methods and

3D TLS measurements only provide discontinuities that are exposed on the rock slope. However,

discontinuities that may have a significant effect in the slope stability may not be exposed for surface

measurements. For this reason, geophysical tool such as GPR may significantly improve the slope


11

stability assessment by providing vital subsurface information on the discontinuity characteristics of

the rock slope.

2.4.1. Theory

Ground penetrating radar (GPR) plays an important role in discontinuity detection by understanding

the underground propagation of electromagnetic waves (Annan, 2001). Thus, a brief theoretical

background is herein presented. GPR generates pulse of electromagnetic (EM) energy into the ground

and measures the time between transmission and reception of pulses reflected back to the instrument

(Conyers, 1997). The generated EM wave travels spherically outward through the medium whose

penetration depend mainly on the electric conductivity and dielectric constant of the materials in the

subsurface and on the frequency of the transmission field (Hack 2000). The transmission of

electromagnetic waves in a medium can be described mathematically by evaluating Maxwell’s

equations into the following equation;

2

22 E.

t

E

t

Eo

∂∂+

∂∂=∇ µεσµ (1)

where ∇ is a divergence operator, E is the electric field strength vector,oµ is the magnetic

permeability of free space, σ is the conductivity, ε is the electric permittivity of the material, and

t

E

∂∂

is the partial derivative of electric field with respect to time (Gueguen and Palciauskas, 1994).

The propagation of an electric field to a material results in a local redistribution of bound electrical

charges known as electric polarization. This phenomenon consists of several processes among others:

(i) distortion of the electron shell relative to the atomic nucleus; (ii) relative displacement and

deformation of charged ions; (iii) reorientation of molecules with electric moment (water) in the

direction of the applied field (Gregoire 2001). This effect can be describe by the permittivity ε [F/m]

through the following equation:

PED o += ε (2)

where vector P is the electric polarization, D is the electric displacement, E the electric field

and ε o is the permittivity in free space. According to Gregoire, for most dielectrics, P and E can be

approximated to:

EP

eo

χε

= , )1( eo χεε += (3)

where eχ is the electrical susceptibility, and ε permittivity. Following this equation, dielectric

constant rε can be derived as the ratio of the permittivity of the material and by the permittivity in

the vacuum.

o

rεεε = (4)


12

Generally, the reflection amplitudes are influenced in order of importance by contrasts in dielectric

constant, electrical conductivity, magnetic permeability, dielectric relaxation and magnetic relaxations

(Gregoire, 2001). The amount of energy reflected increases as the difference between dielectric

constants increases (Conyers, 1997). The reflection strength R of the interface of two medium can be

described as:

)(

)(

21

21

εε

εε

+

−=R (5)

where ε1 and ε2 is the dielectric constant of medium 1 and medium 2, respectively. Di-electric constant

also controls the speed of an EM wave in a particular medium, as shown in the following equation:

r

cv

ε=

(6)

where c is the electromagnetic wave propagation velocity in air ( c = 0.3 m/ns).

2.4.2. GPR Sensitivity and Resolution

Sensitivity is the ability of the GPR to detect small discontinuities and is affected by the signal-to-

noise ratio, S/N (Annan, 2001). This ratio is a measure of how well the reflected signal from the

discontinuity can be deduced from the other background reflections. Absolute reflection strength from

discontinuity depends on a number of factors:

• the frequency, bandwidth and efficiency of the GPR antennas (sensitivity generally increases with higher frequency ),

• the inherent noisiness of the medium and, • the reflectivity (R) of the fracture which is dependent on the contrast between its electromagnetic

properties and those of the medium, its size, shape, orientation and location with respect to the incident energy (Rhazi et al., 2004).

The resolution of a GPR system refers to its ability to distinguish between two reflections induced by

two interfaces that are close together within the material. Vertical imaging resolution is usually

considered one-quarter (1/4) of the predominant wavelength (Annan, 2001).

f

v=λ (7)

where v is the velocity of the electromagnetic energy into the medium, and f can be taken as the

nominal frequency of the GPR used.

2.4.3. GPR Applications in Discontinuity Detection

Discontinuity detection with GPR in a given frequency range depends on the aperture and the filling

of the discontinuities, which control the reflection coefficient (Grégoire, 2001). Studies in different

rocks have shown that open and clay- or water-filled discontinuities are clearly visible when using


13

appropriate wavelengths, while closed discontinuities with no filling do not usually appear (Hack,

2000 ).

Di-electric contrast between discontinuity and in-fill (clay) materials may further increase the

resolution. According to Jeannin, et al., (2006), using Annan’s (1996) reflection-coefficient threshold

of 0.1 (considered as a frame of reference) and the thin-layer approximation, one can compute the

maximum detection power of each antenna for low incidence angles in the transverse electric (TE)

mode. In their research, using a mean velocity of 0.12 m/ns for limestone and 0.07 m/ns for the clay

filling, they derived a detection power equals approximately to 0.375 cm for 400 Mhz. Also, experiments conducted by Rhazi et al., 2004 detected a maximum of 0.5 cm thick concrete fracture

(both air-filled and water-filled) at a depth of 3.85 from the surface. Various researches have also

proven the suitability of 500 Mhz GPR for small scale fractures detection (Maerz et al., 2000; Yoon

2002; Martinez et al., 2001; Galgaro, 2004; Jeannin, et al., 2006; Kovin et al., 2006).

Figure 2-6 shows constant offset GPR survey in detecting subsurface discontinuity and how the

geometric orientation of discontinuity

gives a corresponding reflection event

in the in the radargram. Note that the

slope in the radargram corresponding

to the discontinuity in the ground is

not exactly the same (Gregoire, 2001).

On the other hand, the point reflector

with dimensions smaller than the

wavelength of the radar pulse results

in hyperbola in the GPR profile

(Conyers, 1997). The direct airwave

represents the signal propagating from

the transmitting antenna directly to

the receiving antenna.

Figure 2-6 Principle of GPR constant-offset survey for discontinuity detection ( after Gregoire, 2001)

GPR technique has been extensively applied in various fields of discipline particularly in the domain of geo-engineering, which are presented below: Geohazard and Slope Stability Application In slope stability analysis Roch (2005) used GPR for monitoring rock fall hazards and successfully

created with 3D model of subsurface of the slope and assessed the subsurface discontinuities.

Toshioka et al., (1995) mapped cracks in vertical rock faces in tuff using GPR survey. Tsoflias (2004)

conducted vertical fracture detection by exploiting the polarization properties of ground-penetrating

radar signals. Also, Seol et al., (2001) developed a method to find the strike direction from three

different acquisition modes for the same survey line in a granite rock mass. Dussauge-Peisser et al.


14

(2003) combined GPR measurements and seismic tomography in a 12 m high limestone cliff.

Pettinelli et al. (1996) have conducted GPR investigation and successfully estimated the depth of the

deformational structures induced by the instability phenomena in regularly stratified limestones.

Rashed et al., 2003 has used GPR in imaging a fault zone.

Mining and Quarry Application Further, several studies have shown the suitability of GPR in discontinuity detection for mining and

quarry operation (Porsani et al., 2006; da Silva et al, 2003; Orlando, 2002; Abraham et al., 2000;

Grasmueck ,1996; Grandjean and Gourry 1996; Stevens 1995). Particularly, the combination of GPR

and seismic tomography was used in a gypsum quarry to localize cracks and damage areas inside

pillars (Abraham et al., 2000). Orlando (2002) was able to produce a synthetic map of rock quality

(degree of fracturing) by calculating the square of sample amplitude of real trace and computing the

mean energy of the rock cell in the radargram. However, the spacing and actual orientation of the

discontinuity are not determined. GPR was also used in evaluation of tunnel stability and mining

induced blast fracture detection (Cardarelli, 2002; Grodner, 2001). Porsani et al., (2006) applied GPR

for mapping fractures and optimizing the extraction of ornamental granite from a quarry.

2.4.4. Limitations of GPR methods in discontinuity detection

Major limitation of GPR in discontinuity detection is its limited resolution and depth of penetration,

which are both dependent on the frequency and properties of the media. Further, the interpretation of

GPR image is still subjective and based primarily on the interpreter’s ability to recognize patterns in a

radar image. Because of these limitations, various object-oriented analysis of GPR data have emerged

to minimized the subjectivity in GPR interpretation (Moysey, 2006; Milisavljevi, 2001; Dell’Acqua,

2003 Thuene et al., 2005). Dell’Acqua (2003) effectively detects linear objects in GPR data using 2D

and 3D Hough Transform mathematical algorithm. Thuene et al., (2005) applied generalised image

deconvolution and Radon Transform algorithm to decomposed dipping discontinuity from a noisy

GPR data.

Another limitation of GPR technique is that noise and interference may masks the reflection of

interest in a GPR image, which may also lead to interpretation pit falls. Thus, it is important to be able

distinguished real reflections from noise or interference. Noise is any unwanted signal generated

within the system while interference is a signal originating from a target or some external source.

According to Conyers (1997), radar clutter, mix of reflections from numerous targets, can be also

considered noise as well. Commonly encountered noise and interference in GPR image are: (i)

multiple reflections from layers; (ii)system and background "noise" (iii) antenna coupling; (iii)

horizontal ringing bands in the linescan display (Conyers, 1997);

Particularly, ringing noise caused by the difference in the impedance of the GPR antennae and the

medium may be interpreted as discontinuities in the GPR image (Radzevicius et al., 2000). Several

studies have shown that linear noise features like ringing can be removed by standard 2D Fourier

transform (f-k) methods (Grasmueck, 1996; Young and Sun, 1999). Nuzzo (2003) also showed that

Radon Transform (RT) filtering technique can be used to remove horizontal layer banding noise in the

GPR image.


15

2.5. Discussion

3D TLS provide great advantages in discontinuity characterization as compared to traditional field

measurement technique. However, errors in surveying and processing have been documented. The

success of 3D TLS survey also depends on how well the rock mass discontinuities are exposed or

whether the surrounding area is favourable to perform the appropriate procedures to minimised the

measurement bias. The question that needs to be address in this study is whether these errors and

limitations also occurred during the 3D TLS survey of Montermerlo slope. If so, what slope stability

approach should be adopted to take into account or to minimize these limitations.

In GPR, processing various applications has been done in discontinuity detection, but one of its main

drawbacks is the subjectivity in the interpretation of the radargram. Noise and interference also adds

problem in the interpretation of GPR image. Further, the three-dimensional spherical propagation of

EM waves through the medium implies that the reflection event in the image come from different

reflection directions around its path. This may lead to falls interpretation of the geometrical

orientation of reflection events in the radargram. Thus, these issues should be taken into consideration

in the interpretation of GPR image.


16

3. DESCRIPTION OF THE STUDY AREA AND FIELD PROCEDURES

3.1. Location of the Study Area

Montemerlo Quarry is located in Colli Euganei, the Veneto region of northern Italy. The topography

of Colli Euganei is mountainous that resulted from volcanic eruptions that took place during the

Advance Eocene. The topography is mountainous compared to flat lying area of Padova 14.0 km

northeast. The quarry operations have been going on since the time of the ancient Rome. It was used

for road construction and other infrastructure during that time but also up to date. The slope under

study has a height of 20 meters. The climate in the Colli Euganei, is characterized by dry and hot

summers (temperature ranges from 6 to 28 °C) with moderate winters (-2 to 17 °C). Average

precipitation in the area ranges from 56 to 89 mm.

3.2. Geology

The geology of the area is characterized by mountainous terrain of volcanic origin. In the Tertiary,

extensive mafic volcanism took place in the South-Eastern Alps, along a half-graben structure

bounded by the Schio-Vicenza main fault (Gasperini et al., 2002). This magmatism resulted to four

main volcanic centers; Lessini, Berici, Marostica and Euganei where the Montemerlo Quarry is

situated (Gasperini et al., 2002).

The eruptive activity in the Euganea area begins in the Advanced Eocene, characterized from the

intrusion of basaltic lava until lower Oligocene. Particularly, Montemerlo quarry is predominantly

composed of grey colored trachitic igneous rocks formed indicatively during Oligocene about 33-35

million years ago. Trachyte is an igneous, volcanic rock with an aphanitic to porphyritic texture.

Mineral assemblage is usually, potassium feldspar and plagioclase (in a ratio > 1:4).

Various geologic features can be recognized that described the relationship of magmatic cliff and the

sedimentary cliff in the study area. One of which is the lacolithic structures where the magmatic

bodies are concordant to the sedimentary beds. This geologic structure is the result of magmatic

intrusion into the interfaces of the sedimentary beds that also resulted into contact metamorphism

(Gradizzi, 2005). On the other hand, various discordant structures can be also recognized in the area,

in which case the magma cut across the sedimentary beds.

According to Gradizzi (2005), the contact between the trachite and the host sedimentary rocks appears

to be the concordant. The main tectonic elements that are relevant to the area of Euganea have

direction NNW-SSE and NE-SW, which can be correlated with the Schio-Vi Fault and the Fault of the

Coast of the Berici few kilometers in the south (Gradizzi, 2005). In particular, the prevailing

structures in the area have following directions: N-S, NW-SE, E-W.


17

Figure 3-1 Geology of Montemerlo Quarry Area ( source: Padova University) and aerial photo (source :Google earth) of Montemerlo Quarry. Below right is the 20 m. high rock slope where the 3D TLS survey and GPR measurement were conducted.

Montemerlo, Colli Euganei

14.0 km to Padova

Map of North Italy

Geologic Map of Montemerlo, Colli Euganei, Italy

Slope face- 1

Slope face- 2 Slope face-3

Slope face 4


18

The trachite rock mass of Montemerlo is characterized columnar fracture as a result of cooling and

consequent contraction of the magma. The trachite rock is massive and grey in color. The rock mass

of the quarry consists of various families of joints, resulting to a prismatic shape of the rock mass

blocks. Gradizzi (2005) classified rock mass blocks into two types: parallelepiped shape with a side of

equal length to two meters and the others two of approximately 1 meter; and columnar shape with

quadrangular base and a height ranging 5-8 m.

Geomechanical characterization conducted by Gradizzi, 2005, identified four main fracture system

in the rock face 4: K1 System N 195-75°/80°; K2 system, N 295-86°, N 95-75°/78° and N 70-86°, K2

SYSTEM min: N 290-70°/75° and N 290-65° (superficial of cut), K2 SYSTEM min: N 285-18°

(surface of cut), K3 SYSTEM: N 140-20°/40°; K4 SYSTEM: N 55-45°. Her study also shows that

most of the discontinuity has varying aperture thickness ranging from 1 to 5 cm thick with no in fill

materials. However, during the site visit some discontinuities exhibit an indication of washed clayey

materials.

3.3. Field Survey

3.3.1. Scanline Measurements

Four continuous horizontal scanline measurements, were conducted along the four rock faces in

Montemerlo Quarry. Measuring tape was placed horizontally on the four rock face under investigation

which constitutes the scanline. For every discontinuity that intersected the scanline, the intersection

distance, dip direction, dip, persistence along strike and dip, in fill materials and roughness were

recorded. Fracture near below and above the scanline were projected crossing the scanline. All of the

fracture data collected in the field was entered on a scanline survey logging form (see appendix 5).

Trace discontinuities were projected out of the slope face by aligning a flat wooden field board to

measure its dip direction and dip angle. The trace discontinuity is first observed and interpreted by the

one person relatively far from the slope.

3.3.2. SSPC Measurements

For comparison and validation purposes, the Slope Stability Probability Classification (SSPC) System

rock mass characterization developed by Hack (1995) was used to assess the stability of the slope.

SSPC is a rock mass classification system1 based on a three-step approach and on the

probabilistic assessment of independently different failure mechanisms in a slope (Hack,

1995). First, the exposed rock mass (exposure rock mass) is characterised and corrected for

weathering and excavation disturbance; to derive the parameters critical to geomechanical

behaviour of the slope in its imaginary unweathered and undisturbed state (reference rock mass). Then the design slope (slope rock mass) is assessed based on the derived reference rock mass

1 Rock mass classification system is an slope stability approach which basically conducted by giving a numerical value and

weight to each established parameters critical to slope instability. Depending on the classification system used, this will result

in a final rating which can be related to stability or probability of failure of the slope.


19

parameter, taking into consideration both the method of excavation and future weathering the slope

will be subjected to.

In the SSPC system, the shear strength parameter of a discontinuity is established by the sliding

criterion that converts a visual and tactile (roughness established by touch) characterization of a

discontinuity into an apparent friction angle along the discontinuity plane (Hack and Price 1995).

During field work, graphical representation of roughness parameter were used as guide to established

the roughness parameters of the representative discontinuity as shown in figure 3-2a,b&c. The intact

rock strength is measured by simple method of hammer blows. This seems to be subjective, however,

extensive study by Hack (1998) shows that this simple field tests are at least comparable to the quality

of the results obtained by laboratory UCS tests. Detail of terms and procedure in discontinuity

characterization are provided in the SSPC field form used during fieldwork (see appendix 7a, SSPC

field form).

Figure 3-2 Graphical presentation of roughness parameter used as guide in SSPC field work (after, Hack, 1998)

b. Large-scale roughness

a. Small-scale roughness

c. Interpretation of roughness as function

of amplitude and wavelength


20

3.3.3. 3D Terrestrial Laser Scanning Discontinuity Measurements

3D terrestrial laser scan survey, dated 9/12/2007 was conducted on the abovementioned slope

covering a rock face area of about 30 x 20 m. The measurement was conducted using Optech ILRIS-

3D laser scanner. Optech ILRIS-3D has a scanning capability at a maximum range of 1500 meters,

however, 800 meters has been found to be a typical practical limit for scanning of rock slopes

(Sturzenegger, 2007). The scanning rate is about 2000 points/second with specified range and

positional accuracies of about of 7 mm at specified range of 50 meters. Angular scanning resolutions

are in the order of 0.17 mrad and allow for a very high sampling density on the rock face in relatively

short acquisition times. This results in millions of points known as “point cloud”, which is a three

dimensional (X,Y,Z) representation of the scan rock slope with respect to the laser scanner. Table 1

shows the details of the Optech ILRIS3D specifications.

Two measurements were made: first measurements is about 17 meters from the bottom of Slope

4 (dip direction, 205 degrees); second measurements were conducted 42 meters away from slope

face 1 (229/80). To determine the orientation parameters of the discontinuity the point cloud has to

be reorient relative to the true north and ensure that the data are levelled (Slob et al. 2005). Since the

true north is not indicated in the coordinate of Optech ILRIS system, the two measurements were

merged and geo-referenced in WGS 1984 projection within Polyworks 9 software environment.

Table 1 Specification and accuracy of the Optech ILRIS 3D Terrestrial Laser Scan


21

3.3.4. GPR Survey: Montemerlo Slope Subsurface Discontinuity Extraction

The GPR system used in this field survey was a Geophysical Survey Systems, Inc. Model with

monostatic 500 Mhz frequency shielded antenna. Monostatic GPR consists of built-in integrated

transmitter and receiver antenna. The transmitter produces a short duration, high voltage pulse applied

to the transmitter antenna, which in turn radiates an electromagnetic signal into the ground. The

reflected signal travels back to the receiver antenna and recorded as an amplitude trace. The antenna

was dragged in continuous recording mode along the cliff following the horizontally orientation of the

scanline measurements. Several vertical GPR measurements are also undertaken along the four rock

face.

The GPR survey consists of 12 vertical measurements, V17-28 and 3 horizontal measurements H14-

16. Horizontal GPR H14 and H16 were conducted along the orientation and entire length of the

scanline whereas H16 was conducted 1.0 meter below it. H14 was carried out with two-way travel

time setting of 60 ns per 512 samples per scan, whereas H15&16 was set to a 100 ns per 512 samples.

Horizontal measurements were conducted with the addition of markers every 1.0 m during data

acquisition. This marker where later on used to estimate the position of vertical measurements across

the horizontal measurements.

Figure 3-3 Shows the GPR vertical (blue) and horizontal (green) survey. Also shown is the horizontal scan line measurement S1-4 (pink). GPR equipment used (Top left) and rock slab used in the time-velocity calibration

For propagation velocity determination, the available GPR equipment is not suitable for common

depth point measurement. However, a 1.2 maters thick detached rock slab from the same slope under

V-28 V-17 V-24 V-25 V-26 V-27

V-23 V-22

V-20 V-21 V-18 V-19

S-1 S-2 S-3 S-4

H-15

H-16 Calibration Rock Slab

1.2 m

Control unit / monitor


22

study was used to calibrate the two-way travel time of the reflection events. This led to approximate

estimation of depth of penetration and for time-depth conversion in subsequent processing.

