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Slope stability analysis - Wikipedia. Figure 1: Rotational failure of slope on circular slip surface. Slope stability analysis is performed to assess the safe design of a human- made or natural slopes (e. 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. Today engineers have a lot of possibilities to use analysis software, ranges from simple limit equilibrium techniques through to computational limit analysis approaches (e. Finite element limit analysis, Discontinuity layout optimization) to complex and sophisticated numerical solutions (finite- /distinct- element codes). 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. 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). Current structural design, construction support, inspection and maintenance engineering of all State highway structures. Links to motor vehicle and road information. Improve your climbing technique. Read our expert advice from the climbers at Rock & Ice Magazine. Improve your climbing skills. Click on column titles to sort table in ascending order. Click a second time to order table in descending order. Click on Number to view more information. Small movements of a rough wall can be detected with sub- millimeter accuracy by using interferometry techniques. Limit equilibrium analysis. 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. Transitional or rotational movement is considered on an assumed or known potential slip surface below the soil or rock mass. 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. 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. In this approach, the soil mass is discretized into vertical slices. These variations can produce different results (factor of safety) because of different assumptions and inter- slice boundary conditions. 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. Analytical techniques: Method of slices. 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. 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 caused by forces resisting slope failure. If resisting forces are greater than driving forces, the slope is assumed stable. Ordinary Method 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. 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 (Er,El. The block is assumed to have thickness b. The slices on the left and right exert normal forces El,Er. These forces are balanced by the pore pressure and reactions of the base N,T. Solving for N. A balance of moments for all the slices taken together gives. The moment equation can be used to solve for the shear forces at the interface after substituting the expression for the normal force. The factor of safety is the ratio of the maximum moment from Terzaghi's theory to the estimated moment,Factor of safety=. 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 . An iterative method has to be used to solve for F. 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 1. Gerhardt Lorimer (Dec 2. Oct 1. 9, 1. 96. 1), a student of geotechnical pioneer Karl von Terzaghi. Spencer’s Method. It is not as accurate as the Modified Bishop’s method, but is acceptably accurate in engineering practices. 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. There are no interslice shear forces. Janbu's simplified. An empirical correction factor is used to account for interslice shear forces. Janbu's generalized. The fractions of the function value needed for force and moment balance is computed. Fredlund- Krahn (GLE) . The inclinations of the slice interfaces are varied until a critical criterion is met. The table below shows the statical equilibrium conditions satisfied by some of the popular limit equilibrium methods. 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 Carlo or Latin Hypercube simulation techniques where any input parameter can be defined as a random variable. Probabilistic analysis determine the probability of failure and reliability index, which gives better representation of the level of safety. Back analysis serves for calculation of a reinforcement load with a given required factor of safety. Program enables finite element groundwater seepage analysis. 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. Then a local stability factor for each slice is obtained. Using a Monte Carlo approach, program computes the probability of failure in addition to the conventional factor of safety. 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. The values of the pore pressure in transport domain are imported automatically for the selected time to Stability module. The analysis 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. 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. The software also utilizes Monte Carlo, Latin Hypercube, and the APEM probabilistic approaches. Spatial variability through random fields computations may also be included in the analysis. Slope. The slope can have multiple soils, impenetrable layers, cuts and embankments, multiple groundwater conditions, ponded water, dry and water filled tension cracks, soil reinforcements (anchors, nails, piles and geo- synthetics). Slip surfaces can be defined through six surface generators in order to find the critical case. The program runs on Microsoft Windows, Mac OS X and Android. Problem configurations can involve rotational or non- rotational sliding surfaces, ellipsoids, wedges, compound surfaces, fully specified surfaces and searches. It allows importing arbitrarily complex terrain surfaces which have been digitized beforehand using a topographic map. These surfaces are then extruded to a 3. D solid which 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 safety against sliding is computed using the limit equilibrium method. |
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