seepage-coupled finite element analysis of stress driven
TRANSCRIPT
University of South Florida University of South Florida
Scholar Commons Scholar Commons
Graduate Theses and Dissertations Graduate School
March 2019
Seepage-Coupled Finite Element Analysis of Stress Driven Rock Seepage-Coupled Finite Element Analysis of Stress Driven Rock
Slope Failures for BothNatural and Induced Failures Slope Failures for BothNatural and Induced Failures
Thomas Becket Anyintuo University of South Florida, [email protected]
Follow this and additional works at: https://scholarcommons.usf.edu/etd
Part of the Civil Engineering Commons
Scholar Commons Citation Scholar Commons Citation Anyintuo, Thomas Becket, "Seepage-Coupled Finite Element Analysis of Stress Driven Rock Slope Failures for BothNatural and Induced Failures" (2019). Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/7731
This Thesis is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected].
Seepage-Coupled Finite Element Analysis of Stress Driven Rock Slope Failures for Both Natural
and Induced Failures
by
Thomas Becket Anyintuo
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Science in Civil Engineering
Department of Civil and Environmental Engineering
College of Engineering
University of South Florida
Major Professor: Manjriker Gunaratne, Ph.D.
Andres E. Tejada-Martinez, Ph.D.
Sarah Kruse, Ph.D.
Date of Approval:
March 26, 2019
Keywords: Stress Wave, Blasting, Crack Propagation, Remote Sensing
Copyright © 2019, Thomas Becket Anyintuo
DEDICATION
I dedicate this work to my mum, Madam Lucy Zinale Anyintuo
ACKNOWLEDGEMENTS
I am grateful to my major professor, Dr. M. Gunaratne, for giving me the opportunity to
work with him on this project. I am very appreciative of his support throughout this journey. I also
appreciate the numerous support and encouragement I received from the members of my thesis
committee, Dr. Tejada-Martinez and Dr. Kruse. I am also thankful to all my colleagues at the
Department of Civil Engineering for all their support
i
TABLE OF CONTENTS
LIST OF TABLES .......................................................................................................................... ii
LIST OF FIGURES ....................................................................................................................... iii
ABSTRACT .................................................................................................................................... v
CHAPTER 1: INTRODUCTION ................................................................................................... 1
CHAPTER 2: LITERATURE REVIEW ........................................................................................ 6
2.1 Crack Propagation ......................................................................................................... 6
2.2 Seepage of Water ........................................................................................................ 10
2.3 The Case Study ........................................................................................................... 11
2.4 Remote Sensing .......................................................................................................... 13
CHAPTER 3: METHODOLOGY ................................................................................................ 16
3.1 Finite Element Modeling ............................................................................................ 16
3.1.1 Model Geometry and Properties. ................................................................. 16
3.1.2 Crack Propagation ........................................................................................ 20
3.1.3 Mesh Sensitivity Analysis............................................................................ 23
3.1.4 Seepage of Water Through Existing Cracks ................................................ 26
3.1.5 Stability Analysis. ........................................................................................ 31
3.2 Evidence from Remote Sensing .................................................................................. 32
3.2.1 Data .............................................................................................................. 32
3.2.2 Data Processing ............................................................................................ 33
CHAPTER 4: RESULTS AND DISCUSSION ............................................................................ 34
CHAPTER 5: CONCLUSION ..................................................................................................... 41
REFERENCES ............................................................................................................................. 42
APPENDIX A: STRESSES FOR STABILITY ANALYSIS ....................................................... 47
ii
LIST OF TABLES
Table 1: Model properties for FE analysis (adopted from Styles et al, 2011)……………………………….20
Table 2: Local safety factors after stage 1 cracking……………………………………………….………….……………35
Table 3: Local safety factors after stage 2 cracking………………………………………………..………………………37
Table 4: Local safety factors after stage 3 cracking……………………………………….…..…………..………………39
Table 5: Global factor of safety for each stage of crack extension……………………………..……..………….39
Table A: Stresses for stability analysis………………………………………………………………………………..……………47
iii
LIST OF FIGURES
Figure 1: Illustration of step-path failure mechanism (Camones et al, 2013) ................................ 7
Figure 2: Aerial photo of the pit showing the rock slide (downloaded from SkyTruth.com) ...... 17
Figure 3: NAIP Images of the site, before (left) and after (right) the slide, with slide location ... 17
Figure 4: ASTER digital elevation data in black and white with NAIP image overlain .............. 18
Figure 5: Sample 3-D display of scene before failure .................................................................. 19
Figure 6: Pit geometry used for Finite Element Modeling ........................................................... 19
Figure 7: Graphs showing time of stabilization of gravity loads and start point of detonation .... 21
Figure 8: Applied loads ................................................................................................................. 22
Figure 9: Crack extension path as dictated by stress concentrations ............................................ 23
Figure 10: Coarse mesh (a) and refined mesh (b) for sensitivity analysis .................................... 24
Figure 11: Refinement for single crack location........................................................................... 24
Figure 12: Results with coarse mesh ............................................................................................ 25
Figure 13: Results from refined mesh ........................................................................................... 26
Figure 14: Fracture tooth angle in Patton's model (from Patton, 1966) ....................................... 27
Figure 15: Reduction of tooth angle, i, over time with erosion .................................................... 28
Figure 16: Sample rough pipe used to model crack (a) and mesh used for flow analysis (b). ..... 29
Figure 17: Normal force on crack wall for flow velocity of 0.5m/s ............................................. 30
Figure 18: Normal force on crack wall for flow velocity of 10m/s .............................................. 30
Figure 19: Sliding surface used for stability analysis ................................................................... 32
Figure 20: Images of the slope before (left) and after (right) the failure ...................................... 33
iv
Figure 21: Stage 1 crack extension ............................................................................................... 34
Figure 22: Normal (a) and shear (b) stresses at sample observation points used for stability
analysis for stage 1 cracking ....................................................................................... 35
Figure 23: Stage 2 crack extensions.............................................................................................. 36
Figure 24: Normal (a) and shear (b) stresses at sample observation points used for stability
analysis for stage 2 cracking ....................................................................................... 37
Figure 25: Stage 3 cracking .......................................................................................................... 38
Figure 26: Normal (a) and shear (b) stresses at sample observation points used for stability
analysis for stage 3 cracking ....................................................................................... 39
v
ABSTRACT
Rock slope failures leading to rock falls and rock slides are caused by a multitude of factors,
including seismic activity, weathering, frost wedging, groundwater and thermal stressing.
Although these causes are generally attributed as separate causes, some of them will often act
together to cause rock slope failures. In this work, two of the above factors, seepage of water
through cracks and crack propagation due to the after effects of blasting are considered. Their
combined impact on the development of rock falls and rock slides is modeled on ANSYS
workbench using the Bingham Canyon mine slope failure of 2013 as a case study. Crack path
modeling and slope stability analysis are used to show how a combination of crack propagation
and seepage of water can lead to weakening of rock slopes and ultimate failure. Based on the work
presented here, a simple approach for modeling the development of rock falls and rock slides due
to crack propagation and seepage forces is proposed. It is shown how the information from remote
sensing images can be used to develop crack propagation paths. The complete scope of this method
involves demonstrating the combination of basic remote sensing techniques combined with
numerical modeling on ANSYS workbench.
1
CHAPTER 1: INTRODUCTION
Landslides have various slightly different definitions in different fields such as Geology,
Engineering, Environmental Science, etc. For most common usage, a landslide is simply the
movement of earth material downslope under the action of gravity. Regardless of how they are
defined, landslides are always the result of failure of an existing slope. Therefore, they can be
always related to the shear strength (or tensile strength in some cases) of the material of the failing
slope.
The most commonly used classification of landslides combines the mechanism of the
failure and the properties of the earth material involved in the slide. In terms of mechanism of
failure, landslides may be falls, flows, topples, avalanches etc. The material of the slope may be
rock, debris, mud, etc. Landslides can thus be classified based on the above to result in terms such
as rock falls, mudflows, debris avalanches, etc.
Weerasinghe et al (2011) and Dahigamuwa et al (2017) cite two attributions of the factors
that control the occurrence of landslides. (1) Location based attributes such as geology, slope,
hydrologic factors and surface deposits. (2) Triggering factors such as rainfall, seismic activity,
human activity and volcanic activity. Researchers seem to agree on water and seismicity being the
two most important triggers of landslides, especially rock falls, as an example, N. H. Maerz (2014),
Y. Yin et al (2016) and A. Contino (2017) all cite one or both of these as triggers of the investigated
rock falls. Rock falls are one group of landslides in which dislodged rock moves downslope by
bouncing, rolling, sliding or free-fall under gravity, (J. J. Castleton, 2009). Depending on the
factors such as height of fall, mass of falling blocks and slope of the cliff face, rock falls may attain
2
velocities and reach distances that are threatening to life and property in the vicinity, (J. J.