Figure 3-4 Schematic diagram and detail description of horizontal and vertical GPR measurements.

(Note: file numbers refer to radargram acquired from the GPR survey)


23

4. 3D TERRESTRIAL LASER SCAN DATA PROCESSING AND ANALYSIS

This chapter presents the processing and analysis of point cloud data derived from the laser scan

survey of Montemerlo slope. The analysis will attempt to determine whether the limitations and errors

in 3D Terrestrial Laser Scanning (3D TLS) in rock mass characterization as discussed in Section 3.2.2

occurred in this particular laser scan survey. Establishing these limitations is vital as it have

significant implications on the reliability of slope stability analysis, once the parameters derived from

this method are used. In the last part, the results of laser scan data processing are validated against the

traditional scanline survey.

4.1. Extraction of discontinuity plane from point cloud data

Various methods have been developed to detect discontinuity plane from point cloud data such as

surface reconstruction (Slob et al., 2002;), semi-automated approach (Feng and Roshoff, 2004) and

automatic discontinuity extraction via segmentation (Slob et al., 2002, Vosselman, 2005). Two

mathematical algorithms are currently available that can be used to automatically segment

discontinuity planes in point cloud data: (i) Principal Component Analysis (Slob et al., 2002); and (ii)

Hough Transform (Vosselman, 2005). Both methods give equally successful results, however due to

its faster processing capability, the Hough Transform algorithm was adopted in this study as discussed

below.

4.1.1. Discontinuity Plane Segmentation via Hough Transform

The segmentation of discontinuity plane from point cloud data is implemented with in the Point Cloud

Mapper (PCM) software environment (Vosselman, 2004). The algorithm starts with the selection of a

seed surface, which refers to neighbouring points that fit well to a plane. The mathematical technique

used to detect the seed surface is the 3D Hough transform algorithm.

The 3D Hough transform (HT) was originally developed as a tool for detecting lines in 2D images.

However, Vosselman (2005) has developed extension of this algorithm in segmenting plane in point

cloud data. Every non-vertical plane in Euclidian space can be represented by the equation:

dsyYsxXZ ++= ( 8 )

where sx and sy are the slope of the plane along the x- and y-axis respectively and d is the normal

distance of the plane to the origin. These plane parameters (sx, sy, d) defined the Hough parameter

space. Thus, every plane in the Euclidian space can be represented by a point (sx, sy, d) in Hough

space. Geometrically, an infinite number of planes can pass through a single point of the plane. If that

point has coordinates (x0, y0, Z0) in Euclidian space, all the planes that go through it obey equation 8.

From this, it follows that all the points that lies on the same plane in the Euclidian space corresponds

to a unique point in Hough space.


24

To detect a plane in the point cloud, all points are mapped to planes in the Hough parameter space. All

the points that belong on the same plane in Euclidian space have a unique plane equation, represented

by a point in the Hough space. Thus, the number of times the plane intersects a point in the Hough

space is equal to the number of points that belong to it defined by that equation. From this, the point

or bin in Hough space will be incremented equal to the number of points that belong to it in Euclidian

space. Thus, after all planes have been mapped to the Hough parameter space, a counter represents the

accumulation of number of points that belong to their respective unique plane. The coordinates of the

bin with the highest accumulation represent the plane with the highest amount of points of the point

cloud.

After detecting the seed surface, the next step is to grow the seed surface. To do this, Pu and

Vosselman (2005) outlines the following criteria:

• Proximity of points. Only points within certain distance of a seed surface can be considered to this seed surface as some point may be co-planar to discontinuity plane but actually belong to different discontinuity plane from farther area.

• Only groups greater than a specified number of point should be considered as possible discontinuity surface.

• Points can only be added if the perpendicular distance to the plane is below a certain threshold. The fitness of these points in the plane is quantified by analyzing its residual through least square sum method. The points in the plane are considered a seed surface if the square sum is below a specified threshold.

• The numbers of seeds, the surface growing radius, the maximum distance between surfaces are also the parameters that need to be specified.

After segmenting the discontinuity plane, further processing are performed to compute the orientation

of segmented discontinuity plane and classify each extracted discontinuities into their corresponding

discontinuity sets. The segmented discontinuity planes are exported into matlab environment and

processed using matlab code developed by S. Slob (2006), which can performed the following

operation as discussed below:

4.1.2. Calculation of planar orientations of segmented point cloud

After the segmentation, the orientation of the plane that represents the points needs to be computed

for subsequent processing. A minimum of three points can defined a plane through the following

equation:

0=+++ dczbyax (8)

where d is the orthogonal distance of the plane to the origin while a, b and c are the parameter of

the normal vector, n to the plane, as illustrated below (Fig. 4-1):


25

Figure 4-1 Illustration of the vector normal of the plane defined by points

For instance, if the plane is defined by the coordinates of three points P1 (x1, y1, z1), P2 (x2, y2, z2)

and P3 (x3, y3, z3), the parameters a, b, c and d can be derived by determining the normal, n to the

plane by calculating the cross product of two vectors of the three points. This will lead to the

following equation:

−−−−−−−−−−

−−−−=

=−

)).(()).((

)).(()).((

)()).((

13131312

13121313

13).(121312

xxyyyyxx

zzxxxxzz

yyzzzzyy

c

b

a

n (9)

After finding the parameters a, b and c, the normal the dip angle, θ and dip direction, β of the plane

in degrees can be defined by the following equation:

c1cos−=θ (10)

+= −

22

1cosba

bβ (11)

However, dip directionβ in equation 11 is computed with respect to the quadrant it falls in Cartesian

space, thus, the resulting value only range from 0-90o, instead of 0-360o convention in geologic

compass. To establish the right directions consistent with convention of dip direction used in geologic

compass (azimuth direction), the quadrant where it belongs should be determined. This is indicated by

the sign (+-) of parameters a and b in equation 11.If it is in quadrant I (between 0o-90o) the true dip

direction 'β is equal toβ , whereas if it falls in quadrant II (90o- 180o), 'β is equal to 180 -β . . If it

falls in quadrant III (180-270), 'β is equal to 180+β , whereas if it falls to quadrant IV (270-360), 'β is equal to 360-β .

4.1.3. Discontinuity Set Classification via Fuzzy K-mean clustering

P1

P2

P3


26

After establishing the orientation of the segmented planes, it is further classified into their

corresponding discontinuity sets using the Fuzzy K-mean clustering. It starts by visually establishing

the number of sets in the plotted normal plots of all segmented discontinuity planes. This can also be

done objectively by using various validity indices as proposed of by Hammah and Curran (2000).

Fuzzy k-means clustering implement the classification based on the degrees of membership assigned

to each set, which range from 0 to1. The likelihood that a certain discontinuity pole belongs to a set is

indicated as its membership value is getting near to one. The fuzzy k-means clustering method

implemented in matlab script was improved by Slob (2006), but based mainly on the method proposed

by Hammah and Curran (2000).

According to Hammah and Curran (2000), to optimize the classification of discontinuity pole data, the

following objective function (Jm) should be minimized:

),()( 2

11ij

mij

K

i

N

jm VPduJ ∑∑

−==

(12)

where N is the number of poles; K is the number of clusters; d2(Pj, Vi) is the distance between pole

Pj and the pole cluster centre Vi in a unit sphere (defined by sine of the angle between them) which

can be used as dissimilarity criteria express as 22 )(1),( ijij VPVPd −= (14); uij is the degree of

membership of data point (pole) Pj to cluster i, which is a function of the distances between this pole

and the different centroids of the k clusters (Hammah and Curran, 2000):

[ ][ ]∑

=

−

−

=K

k

m

m

VkPjd

ViPjduij

1

11

2

11

2

,(/1

,(/1 (15)

where m is a weighting parameter that determine the degree of fuzziness of the memberships.

It can be assessed from the equation 15 that as m gets near to one, the membership values also

gets harder (Hammah & Curran, 2000).

Principal Component Analysis (PCA) is the mathematical technique used to find the cluster center. In

implementing this method, it is assumed that the pole dispersion exhibits a Fisher’s distribution: that

is the pole exhibit circular distribution about the mean orientation per discontinuity set. Following the

method of Hammah and Curran (2000), the mean orientation of a cluster can be calculated by

determining the eigenvalues (τ1, τ2, τ3) of the covariance matrix and their corresponding eigenvectors

( 1 2 3ˆ ˆ ˆ, ,ξ ξ ξ ) as express in the following weighted orientation matrix (covariance matrix) S:

1 1 1

1 1 1

1 1 1

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

N N Nm m m

ij j j ij j j ij j jj j j

N N Nm m m


N N Nm m m


u x x u x y u x z

S u x y u y y u y z

u x z u y z u z z

= = =

= = =

= = =

=

∑ ∑ ∑

∑ ∑ ∑

∑ ∑ ∑

(14)


27

where N is the number of direction cosines (xj, yj, zj). The eigenvector 3ξ is related with the highest eigenvalue (τ3) which minimizes the fuzzy objective function. Thus, the mean vector of the group of N unit normal poles is defined by 3ξ .

The eigenvalues derived from the analysis, quantify the spread of the cluster: the higher the ratioτ2 /τ1

the higher the spread. On the other hand, if the ratioτ2 /τ1 is equal or near to 1, it imply that the cluster

exhibit circular pattern which is indicative of Fisher’s distribution. These now can be used as a

criteria to partitioned cluster by rejecting measurements that cause larger variance or spread. Thus, a

better reclassification into discontinuity data is made.

The matlab script developed by Slob (2007) which is used in this study iteratively performed the

process discussed above until difference between the previous and new degree of membership is less

than a specific threshold set by the user.

4.1.4. Discontinuity Spacing Calculation

Now that the mean orientation of the discontinuity sets is established, and the equation of every plane

is defined, the normal mean spacing of each discontinuity set can be computed by mathematically

setting a virtual scanline normal to the established mean orientation of each set. The intersection

distances between the succeeding individual discontinuities that belong to a particular discontinuity

set, traversed by the virtual scanline, are computed and averaged.

4.2. Result Analysis and Discussion The result of discontinuity extraction from Optech ILRIS point cloud data (Fig. 4-2) derived from the

3D terrestrial laser scan survey is depicted in figure 4-3. The segmentation outlined well the face and

edge of major rock mass discontinuities. It also detected some of the trace discontinuity-like features,

which will be validated with scanline measurements in the next section. However, several outliers are

present due to vegetation or loose slope material and naturally and/or blasting induced fractured rock

mass. Slob, 2006 pointed out that these noises will affect the resulting statistics of the discontinuity

set such as the mean orientation and spacing which will be verified in this study.

Outlier removal performed in this data is based mainly on the interpretation of plots of discontinuity

sets and visual observation of the results of the segmentation. The outliers are taken into account by

rejecting those segmented planes with points less than a specified threshold. This is done in several

trials by increasing the threshold until a realistic result is achieved. However, one must be aware that

some small, segmented plane that could be a small exposure of an actual discontinuity may be

included in the removal. After several trials, a threshold of 600 point is found to be appropriate, after

which only 160 planes are left from 493 original segmented planes. This was validated by exhaustive

one by one visual inspection of all 493 segmented individual planes in Deep Exploration software and

removing all those segmented plane identified to be an obvious outliers. After the manual visual

removal of outliers, which resulted in 160 planes left, the model appears to represent the slope well.


28

Various occlusion zones are also identified, which are part of the rock face that are not sampled by 3D

terrestrial laser scan survey. Figure 4-4 illustrates the reason behind these occlusion zones. As shown,

occlusion zone a, comprised a discontinuity face whose orientation is nearly parallel with the line of

sight of the 3D TLS, thus, it was not sampled during the survey. Note that actual position of 3D TLS

in figure 4-4 is a little bit farther to the right, but for the purpose of illustration, it is placed as shown.

Further, some of the rock faces are covered by other discontinuities, which were also not sampled.

During the fieldwork, it was observed that most of the rock face along scanline 1 is irregular with

some indication of blasting relics. Based on the photos of G. Teza, blasting technique was applied in

the excavation of some part of the slope, which may have included the area along scanline 1. Note,

that this irregular plane was also segmented in the point cloud, which if not taken into account will

give some spurious effect on the result of orientation parameter statistics. This is because its

orientation does not represent the actual orientation of the existing discontinuity in the slope.

Figure 4-2Raw ILRIS Optech Point cloud data derived from from 3D TLS survey at Montemerlo slope

RO

CK

MA

SS

SLO

PE

ST

AB

ILIT

Y A

NA

LYS

IS

BA

SE

D O

N 3

D T

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RE

ST

RIA

L LA

SE

R S

CA

NN

ING

AN

D G

RO

UN

D P

EN

ET

RA

TIN

G R

AD

AR

29

F

igur

e 4-

3. D

isco

ntin

uity

pla

ne e

xtra

cted

via

Hou

gh T

rans

form

Seg

men

tatio

n. V

ario

us o

cclu

sion

zon

e ar

e id

entif

ied

and

outli

ers

at t

he u

pper

slo

pe.

Als

o

show

n on

the

upp

er r

ight

is a

line

ar s

egm

ente

d pl

ane

(A)

whi

ch c

orre

spon

ds t

o a

dete

cted

tra

ce d

isco

ntin

uity

.

occl

usio

n

A

Pro

babl

e bl

aste

d Z

one

Pro

babl

e fa

iling

ro

ck b

lock

Roc

k m

ass

slop

e st

abili

ty a

naly

sis

bas

ed o

n 3d

terr

estr

ial l

aser

sca

nnin

g an

d gr

ound

pen

etra

ting

rada

r

30


31

Figure 4-4 Illustration of the cause of occlusion of various rock faces. Note that orientations of occluded discontinuities are almost parallel to the 3D TLS line of sight 1. Occlusion b is parallel with 3D TLS line of sight 2 while occlusion c is covered by other rock face thus not sampled by 3D TLS 2. Trace discontinuities D48&D51also have small exposure at the top of the slope which may or may not exactly represent its actual orientation.

Near the blasted zone, a failing rock mass is visible which can be also related to blasting. Apparently,

this has been outline well after the segmentation process. The orientation of this probable failing rock

mass is found to be 199.98/76.06 whereas the slope where it belongs, slope face 2, has an orientation

of 201.43/83. This again shows how a deformed part of certain discontinuity may affect the actual

mean orientation of particular discontinuity.

The segmented discontinuities are further classified to their corresponding discontinuity sets.

Initially, four discontinuity sets are identified as shown in figure 4-5. The entire stereoplot of

segmented planes have number of points greater than 600, which are significantly bigger than the

obvious outliers. Despite the threshold set, scattered outlier-like, low dipping poles that deviate

significantly from their cluster mean center are still visible. Whether these are really an outlier or not

will be investigated further. However, if it is assumed that these poles are outliers, its removal

significantly affect the resulting clustering and its statistics as shown in figure 4-7.

However, some of these outlier-like features may be an actual discontinuity sets that are under-

sampled due to orientation and occlusion bias. Thus, removing it might aggravate the effect of

orientation bias, which adds uncertainty in the reliability of the resulting discontinuity orientation

D51

3D TLS line sight 1

Occlusion Zone

3D TLS line of sight 2

D48

a

b c

Probable Blasted Zone

Probable Failing Rockmass

d Trace

discontinuity


32

statistics. On the other hand, it may also be a natural or blasting induced fracture which if not

removed may give spurious effect on the resulting discontinuity parameters. Thus, as pointed out by

Slob (2006) the process of outlier removal is intuitive and based largely on the interpretation and

engineering judgment of the user. However, this also makes the processing susceptible to error

especially for user with less experience in rock mass characterization.

Table 2 Statistics of discontinutiy plane model A classified by Fuzzy K-mean Clustering

Figure 4-5. The orientations of the 160 individual planes extracted from point cloud data after the segmentation are plotted in the stereonet (3D TLS Model A). Various poles of the planes are clustered with Fuzzy k-means clustering. Four discontinuity sets are identified. Above it are the statistics of the identified sets which include: mean dip and dip direction and Fisher’s K value and mean normal set spacing. (Note: the projection used is Lambert equal-area in the lower hemisphere)

In view of the above, the outlier-like poles in figure 4-5 are further investigated. Each poles are

labelled according to their plane ID in the segmentation results (see appendix 3) as shown in figure 4-

5. Scattered poles 90, 106 and 400 are small planes found just below occlusion zone a associated with

highly fractured rock face. Pole 275 is a plane also near to a fractured zone just below the occlusion

Disc. Sets Set 1 Set 2 Set3 Set 4

Dip 80.46 47.79 78.51 79.58

Dipdir 254.22 247.99 205.44 295.57

K 42.19 15.93 23.04 15.53

mean N spa 0.5162 0.57772 0.3842 1.2352

stdev N spa 0.952 0.98826 0.7507 1.95035

max N spa 5.2983 5.29622 4.2779 9.99675

3D TLS Model A


33

zone a. Outlier-like poles 38 and 39

are actually a big plane associated

with a low dipping discontinuity.

Pole 120 is a big plane at the top of

slope face 3. Pole 23 is big plane

above the blasting zone in slope

face 1. Pole 180 and 148 is a big

plane at the bottom of slope face 4,

which are associated with an

irregular plane surface. Pole 71 and

76 is also a small, segmented plane

near a highly fractured zone below

occlusion zone a. Pole 16 and 145

are elongated trace-like features

both found in slope face 4. Pole 27

is a relatively big plane on the upper

side of the blasting zone. Pole 367 is

a big plane below occlusion zone a.

Pole 198 is linear trace-like (yellow)

features in slope face 4. At this

moment it is difficult to establish with certainty whether these poles are really an outlier or not.

Based on the above observations, the highly fractured rocks below occlusion zone a are composed of

various segmented planes that significantly contribute to the scattering of plotted poles. Blasting may

have also contributed to the scattered plot but there is no clear evidence to support this conclusion.

With this, it cannot be established with certainty whether these features are actual outliers or not as

this scattering may also be attributed to natural variation of the orientation of discontinuities.

However, if one decide to consider these planes as an outliers the corresponding discontinuity

statistics and orientation give significantly different results as shown in table 5a. Visually, it is also

possible that three (3) discontinuity sets may exist on the same plotted plane poles presented above. If

this interpretation is adopted, the resulting discontinuity orientation statistics and spacing also differ

significantly from previous clustering (based on 4 discontinuity set), as shown in table 5b.

Table3 Statistics of discontinuity plane model B (a) and model C (b) classified by Fuzzy K-mean clustering after the removal outlier-like features in discontinuity plane Model A . This shows how the numbering of cluster affects the discontinuity statistics. The corresponding stereoplot of discontinuity plane model B and C are shown in figure 4-7 and figure 4-8, respectively.

Disc. Sets Set 1 Set 2 Set3 Set 4

Dip 65.86 80.83 79.5 80.81

Dipdir 259.55 238.08 204.09 293.6

K 23.61 50.79 36.18 16.54

mean N spa 0.511 0.285 0.403 1.208

stdev N spa 0.803 0.527 0.769 2.023

max N spa 4.271 2.735 4.176 10.491

Disc. Sets Set1 Set2 Set3

Dip 70.19 79.84 78.06

Dipdir 251.35 206.49 288.94

K 36.18 23.61 50.79

mean N spa 0.317 0.362 0.971

stdev N spa 0.576 0.695 1.624

max N spa 4.216 3.913 8.988

a) b)

Figure 4-6. Label of outlier-like poles from 3D TLS Model A which were further investigated.


34

Figure 4-6 Stereoplots of poles of the same segmented plane after removal of the presumed outliers . Note that the orientation of the mean significantly change from discontinuity plane model A. ( Note that the projection used is Lambert equal-area in the low hemisphere)

Figure 4-7 Stereoplot of the same segmented discontinuity plane after fuzzzy K-mean clustering with 3 discontinuity sets (3D TLS model C).

3D TLS Model B

3D TLS Model C


35

Various validity indices (Gath and Geva, 1989; Xie and Beni, 1991; Fukuyama and Sugeno, 1989)

were used as a guide to assess the optimum of number of cluster in the discontinuity polar plot as

suggested by Hammah and Curran (2000). Validity indices are indication of how many cluster poles

are present on the stereoplot based on how far the cluster are separated from each other or how dense

the distribution of the poles are. This is presented as graph of indices versus number of clusters, in

which depending on the type of index used, the minimum or maximum in the line graph indicate the

optimum number of partition of the stereoplots. The details on derivation of validity indices, which is

beyond the scope of this research, are discussed extensively by Hammah and Curran (2000).

