slope stability analysis instructions

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23/01/2016 Slope stability analysis - W ikipedi a, the fr ee encyclopedia

https://en.wikipedia.org/wiki/Slope_stability_analysis 3/15

A typical cross-section of a slope used in

two-dimensional analyses.

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 influence of

gravity. Transitional or rotational movement is considered

on an assumed or known potential slip surface below the soil

or rock mass.[11] In rock slope engineering, methods may be

highly significant to simple block failure along distinct

discontinuities.[8] 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, defined 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.[11] The most commonly used variation is Terzaghi's theory of

shear strength which states that

where is the shear strength of the interface, is the effective stress ( is the total stress

normal to the interface and is the pore water pressure on the interface), is the effective friction

angle, and is the effective cohesion.

The methods of slices is the most popular limit equilibrium technique. In this approach, the soil mass is

discretized into vertical slices.[10][12] Several versions of the method are in use. These variations can

produce different results (factor of safety) because of different assumptions and inter-slice boundary

conditions.[11][13]

The location of the interface is typically unknown but can be found using numerical optimization

methods.[14] 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 effects, external loading, groundwater

conditions, stabilization forces (i.e., anchors, geo-reinforcements etc.) can also be included.

Analytical techniques: Method of slices

Many slope stability analysis tools use various versions of the methods of slices such as Bishopimplified , 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

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Schematic of the method of slices showing

rotation center.

Division of the slope mass in the method

of slices.

methods can provide more accurate results than non-

rigorous methods. Bishop simplified or Fellenius are non-

rigorous methods satisfying only some of the equilibrium

conditions and making some simplifying assumptions.[12][13]

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 effective 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 cause by forces

resisting slope failure. If resisting forces are greater than driving forces, the slope is assumed stable.

Ordinary 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 satisfied 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.[15]

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 figure 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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Force equilibrium for a slice in the method

of slices. The block is assumed to have

thickness . The slices on the left and right

exert normal forces and shear

forces , the weight of the slice

causes the force . These forces are

balanced by the pore pressure and reactionsof the base .

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,

Modified Bishop’s Method of Analysis

The Modified Bishop’s method[16] is slightly different 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.

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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 effective cohesion, is the effective 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.

Lorimer's method

Lorimer's Method is a technique for evaluating slope stability in cohesive soils. It differs 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 effects of particle cementation. The method was developed in the 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

[17]

requires a computer program capable of cyclic algorithms, but makesslope stability analysis easier. It is not as accurate as the Modified Bishop’s method, but is acceptably

accurate in engineering practices.[18]

Sarma method

The Sarma method,[19] 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. [20]

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Method Assumption

Ordinary method of cells

Interslice forces are neglected

Bishop'ssimplified/modified[16]

Resultant interslice forces are horizontal. There are no interslice shear forces.

Janbu'ssimplified[21]

Resultant interslice forces are horizontal. An empirical correction factor is used toaccount for interslice shear forces.

Janbu's

generalized[21]An assumed line of thrust is used to define the location of the interslice normalforce.

Spencer [17] The resultant interslice forces have constant slope throughout the sliding mass.

Chugh[22] Same as Spencer's method but with a constant acceleration force on each slice.

Morgenstern-

Price[23]

The direction of the resultant interslice forces is defined using an arbitraryfunction. The fractions of the function value needed for force and moment balance

is computed.Fredlund-Krahn

(GLE) [15] Similar to Morgenstern-Price.

Corps of Engineers[24]

The resultant interslice force is either parallel to the ground surface or equal to theaverage slope from the beginning to the end of the slip surface..

Lowe and Karafiath[25]

The direction of the resultant interslice force is equal to the average of the groundsurface and the slope of the base of each slice.

Sarma [19]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 criticalcriterion is met.

The table below shows the statical equilibrium conditions satisfied by some of the popular limit

equilibrium methods.[20]

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Method Force balance

(vertical)

Force balance

(horizontal) Moment balance

Ordinary MS Yes No Yes

Bishop'ssimplified

Yes No Yes

Janbu's

simplified

Yes Yes No

Janbu'sgeneralized

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 andKarafiath

Yes Yes No

Sarma Yes Yes Yes

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 typeof failure); two-dimensional analysis may be used according to the concept of a block resisting on

an inclined plane at limit equilibrium[26][27]

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 iscomposed 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.)[27]

Wedge failure -> three-dimensional analysis enables modelling of the wedge sliding on two planesin a direction along the line of intersection[27][28]

