Sachpazis: Slope Stability Analysis

Slope Stability Analysis
Dr. Costas Sachpazis
Slope stability refers to the condition of inclined soil or rock slopes to withstand or
undergo movement. The stability condition of slopes is a subject of study and research in
soil mechanics, geotechnical engineering and engineering geology.

Slope stability analysis
Table Of Contents
Examples 2
Slope stabilization 5
Analysis methods 6
Limit equilibrium analysis 8
     Analytical techniques: Method of slices 9
     Swedish Slip Circle Method of Analysis 10
     Ordinary Method of Slices 10
     Modi ed Bishop’s Method of Analysis 12
     Lorimer's method 12
     Spencer’s Method 13
     Sarma method 13
     Comparisons 13
     Rock slope stability analysis 16
Limit analysis 17
Stereographic and kinematic analysis 18
Rockfall simulators 19
Numerical methods of analysis 19
     Continuum modelling 20
     Discontinuum modelling 20
     Hybrid/coupled modelling 21
Rock mass classi cation 22
Probability classi cation 22
References 24
Further reading 26
Page 1

Slope stability refers to the condition of inclined soil or rock slopes to withstand or undergo movement. The stability condition of slopes is a
subject of study and research in soil mechanics, geotechnical engineering and engineering geology. Slope stability analyses include static
and dynamic, analytical or empirical methods to evaluate the stability of earth and rock- ll dams, embankments, excavated slopes, and
natural slopes in soil and rock. The analyses are generally aimed at understanding the causes of an occurred slope failure, or the factors
that can potentially trigger a slope movement, resulting in a landslide, as well as at preventing the initiation of such movement, slowing it
down or arresting it through mitigation countermeasures.
The stability of a slope is essentially controlled by the ratio between the available shear strength and the acting shear stress, which can be
expressed in terms of a safety factor if these quantities are integrated over a potential (or actual) sliding surface. A slope can be globally
stable if the safety factor, computed along any potential sliding surface running from the top of the slope to its toe, is always larger than 1.
The smallest value of the safety factor will be taken as representing the global stability condition of the slope. Similarly, a slope can be
locally stable if a safety factor larger than 1 is computed along any potential sliding surface running through a limited portion of the slope
(for instance only within its toe). Values of the global or local safety factors close to 1 (typically comprised between 1 and 1.3, depending
on regulations) indicate marginally stable slopes that require attention, monitoring and/or an engineering intervention (slope stabilization)
to increase the safety factor and reduce the probability of a slope movement.
A previously stable slope can be a ected by a number of predisposing factors or processes that make the safety factor decrease - either
by increasing the shear stress or by decreasing the shear strength - and can ultimately result in slope failure. Factors that can trigger
slope failure include hydrologic events (such as intense or prolonged rainfall, rapid snowmelt, progressive soil saturation, increase of
water pressure within the slope), earthquakes (including aftershocks), internal erosion (piping), surface or toe erosion, arti cial slope
loading (for instance due to the construction of a building), slope cutting (for instance to make space for roadways, railways or buildings),
or slope ooding (for instance by lling an arti cial lake after damming a river).
Examples
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Figure 1: Simple slope slip section
As seen in Figure 1, earthen slopes can develop a cut-spherical weakness area. The probability of this happening can be calculated in
advance using a simple 2-D circular analysis package. A primary di culty with analysis is locating the most-probable slip plane for any
given situation. Many landslides have only been analyzed after the fact. More recently slope stability radar technology has been employed,
particularly in the mining industry, to gather real time data and assist in determining the likelihood of slope failure.
Figure 2: Real life landslide on a slope
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Real life failures in naturally deposited mixed soils are not necessarily circular, but prior to computers, it was far easier to analyse such a
simpli ed geometry. Nevertheless, failures in 'pure' clay can be quite close to circular. Such slips often occur after a period of heavy rain,
when the pore water pressure at the slip surface increases, reducing the e ective normal stress and thus diminishing the restraining
friction along the slip line. This is combined with increased soil weight due to the added groundwater. A 'shrinkage' crack (formed during
prior dry weather) at the top of the slip may also ll with rain water, pushing the slip forward. At the other extreme, slab-shaped slips on
hillsides can remove a layer of soil from the top of the underlying bedrock. Again, this is usually initiated by heavy rain, sometimes
combined with increased loading from new buildings or removal of support at the toe (resulting from road widening or other construction
work). Stability can thus be signi cantly improved by installing drainage paths to reduce the destabilising forces. Once the slip has
occurred, however, a weakness along the slip circle remains, which may then recur at the next monsoon.