However, in this study, this method did not give a consensus results in clustering the discontinuity

poles (Fig.4-9). Again, it depends on the user as to what validity indices to adopt. Also, when some of

this validity index is adopted, for instance Xie-Beni index gives best partition of 2, seems not to

represent well the discontinuity set in the rock slope as it more likely that more than two discontinuity

sets exist. In view of the foregoing, several factors affect the results of discontinuity detection, which

on the process add uncertainty in discontinuity orientation determination from 3D TLS.

It should be noted that some of the rock face consist of many segmented planes as compared to other

due to it large exposed face and variation in smoothness or planarity. Thus, the plotted poles can be an

individual or group of segmented planes that composed a particular discontinuity. The implication is

that a discontinuity consisting of many segmented parts will tend to bias the calculation of the mean

orientation of the cluster, as it contains a dense pole representing its orientation. This affects the

accuracy of validity indices calculation, which depends so much on the density of cluster poles.

.

Figure 4-8 Illustration of validity indices used to assess the optimum partitioning of pole planes (Hammah and Curran 2000) also did not give consensus results. The Xie-Beni index, Fuzzy hypervolume index and partition density index all indicate optimum clustering of the plane poles at 2, while the and Fukuyama-Sugeno and average partition index give 5 and 6 as best cluster, respectively.


36

4.3. Validation of 3D TLS with Scanline Measurements The result 3D TLS survey conducted along the Montemerlo slope was compared with the discontinuity measurements acquired by traditional scanline method. The first two results of fuzzy-k mean clustering (Figure 4-9a&b) presented above are compared with scanline measurements conducted on the same date and on the same slope as 3D TLS survey. The mean orientation of each discontinuity sets from the two 3D TLS models are plotted in the stereonet and visually compared against the stereoplots of the scanline measurements. The discontinuity set 3 (205/79) in Model A strongly correlate with discontinuity set J3 (203/84) in

scanline measurements. While discontinuity set 1 (254/80) and 4 (295/80) fairly correlate with

discontinuity set J2 (262/78) and J4 (112/79), respectively. On the other hand, discontinuity set 2

(248/48) is not clearly defined in scan line measurements. However, field observations and available

photographs show that these low dipping type (<60) of discontinuities are present on the higher part

of the slope. In fact most the sliding wedge failures observed at the upper part of the slope (>10 m)

are caused by low dipping type of discontinuities which will be presented in slope stability analysis

part of this research in Chapter 6. Practically, scan line measurements can be conducted at limited

height only (<3m high) which could be the reason that these discontinuities are not measured. Further,

only horizontal scanline measurement was conducted, which possibly led to under-sampling of the

low dipping or nearly horizontal discontinuities.

The discontinuity 3 (204/79.5) in Model B strongly correlate with discontinuity set J3 scanline

measurements. While discontinuity set 1 (238.08/80.83)), and 4 (294/81) fairly correlate with

discontinuity set J1 and J4, respectively. However, the mean dip of discontinuity set 2 is relatively

lower than the dip of discontinuity set J-2 in scanline measurement. As discussed above, this

difference can be attributed to the presence of low dipping discontinuities on the upper part of the

slope, which are detected by the 3D TLS. Note that model B was derived by manual visual removal of

outlier-like features of Model A. Further, the outlier-like features L-2, in model A is composed of a

point cloud greater than 1000 that is significantly large from the obvious outliers. Thus, there is a

possibility that the scattered low dipping segmented plane poles are real discontinuity in the rock

slope.

A low angle discontinuity plane, L1, was detected both by 3D TLS and by scanline measurements,

which at first glance may look like outliers as they are scattered, and relatively far from the cluster

mean. It should be noted that all these low dipping discontinuities are found in scanline measurement,

S-1, which are conducted near or almost within the presumed blasted zone area, which may suggest

that it is just a blasting induced fractures. In contrary, field measurements conducted by Gradizzi

(2005), before the excavation of the existing slope, shows an outlier-like low dipping discontinuities

(Fig.4-10a and b). This is also supported by field observations and photos of the rock slope before

(Fig.4-11a) and after (Fig.4-11b) the excavation, which shows that low dipping discontinuities (<30

degrees) discontinuities exist. Based from the above observations, 3D TLS Model A are better

representative of the discontinuity set in the rock slope.


37

Figure 4-9 Comparison of the discontinuity set mean orientations of 3D TLS Model A and B against

scanline measurements conducted on September 12, 2007. Discontinuity set 3, 1 and 4 of Model A

stongly to fairly correlate with discontinuity J-3, J-2 and J4 of scanline measurements except for

discontinuity set 2. Discontinuity set 1, 3, and 4 of Model B correlate with J1, J3, and J4, respectively.

However, the dip of discontinuity set 2 is lower than the dip of J2. (note: all the poles are in plotted in

Lambert equal-area stereonet projection )

C. Scanline Measurement

B. 3D TLS Model B (mean)

A. 3D TLS Model A (mean)

L-1

J-1

J-2

J-3

J-4


38

Figure 4-10 a) Photograph of slope face 4 before the excavation of the existing slope and b) stereoplot

of the scanline measurements conducted by Gradizzi (2005) on the same slope. It is apparent that

some discontinuity varies as compared to the discontinuities in existing slope face 4, which explain

the difference of the latest scanline measurements conducted by the author.

Low dipping discontinuities

a b.

k1


39

Figure 4-11 Example of field exposure of low dipping discontinuities L-1 that can be related to

outlier-like features present both in 3D TLS and in scanline measurement stereoplot. Scanline

measurements conducted by Gradizzi, 2005 also show these low dipping discontinuities.

Most of the trace discontinuities in the rock slope are not detected due to insufficient or lack of

surface exposure to be sampled by 3D TLS. High-resolution laser scanner such as Optech 3D TLS

may detect a partly exposed trace discontinuity. However, a detected exposed trace discontinuity may

not represent its actual orientation hidden in the subsurface, due to its limited exposure. For example

the orientation of the detected trace discontinuity A, (as shown in figure 4-3 in section 4). when

compared to the orientation of the corresponding discontinuity in scanline measurements, differs

significantly. The detected trace discontinuity gives an orientation of 256.44/81.499 while the

scanline measurement of the same discontinuity shows an orientation of 276/86. This difference can

be attributed to under sampling on too small exposures, or due to possible erosion and weathering that

changed the orientation of exposed part of the discontinuity.

However, despite its limitations, 3D TLS survey was able to provide large number of data as

compared to scanline measurement due its wider area coverage. As suggested by ISRM (1978),

statistical analysis should be based on a minimum of 150 measurements. In this study, 3D TLS

provide large amount (160 poles), which can be a basis for a more sound statistical analysis. In

contrary, scanline measurements only give 58 discontinuity measurements for 3 days work.

4.4. Conclusion

Several limitations of 3D Terrestrial Laser scan surveys and associated processing in extracting the

discontinuity planes has been established, which include the following:

• Some of the discontinuity are not detected due to occlusion and orientation bias • Most of the trace discontinuities measured by field measurement are not detected. • Some of the partly exposed trace discontinuities are detected but give an orientation

significantly different from the scanline measurements. • In data processing, outlier removal is still based on the judgment of the user that adds

subjectivity and susceptibility to error, especially for users with less experience in rock mass characterizations. As shown above, error in outlier removal significantly affects the resulting statistics of discontinuity orientation of the process data.

• Determination on the number of clustering of plotted discontinuity planes is not straight forward, which forces the user to make his own judgment. The decision to number the cluster again gives different mean orientations, thus, gives different discontinuity spacing results. This gives implications once the data is used for instance in deterministic slope stability analysis, where typically the mean orientation of the discontinuity are the main input in the analysis.


40

5. GROUND PENETRATING RADAR DATA PROCESSING AND ANALYSIS

Presented herein is the proposed method to objectively delineate the subsurface characteristics of rock

mass discontinuities. Particularly, to detect discontinuities that may not be detected by the 3D TLS,

and to verify the continuation of discontinuity planes that are detected by the same method. To

achieve these objectives, a semi-quantitative linear detection approach is carried out. This was

integrated with GPR 3D modelling to correlate and interpret the subsurface geometrical extension of

various linear reflectors corresponding to rock mass discontinuities. The results are finally validated

with scanline measurements.

5.1. Methodology

The method used for Montermerlo GPR datasets consist of three phase which include the following:

1. Standard GPR Radargram Processing 2. Semi-quantitative discontinuity detection based on intensity characteristics 3. GPR 3D Modelling and Visualisation

Figure 5-1 Methodology for GPR Processing


41

5.1.1. Standard GPR Data Processing

Vertical (V18 to 28) and horizontal (H14 to 16) GPR datasets were processed using the processing

software Sandmier, Reflex2D. The processing procedure was a standard one for typical GPR data.

First, the Direct Current (DC) offset was removed, deleting the constant component of the signal in

the data. Next, an automatic gain control (AGC) was carried out, to compensate for the attenuation of

the late arriving EM waves. This allowed some of the deeper reflections to be seen. Then, background

removal was applied to remove the noise that masks the reflection events of interest. Next, a band

pass filter was applied to improve the signal/noise ratio. The band pass gate was centered on the

antenna nominal frequency, 500 Mhz. A running average filter was applied to the data in order to

emphasize horizontally coherent energy (Daniels, 1996). Finally, Stolt F-K Migration was also carried

out. This algorithm reduces diffraction hyperbolas down to a single point and collapse the dipping

event to their true orientation.

The velocity of EM propagation was established through GPR calibration measurements on a 1.2 m

thick trachite rock slab detached from the slope under investigation. GPR profile H13 contains the

GPR calibration measurements, which shows a 30 ns two-way travel time of the first strong coherent

linear reflector. This event is interpreted to correspond to the interface between rock slab and soil

below. From this, it follows that velocity of EM waves in the medium is approximately 0.08 m/ns.

This velocity was then used in time-depth conversion of the radargram.

Figure 5-2a and b show the raw and processed horizontal and vertical profiles acquired in Montemerlo

slope. Layer banding or ringing noise is present at 35 ns and 75 ns in GPR profile H15, which can

lead to false interpretation of discontinuity reflections. According to Sato (2001) ringing is a

periodical system noise signal caused by the resonance of the antennas. The period of antenna ringing

is determined by the amount of time required for currents to travel between the antenna feed and ends

of the antenna elements, whose velocity depends on the antenna design (Radzevicius, 2000). Thus, the

periodical nature of this noise can be used to differentiate noise from real linear reflection events.

After background removal, several realistic linear events are visible between 25 ns downward, except

for events RN, which possibly an artefact of ringing noise (fig. 5-2b). Particularly, on the right side

between 12 m and 24 at slope face 4, several linear reflection events are apparent. Note that these

horizontal linear events are confined within the section of slope face 4 only. Dipping reflection events

are apparent at a of depth 40 ns and 75 ns along the section that corresponds to scan line S-1, starting

from 0 to 5 meter from the left (fig 5-2b). However, despite the standard processing, high amplitude

non-coherent reflections are present which makes the interpretation still difficult.

On the other hand, vertical profile V24&25 even after the processing did not give a satisfactory result

for delineating linear reflection events. Particularly, below 40 ns, delineation of linear coherent event

is hindered by the presence of high amplitude non-coherent background reflections.


42

Figure 5-2. An example of a horizontal GPR profile: (a) raw data and (b) processed data acquired along slope face 4 in Montemerlo Quarry. As shown layer banding noise in the raw profile was remove and some reflection covered previously by background noise seem to appear after processing.

R1

R2

R3

R6

R9

R4=D43

R10

R8=D38

R7

Slope face 4 Slope face 3 Slope face 2 Slope face 1

RN

a GPR H15 raw Data

b GPR H15 processed Data

R5

Ringing noise


43

Figure 5-3 An example of a vertical GPR profile: (a) raw data and (b) processed data acquired along slope face 4 in Montemerlo Quarry. Note that two-way travel and depth of profiles are plotted in horizontal direction. After the time-velocity conversion the maximum depth is 4.0 m.

b GPR V24 process Data a GPR V24 raw Data

c GPR V25 raw Data d GPR V25 process Data


44

5.1.2. GPR object-oriented analysis based on Extreme Intensity Change

Delineation of linear high coherent events is not simple as they are surrounded by high amplitude,

non-coherent reflections. To address this limitation a semi-quantitative approach was carried out to

objectively delineate linear coherent events that correspond likely to rock mass discontinuities. This

was implemented by writing of a series program script within matlab software environment. The

procedures on the proposed algorithm are the following:

1. Conversion of radargram amplitude into GPR gray scale image. 2. Initial assessment of intensity variation in GPR profile image using Matlab improfile function,

which allows for visualization of the variation in intensity of the image along its specified lines or area. Particular emphasis is given to the difference between the maximum and minimum intensity value visualised along the line profile.

3. Automatic delineation of high intensity (local maxima) of the GPR image profile is carried out using the Matlab imextended function. The function also identifies areas of the image where the change in intensity is extreme; that is, the difference between the intensity values of neighboring pixels is greater than a specified threshold. The threshold value that can be applied to delineate coherent linear event can be based on the initial assessment in step 2.

4. This result in a binary image of a high intensity linear event with an extreme changed in intensity value (Fig. 5-4b).

a b Figure 5-4 Illustration show (a) GPR Horizontal image profile H16 between 3.0 m and 6.0 along the transect and (b) the resulting binary intensity image of segmented linear coherent event (local maxima) with extreme intensity change of 56 units (threshold value). Note the delineated high coherent events in binary image b especially in the deeper part are difficult to delineate in image profile a.

Consider the obvious coherent linear event A in the GPR image shown in figure 5-4a. Based on the

visual inspection of its intensity profile, the intensity values directly along the linear event A is

consistently greater than 78. Then, if one inspect the intensity profile just beside the linear event A, a

consistent intensity value lower than 22 will be encountered. The difference of 56 intensity values

indicates a sudden change in the intensity value, thus, can be used as criteria in setting the threshold

value for extreme intensity change.

The intensity value that represents the amplitude reflections of the discontinuities may vary due to

variation in in-fill material, aperture, and degree of weathering of reflecting discontinuities. This

implies that different linear features corresponding to particular discontinuities have a varying

A


45

intensity values. In view of this, the threshold set for extreme intensity change delineation were also

varied based on the assessment of the intensity profile as discussed above. The likely intensity change

corresponding to a linear event can be assessed, first by visual inspection of the intensity profile of the

image. This can serve as a guide in setting appropriate thresholds, which can be done for a number of

trials until sound results are achieved.

Figure 5-5 a and b show the segmented binary intensity image of vertical GPR V24 with varying

threshold in intensity change. First, high intensity coherent events are delineated with a threshold of 4

pixel value. This considers only those events with high intensity value and with extreme change in

intensity higher than 4 units from the surrounding pixel value. The output is a binary image with high

coherent linear events only at first 50 ns while the rest are non-coherent high background reflections

(Fig. 5-5a). Next, a threshold was increased to 18 that give a high coherent linear event between 50 ns

and 100 ns (Fig. 5-5b). The two binary images having different intensity change were combined since

they belong to one profile V24 (Fig.5-5c).

Figure 5-5 Shown above are delineation of linear coherent features (local maxima) with extreme change in intensity of GPR image, V24. The top left (a) and right (b) images have an extreme change of intensity value (threshold) of 4 and 18, respectively. The bottom left (c) is the combination of a and b, while bottom right (d) is combination of a and b, but retaining only the linear coherent features.

5.2. Discontinuity Delineation via GPR 3D Modeling

a

c

b

c d

a b


46

GPR 3D modelling is implemented to help in the correlation of coherent linear features and to

establish its subsurface extension in 3D space. It has been shown that direct interpretation from the

GPR profile image are found to be difficult and highly subjective. Thus, two approaches in 3D

modelling were carried out:

• 3D Model directly from GPR profile image, and; • 3D Model of Binary Intensity Image

Figure 5-6a shows a pseudo-3D view of the 500-MHz vertical and horizontal profile images at slope

face 4 (scanline 4). The combination of these profiles allows to correlating corresponding linear

features in horizontal and vertical profiles. However, difficulties in discriminating the linear coherent

event from direct 3D modelling of GPR images were encountered as some background reflections

also exhibit a high amplitude/intensity. Thus, further processing were undertaken which include the

segmentation of linear coherent events, as discussed in section 5.1.2, prior to plotting the various GPR

profiles to their respective dimensions and coordinates.

5.3. Integration of intensity segmentation with 3D Modelling

The 3D Model of GPR image profile did not give a satisfactory result for the delineation and

interpretation of coherent events due to high background reflections of non-coherent events. To

address this limitation, the GPR image profiles are processed into a binary intensity image following

the algorithm as discussed in section 5.1.2. This is carried out through a series of matlab scripts,

which implement the procedure discussed below:

1. Prior to 3D plotting of various GPR profile, segmentation algorithm as discussed in section

5.1.2 is initially carried out using Matlab imextendedmax command to find the local maxima (high intensity) in the GPR images with specified extreme change in intensity. The values used in setting the thresholds are based on the initial assessment of intensity variation of the GPR image using the Matlab improfile function. This function allows one to see intensity profile of the image along a specified line or transect on the image.

2. The resulting binary images, where plotted and interpolated in their respective dimensions:

where the binary intensity images corresponding to horizontal GPR were plotted along the X axis, whereas vertical binary intensity images corresponding to vertical measurements are plotted along the Z-axis. The time-depth dimension of the horizontal and vertical profile images is plotted along the Y-axis (Fig. 5-6b).

5.3.1. 3D Model of V 24- 28 and H15 at slope face 4

The 3D binary intensity image improves the identification and interpretation of linear events as

compared to the direct 3D Model of GPR image (fig. 5-6b). In this example, several reflection events,

M1 are present at 1 m. These are probably a multiple reflections based on their almost parallel

orientation with each other. However, their irregular and curved like features seem to suggest

reflections from natural rock discontinuities.


47

Figure 5-6. a) 3D Model of GPR image V24-28 and H15 along scanline 4. Various coherent reflection events between vertical and horizontal profiles can be correlated, but still difficult to delineate due to high background reflections from non-coherent events. (b) 3D Model of Binary intensity image, which depicts linear event that are hardly seen in the previous model (note that all the measurement units in XYZ are in meters).

The subsurface extensions of various discontinuities are analyzed by viewing the model in different

perspectives (Fig. 5-7a to f). Figure 5-7c to f, show several linear reflection events in vertical profile

V24-28. Reflection events that correlate with scanline measurements are labeled with D-notation with

corresponding number ID of a discontinuity in scanline measurements. F-notation refers to those

linear events that do not correlate with any of the discontinuities in scanline measurements.

D43

Slope face 4

Slope face 2

????

D38

D43

a

b

M1 M1

M1


48

Note that most of the reflection events that exactly coincide with vertical and horizontal profiles are

nearly parallel to slope face 4. Knowing the azimuth of slope face 4 (N202°), the azimuths of these

reflections can be deduced. Since these major reflection events are almost parallel with slope face 4,

their azimuths are likely to be around N202. This implies that these events correspond to the same

discontinuity sets as slope face 4. Thus, the spacing of these discontinuities is the normal set spacing

as determine in chapter 4.2.

However, in estimating the set spacing, only those linear events in vertical profile that correlate with

horizontal profile is considered. Because some linear events in vertical profile could be a reflections

of discontinuities with an orientation that may be different from the orientation of slope face 4. This

phenomenon can be attributed to three-dimensional effect of EM wave propagation, which may detect

discontinuities in different directions as it travels spherically outward through the medium.

The estimated mean spacing of delineated linear events, which correspond to discontinuity sets

represented by slope face 4 (202/80) is about 0.4 m. This correlates with the discontinuity set 1

(205/79) detected by 3D terrestrial laser scan survey, which has a mean normal discontinuity spacing

of 0.38 m. However, it should be noted that closed discontinuities with no infill material might have

not been detected. This may result to overestimation of set spacing, thus gives uncertainty in spacing

estimation.

Figure 5-7g shows the slope condition of slope face 4 before the excavation. As shown, the nature of

fracturing exhibited by the pre-excavated slope face 4 seems consistent with the dense fracture

spacing of the first 1 m. of linear events in V24-28. The possible reason for these reflection signatures

in the existing rock slope could be the opening of fracture networks due to pressure release upon

excavation of the previous slope. Linear reflection events exhibit variations in reflectivity, suggesting

that the fracture properties such as aperture and filling materials vary in space. Further, reflection

event F9 in GPR V28 are also consistent with the exposed discontinuities on the other part of the

slope as shown in figure 5-7h.

