Semianalytical Solution of Consolidation of Composite Ground with Floating Impervious Column in Unsaturated Soil
Publication: Journal of Engineering Mechanics
Volume 148, Issue 10
Abstract
A novel semi-analytical solution is proposed to analyze the consolidation behavior of composite ground with a floating impervious column in unsaturated soil based on the equal-strain hypothesis. The basic governing equations in the reinforced zone and the underlying stratum are first obtained. Using the Laplace transformation and matrix analysis method, a final solution in the Laplace domain is derived. Afterwards, on the basis of Stehfest’s method, an inverse Laplace transform is conducted to derive the solution in the time domain. The effectiveness of the proposed solution is then evaluated against the results of finite difference analysis. Moreover, a sensitivity analysis is performed to assess the effects of area replacement ratio, depth improvement ratio, and column stiffness on the dissipation of excess pore-water/air pressure and the average degree of consolidation. Results show that only vertical seepage occurs during the consolidation process of unsaturated composite ground under a condition of equal-strain. The consolidation rate of unsaturated soft ground can be improved by introducing floating impervious columns. The use of larger area replacement ratio, depth improvement ratio, and column stiffness can increase the consolidation speed and reduce the settlement of composite ground with a floating impervious column in unsaturated soil.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (52178321, 51878185, 52008124, and 52078506), the China Postdoctoral Science Foundation (2020M683210), the Natural Science Foundation of Guangxi Province (2019GXNSFBA185028), the Bagui Scholars Program (2016A31), the China Scholarship Council (201808455023 and 201906660001), the Systematic Project of Guangxi Key Laboratory of Disaster Prevention and Engineering Safety (2019ZDK041), and the Project Supported by the Foundation of Guangdong Key Laboratory of Oceanic Civil Engineering (LMCE202108).
References
Barden, L. 1965. “Consolidation of compacted and unsaturated clays.” Géotechnique 15 (3): 267–286. https://doi.org/10.1680/geot.1965.15.3.267.
Bergado, D., G. Lorenzo, and T. Duangchan. 2005. “Consolidation settlement of reinforced embankment on deep mixing cement piles.” Geotech. Eng. 36 (1): 77–83.
Biot, M. A. 1941. “General theory of three-dimensional consolidation.” J. Appl. Phys. 12 (2): 155–164. https://doi.org/10.1063/1.1712886.
Castro, J., and C. Sagaseta. 2009. “Consolidation around stone columns. Influence of column deformation.” Int. J. Numer. Anal. Methods Geomech. 33 (7): 851–877. https://doi.org/10.1002/nag.745.
Chai, J., and J. P. Carter. 2011. Deformation analysis in soft ground improvement. Berlin: Springer.
Chai, J., and S. Pongsivasathit. 2010. “A method for predicting consolidation settlements of floating column improved clayey subsoil.” Front. Archit. Civ. Eng. China 4 (2): 241–251. https://doi.org/10.1007/s11709-010-0024-3.
Chen, D., P. Ni, X. Zhang, Z. Chen, G. Mei, and J. Feng. 2021. “Consolidation theory of unsaturated soils with vertical drains considering well resistance and smear effect under time-dependent loading.” J. Eng. Mech. 147 (9): 04021055. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001966.
Chen, Z., P. Ni, X. Zhu, D. Chen, and G. Mei. 2022. “Consolidation of unsaturated soil by vertical drain considering smear and well resistance.” Geosynth. Int. 2022 (Apr): 1–12. https://doi.org/10.1680/jgein.1621.00010.
Conte, E. 2006. “Plane strain and axially symmetric consolidation in unsaturated soils.” Int. J. Geomech. 6 (2): 131–135. https://doi.org/10.1061/(ASCE)1532-3641(2006)6:2(131).
Dakshanamurthy, V., and D. G. Fredlund. 1980. Moisture and air flow in an unsaturated soil, 514–532. Reston, VA: ASCE.
Darkshanamurthy, V., D. G. Fredlund, and H. Rahardjo. 1984. “Coupled three-dimensional consolidation theory of unsaturated porous media.” In Proc., 5th Int. Conf. on Expansive Soils. Melbourne, Australia: ARRB.
Fredlund, D. G. 1996. The scope of unsaturated soil mechanics: An overview. Berkshire: Transport Research Laboratory.
Fredlund, D. G., and J. U. Hasan. 1979. “One-dimensional consolidation theory: Unsaturated soils.” Can. Geotech. J. 16 (3): 521–531. https://doi.org/10.1139/t79-058.
Fredlund, D. G., H. Rahardjo, and M. D. Fredlund. 2012. Unsaturated soil mechanics in engineering practice. New York: Wiley.