Toppling failure -> long thin rock columns formed by the steeply dipping discontinuities mayrotate about a pivot point located at the lowest corner of the block; the sum of the momentscausing toppling of a block (i.e. horizontal weight component of the block and the sum of thedriving forces from adjacent blocks behind the block under consideration) is compared to the sumof the moments resisting toppling (i.e. vertical weight component of the block and the sum of theresisting forces from adjacent blocks in front of the block under consideration); toppling occur if

driving moments exceed resisting moments[29][30]

Limit equilibrium analysis software

SLIDE[31] provides 2D stability calculations in rocks or soils using these rigorous analysismethods: Spencer , Morgenstern-Price/General limit equilibrium; and non-rigorous methods:

Bishop simplified , Corps of Engineers, Janbu simplified/corrected , Lowe-Karafiath and

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Ordinary/Fellenius. Searching of the critical slip surface is realized with the help of a grid or as a slope search in user-defined area. Program includes also probabilistic analysis using Monte Carloor Latin Hypercube simulation techniques where any input parameter can be defined as a randomvariable. Probabilistic analysis determine the probability of failure and reliability index, whichgives better representation of the level of safety. Back analysis serves for calculation of areinforcement load with a given required factor of safety. Program enables finite element

groundwater seepage analysis.[31]

SLOPE/W[32] is formulated in terms of moment and force equilibrium factor of safety equations.Limit equilibrium methods include Morgenstern-Price, General limit equilibrium, Spencer ,

Bishop, Ordinary, Janbu etc. This program allows integration with other applications. For

example, finite element computed stresses from SIGMA/W[33] or QUAKE/W[34] can be used tocalculate a stability factor by computing total shear resistance and mobilized shear stress along theentire slip surface. Then a local stability factor for each slice is obtained. Using a Monte Carloapproach, program computes the probability of failure in addition to the conventional factor of

safety.[32] STABL WV[35] is a limit equilibrium-based, Windows software based on the stablfamily of algorithms. It allows analysis using Bishop's, Spencer's and Janbu's method. Regular slopes as well as slopes with various types of inclusions may be analyzed.

HYDRUS[36]

add-on modules can check the stability of embankments, dams, earth cuts andanchored sheeting structures with the influence of the water. The values of the pore pressure intransport domain are imported automatically for the selected time to Stability module. Theanalysis can be repeated for all time shots of the water movement simulated by basic program.The common method of slices (the Bishop, Fellenius/Petterson, Morgenstern-Price or the Spencer)can be set as well as the different type of Geo-reinforcement or Earthquake effects.

SVSlope[37] is formulated in terms of moment and force equilibrium factor of safety equations.Limit equilibrium methods include Morgenstern-Price, General limit equilibrium, Spencer ,

Bishop, Ordinary, Kulhawy and others This program allows integration with other applications in

the geotechnical software suite. For example, finite element computed stresses from SVSolid[38] or

pore-water pressures from SVFlux[39]

can be used to calculate the factor of safety by computingtotal shear resistance and mobilized shear stress along the entire slip surface. The software alsoutilizes Monte Carlo, Latin Hypercube, and the APEM probabilistic approaches. Spatialvariability through random fields computations may also be included in the analysis.

dotSlope[40] provides limit equilibrium analyses through the methods of Fellenius, Bishop simplified , Janbu simplified/corrected , Corps of Engineers, Lowe & Karafiath, Spencer ,GLE/Morgenstern & Price. The slope can have multiple soils, impenetrable layers, cuts andembankments, multiple groundwater conditions, ponded water, dry and water filled tensioncracks, soil reinforcements (anchors, nails, piles and geo-synthetics). Slip surfaces can be defined

through six surface generators in order to find the critical case. dotSlope[40] can run deterministic

analyses, surface optimization, sensitivity analyses along with probabilistic analyses using the Monte Carlo method. The program runs on Microsoft Windows, Mac OS X and Android .[41]

GALENA[42] - includes stability analysis, back analysis, and probability analysis, using the

Bishop, Spencer-Wright and Sarma methods.[42]

GSLOPE[43] - provides limit equilibrium slope stability analysis of existing natural slopes,unreinforced man-made slopes, or slopes with soil reinforcement, using Bishop’s Modified method

and Janbu’s Simplified method applied to circular, composite or non-circular surfaces.[43]

CLARA-W[44] - three-dimensional slope stability program includes calculation with the help of these methods: Bishop simplified , Janbu simplified , Spencer and Morgenstern-Price. Problem

configurations can involve rotational or non-rotational sliding surfaces, ellipsoids, wedges,compound surfaces, fully specified surfaces and searches.[44]