The model also shows the persistence of some major discontinuities that are hard to establish during

the field measurements. However, one should be aware that variation in aperture and infill materials

might result to some parts of a particular discontinuity not being detected. This may lead into false

interpretation of persistence. This is evident in some discontinuous linear events in the profiles. For

instance, reflection event D43, which seems to be consistently present in vertical profile V24 to V28,

appears to be discontinuous in H15 profile. Thus, it can be inferred that the persistence of this

discontinuity is the same as slope face 4, which is greater than 11 meters. In contrary, the persistence

of this discontinuity was not established during scanline measurements.


49

Figure 5-7 Above are correlation of vertical GPR measurements, V24-28. Based on extreme intensity segmentation, 6 coherent linear reflection events were identified which are labelled as F1 F2, F3, F4, F5, F6, F7. Discontinuities interpreted as consistent with scanline measurement are labelled with D38 and D43, which correspond to discontinuity number 38 and 43, respectively in scanline measurement.(Note: all the measurement units in GPR profiles are in meters).

F3

D43

D38

F1 F3 F6

F6

F7

D38

F1

D43

F6

F7

F8

F3

F2 F2

D38

F3

F1

F6 D43

F6 F7

F8

F2

F2

F1

F6

F9

F8

F6 D43

e. V 26 f. V 28

d. V 25

D43

g. Slope face 4 rock mass condition

3 years ago ( after Gradizzi, 2005)

h. exposed discontinuities similar with

reflections F9 in GPR V28 ( after Gradizzi, 2005)

V26

c. V 24

a. 3D Binary model V 25-H15

H15

F8

F9

V25 V26

a. 3D Binary model V 26-H15

D38 F2

F3

RN RN

M1 M1

RN F6


50

5.3.2. Validation of Model V24, H15 with scanline S3

Figure 5-8c shows the 3D Model of V24-28-H15 at slope face four and parallel with scanline S3. The

interpretation of GPR V24 profile with respect to scanline S3 is depicted in figure 5-8d. Two

reflection events, D38 and D43 are observed at 0.9 m and 2.7 m depth, which correlate with

discontinuity 38 (204/85) and 43 (197/80) in scanline measurements S-3, respectively. Discontinuity

38 and 43 has an intersection distance of 10.1 m and 11.88 m. along scanline 3, respectively. These

intersection distances are approximately equal to 2.88 m and 0.9 m with respect to slope face 4.

Figure 5-8. Photographs of slope face 3 where scanline measurement, S3 was conducted (a&b). D38 and D43 are linear coherent event that correlate with discontinuity 38 and 43 in scanline, S3 (c). Figure d shows the interpretation of GPR Model V24 which shows that D40 is unlikely detected due to its unfavorable orientation with respect to GPR V24.

D38 corresponds to subsurface extension of slope face 2 that was detected by the 3D TLS. However,

D43 corresponds to trace discontinuity 43 (197/80) that was not detected by 3D TLS and the

persistence along strike was hard established during scanline measurements. On the other hand, the

geometrical orientation of discontinuity D40 (293o/85o) is possibly not detected as it is nearly parallel

to GPR profile V24. Further, geometrical analysis of reflection events in V24 and H15 shows no

evidence to support for the detection discontinuity D40.

d. Interpretation

D38

D43

D40

D40

D43 D38

V24

D38

Slope Face 4

D40 D43

V24

D40

Slope Face 3 Slope Face 2

V24

V24

a

b

c

D38

??? D43 D40?

S-3

S-3


51

5.3.3. 3D Model of V22, V23, H15, H16 in Slope Face 3

A coherent linear event D40 is visible at 0.5 m. and 0.6 m. depth in profile H15 and H16,

respectively (Fig. 5-9c and d). This correlates well with the dipping linear event in profile V22.

However, this event is not present in V23. Further, no discontinuity was observed in scanline S4

with a distance of 0.5 meter from the right slope face 3 that can be correlated with event D40.

Figure 5-9. 3D Model of GPR V22-23 at slope face 3. Linear coherent event D40 can be the orthogonal reflection of discontinuity 40 in scanline measurement, S3. However, it is also possible that an unexposed discontinuity parallel to slope face 3 is the source of this linear reflection event.

Base on geometrical evaluation, event D40 can be related to orthogonal reflection from discontinuity

number 40 (293/85) in scanline S3. Knowing the dip direction of slope face 3 (N260o), the inclination

e. Interpretation of Discontinuity D40

V22

V23

H16

H15

D40

D38

D43

D40

D40

V2 V2V22

H15

H16

D40

D50 V22 V23

D40

EMwavefront

V22

V23

Reflection direction of D40

c

a

b

d

Slope face 3

D43 D38

D50


52

D50

D47 D48 D49

angle of discontinuity 40 with respect to slope face 3 can be evaluated as 33o (fig. 5-9e). Note that

V22 intersect scanline S3 at 10.6 m, which gives a 0.8 m distance from the left of D40. From this, it

means that the angle of inclination of D40 should be around 38.67 o. The 5.6o deviation is possibly an

error in scanline measurements. However, existence of an unexposed vertical discontinuity at 0.5 m

depth perpendicular to V22 is also possible .

5.3.4. Validation of V23 with Scanline 4

GPR profile V23, which is oriented parallel with slope face 4 can be validated by scanline

measurements, S4 (Fig. 5-10 b and c). However, only the first 4 meter of the scanline 4 can be used to

validate due to the limited penetration depth of GPR V23. Linear event that correlates with scanline

measurement are indicated with a notation D, with a number corresponding to the number ID of the

discontinuity in scanline measurements. Legends that begin with F refer to discontinuities not

measured in scanline measurements. Tab4 scanline 4

Figure 5-10 GPR 3D Model of V23, H15 and H16 (a) together with the side view of profile V23 (b) validated with scanline S-4 (c). Linear coherent events (indicated by yellow arrow) that does not correlate with scanline measurements are possibly reflections of various discontinuities from different direction due to EM waves 3D propagation effect. Further, some of the linear events correlate with the fractures in the photo. (Note: Figure b and c are viewed in opposite direction of figure a).

ID Intersec distance

Dip dir

Dip

45 12.9 91 87 46 12.9 200 81 47 14.43 129 89 48 14.52 111 86 49 14.78 232 80 50 16.9 262 77 51 17.45 292 80 52 17.6 102 84 53 19.75 276 86 54 20.58 276 85 55 21.6 99 86 56 22.3 99 85 57 22.6 112 83 58 24.75 298 85

V23 V23

D50

D47

D48

D49

V23

D47

D48 D49

D50

V23

Scanline 4

Slope face 4

a

b Table 4. Scanline 4 measurements

c

H15

RN

F45

D45

M1


53

Knowing the orientation of slope-face 4 (202/85), the dip direction of event D50 can be evaluated as

N295o that differs significantly from the measured orientation of discontinuity 50 (262/77) in

scanline, S4. The deviation may be due to compass measurement error or distortion in GPR reflection.

Nevertheless, the azimuth of the reflection event D50 is consistent with the mean orientation of

discontinuity set 4 (296/80) in 3D TLS model A.

Reflection events that are visible at 1.4 m, 1.6m, 3.5 m and 3.8 m closely correlate with major

discontinuity 47, 48, 49, and 50, respectively, as shown in table 5. Note that GPR V23 survey was

conducted slightly inclined above and below the scanline, S4 (Fig. 5-10c). This would explain the

slight deviation in spacing between the reflection events and the scanline 4 discontinuities. For

instance, D47 is about 1.54 in scanline S4, whereas D46 is about 1.40 in the GPR binary profile.

5.3.5. 3D Model H15-16 and V20-V21 in slope face 2

Segmentation processing for GPR V20-21 binary model was set with a higher threshold as the low

linear coherent event at first 1 m is already visible in the GPR image profile. This is to emphasize the

linear coherent events that correspond to the major discontinuities.

Figure 5-11 3D Model of V20,V21, H15 & H16 along scanline 2. Linear coherent event F1 is present only in GPR V20 and on the left side of H15, which is not visible in GPR V21 nor on the right side of GPR H15. Various deeper linear coherent events are also visible.

c d

a

V20 V21

H15

H16

b

F1

F1 F1 ?

F1 ?


54

The threshold used is delineating high coherent event were 12, 42 and 45. These threshold values

were established after the initial analysis of intensity profile in step 2 in (section 5.1.3). As shown in

figure 5-12b-c several reflection events F1, F2, F3, F4, F5 are visible in V20 and H15. The spacing of

these high linear coherent events is also consistent with the discontinuities delineated in V24-28,

which can be considered as its upper continuation. However, reflection event F1 seems not present in

V21 and on the right side of H15. This will be investigated and will be discussed in the succeeding

section.

5.3.6. Validation GPR V20-21 and H15 with field observations

GPR V20-21-H15 3D model is validated with field observations and the photograph of slope face 2,

as some discontinuities that correspond to the reflection events do not intersect the scanline, S2.

However, the distance of some discontinuities with respect to slope face 2 can be estimated from the

3D TLS point cloud data.

a. Photo 10 b. GPR H15 Top View

c. GPR V20 front view d. GPR V21 front view

Figure 5-12 (a) Photo of a failing rock block in between slope face 1 and 2. Apparently, linear coherent event, F1 is present only in GPR V20 and on the left side of GPR H15, which is not visible in GPR V21 and at the right side of H15. This linear coherent events can be related to the plane of failure of the presumed failing rock block. RN are possibly ringing noise artifacts similar as those found in V24-28.

H15

Failing rock block

V20

P4

F2

F1

RN

F1

F1

F2

F3

F2

F3

F5 F6 F7 F6

F5

F6

F7

F5

F5

F2

F2

F8

F8

F1?

F1?

RN

RN

F2

F6 F6

F8

F7

F4

F4

RN F3

F3 F3

F4

F4


55

A failing rock block is apparent during site visit and visible in photo 10 (fig. 5-12 a). Reflection event

F1 could be the fracture networks corresponding to the sliding plane of the failing rock block. Note

that this reflection event is visible only in GPR 20 and at the left side of H15, which directly traversed

the presumed failing rock block. Apparently, this reflection event does not continue in the right side

of H15 (between 8-10 meters), nor can be found in GPR V21.

Several reflection events F2, F3, F4, F5, F6, F7 and F8 are also visible at 1.2 m, 1.7 m, 2.5 m, 3.0 m,

3.5 m, and 3.9 m in GPR profile V20, respectively. These are consistent with the reflection events

found in GPR H15 and V21, except for event F8 that is not visible in V21. However, this observation

can be explained by the F8 orientation in GPR H15 where it disappears at the depth where V21

intersect H15.

Reflection event F5 at 2.5 m depth in GPR profiles V20-21 (figure 5-12b and c) can be related to

discontinuity P4 as indicated in figure 5-12a. The orientation and depth of discontinuity P4 was not

measured in the field as it does not intersect the scanline, S2. However, the depth of this discontinuity

with respect to slope face 2 can be estimated from 3D Terrestrial point cloud data, which gives an

approximate depth of 2.6 m.

5.3.6.1. Validation of Profile V19 with field observation

Figure 5-13a and b show the photo of scanline measurement S-2 and the binary intensity image of

segmented linear events in V35, respectively. The GPR original image is also included to compare it

with the binary intensity image (Fig. 5-13c). The binary image was oriented according to the

inclination of the side slope where the vertical GPR V35 measurement was conducted.

Visually, discontinuities intersecting scanline, S-2 correlate with the virtual scanline VS-2. The

discontinuities found in the photo of slope face 2 correlate with linear events deduced from profile

V22. Particularly, discontinuity number 25, 27 and 33 have an intersection coordinates of 7.77 m,

8.46 m and 9.3m along scanline S-2, respectively. Note that the left edge of the slope face 2 has an

intersection coordinates of 6.0 m in scanline S2. Thus, discontinuities 25, 27 and 33 have a distance of

1.77 m, 2.46 m, and 3.3 m. from the left of the edge of slope face 2, respectively. These distances

correlate with the distances of reflection events D25, D27, and D33 in GPR V19. Based on spatial and

geometrical orientation, discontinuity 23, 24, 36 and 35 can be correlated with D23, D24, D36 and D

35 respectively. F12-15 could be discontinuities below the scanlinethat was not measured and

reflections from other directions.

The degree of fracturing from 0 to 0.6 meter is highly dense as compared to the area between 0.6 to

2.0 m depth. This is exhibited by various reflection events visible at 0 to 0.6 meter in GPR V19

possibly a multiples. The exact sources of these reflection events are hard to decipher as the EM wave

propagates spherically in all direction, which imply that these reflections may come from different

sources from different directions. However, it is interesting to note that the first 0.6 reflection events

delineated the boundary of the probable failing rock mass.


56

Figure 5-13 Validation of Profile V19 (b) with scanline S2 at slope face 2 (a). The GPR profile image (c) was also included for comparison. S-2 refers to Scanline 2 while VS-2 refers to virtual scanline along binary image. Linear coherent event that are not labelled are probably reflection of unexposed discontinuities whose orientation cannot be decipher due to 3D propagation effect of the EM wave.

System noise is visible at the center of the V19. This is possibly antenna coupling noise as described

by Conyers et al., (1997). According to Conyers et al., (1997) changes in antenna orientation with

respect to the ground during survey can potentially cause variations in the recorded reflections known

as antenna coupling loss. Note that this noise occurred exactly when the GPR passed over a curve

(Fig. 5-13b). This is also apparent in H15 profile, which systematically occurred only at sections

???

V19

Failing rock block

c)

b)

a)

D25 D27

D33

Slope Face 2

D27

D23

RN

system noise

D24

F12

D28

D36 D35

F13

F15

F14

S-2

VS-2

system noise


57

where the horizontal GPR measurements passed over a rough, non-levelled surface and every time it

turn from one rock face to another. Reflection events RN are also possibly ringing noise artifacts.

5.3.7. Summary of the Validation

The summary of the validation and correlation of GPR and scanline measurements are presented in

Table 6, 7 and 8.

1.In GPR V23-H15, reflection events D47, D48, D49 and D50 correlate with major discontinuities 47,

48, 49 and 50 in scanline measurements, S4. However, the orientation of reflection D50 (N293) is

different with the corresponding discontinuity 50 (262) in scanline S4. The azimuth of reflection D50

is still consistent with the mean orientation of discontinuity set 4 (296/80) in 3D TLS Model A.

2. GPR V24-28 and H15 profiles show 8 linear coherent events that are nearly parallel with slope

face 4(202/85). Two of which (D38 and D40) correlate with the major discontinuities 38 and 40. D38

can be related to the subsurface continuation of slope face 2 that is detected by the 3D TLS. D40 is a

trace discontinuity that is not detected by the 3D TLS. The estimated spacing of the linear coherent

events that are nearly parallel with slope face 4 is about 0.4 meter, which is fairly the same with the

spacing discontinuity set 3 (205/78) of 3D TLS model A. The coherent linear does not correlate with

any discontinuities at

3. GPRV21-H15 detects reflection event D40, which is possibly an orthogonal reflection of EM

waves from discontinuity 40. However, unexposed discontinuity parallel with slope face 3 can also be

a possible source of the reflection event.

4. GPR V20, V21, H15 detect various discontinuities F1, F2, F3, F4, F5, F6 (see figure 5-12) that

does not intersect scanline S-2. The first coherent linear event F1 possibly corresponds to the plane of

failures of presumed failing rock block in slope face 2.

5. GPR V19 detects various reflection events (D25, D27, and D33) that correlate with the

discontinuities in scanline S-2. Particularly, D27 is consistent with the major discontinuity, based on

visual inspection of the available photograph of slope face 2. However, some discontinuities might

have not been detected by the proposed algorithm, hence, it is better to do the interpretation together

with the original GPR image.


58

GPR

Scanline measurement S-4 V 23-H15

Orientation Persistence Disc.

ID Intersec. Distance

Dip Dir Dip strike dip Reflection ID

45 12.9 91 87 1 0.4 D45

46 12.9 200 81 >10 20

47 14.43 129 89 3 4 D47

48 14.52 111 86 null 1 D48

49 14.78 232 80 4 1 D49

50 16.9 262 77 null 15 D50

51 17.45 292 80 null 15

52 17.6 102 84 null 1

53 19.75 276 86 null 20

54 20.58 276 85 null 1.3

55 21.6 99 86 null 2

56 22.3 99 85 null 1.7

57 22.6 112 83 null 20

58 24.75 298 85 null 20 Table 5. Discontinuities 45, 47, 48, 49, 50 are major discontinuities that correlate with reflection events 45, D47, D48, D49 and D50, respectively. Discontinuity 46 is irrelevant as it is the orientation of slope face 4, which is nearly parallel with GPR V23. As discussed above only 4.0 meters of scanline S4 can be used in the validation. (Note: Null values means the persistence along strike are hard to determine during field measurments)

GPR GPR

Scanline measurement S-3 V24-H15 V22-H15

Orientation Persistence Disc.

ID Intersec.

Distance, m Dip Dir Dip strike dip Reflection ID Reflection ID

38 10.1 204 85 1.5 >20 D38

39 10.1 260 65 1.5 0.5

40 11.42 293 85 2 3 D40

41 11.49 236 68 2 2.5

42 11.49 236 68 0.3 0.5

43 11.88 197 80 1 3 D43

44 12.78 88 87 1 0.3 Table 6 Discontinuities 38 and 43 are major discontinuities that correlate with events D38 and D43, respectively. Discontinuity 40 is a major discontinuity not detected due to its steep inclination with respect to V24. However, this is possibly detected by GPR V22 as explained in section 5.3.3. Discontinuity 39, 42 and 44 are small discontinuities with low persistence, which have no clear evidence of being detected by GPR V21-H15. Discontinuity 41 is steeply inclined with respect to V24, thus probably not detected.


59

GPR Scanline measurement S-2

V19 Orientation Persistence Disc.

ID Intersec.

Distance, m Dip Dir Dip strike dip Reflection ID

19 6 286 83 4 0.05

20 6.3 282 55 0.15 0.15

21 6.44 286 70 0.5 0.3

22 6.9 261 77 0.3 0.2

23 7.04 241 69 0.8 1 D23

24 7.75 112 77 0.15 0.4

25 7.77 284 77 0.3 1 D25

26 7.75 199 85 1 0.3

27 8.46 120 87 0.15 0.3 D27

28 8.64 269 75 null 0.3 D28

29 8.8 108 25 null 0.1

30 9.2 119 75 null 0.05

31 9.15 262 65 null 6

32 10.1 202 86 2 >20

33 9.3 111 86 null 1 D33

34 9.42 301 50 0.15 0.15

35 9.47 111 85 0.15 0.6 D35

36 9.58 281 62 0.15 0.6 D36

37 10.1 209 85 null >20

Table 7 Discontinuities 19, 20, 21 and 23 can be some of the reflection events at first 0.5 meters in

GPR V19 based on its distance with respect to the left edge of slope face 2. Based on spatial and

geometrical orientation, discontinuity 23, 24, 25, 35 and 36 can be related to D 23, D24, D25, D35

and D36, respectively. Discontinuity 26, 32 and 37 are almost parallel with V19, thus, unlikely

detected. Discontinuity 27 and 28 can be related to events D27 and D28. Discontinuity 22, 29, and 30

are small discontinuities, which are not found in their corresponding depth in GPR profile.

Discontinuity 35 and 36 can be related to D35 and D36. (Note: null values in the table means the

persistence along strike are hard to determine during scanline measurements)

5.3.8. Conclusion

Several uncertainties are associated with the interpretation of the geometrical and spatial

characteristics of the detected reflection events. First, 3D spherical propagation effect of EM waves

may give reflection events coming from different directions, thus, the orientation and the source of the

reflection are difficult to determine without a proper validation. Second, one linear coherent events

can be a mixed reflections of two or more discontinuities that have different orientations but with

similar orthogonal distance with respect to GPR measurements. Third, some of the linear events are

possibly just artifacts of ringing noise or multiple reflections after background removal processing.

Particularly, those linear events present between 30ns to 40ns in all the GPR profiles. Thus, it

helpful inspects the raw GPR profile and assessed whether the ringing noise and/or multiples,

correlate with the segmented linear events in the binary intensity image. Fourth, some of the real


60

discontinuity reflections might have been removed during background removal processing (Conyers,

1997).

Nevertheless, the proposed algorithm based on automatic delineation of high intensity and extreme

intensity change can help in providing a more objective way of delineating discontinuities even in the

presence of high, non-coherent, background reflections. Based on the algorithm the objective of this

research has been achieved, viz:

• objective delineation of rock mass discontinuities. • delineation and verification the subsurface extension of major discontinuities that are

detected and not detected by 3D TLS and scanline measurements; • established the persistence along strike of some discontinuities not established in scanline

measurements. • estimation of set spacing of major discontinuity, though, significant uncertainties are

involved.