Slope stability issues can be seen with almost any walk down a ravine in an urban setting. An example is shown in Figure 3, where a river is
eroding the toe of a slope, and there is a swimming pool near the top of the slope. If the toe is eroded too far, or the swimming pool begins
to leak, the forces driving a slope failure will exceed those resisting failure, and a landslide will develop, possibly quite suddenly.
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Slope stabilization
This section needs expansion. You can help by adding to it. (July 2014)
Stability of slopes can be improved by:
Flattening of slope results in reduction in weight which makes the slope more stable
Soil stabilization
Providing lateral supports by piles or retaining walls
Grouting or cement injections into special places
Consolidation by surcharging or electro osmosis increases the stability of slope.
Figure 1: Rotational failure of slope on circular slip surface
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Analysis methods
Figure 3: Slope with eroding river and swimming pool
Figure 4: Method of slices
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If the forces available to resist movement are greater than the forces driving movement, the slope is considered stable. A factor of safety
is calculated by dividing the forces resisting movement by the forces driving movement. In earthquake-prone areas, the analysis is typically
run for static conditions and pseudo-static conditions, where the seismic forces from an earthquake are assumed to add static loads to the
analysis.
Slope stability analysis is performed to assess the safe design of a human-made or natural slopes (e.g. embankments, road cuts, open-pit
mining, excavations, land lls etc.) and the equilibrium conditions. Slope stability is the resistance of inclined surface to failure by sliding or
collapsing. The main objectives of slope stability analysis are nding endangered areas, investigation of potential failure mechanisms,
determination of the slope sensitivity to di erent triggering mechanisms, designing of optimal slopes with regard to safety, reliability and
economics, designing possible remedial measures, e.g. barriers and stabilization.
Successful design of the slope requires geological information and site characteristics, e.g. properties of soil/rock mass, slope geometry,
groundwater conditions, alternation of materials by faulting, joint or discontinuity systems, movements and tension in joints, earthquake
activity etc. The presence of water has a detrimental e ect on slope stability. Water pressure acting in the pore spaces, fractures or other
discontinuities in the materials that make up the pit slope will reduce the strength of those materials. Choice of correct analysis technique
depends on both site conditions and the potential mode of failure, with careful consideration being given to the varying strengths,
weaknesses and limitations inherent in each methodology.
Before the computer age stability analysis was performed graphically or by using a hand-held calculator. Today engineers have a lot of
possibilities to use analysis software, ranges from simple limit equilibrium techniques through to computational limit analysis approaches
(e.g. Finite element limit analysis, Discontinuity layout optimization) to complex and sophisticated numerical solutions ( nite-/distinct-
element codes). The engineer must fully understand limitations of each technique. For example, limit equilibrium is most commonly used
and simple solution method, but it can become inadequate if the slope fails by complex mechanisms (e.g. internal deformation and brittle
fracture, progressive creep, liquefaction of weaker soil layers, etc.). In these cases more sophisticated numerical modelling techniques
should be utilised. Also, even for very simple slopes, the results obtained with typical limit equilibrium methods currently in use (Bishop,
Spencer, etc.) may di er considerably. In addition, the use of the risk assessment concept is increasing today. Risk assessment is
concerned with both the consequence of slope failure and the probability of failure (both require an understanding of the failure
mechanism).
Within the last decade (2003) Slope Stability Radar has been developed to remotely scan a rock slope to monitor the spatial deformation
of the face. Small movements of a rough wall can be detected with sub-millimeter accuracy by using interferometry techniques.
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Limit equilibrium analysis
A typical cross-section of a slope used in two-dimensional analyses.