Castleton, 2009).
Therefore, the ability to locate potentially unstable rock slopes can be a very valuable asset
in investigating rock fall and rock slide risks. A method is presented here where the effect of
seeping water and human activity (mining in this case) as driving forces in developing a step-path
failure are modeled in ANSYS Explicit Dynamics module with supporting evidence obtained from
remote sensing data.
Step-path failure is a common mode of instability in rock slopes with intermittent joints
(Huang et al, 2014). When such slopes are loaded, by self-weight or external loads, the tips of
existing cracks become highly stressed and if the loading is sufficient to create stresses higher than
the strength of the rock material, the cracks will extend into previously intact rock zones. This
could cause a single crack to propagate through intact rock bridges and cause instability or multiple
pre-existing cracks to extend and connect, creating a potential shear failure path. This mechanism
is referred to as the step-path failure mechanism (Huang et al, 2014).
The development of step-path failure in jointed rocks has been extensively studied and
presented in literature. Bonilla et al (2015) combined ground based photogrammetry and numerical
modeling to investigate stability of a hanging rock block under gravity loading. Their work
confirmed possible instability mechanisms such as including both sliding along existing
discontinuities and possible cracking of intact rock bridges. Spreafico et al (2017) investigated the
development of toppling failure at the edge of a fractured rock slope in which slope undercutting
resulting in loss of support was the driving force in the propagation of existing cracks.
In the above cited works, the propagation and coalescence of pre-existing cracks were
considered to be driven only by gravity loading. This is sufficient for the specific cases considered
3
since they were all natural slopes exposed only to self-weight loads. In considering instabilities
involving human activity such as mining as is the case in this research, very complex loading
scenarios can arise which cannot be modeled with the same approach as used for simple gravity
loading.
A mine slope failure which resulted in a rock avalanche is used in this work as a case study
to demonstrate the ability of the proposed method for dealing with complex loading in the
development of step-path failure. According to Hibert et al (2014), the Bingham Canyon Mine
(Copper Mine) is the largest man-made excavation in the world measuring about 4km wide and
1km deep. It is operated by Kennecott Utah Copper but owned by Rio Tinto. In April 2013 one of
the mine’s slopes failed causing a rock avalanche described as being the largest non-volcanic rock
avalanche recorded. Geotechnical personnel had been monitoring the movement along the slope
so that by the time the failure occurred appropriate precautions had been put in place ensuring no
injuries were sustained (Carter, 2014).
The slow movement of a failing slope is a common observation for slopes in which either
a failure path is slowly developing or slopes in which residual strength along a fully formed failure
path is slowly being reduced. These two cases correspond to a developing step-path failure mode
or an eroding fracture surface and thus both scenarios are considered in the following sections.
Since the slope is a man-made excavation, there is the possibility of having loading
conditions more complex than simple self-weight of the slope material. In open cast mining
excavation is commonly done by setting charges to break down rock into rubble which is then
shoveled off to expose more rock for further blasting. A stress wave is generated each time a charge
is set off and this wave travels through the rock at the bottom of the pit as well as on the pit walls.
4
Unfortunately slope pits are usually designed based only on the geological and geotechnical
properties of the wall rock without considering the future load from the mining activity.
By taking advantage of the capabilities of ANSYS Explicit Dynamics module, it is possible
to simulate the blasting process and track the stresses induced in upper parts of a pit wall from the
traveling stress wave at different observation times. Depending on the location of the blast, the
size of the charge and the observation time, stresses in the upper slope can be seen to reach levels
that are higher than the rock strength. In the work presented here, this load is considered as one of
the driving forces that create a step-path failure mode.
In addition to the stresses from the mining operation, water flow through existing cracks
was also investigated. Two particular aspects of seepage were considered, vis, the seepage forces
acting normal and outward to the crack walls and the shear on the wall surfaces which tend to
erode the crack surfaces and reduce the residual shear strength that can be mobilized on these
surfaces.
Remote sensing techniques have found application in many fields of study and research
including study of natural hazards such as landslides. Remote sensing techniques have two
important advantages; (1) is the ability to obtain data for locations that may otherwise be
inaccessible and (2) the method can often reveal details that can be missed in field investigations.
The biggest challenge of remote sensing techniques is the availability of data of the quality
required for the intended study. For this reason, a lot of remote sensing research often includes
some level of field investigation and in most such cases, remote sensing is only applied for
locations that are inaccessible. El Haddad et al (2017) used a combination of field investigations
and satellite images to locate potentially unstable boulders on a rock face along a road cut.
5
M Sečanj et al (2017) used a combination of field investigations and ground based laser scanning
to obtain rock discontinuity data which was used for kinematic analysis.
For the purposes of the current project, the level of remote sensing application required is
basic. Remotely sensed data was used as a source of supporting evidence for constructing the slope
geometry, including both rock material and joint locations. The data was obtained from the vast
database of remotely sensed data provided by the United States Geological Survey (USGS) on its
‘EarthExplorer’ website ( https://earthexplorer.usgs.gov/). Specifically, images obtained as part of
the National Agriculture Imagery Program were used since they provide high levels of visual detail
as required for this project.
The National Agriculture Imagery Program (NAIP) acquires aerial imagery during
agricultural seasons and makes this photographic data available to governmental agencies and the
public within a year of acquisition. The images are acquired at a one-meter ground sample distance
(GSD) with a horizontal accuracy of about six meters of photo-identifiable ground control points.
The default spectral bands was natural color (Red, Green and Blue, or RGB) until 2007 when some
states started being delivered with four bands of data: RGB and Near Infrared
(https://www.fsa.usda.gov)
NAIP imagery products are available in two formats, either as digital ortho quarter quad
tiles (DOQQs) or as compressed county mosaics (CCM). Of the above, DOQQs were used for this
project. They are geotiffs with coverage areas corresponding to the USGS topographic quadrangles
(https://www.fsa.usda.gov). Data processing was limited to visual rendering on two separate image
processing environments, ENVI and ArcGIS Pro. To further enhance visual detail, the 2D image
data was converted into 3D scenes using elevation information from an Aster DEM (Digital
Elevation Model) of the area also downloaded from USGS site.
6
CHAPTER 2: LITERATURE REVIEW
2.1 Crack Propagation
Cracks affect the strength and integrity of rocks and present challenges in designing
structures in, on or even with the rock. Cracks reduce the shear resistance provided by rock
significantly by reducing the area where cohesion and friction are developed. For this reason,
fractured rock slopes can normally become very unstable depending on the interaction between
cracked and intact rock zones. A single crack, favorably oriented may result in enough strength
reduction to lead to failure (Spreafico et al, 2017). Even in situations where there is adequate
strength mobilized from intact rock bridges to hold slope material up, there will still be the
possibility of existing cracks extending into intact zones (Bonilla et al, 2015). Each time a crack
extends into intact rock, the available traction holding up slope material is reduced until a time
when it is not enough to support the weight component of the slope material, at which point failure
will occur. The propagation and coalescence of existing cracks leads to the development of a
preferred failure path known as the step-path failure mechanism as depicted in Figure 1.
7
Figure 1: Illustration of step-path failure mechanism (Camones et al, 2013)
Griffith’s theory of brittle fracture which was proposed in the 1920’s to explain initiation
of fracture in materials such as steel and glass has remained a valid theoretical basis for studying
brittle fracture mechanisms. Griffith (1920) postulated that fracturing of materials initiates at the
tips of micro-fractures under tensile loading, and later extended it to also explain initiation of
cracks under high compressive load. The above theory was based on energy balance approach with
an underlying assumption that crack propagation would only occur if the potential strain energy
released in the process is sufficient to compensate the energy required for the formation of new
surfaces (Irwin 1968, Yarema 1995). Yarema (1995) also discussed in detail the contributions of
Irwin to the topic of brittle fracture and crack propagation. Irwin (1968) showed in his work that
the energy approach could be replaced by an equivalent strength approach which required less
involving computations but produced the same results regarding loads required for crack
propagation. Irwin (1968) further identified three classes of crack propagation based on directions
8
of loads and crack extensions. He also introduced the concept of stress intensity factors which
accounts for the observation that cracks will often withstand loads greater than the strength and
exist in a meta-stable state and then at a certain load intensity, sudden failure at crack tips would
cause propagation of these cracks (Yarema, 1995).
