Analytical Solution for 1D Consolidation of Unsaturated Soil Under Constant Load and DoubleSide Drainage

HE Zizhou; ZHOU Fengxi

doi:10.21656/1000-0887.390292

Volume 40 Issue 9

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HE Zizhou, ZHOU Fengxi. Analytical Solution for 1D Consolidation of Unsaturated Soil Under Constant Load and DoubleSide Drainage[J]. Applied Mathematics and Mechanics, 2019, 40(9): 1035-1047. doi: 10.21656/1000-0887.390292

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Analytical Solution for 1D Consolidation of Unsaturated Soil Under Constant Load and DoubleSide Drainage

doi: 10.21656/1000-0887.390292

HE Zizhou¹,
ZHOU Fengxi^1,2

¹School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, P.R.China;²Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou 730050, P.R.China

Funds: The National Natural Science Foundation of China（11962016）

Received Date: 2018-11-19
Rev Recd Date: 2019-02-15
Publish Date: 2019-09-01

Abstract

Abstract

Based on the elastic theory for porous media and the principle of the effective stress expressed with intergranular suction stresses, the coupled partial differential governing equation for unsaturated soil consolidation was established. For the 1D consolidation problem, the analytical solution for the consolidation of unsaturated soil under constant load and doubleside drainage was obtained through the Laplace integral transform. The effects of soil saturation on the excessive pore water pressure, the effective stress and the soil settlement were analyzed with numerical examples. The results show that, the higher the initial saturation of the soil is, the faster the pore water pressure will dissipate and the faster the effective stress will increase.
- unsaturated soil,
- analytical solution,
- suction stress characteristic curve,
- pore water pressure

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References(26)

