Represention of anisotropy in unsaturated permeabilities for soils based on pore connectivity-tortuosity parameter
ZHANG Zhao1, LIU Feng-yin1, QI Ji-lin1, 2, CHAI Jun-rui3, 4, WANG Shuang1, LI Hui-yang5, GAO Yong-bao6
1. Institute of Geotechnical Engineering, Xi'an University of Technology, Xi'an 710048, China; 2. College of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China; 3. State Key Laboratory Base of Eco-hydraulics in Northwest Arid Region of China (Xi'an University of Technology), Xi'an 710048, China; 4. College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, China; 5. Sinohydro Foundation Engineering Co., Ltd., Tianjin 301700, China; 6. CCCC First Highway Consultants Co., Ltd., Xi'an 710065, China
Abstract:Accurate characterization of the anisotropy in unsaturated permeability for soils is significant in simulating flow and contaminant transport. Based on the Mualem’s unsaturated permeability function, the power type expression for the relationship between the anisotropy coefficient and the effective degree of saturation is derived by introducing the pore connectivity-tortuosity parameter so as to describe the nine types of the anisotropy in unsaturated permeability. In the process of anisotropy coefficients varying with the effective degree of saturation, there exists a critical point at which the dominance of flow direction switches. This expression is then validated using the numerical test results of unsaturated permeability of a pore network for modeling the soil samples in the previous literatures. Combining with the Van Genuchten-Mualem function, this expression can be finally used to represent the effect of matric suction on the anisotropy in permeability for four soils in the existing literatures.
张昭, 刘奉银, 齐吉琳, 柴军瑞, 王爽, 李会勇, 高永宝. 基于孔隙连通-迂曲参数表征土的非饱和渗透各向异性[J]. 岩土工程学报, 2018, 40(S1): 147-152.
ZHANG Zhao, LIU Feng-yin, QI Ji-lin, CHAI Jun-rui, WANG Shuang, LI Hui-yang, GAO Yong-bao. Represention of anisotropy in unsaturated permeabilities for soils based on pore connectivity-tortuosity parameter. Chinese J. Geot. Eng., 2018, 40(S1): 147-152.
[1] DULLIEN F A.Porous media: Fluid transport and pore structure[M]. San Diego: Academic Press, 1991. [2] WARRICK A W.Effective unsaturated hydraulic conductivity for One-dimensional structured heterogeneity[J]. Water Resource Research, 2005, 41(9): 299-317. [3] YEH T-C J, GELHAR L W, GUTJAHR A L. Stochastic analysis of unsaturated flow in heterogeneous soils 2. statistically anisotropic media[J]. Water Resource Research, 1985, 21(4): 465-471. [4] GREEN T R, FREYBERG D L.State-dependent anisotropy: Comparisons of quasi-analytical solutions with stochastic results for steady gravity drainage[J]. Water Resource Research, 1995, 31(1): 2201-2211. [5] BEAR J, BRAESTER C, MENIER P C.Effective and relative permeabilities of anisotropie porous media[J]. Transport in Porous Media, 1987, 2(3): 301-316. [6] LEWANDOWSKA J, SZYMKIEWICZ A, BURZYNSKI K, et al.Modeling of unsaturated water flow in double-porosity soils by the homogenization approach[J]. Advances in Water Resources, 2004, 27(3): 283-296. [7] MUALEM Y.Anisotropy of unsaturated soils[J]. Soil Science Society of America Journal, 1984, 48(3): 505-509. [8] PRUESS K.A composite medium approximation for unsaturated flow in layered sediments[J]. Journal of Contaminant Hydrology, 2004, 70(3/4): 225-247. [9] ZHU J.Effect of layered structure on anisotropy of unsaturated soils[J]. Soil Science, 2012, 177(2): 139-146. [10] DENG P, ZHU J.Anisotropy of unsaturated layered soils: impact of layer composition and domain size[J]. Soil Science Society of America Journal, 2015, 79(2): 487-494. [11] ASSOULINE S, OR D.Anisotropy factor of saturated and unsaturated soils[J]. Water Resources Research, 2006, 42(12): 1675-1679. [12] STEPHENS D B, HEERMANN S.Dependence of anisotropy on saturation in a stratified sand[J]. Water Resource Research, 1988, 24(5): 770-778. [13] MCCORD J T, STEPHENS D B, WILSON J L.Hysteresis and state-dependent anisotropy in modeling unsaturated hillslope hydrologic processes[J]. Water Resource Research, 1991, 27(7): 1501-1518. [14] 徐永福, 黄寅春. 分形理论在研究非饱和土力学性质中的应用[J]. 岩土工程学报, 2006, 28(5): 635-638. (XU Yong-fu, HUANG Yin-chun.Fractal-textured soils and their unsaturated mechanical properties[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(5): 635-638. (in Chinese)) [15] 蔡国庆, 盛岱超, 周安楠. 考虑初始孔隙比影响的非饱和土相对渗透系数方程[J]. 岩土工程学报, 2014, 36(5): 827-835. (CAI Guo-qing, SHENG Dai-chao, ZHOU An-nan.Approach for predicting the relative coefficient of permeability of unsaturated soils with different initial void ratios[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(5): 827-835. (in Chinese)) [16] MUALEM Y.A new model for predicting the hydraulic conductivity of unsaturated porous media[J]. Water Resources Research, 1976, 12(3): 513-522. [17] HU R, CHEN Y F, LIU H H, et al.A relative permeability model for deformable soils and its impact on coupled unsaturated flow and elasto-plastic deformation processes[J]. Science China-Technological Sciences, 2015, 58(11): 1971-1982. [18] LALIBERTE G E, COREY A T, BROOKS R H.Properties of unsaturated porous media[R]. Fort Collins: Colorado State University, 1966. [19] 梁燕, 邢鲜丽, 李同录, 等. 晚更新世黄土渗透性的各向异性及其机制研究[J]. 岩土力学, 2012, 33(5): 1313-1318. (LIANG Yan, XING Xian-li, LI Tong-lu, et al.Study of the anisotropic permeability and mechanism of Q3 loess[J]. Rock and Soil Mechanics, 2012, 33(5): 1313-1318. (in Chinese)) [20] VAN GENUCHTEN M T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J]. Soil Science Society of America Journal, 1980, 44(5): 892-898.