Conventional methods of slope stability analysis can be divided into three groups: kinematic analysis, limit equilibrium analysis, and rock
fall simulators. Most slope stability analysis computer programs are based on the limit equilibrium concept for a two- or three-
dimensional model. Two-dimensional sections are analyzed assuming plane strain conditions. Stability analyses of two-dimensional slope
geometries using simple analytical approaches can provide important insights into the initial design and risk assessment of slopes.
Limit equilibrium methods investigate the equilibrium of a soil mass tending to slide down under the in uence of gravity. Translational or
rotational movement is considered on an assumed or known potential slip surface below the soil or rock mass. In rock slope engineering,
methods may be highly signi cant to simple block failure along distinct discontinuities. All these methods are based on the comparison of
forces, moments, or stresses resisting movement of the mass with those that can cause unstable motion (disturbing forces). The output of
the analysis is a factor of safety, de ned as the ratio of the shear strength (or, alternatively, an equivalent measure of shear resistance or
capacity) to the shear stress (or other equivalent measure) required for equilibrium. If the value of factor of safety is less than 1.0, the
slope is unstable.
All limit equilibrium methods assume that the shear strengths of the materials along the potential failure surface are governed by linear
(Mohr-Coulomb) or non-linear relationships between shear strength and the normal stress on the failure surface. The most commonly
used variation is Terzaghi's theory of shear strength which states that
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where is the shear strength of the interface, is the e ective stress ( is the total stress normal to the interface and is the pore water
pressure on the interface), is the e ective friction angle, and is the e ective cohesion.
The methods of slices is the most popular limit equilibrium technique. In this approach, the soil mass is discretized into vertical slices.
Several versions of the method are in use. These variations can produce di erent results (factor of safety) because of di erent
assumptions and inter-slice boundary conditions.
The location of the interface is typically unknown but can be found using numerical optimization methods. For example, functional slope
design considers the critical slip surface to be the location where that has the lowest value of factor of safety from a range of possible
surfaces. A wide variety of slope stability software use the limit equilibrium concept with automatic critical slip surface determination.
Typical slope stability software can analyze the stability of generally layered soil slopes, embankments, earth cuts, and anchored sheeting
structures. Earthquake e ects, external loading, groundwater conditions, stabilization forces (i.e., anchors, geo-reinforcements etc.) can
also be included.
Analytical techniques: Method of slices
Schematic of the method of slices showing rotation center.
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Many slope stability analysis tools use various versions of the methods of slices such as Bishop simpli ed, Ordinary method of slices
(Swedish circle method/Petterson/Fellenius), Spencer, Sarma etc. Sarma and Spencer are called rigorous methods because they satisfy
all three conditions of equilibrium: force equilibrium in horizontal and vertical direction and moment equilibrium condition. Rigorous
methods can provide more accurate results than non-rigorous methods. Bishop simpli ed or Fellenius are non-rigorous methods satisfying
only some of the equilibrium conditions and making some simplifying assumptions. Some of these approaches are discussed below.
Swedish Slip Circle Method of Analysis
The Swedish Slip Circle method assumes that the friction angle of the soil or rock is equal to zero, i.e., . In other words, when friction angle
is considered to be zero, the e ective stress term goes to zero, thus equating the shear strength to the cohesion parameter of the given
soil. The Swedish slip circle method assumes a circular failure interface, and analyzes stress and strength parameters using circular
geometry and statics. The moment caused by the internal driving forces of a slope is compared to the moment caused by forces resisting
slope failure. If resisting forces are greater than driving forces, the slope is assumed stable.
Ordinary Method of Slices
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Slope stability analysis - Wikipedia
Division of the slope mass in the method of slices.
In the method of slices, also called OMS or the Fellenius method, the sliding mass above the failure surface is divided into a number of
slices. The forces acting on each slice are obtained by considering the mechanical (force and moment) equilibrium for the slices. Each
slice is considered on its own and interactions between slices are neglected because the resultant forces are parallel to the base of each
slice. However, Newton's third law is not satis ed by this method because, in general, the resultants on the left and right of a slice do not
have the same magnitude and are not collinear.
