Three-dimensional limit equilibrium solution to generalized-shaped slope stability

On the basis of the modification of normal stresses on 3D slip surface,a new 3D limit equilibrium method was presented for generalized-shaped slopes.The normal stress distribution over the 3D slip surface was initially assumed,then it was modified by a function with 3 parameters to satisfy three force equilibrium conditions and one moment equilibrium condition about the axis perpendicular to the sliding direction.A cubic algebric equation was derived that would yield an explicit solution to 3D factor of safety.The present method made a feature of simple principle free of assumptions regarding inter-column forces and direct computation of 3D factor of safety without iteration and nonconvergence.The computated results were reliable since 4 equilibrium conditions were satisfied.The method was applicable to asymmetric slopes with arbitrary shapes,thus could be applied in wide fields of slope engineering.The effectiveness and practicability of the present method were shown by the results of example and case history studies.