非饱和土中热-湿-盐耦合作用的稳态分析
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摘要
以多孔介质理论为基础,研究了稳态条件下非饱和土中温度-水分-盐分多场耦合问题。考虑非饱和土的孔隙被液态水、溶解的盐分、水蒸气和干燥气体等填充,在质量和能量守恒的基础上获得了非饱和土中水分、气体、盐分的质量守恒方程以及能量守恒方程。考虑一维稳态问题,选取温度、孔隙气压、孔隙水压和盐溶液浓度以及它们的导数作为状态变量,得到了问题的状态方程组。在给定的边界条件下,采用打靶法求解了该强耦合的非线性变系数微分方程组,通过与已有的试验结果相比较,验证了模型的有效性。基于数值算例,参数分析了含水率、温度边界、孔隙率等条件对非饱和土中温度场、水分场和盐分场分布的影响规律。
The multi-field coupled heat-moisture-salt behavior of unsaturated soils under steady state is investigated using porous media theory. It considers that the pores are filled with liquid water, dissolved salts, water vapor, and dry gas. The mass conservation equations of moisture, gas, and salinity in unsaturated soils and the energy conservation equations are presented. Considering one-dimensional steady-state problems, the state equations are obtained by using the temperature, pore pressure, pore water pressure and salt solution concentration and their first-order derivatives as the state variables. Under given boundary conditions, the coupled nonlinear differential equations for the varying coefficients are solved by shooting method. The validity of the model is verified by comparing with the existing experimental results. Based on numerical examples, the influence of moisture content, temperature boundary and porosity on the distribution of temperature field, water field and salt field in unsaturated soils was discussed in detail.
The multi-field coupled heat-moisture-salt behavior of unsaturated soils under steady state is investigated using porous media theory. It considers that the pores are filled with liquid water, dissolved salts, water vapor, and dry gas. The mass conservation equations of moisture, gas, and salinity in unsaturated soils and the energy conservation equations are presented. Considering one-dimensional steady-state problems, the state equations are obtained by using the temperature, pore pressure, pore water pressure and salt solution concentration and their first-order derivatives as the state variables. Under given boundary conditions, the coupled nonlinear differential equations for the varying coefficients are solved by shooting method. The validity of the model is verified by comparing with the existing experimental results. Based on numerical examples, the influence of moisture content, temperature boundary and porosity on the distribution of temperature field, water field and salt field in unsaturated soils was discussed in detail.
引文
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[8]ABED A A,SO□OWSKI W T.A study on how to couple thermo-hydro-mechanical behaviour of unsaturated soils:physical equations,numerical implementation and examples[J].Computers and Geotechnics,2017,92:132-155.
[9]QIN Bing,CHEN Zheng-han,FANG Zhen-dong,et al.Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I[J].Applied Mathematics and Mechanics,2010,31(12):1561-1576.
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[12]CHEN Y,SHI M,LI X.Experimental investigation on heat,moisture and salt transfer in soil[J].International Communications in Heat and Mass Transfer,2006,33(9):1122-1129.
[13]黄兴法,曾德超,练国平.土壤水热盐运动模型的建立与初步验证[J].农业工程学报,1997,13(3):32-36.HUANG Xing-fa,ZENG De-chao,LIAN Guo-ping.Anumerical model for coupling movement of water heat and salt in soil under the conditions of frozen,unfrozen,saturated and unsaturated[J].Transactions of the Chinese Society of Agricultural Engineering,1997,13(3):32-36.
[14]ADALA M,BENNACER R,SAMMOUDA H,et al.Heat and mass transport in the unsaturated porous media:application to the soil dry drainage method[J].Defect and Diffusion Forum,2009,283-286:589-593.
[15]刘炳成,李庆领.土壤中水、热、盐耦合运移的数值模拟[J].华中科技大学学报(自然科学版),2006,34(1):14-16.LIU Bing-cheng,LI Qing-ling.Numerical simulation of salt,moisture and heat transport in porous soil[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2006,34(1):14-16.
[16]RUTQVIST J,B?RGESSON L,CHIJIMATSU M,et al.Thermo-hydromechanics of partially saturated geological media:governing equations and formulation of four finite element models[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(1):105-127.
[17]OLIVELLA S,CARRERA J,GENS A,et al.Nonisothermal multiphase flow of brine and gas through saline media[J].Transport Porous Media,1994,15(3):271-293.
