A Lateral-Response Analyzed Model for Piles in Sloping Ground Considering Vertical Resistance Based on Transfer Matrix Method

In order to analyze the lateral response of piles subjected to combinational loads located at sloping ground, a simplified physical model is proposed and developed based on the Timoshenko beam theory and tri-parameter elastic foundation beam model. In this model, the effects of vertical resistance, shear deformation and initial inclination of pile shafts are taken into account, and the semi-analytical solution to the lateral behavior of pile is obtained by utilizing the transfer matrix approach. Specifically, the relative transfer matrix coefficients in the free, passive, and active segment of the pile are analytically determined through Laplace transformation. In addition, the validation of this model is conducted by comparing with field observations and predictions obtained from other existing methods. Moreover, the influences of initial inclination angle, vertical resistance in passive segments and the vertical load on the lateral response of the pile are also discussed in depth. The results indicate that, although there is a significant reduction effect emerged in both the lateral displacement and bending moment with the increase in the vertical resistance, a growth trend for those responses can be obtained with an increase in the initial inclination angle and vertical load.