土力学经典问题的极限分析上、下限解

Limit analysis for the classic problems of soil mechanics

摘要: 边坡稳定极限分析的垂直条分法和斜条分法分别建立于塑性力学下限和上限原理之上。垂直条分法可以推广到各种支挡结构主动土压力领域 ,斜条分法可以推广到地基承载力的领域。由于采用数值方法求解临界滑动模式 ,因此 ,适用于土体形状不规则、分层、具有地下水等复杂情况。分析计算的成果表明 ,这一理论体系在简单条件下 ,可以回归为经典的土压力和地基承载力问题 ,获得精确的闭合解 ;在无法获得纯理论解的情况下 ,能给出与目前采用的各种经验方法基本一致的计算结果。这样 ,土力学中边坡稳定、土压力和地基承载力这三个领域可以在同一理论框架下获得实用的数值分析方法。

Abstract: The methods of slices with vertical and inclined interfaces described in this paper are based on the upper bound and lower bound theorems of plasticity respectively. The method of vertical slices can be extended to the area of active earth pressure, while that of inclined slices can be applied in bearing capacity analysis. The numerical approaches included in this method for finding the critical failure modes allows the method to be applied to problems with complicated geometry, layered cross section and ground water conditions.