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

Abstract

External 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.

Analytical solution for Fredlund–Hasan unsaturated consolidation using mode superposition method

“…The above equation is the general solution of the homogeneous problems Equations ( 11) and (12). The integration constants related to the initial condition are…”

“…1,2 After that, many studies have been carried out to seek the analytical solution and numerical solution of the Fredlund-Hasan model. [10][11][12][13][14][15] The finite difference method (FDM) and the finite element method are generally used to obtain the numerical solution. However, the analytical solution is pursued, and its physical implication is explained in this paper.…”

“…The parametric analyses can be easily made through the analytical solution. In the published literature, the Laplace transform method and the Fourier series method are commonly used to develop for 1D and 2D consolidation, 5,[7][8][9][10][11][12][13][14][15] but solving the matrix differential equations and performing Laplace inversion is an inconvenient procedure. Therefore, a precise solution for unsaturated consolidation must be determined.…”

The role of free‐strain assumption in axisymmetric electro‐osmosis‐enhanced preloading consolidation of unsaturated soil

“…In the last decade, some progress has been made in the axisymmetric consolidation theory of unsaturated soil via vertical wells under external preloading 24–29 . However, most of the above studies have adopted equal strain assumption.…”

“…In the last decade, some progress has been made in the axisymmetric consolidation theory of unsaturated soil via vertical wells under external preloading. [24][25][26][27][28][29] However, most of the above studies have adopted equal strain assumption. The real deformation of the soil is closer to free strain 30,31 when the platform bearing the load at the top of the ground is flexible.…”