Abstract
Relative permeability is an indispensable property for characterizing the unsaturated flow and induced deformation in soils. The widely used Mualem model is inadequate for deformable soils because of its assumption of a rigid pore structure and the resultant unique dependence of the tortuosity factor on the volumetric water content. In this study, a unified relationship between the relative permeability and the effective degree of saturation was proposed for deformable soils by incorporating our newly developed water retention curve model into the original Mualem model, in which a new tortuosity factor was defined using the fractal dimension of flow paths and the mean radius of water-filled pores for representing the effect of pore structure variation. The modified deformation-dependent relative permeability model was verified using test data on five types of soils; the verification revealed a much better performance of the proposed model than the original model, which commonly overestimates the relative permeability of deformable soils. Finally, the proposed model was implemented in a coupled numerical model for examining the unsaturated flow and elastoplastic deformation processes in a soil slope induced by rain infiltration. The numerical results showed that the deformation-dependent nature of relative permeability has a remarkable effect on the elastoplastic deformation in the slope and that neglect of the deformation-dependent behavior of relative permeability causes overestimation of the depth of failure.
Similar content being viewed by others
References
Cho S E, Lee S R. Instability of unsaturated soil slopes due to infiltration. Comput Geotech, 2001, 28: 185–208
Hu R, Chen Y, Zhou C. Modeling of coupled deformation, water flow and gas transport in soil slopes subjected to rain infiltration. Sci China Tech Sci, 2011, 54: 2561–2575
Borja R I, White J A, Liu X, et al. Factor of safety in a partially saturated slope inferred from hydro-mechanical continuum modeling. Int J Numer Anal Methods Geomech, 2012, 36: 236–248
Chapuis R P. Predicting the saturated hydraulic conductivity of soils: a review. Bull Eng Geol Environ, 2012, 71: 401–434
Brooks R H, Corey A T. Hydraulic properties of porous media. Fort Collins, CO: Colorado State University. Hydrology Paper No. 3, 1964
Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour Res, 1976, 12: 513–522
Huang S, Barbour S, Fredlund D. Development and verification of a coefficient of permeability function for a deformable unsaturated soil. Can Geotech J, 1998, 35: 411–425
Assouline S. Modeling the relationship between soil bulk density and the hydraulic conductivity function. Vadose Zone J, 2006, 5: 697–705
Li J, Zhang L, Li X. Soil-water characteristic curve and permeability function for unsaturated cracked soil. Can Geotech J, 2011, 48: 1010–1031
Hu R, Chen Y F, Liu H H, et al. A water retention curve and unsaturated hydraulic conductivity model for deformable soils: Consideration of the change in pore size distribution. Géotechnique, 2013, 63: 1389–1405
Borja R I, White J A. Continuum deformation and stability analyses of a steep hillside slope under rainfall infiltration. Acta Geotechnica, 2010, 5: 1–14
Xiong Y, Bao X, Ye B, et al. Soil–water–air fully coupling finite element analysis of slope failure in unsaturated ground. Soils Found, 2014, 54: 377–395
van Genuchten M T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J, 1980, 44: 892–898
Bear J. Dynamics of fluids in porous media. New York: Eisevier Press, 1972. 312–324
Feder J. Fractals. New York: Plenum Press, 1988
van Genuchten M, Leij F, Yates S. The RETC code for quantifying the hydraulic functions of unsaturated soils. Tech. Report, EPA/600/2-91/065. US Environment Protection Agency, 1991
Leij F J, Alves W J, van Genuchten M, et al. The UNSODA unsaturated soil hydraulic database. version 1-0, 1996. http://www.ussl.ars.usda.gov /MODELS/unsoda.htm
Laliberte G E, Corey A T, Brooks R H. Properties of unsaturated porous media. Hydrology paper No. 17, Colorado State University, Fort Collins, Col. 1966
Gao Y B. The Development of the New Auto-Controlling Apparatus for Measuring Air-Water Movement and the Test Investigation of Watering. Dissertation of Master Degree. Xi’an: Xi’an University of Technology, 2006
Li X, Zhang L M. Characterization of dual-structure pore-size distribution of soil. Can Geotech J, 2009, 46: 129–141
Zhang L, Li X. Microporosity structure of coarse granular soils. J Geotech Geoenviron Eng, 2010, 136: 1425–1436
Assouline S. A model for soil relative hydraulic conductivity based on the water retention characteristic curve. Water Resour Res, 2001, 37: 265–271
Hu R, Liu H H, Chen Y, et al. A constitutive model for unsaturated soils with consideration of inter-particle bonding. Comput Geotech, 2014, 59: 127–144
Hu R, Chen Y F, Liu H H, et al. A coupled stress–strain and hydraulic hysteresis model for unsaturated soils: Thermodynamic analysis and model evaluation. Comput Geotech, 2015, 63: 159–170
Li W, Wei C. An efficient finite element procedure for analyzing three-phase porous media based on the relaxed Picard method. Int J Numer Meth Eng, 2015, 101: 825–846
Ma T T, Wei C F, Chen P, et al. Implicit scheme for integrating constitutive model of unsaturated soils with coupling hydraulic and mechanical behavior. Appl Math Mech, 2014, 35: 1129–1154
Iverson R M. Landslide triggering by rain infiltration. Water Resour Res, 2000, 36: 1897–1910
Collins B D, Znidarcic D. Stability analyses of rainfall induced landslides. ASCE J Geotech Geoenviron Engng, 2004, 130: 362–372
Li W C, Lee L M, Cai H, et al. Combined roles of saturated permeability and rainfall characteristics on surficial failure of homogeneous soil slope. Eng Geol, 2013, 153: 105–113
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Hu, R., Chen, Y., Liu, H. et al. A relative permeability model for deformable soils and its impact on coupled unsaturated flow and elasto-plastic deformation processes. Sci. China Technol. Sci. 58, 1971–1982 (2015). https://doi.org/10.1007/s11431-015-5948-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-015-5948-3