The failure mechanism of slope instability is complex

and the characteristics of sliding surface often show complex forms such as compression shear-tension failure. Based on the finite element strength reduction method

the limit stress field and strain field of slope are obtained. Starting from the limit stress field of three-dimensional slope

and considering tension-shear composite failure

the positioning problem of slope critical sliding surface is transformed into the initial value problem for solving the first-order quasilinear partial differential equation

namely

the Cauchy problem. The tensile failure mode is adopted in the equal tensile stress area at the scarp of the slope

and the shear failure mode of Mohr-Coulomb yield criterion is adopted in the passive sliding area. In this way

the critical slip surface is determined without assuming the geometry of the slip surface and specifying the slip mode automatically. The three-dimensional slope of gently inclined structural plane and steeply inclined structural plane are studied respectively. Not only the geometric characteristics and distribution of the two are described

but also compared with the jointed homogeneous slope. Finally

combined with the physical model test

the failure characteristics of homogeneous slope under uniformly distributed load in ultimate stress state are studied to verify the correctness and reliability of the method.