This allows for a simple static equilibrium calculation, considering only soil weight, along with shear and normal stresses along the failure
plane. Both the friction angle and cohesion can be considered for each slice. In the general case of the method of slices, the forces acting
on a slice are shown in the gure below. The normal and shear forces between adjacent slices constrain each slice and make the problem
statically indeterminate when they are included in the computation.
For the ordinary method of slices, the resultant vertical and horizontal forces are
where represents a linear factor that determines the increase in horizontal force with the depth of the slice. Solving for gives
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Next, the method assumes that each slice can rotate about a center of rotation and that moment balance about this point is also needed
for equilibrium. A balance of moments for all the slices taken together gives
where is the slice index, are the moment arms, and loads on the surface have been ignored. The moment equation can be used to solve for
the shear forces at the interface after substituting the expression for the normal force:
Using Terzaghi's strength theory and converting the stresses into moments, we have
where is the pore pressure. The factor of safety is the ratio of the maximum moment from Terzaghi's theory to the estimated moment,
Modi ed Bishop’s Method of Analysis
The Modi ed Bishop's method is slightly di erent from the ordinary method of slices in that normal interaction forces between adjacent
slices are assumed to be collinear and the resultant interslice shear force is zero. The approach was proposed by Alan W. Bishop of
Imperial College. The constraint introduced by the normal forces between slices makes the problem statically indeterminate. As a result,
iterative methods have to be used to solve for the factor of safety. The method has been shown to produce factor of safety values within a
few percent of the "correct" values.
The factor of safety for moment equilibrium in Bishop's method can be expressed as
where
where, as before, is the slice index, is the e ective cohesion, is the e ective internal angle of internal friction, is the width of each slice, is
the weight of each slice, and is the water pressure at the base of each slice. An iterative method has to be used to solve for because the
factor of safety appears both on the left and right hand sides of the equation.
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Lorimer's method
Lorimer's Method is a technique for evaluating slope stability in cohesive soils. It di ers from Bishop's Method in that it uses a clothoid slip
surface in place of a circle. This mode of failure was determined experimentally to account for e ects of particle cementation. The
method was developed in 1930s by Gerhardt Lorimer (Dec 20, 1894-Oct 19, 1961), a student of geotechnical pioneer Karl von Terzaghi.
Spencer’s Method
Spencer's Method of analysis requires a computer program capable of cyclic algorithms, but makes slope stability analysis easier.
Spencer's algorithm satis es all equilibria (horizontal, vertical and driving moment) on each slice. The method allows for unconstrained
slip plains and can therefore determine the factor of safety along any slip surface. The rigid equilibrium and unconstrained slip surface
result in more precise safety factors than, for example, Bishop's Method or the Ordinary Method of Slices.
Sarma method
The Sarma method, proposed by Sarada K. Sarma of Imperial College is a Limit equilibrium technique used to assess the stability of slopes
under seismic conditions. It may also be used for static conditions if the value of the horizontal load is taken as zero. The method can
analyse a wide range of slope failures as it may accommodate a multi-wedge failure mechanism and therefore it is not restricted to
planar or circular failure surfaces. It may provide information about the factor of safety or about the critical acceleration required to
cause collapse.
Comparisons
The assumptions made by a number of limit equilibrium methods are listed in the table below.
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Method Assumption
Ordinary method of
cells
Interslice forces are neglected
Bishop's
simpli ed/modi ed
Resultant interslice forces are horizontal. There are no interslice shear
forces.
Janbu's simpli ed Resultant interslice forces are horizontal. An empirical correction
factor is used to account for interslice shear forces.
Janbu's generalized An assumed line of thrust is used to de ne the location of the
interslice normal force.
Spencer The resultant interslice forces have constant slope throughout the
sliding mass. The line of thrust is a degree of freedom.
Chugh Same as Spencer's method but with a constant acceleration force on
each slice.
Morgenstern-Price The direction of the resultant interslice forces is de ned using an
arbitrary function. The fractions of the function value needed for force
and moment balance is computed.
Fredlund-Krahn
(GLE)
Similar to Morgenstern-Price.
Corps of Engineers The resultant interslice force is either parallel to the ground surface or
equal to the average slope from beginning to end of the slip surface..
