Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with symmetric semi-permeable drainage boundary |
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| Institution: | 1. College of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China;2. Department of Civil Engineering, Shanghai University, Shanghai 200444, China;3. College of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China;4. Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;1. Key Laboratory of Geomechanics and Embankment Engineering of the Ministry of Education, Geotechnical Research Institute, Hohai University, 1 Xikang Road, Nanjing 210098, China;2. Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China;1. Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau, Macau, China;2. UMacau Research Institute, Zhuhai, Guangdong, China;3. Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, College of Civil Engineering and Architecture, Guangxi University, Nanning, China;1. Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University, Changsha 410082, China;2. Institute of Geotechnical Engineering, Hunan University, Changsha 410082, China |
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| Abstract: | This paper presents semi-analytical solutions to Fredlund and Hasan’s one-dimensional consolidation for unsaturated soils under symmetric semi-permeable drainage boundary conditions. Two variables are introduced to transform two coupled governing equations of pore-air and pore-water pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. Then, the pore-air and pore-water pressures, and soil settlement are obtained in the Laplace domain. Crump’s method is adopted to perform the inverse Laplace transform in order to obtain semi-analytical solutions in time domain. It is shown that the present solution is more applicable to various types of drainage boundary conditions, and in a good agreement with existing solutions from the literature. Furthermore, several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with traditional drainage boundary (single or double), and single-sided and double-sided semi-permeable drainage boundaries. Finally, it illustrates the changes in pore-air and pore-water pressures and soil settlement with time at different values of symmetric semi-permeable drainage boundary conditions parameters. In addition, parametric studies are conducted by the variations of pore-air and pore-water pressures at different ratios of air-water permeability coefficient and the depth. |
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| Keywords: | Semi-analytical solution Unsaturated soil One-dimensional consolidation Symmetric semi-permeable drainage boundary Laplace transform |
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