Analytical solution of passive resultant force acting on retaining structure in case of an inner pit

摘要

In the past few years, pit-in-pit excavations have become common to maximize urban underground space. Estimating passive earth pressure is a critical prerequisite to using them. However, Rankine and Coulomb's theory, based on the semi-infinite space assumption, is not suitable for a foundation pit with inner pits. In this study, four cases are identified according to the relative positions of inner pits, and corresponding formulas, based on limit equilibrium analysis, are proposed to calculate the passive resultant force. The analytical expressions of the passive resultant force and the shear failure angle in each case are correspondingly derived. This method is verified with the finite element method (FEM) by comparing the horizontal passive earth pressure and failure surfaces. A few parameters, including the size of the inner pit, the distance between retaining structure and inner pit, the cohesion of soil, and soil-structure interface friction angle, have an effect on the passive resultant force, which is shown by a parametric study. There is one most unfavorable position for an inner pit where the passive resultant force reaches its minimum. This research is intended to provide a theoretical basis for the bracing design of a foundation pit with an inner pit.