Analytical solution for stress and displacement of a finite thickness soil layer subjected to strip footing

Consider an elastic soil layer with a shallow-buried strip footing at the upper boundary and bedrock at the lower boundary, the displacement along the contact surface between the soil layer and the bedrock can be considered as zero when the bedrock is sufficiently rigid relative to the soil layer. The stress and displacement fields in the soil layer are solved on the premise that the displacement on the contact surface between the soil layer and the strip footing is given. The soil layer with the finite thickness on the physical plane is mapped onto the inner domain of the unit circle on the image plane based on the conformal transformation. Then, the complex variable method is applied to give the stress and displacement fields in the soil layer by two analytic functions, the coefficients of which can be determined by the stress and displacement boundary conditions on the upper and lower boundaries of the soil layer. In calculation, the power series method is introduced to establish a set of linear equations containing the analytic function coefficients, and then the coefficients are determined by solving the linear equations. This paper presents the analytical solutions of stress and displacement in the soil layer under two different displacement boundary conditions on the contact surface between the soil layer and the footing. The obtained results are compared with the results of the numerical method based on ANSYS. Finally, the influence of different displacement boundary conditions and soil thickness on the stresses on the surface and internal region of the soil layer is analyzed. (c) 2022 Elsevier Inc.

Automated summary

This paper investigates the stress and displacement in an elastic soil layer with a shallow-buried strip footing. The analytical solutions for stress and displacement in the soil layer are obtained using conformal transformation and complex variable method, and compared with numerical results. The influence of different displacement boundary conditions and soil thickness on the stresses in the soil layer is also analyzed.