Lowe and Kara ath The direction of the resultant interslice force is equal to the average of
the ground surface and the slope of the base of each slice.
Sarma The shear strength criterion is applied to the shears on the sides and
bottom of each slice. The inclinations of the slice interfaces are varied
until a critical criterion is met.
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The table below shows the statical equilibrium conditions satis ed by some of the popular limit equilibrium methods.
Method
Force balance
(vertical)
Force balance
(horizontal) Moment balance
Ordinary MS Yes No Yes
Bishop's
simpli ed
Yes No Yes
Janbu's
simpli ed
Yes Yes No
Janbu's
generalized
Yes Yes Used to compute interslice
shear forces
Spencer Yes Yes Yes
Chugh Yes Yes Yes
Morgenstern-
Price
Yes Yes Yes
Fredlund-
Krahn
Yes Yes Yes
Corps of
Engineers
Yes Yes No
Lowe and
Kara ath
Yes Yes No
Sarma Yes Yes Yes
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Rock slope stability analysis
Rock slope stability analysis based on limit equilibrium techniques may consider following modes of failures:
Planar failure -> case of rock mass sliding on a single surface (special case of general
wedge type of failure); two-dimensional analysis may be used according to the concept
of a block resisting on an inclined plane at limit equilibrium
Polygonal failure -> sliding of a nature rock usually takes place on polygonally-shaped
surfaces; calculation is based on a certain assumptions (e.g. sliding on a polygonal
surface which is composed from N parts is kinematically possible only in case of
development at least (N - 1) internal shear surfaces; rock mass is divided into blocks by
internal shear surfaces; blocks are considered to be rigid; no tensile strength is permitted
etc.)
Wedge failure -> three-dimensional analysis enables modelling of the wedge sliding on
two planes in a direction along the line of intersection
Toppling failure -> long thin rock columns formed by the steeply dipping discontinuities
may rotate about a pivot point located at the lowest corner of the block; the sum of the
moments causing toppling of a block (i.e. horizontal weight component of the block and
the sum of the driving forces from adjacent blocks behind the block under consideration)
is compared to the sum of the moments resisting toppling (i.e. vertical weight
component of the block and the sum of the resisting forces from adjacent blocks in front
of the block under consideration); toppling occur if driving moments exceed resisting
moments
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Limit analysis
A more rigorous approach to slope stability analysis is limit analysis. Unlike limit equilibrium analysis which makes ad-hoc though often
reasonable assumptions, limit analysis is based on rigorous plasticity theory. This enables, among other things, the computation of upper
and lower bounds on the true factor of safety.
Programs based on limit analysis include:
OptumG2 (2014-) General purpose software for geotechnical applications (also includes
elastoplasticity, seepage, consolidation, staged construction, tunneling, and other
relevant geotechnical analysis types).
LimitState:GEO (2008-) General purpose geotechnical software application based on
Discontinuity layout optimization for plane strain problems including slope stability.
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Stereographic and kinematic analysis
Kinematic analysis examines which modes of failure can possibly occur in the rock mass. Analysis requires the detailed evaluation of rock
mass structure and the geometry of existing discontinuities contributing to block instability. Stereographic representation (stereonets) of
the planes and lines is used. Stereonets are useful for analyzing discontinuous rock blocks. Program DIPS allows for visualization
structural data using stereonets, determination of the kinematic feasibility of rock mass and statistical analysis of the discontinuity
properties.
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Rockfall simulators
Rock slope stability analysis may design protective measures near or around structures endangered by the falling blocks. Rockfall
simulators determine travel paths and trajectories of unstable blocks separated from a rock slope face. Analytical solution method
described by Hungr & Evans assumes rock block as a point with mass and velocity moving on a ballistic trajectory with regard to potential
contact with slope surface. Calculation requires two restitution coe cients that depend on fragment shape, slope surface roughness,
momentum and deformational properties and on the chance of certain conditions in a given impact.