Other research in developing the theoretical bases of crack initiation and propagation
include the work of Hoek (1965) who based on Griffith’s theory and Irwin’s modifications with
little additions, developed an extension of this theory to explain fracture mechanism in closed
cracks under compressive loads. These changes and the subsequent extension allowed the theory
to be adopted in the field of rock mechanics to explain crack initiation and propagation in rocks
(Hoek, 1965).
More recent work on the topic of crack propagation has been focused on numerical
techniques and some experimental work to develop approaches to modeling crack propagation and
the application of this knowledge in design of slopes, excavations and tunnels in rock. Huang et al
(2015) used a Particle Flow Code (PFC) to model crack propagation in different model slopes with
the aim of gaining insight into crack propagation and also testing the suitability of particle based
methods for modeling the phenomenon. According to Huang et al (2015), the use of particle based
methods requires extensive data collection in order to obtain grain-level engineering properties of
the rocks involved. They also used the gravity increase method to drive the propagation and
ultimate failure of rock slopes. The principle of this method is to slowly increase the magnitude of
gravitational acceleration until failure is obtained. The above theory has been shown to provide a
good approximation of the final failure surface but it does not represent realistic loading in rock
slopes (Li et al, 2009). In the author’s opinion, the apparent increase in gravitational acceleration
that will result in closely approximating a real failure surface is rather the result of a reduction in
9
shear strength of the slope which could arise from any number of factors including erosion, creep,
internal deformation, and other external load sources.
Paluszny et al (2017) used a finite element approach to model upward crack propagation
as it is applicable in the block cave mining method. In the block caving method, an excavation is
made through a side pit under the block of rock that is to be mined. This leaves a block of rock
above the cave roof with no support, causing it to collapse. This significantly reduces the amount
of blasting that would otherwise be required. Paluszny et al (2017) found that by relying on crack
propagation, it is possible to further reduce the amount of excavation needed for the initial cave
and hence reduce the production cost. Camones et al (2012) conducted a study to test the
applicability of the discrete element method as a tool for understanding the step-path failure
mechanism in fractured rock masses by simulating triaxial tests performed on cracked rock
samples. They found that the results from the DEM simulation closely matched the test results for
the failure modes tested.
Both Bonilla et al (2015) and Spreafico et al (2017) investigated crack propagation in
natural rock slopes where loss of support lead to gravity driven cracking. Bonilla et al studied a
slope where a previous failure had created a hanging block within which multiple existing cracks
could propagate to cause failure. Spreafico et al (2017) investigated a similar loading condition
created by slope undercutting from erosion, with a single near vertical crack propagating through
the intact rock bridge to cause failure.
In the above cited works, the propagation and coalescence of pre-existing cracks were
considered to be driven only by gravity loading. This is sufficient for the specific cases considered
since they were all natural slopes exposed only to self-weight loads. However, in developing an
approach to modeling crack propagation leading to slope instability, it is necessary to consider
10
other loading possibilities. One such alternative load is caused by blasting in mines. The 2013
Bingham Canyon Mine slope failure (Carter, 2014), which resulted in a rock avalanche is used in
this work as a case study to demonstrate the ability of a proposed approach for modeling complex
loading in the development of step-path failure.
2.2 Seepage of Water
In addition to complex stress regimes resulting from mining, the influence of water on the
development and evolution of the slope failure in question is also considered. Two important
influences of water can be recognized as evident in results of various works presented in literature.
Firstly, water trapped in a close-ended crack introduces a destabilizing force due to the static water
pressure (Denby et al, 1985, 2012, Hoek and Bray 1981, Rutqvist et al 2001).
Secondly, when a crack surface is immersed in water, whether by the presence of a high
water table or very slow moving pore water, the water film on the crack surface reduces the contact
between the two walls of the crack and thus reduces the amount of shear strength that can be
mobilized on the surface (Denby et al 1985, 2012, Hopkins et al 1975, Hoek et al 1981, Zare and
Torabi 2008, Rutqvist et al, 2001).
A third and less studied influence arises when water flows through an open-ended crack.
Much like the flow of surface water over rock, seepage forces from the flow can introduce
destabilizing forces while contact shear stresses at the water-rock interface act to erode the surface
of the crack and reduce its residual shear strength (Barton 1973, Hoek and Bray 1981, Barton and
Choubey 1976). Since the cracks in the slope considered in this work were open cracks, priority is
given to the second and third possibilities. The modeling approach and further details are presented
in later sections of this report.
11
2.3 The Case Study
The Bingham Canyon Mine has been described as the largest man-made excavation in the
world (Hibert et al, 2014). The mine is owned by Rio Tinto and operated by Kennecott Utah
Copper (KUCC) (Carter, 2014). It is located about 30km south west of Salt Lake City in Utah. As
of 2011, the mine was approximately 3.6km wide and about 900m deep (Styles et al, 2011). The
mine mainly produces copper but also mines significant amounts of gold, molybdenum and silver
(Krahulec, 1997).
On April 10th 2013, a section of the mine slope failed causing a rock avalanche that has
been described as the biggest non-volcanic rock avalanche ever recorded. The failure initiated at
the northern slope area of the pit known as the Manefey area (Cater, 2014). Field observations and
seismic records led to the conclusion that the slope failed in two stages. The first slide occurred at
about 03:31 UT and the second slide occurred approximately 1.5 hours later at about 5:06 UT
(Hibert et al, 2014). According to Septian et al, 2017, the evidence of the first slide suggested it
was a planar type failure while the second was a rotational type failure.
The massive combined rock avalanche displaced about 150 million tons of slope material
downslope into the pit. Early estimates of recovery operations suggested that it could take up to a
year or more to clean up the debris and for operations to resume. This would cost the mine an
estimated $5 million per day for each day that new ore was not delivered. However, as a result of
a very well-coordinated and time-conscious effort, it only took 17 days after the slide for the mine
to resume sending new ore to the concentrator (Carter, 2014).
The size of the slide was so massive that it has been reported to have caused up to 16 small
earthquakes. The individual slides themselves were recorded on nearby seismographs as reaching
12
magnitudes of 5.1 for the first and 4.9 for the second event making it the first recorded landslide
to have triggered earthquakes (Carter, 2014).
The slide was not unexpected. Geotechnical engineering personnel at the mine had been
monitoring movement on the slope months prior to the failure. Although there was no recognizable
trigger for the movement (Moore et al, 2017), geotechnical personnel relied on heavy slope
instrumentation to monitor the progression of the failure which had been classified as being
inevitable. Some of the monitoring equipment included, a 220-prism network, extensometers, time
domain reflectometers, and ground probe stability radars (Carter, 2014). Based on data obtained
from these instruments, an imminent slope failure was declared in February of 2013, about 2
months before the slide, giving ample time for preparations to be made for the eventual slide
(Carter 2014). For this reason, no casualties were recorded when the slide finally occurred and
damage to equipment was also limited (Hinert et al 2014, and Moore et al 2017).
Geotechnical data for the failed slope has been limited as seen in literature. The mine owner
released some data such as oblique aerial photographs but which were largely insufficient for
geotechnical analysis. This led researchers to resort to various sources of data; Moore et al (2017)
used a combination of the limited data released by the mine owner and press coverage information.
Septian et al (2017) had to simplify their runout model by reducing degrees of freedom and
performing sensitivity analysis to compensate for the lack of sufficient data. Hibert et al (2014)
relied on seismic data to perform runout analysis.
In 2011, Styles et al performed a combined numerical modeling and Insar satellite
monitoring of another slope of the same mine where there was movement. Their work presents an
array of useful geotechnical information about the slope that was investigated. Due to the
proximity of the two slopes, the rock type and properties from this previous work has been adopted
13
for the analysis in this work. From their work two rock types, quartzite and monzonite were seen
as the dominant rock types of the area. Of the two, quartzite is the stronger one with a tensile
strength of 0.27MPa compared to 0.2MPa for monzonite (Styles et al, 2011). The author’s model
used in ANSYS considers the rock as a uniform block of material which makes it difficult to mimic
the aggregate nature of rocks such as monzonite. Quartzite on the other hand is almost entirely
composed of metamorphosed quarts sand grains, making it more uniform and more closely
represented by the model used by the author. For these reasons, quartzite was used in this work as
the slope material. The overall model is stronger than what may have been the real world scenario
due to the use of stronger quartzite and also the lack of contact zones between multiple rock types
which are usually weaker than any one rock material. Other information about the slope, such as
geometry, location of existing cracks and the final slide surface were obtained from the remote
sensing data downloaded from https://www.fsa.usda.gov.
