Hydro-mechanical double-yield-surface model for unsaturated sand and clay
LI Jian1, LIU Kai2, YIN Zhen-yu2, CUI Yu-jun3, YIN Jian-hua2
1. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China; 2. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China; 3. Ecole des Ponts ParisTech, Laboratoire Navier/CERMES, Paris, France
Abstract:Hydro-mechanical coupling behavior analysis with a sophisticated model for both unsaturated sand and clay is still a challenge. In this study, a hydro-mechanical coupling model with two plastic deformation mechanisms, i.e., loading collapse and shear sliding, for unsaturated soils is formulated using the Bishop’s stress as the stress variable and using the void ratio and the effective degree of saturation as the state variables. An expression for the critical state line related to the effective degree of saturation in the void ratio-soil skeleton stress semilog plane is explicitly implemented, which is combined with a non-associated flow rule for the shear sliding yield surface to guarantee the satisfactory simulation of the dilation or contraction during shear for unsaturated soils including sand and clay. The predictive capability of the model to reproduce the main features of unsaturated soil behavior is analyzed by simulating the triaxial tests on silty sand and kaolin.
李舰, 刘凯, 尹振宇, 崔玉军, 殷建华. 非饱和砂土及黏土的水-力耦合双屈服面模型[J]. 岩土工程学报, 2020, 42(1): 72-80.
LI Jian, LIU Kai, YIN Zhen-yu, CUI Yu-jun, YIN Jian-hua. Hydro-mechanical double-yield-surface model for unsaturated sand and clay. Chinese J. Geot. Eng., 2020, 42(1): 72-80.
[1] 陈正汉. 重塑非饱和黄土的变形、强度、屈服和水量变化特性[J]. 岩土工程学报, 1999, 21(1): 82-90. (CHEN Zheng-han.Deformation, strength, yield and moisture change of a remolded unsaturated loess[J]. Chinese Journal of Geotechnical Engineering, 1999, 21(1): 82-90. (in Chinese)) [2] 黄海, 陈正汉, 李刚. 非饱和土在p-s平面上的屈服轨迹及土-水特征曲线的探讨[J]. 岩土力学, 2000, 21(4): 316-321. (HUANG Hai, CHEN Zheng-han, LI Gang.A study on yield locus of unsaturated soil on p-s plane and soil-water characteristic curve[J]. Rock and Soil Mechanics, 2000, 21(4): 316-321. (in Chinese)) [3] 詹良通, 吴宏伟. 吸力对非饱和膨胀土抗剪强度及剪胀特性的影响[J]. 岩土工程学报, 2007, 29(1): 82-87. (ZHAN Liang-tong, NG Charles W W. Effect of suction on shear strength and dilatancy of an unsaturated expansive clay[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(1): 82-87. (in Chinese)) [4] 姚仰平, 牛雷, 韩黎明, 等. 超固结非饱和土的试验研究[J]. 岩土力学, 2011, 32(6): 1601-1606. (YAO Yang-ping, NIU Lei, HAN Li-ming, et al.Experimental study of behaviors of overconsolidated unsaturated clays[J]. Rock and Soil Mechanics, 2011, 32(6): 1601-1606. (in Chinese)) [5] 陈存礼, 张登飞, 董玉柱, 等. 常含水率三轴条件下非饱和原状黄土的吸力和力学特性[J]. 岩土工程学报, 2014, 36(7): 1195-1202. (CHEN Cun-li, ZHANG Deng-fei, DONG Yu-zhu, et al.Suction and mechanical behaviours of unsaturated intact loess from constant water content triaxial tests[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(7): 1195-1202. (in Chinese)) [6] MA T, WEI C, WEI H.Hydraulic and mechanical behavior of unsaturated silt: experimental and theoretical characterization[J]. International Journal of Geomechanics, 2016, 16(6): D4015007. [7] 高登辉, 陈正汉, 郭楠, 等. 干密度和基质吸力对重塑非饱和黄土变形与强度特性的影响[J]. 岩石力学与工程学报, 2017, 36(3): 736-744. (GAO Deng-hui, CHEN Zheng-han, GUO Nan, et al.The influence of dry density and matric suction on the deformation and the strength characteristics of the remolded unsaturated loess soils[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(3): 736-744. (in Chinese)) [8] 徐筱, 赵成刚. 高吸力下黏性土的抗剪强度和体变特性[J]. 岩土力学, 2018, 39(5): 1598-1610. (XU Xiao, ZHAO Cheng-gang.Shear strength and volume change behavior of clay-rich soil at high suctions[J]. Rock and Soil Mechanics, 2018, 39(5): 1598-1610. (in Chinese)) [9] 陈皓, 吕海波, 陈正汉, 等. 考虑温度影响的高庙子膨润土强度与变形特性试验研究[J]. 岩石力学与工程学报, 2018, 37(8): 1962-1979. (CHEN Hao, LÜ Hai-bo, CHEN Zheng-han, et al.Strength and volume change of buffer material under high temperature and pressure[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(8): 1962-1979. (in Chinese)) [10] 朱青青, 苗强强, 陈正汉, 等. 