References

[1]	BARDEN L. Consolidation of compacted and unsaturated clays[J]. Géotechnique,1965,15(3): 267-286.
[2]	BARDEN L. Consolidation of clays compacted ‘dry’ and ‘wet’ of optimum water content[J]. Géotechnique,1974,24(4): 605-625.
[3]	FREDLUND D G. SecondCanadian geotechnical colloquium: appropriate concepts and technology for unsaturated soils[J]. Canadian Geotechnical Journal,1979,16(1): 121-139.
[4]	陈正汉, 谢定义, 刘祖典. 非饱和土固结的混合物理论(Ⅰ)[J]. 应用数学和力学, 1993,14(2): 127-137.(CHEN Zhenghan, XIE Dingyi, LIU Zudian. Consolidation theory of unsaturated soil based on the theory of mixture (Ⅰ)[J]. Applied Mathematics and Mechanics,1993,14(2): 127-137.(in Chinese))
[5]	陈正汉. 非饱和土固结的混合物理论(Ⅱ)[J]. 应用数学和力学, 1993,14(8): 687-698.(CHEN Zhenghan. Consolidation theory of unsaturated soil based on the theory of mixture (Ⅱ)[J]. Applied Mathematics and Mechanics,1993,14(8): 687-698.(in Chinese))
[6]	陈正汉, 秦冰. 非饱和土的应力状态变量研究[J]. 岩土力学, 2012,33(1): 1-11.(CHEN Zhenghan, QIN Bing. On stress state variables of unsaturated soils[J]. Rock and Soil Mechanics,2012,33(1): 1-11.(in Chinese))
[7]	张龙, 陈正汉, 周凤玺, 等. 非饱和土应力状态变量试验验证研究[J]. 岩土工程学报, 2017,39(2): 380-384.(ZHANG Long, CHEN Zhenghan, ZHOU Fengxi, et al. Test verification of stress state variables for unsaturated soils[J].Chinese Journal of Geotechnical Engineering,2017,39(2): 380-384.(in Chinese))
[8]	张龙, 陈正汉, 周凤玺, 等. 从变形、水量变化和强度三方面验证非饱和土的两个应力状态变量[J]. 岩土工程学报, 2017,39(5): 906-915.(ZHANG Long, CHEN Zhenghan, ZHOU Fengxi, et al. Verification of rationality of two stress state variables of unsaturated soil from deformation, moisture change and strength[J]. Chinese Journal of Geotechnical Engineering,2017,39(5): 906-915.(in Chinese))
[9]	陈正汉, 黄海, 卢再华. 非饱和土的非线性固结模型和弹塑性固结模型及其应用[J]. 应用数学和力学, 2001,21(1): 93-103.(CHEN Zhenghan, HUANG Hai, LU Zaihua. Non-linear and elasto-plasticity consolidation models of unsaturated soil and applications[J]. Applied Mathematics and Mechanics,2001,21(1): 93-103.(in Chinese))
[10]	卢再华, 陈正汉, 方祥位, 等. 非饱和膨胀土的结构损伤模型及其在土坡多场耦合分析中的应用[J]. 应用数学和力学, 2006,27(7): 781-788.(LU Zaihua, CHEN Zhenghan, FANG Xiangwei, et al. Structural damage model of unsaturated expansive soil and its application to multi-field coupling analysis of soil slope[J]. Applied Mathematics and Mechanics,2006,27(7): 781-788.(in Chinese))
[11]	秦冰, 陈正汉, 方振东, 等. 基于混合物理论的非饱和土的热-水-力耦合分析模型(Ⅰ)[J]. 应用数学和力学, 2010,31(12): 1476-1487.(QIN Bing, CHEN Zhenghan, FANG Zhendong, et al. Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures Ⅰ[J]. Applied Mathematics and Mechanics,2010,31(12): 1476-1487.(in Chinese))
[12]	LI X K, ZIENKIEWICZ O C, XIE Y M. A numerical model for immiscible two-phase fluid flow in a porous medium and its time domain solution[J]. International Journal for Numerical Methods in Engineering,1990,30(6): 1195-1212.
[13]	LI X K, ZIENKIEWICZ O C. Multiphase flow in deforming porous media and finite element solutions[J]. Computers & Structures,1992,45(2): 211-227.
[14]	杨代泉. 非饱和土二维广义固结非线性数值模型[J]. 岩土工程学报, 1992,14(S1): 2-12.(YANG Daiquan. Nonlinear numerical model of two-dimensional generalized consolidation of unsaturated soils[J]. Chinese Journal of Geotechnical Engineering,1992,14(S1): 2-12.(in Chinese))
[15]	李冰河, 谢康和, 应宏伟, 等. 变荷载下软粘土非线性一维固结半解析解[J]. 岩土工程学报, 1999,21(3): 32-37.(LI Binghe, XIE Kanghe, YING Hongwei, et al. Semi-analytical solution of nonlinear one-dimensional consolidation of soft clay under variable loading[J]. Chinese Journal of Geotechnical Engineering,1999,21(3): 32-37.(in Chinese))
[16]	秦爱芳, 陈光敬, 谈永卫, 等. 非饱和土层一维固结问题的解析解[J]. 应用数学和力学, 2008,29(10): 1208-1218.(QIN Aifang, CHEN Guangjing, TAN Yongwei, et al. Analytical solution to one-dimensional consolidation in unsaturated soils[J]. Applied Mathematics and Mechanics,2008,29(10): 1208-1218.(in Chinese))
[17]	秦爱芳, 孙德安, 谈永卫. 非饱和土一维固结的半解析解[J]. 应用数学和力学, 2010,31(2): 199-209.(QIN Aifang, SUN Dean, TAN Yongwei. Semi-analytical solution for one-dimensional consolidation of unsaturated soils[J]. Applied Mathematics and Mechanics,2010,31(2): 199-209.(in Chinese))
[18]	BIOT M A. Generaltheory of three-dimensional consolidation[J]. Journal of Applied Physics,1941,12(2): 155-164.
[19]	BIOT M A. Mechanics of deformation and acoustic propagation in porous media[J]. Journal of Applied Physics,2004,33(4): 1482-1498.
[20]	LO W C, SPOSITO G, MAJER E. Wave propagation through elastic porous media containing two immiscible fluids [J]. Water Resources Research,2005,41(2): 199-207.
[21]	LO W C, SPOSITO G, CHU H. Poroelastic theory of consolidation in unsaturated soils[J]. Vadose Zone Journal,2014,13(5): 1-12. DOI: 10.2136/vzj2013.07.0117.
[22]	LU N, LIKOS W J. Suction stress characteristic curve for unsaturated soil[J]. Journal of Geotechnical and Geoenvironmental Engineering,2006,132(2): 131-142.
[23]	LU N, GODT J W, WU D T. A closed-form equation for effective stress in unsaturated soil[J]. Water Resources Research,2010,46(5): 567-573.
[24]	RAWLS W J, AHUJA L R, BRAKENSIEK D L. Estimating soil hydraulic properties from soils data[J]. Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils,1992,32(9): 329-340.
[25]	LO W C, YEH C L, TSAI C T. Effect of soil texture on the propagation and attenuation of acoustic wave at unsaturated conditions[J]. Journal of Hydrology(Amsterdam),2007,338(3/4): 273-284.
[26]	GENUCHTEN M T V. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Science Society of America Journal,1980,44(5): 892-898.