Login Register Cart 0
Generic placeholder image

Recent Patents on Engineering

Editor-in-Chief

ISSN (Print): 1872-2121
ISSN (Online): 2212-4047

Back
Journal Home About Journal Editorial Board Journal Insight Current Issue Volumes/Issues
Subscribe
Opinion Article

Analytical Solution and Consolidation Analysis of One-dimensional Large Strain Consolidation Differential Equation

Author(s): Shijia Liu, Huifeng Su*, Tao Yu, Shuo Zhao and Zhicheng Cui

Volume 16, Issue 1, 2022

Published on: 23 November, 2020

Article ID: e211221188280 Pages: 8

DOI: 10.2174/1874476105999201123204611

Price: $65

Abstract

According to the universal one-dimensional consolidation equation introduced by Gibson, the governing equation with the excess pore water pressure as the control variable is derived, and the Fourier series solution under the boundary condition of single-sided drainage is deduced in detail by the standard mathematical and physical method. It verifies the correspondence between the analytical solution and the numerical solution from a theoretical point of view. Using this analytical solution, the nonlinear distribution of the excess pore pressure along the depth direction is obtained, and the traditional small strain consolidation is compared in terms of the average consolidation degree and the final settlement.

In the project, the one-dimensional consolidation theory established by Terzaghi is obviously no longer applicable to the foundation built on saturated soft clay with a compressive amount of 80%, so the research on the large strain theory began.

The purpose of this article is to give a detailed derivation process of the differential equation with excess pore pressure as the control variable in the analytical theory of one-dimensional nonlinear large-strain consolidation, and verify it based on calculation examples, hoping to provide suitable theoretical basis for large-deformation foundations.

This article mainly uses detailed formula derivation and standard mathematical and physical methods to derive the Fourier series solution of the consolidation differential equation according to the boundary conditions of single-sided permeable water and compare and verify the analysis according to an example of calculation.

Based on Gibson's general equation of consolidation and its theory, the detailed derivation process of differential equations with excess pore water pressure as the control variable is given.

According to the example, the image shows the distribution of excess pore pressure with depth, and comparative analysis of large and small strains. If all other conditions are the same, when mv1=1 MPa-1, it can be calculated according to the large and small strains, but when mv1≥3MPa-1, for the soil that should be calculated according to large strain, it is unreasonable to calculate according to small strain. Therefore, the calculation error of the two methods is very large, so it is necessary to distinguish the large and small strains.

Keywords: Large strain, one-dimensional, consolidation, series solution, single-sided drainage, small strain consolidation.