TSLOPE3[45] - two- or three-dimensional analyses of soil and rock slopes using Spencer

method .[45]

A program specific for rock slope analysis is AutoBlock (http://www.igt.ethz.ch/AutoBlock).[46]

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It overcome two problems inherently complicating the analysis in engineering practice: firstlydetermining volumes and magnitudes of sliding areas of potentially unstable blocks based on thereal topography, and secondly finding the critical blocks which are formed by an intersection of various discontinuities. It allows importing arbitrarily complex terrain surfaces which have beendigitized beforehand using a topographic map. These surfaces are then extruded to a 3D solidwhich may be intersected by various sets of discontinuities. By combining all possible locations of all discontinuities potentially unstable blocks are determined. For each block, the factor of safetyagainst sliding is computed using the limit equilibrium method. AutoBlock is an add-on to the

popular program "AutoCAD" and exploits its possibilities and its power (e.g. for 3D-visualizations).

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 (http://www.optumce.com) (2014-) General purpose software for plane straingeotechnical applications including slope stability.

LimitState:GEO (http://www.limitstate.com/geo) (2008-) General purpose geotechnical softwareapplication based on Discontinuity layout optimization for plane strain problems including slopestability.

Stereographic and kinematic analysisKinematic 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.[47][48] Stereographic representation (stereonets) of the planes and lines

is used.[49] Stereonets are useful for analyzing discontinuous rock blocks.[50] Program DIPS[51] allows

for visualization structural data using stereonets, determination of the kinematic feasibility of rock mass

and statistical analysis of the discontinuity properties.[47][51]

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[52] 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 coefficients that depend on fragment

shape, slope surface roughness, momentum and deformational properties and on the chance of certain

conditions in a given impact.[53]

Program ROCFALL[54] 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

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Figure 3: Finite element mesh

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. [54]

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 effects 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. Analysis must be executed by well trained user

with good modelling practise. User also should be aware of boundary effects, 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.[55]

Continuum modelling

Modelling of the continuum is suitable for the analysis of

soil slopes, massive intact rock or heavily jointed rock

masses. This approach includes the finite-difference and

inite element methods that discretize the whole mass to

finite number of elements with the help of generated mesh

(Fig. 3). In finite-difference method (FDM) differential

equilibrium equations (i.e. strain-displacement and stress-

strain relations) are solved. finite 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.[55]

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 satisfied. Discontinuum modelling belongs to the most commonly

applied numerical approach to rock slope analysis and following variations of the DEM exist:[55]

distinct-element methoddiscontinuous deformation analysis (DDA)

particle flow codes

The distinct-element approach describes mechanical behaviour of both, the discontinuities and the solidmaterial. 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.[55]

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Discontinuum program UDEC[56] (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. [56]

Three-dimensional discontinuum code 3DEC[57] contains modelling of multiple intersecting

discontinuities and therefore it is suitable for analysis of wedge instabilities or influence of rock support

(e.g. rockbolts, cables).[55]

In discontinuous deformation analysis (DDA) displacements are unknowns and equilibrium equations

are then solved analogous to finite element method. Each unit of finite 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.[55]

Discontinuous rock mass can be modelled with the help of distinct-element methodology in the form of

article flow code, e.g. program PFC2D/3D.[58][59] Spherical particles interact through frictional sliding

contacts. Simulation of joint bounded blocks may be realized through specified bond strengths. Law of

motion is repeatedly applied to each particle and force-displacement law to each contact. Particle flow

methodology enables modelling of granular flow, 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 [55]

Hybrid/coupled modelling

Hybrid codes involve the coupling of various methodologies to maximize their key advantages, e.g. limit

equilibrium analysis combined with finite element groundwater flow and stress analysis adopted in the

SVOFFICE

[60]

or GEO-STUDIO

[61]

suites of software; coupled particle flow and finite-differenceanalyses used in PF3D[59] and FLAC3D.[62] Hybrid techniques allows investigation of piping slope

failures and the influence of high groundwater pressures on the failure of weak rock slope. Coupled

inite-/distinct-element codes, e.g. ELFEN,[63] provide for the modelling of both intact rock behaviour

and the development and behaviour of fractures.[55]

Rock mass classification

Various rock mass classification 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.