Program ROCFALL provides a statistical analysis of trajectory of falling blocks. Method rely on velocity changes as a rock blocks roll, slide
or bounce on various materials. Energy, velocity, bounce height and location of rock endpoints are determined and may be analyzed
statistically. The program can assist in determining remedial measures by computing kinetic energy and location of impact on a barrier.
This can help determine the capacity, size and location of barriers.
Numerical methods of analysis
Numerical modelling techniques provide an approximate solution to problems which otherwise cannot be solved by conventional methods,
e.g. complex geometry, material anisotropy, non-linear behaviour, in situ stresses. Numerical analysis allows for material deformation and
failure, modelling of pore pressures, creep deformation, dynamic loading, assessing e ects of parameter variations etc. However,
numerical modelling is restricted by some limitations. For example, input parameters are not usually measured and availability of these
data is generally poor. User also should be aware of boundary e ects, meshing errors, hardware memory and time restrictions. Numerical
methods used for slope stability analysis can be divided into three main groups: continuum, discontinuum and hybrid modelling.
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Continuum modelling
Figure 3: Finite element mesh
Modelling of the continuum is suitable for the analysis of soil slopes, massive intact rock or heavily jointed rock masses. This approach
includes the nite-di erence and nite element methods that discretize the whole mass to nite number of elements with the help of
generated mesh (Fig. 3). In nite-di erence method (FDM) di erential equilibrium equations (i.e. strain-displacement and stress-strain
relations) are solved. nite element method (FEM) uses the approximations to the connectivity of elements, continuity of displacements
and stresses between elements. Most of numerical codes allows modelling of discrete fractures, e.g. bedding planes, faults. Several
constitutive models are usually available, e.g. elasticity, elasto-plasticity, strain-softening, elasto-viscoplasticity etc.
Discontinuum modelling
Discontinuum approach is useful for rock slopes controlled by discontinuity behaviour. Rock mass is considered as an aggregation of
distinct, interacting blocks subjected to external loads and assumed to undergo motion with time. This methodology is collectively called
the discrete-element method (DEM). Discontinuum modelling allows for sliding between the blocks or particles. The DEM is based on
solution of dynamic equation of equilibrium for each block repeatedly until the boundary conditions and laws of contact and motion are
satis ed. Discontinuum modelling belongs to the most commonly applied numerical approach to rock slope analysis and following
variations of the DEM exist:
distinct-element method
discontinuous deformation analysis (DDA)
particle ow codes
The distinct-element approach describes mechanical behaviour of both, the discontinuities and the solid material. This methodology is
based on a force-displacement law (specifying the interaction between the deformable rock blocks) and a law of motion (determining
displacements caused in the blocks by out-of-balance forces). Joints are treated as boundary conditions. Deformable blocks are
discretized into internal constant-strain elements.
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Discontinuum program UDEC (Universal distinct element code) is suitable for high jointed rock slopes subjected to static or dynamic
loading. Two-dimensional analysis of translational failure mechanism allows for simulating large displacements, modelling deformation or
material yielding. Three-dimensional discontinuum code 3DEC contains modelling of multiple intersecting discontinuities and therefore it
is suitable for analysis of wedge instabilities or in uence of rock support (e.g. rockbolts, cables).
In discontinuous deformation analysis (DDA) displacements are unknowns and equilibrium equations are then solved analogous to nite
element method. Each unit of nite element type mesh represents an isolated block bounded by discontinuities. Advantage of this
methodology is possibility to model large deformations, rigid body movements, coupling or failure states between rock blocks.
Discontinuous rock mass can be modelled with the help of distinct-element methodology in the form of particle ow code, e.g. program
PFC2D/3D. Spherical particles interact through frictional sliding contacts. Simulation of joint bounded blocks may be realized through
speci ed bond strengths. Law of motion is repeatedly applied to each particle and force-displacement law to each contact. Particle ow
methodology enables modelling of granular ow, fracture of intact rock, transitional block movements, dynamic response to blasting or
seismicity, deformation between particles caused by shear or tensile forces. These codes also allow to model subsequent failure processes
of rock slope, e.g. simulation of rock
Hybrid/coupled modelling
Hybrid codes involve the coupling of various methodologies to maximize their key advantages, e.g. limit equilibrium analysis combined with
nite element groundwater ow and stress analysis ; coupled particle ow and nite-di erence analyses. Hybrid techniques allows
investigation of piping slope failures and the in uence of high groundwater pressures on the failure of weak rock slope. Coupled
nite-/distinct-element codes provide for the modelling of both intact rock behaviour and the development and behaviour of fractures.
