Criterion of shear failure along a surface inside soil-mass and its application to progressive failure analysis

This study extended the strength criterion used to determine the failure of a soil structure from a differential expression at a point or an infinitesimal element to an integral expression along a global consecutive slip surface. In addition, a local failure criterion that described the limit equilibrium state of each area of a sliding surface inside a soil mass was established. Accordingly, it was unnecessary to make any assumptions regarding the sliding surface, along which the soil mass reached its equilibrium state. An arbitrary shape could be investigated without any restrictions, as long as its algorithm followed the above theoretical unification. Along the corresponding surface, the integral of the shear stress equal to that of the shear strength was proven to be a sufficient and necessary condition. Based on this sufficient and necessary condition, a safety factor for soil sliding stability was defined. It indicates the mean value of either the shear strength reduction factor or the overloading coefficient alone the surface, both of which make the soil mass above the surface reach the equilibrium state along the surface. This proposed safety factor could be used not only to evaluate the overall state of soil structural stability but also its local failures. In addition, the gradual development of failure process could be analyzed. Two examples were  presented, involving the studies on stepwise formation of slip curves inside a slope and foundation. These demonstrated that the significantly improved method presented in this paper  could effectively be applied to an analysis of the progressive failure process of a geotechnical structure.