General analytical solutions for the equal‐strain consolidation of prefabricated vertical drain foundation in unsaturated soils under time‐dependent loading

Abstract

AbstractExternal disturbances were scarcely considered in the consolidation of unsaturated vertical drain foundation, in which the ideally permeable or impermeable boundary conditions were always adopted to investigated the consolidation patterns. In view of this, by taking the flows along the vertical and radial orientations simultaneously, this study proposes the general analytical solutions for the axisymmetric consolidation of prefabricated vertical drain foundations in unsaturated soils which consider drain resistance, smear effect, and time‐dependent loading under the equal‐strain assumption. Through theories related to consolidation in unsaturated soils, the governing equations of air and water phases in the matrix form are proposed. Subsequently, Fourier series expansion, matrix analysis and decoupling method are used to acquire the analytical solutions. The separate expressions of smear coefficient and drain resistance factors, which can represent the potential influence of the external boundaries more obviously, are included in the solutions. Degradation validity method is used to verify the credibility of the current solutions, and the vertical flow is found to promote the consolidation process under external conditions. Finally, the solutions obtained in this paper can provide guidance for more complicated consolidation problems in unsaturated soils.