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Rock mass classi cation
Various rock mass classi cation systems exist for the design of slopes and to assess the stability of slopes. The systems are based on
empirical relations between rock mass parameters and various slope parameters such as height and slope dip.
The Q-slope method for rock slope engineering and rock mass classi cation developed by Barton and Bar expresses the quality of the rock
mass for assessing slope stability using the Q-slope value, from which long-term stable, reinforcement-free slope angles can be derived.
Probability classi cation
The slope stability probability classi cation (SSPC) system is a rock mass classi cation system for slope engineering and slope stability
assessment. The system is a three-step classi cation: ‘exposure’, ‘reference’, and ‘slope’ rock mass classi cation with conversion factors
between the three steps depending on existing and future weathering and damage due to method of excavation. The stability of a slope is
expressed as probability for di erent failure mechanisms.
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A rock mass is classi ed following a standardized set of criteria in one or more exposures (‘exposure’ classi cation). These values are
converted per exposure to a ‘reference’ rock mass by compensating for the degree of weathering in the exposure and the method of
excavation that was used to make the exposure, i.e. the ‘reference’ rock mass values are not in uenced by local in uences such as
weathering and method of excavation. A new slope can then be designed in the ‘reference’ rock mass with compensation for the damage
due to the method of excavation to be used for making the new slope and compensation for deterioration of the rock mass due to future
weathering (the ‘slope’ rock mass). If the stability of an already existing slope is assessed the ‘exposure’ and ‘slope’ rock mass values are
the same.
The failure mechanisms are divided in orientation
dependent and orientation independent. Orientation
dependent failure mechanisms depend on the
orientation of the slope with respect to the orientation
of the discontinuities in the rock mass, i.e. sliding
(plane and wedge sliding) and toppling failure.
Orientation independent relates to the possibility that
a slope fails independently from its orientation, e.g.
circular failure completely through newly formed
discontinuities in intact rock blocks, or failing partially
following existing discontinuities and partially new
discontinuities.
In addition the shear strength along a discontinuity ('sliding criterion') and 'rock mass cohesion' and 'rock mass friction' can be determined.
The system has been used directly or modi ed in various geology and climate environments throughout the world. The system has been
modi ed for slope stability assessment in open pit coal mining.
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References
Page 24

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16. Bar, N.; Barton, N.R. (2017). "The Q-slope Method for Rock Slope Engineering". Rock Mechanics & Rock Engineering, Vol 50,
Springer, Vienna, https://doi.org/10.1007/s00603-017-1305-0
17. Sachpazis, CI, (2013), Detailed Slope Stability Analysis and Assessment of the Original Carsington Earth Embankment Dam Failure
in the UK., Electronic Journal of Geotechnical Engineering (E.J.G.E.) 18 (2013), 39.
18. Assefa, E, Li Jian Lin, Dr. Sachpazis, C,I, Deng Hua Feng, Anastasiadis, A,S, Sun Xu Shu, (2016), Discussion on the Analysis,
Prevention and Mitigation Measures of Slope Instability Problems: A case of Ethiopian Railways., Electronic Journal of Geotechnical
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Page 25

Further reading
Devoto, S.; Castelli, E. (September 2007). "Slope stability in an old limestone quarry
interested by a tourist project". 15th Meeting of the Association of European Geological
Societies: Georesources Policy, Management, Environment. Tallinn.
Douw, W. (2009). Entwicklung einer Anordnung zur Nutzung von
Massenschwerebewegungen beim Quarzitabbau im Rheinischen Schiefergebirge.
Hackenheim, Germany: ConchBooks. p. 358. ISBN 978-3-939767-10-7.
Hack, H.R.G.K. (25–28 November 2002). "An evaluation of slope stability classi cation.
