Abstract: 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.

Key words: pit-in-pit, finite soils, passive earth pressure, sliding plane, cohesion force