Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary

doi:10.1007/s10483-017-2243-6

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (10): 1439-1458.doi: https://doi.org/10.1007/s10483-017-2243-6

Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary

Lei WANG^1,2, De'an SUN², Yongfu XU³

1. School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China;
2. Department of Civil Engineering, Shanghai University, Shanghai 200444, China;
3. Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

收稿日期:2016-10-26 修回日期:2017-02-20 出版日期:2017-10-01 发布日期:2017-10-01
通讯作者: De'an SUN E-mail:sundean@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 41630633 and 11672172)

Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary

Lei WANG^1,2, De'an SUN², Yongfu XU³

1. School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China;
2. Department of Civil Engineering, Shanghai University, Shanghai 200444, China;
3. Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2016-10-26 Revised:2017-02-20 Online:2017-10-01 Published:2017-10-01
Contact: De'an SUN E-mail:sundean@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 41630633 and 11672172)

摘要/Abstract

摘要：

The semi-analytical solutions to Fredlund and Hasan's one-dimensional (1D) consolidation for unsaturated soils with a semi-permeable drainage boundary are presented. Two 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 (PDFs), which are easily solved by the Laplace transform method. Then, the pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. The Crump method is adopted to perform the inverse Laplace transform in order to obtain the semi-analytical solutions in the time domain. It is shown that the proposed solutions are more applicable to various types of boundary conditions and agree well with the existing solutions from the literature. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, mixed, and semi-permeable drainage boundaries. The changes in the pore-air and pore-water pressures and the soil settlement with the time factor at different values of the semi-permeable drainage boundary parameters are illustrated. In addition, parametric studies are conducted on the pore-air and pore-water pressures at different ratios (the air permeability coefficient to the water permeability coefficient) and depths.

关键词: transformation toughening ceramics, shear effect, crack growth, asymptotic method, one-dimensional(1D)consolidation, Laplace transform, semi-permeable drainage boundary, unsaturated soil, semi-analytical solution

Abstract:

Key words: transformation toughening ceramics, shear effect, crack growth, asymptotic method, semi-analytical solution, one-dimensional(1D)consolidation, unsaturated soil, semi-permeable drainage boundary, Laplace transform

中图分类号:

74K10
74D05

Lei WANG, De'an SUN, Yongfu XU. Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(10): 1439-1458.

