Analytical Solutions for Consolidation of Combined Composite Ground Reinforced by Short Impervious Columns and Long PVDs
Publication: International Journal of Geomechanics
Volume 23, Issue 10
Abstract
The technology of composite ground has been widely adopted in various engineering projects, and it presents the trend from a single column type to the combined use of multiple types. The combined use of long prefabricated vertical drains (PVDs) and short soil–cement columns (impervious columns) has been proposed and utilized in several ground improvement projects. The research for the consolidation behavior of combined composite ground could facilitate the design and calculation of it in practice. Nevertheless, almost no analytical theories for consolidating such a technique are available in the literature. To fill this gap, an analytical model including multiple long PVDs and short impervious columns is proposed to predict the coupled radial–vertical consolidation of the combined composite ground. The analytical solutions under instantaneously and multistage loading are obtained based on the assumption of equal strain and Darcy’s law. The average degree of consolidation calculated by the current study is then compared with several existing analytical models of composite ground. Furthermore, a parametric study is carried out to investigate the impacts of various factors on consolidation behavior. The results show that the increasing penetration ratio of the short impervious columns can accelerate the consolidation rate. Moreover, the distribution patterns of the construction site, the compression modulus ratio of impervious columns and soil, and the well resistance and smear effect of PVDs can also influence the consolidation behavior of the combined composite ground. Finally, the reasonability of the proposed analytical model is verified by comparing it with the measured test data reported in the literature.
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Acknowledgments
This study is supported by the National Natural Science Foundation of China (Nos. 52178373 and 51878657), which is gratefully acknowledged.
References
Barron, R. A. 1948. “Consolidation of fine-grained soils by drain wells by drain wells.” Trans. ASCE 113 (1): 718–742. https://doi.org/10.1061/TACEAT.0006098.
Chen, L., S. Y. Liu, and Z. S. Hong. 2007. “Study of consolidation calculation of soft ground improved by dry jet mixing combined with vertical drain method.” [In Chinese.] Chin. J. Geotech. Eng. 29 (2): 198–203.
Chu, J., S. W. Yan, and H. Yang. 2000. “Soil improvement by the vacuum preloading method for an oil storage station.” Geotechnique 50 (6): 625–632. https://doi.org/10.1680/geot.2000.50.6.625.
Fang, Z., and J. H. Yin. 2007. “Responses of excess pore water pressure in soft marine clay around a soil–cement column.” Int. J. Geomech. 7 (3): 167–175. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:3(167).
Guo, B., X. N. Gong, M. M. Lu, and Y. Li. 2009. “Theoretical analysis on partiality penetrated and drains foundation with consideration on smear effect.” [In Chinese.] Chin. J. Rock Mech. Eng. 28 (12): 2561–2568.
Indraratna, B., S. Basack, and C. Rujikiatkamjorn. 2013. “Numerical solution of stone column–improved soft soil considering arching, clogging, and smear effects.” J. Geotech. Geoenviron. Eng. 139: 377–394. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000789.
Indraratna, B., I. Sathananthan, C. Rujikiatkamjorn, and A. S. Balasubramaniam. 2005. “Analytical and numerical modeling of soft soil stabilized by prefabricated vertical drains incorporating vacuum preloading.” Int. J. Geomech. 5 (2): 114–124. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:2(114).
Liu, K. W., and R. K. Rowe. 2015. “Numerical modelling of prefabricated vertical drains and surcharge on reinforced floating column-supported embankment behaviour.” Geotext. Geomembr. 43 (6): 493–505. https://doi.org/10.1016/j.geotexmem.2015.05.006.
Liu, S. Y., J. Han, D. W. Zhang, and Z. S. Hong. 2008. “A combined DJM-PVD method for soft ground improvement.” Geosynth. Int. 15 (1): 43–54. https://doi.org/10.1680/gein.2008.15.1.43.
Lu, M. M., H. W. Jing, A. N. Zhou, and K. H. 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. M., D. X. Li, H. W. Jing, and Y. B. Deng. 2019. “Analytical solution for consolidation of band-shaped drain based on an equivalent annular drain.” Int. J. Geomech. 19 (6): 04019043. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001423.
Lu, M. M., S. W. Sloan, B. Indraratna, H. W. Jing, and K. H. Xie. 2016. “A new analytical model for consolidation with multiple vertical drains.” Int. J. Numer. Anal. Methods Geomech. 40 (11): 1623–1640. https://doi.org/10.1002/nag.2508.
Lu, M. M., K. H. Xie, and B. Guo. 2010. “Consolidation theory for a composite foundation considering radial and vertical flows within the column and the variation of soil permeability within the disturbed soil zone.” Can. Geotech. J. 47 (2): 207–217.
Lu, W., and L. Miao. 2015. “A simplified 2-D evaluation method of the arching effect for geosynthetic-reinforced and pile-supported embankments.” Comput. Geotech. 65: 97–103. https://doi.org/10.1016/j.compgeo.2014.11.014.