2.4 Remote Sensing
The use of remote sensing techniques in the study and monitoring of landslides has seen
much success in recent times due to advances in both instrumentation and technology in the field
of remote sensing. One common application of remote sensing in monitoring development of
landslides is the use of data collected over a period of time to determine changes in the developing
slide. Changes could be in terms of land cover (Dahigamuwa et al, 2017), slope material volume
changes and groundwater level changes (Maerz, 2014), and slope material movement (Frodella et
al 2015, Styles et al 2011, Crosta et al 2015). Other researchers have focused on using remote
sensing techniques to identify potentially unstable slopes based on existence and orientation of
discontinuities, hanging blocks, erosion undercuts, etc. Jean et al (2015) employed terrestrial
LiDAR scanning to investigate failure potential of an actively moving slope where they estimated
14
deformation rates, direction and volumes of moving material. They also found that remote sensing
was able to locate moving volumes much smaller than field observations could identify. Dunham
et al (2015) applied Static Terrestrial Laser Scanning techniques in developing a rockfall activity
index (RAI) for assessing rockfall hazards. Other research on the application of remote sensing
techniques in landslide hazard identification and/or monitoring can be found in the works of
Youssef et al (2015) and Molina et al (2015).
For the purposes of the current project, the level of remote sensing application required is
basic. Remotely sensed data was used as a source of supporting evidence for constructing the slope
geometry, including both rock material and joint locations. The data was obtained from the vast
database of remotely sensed data provided by the United States Geological Survey (USGS) on its
‘EarthExplorer’ website (https://earthexplorer.usgs.gov/). Specifically, images obtained as part of
the National Agriculture Imagery Program were used since they provide high levels of visual detail
as required for this project.
The National Agriculture Imagery Program (NAIP) acquires aerial imagery during
agricultural seasons and makes this photographic data available to governmental agencies and the
public within a year of acquisition. The images are acquired at a one-meter ground sample distance
(GSD) with a horizontal accuracy of about six meters of photo-identifiable ground control points.
The default spectral resolution was natural color (Red, Green and Blue, or RGB) until 2007 when
some states started being delivered with four bands of data: RGB and Near Infrared
(https://www.fsa.usda.gov)
NAIP imagery products are available in two formats, either as digital ortho quarter quad
tiles (DOQQs) or as compressed county mosaics (CCM). CCMs are generated by compressing
digital ortho quarter quadrangle image tiles into a single mosaic. The mosaic may cover all or
15
portions of an individual final product. All individual tile images and the resulting mosaic are
rectified in the UTM coordinate system, NAD 83, and cast into a single predetermined UTM zone.
CCMs from 2003 - 2007 are all in a .sid format. Beginning in 2008, CCMs with four bands were
compressed into a .jp2 format. Beginning in 2009, all NAIP CCMs were delivered with a
"seamline" shapefile showing which image swath made up each part of a given image. Of the
above, DOQQs were used for this project. They are geotiffs with coverage areas corresponding to
the USGS topographic quadrangles (https://www.fsa.usda.gov). Data processing was limited to
visual rendering on two separate image processing environments, ENVI and ArcGIS Pro. To
further enhance visual detail, the 2D image data was converted into 3D scenes using elevation
information from an Aster DEM (Digital Elevation Model) of the area also downloaded from
USGS site.
16
CHAPTER 3: METHODOLOGY
3.1 Finite Element Modeling
Finite Element Analysis was carried out with three main targets; (a) to model the
propagation of existing cracks as a result of the combined stresses from gravity and blasting loads,
(b) to determine stresses generated by self-weight for stability analysis, and (c) to model the flow
of water through cracks and how that affects the global stability of the slope.
3.1.1 Model Geometry and Properties
The geometry for the model was constructed based on information from the remote sensing
data. The location of the pit wall of interest, the locations of cracks and their relative positions with
respect to adjacent cracks and the slope face were all collected from the remote sensing images
through visual inspection. Two images, one taken before and the other after the slide were used in
this research. The first image taken before the slide in 2011 formed the basis for constructing the
geometry, particularly the locations of existing cracks while the second image was used to define
the final failure surface which was used for stability analysis.
17
Figure 2: Aerial photo of the pit showing the rock slide (downloaded from SkyTruth.com)
Figure 3: NAIP Images of the site, before (left) and after (right) the slide, with slide location
The images were imported into two separate image processing environments, ArcGIS Pro
and ENVI for analysis. ArcGIS Pro has a measuring tool which is able to measure distances, areas
and even vertical measurements if the right elevation data is available. On the other hand, ENVI
18
produces the better visual rendering of the images. By combining these two, it was possible to
locate existing cracks and make measurements for detailing the geometry. In order to permit 3-D
inspection and measurements, it was necessary to include elevation data in the analysis. Elevation
data was obtained from ASTER Digital Elevation Model (DEM). The Advanced Spaceborne
Thermal Emission and Reflection Radiometer (ASTER) onboard Terra, a multi-national NASA
scientific research satellite, provides high-resolution images of the Earth in 14 different bands,
ranging from visible to thermal infrared light. ASTER data are used to create maps of surface
temperature of land, emissivity, reflectance, and elevation.
Figure 4: ASTER digital elevation data in black and white with NAIP image overlain
A sample 3-D display of the site before the failure is shown in Figure 6. The final geometry
is as shown in Fig. 7, with dimensions of 1.3km width and 900m height with an extension of an
extra 200m at the bottom used to represent a current mining bench. The engineering properties for
the model are summarized in Table 1. These were adopted from the work of Styles et al (2011).
19
Figure 5: Sample 3-D display of scene before failure
Figure 6: Pit geometry used for Finite Element Modeling
Existing cracks
1.5 km
900 m
20
Table 1: Model properties for FE analysis (adopted from Styles et al, 2011).
Parameter Rock
Type
Elastic
Modulus,
E, (GPa)
Poisson’s
Ratio, ν
Density,
ρ, (t/m3)
Bulk
Modulus,
K, (GPa)
Cohesion,
c, (MPa)
Friction
Angle,
φ, (⁰)
Tensile
Strength,
(MPa)
Description Quartzite 23.5 0.27 2.6 17 0.65 35 0.27
3.1.2 Crack Propagation
The extension of existing cracks into intact rock bridges was considered to occur due to
tension, driven by the combined stresses from gravity and blasting. Gravity loading was first
applied to the model and allowed to stabilize. Then a detonation was then set off at the bottom of
the model to mimic the blasting during mining. This sequential application of loads was found to
be necessary due to the fact the two load types depend to different extents on the analysis time
used. While the solution for the gravity loads required at least 2.5 seconds to converge and
stabilize, (as shown in Figure 5), the stresses from the blast needed to be tracked at time steps as
small as 0.1 seconds. Hence if both loads were started at an initial time of zero, then any attempt
to track stress changes resulting from the blast would be futile since the gravity load itself will be
fluctuating for times under 2.5 seconds.
21
Figure 7: Graphs showing time of stabilization of gravity loads and start point of detonation
Ammonium Nitrate Fuel Oxide (ANFO) was used as the explosive material since it is a
common explosive used in mining. A hole is created in the active bench at the bottom of the pit to
hold the explosive material. In the absence of details of the actual mining practices of the mine in
question, a generalized approach was taken where the amount of explosive material was
determined based on the level of stresses it produces upon detonation. The amount of explosive
was decided such that upon detonation, the tensile stresses in the active bench were sufficient to
break the rock within an area of about 50m x 50m.
3.40E+06
5.40E+06
7.40E+06
9.40E+06
1.14E+07
1.34E+07
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Stre
ss, P
a
Time (s)
Max Shear
0.00E+00
5.00E+06
1.00E+07
1.50E+07
2.00E+07
2.50E+07
3.00E+07
3.50E+07
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Stre
ss, P
a
Time (s)
Max Normal
22
Figure 8: Applied loads
Upon detonating the explosive, the stresses in the slope are checked at various observation
times until the point where the tensile stresses in the upper slope are sufficient to cause local failure
at crack tips and cause the extension of existing cracks. It is possible to run the analysis over a few
seconds at a time and then plot only the maximum stresses reached at each point which provides
an easier way of tracking the developing stresses. However, this would consider stresses within
the time periods less than 2.5 seconds and may thus produce results that are not reliable.
