Piecewise-Linear Model for Large-Strain Consolidation with Threshold Hydraulic Gradient
Publication: International Journal of Geomechanics
Volume 22, Issue 5
Abstract
Experimental studies found that water flow in clay might not obey Darcy’s law. In some fine-grained soils, the water flow could occur only when the threshold gradient was exceeded. This study investigates the effects of threshold gradient on the consolidation profile. The well-established model CNDF2 is employed with some modifications. Verification examples demonstrate the accuracy of the numerical simulation in this study. Compared with the existing solution in the literature, modeling results in this study are more reliable because the criterion of seepage is independent of the position of the seepage front. Parametric studies find that the excess pore-water pressure cannot be fully dissipated if there is a threshold gradient. A larger value of normalized threshold hydraulic gradient R will result in a larger value of residual excess pore-water pressure. A permeable bottom boundary can contribute to the dissipation of residual excess pore-water pressure. The final settlement will also be affected by the threshold hydraulic gradient. A larger value of R will lead to a smaller final settlement due to the residual excess pore-water pressure. The average degree of consolidation will not be affected by the threshold hydraulic gradient.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
This research is supported by the National Key R&D Program of China (Grant No. 2016YFC0800200) and the National Natural Science Foundation of China (Grant Nos. 51878313 and 52078236), and the support is gratefully acknowledged.
References
Davis, E. H., and G. P. Raymond. 1965. “A non-linear theory of consolidation.” Géotechnique 15 (2): 161–173. https://doi.org/10.1680/geot.1965.15.2.161.
Fox, P. J., and J. D. Berles. 1997. “CS2: A piecewise-linear model for large strain consolidation.” Int. J. Numer. Anal. Methods Geomech. 21 (7): 453–475. https://doi.org/10.1002/(SICI)1096-9853(199707)21:7%3C453::AID-NAG887%3E3.0.CO;2-B.
Fox, P. J., and H. Pu. 2012. “Enhanced CS2 model for large strain consolidation.” Int. J. Geomech. 12 (5): 574–583. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000171.
Fox, P. J., H.-F. Pu, and J. D. Berles. 2014. “CS3: Large strain consolidation model for layered soils.” J. Geotech. Geoenviron. Eng. 140 (8): 04014041.
Fox, P. J., and T. Qiu. 2004. “Model for large strain consolidation with compressible pore fluid.” Int. J. Numer. Anal. Methods Geomech. 28 (11): 1167–1188. https://doi.org/10.1002/nag.382.
Guo, X., K.-H. Xie, and Y.-B. Deng. 2014. “Consolidation by prefabricated vertical drains with a threshold gradient.” Math. Probl. Eng. 2014: 410390.
Hansbo, S. 1997. “Aspects of vertical drain design: Darcian or non-Darcian flow.” Géotechnique 47 (5): 983–992. https://doi.org/10.1680/geot.1997.47.5.983.
Hansbo, S. 2001. “Consolidation equation valid for both Darcian and non-Darcian flow.” Géotechnique 51 (1): 51–54. https://doi.org/10.1680/geot.2001.51.1.51.
Indraratna, B., R. Zhong, P. J. Fox, and C. Rujikiatkamjorn. 2017. “Large-strain vacuum-assisted consolidation with non-Darcian radial flow incorporating varying permeability and compressibility.” J. Geotech. Geoenviron. Eng. 143 (1): 04016088. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001599.
Li, C., M. Lu, and H. Ma. 2020. “Solutions for one-dimensional rheological consolidation of a clay layer with threshold hydraulic gradient under multistage loading.” Int. J. Geomech. 20 (11): 06020031. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001846.
Li, C. X., X. Q. Dong, D. D. Jin, and K. H. Xie. 2017. “Nonlinear large-strain consolidation analysis of soft clay considering threshold hydraulic gradient.” Rock Soil Mech. 38 (2): 377–384.
Liu, Z., J. Zhang, S. Duan, Y. Xia, and P. Cui. 2020. “A consolidation modelling algorithm based on the unified hardening constitutive relation and Hansbo’s flow rule.” Comput. Geotech. 117: 103233. https://doi.org/10.1016/j.compgeo.2019.103233.
Miller, R. J., and P. F. Low. 1963. “Threshold gradient for water flow in clay systems.” Soil Sci. Soc. Am. J. 27 (6): 605–609. https://doi.org/10.2136/sssaj1963.03615995002700060013x.
Mitchell, J., and J. Younger. 1967. “Abnormalities in hydraulic flow through fine-grained soils.” In Permeability and capillarity of soils, 106–141. West Conshohocken, PA: ASTM.
Olsen, H. W. 1985. “Osmosis: A cause of apparent deviations from Darcy’s law.” Can. Geotech. J. 22 (2): 238–241. https://doi.org/10.1139/t85-032.