[18]DIERSCH H,KOLDITZ O.Variable-density flow and transport in porous media:approaches and challenges[J].Advances in Water Resources,2002,25(8-12):899-944.
[19]VAN GENUCHTEN MT.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Science Society of America Journal,1980,44(5):892-898.
[20]OLIVELLA S,CARRERA J,GENS A,et al.Porosity variations in saline media caused by temperature gradients coupled to multiphase flow and dissolution/precipitation[J].Transport Porous Media,1996,25(1):1-25.
[21]VAN ESCH J M.Adaptive multiscale finite element method for subsurface flow simulation[M].[S.l.]:[s.n.],2010.
[22]RUTQVIST J,B?RGESSON L,CHIJIMATSU M,et al.Thermo-hydromechanics of partially saturated geological media:governing equations and formulation of four finite element models[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(1):105-127.
[23]PHILIP J,DE VRIES D.Moisture movement in porous materials under temperature gradients[J].Eos Trans Am Geophys Union,1957,38(2):222-232.
[24]VAUNAT J,JOMMI C,GENS A.A strategy for numerical analysis of the transition between saturated and unsaturated flow conditions 1997:297-302.
[25]WANG W,RUTQVIST J,G?RKE U,et al.Non-isothermal flow in low permeable porous media:a comparison of Richards’and two-phase flow approaches[J].Environmental Earth Sciences,2011,62(6):1197-1207.
[26]NASSAR I N,HORTON R.Heat,water,and solute transfer in unsaturated porous media.I-theory development and transport coefficient evaluation[J].Transport in Porous Media,1997,27(1):17-38.
[27]ZHOU Feng-xi,MA Qiang.Exact solution for capillary interactions between two particles with fixed liquid volume[J].Applied Mathematics&Mechanics,2016,7(12):1597-1606.
[28]ZHOU Feng-xi,LI Shi-rong,LAI Yuan-ming.Threedimensional analysis for transient coupled thermoelastic response of a functionally graded rectangular plate[J].Journal of Sound and Vibration,2011,330(16):3990-4001.
[29]NASSAR I N,HORTON R.Water transport in unsaturated nonisothermal salty soil:I.experimental results[J].Soil Science Society of America Journal,1989,53(5):1330-1337.
[2]CHEN W,TAN X,YU H,et al.A fully coupled thermohydro-mechanical model for unsaturated porous media[J].Journal of Rock Mechanics and Geotechnical Engineering,2009,1(1):31-40.
[3]李彦龙,王俊,王铁行.温度梯度作用下非饱和土水分迁移研究[J].岩土力学,2016,37(10):2839-2844.LI Yan-long,WANG Jun,WANG Tie-hang.Moisture migration of unsaturated soil due to thermal gradients[J].Rock and Soil Mechanics,2016,37(10):2839-2844.
[4]ZHANG Ming-li,WEN Zhi,XUE Ke,et al.A coupled model for liquid water,water vapor and heat transport of saturated-unsaturated soil in cold regions:model formulation and verification[J].Environmental Earth Sciences,2016,75(8):701.
[5]MOHAMMAD H J,SEYED A S.A new coupled heat,moisture and air transfer model in unsaturated soil[J].Journal of Mechanical Science and Technology,2012,26(11):3661-3672.
[6]TARIKU F,KUMARAN K,FAZIO P.Transient model for coupled heat,air and moisture transfer through multilayered porous media[J].International Journal of Heat&Mass Transfer,2010,53(15):3035-3044.
[7]JAHANGIR M H,SADRNEJAD S A.A new coupled heat,moisture and air transfer model in unsaturated soil[J].Journal of Mechanical Science and Technology,2012,26(11):3661-3672.
[8]ABED A A,SO□OWSKI W T.A study on how to couple thermo-hydro-mechanical behaviour of unsaturated soils:physical equations,numerical implementation and examples[J].Computers and Geotechnics,2017,92:132-155.
[9]QIN Bing,CHEN Zheng-han,FANG Zhen-dong,et al.Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I[J].Applied Mathematics and Mechanics,2010,31(12):1561-1576.
[10]MARTíN M,CUEVAS J,LEGUEY S.Diffusion of soluble salts under a temperature gradient after the hydration of compacted bentonite[J].Applied Clay Science,2000,17(1):55-70.