Once the above time of interest is located, the tips of the various cracks are examined and
the one with the highest stress is taken as the most likely point of local failure. The path of
extension of the next crack is decided based on the concentration of stresses around this tip, with
the likely path being taken as the shortest line between the crack tip and the local maximum stress
in its vicinity. This is shown in Fig 6.
23
Figure 9: Crack extension path as dictated by stress concentrations
After selecting an appropriate crack path, the crack is extended manually in the geometry
and the entire slope re-meshed for further analysis. The next steps include a stability check
performed after each crack extension stage as discussed below.
3.1.3 Mesh Sensitivity Analysis
The influence of mesh properties on the results was checked by performing a simple
sensitivity analysis with a refined mesh. Generally, in finite element analysis, using a finer mesh
results in closer approximation of true results. However, a finer mesh is computationally more
expensive since it requires more time to solve. The purpose of the sensitivity analysis was to check
how much the crack propagation direction is impacted by refining the mesh. The results are
presented in the following figures and seem to suggest that effects are not drastic.
24
Figure 10: Coarse mesh (a) and refined mesh (b) for sensitivity analysis
To put a measure on the computational cost of mesh refinement, the coarse mesh in Figure
10 (a) requires about half hour to reach a solution while the mesh in Figure 10 (b) requires over 70
hours to resolve. Since this was only a comparative study, the 70 hours was too much and so
refinement was only done for one crack location which reduced the time to about 2.5 hours. The
mesh shown in Figure 11 below was thus used to investigate the impact of mesh refinement.
Figure 11: Refinement for single crack location
a b
25
The results from the coarse mesh and the projected cracking path are shown in Figure 12.
In Figure 13, the results of the refined mesh and its projected path (yellow) are shown, with the
projected path from the coarse mesh (red) drawn in for comparison. It is observed that with the
finer mesh, it is possible to follow small scale undulations in the crack path whereas with the coarse
mesh, the path could only be projected along an approximate straight line. However, the deviation
in overall direction of the crack extension was not sufficient to warrant the use of such a fine mesh
with the excessive time requirements. It would however be useful to find an optimal mesh that
allows the user to follow the undulations in the crack path since they may be useful in re-defining
the global slope failure path. The rest of the analysis was done using the coarse mesh.
Figure 12: Results with coarse mesh
26
Figure 13: Results from refined mesh
3.1.4 Seepage of Water Through Existing Cracks
In addition to the propagation of cracks discussed above, flow of water through the open
cracks was considered as another factor that contributes to reduction of global stability of the slope.
Open cracks provide entry and an exit points through which water can flow. Once a crack develops
in a rock, the amount of shear strength that can be mobilized on its surface reduces to a residual
strength value. The magnitude of this residual strength, which itself is the result of the contact and
interlocking of asperities or roughness teeth on the joint surface has been shown by both Patton
(1966) and Barton (1973) to depend on the size of the asperities as well as the normal stress on the
plane of the joint (Hoek, 2007)
𝜏 = 𝜎𝑛 tan(ɸ𝑏 + 𝑖) 𝑃𝑎𝑡𝑡𝑜𝑛′𝑠 𝑚𝑜𝑑𝑒𝑙 (1)
where i is the roughness tooth angle, 𝜎𝑛 is the normal stress and ɸ𝑏 is the basic friction angle.
𝜏 = 𝜎𝑛 tan (ɸ𝑟 + 𝐽𝑅𝐶𝑙𝑜𝑔10𝐽𝐶𝑆
𝜎𝑛) 𝐵𝑎𝑟𝑡𝑜𝑛′𝑠 𝑚𝑜𝑑𝑒𝑙 (2)
27
where JRC and JCS are Joint Roughness Coefficient and Joint surface Compressive Strength
respectively.
Figure 14: Fracture tooth angle in Patton's model (from Patton, 1966)
As water flows through joints, it has the tendency to erode the surface of the joint, thus
reducing the size and also smoothening the asperities. These effects reduce the residual shear
strength on the joint surface. In addition, the flow pressure of the water produces forces normal to
the adjacent joint walls which tends to reduce the normal stress due to the weight of the riding
block. The pressure also causes separation of the adjacent walls, reducing contact. All of these
reduce the magnitude of shear strength that can be mobilized on the joint plane. Over time, erosion
can lead to sufficient strength reduction to cause rock slides.
To model this phenomenon in ANSYS, sections of the joint plane were taken as individual
pipes through which water flow can be simulated. Each pipe is taken as a rough pipe with surface
roughness height equal to the size of asperities used in rating the roughness parameter in the shear
strength model. In the Patton’s model outlined above, a reduction in the value of i results in a
reduction of shear strength. A reduction in the amplitude of asperities results in a reduction in the
magnitude of i as shown by the simple diagram in Figure 7.
28
Figure 15: Reduction of tooth angle, i, over time with erosion
The force driving the erosion process is the wall shear caused by the water flow. As
mentioned earlier in the section, normal forces from the flow also act as destabilizing forces in the
global stability considerations. Figures 8a and 8b below show some results of the flow analysis.
29
Figure 16: Sample rough pipe used to model crack (a) and mesh used for flow analysis (b).
In figure 8a it is seen that the asperities on crack surfaces are drawn as part of the geometry
and the mesh, Figure 8b, shows how the elements near the walls of the pipe are controlled to be
much smaller than that in the middle of the flow, in an attempt to refine the results obtained for
flow near the wall which is the area of interest.
It was realized that in order to produce significant forces for both the wall shear and the
normal forces, unrealistically high inflow velocities are needed. For this reason, it was concluded
that the flow effects were not significant for this case study. The information about the modeling
approach is, however, presented here to complete the proposed method of analysis as it may be
important for other cases such as the ones where flow occurs over much longer periods. Figures 9
a b
30
and 10 show the normal forces on the crack wall corresponding to inflow velocities of 0.5 m/s and
10 m/s respectively. The horizontal axes in both graphs were taken as the length of the flow or
crack with program-controlled divisions which are made to match the scale of the values on the
vertical axes.
Figure 17: Normal force on crack wall for flow velocity of 0.5m/s
Figure 18: Normal force on crack wall for flow velocity of 10m/s
31
3.1.5 Stability Analysis
Every time a crack was extended, global stability of the mine slope was checked using the
limit equilibrium method. Local failure leading to crack propagation was considered to be in
tension while global failure was investigated as a shear failure since this was a slide type failure.
Only gravity loads were considered in assessing global stability for obvious reasons. The failure
path as seen from the remote sensing images was selected and multiple observation points along
this path were considered. At each point, both the normal and shear stresses were recorded from
the FEM output. Stability of the slope was checked by a safety factor against sliding which is
calculated as the ratio of the shear strength along the potential failure surface to the mobilized
shear stress on the surface. The mobilized shear is calculated as
𝜏𝑚𝑎𝑥 = 𝑐 + 𝜎𝑡𝑎𝑛𝜑 (3)
where 𝜏𝑚𝑎𝑥 is the shear strength, c is the cohesion, σ is the normal stress, φ is the angle of friction.
If L is the length of influence, the shear force on the entire surface was calculated as τL where τ is
the shear stress. Since the stresses where taken at the same points along the failure surface, the
influence lengths of corresponding stresses were the same and canceled out. The safety is thus
given as
𝐹 = 𝛴(𝑐+𝜎𝑖𝑡𝑎𝑛𝜑)
𝛴𝜏𝑖 (4)
A factor of safety of 1 means that the slope is at equilibrium where the strength is exactly
enough to balance the stress. When the safety factor falls below a value of 1, the slope is no longer
able to mobilize enough strength to support the stresses induced due to gravity and thus fails.
32
Figure 19: Sliding surface used for stability analysis
The spreadsheet used for the stability analysis is provided in appendix A at the end of the thesis.
3.2 Evidence from Remote Sensing
3.2.1 Data
Images obtained by aircraft scanners as part of the National Agricultural Imagery Program
(NAIP) were downloaded from the USGS website ( https://earthexplorer.usgs.gov/) and used as
the source of information for constructing the slope geometry. These images have high resolutions
of about 60 cm pixel size which permits adequate visual detail for the analysis done for this
research. The images contain four data bands each; the first three being the R-G-B bands of the
visual range and a fourth band of near infrared data.
