Piecewise-Linear Model for One-Dimensional Consolidation Considering Non-Darcian Flow under Continuous Drainage Boundary
Publication: International Journal of Geomechanics
Volume 21, Issue 5
Abstract
Based on the piecewise-linear consolidation model, this paper presents a consolidation model that considers the drainage conditions and non-Darcian flow of clayey soils. In the proposed model, the continuous drainage boundary is used to reflect the drainage performance of the soil's boundary, and Hansbo’s equation is applied to describe non-Darcian flow of clayey soils. The applicability of the proposed model is validated by comparing its results with existing results. Then the influences of drainage conditions, non-Darcian flow, the ratio of compression index to permeability change index. and self-weight of soil on the consolidation process are analyzed through several cases. The results indicate that both a continuous drainage boundary and Hansbo's flow can significantly slow down the consolidation process, and this effect becomes more obvious with the increase of the ratio of compression index to permeability index. In addition, without considering the influence of soil's weight, the consolidation rate and the final settlement of the soil layer will be underestimated and overestimated, respectively.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant No. 51578511), and the support is gratefully acknowledged. All the authors are highly thankful to the reviewers for their fruitful comments to improve the quality of the paper.
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.
Deng, A., and Y. D. Zhou. 2016. “Modeling electroosmosis and surcharge preloading consolidation. II: Validation and simulation results.” J. Geotech. Geoenviron. Eng. 142 (4): 04015094. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001418.
Elnaggar, H. A., R. J. Krizek, and G. M. Karadi. 1973. “Effect of non-Darcian flow on time rate of consolidation.” J. Franklin Inst. 296 (5): 323–337. https://doi.org/10.1016/0016-0032(73)90212-3.
Feng, J. X., P. P. Ni, and G. X. Mei. 2019. “One-dimensional self-weight consolidation with continuous drainage boundary conditions: Solution and application to clay-drain reclamation.” Int. J. Numer. Anal. Methods Geomech. 43 (8): 1634–1652. https://doi.org/10.1002/nag.2928.
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., J. Lee, and T. Qiu. 2005. “Model for large strain consolidation by centrifuge.” Int. J. Geomech. 5 (4): 267–275. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:4(267).
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.
Gray, H. 1945. “Simultaneous consolidation of contiguous layers of unlike compressible soils.” Trans. ASCE 110: 1327–1356.
Hansbo, S. 1960. “Consolidation of clay with special reference to influence of vertical sand drains.” Swedish Geotech. Inst. 18: 45–50.
Hansbo, S. 2003. “Deviation from Darcy’s law observed in one-dimensional consolidation.” Géotechnique 53 (6): 601–605. https://doi.org/10.1680/geot.2003.53.6.601.
Huang, W. X. 1982. “Appliaction of consolidation theory to earth dams built by sluicing-siltation method.” [In Chinese.] J. Hydraul. Eng. (9): 11–21.
Lee, J., and P. J. Fox. 2005. “Efficiency of seepage consolidation for preparation of clay substrate for centrifuge testing.” Geotech. Test J. 28 (6): 577–585. https://doi.org/10.1520/GTJ12516.
Li, C. X., C. J. Wang, M. M. Lu, J. F. Lu, and K. H. Xie. 2017. “One-dimensional large-strain consolidation of soft clay with non-Darcian flow and nonlinear compression and permeability of soil.” J. Central South Univ. 24 (4): 967–976. https://doi.org/10.1007/s11771-017-3499-4.
Li, C. X., and K. H. Xie. 2013. “One-dimensional nonlinear consolidation of soft clay with the non-Dracian flow.” J. Zhejiang Univ. Sci. A 14 (6): 435–446. https://doi.org/10.1631/jzus.A1200343.
Li, C. X., K. H. Xie, A. F. Hu, and B. Hu. 2012. “One-dimensional consolidation of double-layered soil with non-Darcian flow described by exponent and threshold gradient.” J. Central South Univ. 19 (2): 562–571. https://doi.org/10.1007/s11771-012-1040-3.
Li, Y. Y., J. X. Feng, and G. X. Mei. 2019. “One-dimensional consolidation analysis of the trapezoidal cyclic loading under continuous drainage boundary.” [In Chinese.] Eng. Mech. 36 (2): 134–140. https://doi.org/10.6052/j.issn.1000-4750.2017.12.0928.
Liu, J. C., and G. H. Lei. 2013. “One-dimensional consolidation of layered soils with exponentially time-growing drainage boundaries.” Comput. Geotech. 54: 202–209. https://doi.org/10.1016/j.compgeo.2013.07.009.
Liu, J. C., G. G. Lei, and Y. X. Wang. 2011. “One-dimensional consolidation of soft ground considering non-Darcy flows.” Chin. J. Geotech. Eng. 33 (7): 1117–1122.
Liu, Z. Y., P. L. Cui, Z. L. Zheng, Y. Y. Xia, and J. C. Zhang. 2019a. “Analysis of one-dimensional rheological consolidation with flow described by non-Newtonian index and fractional-order Merchant’s model.” Rock Soil Mech. 40 (6): 2029–2038. https://doi.org/10.16285/j.rsm.2018.1085.
