关键词: 矢量和法, 有限元法, 边界元法, 解析解, 极限平衡法, 安全系数

Abstract:

The vector sum method (VSM) has clear physical and mechanical definition, simple calculation and gives reasonable assessment of whole stability according to slope stress distribution; and the stress distribution are usually obtained by finite element method (FEM). The boundary element method (BEM) has gotten extensive application to engineering because of reduced order, discretization error only on the boundary and low computational complexity. For plane problem, using the source point serving as origin, the tangent and normal direction of integral element to establish local coordinate system, analytical solutions are obtained for all integrals of linear element. Therefore, analytical solutions for the variables in the region calculated can be acquired; and it guarantees the accuracy and continuity of the variables of region near the border. Using the stress distribution of two-dimensional slope obtained by BEM, together with VSM, the slope stability can be analyzed; the results obtained are compared and analyzed with the VSM based on FEM and the limit equilibrium method (LEM). The results of circle and fold line slip surface slopes show that the vector sum safety factor based on BEM is very close to the VSM based on FEM and LEM; the vector sum factor of safety based on BEM is not sensitive to boundary element size.

Key words: vector sum method, finite element method, boundary element method, analytical solutions, limit equilibrium method, safety factor