Large-Strain Elastic Viscoplastic Consolidation of Vertical Drains with Non-Darcian Flow Incorporating Well Resistance and Smear Zone
Publication: International Journal of Geomechanics
Volume 23, Issue 1
Abstract
Vertical drains improve the consolidation of soft clay, characterized by the large void ratio, high compressibility, and high water content, but the consolidation theory still needs to be improved. This paper investigated the large-strain consolidation of soft clay with vertical drains under free-strain theory, considering the elastic viscoplastic constitutive relation of soft soil, the coupled vertical–radial non-Darcian flow, and the logarithmic relationship of the permeability coefficients. Meanwhile, the nonideal cylindrical unit cell of the soil was captured by taking into account the permeability of the vertical drain decreasing with time (variable well resistance) and the smear effect. The proposed model was verified by degenerating into the cases in the extant literature and applying it to two laboratory tests using the finite-difference method. The most salient finding of the parametric analysis was that the average degree of consolidation curve might show two ups and downs due to the rheological property of soft clay. Several parameters reflecting the impacts of the smear zone and well resistance were also studied. The results demonstrated that some factors related to soil permeability and boundary conditions could enhance the phenomenon of increasing pore pressure.
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 code that support the findings of this study are available from the corresponding author upon reasonable request. All data related to this study are shown in the corresponding figures or tables.
Acknowledgments
The authors sincerely appreciate the support of the National Natural Science Foundation of China (Grant No. 51578511). All authors are highly thankful to the reviewers for their insightful comments to improve the quality of the paper.
References
Barron, R. A. 1948. “Consolidation of fine-grained soils by drain wells by drain wells.” Trans. Am. Soc. Civ. Eng. 113: 718–742. https://doi.org/10.1061/TACEAT.0006098.
Basack, S., and S. Nimbalkar. 2017. “Free strain analysis of the performance of vertical drains for soft soil improvement.” Geomech. Eng. 13 (6): 963–975. https://doi.org/10.12989/gae.2017.13.6.963.
Basu, D., P. Basu, and M. Prezzi. 2006. “Analytical solutions for consolidation aided by vertical drains.” Geomech. Geoeng. 1 (1): 63–71. https://doi.org/10.1080/17486020500527960.
Bo, M. W. 2004. “Discharge capacity of prefabricated vertical drain and their field measurements.” Geotext. Geomembr. 22: 37–48. https://doi.org/10.1016/S0266-1144(03)00050-5.
Cao, Y., J. Yang, G. Xu, and J. Xu. 2018. “Analysis of large-strain consolidation behavior of soil with high water content in consideration of self-weight.” Adv. Civ. Eng. 2018: 6240960. https://doi.org/10.1155/2018/6240960.
Chen, Z., P. Ni, G. Mei, and Y. Chen. 2021. “Semi-analytical solution for consolidation of ground with partially penetrating PVDs under the free-strain condition.” J. Eng. Mech. 147 (2): 04020148. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001884.
Chu, J., M. Bo, and V. Choa. 2006. “Improvement of ultra-soft soil using prefabricated vertical drains.” Geotext. Geomembr. 24 (6): 339–348. https://doi.org/10.1016/j.geotexmem.2006.04.004.
Deng, Y.-B., G.-B. Liu, M.-M. Lu, and K.-h. Xie. 2014. “Consolidation behavior of soft deposits considering the variation of prefabricated vertical drain discharge capacity.” Comput. Geotech. 62: 310–316. https://doi.org/10.1016/j.compgeo.2014.08.006.
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.
Fox, P. J., M. Di Nicola, and D. W. Quigley. 2003. “Piecewise-linear model for large strain radial consolidation.” J. Geotech. Geoenviron. Eng. 129 (10): 940–950. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:10(940).
Geng, X., B. Indraratna, and C. Rujikiatkamjorn. 2012. “Analytical solutions for a single vertical drain with vacuum and time-dependent surcharge preloading in membrane and membraneless systems.” Int. J. Geomech. 12 (1): 27–42. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000106.
Geng, X., and H.-S. Yu. 2017. “A large-strain radial consolidation theory for soft clays improved by vertical drains.” Géotechnique 67 (11): 1020–1028. https://doi.org/10.1680/jgeot.15.T.013.
Gibson, R. E., G. L. England, and M. J. L. Hussey. 1967. “The theory of one-dimensional consolidation of saturated clays.” Géotechnique 17 (3): 261–273. https://doi.org/10.1680/geot.1967.17.3.261.
Gibson, R. E., R. L. Schiffman, and K. W. Cargill. 1981. “The theory of one-dimensional consolidation of saturated clays. II: Finite nonlinear consolidation of thick homogeneous layers.” Can. Geotech. J. 18 (2): 280–293. https://doi.org/10.1139/t81-030.
Guo, X., K.-H. Xie, and Y.-B. Deng. 2014. “Consolidation by prefabricated vertical drains with a threshold gradient.” Math. Probl. Eng. 2014: 410390. https://doi.org/10.1155/2014/410390.
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.
Hu, Y.-Y., W.-H. Zhou, and Y.-Q. Cai. 2014. “Large-strain elastic viscoplastic consolidation analysis of very soft clay layers with vertical drains under preloading.” Can. Geotech. J. 51 (2): 144–157. https://doi.org/10.1139/cgj-2013-0200.
Indraratna, B., and S. Nimbalkar. 2013. “Stress–strain degradation response of railway ballast stabilized with geosynthetics.” J. Geotech. Geoenviron. Eng. 139 (5): 684–700. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000758.