Han, J. 2015. “Recent research and development of ground column technologies.” Proc. Inst. Civ. Eng. Ground Improv. 168 (4): 246–264. https://doi.org/10.1680/grim.13.00016.
Ho, L., and B. Fatahi. 2015. “Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading.” Comput. Geotech. 67 (Feb): 1–16. https://doi.org/10.1016/j.compgeo.2015.02.011.
Ho, L., and B. Fatahi. 2017. “Axisymmetric consolidation in unsaturated soil deposit subjected to time-dependent loadings.” Int. J. Geomech. 17 (2): 04016046. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000686.
Ho, L., and B. Fatahi. 2018. “Analytical solution to axisymmetric consolidation of unsaturated soil stratum under equal strain condition incorporating smear effects.” Int. J. Numer. Anal. Methods Geomech. 42 (15): 1890–1913. https://doi.org/10.1002/nag.2838.
Ho, L., B. Fatahi, and H. Khabbaz. 2014. “Analytical solution for one-dimensional consolidation of unsaturated soils using eigenfunction expansion method.” Int. J. Numer. Anal. Methods Geomech. 38 (10): 1058–1077. https://doi.org/10.1002/nag.2248.
Ho, L., B. Fatahi, and H. Khabbaz. 2015. “A closed form analytical solution for two-dimensional plane strain consolidation of unsaturated soil stratum.” Int. J. Numer. Anal. Methods Geomech. 39 (15): 1665–1692. https://doi.org/10.1002/nag.2369.
Ho, L., B. Fatahi, and H. Khabbaz. 2016. “Analytical solution to axisymmetric consolidation in unsaturated soils with linearly depth-dependent initial conditions.” Comput. Geotech. 74 (Dec): 102–121. https://doi.org/10.1016/j.compgeo.2015.12.019.
Kim, P., M. Ri, Y. Kim, G. Ri, and H. Myong. 2020. “One-dimensional consolidation analysis of unsaturated soils under cyclic loadings.” Shock Vib. 2020 (1): 1–16. https://doi.org/10.1155/2020/7285323.
Lang, R. Q., and A. W. Yang. 2020. “A quasi-equal strain solution for the consolidation of a rigid pile composite foundation under embankment loading condition.” Comput. Geotech. 117 (Jan): 103232. https://doi.org/10.1016/j.compgeo.2019.103232.
Lu, M., H. Jing, A. Zhou, and K. Xie. 2018. “Analytical models for consolidation of combined composite ground improved by impervious columns and vertical drains.” Int. J. Numer. Anal. Methods Geomech. 42 (6): 871–888. https://doi.org/10.1002/nag.2770.
Lu, M., H. Jing, Y. Zhou, and K. Xie. 2017. “General analytical model for consolidation of stone column–reinforced ground and combined composite ground.” Int. J. Geomech. 17 (6): 04016131. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000836.
Lu, M. M., K. H. Xie, S. Y. Wang, and C. X. Li. 2013. “Analytical solution for the consolidation of a composite foundation reinforced by an impervious column with an arbitrary stress increment.” Int. J. Geomech. 13 (1): 33–40. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000176.
Lu, M. M., K. H. Xie, G. Q. Zhou, and B. Guo. 2011. “Analytical solution for consolidation of composite ground with impervious pile.” Chin. J. Geotech. Eng. 33 (4): 574–579.
Miao, L., F. Wang, and X. Wang. 2010. “One dimensional consolidation of double-layered foundation with multi-level load.” Mar. Georesour. Geotechnol. 28 (1): 1–24. https://doi.org/10.1080/10641190903170440.
Miao, L., X. Wang, and E. Kavazanjian Jr. 2008. “Consolidation of a double-layered compressible foundation partially penetrated by deep mixed columns.” J. Geotech. Geoenviron. Eng. 134 (8): 1210–1214. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:8(1210).
Ni, P., S. Mangalathu, G. Mei, and Y. Zhao. 2018. “Laboratory investigation of pore pressure dissipation in clay around permeable piles.” Can. Geotech. J. 55 (9): 1257–1267. https://doi.org/10.1139/cgj-2017-0180.
Ni, P., Y. Yi, and S. Liu. 2019. “Bearing capacity of composite ground with soil-cement columns under earth fills: Physical and numerical modeling.” Soils Found. 59 (6): 2206–2219. https://doi.org/10.1016/j.sandf.2019.12.004.
Qin, A., D. A. Sun, L. Yang, and Y. Weng. 2010. “A semi-analytical solution to consolidation of unsaturated soils with the free drainage well.” Comput. Geotech. 37 (7): 867–875. https://doi.org/10.1016/j.compgeo.2010.07.006.
