Axisymmetric Consolidation in Unsaturated Soil Deposit Subjected to Time-Dependent Loadings

Abstract

This paper presents an analytical solution to predict the axisymmetric consolidation in unsaturated soil deposits subjected to different time-dependent loadings. The mathematical procedure uses the separation of variables and Laplace transformation methods to obtain the final solution. A set of polar governing equations of flow are obtained and presented under the partial differential equations (PDEs), and then the variable separation technique is used to alter the PDEs to ordinary differential equations (ODEs) consisting of distinctive variables. Fourier Bessel and sine series are used to present functions of radial and vertical flows, respectively, and the Laplace transformation is used to obtain a function of time. Four primary time-dependent loading functions, including ramping, asymptotic, sinusoid, and damped sine wave, are mathematically simulated and incorporated into the proposed solutions. This study investigates changes in excess pore-air and pore-water pressures as well as consolidation settlement against the air-to-water permeability ratio and various loading parameters. Moreover, changes in suction and net stress induced by ramped and asymptotic loadings are also presented in the worked examples.