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.
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.
Kim, P., T.-C. Kim, Y.-G. Kim, H.-B. Myong, K.-S. Jon, and S.-H. Jon. 2021. “Nonlinear consolidation analysis of soft soil with vertical drains considering well resistance and smear effect under cyclic loadings.” Geotext. Geomembr. 49 (1): 1440–1446. https://doi.org/10.1016/j.geotexmem.2021.05.012.
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.
Lee, H., T. Kwak, D. Kim, and H. Choi. 2020. “Consideration of radial flow in nonlinear finite-strain self-weight consolidation of dredged soil.” Ocean Eng. 197: 106889. https://doi.org/10.1016/j.oceaneng.2019.106889.
Leo, C. J. 2004. “Equal strain consolidation by vertical drains.” J. Geotech. Geoenviron. Eng. 130 (3): 316–327. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:3(316).
Liu, S.-j., X.-y. Geng, H.-l. Sun, Y.-q. Cai, X.-d. Pan, and L. Shi. 2019. “Nonlinear consolidation of vertical drains with coupled radial–vertical flow considering time and depth dependent vacuum pressure.” Int. J. Numer. Anal. Methods Geomech. 43 (4): 767–780. https://doi.org/10.1002/nag.2888.
Lu, M., S. Wang, S. W. Sloan, D. Sheng, and K. Xie. 2015. “Nonlinear consolidation of vertical drains with coupled radial–vertical flow considering well resistance.” Geotext. Geomembr. 43 (2): 182–189. https://doi.org/10.1016/j.geotexmem.2014.12.001.
Nguyen, B.-P., T.-H. Do, and Y.-T. Kim. 2020. “Large-strain analysis of vertical drain-improved soft deposit consolidation considering smear zone, well resistance, and creep effects.” Comput. Geotech. 123: 103602. https://doi.org/10.1016/j.compgeo.2020.103602.
Nguyen, B.-P., and Y.-T. Kim. 2019. “Radial consolidation of PVD-installed normally consolidated soil with discharge capacity reduction using large-strain theory.” Geotext. Geomembr. 47 (2): 243–254. https://doi.org/10.1016/j.geotexmem.2019.01.008.
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.
Rujikiatkamjorn, C., and B. Indraratna. 2009. “Design procedure for vertical drains considering a linear variation of lateral permeability within the smear zone.” Can. Geotech. J. 46 (3): 270–280. https://doi.org/10.1139/T08-124.
Rujikiatkamjorn, C., and B. Indraratna. 2015. “Analytical solution for radial consolidation considering soil structure characteristics.” Can. Geotech. J. 52 (7): 947–960. https://doi.org/10.1139/cgj-2014-0277.
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.
Walker, R., and B. Indraratna. 2006. “Vertical drain consolidation with parabolic distribution of permeability in smear zone.” J. Geotech. Geoenviron. Eng. 132 (7): 937–941. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:7(937).
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, J., J. Ding, H. Wang, and C. Mou. 2020. “Large-strain consolidation model considering radial transfer attenuation of vacuum pressure.” Comput. Geotech. 122: 103498. https://doi.org/10.1016/j.compgeo.2020.103498.
Xu, C., Z. Liu, J. Zhang, and J. Huang. 2021. “Analysis of large-strain elastic viscoplastic consolidation for soft clay with vertical drains considering non-Darcian flow.” Appl. Math. Modell. 92: 770–784. https://doi.org/10.1016/j.apm.2020.11.038.
Yao, Y. P., L. M. Kong, and J. Hu. 2013. “An elastic–viscous–plastic model for overconsolidated clays.” Sci. China Technol. Sci. 56 (2): 441–457. https://doi.org/10.1007/s11431-012-5108-y.
Yin, J.-H., and J. Graham. 1989. “Viscous–elastic–plastic modelling of one-dimensional time-dependent behaviour of clays.” Can. Geotech. J. 26 (2): 199–209. https://doi.org/10.1139/t89-029.
Yin, J., J. Graham, J. I. Clark, and L. Guo. 1994. “Modelling unanticipated pore-water pressures in soft clays.” Can. Geotech. J. 31 (5): 773–778. https://doi.org/10.1139/t94-088.
Zhang, Y., W. Wu, G. Mei, and L. Duan. 2019. “Three-dimensional consolidation theory of vertical drain based on continuous drainage boundary.” J. Civ. Eng. Manage. 25 (2): 145–155. https://doi.org/10.3846/jcem.2019.8071.
Zhou, Y., P. Wang, L. Shi, Y. Cai, and J. Wang. 2021. “Analytical solution on vacuum consolidation of dredged slurry considering clogging effects.” Geotext. Geomembr. 49 (3): 842–851. https://doi.org/10.1016/j.geotexmem.2020.12.013.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 23 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 13, 2022
Accepted: Jul 27, 2022
Published online: Oct 21, 2022
Published in print: Jan 1, 2023
Discussion open until: Mar 21, 2023
ASCE Technical Topics:
- Consolidated soils
- Design (by type)
- Drainage
- Elastic analysis
- Engineering fundamentals
- Geomechanics
- Geotechnical engineering
- Irrigation engineering
- Load and resistance factor design
- Load factors
- Material mechanics
- Materials engineering
- Permeability (soil)
- Soft soils
- Soil mechanics
- Soil properties
- Soils (by type)
- Strain
- Structural analysis
- Structural design
- Structural engineering
- 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.