Slope Stability And Stabilization Methods Abramson Pdf 115
Gabelo Clancy
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, 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.
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.
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.
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 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. 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.[39]
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 finite 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.[40] 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.[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.[45] Hybrid techniques allows investigation of piping slope failures and the influence of high groundwater pressures on the failure of weak rock slope. Coupled finite-distinct-element codes provide for the modelling of both intact rock behavior and the development and behavior of fractures.
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