Technical Papers
May 9, 2024

Analytical Solution for Radial Consolidation of Combined Electroosmotic, Vacuum, and Surcharge Preloading Considering Smear Effects

Publication: International Journal of Geomechanics
Volume 24, Issue 7

Abstract

The combining of electroosmotic, vacuum, and surcharge preloading is an emerging technique for soft foundation treatment. Considering smear effects and free strain, an analytical solution for the radial consolidation of combined electroosmotic, vacuum, and surcharge preloading was derived based on the characteristic function method and Bessel function. The correctness of the proposed solution was verified by comparing with existing solutions and numerical results. On this basis, the influence of smear effects, vacuum pressure, surcharge load, and applied voltage on the consolidation characteristics of soil was further analyzed. The results showed that when the electroosmosis permeability coefficient of the undisturbed zone was greater than that of the smear zone, the excess pore-water pressure at the interface between the smear zone and the undisturbed zone increased in the early stage of consolidation owing to the electroosmotic effect. Vacuum pressure had a great influence on soil consolidation in the smear zone, while applied voltage had a great influence on the consolidation of soil in the undisturbed zone.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

This research is supported by the National Natural Science Foundation of China (Grant Nos. 52178371, 52178321, 52108322, and 51878634) and the Outstanding Youth Project of the Natural Science Foundation of Zhejiang Province (LR21E080005). The China Postdoctoral Science Foundation Funded Project (Grant No. 2022M712964), the China Scholarship Council (CSC) (Grant No. 201906660001), and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 23KJB560004) are also acknowledged.
Author contributions: Mengfan Zong: Conceptualization, Writing—Original draft, Formal analysis. Lichen Li: Formal analysis, Data Curation, Writing—Review and Editing. Wenbing Wu: Project administration, Funding acquisition, Conceptualization, Writing—Review and Editing. Yi Zhang: Formal analysis, Data Curation. Guoxiong Mei: Conceptualization, Writing—Review and Editing.