61

6. SLOPE STABILITY ANALYSIS BASED ON 3D TERRESTRIAL LASER SCANNING AND GROUND PENETRATING RADAR

6.1. Introduction

This chapter presents the application of discontinuity measurements derived from 3D TLS and GPR

measurements, for slope stability analysis. Discontinuity orientations data derived from 3D terrestrial

laser scanning have some uncertainty associated with the field procedure and the subsequent data

processing routine as discussed in chapter IV. GPR measurements also show that some of the

discontinuities are not detected by 3D TLS. Further, GPR depicts the inherent variability of

discontinuity orientation in 3D space. Considering the uncertainty and variability inherent in the data

derived from the two methods, a probabilistic approach in slope stability analysis is adopted. First, the

fundamentals of kinematic and kinetic slope stability will be presented, followed by a discussion on

the probabilistic slope stability analysis and its implementation for the slope under study. Then, the

orientation and spacing measurements from the 3D TLS and GPR measurements are used as an input

SSPC analysis and compared with SSPC analysis based on the data from the manual field

measurement. Finally, the probabilistic analysis will be compared to SSPC analysis.

6.2. Kinematic and Kinetic Stability of the slope

Based on the discontinuity orientation data derived from 3D Terrestrial Laser Scan and GPR survey

of Montemerlo slope, the kinematic stability of the slope can be evaluated. Kinematic analysis is

typically done using stereographic projection, in which the orientation of discontinuities critical to

slope instability are analysed. In this analysis three different mode of failure (i.e., planar; wedge and

toppling) can be evaluated. However, this study will focus more on the wedge failure analysis of the

slope, which are the commonly observed failure mode in the study site (Figure 6-1a and b). However,

the other mode of failures should be also analysed.

Figure 6-1. Photo a depicts the condition of slope face 1 (229/80), which shows various wedge sliding failures. Photo b is the condition of slope face 4 before the excavation of the existing rock slope. (after, Gradizzi, 2005). Apparently, low-dipping discontinuities (L1-3) are visible mostly at the upper part of the slope. Some of which resulted to various wedge and planar sliding failures.

Wedge

a) b)

L1

L2

L3


62

According to, Hoek and Bray (1981) and Norrish and Wyllie (1996), kinematic wedge failure can be

assessed through the following criteria:

• the line made by the intersection of the planes creating the wedge must plunge more steeply

than the friction angle , but;

• less steeply than the dip of the slope face, and;

• in a direction such that it daylights from the slope face.

After kinematic analysis of wedge stability indicates the

possibility of a wedge failure, kinetic analysis can be performed.

Kinetic analysis takes into account not only the geometrical

aspect of slope stability but also the forces that contribute to the

instability. This is typically implemented using the Limit

Equilibrium analysis such as the method proposed by Hoek and

Bray (1981). This analysis needs the details of the wedge

geometry as defined by the location and orientation of the

bounding surfaces of the discontinuities and the slope (Fig.6-2). In Hoek and Bray (1981) geometrical

model, the four planes representing, the combination of two discontinuities (plane A and B), the

slope face, and the upper ground face, are considered for wedge stability analysis (Fig. 6-2 and 6-3).

Then, the wedge stability are analysed by resolving the forces acting normal to the discontinuities and

in the direction parallel to the line of intersection. This analysis can be represented by the following

equation.

Bw

AwBA Y

BAH

Yc

H

XcFS φ

γγφ

γγ

γγtan)

2(tan)

2(

33 −+−++= (17)

naX

,235

24

cossin

sin

θθθ= (18)

nbY

,1cos35

13

sin

sin

θθθ= (19)

nbna

nbnabbaA

,2

5

,cos

sinsin

coscos

θψθψψ −= (20)

nbna

nbnababB

,2

5

,cos

sinsin

coscos

θψθψψ −= (21)

Figure 6-2. Schematic diagram of wedge Figure 6-3. Stereonet for deriving the coefficients X,Y,A,B (after, Hoek and Bray,1981)

where FS is the factor of safety, cA and cB are the cohesive strengths of planes A and B; θA and θB the

angles of friction on planes A and B; γ the unit weight of the rock; Ψ the unit weight of water; H the

total height of the wedge.

Figure 6-2. Schematic diagram

of wedge failure model

Figure 6-3. Illustration of stereonet for deriving the coefficients X,Y,A,B (after, Hoek

and Bray,1981)

Upper ground face

slope face

Plane B

Plane A

Line of intersection


63

6.3. Deterministic approach in Rock Slope Stability Analysis

Kinematic and kinetic slope stability analysis can be implemented using two different approaches:

deterministic and probabilistic approach. The deterministic approach of slope stability analysis used a

fixed value for each parameter to compute the factor of safety, without taking into account the

uncertainty and variability inherent in the data. For instance, in deterministic kinematic analysis, the

mean value for each discontinuity set is typically used in stereographic analysis to compute the

stability of the slope (Yoon, 2002; Lana 2003; Kentli, 2004). However, it has been established in

chapter 4 and 5 that the mean orientation of discontinuity parameter derived from laser scanning

significantly varies and are sensitive to various factors associated with the processing and modelling.

The data also show some scatter, which is inherent in nature itself. Considering these limitations and

the uncertainties in measurements and modelling of the 3D TLS data, the probabilistic analysis

method may be a more suitable approach.

6.4. Probabilistic approach in Rock Slope Stability Analysis

In view of the variability of some plots in discontinuity derived from laser scanning and uncertainty in

discontinuity plane modelling, a probabilistic approach is adopted. The basis for the probabilistic

analysis is the recognition that most of the factors that contribute to slope instability have

some natural variation. Further, probabilistic analysis is used to quantify the variability in the

parameters and the uncertainty associated in modelling (Park and West, 2001). In this approach, the

parameter in slope stability are treated as random variable with a particular probability density

function (PDF), which describes the relative likelihood that a random variable will assume a

particular value (Sjoberg, 1996)).

In probabilistic analysis, the stability of the slope is defined in terms of probability of failure, which

treat the factor of safety as random variable with a certain PDF, instead of one fixed value. Then, the

probability of failure is taken as the percentage of factor of safety (FS) less than 1.0 to the total area

within the probability density function (PDF) of factor of safety (Park and West, 2001). Assessing the

stability of the slope in terms of probabilities of failure than factor of safety means that one consider

that there is a finite possibility of failure, even if it can be very small (Sjoberg, 1996). This is more

realistic assumption than saying that the slope with a certain factor of safety is totally stable or

absolutely unstable.

The first step in probabilistic approach is to define the statistical parameter (e.g., mean, variance) of

the random variables that affect the slope instability. The mean value of the PDF represents the best

estimate of the random variable, and the variance or standard deviation of the PDF represents an

evaluation of variability or uncertainty (Park and West, 2001). In this research, the statistical

parameter for discontinuity orientation is the mean orientation and Fisher’s constant K, which

indicates the degree of dispersion or variability.

In the probabilistic slope stability approach, the parameters that are critical to slope instability such as

orientation of discontinuities, length, spacing, persistence, and shear strength of discontinuities should

be given a proper statistical model as it affect significantly the analysis (Kuletake, 1993). As pointed

out by Park and West (2001) most of these parameters should be considered as random variables and

the types of distribution functions for each random variable should be established carefully in the


64

probabilistic analysis. However, in many cases, the available data are usually insufficient for a sound

statistical analysis, thus a certain degree of experience and engineering judgement are always needed

(Muralha and Trunk, 1993).

Then, once the statistical parameters and the probability density distribution have been established,

the probability of failure can be evaluated by various risk analysis procedures. One of the most

commonly applied methods is the Monte Carlo simulation.

6.4.1. Probabilistic Rock Slope stability assessment via Monte Carlo Simulation

In rock slope stability analysis, the Monte Carlo simulation method is utilized for reliability analysis

to evaluate the probability of failure (Park and West, 2001). The Monte Carlo technique is a

numerical simulation that solves a mathematical problems through random sampling and repeated

calculation. In this procedure, values of each variable are generated randomly corresponding to their

probability density function (PDF). Then, the generated values are used to calculate the factor of

safety. The calculation is repeated for large number of times, which result to the PDF of factor of

safety. Then, the ratio of the area under the distribution curve for FS less than 1 is divided by the total

area under the PDF that gives the probability of failure of the slope.

According to Park and West (2001), for complete probabilistic analysis, kinematic and kinetic

analysis of the slope should be done. However, several difficulties are encountered in implementing

kinematic and kinetic analysis in a Monte Carlo simulation. This is because kinematic analyses are

commonly performed using stereographic projections, which implies that to use the equation for

repeated calculation, one needs to make many calculation from stereonet projection, which is not

suitable for Monte Carlo simulation. As discussed above, calculation of wedge failure using the

method of Hoek and Bray (1981), needs the complicated calculation procedures of equation 17-19,

where the coefficient X, Y, A, B also requires calculation in stereographic projections. Thus, if Monte

Carlo simulation is implemented, for each set of parameter combinations, a large number of

stereographic projections must be performed, and the input values for each simulation must be

measured from the stereoplot.

In view of the above, Park and West (2001) proposed a simple kinematic instability check, which can

be express in the following equation:

apparentδ<Ω<Φ (22)

[ ])cos(tantan 1siapparent ρρδδ −

−= (23)

where, Φ is the dip angles of the top slope face, Ω is the dip angle of the line of intersection between

two discontinuities, and δapparent is the apparent dip of the slope face in the dip direction of the line

of intersection. δ is the dip of the slope face, ρi are the dip directions of the lines of intersection, and

ρs dip directions of the slope face.


65

After the kinematic analysis, the kinetic stability analysis can be solved by using a closed form

equation formulated by, Hoek and Bray (1981) which are presented in the appendix 2 of their

textbook. This solution can be easily used for the probabilistic analysis because it is based on

straightforward calculation of equations and does not require any stereographic projections.

In this method, the unit vectors of each plane and vectors of the lines of intersection of the two

discontinuity planes are first evaluated. Then the volume of the wedge is calculated, based on the

geometrical arrangement of: (i) the combination of two discontinuity planes and the slope, (ii) the

orientation of the line of intersection of the two discontinuities, and; (iii) the areas of the faces. Then,

considering the sliding mode, the forces acting parallel to the line of intersection and normal to the

discontinuity planes, the factor of safety is computed. Due to its straightforward and systematic

calculation procedure, a number of calculations can be easily repeated, thus, suitable for Monte Carlo

simulation.

According to Einstein (1996) and Park and West (2001) the probability of failure of the slope should

be considered as the product of the probability of kinematic instability and the probability of kinetic

instability. This is based on the assumption that the probability of kinematic instability is a

conditional probability of kinetic instability. Meaning, even if the limit equilibrium analysis shows

that the factor of safety is less than one (1), the wedge on the slope will not fail if its orientation have

no possibility to slide down slope.

Thus, in the simulation procedure only wedges that are kinematically unstable will be analysed for

kinetic stability. Then, the probability of kinematic instability, Pkim can be evaluated as:

mi

mukim

K

KP = (24)

where Kmu is the total number of iteration resulting to kinematically unstable wedges, while Kmi is the

total number of iteration. After evaluating the probability of kinematic instability, the probability of

kinetic instability will be:

mu

nukin

K

KP = (25)

where Knu is the total number of wedges with a factor of safety less than one (1), while Kmu is the total

number of kinematically unstable wedge. Finally, the overall probability of failure of the slope is

express as:

kinkimf PPP *= (26)

6.5. Implemenation of Monte Carlo Simulation in Montemerlo Slope Stability

Monte Carlo simulation was implemented in Matlab software, the script used was developed

following the concepts and procedures as discussed above. Mathlab built-in function randtool can

generate random samples based on the specified probability density function (PDF) and statistical

parameters of each random variable that affect the stability of the slope. The program generate 25,000


66

random samples from each discontinuity sets. Then, all the wedge formed by the combination of two

pair of discontinuities generated from their respective parent discontinuity sets are analysed for

kinematic and kinetic failure. The programmed script composed basically of four components: (i)

input parameters; (ii) generation of random orientation; followed by the computation of (iii)

probability of kinematic wedge failure; (iv) probability of kinetic failure; and (v) the total probability

of failure, successively. This is discussed in detail below:

1. Input Parameter

The parameters used for probabilistic analysis can be classified into two types depending on their

variability: (i) deterministic parameters, and (ii) probabilistic parameters. The deterministic

parameters are those that are considered as having fixed value and do not significantly vary, such as

density of materials, γm (27 kN/m2); height of slope, H (20 m); dip and dip direction of the slope and

orientation of the slope ground surface. The analysis is done for two slope orientation: slope face 4

(202/85) and slope face1 (229/80), while the upper ground surface corresponding to the two slope

face are taken as 202/0 and 229/0, respectively.

The shear strength parameter (angle of friction and cohesion) are considered only as deterministic

parameters. The cohesion is taken as equal to zero. The internal angle of friction is taken as 29.2o for

discontinuity set 3, and 36.9 o for the other discontinuity sets 1, 2 and 4. The internal angle of friction

is derived from sliding angle computation based on the discontinuity properties of each discontinuity

sets measured by SSPC field measurements (Hack, 1998). This can be express through the following

equation.

0113.0

Im*** KaRsRlslding =ϕ (27)

where Rl, and Rs is the large scale and small scale roughness, respectively, Im is the infill materials,

Ka is the karst. According to Hack (1998) this is comparable to i-angle principle under which a block

lying on the slope is stable.

On the other hand, the probabilistic parameters that are considered in this study are those that exhibit

significant variation, such as discontinuity orientation, water pressure, and height of the wedge. As

discussed above, the statistical parameter for the discontinuity orientation is the mean value and

Fisher’s constant K for each discontinuity sets (Table 8). In wedge failure analysis, two conditions are

evaluated: dry and random uniform saturation. In random saturation condition, the water pressure

distribution acting against the discontinuity surface is adopted from Hoek and Bray (1981) model of

pore distribution express as;

6

wwhγµ = (28)

where wγ is the unit weight of water and hw is the height of groundwater surface that varies

uniformly depending on the height of the wedge. The height of the wedge varies uniformly based on

the height of the slope.


67

Statistical Parameter of 3D TLS discontinuity model A Set 1 Set 2 Set 3 Set 4 Dip 80.46 47.79 78.51 79.58 Dipdir 254.22 247.99 205.44 295.57 K 42.19 15.93 23.04 15.53 mean N spa 0.5161 0.5777 0.3841 1.2352 stdev N spa 0.952 0.9882 0.7506 1.9503 max N spa 5.298 5.296 4.2778 9.9967

Table 8 Statistical parameter of discontinuity sets derived from 3D TLS, which are used as an input for Monte Carlo simulation

2. Generation of Discontinuity Orientation

The next step of the simulation procedure is the random generation of discontinuity orientation from

each of the two combination of discontinuity sets that can form a wedge. From each of the two

combination of discontinuity set, 25,000 discontinuity orientations are randomly generated based on

their statistical input parameter: (i) mean orientation (dip and dip direction) and (ii) the Fisher’s

constant, K, of their parent discontinuity sets. To understand how the discontinuity orientations are

randomly generated, a number of equations are presented. The generation of discontinuities are based

on the Fisher Probability function, which can be express as

θθθ cossin)( K

KKe

ee

KP −−

= (29)

where P(θ) is Fisher frequency density function, θ is the angular distance from the true position(θ=0),

and K is the Fisher’s constant. K is an indication of the dispersion of the distribution of the

discontinuity set: that is the lower the K value the higher the spread of the distribution. K value can be

derived through the following equation

RwNw

NwK

−−= 1

(30)

where Nw is the total weighted size of N observations (poles) and Rw is the magnitude of the resultant

true (mean) normal vector rn. . However, according to Queck and Leung (1995), equation 29 can be

approximated to

)1(cos1)( −−≈ θθ KeP (31)

Then, in order to implement the simulation, equation 31 can be rearrange, and a uniform random

variable Ru (0-1) can be substituted to P(θ), to get the angular distance, θ. This can be express to the

following equation (Park and West, 2001)

+−= − 1)1ln(

cos 1

K

Ruθ (32)


68

Then, Queck and Leung (1995) have shown that the plunge ß1 and trend α1 of a pole with an angular

distance θ from the mean value can be computed by the geometrical evaluation of its direction

cosines. This leads to equations 33 and 34, respectively;

θ

λθβθθββ sin

2sin

2sincos8sin)sin(

sin

22

1

nn +=

−

(33)

1

11

coscossinsincos

)cos(ββ

ββθααn

nn

−=−

(34)

where ßn is the plunge and αn is the trend of the mean (normal vector) while λ is an angle that can

be generated randomly following a uniform distribution over the interval 0 to 2 Π (Queck and

Leung.,1995). This is to ensure that the generated discontinuity will be sampled randomly and

circularly around the true value (θ=0,) following its probability distribution express in equation 26.

To calculate equations 32 and 33, the random parameter Ru (0-1) and λ (0o-360 o), respectively, were

generated randomly following uniform distribution using the built-in Matlab function randtool.

3. Determination of orientation of intersection line. After the generation of random dip and dip

direction from each of the two combinations of discontinuities, the orientation (trend and plunge) of

their intersection line is calculated. This is implemented in Rockworks software using Beta pair

function that can calculate plunge and trend of intersection line for every pair of two discontinuities.

4. Probabilistic Kinematic Wedge Analysis After getting the dip and dip direction of each of the combination of the two discontinuities and the

orientation of their line of intersections, the next step is to evaluate the probability of kinematic

wedge failure. The entire wedge that formed were analysed for kinematic failure using the criteria set

in equation 22 and 23. All the wedge with a line of intersections having a trend of less than 90o

(absolute) with respect to the dip direction of the slope are taken as an additional criterion to the

kinematic failure. This is to ensure the daylighting condition of kinematic failure. Then, the total

number of wedge kinematically unstable is divided by the total number of wedges formed. This gives

the probability of kinematic wedge failure.

5. Probabilistic Kinetic Analysis. Then, only those wedges found to be kinematically unstable are

evaluated for kinetic analysis using Limit Equilibrium analysis method proposed by Hoek and Bray

(1981). Limit equilibrium analysis for every wedge formed were carried out based on the

deterministic and probabilistic input parameters as discussed in step 1. Then, the total number of

wedge found to be kinetically unstable is divided by the total number of wedge that are kinematically

unstable. This gives the kinetic probability of failure.

6. Calculation of Rock slope Total Probability of Failure. Finally, the total probability of the slope failure is taken as the product of Probability of Kinematic

instability and Probability of Kinetic instability (Einstein, 1996; Park and West 2001; Park and West,

2005).


69

6.6. RESULTS

The results of the deterministic analysis and the probabilistic analysis for wedge failure in dry

conditions are shown in table 9 and 10, respectively. The input parameters used for deterministic

analysis are the same with the deterministic input parameter used in Monte Carlo simulation, except

for the height of the wedge, which is assumed as 10 m. Also, shown below are the histogram of factor

of safety (FS) based on the results of calculation using the repeated simulation procedure (Fig. 6-4

and 6-5).

6.6.1. Stability analysis of Slope 4 (202/85)

Based on the deterministic analysis, most of the combinations of two discontinuity sets are found to

be kinematically unstable except for the combination of discontinuity set 1 and 4. The plunge of the

line of intersection of the combination of discontinuity sets 1 and 4 is 79.27o, which is greater than

the apparent dip of the slope face (63.95). Thus, based on criteria set in equation 22 and 23, the

combination of discontinuity sets 1 and 4 is kinematically stable. Based on the deterministic analysis,

the combination of discontinuity set1 and 2 is kinetically stable, which is consistent with the result of

the probabilistic analysis that show a very low probability of kinetic failure. In probabilistic analysis,

the combination of discontinuity set 1 and 3, set 2 and 3, and set 4 and 3, give a total probability of

failure of 91.9%, 62.71% and 92.82%, respectively, which agree with the results of deterministic

analysis all having a factor of safety less than 1.

However, the combination of discontinuity set 2 and 4, which is kinetically stable (FS=1.399) in

deterministic analysis, is shown to be kinematically (91.01%) and kinetically (8.79%) unstable in

probabilistic analysis, which gives a total probability of failure of 8 %. This shows that the mean

orientation of combination set 2 and 4 when used in slope stability analysis does not show any

possibility of kinetic instability. However, when the variation in orientation is considered, it indicates

the possibility of kinetic instability. Thus, deterministic analysis based on a fixed representative

orientation of discontinuities fails to show the possibility of kinetic instability.

