Incorporating Hydromechanical Coupling of Unsaturated Soils into the Analysis of Rainwater-Induced Groundwater Ponding
Publication: International Journal of Geomechanics
Volume 18, Issue 6
Abstract
The moisture contents and coefficients of permeability of partially saturated soils are assumed to follow an exponential function of the pressure head. A partial differential equation is proposed here to describe the groundwater flow in a partially saturated and deformable soil mass based on Darcy’s law, conservation of mass law, and elasticity theory. An accurate solution to the one-dimensional (1D) seepage equation was obtained using the Fourier integral transform. This solution was then applied to examine 1D infiltration into deformable soil that caused the groundwater table to rise. The model developed here can be applied to a 1D seepage problem in deformable soil with recharge at the surface and no flux at the base. As rainwater accumulates up from the lower boundary, the coupling effect increases. The thinner the soil layer, the faster the pressure-head profile builds up in coupled conditions (F < 0, swelling soils). The rise of the groundwater table is closely correlated to the coupling effect and is also affected by the soil properties, rainfall intensity, and depth of the soil layer.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors are grateful for the supports by the Funds for Creative Research Groups of China (No. 41521002), the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (No. SKLGP2016Z017), the National Natural Science Foundation of China (No. 41572313), China Geological Survey Program (No. DD20160271). The first author thanks the Innovative Team of the Chengdu University of Technology. The first author would also like to thank Professor Daichao Sheng for the hospitality shown during a research visit at the Centre for Geotechnical Science and Engineering, University of Newcastle.
References
Basha, H. A. (1999). “Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface.” Water Resour. Res., 35(1), 75–83.
Basha, H. A. (2000). “Multidimensional linearized nonsteady infiltration toward a shallow water table.” Water Resour. Res., 36(9), 2567–2573.
Batu, V. (1983). “Time-dependent linearized two-dimensional infiltration and evaporation from nonuniform and periodic strip sources.” Water Resour. Res., 19(6), 1523–1529.
Chen, J.-M., Tan, Y.-C., and Chen, C.-H. (2001a). “Multidimensional infiltration with arbitrary surface fluxes.” J. Irrig. Drain. Eng., 370–377.
Chen, J. M., Tan, Y.-C., Chen, C.-H., and Parlange, J.-Y. (2001b). “Analytical solutions for linearized Richards equation with arbitrary time-dependent surface fluxes.” Water Resour. Res., 37(4), 1091–1093.
Fredlund, D. G., and Rahardjo, H. (1993). Soil mechanics for unsaturated soils. Wiley, New York.
Garcia, E., Oka, F., and Kimoto, S. (2011). “Numerical analysis of a one-dimensional infiltration problem in unsaturated soil by a seepage–deformation coupled method.” Int. J. Numer. Anal. Methods Geomech., 35(5), 544–568.
Ho, L., and Fatahi, B. (2015). “Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading.” Comput. Geotech., 67, 1–16.
Ho, L., and Fatahi, B. (2016). “One-dimensional consolidation analysis of unsaturated soils subjected to time-dependent loading.” Int. J. Geomech., 04015052.
Ho, L., Fatahi, B., and Khabbaz, H. (2016). “Analytical solution to axisymmetric consolidation in unsaturated soils with linearly depth-dependent initial conditions.” Comput. Geotech., 74, 102–121.
Huang, R. Q., and Wu, L. Z. (2012). “Analytical solutions to 1-D horizontal and vertical water infiltration in saturated/unsaturated soils considering time-varying rainfall.” Comput. Geotech., 39, 66–72.
Ichikawa, Y., and Selvadurai, A. P. S. (2012). Transport phenomena in porous media: Aspects of micro/macro behaviour. Springer-Verlag, Berlin.
Kim, J.-M. (2000). “A fully coupled finite element analysis of water-table fluctuation and land deformation in partially saturated soils due to surface loading.” Int. J. Numer. Methods Eng., 49(9), 1101–1119.
Lloret, A., Gens, A., Batlle, F., and Alonso, E. E. (1987). “Flow and deformation analysis of partially saturated soils.” Proc., 9th European Conf. on Soil Mechanics, E. T. Hanrahan, T. L.L. Orr, and T. F. Widdis, eds., Balkema, Rotterdam, Netherlands, Dublin, 2, 565–568.
Mansuco, C., Jommi, C., and D’Onza, F. (Eds) (2012), Unsaturated soils: Research and applications, Vols. 1and2, Springer-Verlag, Berlin.
Ng, C. W. W., Liu, H. W., and Feng, S. (2015). “Analytical solutions for calculating pore-water pressure in an infinite unsaturated slope with different root architectures.” Can. Geotech. J., 52(12), 1981–1992.
