1. Limit equilibrium Method (LEM) Advantage of LEM Limitation of LEM
STABILITY ANALYSIS OF SLOPE
Limit equilibrium Method (LEM)
Advantage of LEM
Limitation of LEM
Numerical modeling
Advantage
Limitation
limit equilibrium methods still remain the most commonly adopted solution method in rock slope engineering, even though most failures involve complex internal deformation and fracturing which bears little resemblance to the 2-D rigid block assumptions required by most limit equilibrium back-analyses.
Both the stress and the displacements can be calculated,
Different constitutive relations can be employed.
No assumption needs to be made in advance about the shape or location of the failure surface. Failure occurs `naturally' through the zones within the soil mass in which the soil shear strength is unable to sustain the applied shear stresses.
(b) Since there is no concept of slices in the Numerical approach, there is no need for assumptions about slice side forces. The Numerical method preserves global equilibrium until `failure' is reached.
(c) If realistic soil compressibility data are available, the Numerical solutions will give information about deformations at working stress levels.
(d) The Numerical method is able to monitor progressive failure up to and including overall shear failure.

2. Software based on Limit equilibrium Method
SLIDE (rocscience group)
GALENA
GEO-SLOPE
GEO5
GGU
SOILVISION

3. Software based on Numerical modeling
PHASES2
PLAXIS
FLAC-SLOPE / UDEC / PPF
ANSYS
FEFLOW
GEOSLOPE/SIGMA
SOIL-VISION

4. Required input properties
Young modulus
Poisson ratio
Density
Failure criterion:
M-C H-B
Cohesion UCS
Friction angle m & s 4

5. Type of failure mechanism
Numerical modeling
Type of failure mechanism
Physico-mechanical behaviour of slope material
Types of analysis
Types of analysis: long or Short term analysis, static or dynamic analysis
Joint analysis, water pressure analysis, fault or bedding plane, analysis jointed rock mass,

6. • Discontinuum modelling DEM, UDEC • Hybrid modelling
Numerical modeling
• Continuum modelling
FEM, BEM and FDM
• Discontinuum modelling
DEM, UDEC
• Hybrid modelling
PPF,

7. What are the conditions of slope in the field
Simple slope with single, two or three joints
Large number of joint sets present in the slope
Heavily jointed rock slope
Waste dump / very weak rock / soil
When simulating the mathematical model of slope that represent the nearly actual/real behaviour of the slope in the field. That requires the precise behavior of slope material i.e. constitute equations (stress- strain relationship)

8. Simple slope with single, two or three joints
large number of joint sets present in the slope
Heavily jointed rock
Waste dump / very weak rock / soil
Properties of each Joints strength
Properties of each joint set or combined properties
Properties of jointed rock mass
Properties of waste rock
When simulating the mathematical model of slope that represent the nearly actual/real behaviour of the slope in the field. That requires the precise behavior of slope material i.e. constitute equations (stress- strain relationship)

9. Continuum modelling
Continuum modeling is best suited for the analysis of slopes that are comprised of massive, intact rock, weak rocks, and soil-like or heavily jointed rock masses. Discontinuum modeling is appropriate for slopes controlled by discontinuity behaviour.
Critical Parameters: shear strength of material, constitutive criteria, water condition, insitu stress state
Advantages: Allows for material deformation and failure, model complex behaviour, pore pressures, creep deformation and/or dynamic loading can be simulated
Limitations: inability to model effects of highly jointed rock
Continuum methods are best suited for the analysis of rock slopes that are comprised of massive
intact rock, weak rocks, or heavily fractured rock masses. For the most part, earlier studies were
often limited to elastic analyses and as such were limited in their application. Most continuum
codes, however, now incorporate a facility for including discrete fractures such as faults and
bedding planes. Numerous commercial codes are available, which often offer a variety of
constitutive models including elasticity, elasto-plasticity, strain-softening and elastoviscoplasticity
(allowing for the modelling of time-dependent behaviour).