Nguyen, B. P., T. T. Nguyen, T. H. Y. Nguyen, and T. D. Tran. 2022. “Performance of composite PVD–SC column foundation under embankment through plane-strain numerical analysis.” Int. J. Geomech. 22 (9): 04022155. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002494.
Rujikiatkamjorn, C., and B. Indraratna. 2007. “Analytical solutions and design curves for vacuum-assisted consolidation with both vertical and horizontal drainage.” Can. Geotech. J. 44 (2): 188–200. https://doi.org/10.1139/t06-111.
Si, H. Y., H. T. Chang, Q. Y. Chen, G. B. Ye, and G. L. Tian. 2011. “Centrifugal model tests on D-M method.” [In Chinese.] Chin. J. Geotech. Eng. 33 (S1): 406–409.
Tang, X. W., and K. Onitsuka. 2000. “Consolidation by vertical drains under time-dependent loading.” Int. J. Numer. Anal. Methods Geomech. 24 (9): 739–751. https://doi.org/10.1002/1096-9853(20000810)24:9%3C739::AID-NAG94%3E3.0.CO;2-B.
Tian, Y., W. B. Wu, G. S. Jiang, M. H. El Naggar, G. X. Mei, and P. P. Ni. 2019. “Analytical solutions for vacuum preloading consolidation with prefabricated vertical drain based on elliptical cylinder model.” Comput. Geotech. 116: 103202. https://doi.org/10.1016/j.compgeo.2019.103202.
Wang, R. C., and K. H. Xie. 2002. “General analytical solution for consolidation of double-layered composite ground with granular columns.” [In Chinese.] China J. Highway Transp. 15 (3): 33–37.
Xu, C., G. B. Ye, Z. S. Jiang, and Q. Z. Zhou. 2006. “Research on mechanism of combined improvement of soft soils based on field monitoring.” [In Chinese.] Chin. J. Geotech. Eng. 28 (7): 918–921.
Ye, G. B., J. Chen, H. F. Xing, and M. S. Huang. 2010a. “In-situ tests on consolidation of composite foundation composed of short cement–soil piles and long plastic drainage plates.” [In Chinese.] J. Tongji Univ. (Nat. Sci.) 38 (12): 1725–1729.
Ye, G. B., Z. Zhang, H. F. Xing, M. S. Huang, and H. T. Chang. 2010b. “Consolidation of combined composite foundation.” [In Chinese.] Chin. J. Geotech. Eng. 33 (1): 45–49.
Ye, G. B., Z. Zhang, H. F. Xing, M. S. Huang, and C. Xu. 2012. “Consolidation of a composite foundation with soil–cement columns and prefabricated vertical drains.” Bull. Eng. Geol. Environ. 71: 87–98. https://doi.org/10.1007/s10064-011-0354-y.
Ye, G. B., Q. Zhang, Z. Zhang, and H. T. Chang. 2015. “Centrifugal modeling of a composite foundation combined with soil–cement columns and prefabricated vertical drains.” Soils Found. 55 (5): 1259–1269. https://doi.org/10.1016/j.sandf.2015.09.024.
Zeng, G. X., and K. H. Xie. 1989. “New development of the vertical drain theories.” In Vol. 2 of Proc., 12th Int. Conf. on Soil Mechanics and Foundation Engineering, 1435–1438. Rotterdam, Netherlands: A. A. Balkema.
Zhang, D. W., S. Y. Liu, W. J. Han, and G. Y. Du. 2013. “A combined dry jet mixing-prefabricated vertical drain method for soft ground improvement: A case study.” Mar. Georesour. Geotechnol. 31 (4): 332–347. https://doi.org/10.1080/1064119X.2012.680679.
Zhang, D. W., S. Y. Liu, and Z. S. Hong. 2006. “Consolidation calculation method of soft ground improved by DJM-PVD combined method.” In Ground Modification and Seismic Mitigation, Geotechnical Special Publication 152, edited by A. Porbaha, S. L. Shen, J. Wartman, and J. C. Chai, 29–36. Reston, VA: ASCE.
Zhang, Z., G. B. Ye, and H. F. Xing. 2015. “Consolidation analysis of soft soil improved with short deep mixed columns and long prefabricated vertical drains (PVDs).” Geosynth. Int. 22 (5): 366–379. https://doi.org/10.1680/jgein.15.00018.
Zhuang, Y., and K. Y. Wang. 2017. “Numerical simulation of high-speed railway foundation improved by PVD-DCM method and compared with field measurements.” Eur. J. Environ. Civ. Eng. 21 (11): 1363–1383. https://doi.org/10.1080/19648189.2016.1170728.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 10 • October 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jan 18, 2023
Accepted: Apr 25, 2023
Published online: Jul 26, 2023
Published in print: Oct 1, 2023
Discussion open until: Dec 26, 2023
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