Analytical solution to interaction between passive piles and soils

In order to analyze mechanical mechanism of passive pile-soil interaction in slope, based on the Winkler elastic model which assumes that soil displacement is elastic, a fourth-order differential equation considering passive pile-soil interaction is presented to describe the stabilizing pile subjected to an arbitrary profile of residual thrust, and the analytical solution is derived. The procedure is programmed with Matlab code. Meantime, the computed values are in good agreement with the in field monitoring data, which means that the suggested analytical solutions are reliable. Finally, the model is conducted in a case history of Shenzhen to verify the proposed analytical solution. The analysis is carried out to investigate the effects of subgrade modulus and distribution function of residual thrust on behavior of passive piles embedded in slope considering the interaction between passive piles and soils. The results show that the triangular distribution forms of residual trust will have the largest moment of passive piles, followed by a parabola, uniform distribution of the smallest. The relatively large gap can be up to 47%. Under the same level of subgrade modulus conditions, the uniform distribution of residual trust has large displacement of passive piles at the top around the piles than that of triangle and parabola distribution. The approach can provide theoretical helpful for calculating internal forces and displacements of stabilizing piles.