预留土支护基坑旋转破坏模式下的极限抗力上限解

对于支撑式或锚拉式支挡结构，进行预留土辅助支护时需验算绕支点的抗倾覆稳定性，然而目前还未找到合理的计算方法。基于极限分析上限定理，提出预留土支护基坑的3种可能破坏模式，运用斜条分法对被动区土体进行离散，并构建相容速度场，分别推导3种破坏模式下基坑抗倾覆力矩的计算表达式，采用遗传算法编程，分析支挡结构与土体间摩擦系数、土体黏聚力及预留土几何参数等对破裂角及抗倾覆力矩的影响规律。结果表明：当墙背光滑且土体黏聚力为零时，利用朗肯被动土压力理论计算得到的抗倾覆力矩为一上限解；存在黏聚力时，朗肯被动土压力理论计算值偏于保守，存在摩擦系数时，库伦土压力理论计算的抗倾覆力矩偏大；与预留土宽度和坡度相比，预留土高度对抗倾覆力矩的影响更加显著。

Upper bound solution of ultimate resistance of berm-retained excavations under rotating failure mode

For strutted or anchored retaining structures, the anti-overturning stability around the fulcrum needs to be checked for the berm-retained excavations. However, a reasonable calculation method has not yet been found. Based on the upper limit theorem of limit analysis, three possible failure modes of the berm-retained excavations were proposed, the slice method with inclined interfaces was used to separate the passive soil area, and a compatible velocity field was constructed. The expressions for calculating the anti-overturning moment of foundation pit under three failure modes were derived respectively. Through the calculation example, the effects of friction coefficient between retaining structure and soil, soil cohesive force and the berm-retained geometric parameters on the rupture angle and anti-overturning moment were analyzed by using genetic algorithm. The results show that when the wall is smooth and the soil cohesion is zero, the anti-overturning moment calculated by Rankine''s passive earth pressure theory is an upper bound solution. When cohesive force exists, the theoretical value of Rankine''s passive earth pressure theory is conservative, when friction coefficient exists, the anti-overturning moment calculated by coulomb earth pressure theory is too large. In addition, the berm-retained height has a more significant influence on the anti-overturning moment than the berm-retained width and slope.