Ozisik, M. N. (1989). Boundary value problems of heat conduction. Dover, New York.
Parlange, J.-Y. et al. (1999). “Analytical approximation to the solutions of Richards’ equation with applications to infiltration, ponding, and time compression approximation.” Adv. Water Resour., 23(2), 189–194.
Philip, J. R. (1969). “Theory of infiltration.” Advances in Hydroscience, V. T. Chow, ed., Vol. 5, Academic Press, Cambridge, MA, 215–296.
Pullan, A. J. (1990). “The quasilinear approximation for unsaturated porous media flow.” Water Resour. Res., 26(6), 1219–1234.
Raats, P. A. C. (1970). “Steady infiltration from line sources and furrows.” Soil Sci. Soc. Am. J., 34(5), 709–714.
Schnellmann, R., Busslinger, M., Schneider, H. R., and Rahardjo, H. (2010). “Effect of rising water table in an unsaturated slope.” Eng. Geol., 114(1–2), 71–83.
Srivastava, R., and Yeh, T.-C. J. (1991). “Analytical solutions for one-dimensional, transient infiltration toward the water table in homogeneous and layered soils.” Water Resour. Res., 27(5), 753–762.
Tartakovsky, D. M., Neuman, S. P., and Lu, Z. (1999). “Conditional stochastic averaging of steady state unsaturated flow by means of Kirchhoff transformation.” Water Resour. Res., 35(3), 731–745.
Tsai, T.-L., and Wang, J.-K. (2011). “Examination of influences of rainfall patterns on shallow landslides due to dissipation of matric suction.” Environ. Earth Sci., 63(1), 65–75.
van Gaalen, J. F., Kruse, S., Lafrenz, W. B., and Burroughs, S. M. (2013). “Predicting water table response to rainfall events, central Florida.” Ground Water, 51(3), 350–362.[
van Genuchten, M. T. (1980). “A closed form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J., 44(5), 892–898.
Warrick, A. W. (1975). “Analytical solutions to the one-dimensional linearized moisture flow equation for arbitrary input.” Soil Sci., 120(2), 79–84.
Warrick, A. W., and Parkin, G. W. (1995). “Analytical solution for one-dimensional drainage: Burgers’ and simplified forms.” Water Resour. Res., 31(11), 2891–2894.
Wu, L. Z., and Selvadurai, A. P. S. (2016). “Rainfall infiltration-induced groundwater table rise in an unsaturated porous medium.” Environ. Earth Sci., 75, 135.
Wu, L. Z., Selvadurai, A. P. S., and Huang, R. Q. (2013). “Two-dimensional coupled hydro-mechanical modeling of water infiltration into a transversely isotropic unsaturated soil region.” Vadose Zone J., 12(4).
Wu, L. Z., and Zhang, L. M. (2009). “Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils.” Int. J. Numer. Anal. Met, 33(6), 773–790.
Wu, L. Z., Selvadurai, A. P. S., Zhang, L. M., Huang, R. Q., and Huang, J. (2016a). “Poro-mechanical coupling influences on potential for rainfall-induced shallow landslides in unsaturated soils.” Adv. Water Res., 98, 114–121.
Wu, L. Z., Sun, P., and Huang, R. Q. (2017). “Analytical analysis of partially saturated infiltration coupled with deformation in a semi-infinite region.” Int. J. Geomech., 06016040.
Wu, L. Z., Zhang, L. M., and Huang, R. Q. (2012). “Analytical solution to 1D coupled water infiltration and deformation in two-layer unsaturated soils.” Int. J. Numer. Anal. Methods Geomech., 36(6), 798–816.
Wu, L. Z., Zhang, L. M., and Li, X. (2016b). “One-dimensional coupled infiltration and deformation in unsaturated soils subjected to varying rainfall.” Int. J. Geomech., 06015004.
Zhan, T. L. T., and Ng, C. W. W. (2004). “Analytical analysis of rainfall infiltration mechanism in unsaturated soils.” Int. J. Geomech., 273–284.
Zhan, T. L. T., Jia, G. W., Chen, Y.-M. Fredlund, D. G, and Li, H. (2013). “An analytical solution for rainfall infiltration into an unsaturated infinite slope and its application to slope stability analysis.” Int. J. Numer. Anal. Methods Geomech., 37(12), 1737–1760.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 18 • Issue 6 • June 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Jun 20, 2017
Accepted: Nov 28, 2017
Published online: Mar 20, 2018
Published in print: Jun 1, 2018
Discussion open until: Aug 20, 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.