Asymptotic Solution for the One-Dimensional Nonlinear Consolidation Equation Including the Pore Evolution Effect
Publication: International Journal of Geomechanics
Volume 18, Issue 10
Abstract
Soil consolidation causes pore compression and ground subsidence. Accordingly, void ratio, compressibility, and permeability change, thereby affecting the consolidation process. Thus, the consolidation generates a nonlinear coupling interaction with pore compression. Considering the effect of pore evolution on consolidation is important for accurate analysis of the consolidation process. In this article, a one-dimensional (1D) nonlinear consolidation equation is reformulated based on the property relationships related to pore evolution, and a consolidation coefficient is provided as an independent variable. The nonmonotonic change in the consolidation coefficient with an increase in the effective stress is described. In addition, an asymptotic solution for the present consolidation equation is obtained by adopting the Galerkin–iterative method. In this solution, the pore-water pressure is decoupled into two physical quantities: pore-water pressures of Terzaghi’s consolidation theory and pore evolution effect; the latter characterizes the effect of pore evolution on the dissipation of pore-water pressure. On the basis of the present consolidation equation and its asymptotic solution, some complex consolidation characteristics reported in the literature are clarified. The predicted results of the asymptotic solution and the corresponding experimental results have a better consistency compared with the results calculated by Terzaghi’s solution.
Get full access to this article
View all available purchase options and get full access to this article.
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.
Abuel-Naga, H. M., and M. J. Pender. 2012. “Modified Terzaghi consolidation curves with effective stress-dependent coefficient of consolidation.” Géotechnique Lett. 2 (2): 43–48. https://doi.org/10.1680/geolett.12.00005.
Anderson, D. A., J. C. Tannehill, and R. H. Pletcher. 1984. Computational fluid mechanics and heat transfer. New York: Hemisphere.
ASTM. 2004. Standard test methods for one-dimensional consolidation properties of soils using incremental loading. ASTM D2435-04. West Conshohocken, PA: ASTM.
Brandenberg, S. J. 2017. “iConsol.js: JavaScript implicit finite-difference code for nonlinear consolidation and secondary compression.” Int. J. Geomech. 17 (6): 04016149. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000843.
Chan, A. H. C. 2003. “Determination of coefficient of consolidation using a least squares method.” Géotechnique 53 (7): 673–678. https://doi.org/10.1680/geot.2003.53.7.673.
Davis, E. H., and G. P. Raymond. 1965. “A non-linear theory of consolidation.” Géotechnique 15 (2): 161–173. https://doi.org/10.1680/geot.1965.15.2.161.
Dominijanni, A., M. Manaseero, and S. Puma. 2013. “Coupled chemical-hydraulic-mechanical behaviour of bentonites.” Géotechnique 63 (3): 191–205. https://doi.org/10.1680/geot.SIP13.P.010.
Duncan, J. M. 1993. “Limitations of conventional analysis of consolidation settlement.” J. Geotech. Eng. 119 (9): 1333–1359. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:9(1333).
Emmanuel, S., L. M. Anovitz, and R. J. Day-Stirrat. 2015. “Effects of coupled chemo-mechanical processes on the evolution of pore-size distributions in geological media.” Rev. Mineral Geochem. 80 (1): 45–60. https://doi.org/10.2138/rmg.2015.03.
Evans, L. C. 1998. Partial differential equation. Providence, RI: American Mathematical Society.
Fang, Y. G., and B. Li. 2016. “Multiscale problems and analysis of soil mechanics.” Mech. Mater. 103: 55–67. https://doi.org/10.1016/j.mechmat.2016.09.003.
Feng, T. W., and Y. J. Lee. 2001. “Coefficient of consolidation from the linear segment of the t1/2 curve.” Can. Geotech. J. 38 (4): 901–909. https://doi.org/10.1139/t01-008.
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.
Han, G., and R. Wang. 2002. “Richardson extrapolation of iterated discrete Galerkin solution for two-dimensional Fredholm integral equations.” J. Comput. Appl. Math. 139 (1): 49–63. https://doi.org/10.1016/S0377-0427(01)00390-9.
Hayashi, Y., K. Ken’ichirou, and T. Mizuyama. 2006. “Changes in pore size distribution and hydraulic properties of forest soil resulting from structural development.” J. Hydrol. 331 (1–2): 85–102. https://doi.org/10.1016/j.jhydrol.2006.05.003.
Indraratna, B., C. Rujikiatkamjorn, and I. Sathananthan. 2005. “Radial consolidation of clay using compressibility indices and varying.” Can. Geotech. J. 42 (5): 1330–1341. https://doi.org/10.1139/t05-052.
Karunaratne, G. P., S. H. Chew, S. L. Lee, and A. N. Sinha. 2001. “Bentonite: Kaolinite clay liner.” Geosynth. Int. 8 (2): 113–133. https://doi.org/10.1680/gein.8.0189.
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).
Mesri, G. 1971. “Mechanisms controlling the permeability of clays.” Clays Clay Miner. 19 (3): 151–158. https://doi.org/10.1346/CCMN.1971.0190303.
Mesri, G., and Y. K. Choi. 1985. “Settlement analysis of embankments on soft clays.” J. Geotech. Eng. 111 (4): 441–464. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:4(441).
Mesri, G., T. W. Feng, and M. Shahien. 1999. “Coefficient of consolidation by inflection point method.” J. Geotech. Geoenviron. Eng. 125 (8): 716–718. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:8(716).
Mitchell, J. K., and K. Soga. 2005. Fundamentals of soil behavior. Hoboken, NJ: Wiley.