[11]李毅,王文焰,王全九,等.温度势梯度下土壤水平一维水盐运动特征的实验研究[J].农业工程学报,2002,18(6):4-8.LI Yi,WANG Wen-yan,WANG Quan-jiu,et al.Experimental study on the characteristics of one-dimensional water salinity movement in soil under temperature potential gradient[J].Transactions of the Chinese Society of Agricultural Engineering,2002,18(6):4-8.
[12]CHEN Y,SHI M,LI X.Experimental investigation on heat,moisture and salt transfer in soil[J].International Communications in Heat and Mass Transfer,2006,33(9):1122-1129.
[13]黄兴法,曾德超,练国平.土壤水热盐运动模型的建立与初步验证[J].农业工程学报,1997,13(3):32-36.HUANG Xing-fa,ZENG De-chao,LIAN Guo-ping.Anumerical model for coupling movement of water heat and salt in soil under the conditions of frozen,unfrozen,saturated and unsaturated[J].Transactions of the Chinese Society of Agricultural Engineering,1997,13(3):32-36.
[14]ADALA M,BENNACER R,SAMMOUDA H,et al.Heat and mass transport in the unsaturated porous media:application to the soil dry drainage method[J].Defect and Diffusion Forum,2009,283-286:589-593.
[15]刘炳成,李庆领.土壤中水、热、盐耦合运移的数值模拟[J].华中科技大学学报(自然科学版),2006,34(1):14-16.LIU Bing-cheng,LI Qing-ling.Numerical simulation of salt,moisture and heat transport in porous soil[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2006,34(1):14-16.
[16]RUTQVIST J,B?RGESSON L,CHIJIMATSU M,et al.Thermo-hydromechanics of partially saturated geological media:governing equations and formulation of four finite element models[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(1):105-127.
[17]OLIVELLA S,CARRERA J,GENS A,et al.Nonisothermal multiphase flow of brine and gas through saline media[J].Transport Porous Media,1994,15(3):271-293.
[18]DIERSCH H,KOLDITZ O.Variable-density flow and transport in porous media:approaches and challenges[J].Advances in Water Resources,2002,25(8-12):899-944.
[19]VAN GENUCHTEN MT.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Science Society of America Journal,1980,44(5):892-898.
[20]OLIVELLA S,CARRERA J,GENS A,et al.Porosity variations in saline media caused by temperature gradients coupled to multiphase flow and dissolution/precipitation[J].Transport Porous Media,1996,25(1):1-25.
[21]VAN ESCH J M.Adaptive multiscale finite element method for subsurface flow simulation[M].[S.l.]:[s.n.],2010.
[22]RUTQVIST J,B?RGESSON L,CHIJIMATSU M,et al.Thermo-hydromechanics of partially saturated geological media:governing equations and formulation of four finite element models[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(1):105-127.
[23]PHILIP J,DE VRIES D.Moisture movement in porous materials under temperature gradients[J].Eos Trans Am Geophys Union,1957,38(2):222-232.
[24]VAUNAT J,JOMMI C,GENS A.A strategy for numerical analysis of the transition between saturated and unsaturated flow conditions 1997:297-302.
[25]WANG W,RUTQVIST J,G?RKE U,et al.Non-isothermal flow in low permeable porous media:a comparison of Richards’and two-phase flow approaches[J].Environmental Earth Sciences,2011,62(6):1197-1207.
[26]NASSAR I N,HORTON R.Heat,water,and solute transfer in unsaturated porous media.I-theory development and transport coefficient evaluation[J].Transport in Porous Media,1997,27(1):17-38.
[27]ZHOU Feng-xi,MA Qiang.Exact solution for capillary interactions between two particles with fixed liquid volume[J].Applied Mathematics&Mechanics,2016,7(12):1597-1606.
[28]ZHOU Feng-xi,LI Shi-rong,LAI Yuan-ming.Threedimensional analysis for transient coupled thermoelastic response of a functionally graded rectangular plate[J].Journal of Sound and Vibration,2011,330(16):3990-4001.
[29]NASSAR I N,HORTON R.Water transport in unsaturated nonisothermal salty soil:I.experimental results[J].Soil Science Society of America Journal,1989,53(5):1330-1337.