Pascal, F., H. Pascal, and D. W. Murray. 1981. “Consolidation with threshold gradients.” Int. J. Numer. Anal. Methods Geomech. 5 (3): 247–261. https://doi.org/10.1002/nag.1610050303.
Pu, H., and P. J. Fox. 2016. “Model for coupled large strain consolidation and solute transport in layered soils.” Int. J. Geomech. 16 (2): 04015064. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000539.
Pu, H., P. Yang, M. Lu, Y. Zhou, and J. Chen. 2020. “Piecewise-linear large-strain model for radial consolidation with non-Darcian flow and general constitutive relationships.” Comput. Geotech. 118: 103327. https://doi.org/10.1016/j.compgeo.2019.103327.
Pu, H.-F., P. J. Fox, and Y. Liu. 2013. “Model for large strain consolidation under constant rate of strain.” Int. J. Numer. Anal. Methods Geomech. 37 (11): 1574–1590. https://doi.org/10.1002/nag.2100.
Walker, R., B. Indraratna, and C. Rujikiatkamjorn. 2012. “Vertical drain consolidation with non-Darcian flow and void-ratio-dependent compressibility and permeability.” Géotechnique 62 (11): 985–997. https://doi.org/10.1680/geot.10.P.084.
Wang, H.-X., W. Xu, Y.-Y. Zhang, and D.-A. Sun. 2021. “Simplified solution to one-dimensional consolidation with threshold gradient.” Comput. Geotech. 131 (3): 103943.
Wang, K. 2011. Studies on one dimensional consolidation for soft soils with threshold gradient. Hangzhou, China: Zhengjiang Univ.
Wen, Z., F. Wu, and Q. Feng. 2016. “Non-Darcian flow to a partially penetrating pumping well in a leaky aquifer considering the aquitard–aquifer interface flow.” J. Hydrol. Eng. 21 (12): 06016011. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001446.
Xie, K.-H., K. Wang, Y.-L. Wang, and C.-X. Li. 2010. “Analytical solution for one-dimensional consolidation of clayey soils with a threshold gradient.” Comput. Geotech. 37 (4): 487–493. https://doi.org/10.1016/j.compgeo.2010.02.001.
Zhao, X. D., and W.-H. Gong. 2019. “Model for large strain consolidation with non-Darcian flow described by a flow exponent and threshold gradient.” Int. J. Numer. Anal. Methods Geomech. 43 (14): 2251–2269. https://doi.org/10.1002/nag.2946.
Zhao, X. D., Y. Liu, and W.-H. Gong. 2020. “Analytical solution for one-dimensional electro-osmotic consolidation of double–layered system.” Comput. Geotech. 122: 103496. https://doi.org/10.1016/j.compgeo.2020.103496.
Zhou, Y., W.-k. Bu, and M.-m. Lu. 2013. “One-dimensional consolidation with a threshold gradient: A Stefan problem with rate-dependent latent heat.” Int. J. Numer. Anal. Methods Geomech. 37 (16): 2825–2832. https://doi.org/10.1002/nag.2219.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 5 • May 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Feb 1, 2021
Accepted: Dec 19, 2021
Published online: Mar 2, 2022
Published in print: May 1, 2022
Discussion open until: Aug 2, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Wenhao Jiang, Chen Feng, Shangqi Ge, Saiou Fu, Jiangshan Li, Fully Coupled Model for One-Dimensional Large-Strain Consolidation and Heat Conduction in Saturated Clay, Journal of Engineering Mechanics, 10.1061/JENMDT.EMENG-6852, 149, 4, (2023).
- Yang Liu, Jun‐Jie Zheng, Jia‐Tai Lu, An analytical model for 2D consolidation of unsaturated soil with semi‐permeable boundaries considering self‐weight stress and time‐dependent loading, International Journal for Numerical and Analytical Methods in Geomechanics, 10.1002/nag.3498, (2023).
- Yuguo Zhang, Yamin Zhao, Chuang Wang, Wenbing Yang, Theoretical Study on the Consolidation of Multiple Composite Foundations with Vertical Drains-Impervious Piles considering Temperature Effect and Nonuniform Distribution of Initial Pore Pressure, Advances in Civil Engineering, 10.1155/2022/6238841, 2022, (1-11), (2022).
- Yuguo Zhang, Yamin Zhao, Analytical Solution for Consolidation of Vertical Drains-Impervious Piles with Multiple Composite Foundations under Nonuniform Initial Pore Pressure and Time-Dependent Well Resistance, Advances in Civil Engineering, 10.1155/2022/2181792, 2022, (1-13), (2022).
- Wenhao Jiang, Shangqi Ge, Xiao Huang, Zhen Chen, Jiangshan Li, General analytical solutions for one-dimensional large strain consolidation of soft soils under electro-osmosis–surcharge preloading, Soils and Foundations, 10.1016/j.sandf.2022.101211, 62, 5, (101211), (2022).