非饱和含黏砂土的弹塑性剪胀特性研究[J]. 岩土工程学报, 2018, 40(增刊1): 65-72. (ZHU Qing-qing, MIAO Qiang-qiang, CHEN Zheng-han, et al.Elastoplastic dilatancy relations of unsaturated clayey sand[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(S1): 65-72. (in Chinese)) [11] BISHOP A W.The principle of effective stress[J]. Teknisk Ukeblad, 1959, 39: 113-143. [12] GALLIPOLI D, GENS A, SHARMA R, et al.An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour[J]. Géotechnique, 2003, 53(1): 123-135. [13] WHEELER S J, SHARMA R S, BUISSON M S R. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils[J]. Géotechnique, 2003, 53(1): 41-54. [14] FREDLUND D G, MORGENSTERN N R.Stress state variables for unsaturated soils[J]. Journal of Geotechnical Engineering, 1977, 103(GT5): 447-466. [15] TARATINO A, MONGIOVÕÁ L, BOSCO G.An experimental investigation on the independent isotropic stress variables for unsaturated soils[J]. Géotechnique, 2000, 50(3): 275-282. [16] 张龙, 陈正汉, 周凤玺, 等. 非饱和土应力状态变量试验验证研究[J]. 岩土工程学报, 2017, 39(2): 380-384. (ZHANG Long, CHEN Zheng-han, ZHOU Feng-xi, et al.Test verification of stress state variables for unsaturated soils[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(2): 380-384. (in Chinese)) [17] 张龙, 陈正汉, 周凤玺, 等. 从变形、水量变化和抗剪强度三个方面验证非饱和土的两个应力状态变量[J]. 岩土工程学报, 2017, 39(5): 906-915. (ZHANG Long, CHEN Zheng-han, ZHOU Feng-xi, et al.Verification of rationality of two stress state variables of unsaturated soil from deformation, moisture change and strength[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 39(2): 380-384. (in Chinese)) [18] ZHOU A N, SHENG D, SLOAN S W, et al.Interpretation of unsaturated soil behaviour in the stress-saturation space I: volume change and water retention behaviour[J]. Computers and Geotechnics, 2012, 43: 178-187. [19] ZHANG F, IKARIYA T.A new model for unsaturated soil using skeleton stress and degree of saturation as state variables[J]. Soils and Foundations, 2011, 51(1): 67-81. [20] ALONSO E E, GENS A, JOSA A.A constitutive model for partially saturated soils[J]. Géotechnique, 1990, 40(3): 405-430. [21] 孙德安. 非饱和土的水力和力学特性及其弹塑性描述. 岩土力学, 2009, 30(11): 3217-3231. (SUN De-an.Hydro-mechanical behaviours of unsaturated soils and their elastoplastic modelling[J]. Rock and Soil Mechanics, 2009, 30(11): 3217-3231. (in Chinese)) [22] 马田田, 韦昌富, 陈盼, 等. 非饱和土毛细滞回与变形耦合弹塑性本构模型. 岩土力学, 2012, 33(11): 3263-3270. (MA Tian-tian, WEI Chang-fu, CHEN Pan, et al.An elastoplastic constitutive model of unsaturated soils with capillary hysteresis and deformation coupling[J]. Rock and Soil Mechanics, 2012, 33(11): 3263-3270. (in Chinese)) [23] LI J, YIN Z Y, CUI Y J, et al.Work input analysis for soils with double porosity and application to the hydro-mechanical modeling of unsaturated expansive clays[J]. Canadian Geotechnical Journal, 2017, 54(2): 173-187. [24] YAO Y P, NIU L, CUI W J.Unified hardening (UH) model for overconsolidated unsaturated soils[J]. Canadian Geotechnical Journal, 2014, 51(7): 810-821. [25] LI X S.Thermodynamics-based constitutive framework for unsaturated soils: 2 a basic triaxial model[J]. Géotechnique, 2007, 57(5): 423-435. [26] 卢再华, 陈正汉, 曹继东. 原状膨胀土的强度变形特性及其本构模型研究[J]. 岩土力学, 2001, 22(3): 339-342. (LU Zai-hua, CHEN Zheng-han, CAO Ji-dong.A study on the strength and deformation characteristics and the constitutive model of natural expansive soils[J]. Rock and Soil Mechanics, 2001, 22(3): 339-342. (in Chinese)) [27] 卢再华, 陈正汉. 非饱和原状膨胀土的弹塑性损伤本构模型研究[J]. 岩土工程学报, 2003, 25(4): 422-426. (LU Zai-hua, CHEN Zheng-han.An elastoplastic damage constitutive model of unsaturated undisturbed expansive soil[J]. Chinese Journal of Geotechnical Engineering, 2003, 25(4): 422-426. (in Chinese)) [28] CHIU C F, NG C W W. A state-dependent elasto-plastic model for saturated and unsaturated soils[J]. Géotechnique, 2003, 53(9): 809-829. [29] 殷宗泽. 一个土体的双屈服面应力-应变模型[J]. 