An Analytical Solution for Nonlinear Consolidation of Composite Foundations Improved by Impermeable Columns and Vertical Drains with Time-Dependent Well Resistance
Publication: International Journal of Geomechanics
Volume 24, Issue 10
Abstract
Composite foundations improved by impermeable columns and vertical drains are widely applied in various actual projects. However, few existing studies have reported nonlinear consolidation solutions for such composite foundations. In this study, a nonlinear consolidation model is developed with a time-dependent permeability coefficient for vertical drains. Then, the equation governing the consolidation of the composite foundation is derived, and the corresponding analytical solution is obtained. An iterative approach is adopted to minimize the errors generated in the simplified solution process. Through extensive calculations, the effect of time-dependent well resistance of vertical drains on the consolidation of such composite foundations is analyzed. The results show that ignoring changes in well resistance over time leads to an overestimation of the stress concentration effect of impermeable columns, consolidation of the composite foundation, and settlement rates. Finally, the proposed analytical solution is applied to the settlement calculations for a section of the Huai-Yan Highway and a section of the Lin-Lian Highway. Compared with the consolidation model with constant well resistance, the one with variable well resistance provides results that are more consistent with the measured data.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or codes generated or used during the study are available in a repository online in accordance with funder data retention policies. (Bai and Yang 2021; Chai et al. 2004; Kim et al. 2011; Li et al. 2014; Zhang et al. 2006; Lu et al. 2018).
Acknowledgments
This research was supported by the National Natural Science Foundation of China (Grant No. 42377183).
References
Bai, Y. C., and T. Yang. 2021. “Consolidation analysis of composite ground with undrained columns under flexible foundation.” [In Chinese.] J. Univ. Shanghai Sci. Technol. 43 (6): 560–566. https://doi.org/10.13255/j.cnki.jusst.20210619003.
Basack, S., B. Indraratna, C. Rujikiatkamjorn, and F. Siahaan. 2017. “Modeling the stone column behavior in soft ground with special emphasis on lateral deformation.” J. Geotech. Geoenviron. Eng. 143 (6): 04017016. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001652.
Basack, S., F. Siahaan, B. Indraratna, and C. Rujikiatkamjorn. 2018. “Stone column‒stabilized soft-soil performance influenced by clogging and lateral deformation: Laboratory and numerical evaluation.” Int. J. Geomech. 18 (6): 04018058. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001148.
Bergado, D. T., R. Manivannan, and A. S. Balasubramaniam. 1996. “Proposed criteria for discharge capacity of prefabricated vertical drains.” Geotext. Geomembr. 14 (9): 481–505. https://doi.org/10.1016/S0266-1144(96)00028-3.
Bo, M. W. 2004. “Discharge capacity of prefabricated vertical drain and their field measurements.” Geotext. Geomembr. 22 (1): 37–48. https://doi.org/10.1016/S0266-1144(03)00050-5.
Cao, W. P., and Y. M. Chen. 2007. “Analysis of sliding failure mechanism and treatment for Taihua highway embankment slope over soft soils.” [In Chinese.] Chin. J. Rock Mech. Eng. 26 (7): 1504–1510.
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.
Castro, J., and C. Sagaseta. 2011. “Deformation and consolidation around encased stone columns.” Geotext. Geomembr. 29 (3): 268–276. https://doi.org/10.1016/j.geotexmem.2010.12.001.
Chai, J.-C., N. Miura, and T. Nomura. 2004. “Effect of hydraulic radius on long-term drainage capacity of geosynthetics drains.” Geotext. Geomembr. 22 (1): 3–16. https://doi.org/10.1016/S0266-1144(03)00048-7.
Chai, J.-C., N. Miura, S. Sakajo, and D. Bergado. 1995. “Behavior of vertical drain improved subsoil under embankment loading.” Soils Found. 35 (4): 49–61. https://doi.org/10.3208/sandf.35.4_49.
Chen, Y., A.-F. Hu, S.-L. Xie, Y.-Y. Chen, and Z.-Q. Gong. 2021. “Consolidation theory for the stone column reinforced ground with time-dependent drainage boundary considering the foundation stiffness.” Comput. Geotech. 136: 104218. https://doi.org/10.1016/j.compgeo.2021.104218.
