A Simple Monte Carlo Method for Locating the Three-dimensional Critical Slip Surface of a Slope

Based on the assumption of the plain-strain problem, various optimization or random search methods have been developed for locating the critical slip surfaces in slope-stability analysis, but none of such methods is applicable to the 3D case. In this paper, a simple Monte Carlo random simulation method is proposed to identify the 3D critical slip surface. Assuming the initial slip to be the lower part of a slip ellipsoid, the 3D critical slip surface is located by means of a minimized 3D safety factor. A column-based 3D slope stability analysis model is used to calculate this factor. In this study, some practical cases of known minimum safety factors and critical slip surfaces in 2D analysis are extended to 3D slope problems to locate the critical slip surfaces. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference in terms of only cross section, but the associated 3D safety factor is definitely higher.

Determination of critical slip surface of fractured rock slopes based on fracture orientation data

The critical slip surface of a fractured rock slope tends to extend along the fractures.Thus,fracture orientation plays a critical role in determining the critical slip surface.Based on fracture orientation data,this paper examines the critical slip surfaces of fractured rock slopes.Given that the surface of a fractured rock slope extends along the fracture surfaces,or the wedges,with each composed of two arbitrary fractures,the critical slip surface is determined via stochastic dynamics.In addition,a fracture frequency method is proposed as a means of analyzing the critical slip surface.According to this method,the critical slip surface slips in whichever direction has the lowest fracture frequency.Based on the stochastic dynamics method and the fracture frequency method,the critical slip surface of the slope is finally determined,that is,the critical slip surface takes the form of a plane passing the slope toe with a dip of 120° and a dip angle of 45°.

Effect of Inclined Tension Crack on Rock Slope Stability by SSR Technique

The tension cracks and joints in rock or soil slopes affect their failure stability.Prediction of rock or soil slope failure is one of the most challenging tasks in the earth sciences.The actual slopes consist of inhomogeneous materials,complex morphology,and erratic joints.Most studies concerning the failure of rock slopes primarily focused on determining Factor of Safety(FoS)and Critical Slip Surface(CSS).In this article,the effect of inclined tension crack on a rock slope failure is studied numerically with Shear Strength Reduction Factor(SRF)method.An inclined Tension Crack(TC)influences the magnitude and location of the rock slope’s Critical Shear Strength Reduction Factor(CSRF).Certainly,inclined cracks are more prone to cause the failure of the slope than the vertical TC.Yet,all tension cracks do not lead to failure of the slope mass.The effect of the crest distance of the tension crack is also investigated.The numerical results do not show any significant change in the magnitude of CSRF unless the tip of the TC is very near to the crest of the slope.ATC is also replaced with a joint,and the results differ from the corresponding TC.These results are discussed regarding shear stress and Critical Slip Surface(CSS).

A Generalized Limit Equilibrium Method for the Solution of Active Earth Pressure on a Retaining Wall

In this paper, a generalized limit equilibrium method of solving the active earth pressure problem behind a retaining wall is proposed.Differing from other limit equilibrium methods, an arbitrary slip surface shape without any assumptions of pre-defined shapes is needed in the current framework, which is verified to find the most probable failure slip surface. Based on the current computational framework, numerical comparisons with experiment, discrete element method and other methods are carried out. In addition, the influences of the inclination of the wall, the soil cohesion, the angle of the internal friction of the soil, the slope inclination of the backfill soil on the critical pressure coefficient of the soil, the point of application of the resultant earth pressure and the shape of the slip surface are also carefully investigated. The results demonstrate that limit equilibrium solution from predefined slip plane assumption, including Coulomb solution, is a special case of current computational framework. It is well illustrated that the current method is feasible to evaluate the characteristics of earth pressure problem.

Back analysis of general slope under earthquake forces using upper bound theorem

Long time monitoring is acquired to obtain the displacement data for displacement-based geotechnical material back analysis, and these data are hard to be measured under some special condition, such as earthquake. For a simple homogeneous slope, the position of a critical failure surface is determined by value of c/tan ~b. Utilizing upper bound theorem of limit analysis, the external work rate and internal energy for normal slope under earthquake forces are given, and the formula for minimum safety factor is derived. On this basis, the equation of slip surface and the surface depth of a given position are solved. In this way, the strength parameter can be analyzed by known slip surface depth. For practical use, the surface depth for a given slope under varying strength parameter is presented. Finally, two examples are given to show its simplicity and effectiveness.

Effects of nonlinear strength parameters on stability of 3D soil slopes

Actual slope stability problems have three-dimensional(3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.

Comparative study of material point method and upper bound limit analysis in slope stability analysis

The upper bound limit analysis(UBLA)is one of the key research directions in geotechnical engineering and is widely used in engineering practice.UBLA assumes that the slip surface with the minimum factor of safety(FSmin)is the critical slip surface,and then applies it to slope stability analysis.However,the hypothesis of UBLA has not been systematically verified,which may be due to the fact that the traditional numerical method is difficult to simulate the large deformation.In this study,in order to systematically verify the assumption of UBLA,material point method(MPM),which is suitable to simulate the large deformation of continuous media,is used to simulate the whole process of the slope failure,including the large-scale transportation and deposition of soil mass after slope failure.And a series of comparative studies are conducted on the stability of cohesive slopes using UBLA and MPM.The proposed study indicated that the slope angle,internal friction angle and cohesion have a remarkable effect on the slip surface of the cohesive slope.Also,for stable slopes,the calculation results of the two are relatively close.However,for unstable slopes,the slider volume determined by the UBLA is much smaller than the slider volume determined by the MPM.In other words,for unstable slopes,the critical slip surface of UBLA is very different from the slip surface when the slope failure occurs,and when the UBLA is applied to the stability analysis of unstable slope,it will lead to extremely unfavorable results.