References

Bergado, D. T., P. Jamsawang, P. Jongpradist, S. Likitlersuang, C. Pantaeng, N. Kovittayanun, and F. Baez. 2022. “Case study and numerical simulation of PVD improved soft Bangkok clay with surcharge and vacuum preloading using a modified air‒water separation system.” Geotext. Geomembr. 50 (1): 137–153. https://doi.org/10.1016/j.geotexmem.2021.09.009.
Bjerrum, L., J. Moum, and O. Eide. 1967. “Application of electro-osmosis to a foundation problem in a Norwegian quick clay.” Géotechnique 17 (3): 214–235. https://doi.org/10.1680/geot.1967.17.3.214.
Chen, D. Q., P. P. Ni, X. L. Zhang, Z. Chen, G. X. Mei, and J. X. Feng. 2021a. “Consolidation theory of unsaturated soils with vertical drains considering well resistance and smear effect under time-dependent loading.” J. Eng. Mech. 147 (9): 04021055.
Chen, Z., P. P. Ni, G. X. Mei, and Y. F. Chen. 2021b. “Semi-analytical solution for consolidation of ground with partially penetrating PVDs under the free-strain condition.” J. Eng. Mech. 147 (2): 04020148.
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. 29 (3): 1–12.
Chew, S. H., G. P. Karunaratne, V. M. Kuma, L. H. Lim, M. L. Toh, and A. M. Hee. 2004. “A field trial for soft clay consolidation using electric vertical drains.” Geotext. Geomembr. 22 (1–2): 17–35. https://doi.org/10.1016/S0266-1144(03)00049-9.
Chu, J., and S. W. Yan. 2005. “Estimation of degree of consolidation for vacuum preloading projects.” Int. J. Geomech. 5 (2): 158–165. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:2(158).
Deng, A., and Y. Zhou. 2016a. “Modeling electroosmosis and surcharge preloading consolidation. I: Model formulation.” J. Geotech. Geoenviron. Eng. 142 (4): 04015093. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001417.
Deng, A., and Y. Zhou. 2016b. “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.
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.
Esrig, M. I. 1968. “Pore pressures, consolidation, and electrokinetics.” J. Soil Mech. Found. Div. 94 (4): 899–921. https://doi.org/10.1061/JSFEAQ.0001178.
Estabragh, A. R., M. Naseh, and A. A. Javadi. 2014. “Improvement of clay soil by electro-osmosis technique.” Appl. Clay Sci. 95: 32–36. https://doi.org/10.1016/j.clay.2014.03.019.
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.
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.
Indraratna, B., C. Bamunawita, and H. Khabbaz. 2004. “Numerical modeling of vacuum preloading and field applications.” Can. Geotech. J. 41 (6): 1098–1110. https://doi.org/10.1139/t04-054.
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., K. Kianfar, and C. Rujikiatkamjorn. 2012. “Laboratory evaluation of coefficient of radial consolidation based on pore-water-pressure dissipation and settlement.” Geotech. Test. J. 36 (1): 107–118. https://doi.org/10.1520/GTJ20120032.
Jiang, W., S. Ge, X. Huang, Z. Chen, and J. Li. 2022. “General analytical solutions for one-dimensional large strain consolidation of soft soils under electro-osmosis-surcharge preloading.” Soils Found. 62 (5): 101211. https://doi.org/10.1016/j.sandf.2022.101211.
Kim, P., T.-C. Kim, Y.-G. Kim, H.-B. Myong, K.-S. Jon, and S.-H. Jon. 2021a. “Nonlinear consolidation analysis of soft soil with vertical drains considering well resistance and smear effect under cyclic loadings.” Geotext. Geomembr. 49 (5): 1440–1446. https://doi.org/10.1016/j.geotexmem.2021.05.012.
Kim, P., M.-C. Ri, K.-S. Ri, M.-C. Rim, and S.-G. Jong. 2021b. “Radial consolidation analysis of unsaturated soil with vertical drains under various cyclic loadings.” Int. J. Numer. Anal. Methods Geomech. 45 (11): 1549–1568. https://doi.org/10.1002/nag.3213.
Liu, Y., J.-J. Zheng, and J.-T. Lu. 2023b. “An analytical model for 2D consolidation of unsaturated soil with semi-permeable boundaries considering self-weight stress and time-dependent loading.” Int. J. Numer. Anal. Methods Geomech. 47: 903–935. https://doi.org/10.1002/nag.3498.
Liu, Y., J.-J. Zheng, L. You, J.-T. Lu, L. Cui, W.-Y. Yang, and Z.-F. Huang. 2022a. “An analytical solution for 2D plane strain consolidation in unsaturated soils with lateral and vertical semipermeable drainage boundaries under time-dependent loading.” Int. J. Geomech. 22 (12): 06022032. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002508.
Liu, Y., J. J. Zheng, X. Zhao, W. Cao, and Z. Huang. 2022b. “A closed-form solution for axisymmetric electro-osmotic consolidation considering smear effects.” Acta Geotech. 17 (6): 2597–2609. https://doi.org/10.1007/s11440-021-01353-z.
Liu, Y., J. J. Zheng, X. Zhao, and L. You. 2023a. “Analytical model for two-dimensional electro-osmosis-enhanced preloading consolidation of unsaturated soil.” Acta Geotech. 18: 1093–1110. https://doi.org/110.1007/s11440-022-01585-7.
Lu, M., and J. Sun. 2022. “Analytical model for consolidation of soft ground improved by PVDs with air-boosted system.” Comput. Geotech. 151: 104968. https://doi.org/10.1016/j.compgeo.2022.104968.
