Nonlinear Consolidation Analysis of a Saturated Clay Layer with Variable Compressibility and Permeability under Various Cyclic Loadings
Publication: International Journal of Geomechanics
Volume 20, Issue 8
Abstract
This paper presents an analytical solution for one-dimensional nonlinear consolidation of a saturated clay layer with variable compressibility and permeability under various cyclic loadings. Based on the assumption that the initial effective stress was constant with depth and the nonlinear variations of compressibility and permeability were expressed by the logarithm relations (e − log σ′ and e − log kv), two new variables were introduced to the 1D nonlinear consolidation equation. The analytical solutions were derived for trapezoidal, rectangular, and triangular cyclic loadings. The presented solution could degenerate into all of the existing solutions for nonlinear consolidation, which showed the analytical solution proposed in this paper was the most general one for nonlinear consolidation. The validity of the proposed solutions was verified against the numerical results from the finite difference method (FDM). The effects of different parameters on nonlinear consolidation behavior of the saturated clay layer subjected to various cyclic loadings were investigated using the solutions developed. The proposed solutions could be effectively utilized in the analysis of nonlinear consolidation of a saturated clay layer under various cyclic loadings.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by Kim Il Sung University in DPR of Korea.
References
Abbasi, N., H. Rahimi, A. A. Javadi, and A. Fakher. 2007. “Finite difference approach for consolidation with variable compressibility and permeability.” Comput. Geotech. 34 (1): 41–52. https://doi.org/10.1016/j.compgeo.2006.09.003.
Baligh, M. M., and J. N. Levadoux. 1978. “Consolidation theory for cyclic loading.” J. Geotech. Engrgy Div. 104 (4): 415–431.
Berry, P. L., and W. R. Wilkinson. 1969. “The radial consolidation of clay soils.” Geotechnique 19 (2): 253–284. https://doi.org/10.1680/geot.1969.19.2.253.
Cai, Y. Q., X. Y. Geng, and C. J. Xu. 2007. “Solution of one-dimensional finite-strain consolidation of soil with variable compressibility under cyclic loadings.” Comput. Geotech. 34 (1): 31–40. https://doi.org/10.1016/j.compgeo.2006.08.008.
Cheng, D., W. Wang, X. Chen, and Z. Zhang. 2017. “Finite analytic method for one-dimensional nonlinear consolidation under time-dependent loading.” Shock Vib. 2017: 4071268. https://doi.org/10.1155/2017/4071268.
Conte, E., and A. Troncone. 2007. “Nonlinear consolidation of thin layers subjected to time-dependent loading.” Can. Geotech. J. 44 (6): 717–725. https://doi.org/10.1139/t07-015.
Davis, E. H., and G. P. Raymond. 1965. “A non-linear theory of consolidation.” Geotechnique 15 (2): 161–173. https://doi.org/10.1680/geot.1965.15.2.161.
Favaretti, M., and M. Soranzo. 1995. “A simplified consolidation theory in cyclic loading conditions.” In Proc., Int. Symp. on Compression and Consolidation of Clayey Soils, 405–409. Rotterdam, Netherlands: A. A. Balkema.
Geng, X. Y., C. J. Xu, and Y. Q. Cai. 2006. “Non-linear consolidation analysis of soil with variable compressibility and permeability under cyclic loadings.” Int. J. Numer. Anal. Methods Geomech. 30 (8): 803–821. https://doi.org/10.1002/nag.505.
Kim, P., Y. G. Kim, H. B. Myong, C. H. Paek, and J. Ma. 2019a. “Numerical analysis for nonlinear consolidation of saturated soil using lattice Boltzmann method.” Int. Res. J. Eng. Technol. 6 (4): 3611–3618.
Kim, P., Y. G. Kim, C. H. Paek, and J. Ma.2019b. “Lattice Boltzmann method for consolidation analysis of saturated clay.” J. Ocean. Eng. Sci. 4 (3): 193–202. https://doi.org/10.1016/j.joes.2019.04.004.
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, C., J. Huang, L. Wu, J. Lu, and C. Xia. 2018. “Approximate analytical solutions for one-dimensional consolidation of a clay layer with variable compressibility and permeability under a ramp loading.” Int. J. Geomech. 18 (1): 06018032. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001296.
Olson, R. E. 1977. “Consolidation under time-dependent loading.” J. Geotech. Engrgy Div. 103 (1): 55–60.
Razouki, S. S., P. Bonnier, M. Datcheva, and T. Schanz. 2013. “Analytical solution for 1D consolidation under haversine cyclic loading.” Int. J. Numer. Anal. Methods Geomech. 37 (14): 2367–2372. https://doi.org/10.1002/nag.2188.
Razouki, S. S., and T. Schanz. 2011. “One-dimensional consolidation under haversine repeated loading with rest period.” Acta Geotech. 6 (1): 13–20. https://doi.org/10.1007/s11440-010-0132-1.
Schiffman, R. L. 1958. “Consolidation of soil under time-dependent loading and varying permeability.” Highway Res. Board 37: 584–617.
Wilson, N. E., and M. M. Elgohary. 1974. “Consolidation of soils under cyclic loading.” Can. Geotech. J. 11 (3): 420–423. https://doi.org/10.1139/t74-042.
Xie, K., T. Qi, and Y. Dong. 2006. “Nonlinear analytical solution for one-dimensional consolidation of soft soil under cyclic loading.” J. Zhejiang Univ. Sci. A 7 (8): 1358–1364. https://doi.org/10.1631/jzus.2006.A1358.
Zheng, G. Y., P. Li, and C. Y. Zhao. 2013. “Analysis of non-linear consolidation of soft clay by differential quadrature method.” Appl. Clay Sci. 79: 2–7. https://doi.org/10.1016/j.clay.2013.02.025.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 20 • Issue 8 • August 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jun 7, 2019
Accepted: Jan 21, 2020
Published online: May 21, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 21, 2020
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.