岩土工程学报, 1988, 10(4): 64-71. (YIN Zong-ze.A stress-strain model of soil with double yield surfaces[J]. Chinese Journal of Geotechnical Engineering, 1988, 10(4): 64-71. (in Chinese)) [30] YIN Z Y, XU Q, HICHER P Y.A simple critical-state-based double-yield-surface model for clay behavior under complex loading[J]. Acta Geotechnica, 2013, 8(5): 509-523. [31] ALONSO E E, PEREIRA M J, VAUNAT J, et al.A microstructurally-based effective stress for unsaturated soils[J]. Géotechnique, 2010, 60(12): 913-925. [32] KHALILI N, ZARGARBASHI S.Influence of hydraulic hysteresis on effective stress in unsaturated soils[J]. Géotechnique, 2010, 60(9): 729-734. [33] LU N, GODT J W, WU D T.A closed-form equation for effective stress in unsaturated soil[J]. Water Resources Research, 2010, 46(5): W05515. [34] 陈正汉, 郭楠. 非饱和土与特殊土力学及工程应用研究的新进展[J]. 岩土力学, 2019, 40(1): 1-54. (CHEN Zheng-han, GUO Nan.New developments of mechanics and application for unsaturated soils and special soils[J]. Rock and Soil Mechanics, 2019, 40(1): 1-54. (in Chinese)) [35] CHRISTENSON H K.Capillary condensation due to van der Waals attraction in wet slits[J]. Physical Review Letters, 1994, 73(13): 1821-1824. [36] TULLER M, OR D, DUDLEY L M.Adsorption and capillary condensation in porous media: liquid retention and interfacial configurations in angular pores[J]. Water Resources Research, 1999, 35(7): 1949-1964. [37] TULLER M, OR D.Water films and scaling of soil characteristic curves at low water contents[J]. Water Resources Research, 2005, 41(9): W09403. [38] KONRAD J M, LEBEAU M.Capillary-based effective stress formulation for predicting shear strength of unsaturated soils[J]. Canadian Geotechnical Journal, 2015, 52(12): 2067-2076. [39] ZHOU A N, HUANG R Q, SHENG D.Capillary water retention curve and shear strength of unsaturated soils[J]. Canadian Geotechnical Journal, 2016, 53(6): 974-987. [40] SIVAKUMAR V.A Critical State Framework for Unsaturated Soil[D]. Sheffield: University of Sheffield, 1993. [41] WEI C F, DEWOOLKAR M M.Formulation of capillary hysteresis with internal state variables[J]. Water Resources Research, 2006, 42(7): W074051-16. [42] 胡冉, 陈益峰, 周创兵. 基于孔隙分布的变形土土水特征曲线模型[J]. 岩土工程学报, 2013, 35(8): 1451-1462. (HU Ran, CHEN Yi-feng, ZHOU Chuang-bing.A water retention curve model for deformable soils based on pore size distribution[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(8): 1451-1462. (in Chinese)) [43] 张俊然, 许强, 孙德安. 多次干湿循环后土-水特征曲线的模拟[J]. 岩土力学, 2014, 35(3): 689-695. (ZHANG Jun-ran, XU Qiang, SUN De-an.Simulation of soil-water characteristic curves during drying and wetting cycles[J]. Rock and Soil Mechanics, 2014, 35(3): 689-695. (in Chinese)) [44] 刘艳, 赵成刚, 李舰, 等. 相间交界面对非饱和土应力状态的影响[J]. 力学学报, 2017, 49(2): 335-343. (LIU Yan, ZHAO Cheng-gang, LI Jian, et al.The influence of interfaces on the stress state in unsaturated soils[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 335-343. (in Chinese)) [45] SHENG D, SLOAN S W, GENS A, et al.Finite element formulation and algorithms for unsaturated soils: part I theory[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2003, 27(9): 745-765. [46] 李锡夔, 范益群. 非饱和土变形及渗流过程的有限元分析[J]. 岩土工程学报, 1998, 20(4): 20-24. (LI Xi-kui, FAN Yi-qun.Finite element analysis of deformation and seepage process in unsaturated soils[J]. Chinese Journal of Geotechnical Engineering, 1998, 20(4): 20-24. (in Chinese)) [47] 李舰, 赵成刚, 刘艳, 等. 适用于膨胀性非饱和土的边界面模型的数值实现[J]. 岩石力学与工程学报, 2017, 36(10): 215-226. (LI Jian, ZHAO Cheng-gang, LIU Yan, et al.Numerical implementation of a bounding surface model for unsaturated expansive clays[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(10): 215-226. (in Chinese)) [48] 李舰, 王鹏月, 海路, 等. 膨胀性非饱和土本构模型的隐式和显式积分算法的比较[J]. 岩石力学与工程学报, 2018, 37(7): 1731-1740. (LI Jian, WANG Peng-yue, HAI Lu, et al.Implicit and explicit integration schemes of a constitutive model for unsaturated expansive clays[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(7): 1731-1740. (in Chinese)) [49] RAMPINO C, MANCUSO C, VINALE F.Experimental behaviour and modelling of an unsaturated compacted soil[J]. Canadian Geotechnical Journal, 2000, 37(4): 748-763.