Keynote Lecture.". In Dinis da Gama, C.; Ribeira e Sousa, L. (eds.). Proc. ISRM
EUROCK’2002. Funchal, Madeira, Portugal: Sociedade Portuguesa de Geotecnia, Lisboa,
Portugal. pp. 3–32. ISBN 972-98781-2-9.
Liu, Y.-C.; Chen, C.-S. (2005). "A new approach for application of rock mass classi cation
on rock slope stability assessment". Engineering Geology. 89 (1–2): 129–143.
doi:10.1016/j.enggeo.2006.09.017.
Pantelidis, L. (2009). "Rock slope stability assessment through rock mass classi cation
systems". International Journal of Rock Mechanics and Mining Sciences. 46 (2, number 2):
315–325. doi:10.1016/j.ijrmms.2008.06.003.
Rupke, J.; Huisman, M.; Kruse, H.M.G. (2007). "Stability of man-made slopes". Engineering
Geology. 91 (1): 16–24. doi:10.1016/j.enggeo.2006.12.009.
Singh, B.; Goel, R.K. (2002). Software for engineering control of landslide and tunnelling
hazards. 1. Taylor & Francis. p. 358. ISBN 978-90-5809-360-8.
Coduto, Donald P. (1998). Geotechnical Engineering: Principles and Practices. Prentice-
Hall. ISBN 0-13-576380-0
Fredlund, D. G., H. Rahardjo, M. D. Fredlund (2014). Unsaturated Soil Mechanics in
Engineering Practice. Wiley-Interscience. ISBN 978-1118133590
Page 26

Kliche, Charles A. (1999), Rock Slope Stability, Colorado, USA: Society for Mining,
Metallurgy, and Exploration, ISBN 0-87335-171-1
Eberhardt, Erik (2003), Rock Slope Stability Analysis - Utilization of Advanced Numerical
Techniques (PDF), Vancouver, Canada: Earth and Ocean Sciences, University of British
Columbia
US Army Corps of Engineers (2003), Engineering and Design - Slope Stability (PDF),
Washington DC, USA: US Army Corps of Engineers
Stead, Doug; Eberhardt, E.; Coggan, J.; Benko, B. (2001), M. Kühne; H.H. Einstein; E.
Krauter; H. Klapperich; R. Pöttler (eds.), Advanced numerical techniques in rock slope
stability analysis - Applications and limitations (PDF), Davos, Switzerland: Verlag
Glückauf GmbH, pp. 615–624
Abramson, Lee W.; Lee, Thomas S.; Sharma, Sunil; Boyce, Glenn M. (2002), Slope Stability
and Stabilization Methods (2nd ed.), New York, USA: John Wiley & Sons, ISBN 0-471-
38493-3
Zhu, D.Y.; Lee, C.F.; Jiang, H.D. (2003), "Generalised framework of limit equilibrium
methods for slope stability analysis", Geotechnique, Telford, London, Great Britain, 53 (4):
377–395, doi:10.1680/geot.2003.53.4.377, ISSN 0016-8505
Kovári, Kalman; Fritz, P. (1978), Slope Stability with Plane, Wedge and Polygonal Sliding
Surfaces, Rio de Janeiro, Brazil, pp. 103–124
Yang, Xiao-Li; Li, L.; Yin, J.H. (2004), "Stability analysis of rock slopes with a modi ed
Hoek-Brown failure criterion", International Journal for Numerical and Analytical Methods
in Geomechanics, Chichester, Great Britain: John Wiley & Sons, 28 (2): 181–190,
Bibcode:2004IJNAM..28..181Y, doi:10.1002/nag.330, ISSN 0363-9061
Barton, N.R.; Bandis, S.C. (1990), Barton, Nick (ed.), Review of predictive capabilities of
JRC-JCS model in engineering practice, Rotterdam: Balkema, pp. 603–610, ISBN 978-90-
6191-109-8
Hungr, O.; Evans, S.G. (1988), Bonnard, C. (ed.), Engineering evaluation of fragmental
rockfall hazards, Rotterdam: Balkema, pp. 685–690
Page 27

Dr. Costas Sachpazis

Sachpazis: Slope Stability Analysis

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