A rigid finite element method for upper bound limit analysis of soil slopes subjected to pore water pressure

Abstract

An upper bound limit analysis method using rigid finite elements is developed. Rigid finite elements are used to discretize the slope media. Kinematically admissible velocity discontinuities are permitted to occur at all inter element boundaries. The traditional definition of factor of safety is adopted in the present method so that the results from the limit analysis can be directly compared with those from methods of slices. The presence of water can be considered through work terms in the energy work balance equation. To do this effectively, the pore water pressure is considered as an external force, similar to gravity and surface tractions. The proposed method formulates the slope stability problem as a non linear optimization problem with constraints based on the yield criterion, flow rule, boundary conditions, and the energy work balance equation. The optimization problem is solved by a sequential quadratic algorithm.

采用一種結合剛體有限元與極限分析上限法來求解邊坡穩定性問題的新方法。借助剛體有限單元離散計算區域并構造運動許可速度場 ,利用傳統的安全系數作為評價邊坡穩定的定量指標。水對邊坡的影響作用可通過虛功方程表現出來 ,將孔隙水壓力當作外力荷載做功。在滿足屈服條件、流動法則、虛功方程以及相應的邊界條件的基礎上 ,引入非線性數學規劃方法求解最小安全系數