Slope Stability Analysis Software Free Download
Amice Golden
Slope stability analysis is a static or dynamic, analytical or empirical method to evaluate the stability of slopes of soil- and rock-fill dams, embankments, excavated slopes, and natural slopes in soil and rock. 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.) and the equilibrium conditions.[1][2] Slope stability is the resistance of inclined surface to failure by sliding or collapsing.[3] The main objectives of slope stability analysis are finding endangered areas, investigation of potential failure mechanisms, determination of the slope sensitivity to different triggering mechanisms, designing of optimal slopes with regard to safety, reliability and economics, and designing possible remedial measures, e.g. barriers and stabilization.[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.[4][5] The presence of water has a detrimental effect 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.[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.[7]
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 (finite-/distinct-element codes).[1] 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 differ 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).[8][9]
Conventional methods of slope stability analysis can be divided into three groups: kinematic analysis, limit equilibrium analysis, and rock fall simulators.[10]Most slope stability analysis computer programs are based on the limit equilibrium concept for a two- or three-dimensional model.[11][12] 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 influence of gravity. 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.[10] 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.[13] The most commonly used variation is Terzaghi's theory of shear strength which states that
The methods of slices is the most popular limit equilibrium technique. In this approach, the soil mass is discretized into vertical slices.[12][14] 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.[13][15]
The location of the interface is typically unknown but can be found using numerical optimization methods.[16] 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.
Many slope stability analysis tools use various versions of the methods of slices such as Bishop simplified, 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 simplified or Fellenius are non-rigorous methods satisfying only some of the equilibrium conditions and making some simplifying assumptions.[14][15] Some of these approaches are discussed below.
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.[17]
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 ( E r , E l \displaystyle E_r,E_l ) and shear ( S r , S l \displaystyle S_r,S_l ) forces between adjacent slices constrain each slice and make the problem statically indeterminate when they are included in the computation.
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
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 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.
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 of analysis[19] requires a computer program capable of cyclic algorithms, but makes slope stability analysis easier. Spencer's algorithm satisfies 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.[19]
The Sarma method,[20] 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.
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.
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