坑中坑条件下基坑有限土体的被动土压力计算

坑中坑在基坑工程实践中普遍存在，使得基坑底部土体成为有限土体，因此，常规的建立在半无限空间土体假定上的朗肯土压力理论对于坑中坑条件下的基坑不再适用。基于极限平衡理论和平面滑裂面假定，考虑土体黏聚力和滑动土体不同的形状，推导了4种情况下被动土压力的计算公式，并给出了滑裂面剪切破坏角的数学表达式。通过算例，计算了不同内坑位置条件下被动土压力的大小和变化趋势。结果表明，滑裂面剪切破坏角是与土体内摩擦角、黏聚力、计算深度、内坑大小及位置有关的变量，内坑的存在将降低围护结构上的被动土压力，且存在一个内坑影响最不利位置，此时的被动土压力值最小。成果为基坑围护设计中被动土压力的计算提供了理论基础。

Calculation of passive earth pressure for finite soil in foundation pit under pit-in-pit condition

Pit-in-pit usually occurs in pit engineering practices, making the soil at the bottom of the foundation pit become a limited soil. Thus, Rankine earth pressure theory based on conventional semi-infinite space is not applicable for calculating the earth pressure acting on retaining structure in case of pit-in-pit. This also makes it difficult to correctly estimate the excavation depth of the foundation pit for design. Based on the limited equilibrium theory and the hypothesis of planar sliding plane, four formulas for calculating passive earth pressure are deduced with cohesion force and different shapes of sliding soil mass taken into account, and corresponding mathematical expressions of shear failure angles are given. By example, the values and variation trends of passive earth pressures for different internal pit positions are calculated. The results show that the angle of shear failure is a variate that are related to the friction angle of soil, the cohesion of soil, the depth, the size and the position of inner pit. The inner pit will lead to decrease of the passive earth pressure acting on retaining structure, and there is a most unfavorable position for inner pit, where the value of passive earth pressure is minimum. This study provides a theoretical basis for the calculation of passive earth pressure in foundation pit design.