Abstract
In the research field of ground water, hydraulic gradient is studied for decades. In the consolidation field, hydraulic gradient is yet to be investigated as an important hydraulic variable. So, the variation of hydraulic gradient in nonlinear finite strain consolidation was focused on in this work. Based on lab tests, the nonlinear compressibility and nonlinear permeability of Ningbo soft clay were obtained. Then, a strongly nonlinear governing equation was derived and it was solved with the finite element method. Afterwards, the numerical analysis was performed and it was verified with the existing experiment for Hong Kong marine clay. It can be found that the variation of hydraulic gradient is closely related to the magnitude of external load and the depth in soils. It is interesting that the absolute value of hydraulic gradient (AVHG) increases rapidly first and then decreases gradually after reaching the maximum at different depths of soils. Furthermore, the changing curves of AVHG can be roughly divided into five phases. This five-phase model can be employed to study the migration of pore water during consolidation.
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HUSAIN M M, CHERRY J A, FIDLER S, FRAPE S K. On the long-term hydraulic gradient in the thick clayey aquitard in the Sarnia region, Ontario [J]. Canadian Geotechnical Journal, 1998, 35(6): 986–1003.
DEVLIN J F, MCELWEE C D. Effects of measurement error on horizontal hydraulic gradient estimates [J]. Ground Water, 2007, 45(1): 62–73.
FRITZ B G, MACKLEY R D. A wet/wet differential pressure sensor for measuring vertical hydraulic gradient [J]. Ground Water, 2010, 48(1): 117–121.
BAIR E S. Analysis of hydraulic gradients across the host rock at the proposed Texas panhandle nuclear-waste repository site [J]. Ground Water, 1987, 25(4): 440–447.
SILLIMAN S E, FROST C. Monitoring hydraulic gradient using three-point estimator [J]. Journal of Environmental Engineering, ASCE, 1998, 124(6): 517–523.
DEVLIN J F. A spreadsheet method of estimating best-fit hydraulic gradients using head data from multiple wells [J]. Ground Water, 2003, 41(3): 316–320.
FENTONL G A, GRIFFITHS D V. Extreme hydraulic gradient statistics in stochastic earth dam [J]. Journal of Geotechnical and Geoenvironmental Engineering, 1997, 123(11): 995–1000.
MOUTIER M, SHAINBERG I, LEVY G J. Hydraulic gradient and wetting rate effects on the hydraulic conductivity of two calcium vertisols [J]. Soil Science Society of America Journal, 2000, 64(4): 1211–1219.
LIU Hui-hai, BIRKHOLZER J. On the relationship between water flux and hydraulic gradient for unsaturated and saturated clay [J]. Journal of Hydrology, 2012, 475: 242–247.
GIBSON R E, ENGLAND G L, HUSSEY M J L. The theory of one-dimensional consolidation of saturated clays. I. Finite non-linear consolidation of thin homogeneous layers [J]. Géotechnique, 1967 (17): 261–273.
GIBSON R E, SCHIFFMAN R L, CARGILL K W. The theory of one-dimensional consolidation of saturated clays. II. Finite non-linear consolidation of thick homogeneous layers [J]. Canadian Geotechnical Journal, 1981, 18(2): 280–293.
SCHIFFMAN R L, CARGILL K W. Finite strain consolidation of sedimenting clay deposits [C]// Proceedings of the Tenth International Conference on Soil Mechanics and Foundation Engineering. Stockholm, Sweden, 1981: 239–242.
JEERAVIPOOLVARN S, CHALATURNYK R J, SCOTT J D. Sedimentation-consolidation modeling with an interaction coefficient [J]. Computers and Geotechnics, 2009, 36: 751–761.
POSKITT T J. Consolidation of saturated clay with variable permeability and compressibility [J]. Géotechnique, 1969, 19(2): 234–252.
CARTER J P, SMALL J C, BOOKER J R. A theory of finite elastic consolidation [J]. International Journal of Solids Structures, 1977, 13: 467–478.
XIE Kang-he, LEO C J. Analytical solutions of one-dimensional large strain consolidation of saturated and homogeneous clays [J]. Computers and Geotechnics, 2004, 31: 301–314.
XIE Xin-yu, ZHANG Ji-fa, ZENG Guo-xi. Similarity solution of self-weight consolidation problem for saturated soil [J]. Applied Mathematics and Mechanics, 2005, 26(9): 1061–1066.
DUNCAN J M. Limitation of conventional analysis of consolidation settlement [J]. Journal of Geotechnical Engineering, 1993, 119(9): 1333–1359.
LEROUEIL S. Recent developments in consolidation of natural clays [J]. Canadian Geotechnical Journal, 1988, 25(1): 85–105.
MESRI G, ROKHSAR A. Theory of consolidation for clays [J]. Journal of Geotechnical Engineering, 1974, 100(8): 889–904.
TAVENAS F, JEAN P, LEBLOND P, LEROUEIL S. The permeability of natural soft clays. Part II: Permeability characteristics [J]. Canadian Geotechnical Journal, 1983, 20(4): 645–660.
ZHU Qing-jie, CHEN Yan-hua, LIU Ting-quan, DAI Zhao-li. Finite element analysis of fluid-structure interaction in buried liquid-conveying pipeline [J]. Journal of Central South University of Technology, 2008, 15(sl): 307–310.
YU Hai-liang, LIU Xiang-hua. Longitudinal crack on slab surface at straightening stage during continuous casting using finite element method [J]. Journal of Central South University of Technology, 2010, 17(2): 235–238.
LEE S R, KIM Y S, KIM Y S. Analysis of sedimentation/consolidation by finite element method [J]. Computers and Geotechnics, 2000, 27: 141–160.
TAIEBAT H A, CARTER J P. A semi-analytical finite element method for three-dimensional consolidation analysis [J]. Computers and Geotechnics, 2001, 28: 55–78.
MENENDEZ C, NIETO P J G, ORTEGA F A, BELLO A. Non-linear analysis of the consolidation of an elastic saturated soil with incompressible fluid and variable permeability by FEM [J]. Applied Mathematics and Computation, 2010, 216: 458–476.
FANG Zhen, YIN Jian-hua. Responses of excess pore water pressure in soft marine clay around a soil-cement column [J]. International Journal of Geomechanics, 2007, 3: 167–175.
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Foundation item: Project(51378469) supported by the National Natural Science Foundation of China; Project(Y1111240) supported by the Zhejiang Provincial Natural Science Foundation of China; Project(2013A610196) supported by the Natural Science Foundation of Ningbo City, China
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Xie, Xy., Huang, Jq., Wang, Wj. et al. Variation of hydraulic gradient in nonlinear finite strain consolidation. J. Cent. South Univ. 21, 4698–4706 (2014). https://doi.org/10.1007/s11771-014-2479-1
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DOI: https://doi.org/10.1007/s11771-014-2479-1