A method of three-dimensional limited slope stability analysis is presented here based on the upperbound theorem of the limit analysis approach.A rotating collapse mechanism is considered in which energy dissipation takes place along curve velocity discontinuities.In the frictional soils,the failure surface has the shape of logarithm helicoids,with track outline defined by log-spirals.In the cohesive soils,the shape of the failure surface is torus.Angle is considered at slope top,and the critical height is less than top with no inclination.Numerical results of the proposed algorithm are presented in the form of nondimensional graphs.Some examples illustrate the practical use of the results.
A method of three-dimensional loaded slope stability for anisotropic and nonhomogeneous slopes was presented based on the upper-bound theorem of the limit analysis approach. The approach can be considered as a modification and extension of the solutions. The influences of friction angle, anisotropy factor, nonhomogeneous factor, slope angle, ratio of width to depth, and load on the slope crest were investigated. The results show that solutions are suitable to deal with the purely cohesive soils and frictional/cohesive soils, isotropic and anisotropic, homogeneous and nonhomogeneous, loaded and unloaded cases.
