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.

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).

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.