Graphical Abstract

[1]
L. Ting-Hao, Soil mechanics., Hohai Unversity Press: Nan Jing, 2005.
[2]
H.J. Qing, Theoretical and Experimental Study on Nonlinear Finite Strain Consolidation., Zhejiang University, 2015.
[3]
L.J. Zhu, Study on Large Strain Consolidation of Soft Soil Considering Rheological Effect., Zhejiang University, 2011.
[4]
R.E. Gibson, G.L. England, and M.J.L. Hussey, "The theory if one-dimensional Consolidation of saturated clays(I): Finite Non-Linear Consolidation of Thin Homogeneous Layers", Geotechnique, vol. 17, pp. 261-273, 1967.
[http://dx.doi.org/10.1680/geot.1967.17.3.261]
[5]
R.E. Gibson, R.L. Schiffman, and K.W. Cargill, "Theory of one dimensional consolidation of saturated clays(II): Finite Non-Linear Consolidation of Thick Homogeneous Layers", Can. Geotech. J., vol. 18, pp. 280-293, 1981.
[http://dx.doi.org/10.1139/t81-030]
[6]
J. Fox Patrick, and H. Pu, "Benchark Problems for Large Strain Consolidation", J. Geotech. Geoenviron. Eng., vol. 141, p. no. 11, 2015.
[7]
I. Buddhima, Z. Rui, P.J. Fox, and R. Cholachat, "Large-strain vacuum-assisted consolidation with non-Darcian radial flow incorporating varying permeability and compressibility", J. Geotech. Geoenviron. Eng., vol. 143, p. no. 1, 2017.
[8]
B. Li, K. Xie, H. Ying, and G. Zeng, "Semi-analytical solution of one dimensional non-linear consolidation of soft clay under time-dependent loading", Chin. J. Geotechn. Eng., vol. 21, pp. 288-293, 1999.
[9]
P.J. Fox, H-F. Pu, and J.D. Berles, "CS3: Large Strain Consolidation Model for Layered Soils", J. Geotech. Geoenviron. Eng., vol. 140, p. no. 8, 2014.
[http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001128]
[10]
B. Malengier, H. Peiffer, and G. Di Emidio, "One-dimensional model for large-strain consolidation in a bench-scale centrifuge", Transp. Porous Media, vol. 114, pp. 675-693, 2016.
[http://dx.doi.org/10.1007/s11242-016-0739-2]
[11]
X. Geng, and H.S. Yu, "A large-strain radial consolidation theory for soft clays improved by vertical drain", Geotechnique, vol. 67, pp. 1020-1028, 2017.
[http://dx.doi.org/10.1680/jgeot.15.T.013]
[12]
P.J. Fox, and H. Pu, "Enhanced CS2 model for large strain consolidation", Int. J. Geomech., vol. 12, pp. 574-583, 2012.
[http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0000171]
[13]
B.T. Fisseha, G.W. Wilson, and D.G. Fredlund, "Large-Strain Consolidation Column with Applied Negative Water Pressure", 2nd Pan-American Conference on Unsaturated Soils ((PanAm- UNSAT), Dallas, TX, USA, 2018, pp. 476-485.
[http://dx.doi.org/10.1061/9780784481684.048]
[14]
Y. Cao, Z. Sun, J. Ding, and J. Feng, "Axisymmetric large-strain consolidation model for dredged clay with high water content", Chin. J. Geotechnical Eng., vol. 38, pp. 1904-1910, 2016.
[15]
C. Li, X. Chao, and K. Xie, "Analysis of one-dimensional large strain consolidation of soft clay with threshold gradient", Chin. J. Rock Mech. Eng., vol. 34, pp. 3525-3533, 2015.
[16]
C. Li, and K. Xie, "Large-strain consolidation of soft clay with non-Darcian flow by considering time-dependent load", Chin. J. Geotec. Eng., vol. 37, pp. 1002-1009, 2015.
[17]
W. Zhang, and X. Gu, "General solution to one-dimentional consolidation theories and simple computation method for consolidation settlement", Chinese Journal of Geotechnical Engineering, vol. 38, pp. 35-42, 2016.
[18]
K. Xie, Z. Hun, and C.J. Leo, "An analytical theory for 1-D nonlinear large strain consolidation of soft clay", Chin. J. Geotec. Eng., vol. 24, pp. 681-684, 2002.
[19]
L. Chang, J. Wang, and X. Zhu, "An analytical solution of 1-D finite strain consolidation of saturated soft clay under multistep linear loading", Rock and Soil Menchanics, vol. 30, pp. 2343-2347, 2009.
[20]
J. Zhang, X. Xie, J. Zheng, and G. Zeng, "An analytical solution of one-dimensional finite strain consolidation theory", Chin. J. Solid Mechan., vol. 24, pp. 384-390, 2003.
[21]
M. Kaitlin, and J. Fox Patrick, "Large Strain Consolidation Model for Land Subsidence", int. j. geomechanics, vol. 18, 2018.
[22]
C. Li, X. Dong, D. Jin, and Y. Wang, "Large-strain nonlinear consolidation of double-layered soft clay with threshold gradient", Rock Soil Mench., vol. 39, pp. 1877-1884, 2018.
[23]
H. Shen, and S. Jiang, "Analytical calculation of one-dimensional consolidation differential equation and consolidation degree", J. Guang. University Education, vol. 34, pp. 43-47, 2014.
[24]
A. Hu, J. Huang, X. Xie, W. Jian, J. Li, and K. Liu, "Study on properties of one-dimensional complex nonlinear consolidation considering self-weight of saturated soils", J. Zhejiang Univ. Eng. Sci., vol. 46, pp. 441-447, 2012.
[25]
A. Ferrari, V. Faverz, and L. Laloui, "One-dimensional compression and consolidation of shales", Int. J. Rock Mech. Min. Sci., vol. 88, pp. 286-300, 2016.
[http://dx.doi.org/10.1016/j.ijrmms.2016.07.030]
[26]
X. Xie, Y.M. Liu, and Q. Pan, "Effects of variable permeability on one-dimensional large strain consolidation", Chin. J. Geotech. Eng., vol. 22, pp. 509-511, 2000.
[27]
"Hu, YaYuan, Zhou, Wan-Huan; Cai, Yuan-Qiang, Large-strain elastic viscoplastic consolidation analysis of very soft clay layers with vertical drains under preloading", Can. Geotech. J., vol. 51, pp. 144-157, 2014.
[http://dx.doi.org/10.1139/cgj-2013-0200]

Rights & Permissions Print Cite
Article Metrics
13
1
© 2024 Bentham Science Publishers | Privacy Policy