Slope stability analysis
It is performed to assess the safe design of a human-made or natural slopes (e.g. embankments, road cuts, open-pit mining, excavations, landfills etc.)
[1][2] 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.
[6] 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.
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.).
Also, even for very simple slopes, the results obtained with typical limit equilibrium methods currently in use (Bishop, Spencer, etc.)
[10] Most slope stability analysis computer programs are based on the limit equilibrium concept for a two- or three-dimensional model.
Translational or rotational movement is considered on an assumed or known potential slip surface below the soil or rock mass.
[13] In rock slope engineering, methods may be highly significant to simple block failure along distinct discontinuities.
A wide variety of slope stability software use the limit equilibrium concept with automatic critical slip surface determination.
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.
[17] This allows for a simple static equilibrium calculation, considering only soil weight, along with shear and normal stresses along the failure plane.
The factor of safety is the ratio of the maximum moment from Terzaghi's theory to the estimated moment, The Modified Bishop's method[18] 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 method was developed in the 1930s by Gerhardt Lorimer (Dec 20, 1894-Oct 19, 1961), a student of geotechnical pioneer Karl von Terzaghi.
Analysis requires the detailed evaluation of rock mass structure and the geometry of existing discontinuities contributing to block instability.
[35] Program DIPS allows for visualization structural data using stereonets, determination of the kinematic feasibility of rock mass and statistical analysis of the discontinuity properties.
[32] 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.
[36] Analytical solution method described by Hungr & Evans[37] 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.
[38] 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 behavior, in situ stresses.
Numerical methods used for slope stability analysis can be divided into three main groups: continuum, discontinuum and hybrid modelling.
Rock mass is considered as an aggregation of distinct, interacting blocks subjected to external loads and assumed to undergo motion with time.
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.
[39] Discontinuum program UDEC[41] (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.
[41] Three-dimensional discontinuum code 3DEC[42] 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).
[39] In Discontinuous Deformation Analysis (DDA) displacements are unknowns and equilibrium equations are then solved analogous to finite element method.
Advantage of this methodology is possibility to model large deformations, rigid body movements, coupling or failure states between rock blocks.
[39] Discontinuous rock mass can be modelled with the help of distinct-element methodology in the form of particle flow code, e.g. program PFC2D/3D.
These codes also allow to model subsequent failure processes of rock slope, e.g. simulation of rock[39] 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; coupled particle flow and finite-difference analyses; hydro-mechanically coupled finite element and material point methods for simulating the entire process of rainfall-induced landslides.