10. Continuum modelling • Typical Input required Moduls of Elasticity
Poision ratio
Density
Shear strength
(cohesion and friction angle)
Model Behavior

11. Continuum modelling

12. 12

13. Typical Input required
Moduls of Elasticity for rock and joints
Poision ratio for rock and joints
Density
Shear strength for rock and joints
Joint behaviour
Water pressure

14. • Continuum modelling (water simulation)
Pore water pressure
Ground water table
Infiltration of rain water 14

15. 15

20. Mohr-Coulomb model; The Mohr-Coulomb model is the conventional model used to represent shear
failure in soils and rocks. Vermeer and deBorst (1984), for example, report
laboratory test results for sand and concrete that match well with the Mohr-
Coulomb criterion.
ubiquitous-joint model; The ubiquitous-joint model is an anisotropic plasticity model that includes
weak planes of specific orientation embedded in a Mohr-Coulomb solid.
strain-hardening / softening model;
The strain-hardening/softening model allows representation of non-linear material
softening and hardening behavior based on prescribed variations of the
Mohr-Coulomb model properties (cohesion, friction, dilation, tensile strength)
as functions of the deviatoric plastic strain.
double-yield model; The doube-yield model is intended to represent materials in which there may
be significant irreversible compaction in addition to shear yielding, such as
hydraulically-placed backfill or lightly-cemented granular material.

21. Mohr-Coulomb model; The Mohr-Coulomb model is the conventional model used to represent shear
failure in soils and rocks. Vermeer and deBorst (1984), for example, report
laboratory test results for sand and concrete that match well with the Mohr-
Coulomb criterion.
ubiquitous-joint model; The ubiquitous-joint model is an anisotropic plasticity model that includes
weak planes of specific orientation embedded in a Mohr-Coulomb solid.
strain-hardening / softening model;
The strain-hardening/softening model allows representation of non-linear material
softening and hardening behavior based on prescribed variations of the
Mohr-Coulomb model properties (cohesion, friction, dilation, tensile strength)
as functions of the deviatoric plastic strain.
double-yield model; The double-yield model is intended to represent materials in which there may
be significant irreversible compaction in addition to shear yielding, such as
hydraulically-placed backfill or lightly-cemented granular material. 21

22. 22

23. 23

24. Discontinuum modelling
Discontinuum modeling is appropriate for slopes controlled by discontinuity behaviour
Critical Parameters: discontinuity stiffness and shear strength; groundwater characteristics; in situ stress state.
Advantages: Allows for block deformation and movement of blocks relative to each other, can modeled with combined material and discontinuity behaviour coupled with hydro - mechanical and dynamic analysis
Limitations: need to simulate representative discontinuity geometry (spacing, persistence, etc.); limited data on joint properties available
Although 2-D and 3-D continuum codes are extremely useful in characterizin g rock slope failure
mechanisms it is important to recognize their limitations, especially with regards to whether they
are representative of the rock mass under consideration. Where a rock slope comprises multiple
joint sets, which control the mechanism of failure, then a discontinuum modelling approach may
be considered more appropriate. Discontinuum methods treat the problem domain as an
assemblage of distinct, interacting bodies or blocks that are subjected to external loads and are
expected to undergo significant motion with time. This methodology is collectively referred to as
the discrete-element method (DEM).
The development of discrete-element procedures represents an important step in the modelling
and understanding of the mechanical behaviour of jointed rock masses. Although continuum
codes can be modified to accommodate discontinuities, this procedure is often difficult and time
consuming. In addition, any modelled inelastic displacements are further limited to elastic orders
of magnitude by the analytical principles exploited in developing the solution procedures. In
contrast, discontinuum analysis permits sliding along and opening/closure between blocks or
particles. The underlying basis of the discrete-element method is that the dynamic equation of
equilibrium for each block in the system is formulated and repeatedly solved until the boundary
conditions and laws of contact and motion are satisfied (Fig. 17). The method thus accounts for
complex non-linear interaction phenomena between blocks.

25. Discontinuum modelling
The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope

26. Discontinuum modelling
The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope

27. The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope

28. The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope

29. The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope

30. joint normal stiffness joint shear stiffness
The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope
cohesion joint
dilation joint
friction joint
joint normal stiffness
joint shear stiffness

31. Critical Parameters: Combination of input parameters
Hybrid modelling
Hybrid codes involve the coupling of these two techniques (i.e. continuum and discontinuum) to maximize their key advantages.
Critical Parameters: Combination of input parameters
Advantages: Coupled finite-/distinctelement models able to simulate intact fracture propagation and fragmentation of jointed and bedded rock.
Limitations: high memory capacity;
The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope