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.
Lu, M. M., K. H. Xie, and S. Y. Wang. 2011. “Consolidation of vertical drain with depth-varying stress induced by multi-stage loading.” Comput. Geotech. 38 (8): 1096–1101. https://doi.org/10.1016/j.compgeo.2011.06.007.
Nguyen, B.-P. 2021. “Nonlinear analytical modeling of vertical drain-installed soft soil considering a varied discharge capacity.” Geotech. Geol. Eng. 39 (1): 119–134. https://doi.org/10.1007/s10706-020-01477-1.
Shang, J. Q. 1998. “Electroosmosis-enhanced preloading consolidation via vertical drains.” Can. Geotech. J. 35 (3): 491–499. https://doi.org/10.1139/t98-018.
Su, J. Q., and Z. Wang. 2003. “The two-dimensional consolidation theory of electro-osmosis.” Géotechnique 53 (8): 759–763. https://doi.org/10.1680/geot.2003.53.8.759.
Tang, M., and J. Q. Shang. 2000. “Vacuum preloading consolidation of Yaoqiang Airport runway.” Géotechnique 50 (6): 613–623. https://doi.org/10.1680/geot.2000.50.6.613.
Tian, Y., G. Jiang, W. Wu, M. Wen, M. H. El Naggar, and G. Mei. 2022. “Elliptical cylindrical equivalent model for consolidation of unsaturated soil improved by PVD.” Int. J. Numer. Anal. Methods Geomech. 46 (17): 3123–3153. https://doi.org/10.1002/nag.3443.
Wan, T.-Y., and J. K. Mitchell. 1976. “Electro-osmotic consolidation of soils.” J. Geotech. Eng. Div. 102 (5): 473–491. https://doi.org/10.1061/AJGEB6.0000270.
Wang, J., H. Fu, F. Liu, Y. Cai, and J. Zhou. 2018. “Influence of electro-osmosis activation time on vacuum electro-osmosis consolidation of a dredged slurry.” Can. Geotech. J. 55 (1): 147–153. https://doi.org/10.1139/cgj-2016-0687.
Wang, L., P. Huang, S. Liu, and E. Alonso. 2020. “Analytical solution for nonlinear consolidation of combined electroosmosis-vacuum-surcharge preloading.” Comput. Geotech. 121: 103484. https://doi.org/10.1016/j.compgeo.2020.103484.
Wang, L. J., Y. M. Wang, S. H. Liu, and P. H. Huang. 2021. “Analytical investigation of electroosmotic consolidation in unsaturated soils considering the coupling effect and a nonuniform initial water content.” Int. J. Geomech. 21 (8): 06021018. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002053.
Wu, H., and L. M. Hu. 2012. “Analytical models of the coupling of vacuum preloading and electro-osmosis consolidation for ground stabilization.” [In Chinese.] J. Tsinghua Univ. (Sci. Tech.) 52 (2): 182–185.
Wu, H., and L. Hu. 2013. “Analytical solution for axisymmetric electro-osmotic consolidation.” Géotechnique 63 (12): 1074–1079. https://doi.org/10.1680/geot.12.P.133.
Wu, H., L. Hu, W. Qi, and Q. Wen. 2017a. “Analytical solution for electroosmotic consolidation considering nonlinear variation of soil parameters.” Int. J. Geomech. 17 (5): 06016032. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000821.
Wu, H., W. Qi, L. Hu, and Q. Wen. 2017b. “Electro-osmotic consolidation of soil with variable compressibility, hydraulic conductivity and electro-osmosis conductivity.” Comput. Geotech. 85: 126–138. https://doi.org/10.1016/j.compgeo.2016.12.026.
Zhao, X.-D., Y. Liu, and W.-H. Gong. 2020. “Analytical solution for one-dimensional electro-osmotic consolidation of double-layered system.” Comput. Geotech. 122: 103496. https://doi.org/10.1016/j.compgeo.2020.103496.
Zhou, T., T. Y. Li, L. Wang, M. J. Wen, and Y. Chen. 2022. “Analytical solution for the consolidation of unsaturated vertical drain foundation under depth-dependent initial conditions.” Int. J. Numer. Anal. Methods Geomech. 46: 2754–2769. https://doi.org/10.1002/nag.3425.
Zhou, Y., A. Deng, and J. Y. Fu. 2019. “Modelling electro-osmosis-surcharge preloading combined consolidation of unsaturated soils.” Comput. Geotech. 114: 103145. https://doi.org/10.1016/j.compgeo.2019.103145.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 24Issue 7July 2024

History

Received: May 9, 2023
Accepted: Jan 31, 2024
Published online: May 9, 2024
Published in print: Jul 1, 2024
Discussion open until: Oct 9, 2024

Permissions

Request permissions for this article.

Authors

Affiliations

Mengfan Zong [email protected]
Lecturer, School of Civil and Ocean Engineering, Jiangsu Ocean Univ., Lianyungang, Jiangsu 222005, China. Email: [email protected]
Professor, Faculty of Engineering, China Univ. of Geosciences, Wuhan, Hubei 430074, China (corresponding author). Email: [email protected]
Professor, Faculty of Engineering, China Univ. of Geosciences, Wuhan, Hubei 430074, China. Email: [email protected]
Lecturer, School of Civil and Ocean Engineering, Jiangsu Ocean Univ., Lianyungang, Jiangsu 222005, China. Email: [email protected]
Guoxiong Mei [email protected]
Professor, Ocean College, Zhejiang Univ., Zhoushan, Zhejiang 316021, China. Email: [email protected]

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.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share