MWR (Ministry of Water Resources). 1999. Standard for soil test measurement. GB/T 50123-1999. Beijing: China Planning Press.
Musso, G., E. Romero, and G. D. Vecchia. 2013. “Double-structure effects on the chemo-hydro-mechanical behaviour of a compacted active clay.” Géotechnique 63 (3): 206–220. https://doi.org/10.1680/geot.SIP13.P.011.
Olson, R. E., and G. Mesri. 1970. “Mechanisms controlling compressibility of clays.” J. Soil Mech. Found. Div. 96 (6): 1863–1878.
Penumadu, D., and J. Dean. 2000. “Compressibility effect in evaluating the pore-size distribution of kaolin clay using mercury intrusion porosimetry.” Can. Geotech. J. 37 (2): 393–405. https://doi.org/10.1139/t99-121.
Poskitt, T. J. 1969. “The consolidation of saturated clay with variable permeability and compressibility.” Géotechnique 19 (2): 234–252. https://doi.org/10.1680/geot.1969.19.2.234.
Robinson, R. G., and M. M. Allam. 1996. “Determination of coefficient of consolidation from early stage of log t plot.” Geotech. Test. J. 19 (3): 316–320. https://doi.org/10.1520/GTJ10358J.
Robinson, R. G., and M. M. Allam. 1998. “Effect of clay mineralogy on coefficient of consolidation.” Clays Clay Miner. 46 (5): 596–600. https://doi.org/10.1346/CCMN.1998.0460514.
Romero, E., and P. H. Simms. 2008. “Microstructure investigation in unsaturated soils: A review with special attention to contribution of mercury intrusion porosimetry and environmental scanning electron microscopy.” Geotech. Geol. Eng. 26 (6): 705–727. https://doi.org/10.1007/s10706-008-9204-5.
Sharma, S. M., A. K. Srivastava, and N. Aravas. 1994. “Higher order crack tip asymptotic solutions for quasi-static steady crack growth in nonlinear viscous solids.” J. Mech. Phys. Solids 42 (2): 159–179. https://doi.org/10.1016/0022-5096(94)90007-8.
Shear, D. L., H. W. Olsen, and K. R. Nelson. 1993. “Effects of desiccation on the hydraulic conductivity versus void ratio relationship fora natural clay.” Transp. Res. Rec. (1369): 130–135.
Singh, S. K. 2005. “Estimating consolidation coefficient and final settlement: Triangular excess pore-water pressure.” J. Geotech. Geoenviron. Eng. 131 (8): 1050–1055. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:8(1050).
Singh, S. K. 2008. “Identifying consolidation coefficient: Linear excess pore-water pressure.” J. Geotech. Geoenviron. Eng. 134 (8): 1205–1209. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:8(1205).
Sridharan, A., and H. B. Nagaraj. 2004. “Coefficient of consolidation and its correlation with index properties of remolded soils.” Geotech. Test. J. 27 (5): 469–474. https://doi.org/10.1520/GTJ10784.
Sun, Z., M. Gao, and X. Yu. 2015. “Vacuum preloading combined with electro-osmotic dewatering of dredger fill using electric vertical drains.” Drying Technol. 33 (7): 847–853. https://doi.org/10.1080/07373937.2014.992529.
Terzaghi, K. 1925. Erdbaumechanik auf bodenphysikalischer grundlage. Leipzig, Vienna: Franz Deuticke.
Terzaghi, K., R. B. Peck, and G. Mersi. 1996. Soil mechanics in engineering practice. 3rd ed. Hoboken, NJ: Wiley.
Wang, D., and N. E. Abriak. 2015. “Compressibility behavior of Dunkirk structured and reconstituted marine soils.” Mar. Georesour. Geotechnol. 33 (5): 419–428. https://doi.org/10.1080/1064119X.2014.950798.
Wang, D., N. E. Abriak, and R. Zentar. 2015. “One-dimensional consolidation of lime-treated dredged harbour sediments.” Eur. J. Environ. Civ. Eng. 19 (2): 199–218. https://doi.org/10.1080/19648189.2014.939309.
Xie, K. H., and C. J. Leo. 2004. “Analytical solutions of one-dimensional large strain consolidation of saturated and homogeneous clays.” Comput. Geotech. 31 (4): 301–314. https://doi.org/10.1016/j.compgeo.2004.02.006.
Xie, K. H., X. Y. Xie, and W. Jiang. 2002. “A study on one-dimensional nonlinear consolidation of double-layered soil.” Comput. Geotech. 29 (2): 151–168. https://doi.org/10.1016/S0266-352X(01)00017-9.
Yang, Y., and A. C. Aplin. 2010. “A permeability–porosity relationship for mudstones.” Mar. Pet. Geol. 27 (8): 1692–1697. https://doi.org/10.1016/j.marpetgeo.2009.07.001.
Zhou, H., Y. G. Fang, R. G. Gu, and C. Zeng. 2011. “Microscopic analysis of saturated soft clay in Pearl River Delta.” J. Cent. South Univ. Technol. 18 (2): 504–510. https://doi.org/10.1007/s11771-011-0724-4.
Zhu, G., and J. H. Yin. 2012. “Analysis and mathematical solutions for consolidation of a soil layer with depth-dependent parameters under confined compression.” Int. J. Geomech. 12 (4): 451–461. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000152.
Information & Authors
Information
Published In
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Nov 10, 2017
Accepted: Mar 16, 2018
Published online: Jul 23, 2018
Published in print: Oct 1, 2018
Discussion open until: Dec 23, 2018
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.