To further enhance visualization in ENVI, the 2D image data was converted into 3D scenes
using elevation information from an Aster DEM (Digital Elevation Model) of the area also
downloaded from the USGS site ( https://earthexplorer.usgs.gov/). Unfortunately, the DEM was
only valid for 2011, and hence it could only be used accurately for rendering the image taken in
2011prior to the failure. The two images are shown in Figure 12 with the approximate location of
33
the failure line shown on both. It is clearly seen that the failure line is more easily depicted in the
scene prior to the failure due to the 3D display.
Figure 20: Images of the slope before (left) and after (right) the failure
3.2.2 Data Processing
Two software programs, ENVI and ArcGIS Pro were used for the image processing. While
ENVI is primarily an image processing software, ArcGIS Pro boasts of a host of capabilities
including GIS and image processing applications. ENVI software allows higher resolutions to be
used when the data is converted to 3D whereas ArcGIS Pro provides a wider range of measuring
capabilities. Hence by using the above software, it was possible to display the images in high
resolution for visual analysis and at the same time make necessary measurements of relevant
distances in constructing the slope geometry.
34
CHAPTER 4: RESULTS AND DISCUSSION
Three stages of crack propagation were attained before slope failure. A stage of cracking
is complete when a probable crack extension path has been identified and the new crack surface
created. Stability analysis was performed at the end of each stage and the procedure was repeated
until the safety factor of the slope was below 1. At the end of the first simulation, two crack tips
were seen to be highly stressed with similar maximum stresses. Since these stressed tips are for
different cracks, the possibility exists for both to extend at the same time. The extended cracks are
as shown in Figure 13.
Figure 21: Stage 1 crack extension
Stability analysis confirmed that the slope was stable at this stage with a factor of safety of
1.6. Multiple observation points were selected along the failure line and at each point the normal
35
and shear stresses were determined in order to calculate the global safety factor of the slope. Figure
18 shows the required stresses at 5 sample observation points. Table 2 summarizes the calculation
of local safety factors at each of these points.
Figure 22: Normal (a) and shear (b) stresses at sample observation points used for stability
analysis for stage 1 cracking
Table 2: Local safety factors after stage 1 cracking
Point Normal Stress, MPa Strength (𝑐 + 𝜎𝑡𝑎𝑛𝜑), MPa Shear Stress, MPa F.O.S
A -5.707 4.647 1.954 2.4
B -6.644 5.304 2.262 2.3
C -5.564 4.547 2.586 1.8
D -5.216 4.303 3.529 1.2
E -3.571 3.151 3.757 0.84
a b
36
For the second stage of cracking, 3 crack tips were identified as being stressed enough to cause
further cracking. The 3 cracks were thus extended as shown below in Figure 19
Figure 23: Stage 2 crack extensions
At this stage the slope was still stable with stability analysis yielding a safety factor of 1.2,
less than the value at the previous stage but still satisfactory. The stresses and corresponding local
safety factors at 5 sample observation points are summarized in Figure 20 and Table 3.
37
Figure 24: Normal (a) and shear (b) stresses at sample observation points used for stability
analysis for stage 2 cracking
Table 3: Local safety factors after stage 2 cracking
Point Normal Stress, MPa Strength (𝑐 + 𝜎𝑡𝑎𝑛𝜑),
MPa
Shear Stress,
MPa
F.O.S
A -6.783 5.401 3.038 1.8
B -10.841 8.243 4.777 1.7
C -4.862 4.055 3.348 1.2
D -5.346 4.394 3.811 1.2
E -5.166 4.268 3.833 1.1
a b
38
Stage three of cracking is shown in Figure 15 with the failure surface inserted to show the
interaction of the extended cracks and the final failure line.
Figure 25: Stage 3 cracking
Stability analysis at this stage showed that the slope was no longer able to mobilize enough
resistance along the failure line to remain stable. The safety factor dropped to 0.53 at this stage.
Sample calculations for the 5 observation points are summarized in Figure 22 and Table 4.
39
Figure 26: Normal (a) and shear (b) stresses at sample observation points used for stability
analysis for stage 3 cracking
Table 4: Local safety factors after stage 3 cracking
Point Normal Stress, MPa Strength (𝑐 + 𝜎𝑡𝑎𝑛𝜑), MPa Shear Stress, MPa F.O.S
A -5.815 4.723 2.211 2.1
B -10.494 8.000 4.189 1.9
C -5.541 4.531 2.873 1.6
D -7.730 6.064 4.028 1.5
E -6.167 4.969 5.503 0.9
Table 5 summarizes the safety factors for the cracking stages.
Table 5: Global factor of safety for each stage of crack extension
Stage of cracking Stage 1 Stage 2 Stage 3
Safety Factor 1.68 1.30 0.57
a b
40
Besides using the stability analysis to confirm the possibility of failure arising from the
crack extensions, an interesting observation can also be made of how the crack extension paths
interact with the final failure line. First, it is seen that all through the analysis until failure, the
cracks that are presently on the failure line do not show any sign of extension. Secondly, the cracks
that have showed signs of extension have extended in paths directed towards the failure line. And
finally, the only crack that continued to extend after getting to the failure line did so along the line
instead of continuing beyond it.
41
CHAPTER 5: CONCLUSION
Based on the work and results presented in the foregoing sections, it is seen that crack
propagation driven by blasting induced stresses could be the cause of the 2013 rock avalanche
described in the case study presented. The crack propagation has been shown to cause enough
reduction in strength to cause failure along the suspected failure line to cause failure. Also, the
direction of propagation of cracks supports the above conclusion since it follows the final failure
line determined from remote sensing images.
The basis of modeling the flow of water through cracks and how it affects global slope
stability was demonstrated here although it was found to not be a significant contributing factor to
the slope failure considered in this research.
The use of remotely sensed data has been shown to be a useful asset in analyses such as
the one presented here. The use of remote sensing made the work possible without the need for
actual field visits to the site. It should also be noted that even if field visits were made, it may have
been impossible to reconstruct the geometry of the slope prior to failure for back analysis.
Finally, the results of this research show that the modeling capabilities of ANSYS can be
employed to study crack propagation for complex loading scenarios such as those present in
mining settings. There is also a potential for extending this work to be useful for studying stability
concerns resulting from other seismic loading conditions such as earthquakes.
42
REFERENCES
A.A.Griffith. (1921). “The Phenomena of Rupture and Flow in Solids.” Philosophical
Transactions of the Royal Society, 221(582–593), 163–198.
Alejano, L. R., & Alonso, E. (2005). Considerations of the dilatancy angle in rocks and rock
masses. International Journal of Rock Mechanics and Mining Sciences, 42(4), 481–507.
https://doi.org/10.1016/j.ijrmms.2005.01.003
Atkinson, B. K. (1982). Subcritical crack propagation in rocks: theory, experimental results and
applications. Journal of Structural Geology, 4(1), 41–56. https://doi.org/10.1016/0191-
8141(82)90005-0
Babiker, A. F. A., Smith, C. C., Gilbert, M., & Ashby, J. P. (2014). Non-associative limit
analysis of the toppling-sliding failure of rock slopes. International Journal of Rock
Mechanics and Mining Sciences, 71, 1–11. https://doi.org/10.1016/j.ijrmms.2014.06.008
Barton, N. (2013). Shear strength criteria for rock, rock joints, rockfill and rock masses:
Problems and some solutions. Journal of Rock Mechanics and Geotechnical Engineering,
5(4), 249–261. https://doi.org/10.1016/j.jrmge.2013.05.008
Barton, N., & Choubey, V. (1977). The shear strength of rock joints in theory and practice. Rock
Mechanics Felsmechanik Mécanique Des Roches, 10(1–2), 1–54.
https://doi.org/10.1007/BF01261801
Barton1973.Anewshearstrengthcriterionforrockjoints.Eng.Geol..pdf. (n.d.).
Bineshian, H., Ghazvinian, A., & Bineshian, Z. (2012). Comprehensive compressive-tensile
strength criterion for intact rock. Journal of Rock Mechanics and Geotechnical Engineering,
4(2), 140–148. https://doi.org/10.3724/sp.j.1235.2012.00140
Bonilla-Sierra, V., Scholtès, L., Donzé, F. V., & Elmouttie, M. K. (2015). Rock slope stability
analysis using photogrammetric data and DFN–DEM modelling. Acta Geotechnica, 10(4),
497–511. https://doi.org/10.1007/s11440-015-0374-z
Camones, L. A. M., Vargas, E. do A., de Figueiredo, R. P., & Velloso, R. Q. (2013). Application
of the discrete element method for modeling of rock crack propagation and coalescence in
the step-path failure mechanism. Engineering Geology, 153, 80–94.
https://doi.org/10.1016/j.enggeo.2012.11.013
Castleton, J. J. (n.d.). Rock-Fall Hazards in Utah, (January 2009).