6.6.2. Stability analysis of Slope 1 (229/80)

Based on deterministic analysis, the combination of discontinuity set1 and 2, and set 1 and 4

shows consistent results in deterministic and probabilistic analysis which are kinetically

stable. In deterministic analysis, the combination of discontinuity set 1 and 4 kinematically stable.

However, according to probabilistic analysis the combination of discontinuity set 1 and 4 can formed

a wedge with kinematic probability of failure of 23.53 %. Nevertheless, none of the formed wedges

are kinetically unstable.

In probabilistic analysis, the combination of discontinuity sets 1 and 3, set 2 and 3, and set 4

and 3, give a total probability of failure of 79.77%, 69.71% and 86.5%, respectively, which are

consistent with the result of deterministic analysis with corresponding factor of safety of 0.169,

0.68, and 0.23.


70

Deterministic analysis of the combination of discontinuity set 1 and 4 gives a FS of 1.4. This is

contrary to the result of probabilistic analysis, which shows a kinematic and kinetic probability of

failure of 91.99% and 9.54%, respectively. This gives a total probability of failure of 8.78%. In this

slope orientation, the combination of discontinuity set 1 and 3, set 2 and 3, and set 4 and 3 have the

critical influenced in the stability of the slope.

The Limit Equilibrium analysis adapted both for deterministic and probabilistic analysis is sensitive to

pore pressure input parameter as shown by Hoek and Bray (1981). Thus, limit equilibrium analysis

based on saturated condition is expected to give a significant increased in the probability of failure

for probabilistic analysis, or a significant decreased in the factor of safety for deterministic analysis.


71

Deterministic Wedge failure Analysis at slope orientation 202/85

(dry condition) Discontinuity

Combination Disc dip1

Disc dip1

Disc dir1

Disc dir1

Intersec. trend

Intersec. plunge Kinetic FS

Set 1 and 2 80.46 47.79 254.22 247.99 165.63 8.34 16.1193

Set 1 and 3 80.46 78.31 254.22 205.44 233.04 78.08 0.116

Set 1 and 4 80.46 79.58 254.22 295.57 281.69 79.27 Kinematic stable

Set 2 and 3 47.79 78.31 247.99 205.44 284.94 41.38 0.68

Set 2 and 4 47.79 79.58 247.99 295.57 234.59 42.89 1.3989

Set 3 and 4 78.31 79.58 205.44 295.57 202.86 74.51 0.2531

Deterministic Wedge Failure Analysis at slope

orientation 229/80 (dry condition)

Set 1 and 2 80.46 47.79 254.22 247.99 165.63 8.34 16

Set 1 and 3 80.46 78.31 254.22 205.44 233.04 78.08 0.169

Set 1 and 4 80.46 79.58 254.22 295.57 281.69 79.27 Kinematic stable

Set 2 and 3 47.79 78.31 247.99 205.44 284.94 41.38 0.70

Set 2 and 4 47.79 79.58 247.99 295.57 234.59 42.89 1.4

Set 3 and 4 78.31 79.58 205.44 295.57 202.86 74.51 0.2467 Table 9 Result of Deterministic wedge failure analysis at slope orientation 202/85 and 229/80 at dry condition

Probabilistic Wedge Failure Analysis at slope 229/80

(dry condition) Probability of Failure (x100)

Disc dip1 Disc dip2 Disc dir1 Disc dir2

Kinematic wedge failure

Kinetic wedge

Total failure

Set 1 and 2 80.46 47.79 254.22 247.99 0.0447 0.0098 4.40E-04

Set 1 and 3 80.46 78.31 254.22 205.44 0.9226 0.9961 0.919

Set 1 and 4 80.46 79.58 254.22 295.57 0.2094 0 0

Set 2 and 3 47.79 78.31 247.99 205.44 0.7369 0.851 0.6271

Set 2 and 4 47.79 79.58 247.99 295.57 0.9101 0.0879 0.08

Set 3 and 4 78.31 79.58 205.44 295.57 0.93 0.9981 0.9282

Probabilistic Wedge Failure Analysis at slope 229/80

(dry condition) Probability of Failure (x100)

Disc dip1 Disc dip2 Disc dir1 Disc dir2

Kinematic wedge failure

Kinetic wedge

Total failure

Set 1 and 2 80.46 47.79 254.22 247.99 0.0447 0.0027 1.20E-04

Set 1 and 3 80.46 78.31 254.22 205.44 0.7981 0.9995 0.7977

Set 1 and 4 80.46 79.58 254.22 295.57 0.2353 0 0

Set 2 and 3 47.79 78.31 247.99 205.44 0.9578 0.7278 0.6971

Set 2 and 4 47.79 79.58 247.99 295.57 0.9199 0.0954 0.0878

Set 3 and 4 78.31 79.58 205.44 295.57 0.8764 0.9869 0.865 Table10 Result of Probabilistic wedge failure analysis at slope orientation 202/85 and 229/80 at dry condition


72

Figure 6-4 Histogram factor of safety derived from Probabilistic analysis of slope 202/85

Disc. Set 1 and 2 Disc. Set 1 and 3




73

Figure 6-5 Histogram factor of safety derived from Probabilistic analysis of slope 229/80

6.7. SSPC Slope Stability Analysis

The data derived from 3D TLS and GPR measurements are used as an input for SSPC slope

stability analysis. This was compared with SSPC analysis using the manual filed data. Further,

the result of the adopted probabilistic analysis is compared with the result of SSPC slope





74

stability analysis. (SSPC slope stability method and procedures are discussed in chapter 3.2,

while the details of the computation for SSPC analysis are shown in appendix 6 and 7).

SSPC analysis, based on manual field data shows that the slope can stand up to a maximum

height of 640 meters, which is greater than the maximum height of the existing slope of 20

meters, thus, have a probability to be stable of 100%. Assessment of orientation-independent

analysis of slope face 1(229/80) also shows a probability to be stable of 100%. However,

SSPC analysis based on the orientation and spacing data of the 3D TLS and GPR, shows that

a slope with an orientation of 229/80 can stand up to a maximum height of 28.36 meter. This

implies only about 90% probability to be stable for the slope height of 20 meters.

The difference in the results SSPC analysis using manual field data as compared to 3D TLS

and GPR data is influence mainly by the spacing measurements. As compared to the 3D TLS

and GPR spacing data, SSPC field measurements of discontinuity spacing is relatively wide.

In manual field measurements, the spacing of 3 m for discontinuity set 1 (205/82) is based on

the distance of slope face 2 and 4. However, in between these two rock faces are two trace

discontinuities D40 and D43. During the fieldwork, the actual orientation and persistence

these discontinuities are hard to establish, thus, these were not considered in the computation

of spacing of SSPC discontinuity set 1. Based on GPR measurements, D43 has high

persistence along strike (>11 m.), and parallel to the orientation of the slope face 4 and slope

face 2. Thus, these discontinuities can be consider similar with discontinuity set 1, thus, the

spacing of discontinuity set 1 should be less than as measured in the field.

SSPC orientation-dependent analysis based on the manual field measurements shows that only

discontinuity set 2 (270/82) may cause instability at a slope with an orientation of 202/85,

while none of the other discontinuity sets may cause instability at the same slope (Table 11).

At slope with an orientation of 229/80 no discontinuity sets may cause orientation-dependent

instability.

However, SSPC orientation-dependent stability analysis based on 3D TLS shows that

discontinuity set 2 (247.99/47.79) and discontinuity set 4(295.57/79.58) will cause instability

at a slope with an orientation of 229/80, resulting to probability to be stable of <5%. This

result is in agreement with the condition of slope face 1 (229/80), which clearly shows several

sliding failures mostly at the upper part of the slope (Fig. 6-6). This is also consistent with the

result of probabilistic wedge failure analysis, which shows that the combination of

discontinuity set 2 and 3, and set 3 and 4 give a total probability of failure 91.9% and 86.5%,

respectively at a slope with an orientation of 229/80.


75

Table 11. Comparison of SSPC orientation-dependent slope stability analysis based manual field measurements against SSPC orientation-dependent analysis based on 3D TLS measurements.

Figure 6-6. Slope condition of slope face 1 (229/80) which shows several sliding failure planes of low relatively low dipping discontinuities (after, Gradizzi, 2005).

SSPC analysis based on Manual Field Measurements Disc. Set #

Disc. Dip Direction

Disc. Dip

Slope orientation

Apparent Slope Dip

Orientation-dependent stability

1 205 82 202/85 81.9892 stable 2 270 82 202/85 69.4356 5% 3 292 89 202/85 0.0121 stable 1 205 82 229/80 81.2541 stable 2 270 82 229/80 79.4513 stable 3 292 89 229/80 87.7984 stable SSPC analysis based on 3D TLS Measurements

Disc. Set #

Disc. Dip Direction

Disc. Dip

Slope orientation

Apparent Slope Dip

Orientation-dependent stability

1 254.22 80.46 202/80 74.6598 <5% 2 247.99 47.79 202/80 37.451 70% 3 205.44 78.31 202/80 78.2895 stable 4 295.57 79.58 202/80 -18.7077 95% 1 254.22 80.46 229/80 79.4763 stable 2 247.99 47.79 229/80 46.1909 <5 3 205.44 78.31 229/80 77.2802 stable 4 295.57 79.58 229/80 65.1805 <5


76

6.8. Discussion and Conclusion

The results of the analysis show that probabilistic analysis gives a more realistic result than

deterministic approach because it considers the uncertainty inherent in the 3D TLS data. Particularly,

when only the mean orientation of the discontinuity set is used in the analysis, it did not show any

possibility of failure, whereas if it varied it indicates a probability of failure.

However, one of the main limitations of the adapted probabilistic analysis is that the computation of

probability of failure is based on the conditional probability of kinetic failure from kinematic failure.

It means that the assessment depend so much on the orientation-dependent stability of the slope.

However, orientation-independent slope failure also occurs due to breaking of intact rocks or buckling

mechanism (Hack, 1998). Thus, SSPC gives better assessment of the stability of the slope as it

incorporate both the orientation-dependent and orientation–independent slope stability analysis and

compute it separately. Second, SSPC analysis separate various geotechnical unit in a particular slope

and conduct the analysis per geotechnical unit in a slope. This is important as one slope may contain

several geotechnical units that geomechanically behave differently from each other.

Incorporation of 3D TLS and GPR in SSPC slope stability analysis may also helps in the modelling

and in the assessment of the stability of the slope. Particularly, 3D TLS can help to detect those

discontinuities in the upper part of the slope, which are beyond the reach of manual field

measurements. In this study, GPR provide orientation and persistence of trace discontinuities which

hard to establish during field measurement. This leads to a better estimation of spacing of the actual

discontinuity set which is one of the major parameter in SSPC analysis. However, there are

considerable uncertainties and limitations associated in the two methods, which should be taken into

account.


77

7. CONCLUSION AND RECOMMENDATION

7.1. Conclusion

The main objective of this research is to assess the stability of Montemerlo slope based on the 3D

TLS and GPR data. To achieve this objective, discontinuity plane modeling was carried out separately

with the data derived from the two survey methods. The reliability and the limitations of both methods

were analyzed and were validated with field measurements. Then, the orientation and spacing data

derived from the two methods were used as an input in probabilistic analysis and SSPC slope stability

analysis. Based on the results discussed in the previous chapters, the following conclusions can be

drawn:

7.1.1. 3D Terrestrial Laser Scanning Reliability analysis

This study showed the limitations of 3D Terrestrial Laser scan survey and associated uncertainty to

derive the discontinuity orientation and spacing, which include the following:

• Some of the discontinuities are not detected due to occlusion and orientation bias

• Most of the traces from discontinuities measured by field measurements are not detected.

Some of the traces are detected but the measured orientations may not represent the actual

orientation due to under sampling on too small exposures, or due to possible erosion and

weathering that changed the orientation of exposed part of the discontinuity.

• In the data processing, outlier removal is based mainly on the judgment of the user, which

adds subjectivity and susceptibility to error especially for users with less experience in rock

mass characterization. Error in outlier removal significantly affects the resulting statistics of

the discontinuity orientation of the processed data.

• Determination of the number of clusters in the plot of the discontinuity orientation is often not

unambiguous and the user may have to make his own (engineering) judgment. This may also

cause over- or under-estimation of the discontinuity set spacing, as the latter is dependent on

the number of clusters.

• Some of the discontinuity set in 3D TLS model weakly correlate with scanline measurements,

while others have fair to strong correlation. The weak correlation with scanline

measurements, is mainly due to the low dipping discontinuities at the upper part of the slope

that are detected by 3D TLS, but obviously out of reach of scanline measurements. Non-

detection of several trace discontinuities and possible outlier-effect also contribute to the

difference.

• Despite these limitations, 3D TLS was able to provide a large number of discontinuity

orientation data as compared to the scanline technique that can be a basis for a sound

statistical analysis.


78

7.1.2. Ground penetrating radar discontinuity measurements

The proposed discontinuity detection algorithm for Ground Penetrating Radar (GPR) data discontinuity measurements helps in objectively delineating the linear coherent events, amidst the presence of high amplitude, non-coherent reflections. This detection technique when integrated with GPR 3D modeling significantly improved the correlation and the interpretation of various linear events in the GPR images. This led to the determination of vital information on subsurface discontinuity characteristics, which include the following:

• delineation and verification of the subsurface extension of discontinuities detected by the 3D TLS and scanline measurements;

• detection of discontinuities not detected by 3D TLS and scanline measurements; • determination of the persistence along the strike of some trace discontinuities, whose

persistence are hard to determine by a scanline technique; • estimation of set spacing of exposed major discontinuities compared to 3D TLS and scanline

measurements, although, significant uncertainties are involved.

Although the usefulness of GPR is limited by several limitations and uncertainties in the proposed

processing algorithm and in the application of GPR, in general, for discontinuity detection; GPR is

considered as useful addition for discontinuity identification and characterization.

The limitations are due to:

1) the proposed detection technique might not detect some of the linear events that do not fall

within the threshold set.

2) the detected linear event may not give the actual orientation and spacing of discontinuities

due to three-dimensional spherical propagation effect of the EM waves. This gives difficulties

in the interpretation on the true geometrical orientation of the source linear reflections. Thus,

a proper analysis on the wave propagation and geometrical orientation of possible reflector

should be taken into account in the interpretation of linear event. All of these limitations

introduce uncertainty in the interpretation of the orientation and spacing of the

discontinuities.

7.1.3. Stability Analysis of Montemerlo SLope

Probabilistic approach gives a more realistic assessment of the stability of the slope as compared to

deterministic approach, as it considers the uncertainties and variation inherent in the 3D TLS.

However, one of the main limitations of the adapted probabilistic analysis is that the computation of

probability of failure is based on the conditional probability of kinetic failure. It means that the

assessment depend so much on the orientation-dependent stability of the slope. However, orientation-

independent slope failure also occurs due to breaking of intact rocks or buckling mechanism (Hack,

1998; Hack et al., 2003). Thus, SSPC gives better assessment of the stability of the slope as it

incorporate both the orientation-dependent and orientation–independent slope stability analysis and

compute it separately.


79

Second, SSPC analysis separates various geotechnical units in a particular slope and conducts the

analysis per geotechnical unit in a slope. This is important as one slope may contain several

geotechnical units that geomechanically behave differently from each other.

3D TLS and GPR measurements can be used in slope stability analysis with due consideration to the

limitations and uncertainty involved. However, GPR should be used only as a complementary

technique in rock mass characterisation and should be given a proper field validation due to

considerable uncertainty involved. Probabilistic analysis shows that combination of various

combinations of discontinuity may lead to wedge failures on the slope under investigation. SSPC

analysis based on 3D TLS data shows that various orientation-dependent instabilities are possible.

7.2. Limitation and Recommendation

Limitation of the Study

• This study investigates the effect of using 3D TLS orientation data when used in probabilistic

analysis. Thus, only orientation data was considered as a random variable in probabilistic

analysis so that a comparison can be made against deterministic analysis that used only the

mean orientation of the of 3D TLS discontinuity sets as an orientation input parameter. Other

rock mass parameters such as shear strength should be also considered as random variables.

• Discontinuity surface roughness was not derived from the 3D TLS point cloud data.

• The orientation of the detected linear events were not quantitatively defined, however, this

can be done using the Hough Transform and/or Radon Transform mathematical algorithm

which suited for mathematically defining linear features in a binary image such as the result

of segmentation carried out in this research.

Recommendation

1. Roughness can be also derived from 3D TLS point cloud data and can be incorporated as

shear strength parameter for slope stability analysis.

2. Other rock mass parameter should be considered as probabilistic parameter for probabilistic

slope analysis.

3. The orientation of segmented linear coherent event can be objectively defined using Hough

Transform and Radon Transform mathematical algorithm.


80

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Theune, U., Schmitt D.R., and Sacchi, M.D.2005. Mapping fractures with GPR at Turtle Mountain,

submitted to CSEG annual convention, CSEG, Calgary,

Toshioka, T., Tsuchida, T., and Sasahara, K. (1995). Application of GPR to detecting and mapping

cracks in rock slopes. Journal of Applied Geophysics v. 33 (1): 119-124.

Xie, X. L. and Beni, G., 1991. A validity measure for fuzzy clustering.IEEE Trans. Pattern Anal.

Machine InteN., 13(8), 841-847.

Yoon W.S., Jeong U.J., Kim J.H., 2002. Kinematic analysis for sliding failure of multi-faced rock

slopes. Q. J. Eng. Geol. 2002: p. 22, 19–30.

Zillur Rahman, M., 2005. Deriving roughness characteristics of rock mass discontinuities from

terrestrial laser scan data. MSc. Thesis, ITC, Enschede, 100 pp.

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87

9. APPENDICES

Appendix 1 Matlab Script used in 3D Modelling GPR Binary Intensity Image

This is the script for the 3D Model of GPR profile V24-V28 and H15-16 along SCanline#4

Author: Mark Anthony Pernito

The script in the last part (script 68-75) used for plotting vertical and horizontal GPR in their

respective coordinates was adopted partly from method developed by Theune(2004)

1 V24croprx=double(imextendedmax(V24cropr,4));

2 V24croprx0=double(imextendedmax(V24cropr,5));


4 V24croprx(:,190:512)=0;V24croprx0(:,200:512)=0;V24croprx4(:,190:512)=0;




8 V24croprx2(:,300:512)=0;V24croprx3(:,300:512)=0;

9 V24croprx=V24croprx+V24croprx0+V24croprx4+V24croprx1+V24croprx2+V24croprx3;

Command line 1-3 and 5-7 are command to delineate maximum linear events with a threshold on

sudden change in intensity of 3, 4,5 and 18,14,11 respectively. The output is a binary image showing

coherent linear event based on the specified threshold of extreme change in intensity. Script 4 and 8 is

command to removed non-linear/non-coherent events. Command 9 is a command to combine all the

resulting binary maps with different extreme intensity threshold into one image representing GPR

V24.

10 V25croprx=double(imextendedmax(V25cropr,4));V25croprx5=double(imextendedmax(V25cropr,5));

11 V25croprx0=double(imextendedmax(V25cropr,3));V25croprx4=double(imextendedmax(V25cropr,2));

12V25croprx(:,190:512)=0;V25croprx0(:,200:512)=0;V25croprx4(:,170:512)=0;V25croprx5(:,170:512)=0;




16 V25croprx6=double(imextendedmax(V25cropr,11));V25croprx3(:,300:512)=0;V25croprx6(:,300:512)=0;

17 V25croprx=V25croprx+V25croprx0+V25croprx1+V25croprx4+V25croprx5+V25croprx6+V25croprx2;

Command line 10 to 17 are command to delineate coherent linear reflection events in vertical GPR image, V25.

The procedure for delineating linear coherent event is the same as in command line 1-9.







24V26croprx3(:,300:512)=0;V26croprx6(:,300:512)=0;V26croprx7(:,300:512)=0;V26croprx6(:,300:512)=0;


88

25 V26croprx=V26croprx+V26croprx0+V26croprx+V26croprx4+V26croprx6+V26croprx7+V26croprx2;

The script 18 to 25 are command to delineate coherent linear reflection in Vertical GPR image, V26. The step by

step procedure for delineating linear coherent event is the same as in script 1-9.

