Complex Variable Solution of Interference Effect of Two Nearby Strip Footings on Layered Soil

Abstract

This study provides a solution for determining stress and displacement measurements of layered soil under the interaction of two adjacent strip footings by using conformal transformation methods (CTMs) in complex variable functions. Using the CTM, this research maps each layer of soil to a unit circle and calculates two single-valued analytic functions of each layer based on continuous conditions and boundary conditions to obtain the stress and displacement fields of the entire soil. The results were verified after being compared with the numerical solution of the Analysis Systems (ANSYS) finite-element software. In addition, this research uses two layers (as an example) to analyze influences of clear spacing of the footings and shear modulus of the soil on the interaction of two strip footings, as well as the influence of the center spacing of the footings and shear modulus of the bottom layer on differential settlements. The results indicate that an increase in the clear spacing of the footings and shear modulus of the soil sublayer greatly reduces the interaction between the two footings. Moreover, the differential settlement will increase with the center spacing, but will not vary with a changing shear modulus of the sublayer soil.