Cimentada, A., A. Da Costa, J. Cañizal, and C. Sagaseta. 2011. “Laboratory study on radial consolidation and deformation in clay reinforced with stone columns.” Can. Geotech. J. 48 (1): 36–52. https://doi.org/10.1139/T10-043.
Deb, K., and A. Behera. 2017. “Rate of consolidation of stone column-improved ground considering change in permeability and compressibility during consolidation.” Appl. Math. Modell. 48: 548–566. https://doi.org/10.1016/j.apm.2017.04.016.
Deb, K., and S. Shiyamalaa. 2016. “Effect of clogging on rate of consolidation of stone column-improved ground by considering particle migration.” Int. J. Geomech. 16 (1): 04015017. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000492.
Deng, Y.-B., K.-H. Xie, M.-M. Lu, H.-B. Tao, and G.-B. Liu. 2013. “Consolidation by prefabricated vertical drains considering the time dependent well resistance.” Geotext. Geomembr. 36: 20–26. https://doi.org/10.1016/j.geotexmem.2012.10.003.
Dingwen, Z., L. Songyu, H. Wenjun, and D. Guangyin. 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.
Doan, S., and B. Fatahi. 2020. “Analytical solution for free strain consolidation of stone column-reinforced soft ground considering spatial variation of total stress and drain resistance.” Comput. Geotech. 118: 103291. https://doi.org/10.1016/j.compgeo.2019.103291.
Doan, S., and B. Fatahi. 2021. “Green’s function analytical solution for free strain consolidation of soft soil improved by stone columns subjected to time-dependent loading.” Comput. Geotech. 136: 103941. https://doi.org/10.1016/j.compgeo.2020.103941.
Feng, J., Z. Chen, D. Chen, T. Xiao, Z. Wu, and G. Mei. 2022. “Semianalytical solution of consolidation of composite ground with floating impervious column in unsaturated soil.” J. Eng. Mech. 148 (10): 04022061. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002143.
Gang, Z., G. Xiaonan, X. Yongli, and L. Guangxin. 2012. “State-of-the-art techniques for ground improvement in China.” [In Chinese.] China Civ. Eng. J. 45 (2): 127–146.
Guo, X. 2016. Analytical study on consolidation theory of soft soils with vertical drains under complicated condition. Hangzhou, China: Zhejiang Univ.
Indraratna, B., C. Rujikiatkamjorn, and I. Sathananthan. 2005. “Radial consolidation of clay using compressibility indices and varying horizontal permeability.” Can. Geotech. J. 42 (5): 1330–1341. https://doi.org/10.1139/t05-052.
Kim, R., S.-J. Hong, M.-J. Lee, and W. Lee. 2011. “Time dependent well resistance factor of PVD.” Mar. Georesour. Geotechnol. 29 (2): 131–144. https://doi.org/10.1080/1064119X.2010.525145.
Lang, R., and A. Yang. 2020. “A quasi-equal strain solution for the consolidation of a rigid pile composite foundation under embankment loading condition.” Comput. Geotech. 117: 103232. https://doi.org/10.1016/j.compgeo.2019.103232.
Lekha, K. R., N. R. Krishnaswamy, and P. Basak. 1998. “Consolidation of clay by sand drain under time-dependent loading.” J. Geotech. Geoenviron. Eng. 124 (1): 91–94. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:1(91).
Lekha, K. R., N. R. Krishnaswamy, and P. Basak. 2003. “Consolidation of clays for variable permeability and compressibility.” J. Geotech. Geoenviron. Eng. 129 (11): 1001–1009. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:11(1001).
Li, Y., J. Ji, W. J. Zhang, and X. Han. 2014. “Analysis of seepage and consolidation properties of rigid-pile composite foundation.” [In Chinese.] J. Build. Struct. 35 (3): 208–214. https://doi.org/ 10.14006/j.jzjgxb.2014.03.028.
