Determination of Passive Earth Pressure on a Cantilever Retaining Wall in a Narrow Foundation Pit Based on Logarithmic Spiral Sliding Surface

Abstract

The distribution of passive earth pressure on a cantilever flexible retaining wall in a narrow foundation pit is significantly affected by the adjacent retaining wall and the width of the foundation pit. The deformation mode of the cantilever retaining wall rotating around the displacement zero point makes the soil layer below the displacement zero point retain a nonlimit passive state. The functional relationship between soil mechanical parameters and horizontal displacement in the nonlimit state region, considering the influence of displacement, is established. A new combined failure mode of the soil mass in the passive zone of the narrow foundation pit is proposed, which is the logarithmic spiral fracture surface in the nonlimit state region and the broken line fracture surface in the limit-state region. On this basis, a passive earth pressure calculation model of a narrow foundation pit is proposed and solved by differential layer method. The solution of the passive earth pressure coefficient strictly meets the static equilibrium conditions in vertical and horizontal directions as well as the moment equilibrium conditions. A numerical example is used to analyze the influence of the width of the foundation pit. The smaller the narrow foundation pit width, the greater the passive earth pressure in the lower soil layer and it even greatly exceeds the Coulomb earth pressure distribution. The earth pressure distribution acting on the lower part of the wall near the zero point of displacement decreases sharply and bends. The passive earth pressure distribution is calculated by the theoretical method and compared with the laboratory model test results as well as the engineering test results. It is found that the proper selection of the initial soil mechanical parameters affects significantly the magnitude and distribution of lateral pressure in the nonlimit state region. When the internal friction angle of soil φ0 is small, the lateral pressure in the lower nonlimit state area is relatively small. When both φ0 and δ0 are small, the pressure distribution is closer to the test results and the existing theoretical calculation results.