A simple analytical solution to one-dimensional consolidation for unsaturated soils

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 38; no. 8; pp. 794 - 810
• Main Authors: Zhou, Wan-Huan, Zhao, Lin-Shuang, Li, Xi-Bin
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 10.06.2014; Wiley; Wiley Subscription Services, Inc
• Subjects: analytical solution; Applied sciences; boundary condition; Buildings. Public works; Computation methods. Tables. Charts; Consolidation; Drainage; Exact sciences and technology; Geotechnics; initial condition; Mathematical analysis; Mathematical models; one-dimensional consolidation; Porosity; ramp loading; Soil mechanics. Rocks mechanics; Soils; Structural analysis. Stresses; Tables; Unsaturated; unsaturated soil; ramp loading; Initial condition; one-dimensional consolidation; One dimensional model; Analytical method; analytical solution; Soil consolidation; Boundary condition; Mathematical model; Unsaturated soil; Modeling; Soil mechanics
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2231

SUMMARY This paper presents a simple analytical solution to Fredlund and Hasan's one‐dimensional (1‐D) consolidation theory for unsaturated soils. The coefficients of permeability and volume change for unsaturated soils are assumed to remain constant throughout the consolidation process. The mathematical expression of the present solution is much simpler compared with the previous available solutions in the literature. Two new variables are introduced to transform the two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved with standard mathematical formulas. It is shown that the present analytical solution can be degenerated into that of Terzaghi consolidation for fully saturated condition. The analytical solutions to 1‐D consolidation of an unsaturated soil subjected to instantaneous loading, ramp loading, and exponential loading, for different drainage conditions and initial pore pressure conditions, are summarized in tables for ease of use by practical engineers. In the case studies, the analytical results show good agreement with the available analytical solution in the literature. The consolidation behaviors of unsaturated soils are investigated. The average degree of consolidation at different loading patterns and drainage conditions is presented. The pore‐water pressure isochrones for two different drainage conditions and three initial pore pressure distributions are presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.