32. The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope

33. The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope 33

34. The dip of the slope must exceed the dip of the potential slide plane
The potential slip plane must daylight on the slope plane
The dip of the potential slip plane must be such that the strength of the plane is reached
The dip direction of the sliding plane should lie approximately ±20° of the dip direction of the slope

35. Important considerations

36. Two-dimensional analysis versus three-dimensional analysis
2D Simulation by Geoslope software based on Finite element method
3D Simulation by Ansys software based on Finite element method

37. Continuum versus discontinum models
2D simulation of bench slope by FLAC based on finite difference method
3D simulation of slope 3DEC software based on discontinum modeling

38. Selecting appropriate zone size
Different view discritized view of internal dump slope

39. Boundary conditions
Typical recommendations for locations of artificial far-field boundaries in slope stability analyses.

40. Water pressure
Simulation of rain water infiltration and generation of water table

41. Excavation sequence
Show the sequential excavation

42. Stability / failure indicators
Factor of safety
Displacement ( x and Y)
Shear Strain
Yield Points
Plastic Points
unbalance force/ convergence of solution
Velocity
2.7.2 Unbalanced Force
A grid point in a model is surrounded by up to eight zones that contribute forces to the grid point. At equilibrium, the algebraic sum of these forces is almost zero (i.e., the forces acting on one side of the grid point nearly balance those acting on the other). Unbalanced force approaching a constant non-zero value indicates elastic equilibrium and /or plastic flow occurring within the model. Only very low value of unbalanced forces indicates that force balance at all grid points; however, steady plastic flow may occur, without acceleration. In order to distinguish between these two conditions and “true” equilibrium, other indicators such as those described below should be examined.
2.7.3 Grid point Velocities
The grid velocities may be assessed either by plotting out the whole field of velocities or by selecting certain key points in the grid and tracking their velocities with histories. Steady-state conditions are indicated, if the velocity histories show horizontal traces in their final stages. If they have all converged to “near zero” (in comparison to their starting values), then absolute equilibrium has occurred. If a history has converged to a “non-zero” value, then steady plastic flow occurs at the grid point corresponding to the recorded history. If one or more velocity history plots show fluctuating velocities, then the system is likely to be in a transient condition. To confirm that continuing plastic flow is occurring, a plot of plasticity should be examined. When the model is stable, the gridpoint velocities decrease to zero and the velocity vectors often appear random in direction. However, for unstable model, the gridpoint velocities have converged to a non-zero value; it is likely that steady plastic flow is occurring in the model. In this case, the velocity vectors show some systematic orientation.
2.7.4 Plastic Indicators
For the plasticity models, the FLAC code can display those zones in which the stresses satisfy the yield criterion. Such an indication usually denotes that plastic flow is occurring, but it is possible for an element to simply “sit” on the yield surface without any significant flow taking place. It is important to look at the whole pattern of plasticity indicators to see if a “failure mechanism” has developed. Two types of failure mechanisms are indicated by the plasticity state; shear failure and tensile failure.
2.7.5 Displacement
The system can also be unstable, meaning that it is heading for ultimate failure or collapse. In addition to the above criterion for steady plastic flow, an unstable model is usually characterized by a non-zero, often fluctuating, maximum unbalanced force, as well as increasing velocities and displacements. The model can also collapse due to displacements becoming very large, thus distorting the individual elements badly and prohibiting further timestepping
2.7.6 Failure Surface
Once unstable or steady plastic flow has been identified, the question of failure surface formation needs to be answered. The location of a failure surface can be judged by plasticity indicators, displacement field and localization of shear strain. The extent of the zone of actively yielding elements forms the outer limit as to where the failure surface can develop. By looking at the displacement pattern in the model, a more precise estimate can be made. 42

43. Stability / failure indicators Factor of safety
To perform slope stability analysis with the shear strength technique, simulations are run for a series of increasing trial factor of safety, F, actual shear strength properties cohesion (c) and internal friction angle ( ) are reduced for each trial according to the equations 2.1 and 2.2. If the multiple materials are present, the reduction is made simultaneously for all materials. The trial factor of safety is gradually increased until the slope fails. At failure, the safety factor equals the trial safety factor. The factor of safety is defined according to the equation 43

44. Stability / failure indicators Displacement ( x and Y)44

45. Stability / failure indicators Shear Strain45

46. Stability / failure indicators Yield Points46

47. Stability / failure indicators Velocity Vector47

48. Stability / failure indicators
unbalance force/ convergence of solution 48