参考文献

[1] Xie, K. H., Xie, X. Y., and Gao, X. Theory of one dimensional consolidation of two-layered soil with partially drained boundaries. Computers & Geotechnics, 24, 265-278(1999)
[2] Gray, H. Simultaneous consolidation of contiguous layers of unlike compressible soils. Transactions, ASCE, 110, 1327-1356(1945)
[3] Schiffman, R. L. and Stein, J. R. One-dimensional consolidation of layered systems. Journal of the Soil Mechanics and Foundations Division, 96, 1499-1504(1970)
[4] Scott, R. F. Principles of Soil Mechanics, Addison-Wesley Pub. Co., Boston (1963)
[5] Biot, M. A. General theory of three-dimensional consolidation. Journal of Applied Physics, 12, 155-164(1941)
[6] Barden, L. Consolidation of compacted and unsaturated clays. Geotechnique, 15, 267-286(1965)
[7] Fredlund, D. G. and Hasan, J. U. One-dimensional consolidation theory:unsaturated soils. Canadian Geotechnical Journal, 17, 521-531(1979)
[8] Dakshanamurthy, V., Fredlund, D. G., and Rahardjo, H. Coupled three-dimensional consolidation theory of unsaturated porous media. Proceedings of 5th International Conference on Expansive Soils, Adelaide, 99-103(1984)
[9] Fredlund, D. G., Rahardjo, H., and Fredlund, M. D. Unsaturated Soil Mechanics in Engineering Practice, John Wiley & Sons, Hoboken (2012)
[10] Qin, A. F., Chen, G. J., Tan, Y. W., and Sun, D. A. Analytical solution to one dimensional consolidation in unsaturated soils. Applied Mathematics and Mechanics (English Edition), 29(10), 1329-1340(2008) DOI 10.1007/s10483-008-1008-x
[11] Qin, A. F., Sun, D. A., and Tan, Y. W. Semi-analytical solution to one-dimensional consolidation in unsaturated soils. Applied Mathematics and Mechanics (English Edition), 31(2), 215-226(2010) DOI 10.1007/s10483-010-0209-9
[12] Shan, Z. D., Ling, D. S., and Ding, H. J. Exact solutions for one-dimensional consolidation of single-layer unsaturated soil. International Journal for Numerical and Analytical Methods in Geomechanics, 36, 708-722(2012)
[13] Shan, Z. D., Ling, D. S., and Ding, H. J. Analytical solution for 1D consolidation of unsaturated soil with mixed boundary condition. Journal of Zhejiang University-Science A, 14, 61-70(2013)
[14] Zhou, W. H., Zhao, L. S., and Li, X. B. A simple analytical solution to one-dimensional consolidation for unsaturated soils. International Journal for Numerical and Analytical Methods in Geomechanics, 38, 794-810(2014)
[15] Zhou, W. H. and Zhao, L. S. One-dimensional consolidation of unsaturated soil subjected to time-dependent loading with various initial and boundary conditions. International Journal of Geomechanics, 14, 291-301(2014)
[16] Ho, L. and Fatahi, B. One-dimensional consolidation analysis of unsaturated soils subjected to time-dependent loading. International Journal of Geomechanics, 16, 04015052(2015)
[17] Ho, L. and Fatahi, B. Axisymmetric consolidation in unsaturated soil deposit subjected to timedependent loadings. International Journal of Geomechanics, 17, 04016046(2016)
[18] Ho, L., Fatahi, B., and Khabbaz, H. A closed form analytical solution for two-dimensional plane strain consolidation of unsaturated soil stratum. International Journal for Numerical and Analytical Methods in Geomechanics, 39, 1665-1692(2015)
[19] Crump, K. S. Numerical inversion of Laplace transforms using a Fourier series approximation. Journal of the Association for Computing Machinery, 23, 89-96(1976)
[20] Wang, L., Sun, D. A., and Qin, A. F. General semi-analytical solutions to one-dimensional consolidation for unsaturated soils. Applied Mathematics and Mechanics (English Edition), 38(6), 831-850(2017) DOI 10.1007/s10483-017-2209-8

Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary

Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Xiaodong GUO, Zhu SU, Lifeng WANG. Dynamic characteristics of multi-span spinning beams with elastic constraints under an axial compressive force[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 295-310.
[2]	Hai QING, Huidiao SONG. Nonlocal stress gradient formulation for damping vibration analysis of viscoelastic microbeam in thermal environment[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 773-786.
[3]	Jingming FAN, Bo CHEN, Yinghui LI. Closed-form steady-state solutions for forced vibration of second-order axially moving systems[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(10): 1701-1720.
[4]	A. BAKHTIYARI, M. BAGHANI, S. SOHRABPOUR. An investigation on multilayer shape memory polymers under finite bending through nonlinear thermo-visco-hyperelasticity[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 73-88.
[5]	Peiliang BIAN, Hai QING. Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(3): 425-440.
[6]	Pei ZHANG, Hai QING. Two-phase nonlocal integral models with a bi-Helmholtz averaging kernel for nanorods[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(10): 1379-1396.
[7]	T. SAEED, I. A. ABBAS. Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(6): 927-938.
[8]	M. SHOJAEIFARD, M. BAGHANI. Finite deformation swelling of a temperature-sensitive hydrogel cylinder under combined extension-torsion[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(3): 409-424.
[9]	Peng JIANG, Hai QING, Cunfa GAO. Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(2): 207-232.
[10]	K. LOTFY, R. KUMAR, W. HASSAN, M. GABR. Thermomagnetic effect with microtemperature in a semiconducting photothermal excitation medium[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(6): 783-796.
[11]	Rong WANG, Guohua NIE. Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(12): 1825-1836.
[12]	Chunbao XIONG, Yanbo NIU. Fractional-order generalized thermoelastic diffusion theory[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(8): 1091-1108.
[13]	Lei WANG, De'an SUN, Aifang QIN. General semi-analytical solutions to one-dimensional consolidation for unsaturated soils[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(6): 831-850.
[14]	Yaqing LIU, Boling GUO. Coupling model for unsteady MHD flow of generalized Maxwell fluid with radiation thermal transform[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(2): 137-150.
[15]	马田田;韦昌富;陈盼;魏厚振. Implicit scheme for integrating constitutive model of unsaturated soils with coupling hydraulic and mechanical behavior[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1129-1154.