Analytical solution for evaluating the responses of existing pile caused by adjacent tunnel excavation

Tunnel excavation in short distance will change the physical equilibrium stress field of stratum and cause adverse effects on adjacent existing pile. In this paper, a simplified analytical solution is thus proposed to evaluate the existing pile behaviors due to adjacent tunnel excavation. First, tunneling-induced horizontal free field soil movement calculated by a modified Loganathan's formula during shield tunnel excavation is presented. Then, consider that the existing pile is a Euler-Bernoulli beam resting on the Pasternak foundation model. The differential equation of lateral displacement of existing pile is established by combining the coupling condition of soil-pile interaction. Finally, the analytical solution of lateral displacement of the existing pile caused by adjacent tunneling is obtained by finite difference method. The reliability of the analytical solution is validated by comparing with boundary element program, finite element simulation and field measurements. Parametric studies are also preformed to estimate the effects of various factors on an existing pile, including the clearance distance, tunnel depth, tunnel radius, pile diameter and tunneling-induced soil loss rate. A prediction formula for evaluating the maximum lateral displacement of a pile caused by adjacent tunneling was presented, which the deviation rate between predictions and the results of published case reports is less than 10%.