43
Chen, H. M., Zhao, Z. Y., Choo, L. Q., & Sun, J. P. (2016). Rock Cavern Stability Analysis
Under Different Hydro-Geological Conditions Using the Coupled Hydro-Mechanical
Model. Rock Mechanics and Rock Engineering, 49(2), 555–572.
https://doi.org/10.1007/s00603-015-0748-4
Crosta, G. B., Agliardi, F., Frattini, P., & Lari, S. (2014). Engineering Geology for Society and
Territory - Volume 8. Engineering Geology for Society and Territory - Volume 8, 2, 43–58.
https://doi.org/10.1007/978-3-319-09408-3
Cruden, D. M. (2008). Rock slope stability analysis. Canadian Geotechnical Journal, 31(2),
319–319. https://doi.org/10.1139/t94-039
Dahigamuwa, T., & Gunaratne, M. (2017). Stochastic Investigation of the Feasibility of Using
Remotely Sensed Moisture Data for Rainfall Induced Landslide Hazard Assessment.
Advancing Culture of Living with Landslides, 679–688. https://doi.org/10.1007/978-3-319-
53498-5_78
Dahigamuwa, T., Yu, Q., & Gunaratne, M. (2016). Feasibility Study of Land Cover
Classification Based on Normalized Difference Vegetation Index for Landslide Risk
Assessment. Geosciences, 6(4), 45. https://doi.org/10.3390/geosciences6040045
Dunham, L., Wartman, J., Olsen, M. J., O’Banion, M., & Cunningham, K. (2017). Rockfall
Activity Index (RAI)A lidar-derived, morphology-based method for hazard assessment.
Engineering Geology, 221, 184–192. https://doi.org/10.1016/j.enggeo.2017.03.009
Eberhardt, E. (2013). Rock Slope Stability Analysis-Utilization of Advanced Numerical
Techniques Rock Slope Stability Analysis – Utilization of Advanced Numerical
Techniques, (December).
Frodella, W., Nocentini, M., Scardigli, C., Gigli, G., Lombardi, L., Casagli, N., … Ciampalini,
A. (2016). Synergic use of satellite and ground based remote sensing methods for
monitoring the San Leo rock cliff (Northern Italy). Geomorphology, 264, 80–94.
https://doi.org/10.1016/j.geomorph.2016.04.008
Haeri, H., Shahriar, K., Marji, M. F., & Moarefvand, P. (2014). Experimental and numerical
study of crack propagation and coalescence in pre-cracked rock-like disks. International
Journal of Rock Mechanics and Mining Sciences, 67, 20–28.
https://doi.org/10.1016/j.ijrmms.2014.01.008
Henry, J. P., Paquet, J., & Tancrez, J. P. (1977). Experimental study of crack propagation in
calcite rocks. International Journal of Rock Mechanics and Mining Sciences And, 14(2),
85–91. https://doi.org/10.1016/0148-9062(77)90200-5
Hibert, C., Ekström, G., & Stark, C. P. (2014). Dynamics of the Bingham Canyon Mine
landslides from seismic signal analysis. Geophysical Research Letters, 41(13), 4535–4541.
https://doi.org/10.1002/2014GL060592
44
Highland, L. M., & Bobrowsky, P. (2008). Basic Information About Landslides. The Landslide
HanHighland, L. M., & Bobrowsky, P. (2008). Basic Information About Landslides. The
Landslide Handbook — A Guide to Understanding Landslides, 129.Dbook — A Guide to
Understanding Landslides, 129.
Hoek, E., & Martin, C. D. (2014). Fracture initiation and propagation in intact rock - A review.
Journal of Rock Mechanics and Geotechnical Engineering, 6(4), 287–300.
https://doi.org/10.1016/j.jrmge.2014.06.001
Hopkins, T. C., Allen, D. L., & Deen, R. C. (1975). Effect of water on slope stability, 44.
Huang, D., Cen, D., Ma, G., & Huang, R. (2015). Step-path failure of rock slopes with
intermittent joints. Landslides, 12(5), 911–926. https://doi.org/10.1007/s10346-014-0517-6
Irwin, G. R. Linear fracture mechanics, fracture transition, and fracture control, Engineering
Fracture Mechanics, (August 1968).
Kemeny, J. (2003). The time-dependent reduction of sliding cohesion due to rock bridges along
discontinuities: A fracture mechanics approach. Rock Mechanics and Rock Engineering,
36(1), 27–38. https://doi.org/10.1007/s00603-002-0032-2
Krahulec, K. (1997). History and production of the West Mountain Bingham mining district,
Utah. Geology and Ore Deposits of the Oquirrh and Wasatch Mountains, Utah. Guidebook
Series of the Society of Economic Geologists, 29(January 1997), 189−217.
Krautblatter, M., & Moser, M. (2009). A nonlinear model coupling rockfall and rainfall intensity
based on a four year measurement in a high Alpine rock wall (Reintal, German Alps).
Natural Hazards and Earth System Science, 9(4), 1425–1432.
https://doi.org/10.5194/nhess-9-1425-2009
Maerz, N. H. (2014). An Investigation of Rock Fall and Pore Water Pressure using LiDAR in
Highway 63 Rock Cuts An Investigation of Rock Fall and Pore Water Pressure.
Monteleone, S., Contino, A., Bova, P., Esposito, G., & Giuffré, I. (2017). Historical analysis of
rainfall-triggered rockfalls: the case study of the disaster of the ancient hydrothermal
Sclafani Spa (Madonie Mts, northern-central Sicily, Italy) in 1851. Natural Hazards and
Earth System Sciences, 17(12), 2229–2243. https://doi.org/10.5194/nhess-17-2229-2017
Moore, J. R., Pankow, K. L., Ford, S. R., Koper, K. D., Hale, J. M., Aaron, J., & Larsen, C. F.
(2017). Dynamics of the Bingham Canyon rock avalanches (Utah, USA) resolved from
topographic, seismic, and infrasound data. Journal of Geophysical Research: Earth Surface,
122(3), 615–640. https://doi.org/10.1002/2016JF004036
Oppikofer, T., Böhme, M., Saintot, A., & Hermanns, R. (2014). Engineering Geology for
Society and Territory - Volume 8. Engineering Geology for Society and Territory - Volume
8, 2, 243–248. https://doi.org/10.1007/978-3-319-09408-3
45
Paluszny, A., & Zimmerman, R. W. (2017). Modelling of primary fragmentation in block caving
mines using a finite-element based fracture mechanics approach. Geomechanics and
Geophysics for Geo-Energy and Geo-Resources, 3(2), 121–130.
https://doi.org/10.1007/s40948-016-0048-9
Paronuzzi, P., & Bolla, A. (2014). Engineering Geology for Society and Territory - Volume 8.
Engineering Geology for Society and Territory - Volume 8, 2, 213–216.
https://doi.org/10.1007/978-3-319-09408-3
Regmi, A. D., Yoshida, K., Nagata, H., & Pradhan, B. (2014). Rock toppling assessment at
mugling-narayanghat road section: “A case study from mauri khola landslide”, nepal.
Catena, 114, 67–77. https://doi.org/10.1016/j.catena.2013.10.013
Rutqvist, J. & Stephansson, O. (2003). The role of hydrochemical coupling in fractured rock
engineering.Hydrogeology Journal, 11(1) 7–40. https://doi.org/10.1007/s10040-002-0241-5
Sagaseta, C., Sánchez, J. M., & Cañizal, J. (2001). A general analytical solution for the required
anchor force in rock slopes with toppling failure. International Journal of Rock Mechanics
and Mining Sciences, 38(3), 421–435. https://doi.org/10.1016/S1365-1609(01)00011-9
Septian, A., Llano-Serna, M. A., Ruest, M. R., & Williams, D. J. (2017). Three-dimensional
Kinematic Analysis of Bingham Canyon Mine Pit Wall Slides. Procedia Engineering, 175,
86–93. https://doi.org/10.1016/j.proeng.2017.01.030
Spreafico, M. C., Cervi, F., Francioni, M., Stead, D., & Borgatti, L. (2017). An investigation into
the development of toppling at the edge of fractured rock plateaux using a numerical
modelling approach. Geomorphology, 288, 83–98.
https://doi.org/10.1016/j.geomorph.2017.03.023
Sternik, K. (2013). Comparison of Slope Stability Predictions By Gravity Increase and Shear
Strength Reduction Methods Metodami Rosnącej Grawitacji I Redukcji.