26 V27croprx=double(imextendedmax(V27cropr,4));V27croprx5=double(imextendedmax(V27cropr,5));


28 V27croprx(:,190:512)=0;V27croprx0(:,200:512)=0;V27croprx4(:,200:512)=0;V27croprx5(:,200:512)=0;




32 V27croprx6=double(imextendedmax(V27cropr,11));V27croprx3(:,300:512)=0;

33 V27croprx6(:,300:512)=0;V27croprx7(:,400:512)=0;

34 V27croprx=V27croprx+V27croprx0+V27croprx8+V27croprx1+V27croprx4+V27croprx7+

V27croprx5+V27croprx6+V27croprx2;

Command line 26 to 34 is command to delineate coherent linear reflection in Vertical GPR image, V27. The

procedure for delineating linear coherent event is the same as in command line 1-9.







41 V28croprx3(:,300:512)=0;

42 V28croprx=V28croprx+V28croprx0+V28croprx+V28croprx4+V28croprx2;

Command line 35 to 42 are command to delineate coherent linear reflection in Vertical GPR image, V28. The

procedure for delineating linear coherent event is the same as command line 1-9.

43 H15crop2rx=double(imextendedmax(H15crop2,10));

44 H15crop2rx0=double(imextendedmax(H15crop2,4));


46 H15crop2rx0(190:512,:)=0;H15crop2rx1(190:512,:)=0;





51 H15crop2rx=H15crop2rx0+H15crop2rx1+H15crop2rx+H15crop2rx3+H15crop2rx4+H15crop2rx4;

Command line 43 to 51 are command to delineate coherent linear reflection in Horizontal GPR image H15

along slope 4. The procedure for delineating linear coherent event is the same as in command line 1-9.

52 H16crop2rx=double(imextendedmax(H15crop2,10));



55 H16crop2rx0(190:512,:)=0;H15crop2rx1(190:512,:)=0;




89



60 H16crop2rx=H15crop2rx0+H15crop2rx1+H15crop2rx+H15crop2rx3+H15crop2rx4+H15crop2rx4;

Command line 52 to 60 are command to delineate coherent linear reflection in Horizontal GPR image H16

along slope 4. The procedure for delineating linear coherent event is the same as in script 1-9.

61 V24croprx(V24croprx(:,:)>0)=1;





66 H15crop2rx(H15crop2rx(:,:)>0)=1;

67H15crop2rx(H15crop2rx(:,:)>0)=1;

Script 61-67 is to ensure that the combined binary images consisting linear coherent event with different

extreme intensity threshold, will have consistent maximum value of one (as in a binary image). This is necessary

as during 3D plotting, color rendering will be based on the pixel value. To avoid confusion in the interpretation

arising from variation in different color, the combined imaged is maintain as binary map showing only linear

coherent events.

68 x=1:1270;y=1:512;z=1:627;

69 h=hslice(x',y,H15crop2rx,313);

70 h=hslice(x',y,H15crop2rx,1);

71 v2=vslice(ones(1,512).*1219,y,z,V28croprx);





Command line 68-75 is a command for 3-Dimensional Plotting of various Vertical and Horizontal

GPR profile, V24-28 and H15-16, respectively. In script 68, X represent the horizontal dimension of

horizontal GPR, Y represents the depth of vertical and horizontal profile, while Z is the height of

vertical profile.


90

Appendix 2 Mathlab Script for Probabilistic Slope Wedge Analysis Author: Mark Anthony Pernito The script partly adapted the Limit Equilibrium An alysis by Hoek and Bray(1981) and procedure on the probabilistic wedge slope stability analysis proposed by Park and West, 2001 1 Randtool % This is the command to generate random variable based on specified probability density

function and statistical input parameter

2 R=rand(25000,1); % This is the uniformly distributed random number from 0 to 1

3 Z = zeros(25000,10); This is to create a matrix for Monte Carlo simulation with 25, 000 iteration

% Command Line 4-9 are the input statistical parameters of two discontinuities from 3D TLS data

input statistical parameters of two discontinuities from 3D TLS data 4 Z(:,1)=205; % This is the mean dip direction of discontinuity 1

5 Z(:,2)=292; % This is the mean dip direction of discontinuity 2

6 Z(:,3)=82; % This is the mean dip angle of discontinuity 1

7 Z(:,4)=89; % This is the mean dip angle of discontinuity 2

8 Z(:,5)=26; % This is the Fisher’s constant K of Discontinuity 1

9 Z(:,6)=35; % This is the Fisheris constant K of Discontinuity2

10 Z(:,7)=360.*R; %This is the uniform distribution from 0 to 360o necessary to generate random discontinuity

based on equation 32 (Queck and Lueng,1995)

11 Z(:,9)=rand(25000,1);

12 Z(:,8)=rand(25000,1); %uniformly distributed random number from 0 to 1 to derived angle of deviation

based on Fisher's K constant ( Queck and Lueng, 1995; Park, 2001)

13 Z(:,10)=(acos(log(1-Z(:,8))./Z(:,5)+1)).*180./pi;

14 Z(:,11)=(acos(log(1-Z(:,9))./Z(:,6)+1)).*180./pi;

%command line 13 and 14 are calculation of the angular distance of the generated poles from mean

(equation 32)

15 B=zeros(25000,17);

16 x=pi/180;

17 B(:,1)=abs(rad2deg(asin((sin(deg2rad(Z(:,3))-18

deg2rad(Z(:,10))).*sin(deg2rad(Z(:,10)))+8.*cos(deg2rad(Z(:,3))).*(sin(deg2rad(Z(:,10))./2)).^2.*(sin(deg2r

ad(1(:,7))./2)).^2)./sin(deg2rad(Z(:,10))))));

18 B(:,2)=abs(rad2deg(asin((sin(deg2rad(Z(:,4))-

deg2rad(Z(:,11))).*sin(deg2rad(Z(:,11)))+8.*cos(deg2rad(Z(:,4))).*

(sin(deg2rad(Z(:,11))./2)).^2.*(sin(deg2rad(Z(:,7))./2)).^2)./sin(deg2rad(Z(:,11)))))); %beta2

% command line 17 and 18 is calculation of the dip angle of all the generated pole vectors (equation 33)

19 B(:,3)=abs(Z(:,1)-acos((cos(Z(:,10).*x)-sin(Z(:,3).*x).*sin(B(:,1).*x))./cos(Z(:,3).*x).*cos(B(:,1).*x))./x)+90;

20 B(:,4)=abs(Z(:,2)-acos((cos(Z(:,11).*x)-sin(Z(:,4).*x).*sin(B(:,2).*x))./cos(Z(:,4).*x).*cos(B(:,2).*x))./x)+90;


91

% Above is the calculation of the trend of the randomly generated pole vectors as express by equation 34

21 K1=B(:,1:4); %This is to get all the pair of generated discontinuity orientation (dip angle and dip direction)

from the simulation

%dlmwrite('kinematics1.txt',K1,'\t'); %This is to export all the pair of dip angle and dip direction to

Rockworks software. This is to compute for the plunge and the trend of the line of intersections of every

combination of two discontinuities

22 KTin=dlmread('kinematics10.txt'); %This is to import the plunge and trend of the line of intersection of

all the pair of discontinuity set 1 and 2 that formed a wedge (from Rockworks to Matlab)

23 KTin(:,5)+90; %

%//////////////////////////////////////////////////////////////////////////

% PROBABILISTIC KINEMATIC ANALYSIS %//////////////////////////////////////////////////////////////////////////

% input parameters for KINEMATIC Analysis 24 P1=80; %slope dip

25 P2=229; %slope direction

26 P3=0; %dip of upper ground surface

27 P3a=229; %dip direction of upper ground surface

28 P4=36.9; %Angle of friction1

29 P4a=29.2; %Angle of friction2

30 B(:,5)=P1; %

31 B(:,6)=0; % top slope dip

32 B(:,7)=P2; %slope direction

33 B(:,8)=P3a; % top slope direction

34 B(:,5)=abs(atan(tan(B(:,5).*x).*cos(abs(KTin(:,5)-B(:,7)).*x))./x); %this is the apparent slope dip

% Command line 30 to 31 represents the table of the generated discontinuity orientation of each discontinuity

set. Included in the table are the plunge and trend of intersections of each pair of two discontinuities that formed

wedges.

% Probabilistic Kinematic Analysis For Planar Sliding Failure

35 KTin(:,8)=B(:,7);

36 KTin(:,9)=abs(KTin(:,8)-KTin(:,3)); % difference of slope direction and direction of discontinuity 1

37 KTin(:,10)=abs(KTin(:,8)-KTin(:,4)); % difference of slope direction and direction of discontinuity 2

38 KFP1=find(KTin(:,1)<P1 & KTin(:,1)>P4 & KTin(:,9)<=20); %condition for Planar Sliding Failure for

discontinuity 1(dip slope>dip discotinuity>angle friction)

39 KFP2=find(KTin(:,2)<P1 & KTin(:,2)>P4 & KTin(:,10)<=20); %condition for Planar Sliding Failure for

discontinuity 2

40 FSP=size(cat(1,KFP2,KFP1));

41 YP=(size(KTin))*2;

42 KINEMATIC_PROBABILITY_PlanarFailure=FSP(:,1)/YP(:,1) %( total number of kinematically unstable

discontinuities/total number of generated discontinuities)

% Command line 35 to 42 is an optional analysis for planar sliding failure of all the generated discontinuity

orientations


92

% Probabilistic Kinematic Analysis For Wedge Failure 43 KTin(:,13)=abs(KTin(:,5)-B(:,7)); % This is the difference between the slope dip direction and trend of the

line of intersection of the formed wedge.

44 KFW=find(KTin(:,6)<B(:,5) & KTin(:,6)>P3 & KTin(:,13)<=90);

%condition for Wedge Sliding Failure (top dip<intersection dip < apparent slope dip) as express in equation 22

and 23 (Park,2001).

44 FSW=size(KFW); This is the total number of kinematically unstable wedge

45 Y1=size(KTin); This is the total number of wedge formed

46 KINEMATIC_PROBABILITY_WedgeFailure=FSW(:,1)/Y1(:,1)

%(number of kinematically unstable wedge/total number of iteration)

% command line 43-46 are the implementation of kinematic wedge failure analysis. Command line 44 is used

to find all the wedge that satisfy the condition for kinematic wedge failure as specified in equation 22 and 23.

%//////////////////////////////////////////////////////////////////////////

% PROBABILISTIC KINETIC ANALYSIS

%/////////////////////////////////////////////////////////////////////////

%Only wedges evaluated as kinetically unstable will be analysed for

%Wedge failure Limit equilibrium analysis based on Hoek and Bray (1981) Algorithm.

Notation on the Limit Equilibrium Analysis by Hoek and Bray (1981)

45 % KFW2=find(KTin(:,6)<P1 & KTin(:,6)>P3 & KTin(:,13)>90);

46 % This is the the matrix of kinematically stable wedge

47 B=KTin(KFW,1:6); % This is the matrix of kinematically unstable wedge

48 Y3=size(B); This is to create a matrix (table) with a size based on the number of kinematically unstable

wedge

% input parameters for KINETIC ANALYSIS (Limit equilibrium analysis)

49 B(:,7)=P1;%slope dip

50 B(:,8)=P3; % top slope dip

51 B(:,9)=P2; %slope direction

52 B(:,10)=P3a; %top slope direction

53 B(:,11)=P4; %angle of internal friction of discontinuity 1

54 B(:,12)=P4a; %angle of internal friction of discontinuity 2

55 B(:,13)=27; %Unit weight rocks

56 B(:,14)=20; %slope height

57 B(:,5)=abs(atan(tan(B(:,7).*x).*cos(abs(B(:,5)-B(:,9)).*x))./x); % this is the apparent slope dip

58 %B(:,14)=B(:,14).*abs(tan(B(:,6).*x)./(tan(B(:,5).*x))); % optional height of the wedge based on the

apparent slope dip.

59 B(:,14)=B(:,14).* rand(Y3,1) % this is an optional command to randomly generate height of a wedge with

uniform distribution based on the height of the slope

60 B(:,15)=32; %cohesion of discontinuity 1

61 B(:,16)=32; %cohesion of discontinuity 2

62 B(:,17)=0; %pore pressure 1

63 B(:,18)=0; %pore pressure 2

64 B(:,19)=1; %slope doesnt overhang

65 %B(:,17)=10.*B(:,14).*rand(Y3,1)./6; %this is an optional command to randomly generate a pore water

pressure with uniform distribution based on the height of the


93

66 %B(:,18)=10.*B(:,14).*rand(Y3,1)./6; %this is an optional pore water pressure 2 generated from uniform

distribution

% Command line 49-64 are the input parameters for limit equilibrium analysis method by Hoek and Bray,

(1981). Command line 59 is the command to generate the height of wedge based on uniform distribution.

Command line 58 is used to generate uniform distribution of pore pressure depending on the height of the

wedge.

This is the notations used in Limit Equilibrium analysis, which can be found at appendix 2 of Rock Slope

Engineering by Hoek and Bray (1981).

% Limit Equilibrium Analysis Hoek & Bray, 1981 algorithm;

67 C = zeros(Y3,24); This is to create a matrix for all the kinematically unstable wedge, all of which will be

further analyzed for kinetic stability using limit equilibrium analysis


94

68 C(:,1)=((sin(B(:,1).*x).*sin(B(:,3).*x-B(:,4).*x)).^2).^.5;

69 C(:,2)=((sin(B(:,1).*x).*cos(B(:,3).*x-B(:,4).*x)).^2).^.5;

70 C(:,3)=((cos(B(:,1).*x)).^2).^.5;%az

% Command line 68, 69, 70 is the component of unit vector (ax, ay, az) in the direction normal to the plane 1

71 C(:,4)=((sin(B(:,7).*x).*sin(B(:,7).*x-B(:,4).*x)).^2).^.5;%fx

72 C(:,5)=((sin(B(:,7).*x).*cos(B(:,7).*x-B(:,4).*x)).^2).^.5;%fy

73 C(:,6)=((cos(B(:,11).*x)).^2).^.5;

% Command line 71-73 are the component of unit vector in the direction normal to the plane 2

75 C(:,7)=((sin(B(:,2).*x)).^2).^.5; % by

76 C(:,8)=((cos(B(:,2).*x)).^2).^.5; % bz

77 C(:,9)=C(:,1).*C(:,7); % i

78 C(:,10)=C(:,4).*C(:,2)-C(:,5).* C(:,1); % gz

79 C(:,11)=C(:,7).*(C(:,6).*C(:,1)-C(:,4).* C(:,3))+C(:,8).*C(:,10);% q

60 C(:,12)=C(:,11)./C(:,9); %

61 C(:,13)=C(:,2).*C(:,7)+C(:,3).* C(:,8);% r

62 C(:,14)=1-C(:,13).^2; % k

63 C(:,15)=B(:,11).*B(:,12).*C(:,11)./3./C(:,10); % z

64 C(:,16)=(-1).*C(:,7).*C(:,4)./C(:,10); % p

65 C(:,17)=((C(:,15)./C(:,14)).*(C(:,3)-C(:,13).* C(:,8))-C(:,16).*B(:,15)).*C(:,16)./((C(:,16)).^2).^.5; % n1

66 C(:,18)=((C(:,15)./C(:,14)).*(C(:,8)-C(:,13).* C(:,3))-B(:,16)); % n2

67 C(:,19)=(C(:,15).*C(:,3)-C(:,13).* B(:,16)-C(:,16).*B(:,15)).*C(:,16)./((C(:,16)).^2).^.5; % m1

68 C(:,20)=(C(:,15).*C(:,8)-C(:,13).* C(:,16).*B(:,15)-B(:,16)); % m2

69 C(:,21)=(C(:,17).*tan(B(:,11).*x)+C(:,18).*tan(B(:,10).*x)+(((C(:,16)).^2).^.5).*B(:,13)+B(:,14)).*

((C(:,14)).^.5)./((( C(:,15).*C(:,9)).^2).^.5);

% this the equation for calculating the factor of safety when there is contact on plane 1 only

70 C(:,22)= ((C(:,19).*tan(B(:,11).*x)+(((C(:,16)).^2).^.5).*B(:,13))./((C(:,15).^2).*(1-71

C(:,3).^2)+C(:,14).*(B(:,16).^2)+2.*(C(:,13).*C(:,3)-C(:,8)).*C(:,15).*B(:,16)).^.5);%FS2

% FS2= Factor of Safety when there is contact on plane1 only

72C(:,23) = ((C(:,20).*tan(B(:,16).*x)+B(:,16))./((C(:,15).^2).*C(:,7).^2+C(:,14).*(C(:,16)).^2.*(B(:,17).^2)+

2.*(C(:,13).*C(:,8)-C(:,3)).*C(:,16).*C(:,15).*B(:,19)).^.5);%FS3

%FS3 = this the equation for calculating the factor of safety when there is contact on plane 2 only

73 C(:,24)=0;%FS4

% FS4 = This is the factor of safety when contact is lost on both planes and the wedge floats as a result of water

pressure acting on planes 1 and 2. In this case, the factor of safety falls to zero.

74 F1=find(C(:,17)>0 & C(:,18)>0);

% This is the table of all wedges with factor of safety for wedge with contact on plane 1 only

75 F2=find(C(:,18)<0 & C(:,19)>0);

% This is the table of wedges with factor of safety that lost contact on both

76 F3=find(C(:,17)<0 & C(:,20)>0);

% This is the table of all wedges with factor of safety for wedge with contact on plane 2 only


95

77 F4=find(C(:,19)<0 & C(:,20)<0);

% This is the table of all wedges with factor of safety for wedge with contact lost on both planes

78 FS1=C(F1,21);

79 FS2=C(F2,22);

80 FS3=C(F3,23);

81 FS4=C(F4,24);Y1=size(FS4);FS41=rand(Y1,1);

82 FS=cat(1,FS1,FS2,FS3,FS41);% this is the combined table of FS1, FS2, FS3, FS4 selected based on

n1,n2,m1,m3 criteria

% Command line 78-82 is used to tabulate all the factor of safety based on n1, n2, m1 and m3 criteria