Lu, M.-m, Y. Bai, and Y. Kang. 2023. “Consolidation behaviors of multi-reinforcement composite ground considering time-and depth-dependent clogging effects of prefabricated vertical drains.” [In Chinese.] Chin. J. Geotech. Eng. 45 (8): 1564–1573.
Lu, X., and C. Li. 2023a. “Analytical solutions for consolidation of stone column composite foundations considering time-dependent boundary and loading.” Rock Mech. Bull. 2 (3): 100058. https://doi.org/10.1016/j.rockmb.2023.100058.
Lu, X., and C. Li. 2023b. “An analytical solution for nonlinear consolidation of composite foundations improved by stone columns and vertical drains.” Comput. Geotech. 161: 105598. https://doi.org/10.1016/j.compgeo.2023.105598.
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.-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. https://doi.org/10.1139/T09-086.
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, and G.-g. Zhou. 2011. “Analytical solution for consolidation of composite ground with impervious pile.” [In Chinese.] Chin. J. Geotech. Eng. 33 (4): 574–579.
Miura, N., and J. C. Chai. 2000. “Discharge capacity of prefabricated vertical drains confined in clay.” Geosynth. Int. 7 (2): 119–135. https://doi.org/10.1680/gein.7.0169.
Pal, S., and K. Deb. 2019. “Effect of clogging of stone column on drainage capacity during soil liquefaction.” Soils Found. 59 (1): 196–207. https://doi.org/10.1016/j.sandf.2018.10.005.
Sun, J., M. Lu, K. Yang, and B. Han. 2023. “Nonlinear consolidation analysis for composite ground with combined use of impervious columns and prefabricated vertical drains under time-dependent loading.” Comput. Geotech. 161: 105563. https://doi.org/10.1016/j.compgeo.2023.105563.
Tai, P., B. Indraratna, and C. Rujikiatkamjorn. 2018. “Experimental simulation and mathematical modelling of clogging in stone column.” Can. Geotech. J. 55 (3): 427–436. https://doi.org/10.1139/cgj-2017-0271.
Wang, L., A. Zhou, Y. Xu, and X. Xia. 2020. “Consolidation of unsaturated composite ground reinforced by permeable columns.” Comput. Geotech. 125: 103706. https://doi.org/10.1016/j.compgeo.2020.103706.
Wang, L., A. Zhou, Y. Xu, and X. Xia. 2022. “Consolidation of partially saturated ground improved by impervious column inclusion: Governing equations and semi-analytical solutions.” J. Rock Mech. Geotech. Eng. 14 (3): 837–850. https://doi.org/ 10.1016/j.jrmge.2021.09.017.
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: 30–36. https://doi.org/10.1016/j.compgeo.2014.01.001.
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 (1): 87–98. https://doi.org/10.1007/s10064-011-0354-y.
Yoshikuni, H. 1979. Design and control of construction in the vertical drain method. Tokyo: Gihoudou.
Yu, C., A. Zhang, Y. Wang, and W. Ren. 2020. “Analytical solution for consolidation of combined composite foundation reinforced with penetrated impermeable columns and partially penetrated permeable stone columns.” Comput. Geotech. 124: 103606. https://doi.org/10.1016/j.compgeo.2020.103606.
Zhang, D. W., S. Y. Liu, and Z. S. Hong. 2006. “Consolidation calculating method of soft ground improved by DJM-PVD combined method.” In Proc., 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.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 10 • October 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jul 26, 2023
Accepted: Apr 15, 2024
Published online: Aug 2, 2024
Published in print: Oct 1, 2024
Discussion open until: Jan 2, 2025
ASCE Technical Topics:
- Columns
- Composite columns
- Composite materials
- Consolidated soils
- Design (by type)
- Drainage
- Engineering fundamentals
- Engineering materials (by type)
- Foundation settlement
- Foundations
- Geomechanics
- Geotechnical engineering
- Irrigation engineering
- Load and resistance factor design
- Load factors
- Materials engineering
- Measurement (by type)
- Soil mechanics
- Soils (by type)
- Structural design
- Structural engineering
- Structural members
- Structural systems
- Time dependence
- Water and water resources
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.