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

## Authors

• ### Wan-Huan Zhou,

Corresponding author
1. Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau, Macau, China
• Correspondence to: Zhou Wan-Huan, Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau, Macau, China.

E-mail: hannahzhou@umac.mo

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• ### Lin-Shuang Zhao,

1. Department of Civil and Environmental Engineering, University of Macau, Macau, China
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• ### Xi-Bin Li

1. Department of Civil Engineering, Zhejiang Agriculture and Forestry University, Hangzhou, China
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## 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.