Liu, Z. Y., L. Y. Sun, and J. C. Yue. 2010. “One-dimensional consolidation of saturated clays under time-dependent loadings considering non-Darcy flow.” In GeoShanghai Int. Conf. 2010 Shanghai, Geotechnical Special Publication 200, edited by R. Meier, A. Abbo, and L. Wang, 1–7. Reston, VA: ASCE.
Liu, Z. Y., Y. Y. Xia, M. S. Shi, J. C. Zhang, and X. M. Zhu. 2020a. “One-dimensional elastic viscoplastic consolidation analysis of saturated clay considering gravity stress and Hansbo’s flow.” Chin. J. Geotech. Eng. 42 (2): 221–229.
Liu, Z. Y., J. C. Zhang, S. Q. Duan, Y. Y. Xia, and P. L. Cui. 2020b. “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.
Liu, Z. Y., J. C. Zhang, Y. Y. Xia, and X. M. Zhu. 2019b. “One-dimensional rheological consolidation analysis of saturated soft clay based on piecewise-linear model.” [In Chinese.] J. Tongji Univ.: Nat. Sci. Ed. 47 (5): 640–647. https://doi.org/10.11908/j.issn.0253-374x.2019.05.007.
Mei, G. X., J. Xia, and L. Mei. 2011. “Terzaghi’s one-dimensional consolidation equation and its solution based on asymmetric continuous drainage boundary.” [In Chinese.] Chin. J. Geotech. Eng. 33 (1): 28–31.
Moradi, M., A. Keshavarz, and A. Fazeli. 2019. “One dimensional consolidation of multi-layered unsaturated soil under partially permeable boundary conditions and time-dependent loading.” Comput. Geotech. 107: 45–54. https://doi.org/10.1016/j.compgeo.2018.11.020.
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. 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.
Pu, H. F., Z. Y. Li, D. B. Song, and L. Li. 2019a. “Large-strain nonlinear consolidation model for soil layer with impeded drainage boundaries.” [In Chinese.] J. Huazhong Univ. Sci. Techno.: Nat. Sci. Ed. 47 (9): 107–112.
Pu, H. F., D. B. Song, J. J. Zheng, Y. Zhou, J. Yan, and Z. Y. Li. 2019b. “Non-linear self-weight consolidation model of saturated soft soil under large-strain condition.” [In Chinese.] Rock Soil Mech. 40 (5): 1683–1692.
Pu, H. F., P. Yang, M. M. Lu, Y. Zhou, and J. N. 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.
Schiffman, R. L., and J. R. Stein. 1970. “One-dimensional consolidation of layered systems.” J. Soil Mech. Found. Div. 96 (4): 1499–1504. https://doi.org/10.1061/JSFEAQ.0001453.
Swartzendruber, D. 1962. “Modification of darcy's law for the flow of water in soils.” Soil Sci. 93 (1): 22–29. https://doi.org/10.1097/00010694-196201000-00005.
Taylor, D. W. 1948. Fundamentals of soil mechanics. New York: John Wiley & Sons.
Terzaghi, K. 1925. Erdbaumechanik and bodenphysikalischer grundlage, 175–176. Vienna, Austria: Leipzig Deuticke.
Tong, L. H., J. Wang, S. G. Guo, H. L. Zhu, and C. J. Xu. 2019. “One-dimensional consolidation characteristics of viscoelastic foundation with continuous drainage boundary under time-dependent loading.” [In Chinese.] Rock Soil Mech. 40 (5): 1862–1868. https://doi.org/10.16285/j.rsm.2018.0124.
Wang, S. W., W. Zhu, X. D. Qian, H. Q. Xu, and X. H. Fan. 2017. “Temperature effects on non-Darcy flow of compacted clay.” Appl. Clay Sci. 135: 521–525. https://doi.org/10.1016/j.clay.2016.09.025.
Wu, W. B., M. F. Zong, M. H. El Naggar, G. X. Mei, and R. Z. Liang. 2018. “Analytical solution for one-dimensional consolidation of double-layered soil with exponentially time-growing drainage boundary.” Int. J. Distrib. Sens. Netw. 14 (10): 1550147718806716. https://doi.org/10.1177/1550147718806716.
Xie, K. H. 1996. “One dimensional consolidation analysis of layered soils with impeded boundaries.” [In Chinese.] J. Zhejiang Univ.: Eng. Sci. 30 (5): 567–575.
Zhao, X. D., W. H. Gong, and H. Yang. 2019. “Model for large strain consolidation based on exponential flow law.” Eur. J. Environ. Civ. Eng. https://doi.org/10.1080/19648189.2019.1570873.
Zhou, Y. D., and A. Deng. 2019. “Modelling combined electroosmosis-vacuum-surcharge preloading consolidation considering large-scale deformation.” Comput. Geotech. 109: 46–57. https://doi.org/10.1016/j.compgeo.2019.01.013.
Zong, M. F., W. B. Wu, G. X. Mei, R. Z. Liang, and Y. Tian. 2018. “An analytical solution for one-dimensional nonlinear consolidation of soils with continuous drainage boundary.” [In Chinese.] Chin. J. Rock Mech. Eng. 37 (12): 2829–2838. https://doi.org/10.13722/j.cnki.jrme.2018.0602.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 21 • Issue 5 • May 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Sep 11, 2020
Accepted: Dec 29, 2020
Published online: Mar 11, 2021
Published in print: May 1, 2021
Discussion open until: Aug 11, 2021
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.