Solutions for one‐dimensional consolidation of unsaturated soil with general boundary conditions subjected to time‐dependent load

Abstract

Based on the governing equations proposed by Fredlund and Hasan, this paper firstly establishes a mathematical model for one-dimensional consolidation of single-layer unsaturated soil with general boundary conditions, arbitrary initial conditions and time-dependent external load. Then the eigenfunction expansion method is used to derive series solutions for excess pore water pressure and excess pore air pressure in time domain directly. It can be inferred that the series solutions in this paper for one-dimensional consolidation of unsaturated soil are more general compared with previous researches, due to the generality of boundary conditions and time-dependent load. They could be degenerated into solutions for one-dimensional consolidation of unsaturated soil in various conditions. Finally, comparisons with results from previous literatures are made to validate the general series solutions in this research. More examples are provided to illustrate the consolidation behaviors of unsaturated soil with different impeded drainages on air and water phases at the boundary, and different types of external load.

Time scales in the primary and secondary compression of soils

“…Before stating the boundary and initial conditions, we first note that the constrained 1D condition allows the displacement and fluid pressures to be uncoupled. This is facilitated by using the elasto-viscoplastic constitutive relation (7) to express 𝜎 ′ v in terms of 𝜀 v in the equilibrium condition, solving for 𝜀 v in terms of 𝑝 1 and 𝑝 2 , and substituting the result into the fluid mass balance conditions. The equivalent strong form then reads: find 𝑝 1 and 𝑝 2 such that for 0 < 𝑧 < 𝐻,…”

“…This theory as well as its variations has dominated the literature in the past several decades. In the context of one-dimensional deformation and flow processes, some major improvements on the theory have been made taking into consideration the effect of partial saturation, [1][2][3][4][5][6][7][8][9][10] time-dependent surface loading, [11][12][13][14][15][16][17] layered soil systems, [18][19][20][21][22][23][24] and simple nonlinearity including plasticity [25][26][27][28] and varying compressibility and permeabilitiy, 23,[29][30][31][32][33] among others. Even though the 1D kinematics have imposed limits on the applicability of these theories, they are still valuable contributions to the literature because they can be represented with closed-form analytical solutions.…”

Consolidation calculation of a foundation partially penetrated by concrete‐cored gravel (CCG) columns

“…The proposed analytical solutions will be promoted if the time-dependent variations of these consolidation-related parameters are involved. 28,29 In addition, the proposed analytical solutions are expected to spread into more circumstances, such as unsaturated soft soils causing varying negative and positive friction along the pile shaft 30,22 and nonlinear constitutive models of subsoils. 31,32 Notation: Basic SI units are given in parentheses…”

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

“…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.…”