Qin, A.-F., G.-J. Chen, Y.-W. Tan, and D.-A. Sun. 2008. “Analytical solution to one-dimensional consolidation in unsaturated soils.” Appl. Math. Mech. 29 (10): 1329–1340. https://doi.org/10.1007/s10483-008-1008-x.
Shan, Z., D. Ling, and H. Ding. 2012. “Exact solutions for one-dimensional consolidation of single-layer unsaturated soil.” Int. J. Numer. Anal. Methods Geomech. 36 (6): 708–722. https://doi.org/10.1002/nag.1026.
Shan, Z., D. Ling, and H. Ding. 2014. “Analytical solution for the 1D consolidation of unsaturated multi-layered soil.” Comput. Geotech. 57 (Apr): 17–23. https://doi.org/10.1016/j.compgeo.2013.11.009.
Shan, Z.-D., D.-S. Ling, and H.-J. Ding. 2013. “Analytical solution for 1D consolidation of unsaturated soil with mixed boundary condition.” J. Zhejiang Univ. Sci. A. 14 (1): 61–70. https://doi.org/10.1631/jzus.A1200167.
Stehfest, H. 1970. “Numerical inversion of Laplace transforms.” Commun. ACM 13 (1): 47–49. https://doi.org/10.1145/361953.361969.
Wang, L., Y. Xu, X. Xia, and Y. He. 2019a. “Semi-analytical solutions of two-dimensional plane strain consolidation in unsaturated soils subjected to the lateral semipermeable drainage boundary.” Int. J. Numer. Anal. Methods Geomech. 43 (17): 2628–2651. https://doi.org/10.1002/nag.2986.
Wang, L., Y. Xu, X. Xia, Y. He, and T. Li. 2019b. “Semi-analytical solutions to two-dimensional plane strain consolidation for unsaturated soils under time-dependent loading.” Comput. Geotech. 109 (Jan): 144–165. https://doi.org/10.1016/j.compgeo.2019.01.002.
Wang, S., P. Ni, Z. Chen, and G. Mei. 2019c. “Consolidation solution of soil around a permeable pipe pile.” Mar. Georesour. Geotechnol. 38 (9): 1097–1105. https://doi.org/10.1080/1064119X.2019.1655119.
Xu, M., P. Ni, G. Mei, and Y. Zhao. 2018. “Time effects on settlement of rigid pile composite foundation: Simplified models.” Int. J. Comput. Methods 15 (7): 1850066. https://doi.org/10.1142/S0219876218500664.
Xu, Y., K.-H. Xie, and H.-T. Lu. 2002. “Consolidation analysis of composite ground with lime-flyash columns by 3D FEM.” Chin. J. Geotech. Eng. 24 (2): 254–256.
Yang, T., Y. Ruan, J. Ni, and C. Li. 2019. “Consolidation analysis of an impervious multi-pile composite ground under rigid foundation.” Eur. J. Environ. Civ. Eng. 25 (7): 1287–1301. https://doi.org/10.1080/19648189.2019.1574608.
Yang, T., J. Z. Yang, and J. Ni. 2014. “Analytical solution for the consolidation of a composite ground reinforced by partially penetrated impervious columns.” Comput. Geotech. 57 (2): 30–36. https://doi.org/10.1016/j.compgeo.2014.01.001.
Ye, G., X. Liao, Y. Gao, and C. Xu. 2008. “Numerical analysis of improved deep soft foundation for highways by use of D-M method.” Chin. J. Geotech. Eng. 30 (2): 232–236.
Zhang, J., X. Cui, D. Huang, Q. Jin, J. Lou, and W. Tang. 2016. “Numerical simulation of consolidation settlement of pervious concrete pile composite foundation under road embankment.” Int. J. Geomech. 16 (1): B4015006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000542.
Zhou, F., Z. Chen, and X. Wang. 2018. “An equal-strain analytical solution for the radial consolidation of unsaturated soils by vertical drains considering drain resistance.” Adv. Civ. Eng. 2018 (1): 1–9. https://doi.org/10.1155/2018/5069159.
Zhou, W.-H. 2013. “Axisymmetric consolidation of unsaturated soils by differential quadrature method.” Math. Probl. Eng. 2013 (Jan): 1–14. https://doi.org/10.1155/2013/497161.
Zhou, Y., G.-Q. Zhou, M.-M. Lu, and X.-Y. Shi. 2018. “Analytical solution for the consolidation process of a stone-column reinforced foundation under partially drained boundaries.” Int. J. Geomech. 18 (1): 06017023. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001053.
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 10 • October 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 6, 2022
Accepted: May 12, 2022
Published online: Aug 1, 2022
Published in print: Oct 1, 2022
Discussion open until: Jan 1, 2023
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