See also

Angle of reposeRetaining wallDiscontinuous Deformation AnalysisDiscontinuity layout optimizationDiscrete element methodFinite difference methodFinite element limit analysisFinite element methodStereonet

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-https://en.wikipedia.org/wiki/Stereonet#Geologyhttps://en.wikipedia.org/wiki/Finite_element_methodhttps://en.wikipedia.org/wiki/Finite_element_limit_analysishttps://en.wikipedia.org/wiki/Finite_difference_methodhttps://en.wikipedia.org/wiki/Discrete_element_methodhttps://en.wikipedia.org/wiki/Discontinuity_layout_optimizationhttps://en.wikipedia.org/wiki/Discontinuous_Deformation_Analysishttps://en.wikipedia.org/wiki/Retaining_wallhttps://en.wikipedia.org/wiki/Angle_of_reposehttps://en.wikipedia.org/wiki/Rock_mass_classificationhttps://en.wikipedia.org/wiki/Discrete_element_methodhttps://en.wikipedia.org/wiki/Finite_difference_methodhttps://en.wikipedia.org/wiki/Discrete_element_methodhttps://en.wikipedia.org/wiki/Discontinuous_Deformation_Analysis


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11. USArmyCorps 2003, p. 2

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Systems Ltd.), retrieved 24 July 2010 External link in (help)

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41. "dotSlope for Android", https://play.google.com/store/apps/details?id=com.nebulare.dotSlope (Google PlayStore), retrieved 16 March 2015 External link in (help)

42. "GALENA – Slope Software System", http://www.scisoftware.com (Utah, USA: Scientific Software Group),

retrieved 20 July 2009 External link in (help)

43. "GSLOPE – Limit Equilibrium Slope Stability Analysis for Reinforced Slopes",

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TAGA Engineering Software), retrieved 21 July 2009 External link in (help)

46. "Computer Program AutoBlock for Analyzing the Stability of Foundations and Slopes in Rock based on aDigital Terrain Model", http://www.igt.ethz.ch/www/search/PublicationDisplay.asp?publication=761

(Zurich, Switzerland: ETH), retrieved 2004 External link in (help)


48. Kliche 1999, p. 111

49. Kliche 1999, pp. 111–123

50. Kliche 1999, pp. 43–65

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Canada: Rocscience), retrieved 21 July 2009 External link in (help)

52. Hungr 1988, pp. 685–690

53. Eberhardt 2003, pp. 15–17

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55. Eberhardt 2003, pp. 17–38

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27 July 2009 External link in (help)

57. "3DEC - Three Dimensional Distinct Element Code", http://www.itascacg.com (Minneapolis, USA: Itasca),


58. "PFC2D - Particle Flow Code in Two Dimensions", http://www.itascacg.com (Minneapolis, USA: Itasca),


59. "PFC3D - Particle Flow Code in Three Dimensions", http://www.itascacg.com (Minneapolis, USA: Itasca),


60. "SVOffice - Next generation geotechnical software", http://www.soilvision.com (Saskatoon, Canada:SoilVision Systems Ltd), retrieved 1 August 2009 External link in (help)

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Kliche, Charles A. (1999), Rock Slope Stability, Colorado, USA: Society for Mining, Metallurgy, and

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Vancouver, Canada: Earth and Ocean Sciences, University of British Columbia

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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 and R. Pöttler, ed., Advanced numerical techniques in rock slope stability analysis - Applications

and limitations (PDF), Davos, Switzerland: Verlag Glückauf GmbH, pp. 615–624 Cite uses deprecated

parameter (help)

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 slopestability analysis", Geotechnique (Telford, London, Great Britain) 53 (4): 377–395,

doi:10.1680/geot.2003.53.4.377, ISSN 0016-8505 Cite uses deprecated parameter (help)

Kovári, Kalman; Fritz, P. (1978), Slope Stability with Plane, Wedge and Polygonal Sliding Surfaces , Rio de

Janeiro, Brazil, pp. 103–124 Cite uses deprecated parameter (help)

Yang, Xiao-Li; Li, L.; Yin, J.H. (2004), "Stability analysis of rock slopes with a modified 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 Cite uses deprecated parameter (help)

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 Cite uses deprecated

parameter (help)Hungr, O.; Evans, S.G. (1988), Bonnard, C., ed., Engineering evaluation of fragmental rockfall hazards,

Rotterdam: Balkema, pp. 685–690 Cite uses deprecated parameter (help)

External links

Geotechnical Software(https://www.dmoz.org/Science/Technology/Civil_Engineering/Geotechnical/Software) at DMOZInformation on the methods of limit equilibrium analysis(http://www.finesoftware.eu/help/geo5/en/slope-stability-01/)

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