Styles, T., Stead, D., Eberhardt, E., Rabus, B., Gaida, M., & Bloom, J. (2011). Integrated
Numerical Modelling and Insar Monitoring of a Slow Moving Slope Instability at Bingham
Canyon Mine. Slope Stability 2011: International Symposium on Rock Slope Stability in
Open Pit Mining and Civil Engineering, (October 2015).
Tenggara, N. (2014). Engineering Geology for Society and Territory - Volume 8. Engineering
Geology for Society and Territory - Volume 8, 2(Anonim 2003), 797–800.
https://doi.org/10.1007/978-3-319-09408-3
Walker, L. R., & Shiels, A. B. (2013). Physical causes and consequences for Landslide Ecology.
Landslide Ecology, 46–82.
Yarema, S. Y. (2004). On the contribution of G. R. Irwin to fracture mechanics. Materials
Science, 31(5), 617–623. https://doi.org/10.1007/bf00558797
46
Youssef, A. M., Pradhan, B., Al-Kathery, M., Bathrellos, G. D., & Skilodimou, H. D. (2015).
Assessment of rockfall hazard at Al-Noor Mountain, Makkah city (Saudi Arabia) using
spatio-temporal remote sensing data and field investigation. Journal of African Earth
Sciences, 101, 309–321. https://doi.org/10.1016/j.jafrearsci.2014.09.021
Zare, M., & Torabi, S. R. (2008). The effect of moisture on the stability of rock slopes: An
experimental study on the rock slopes of Khosh Yeylagh Main Road, Iran. 1st International
Conference on Transportation Geotechnics, ICTG-1, (January), 355–359.
47
APPENDIX A: STRESSES FOR STABILITY ANALYSIS
Table A: Stresses for stability analysis
Stage 1
Normal
Stress
Shear
Stress
Shear
strength
-0.81 0.173 0.632
-0.841 0.224 0.654
-0.881 0.265 0.682
-0.915 0.307 0.706
-0.952 0.352 0.732
-0.983 0.477 0.754
-1 0.561 0.765
-1.03 0.658 0.786
-1.07 0.756 0.814
-1.1 0.856 0.835
-1.17 0.981 0.884
-1.24 1.06 0.934
-1.33 1.18 0.997
-1.4 1.26 1.046
-1.49 1.36 1.109
-1.55 1.44 1.151
-2.17 1.55 1.585
-1.08 1.7 0.821
-1.2 1.67 0.905
-1.3 1.64 0.976
-1.3 1.63 0.976
-1.4 1.61 1.046
-1.55 1.61 1.151
-1.77 1.69 1.305
-2.01 1.74 1.473
-2.21 1.79 1.613
-2.42 1.85 1.760
-2.62 1.92 1.900
-2.83 2.02 2.047
48
Table A (Continued)
-3.01 2.07 2.173
-3.2 2.14 2.306
-3.26 2.2 2.348
-3.31 2.27 2.383
-3.31 2.29 2.383
-3.36 2.13 2.418
-3.49 2.08 2.509
-3.6 2.02 2.586
-3.74 1.98 2.685
-3.87 1.87 2.776
-4.06 1.77 2.909
-4.17 1.7 2.986
-4.28 1.63 3.063
-4.4 1.56 3.147
-4.75 1.59 3.392
-5.22 1.72 3.721
-5.32 1.79 3.791
-5.12 1.81 3.651
-4.92 1.87 3.511
-4.68 1.93 3.343
-4.24 2.42 3.035
-3.76 2.22 2.699
-2.89 1.99 2.089
-2.08 1.69 1.522
-9.95 1.36 7.034
-1.75 0.387 1.291
-2.14 -0.541 1.564
-2.39 -1.31 1.739
-3.27 -1.44 2.355
-4.59 -1.19 3.280
-5.68 -0.846 4.043
-6.88 -0.536 4.884
-7.68 0.371 5.444
-8.47 1.63 5.997
-9.28 2.96 6.565
-9.33 3.62 6.600
-9.18 4.07 6.495
-8.84 4.35 6.257
49
Table A (Continued)
-8.64 4.62 6.117
-8.55 4.96 6.053
103.535 174.181
FOS 1.68
Stage 2
Normal
Stress
Shear
Stress
Shear
strength
-0.468 0.58 0.393
-0.508 0.679 0.421
-0.56 0.791 0.457
-0.608 0.898 0.491
-0.619 1.03 0.499
-0.598 1.12 0.484
-0.545 1.22 0.447
-0.479 1.33 0.400
-0.382 1.45 0.333
-0.255 1.66 0.244
-0.081742 1.93 0.122
0.085724 2.12 0.005
0.436 2.59 -0.240
-0.25 2.56 0.240
-0.31 2.47 0.282
-0.386 2.36 0.335
-0.442 2.26 0.375
-0.489 2.15 0.407
-0.522 2.14 0.431
-0.559 2.12 0.457
-0.664 2.11 0.530
-0.77 2.1 0.604
-0.864 2.1 0.670
-1.01 2.09 0.772
-1.1 2.09 0.835
-1.31 2.13 0.983
-1.51 2.17 1.123
-1.78 2.2 1.312
-2.1 2.13 1.536
50
Table A (Continued)
-2.48 2.41 1.802
-2.82 2.62 2.040
-3.07 2.71 2.215
-2.99 2.78 2.159
-2.96 2.3 2.138
-3.12 2.19 2.250
-3.36 2.07 2.418
-3.61 2.02 2.593
-4.48 2.25 3.203
-4.87 2.26 3.476
-5.31 2.26 3.784
-5.59 2.25 3.980
-5.88 2.21 4.183
-6.16 2.17 4.380
-6.35 2.15 4.513
-6.64 2.14 4.716
-6.93 2.13 4.919
-7.32 2.1 5.192
-7.84 2.4 5.556
-8.56 2.78 6.060
-9.23 3.18 6.530
-11 4.74 7.769
-9.46 4.07 6.691
-7.95 3.5 5.633
-6.37 2.87 4.527
-4.73 2.27 3.378
-4.99 2.5 3.560
-5.22 2.79 3.721
-4.59 2.56 3.280
-3.6 2.59 2.586
-2.71 1.58 1.963
-2.19 0.9 1.599
-3.2 0.348 2.306
-4.62 -0.271 3.301
-5.93 0.198 4.218
-6.71 0.484 4.765
-7.2 0.812 5.108
-7.86 1.38 5.570
51
Table A (Continued)
-8.04 2.09 5.696
-8.24 2.62 5.836
-8.4 3.17 5.948
-8.58 3.85 6.075
-8.6 4.17 6.089
-8.62 4.59 6.103
-8.62 5.15 6.103
160.919 202.860
FOS 1.261
Stage 3
Normal
Stress
Shear
Stress
Shear
strength
-2.52 -0.216 1.830
-2.79 -0.087722 2.019
-3.19 0.083258 2.299
-3.26 0.299 2.348
-3.36 0.589 2.418
-3.57 0.926 2.565
-3.82 0.134 2.741
-3.59 1.35 2.579
-2.74 0.774 1.984
-2.53 2.21 1.837
-2.31 2.47 1.683
-2.06 2.81 1.508
-1.88 3.18 1.382
-1.73 3.62 1.277
-1.46 3.99 1.088
-1.14 4.36 0.863
-1.09 4.56 0.828
-1.02 4.78 0.779
-4.96 3.45 3.539
-3.05 2.93 2.201
-1.62 3.35 1.200
-1.17 3.37 0.884
-1.49 3.36 1.109
-1.75 3.33 1.291
-2.08 3.26 1.522
52
Table A (Continued)
-1.68 3.35 1.242
-2.96 4.23 2.138
1.52 5.31 -1.000
-1.1 3.81 0.835
-1.32 3.52 0.990
4.64 3.29 -3.185
8.53 3.87 -5.909
5.37 4.42 -3.696
0.069 5.13 0.016
-3.61 4.15 2.593
-1.17 2.96 0.884
-1.6 1.84 1.186
-1.64 5.47 1.214
-1.76 -0.947 1.298
-1.64 -0.957 1.214
-1.43 -0.82 1.067
-1.32 -0.672 0.990
-1.73 0.387 1.277
-2.08 1.55 1.522
-2.52 2.63 1.830
-3.03 3.61 2.187
-3.44 4.53 2.474
-3.74 5.25 2.685
124.79254 71.416
FOS 0.572