Nonlinear Analysis of Slope Stability Considering Geomaterial Dilatancy

Shear dilation occurs during the failure of geomaterials subjected to shear stress. To account for the dilatancy and nonlinearity of geomaterials, a nonlinear upper-bound analysis method was proposed for evaluating the stability of homogeneous slopes based on the coaxial nonassociated flow rule. The rotational failure mechanism of a homogeneous slope was established within the kinematic approach of limit analysis, using the Davis approach to convert the nonassociated flow rule into an associated one. By applying the variation principle, ordinary differential equations of the potential sliding surface and its corresponding stress were derived, which were then solved using a fourth-order Runge–Kutta method in conjunction with appropriate boundary conditions. Furthermore, the balance equation was derived from the virtual power principle, and the critical height of the slope was calculated using a particle swarm optimization algorithm. The strength reduction technique was then introduced to determine the factor of safety of the slope. The accuracy and effectiveness of the proposed nonlinear upper-bound variation method for evaluating the stability of homogeneous slopes under nonassociated flow rule and nonlinear failure criteria were verified when compared with existing studies and techniques, such as the finite-element limit analysis and the finite difference method. This study accurately reflects the nonlinearity and dilatancy of geomaterials and avoids assumptions regarding the sliding surface and its corresponding stress, making it a valuable reference for future research.