83 Proba=find(FS(:,1)>1) ; % This is to find all the results with a factor of safety ( FS) greater than 1

84 FSLES1=size(FS)-size(Proba); % This is to find the total number of FS less than 1

85 Y=size(FS); % This is the total number of wedge kinematically unstable

86 KINETIC_PROBABILITYFailure=FSLES1(:,1)/Y(:,1) % this the total number of wedge kinetically

unstable/Total number of wedge kinematically unstable

87 TOTAL_PROBABILITYFAILURE=KINETIC_PROBABILITYFailure.*KINEMATIC_PROBABILITY_WedgeFailure

89 FS=FS(FS,1);hist(FS) % This is the histogram of the calculated factor of safety of all the iteration


96

Appendix 3 160 Segmented discontinuity plane extracted from Optech ILRIS

3D TLS point cloud data of Montemerlo SLope

LABEL DIPDIR DIP a b c d SIZE NOPNTS FUZZY C5 Xi Yi Zi

1 224.378 78.661 -0.69 -0.7008 0.1966 7167.8 46.789 3760 3 0.69 0.7 0.197

2 200.909 84.2453 -0.36 -0.9294 0.1003 8483.3 20.026 223074 1 0.36 0.93 0.1

3 201.428 83.1265 -0.36 -0.9242 0.1197 8455.2 18.904 197210 1 0.36 0.92 0.12

4 263.109 87.3465 -0.99 -0.1199 0.0463 2842.5 3.962 9523 2 0.99 0.12 0.046

5 199.984 76.0618 -0.33 -0.9121 0.2409 8292.8 6.3177 50834 1 0.33 0.91 0.241

6 267.936 86.6686 -1 -0.036 0.0581 2142.2 11.006 33116 2 1 0.04 0.058

8 236.91 67.3371 -0.77 -0.5038 0.3853 5663 3.2486 8025 3 0.77 0.5 0.385

10 261.147 69.1504 -0.92 -0.1438 0.3559 2906.1 1.2625 1119 2 0.92 0.14 0.356

11 209.361 65.7281 -0.45 -0.7945 0.4111 7511.3 12.163 5438 1 0.45 0.79 0.411

12 224.537 76.8119 -0.68 -0.694 0.2281 7104.5 1.6484 1367 3 0.68 0.69 0.228

13 215.351 81.7619 -0.57 -0.8072 0.1433 7857 1.1418 1665 1 0.57 0.81 0.143

14 284.947 77.9523 -0.94 0.25224 0.2087 -388.7 1.6294 1187 4 0.94 0.25 0.209

15 211.901 75.3248 -0.51 -0.8213 0.2533 7860 5.5464 9287 1 0.51 0.82 0.253

17 262.263 73.2576 -0.95 -0.1289 0.2881 2833.6 6.6319 88442 2 0.95 0.13 0.288

18 243.232 76.9127 -0.87 -0.4387 0.2264 5294.8 7.1666 39807 3 0.87 0.44 0.226

19 242.521 84.8841 -0.88 -0.4596 0.0892 5500.1 12.656 128170 3 0.88 0.46 0.089

20 219.901 74.6677 -0.62 -0.7399 0.2644 7371.3 9.2066 29460 1 0.62 0.74 0.264

21 199.701 84.6692 -0.34 -0.9374 0.0929 8517.1 2.3644 9224 1 0.34 0.94 0.093

23 246.747 37.5245 -0.56 -0.2405 0.7931 3038.9 2.187 2811 2 0.56 0.24 0.793

25 96.3568 74.6633 0.958 -0.1068 0.2645 -881.3 2.4445 773 4 0.96 0.11 0.264

26 218.508 78.9434 -0.61 -0.768 0.1918 7596.9 6.2333 41163 1 0.61 0.77 0.192

34 257.995 75.045 -0.94 -0.201 0.2581 3430.6 5.9826 28325 2 0.94 0.2 0.258

35 204.28 82.9143 -0.41 -0.9046 0.1234 8371.5 16.468 101893 1 0.41 0.9 0.123

36 214.896 87.5483 -0.57 -0.8194 0.0428 7962.4 12.143 31684 1 0.57 0.82 0.043

37 268.088 89.9337 -1 -0.0334 0.0012 2125.1 7.9842 110774 4 1 0.03 0.001

38 28.1348 51.9769 0.371 0.69468 0.6160 -6560 1.4569 2181 1 0.37 0.69 0.616

39 70.371 50.4457 0.726 0.25901 0.6368 -3539 1.1691 1647 4 0.73 0.26 0.637

40 254.87 64.4934 -0.87 -0.2356 0.4306 3578.5 1.8116 4421 2 0.87 0.24 0.431

41 62.7008 89.208 0.889 0.45859 0.0138 -5504 2.711 11851 3 0.89 0.46 0.014

42 214.044 69.3783 -0.52 -0.7755 0.3522 7496.1 2.5303 7427 1 0.52 0.78 0.352

43 15.2321 67.257 0.242 0.88985 0.3866 -7961 1.2105 1255 1 0.24 0.89 0.387

45 264.315 67.4639 -0.92 -0.0915 0.3833 2460.8 10.678 83477 2 0.92 0.09 0.383

46 186.721 77.5759 -0.11 -0.9699 0.2151 8383.4 6.1546 12208 1 0.11 0.97 0.215

47 123.278 89.0974 0.836 -0.5486 0.0158 3074.2 3.371 10485 4 0.84 0.55 0.016

48 207.705 82.188 -0.46 -0.8771 0.1359 8238.9 17.455 56850 1 0.46 0.88 0.136

49 18.7579 88.3053 0.321 0.94647 0.0296 -8576 1.995 6633 1 0.32 0.95 0.03

50 245.53 76.4116 -0.88 -0.4026 0.2349 5023.5 2.4843 2509 3 0.88 0.4 0.235

51 257.714 74.7622 -0.94 -0.2053 0.2628 3459.5 4.6038 40468 2 0.94 0.21 0.263

52 202.477 89.1513 -0.38 -0.9239 0.0148 8489.7 10.095 92116 1 0.38 0.92 0.015

53 45.3998 74.0812 0.685 0.67523 0.2743 -6964 2.1097 4492 1 0.68 0.68 0.274

54 206.377 84.9697 -0.44 -0.8924 0.0877 8336 2.092 5626 1 0.44 0.89 0.088

59 210.667 80.3371 -0.5 -0.8479 0.1679 8072.9 6.7831 14903 1 0.5 0.85 0.168

60 218.402 80.9486 -0.61 -0.7739 0.1573 7652.1 10.796 71760 1 0.61 0.77 0.157

62 255.841 77.2972 -0.95 -0.2386 0.2199 3746.9 4.2485 11693 2 0.95 0.24 0.22

64 240.284 51.773 -0.68 -0.3894 0.6188 4521.4 1.5051 1734 2 0.68 0.39 0.619

65 199.17 89.322 -0.33 -0.9445 0.0118 8563 7.3846 72577 1 0.33 0.94 0.012

66 202.963 83.5605 -0.39 -0.915 0.1122 8428.5 5.5715 8651 1 0.39 0.91 0.112

68 252.265 77.9861 -0.93 -0.2979 0.2081 4221.5 3.8787 3922 2 0.93 0.3 0.208

71 124.453 60.601 0.718 -0.4929 0.4909 2820.3 1.5859 836 4 0.72 0.49 0.491


97

LABEL DIPDIR DIP a b c d SIZE NO

PNTS FUZZY

C5 Xi Yi Zi

72 117.91 88.6261 0.883 -0.4679 0.0240 2320.6 3.0859 6276 4 0.88 0.47 0.024

73 204.662 79.2151 -0.41 -0.8927 0.1871 8279.1 2.845 5437 1 0.41 0.89 0.187

74 257.401 66.8139 -0.9 -0.2005 0.3937 3330.9 3.5106 13538 2 0.9 0.2 0.394

76 248.842 38.3532 -0.58 -0.224 0.7842 2929 0.8157 704 2 0.58 0.22 0.784

77 202.834 85.4696 -0.39 -0.9188 0.0790 8455.3 7.7175 61626 1 0.39 0.92 0.079

78 125.85 86.2586 0.809 -0.5844 0.0653 3439.5 1.3383 606 4 0.81 0.58 0.065

82 217.207 54.0377 -0.49 -0.6447 0.5873 6319.2 0.6859 696 1 0.49 0.64 0.587

83 260.687 48.5862 -0.74 -0.1214 0.6615 2364.3 1.4348 883 2 0.74 0.12 0.661

89 120.015 88.3842 0.866 -0.5 0.0282 2621.9 3.1502 5509 4 0.87 0.5 0.028

93 269.919 57.2761 -0.84 -0.0012 0.5406 1544.4 6.7588 11879 2 0.84 0 0.541

96 260.499 71.9186 -0.94 -0.1569 0.3104 3048.4 6.4146 26099 2 0.94 0.16 0.31

101 187.784 78.5394 -0.13 -0.971 0.1987 8416.8 3.648 3510 1 0.13 0.97 0.199

111 213.816 84.4241 -0.55 -0.8269 0.0972 7991 12.289 78317 1 0.55 0.83 0.097

112 303.359 73.36 -0.8 0.52685 0.2864 -2982 0.5487 747 4 0.8 0.53 0.286

120 81.3845 68.7184 0.921 0.13959 0.3630 -2896 2.2538 4496 4 0.92 0.14 0.363

121 325.895 83.6232 -0.56 0.82289 0.1111 -5902 2.3717 600 4 0.56 0.82 0.111

122 266.668 50.7919 -0.77 -0.045 0.6321 1786 3.8978 16468 2 0.77 0.05 0.632

124 325.549 69.2644 -0.53 0.77119 0.3541 -5543 0.7263 720 4 0.53 0.77 0.354

125 276.152 84.3783 -0.99 0.10665 0.0980 932 1.6278 2626 4 0.99 0.11 0.098

127 279.812 77.9082 -0.96 0.16664 0.2095 374.81 3.4798 4170 4 0.96 0.17 0.209

128 211.536 83.7488 -0.52 -0.8472 0.1089 8097.3 11.986 25644 1 0.52 0.85 0.109

130 239.568 80.6014 -0.85 -0.4997 0.1633 5774.5 0.583 613 3 0.85 0.5 0.163

131 219.228 59.0898 -0.54 -0.6646 0.5137 6587.5 2.6878 3901 1 0.54 0.66 0.514

133 273.554 68.9647 -0.93 0.05785 0.3589 1226.8 2.4414 717 2 0.93 0.06 0.359

134 202.096 84.6319 -0.37 -0.9225 0.0936 8460.6 5.3541 14415 1 0.37 0.92 0.094

135 299.985 89.2419 -0.87 0.49972 0.0132 -2622 1.3721 2510 4 0.87 0.5 0.013

136 223.177 85.4253 -0.68 -0.7269 0.0798 7385.2 3.6737 13180 1 0.68 0.73 0.08

139 200.609 84.451 -0.35 -0.9316 0.0967 8493 15.065 399849 1 0.35 0.93 0.097

151 239.561 52.2259 -0.68 -0.4004 0.6125 4619.1 1.476 1391 2 0.68 0.4 0.613

156 200.67 79.9015 -0.35 -0.9211 0.1753 8397.5 2.5435 2678 1 0.35 0.92 0.175

162 301.519 88.1319 -0.85 0.5225 0.0326 -2830 1.2254 1054 4 0.85 0.52 0.033

163 254.735 48.239 -0.72 -0.1964 0.6660 2958.7 1.4856 1519 2 0.72 0.2 0.666

167 269.17 80.192 -0.99 -0.0143 0.1703 1931.3 7.5855 44936 2 0.99 0.01 0.17

168 247.514 79.1263 -0.91 -0.3756 0.1886 4833.5 2.4856 10809 3 0.91 0.38 0.189

169 199.964 74.6406 -0.33 -0.9063 0.2649 8244.8 3.0316 1592 1 0.33 0.91 0.265

171 257.174 80.6742 -0.96 -0.2191 0.1620 3616 3.8572 6963 2 0.96 0.22 0.162

176 204.591 86.364 -0.42 -0.9075 0.0634 8413.2 12.113 28379 1 0.42 0.91 0.063

178 198.379 81.3876 -0.31 -0.9383 0.1497 8478.8 6.7926 28265 1 0.31 0.94 0.15

179 197.266 89.274 -0.3 -0.9549 0.0127 8595.3 2.1975 2821 1 0.3 0.95 0.013

180 239.44 33.6753 -0.48 -0.2819 0.8322 3242 1.9374 1229 2 0.48 0.28 0.832

189 194.865 59.1975 -0.22 -0.8302 0.5121 7387.4 2.9865 7220 1 0.22 0.83 0.512

191 256.445 81.4993 -0.96 -0.2318 0.1478 3735 4.2566 2414 2 0.96 0.23 0.148

195 199.134 87.0013 -0.33 -0.9435 0.0523 8551.4 11.748 89782 1 0.33 0.94 0.052

197 200.305 85.5266 -0.35 -0.935 0.0780 8513.6 6.0237 37123 1 0.35 0.93 0.078

198 337.525 83.3594 -0.38 0.91785 0.1156 -7024 3.3823 2639 4 0.38 0.92 0.116

199 196.157 89.4767 -0.28 -0.9605 0.0091 8605 5.6894 8621 1 0.28 0.96 0.009

200 204.374 83.9936 -0.41 -0.9059 0.1046 8387.6 7.1814 28531 1 0.41 0.91 0.105

201 84.2876 89.3354 0.995 0.09953 0.0116 -2691 5.1828 4601 2 0.99 0.1 0.012

202 175.095 69.5141 0.08 -0.9333 0.3500 7698.3 2.9813 5013 1 0.08 0.93 0.35

203 200.573 83.3588 -0.35 -0.9299 0.1157 8476.6 3.5717 8462 1 0.35 0.93 0.116


98

Continuation

LABEL DIPDIR DIP a b c d SIZE NOPNTS FUZZYC5 Xi Yi Zi

204 195.647 88.9407 -0.27 -0.9628 0.0185 8607.9 8.3215 62304 1 0.27 0.96 0.018

205 1.83024 75.6687 0.031 0.96839 0.2475 -8220 1.8692 3866 1 0.03 0.97 0.248

207 196.734 88.8174 -0.29 -0.9574 0.0206 8596.7 5.8214 35932 1 0.29 0.96 0.021

209 255.494 70.0779 -0.91 -0.2355 0.3407 3654.2 1.3105 2127 2 0.91 0.24 0.341

211 248.656 58.3364 -0.79 -0.3098 0.5249 4059.3 1.6077 1695 2 0.79 0.31 0.525

215 267.538 89.1367 -1 -0.043 0.0151 2197.9 6.8384 62087 4 1 0.04 0.015

217 265.284 72.2458 -0.95 -0.0783 0.3049 2403.5 2.6199 3725 2 0.95 0.08 0.305

230 240.566 80.3263 -0.86 -0.4844 0.1680 5661.7 1.9088 1833 3 0.86 0.48 0.168

231 239.639 85.3484 -0.86 -0.5038 0.0811 5829.8 2.305 4967 3 0.86 0.5 0.081

235 243.341 85.4365 -0.89 -0.4473 0.0796 5409.6 2.615 12933 3 0.89 0.45 0.08

244 236.281 85.3335 -0.83 -0.5533 0.0814 6190.5 9.3335 47455 3 0.83 0.55 0.081

245 253.799 73.3035 -0.92 -0.2672 0.2873 3938.1 1.5279 2271 2 0.92 0.27 0.287

247 129.426 84.4472 0.769 -0.6321 0.0968 3907.8 1.8615 2881 4 0.77 0.63 0.097

248 235.165 79.5356 -0.81 -0.5617 0.1816 6218.6 8.4951 25192 3 0.81 0.56 0.182

249 5.16487 78.6259 0.088 0.97638 0.1972 -8407 2.2275 1177 1 0.09 0.98 0.197

250 83.0188 87.9591 0.992 0.12147 0.0356 -2849 6.576 71490 2 0.99 0.12 0.036

253 89.8621 89.8191 1 0.00241 0.0032 -1865 3.1591 13562 4 1 0 0.003

255 250.834 85.7236 -0.94 -0.3274 0.0746 4492.5 6.1696 19846 3 0.94 0.33 0.075

257 266.988 65.499 -0.91 -0.0478 0.4147 2060.8 5.3577 57044 2 0.91 0.05 0.415

262 235.484 77.9819 -0.81 -0.5542 0.2082 6152.3 5.9697 12739 3 0.81 0.55 0.208

263 247.293 86.9793 -0.92 -0.3855 0.0527 4945.1 4.3827 12013 3 0.92 0.39 0.053

269 263.586 89.1469 -0.99 -0.1117 0.0149 2769.7 1.9818 6445 2 0.99 0.11 0.015

276 294.827 89.5103 -0.91 0.41986 0.0085 -1864 9.2765 66040 4 0.91 0.42 0.009

280 280.352 87.6979 -0.98 0.17955 0.0402 291.54 3.752 12892 4 0.98 0.18 0.04

283 268.372 82.1494 -0.99 -0.0281 0.1366 2054.3 2.684 7778 2 0.99 0.03 0.137

290 227.51 86.7618 -0.74 -0.6744 0.0565 7043.5 3.9157 2868 3 0.74 0.67 0.056

294 108.693 88.1222 0.947 -0.3203 0.0328 941.94 3.8308 9441 4 0.95 0.32 0.033

296 125.103 89.1563 0.818 -0.575 0.0147 3340.2 5.8549 13378 4 0.82 0.57 0.015

298 316.275 74.5118 -0.67 0.69642 0.2670 -4654 1.1116 1396 4 0.67 0.7 0.267

306 106.4 86.4641 0.957 -0.2818 0.0617 595.68 3.8283 9639 4 0.96 0.28 0.062

316 293.064 73.0258 -0.88 0.37469 0.2919 -1536 1.1272 889 4 0.88 0.37 0.292

318 258.773 80.2564 -0.97 -0.1919 0.1692 3402.8 4.0672 6936 2 0.97 0.19 0.169

323 265.202 73.7101 -0.96 -0.0803 0.2805 2427.1 6.323 42955 2 0.96 0.08 0.28

330 264.362 55.2692 -0.82 -0.0807 0.5697 2166.9 0.7924 893 2 0.82 0.08 0.57

339 255.242 77.394 -0.94 -0.2486 0.2182 3826.3 1.9459 7842 2 0.94 0.25 0.218

342 230.335 64.9031 -0.7 -0.578 0.4241 6144.9 1.8683 886 3 0.7 0.58 0.424

346 236.008 65.9991 -0.76 -0.5107 0.4068 5688.9 0.7916 696 3 0.76 0.51 0.407

348 228.646 86.7622 -0.75 -0.6597 0.0565 6944.7 2.2464 4561 3 0.75 0.66 0.056

350 268.121 49.9518 -0.77 -0.0251 0.6434 1605 1.6225 1033 2 0.77 0.03 0.643

355 287.707 89.5935 -0.95 0.30414 0.0071 -805.5 5.0771 23401 4 0.95 0.3 0.007

359 268.53 71.2145 -0.95 -0.0243 0.3220 1947.5 1.8451 1278 2 0.95 0.02 0.322

360 274.399 40.4253 -0.65 0.04974 0.7613 749.62 2.0605 1308 2 0.65 0.05 0.761

370 268.32 76.2137 -0.97 -0.0285 0.2383 2017.7 5.4306 46695 2 0.97 0.03 0.238

381 224.259 85.753 -0.7 -0.7142 0.0741 7302.3 7.1489 15683 3 0.7 0.71 0.074

383 252.236 89.4467 -0.95 -0.3051 0.0097 4329.4 4.2643 19075 3 0.95 0.31 0.01

395 237.151 86.3546 -0.84 -0.5413 0.0636 6109.4 1.8286 3116 3 0.84 0.54 0.064

404 216.491 85.149 -0.59 -0.8011 0.0846 7847.7 3.5976 3846 1 0.59 0.8 0.085

413 237.703 87.2255 -0.84 -0.5337 0.0484 6057.7 4.24 13922 3 0.84 0.53 0.048

435 252.947 87.4998 -0.96 -0.293 0.0436 4229.9 1.2565 1870 3 0.96 0.29 0.044

443 254.214 64.8641 -0.87 -0.2463 0.4248 3665.8 0.8059 1271 2 0.87 0.25 0.425

450 254.125 50.0854 -0.74 -0.2098 0.6416 3104.5 1.9707 1386 2 0.74 0.21 0.642

451 94.761 86.3031 0.994 -0.0828 0.0645 -1134 1.5395 5165 4 0.99 0.08 0.064


99

LABEL DIPDIR DIP a b c d SIZE NO

PNTS FUZZY

C5 Xi Yi Zi

455 261.302 79.3624 -0.97 -0.1486 0.1846 3038.8 1.9989 2173 2 0.97 0.15 0.185

457 230.427 84.9811 -0.77 -0.6346 0.0875 6767 2.252 6033 3 0.77 0.63 0.087

464 286.754 61.5723 -0.84 0.25351 0.4761 -603.6 4.1867 1902 4 0.84 0.25 0.476

467 242.189 54.8935 -0.72 -0.3817 0.5751 4530.7 1.2799 730 2 0.72 0.38 0.575

469 281.621 47.1663 -0.72 0.14772 0.6799 52.954 1.7379 1337 2 0.72 0.15 0.68

471 231.617 62.9743 -0.7 -0.5531 0.4544 5934.5 1.5186 658 3 0.7 0.55 0.454

495 272.48 83.0721 -0.99 0.04296 0.1206 1462.4 5.4669 42546 4 0.99 0.04 0.121

496 276.03 49.17 -0.75 0.07948 0.6538 690.92 1.4147 855 2 0.75 0.08 0.654

501 274.474 53.2185 -0.8 0.06248 0.5988 921.51 1.6684 936 2 0.8 0.06 0.599

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104


105

Appendix 7 SSPC Analysis of the Montemerlo Slope based on Manual Field

Measurement Appendix 7 a SSPC Manual Field Data


106

Appendix 7 b Reference rock mass calculation

Disc 1 & 3 Disc 2


107

Appendix 7 b Slope Stability Probability Calculation at slope orientation of 229/80 based on manual field measurments


108

Appendix 7 d Slope Stability Probability Calculation at slope orientation of 202/85 based on manual field measurements


109

Appendix 8 SSPC Analysis of the Montemerlo Slope based on 3D TLS Discontinuity Orientation Data

Appendix 8a Discontinuity orientation data derived from TLS measurement are used as an input in SSPC analysis.

The condition of discontinuities of each 3D TLS discontinuity set are assumed equal to the condition of discontinuities of

manually measured discontinuity sets with an orientation, nearly the same with its orientation. For example, the condition of

discontinuity used for 3D TLS discontinuity set 3 (205. 44/ 78.31) is the same with the condition of discontinuity with

manual field measurement discontinuity set 1 ( 202/ 82).


110

Appendix 8 b Reference rock mass calculation

Disc 1 & 2 Disc 3


111

Appendix 8 c Slope Stability Probability Calculation at slope orientation of 229/80


112

Appendix 8d Slope Stability Probability Calculation at slope orientation of 202/85

rock mass slope stability analysis based on 3d … · rock mass slope stability analysis based on...

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