正冻土水热力耦合的数值机理研究
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摘要
在土体的冻结与融化过程中,土体中温度、水分和应力之间相互耦合机理是一个涉及到热传质学、热力学、流体力学和物理化学的极其复杂的综合问题。由于冻土的特殊性质,尤其是冻土中冰透镜体的出现,使得对冻土的研究与一般土体相比更为复杂,要有效的预防和抑制土体在冻结与融化过程中的冻胀与融沉现象,就必须充分考虑温度、水分和应力的三场耦合作用机理。
本文在Harlan模型的基础上,综合考虑了刚性冰假定和水动力学模型,将土体视为空间弹性体,以等效含水量代替冰含量简化水分迁移方程,并采用冰阻抗因子求解冻结区的各计算参数,运用显热容法处理冰水相变潜热,进一步考虑了土体应变对含水量的影响,建立了土体冻结过程中水—热—力的三场耦合模型。
运用有限元法和差分法对饱和土冻结过程中水—热—力的耦合机理进行了数值离散,给出了离散后的有限元方程,并在论文最后模拟了土柱和冻土路基的冻结过程,给出了冻土中含水量分布、应力分布规律,以及冻结时间、温度边界条件对冻土中含水量分布、应力分布的影响,经过对计算结果的分析研究,认为为保护冻土区的建筑物的稳定性和运营安全,对冻土路面采取保温措施和降低路基中温度是切实可行的。
The coupled mechanism of the moisture-heat-stress fields is an extremely complex problem concerning thermodynamics, hydrodynamics, fluid mechanics, physics and chemistry in the process of freezing and thawing of the soil. The special characteristics of the frozen soil, especially the emergence of ice lens, make the research of the frozen soil more complex than the common soil. To prevent and control the phenomenon of frost-heaving and thawing-settlement during freezing and thawing of the soil, sufficient attention should be paid to the coupled mechanism of the moisture-heat-stress fields.
Based on the model of Harlan, this paper synthetically considers the hypothesis of rigid ice and the model of hydrodynamics, and regards the soil as elastic. Most of the earlier scholars treat the ice content as a coupled factor. This paper simplifies the moisture-migration-equation through substituting equivalent water content for ice content, adopts ice-impedance-factors to solve calculation-parameter, uses apparent heat capacity to deal with phase change latent heat, and considers the influence of soil strain on the water content. The model of the coupled moisture-heat-stress field in freezing soil is established.
At the end of this paper, FEM and FDM are employed to solve the coupled equation of the moisture-heat-stress field during the freezing of the saturated soil, simulate the freezing process of soil-pole and frozen bed, and summarize the laws of water-content-distribution and the stress distribution, and the influence of frozen time, temperature boundary on water-content-distribution and the stress distribution. From analysis of the results, the conclusion is drawn that it is effective to protect the stability and the security of buildings in the frozen region through heat preservation and temperature control of the bed.
本文在Harlan模型的基础上,综合考虑了刚性冰假定和水动力学模型,将土体视为空间弹性体,以等效含水量代替冰含量简化水分迁移方程,并采用冰阻抗因子求解冻结区的各计算参数,运用显热容法处理冰水相变潜热,进一步考虑了土体应变对含水量的影响,建立了土体冻结过程中水—热—力的三场耦合模型。
运用有限元法和差分法对饱和土冻结过程中水—热—力的耦合机理进行了数值离散,给出了离散后的有限元方程,并在论文最后模拟了土柱和冻土路基的冻结过程,给出了冻土中含水量分布、应力分布规律,以及冻结时间、温度边界条件对冻土中含水量分布、应力分布的影响,经过对计算结果的分析研究,认为为保护冻土区的建筑物的稳定性和运营安全,对冻土路面采取保温措施和降低路基中温度是切实可行的。
The coupled mechanism of the moisture-heat-stress fields is an extremely complex problem concerning thermodynamics, hydrodynamics, fluid mechanics, physics and chemistry in the process of freezing and thawing of the soil. The special characteristics of the frozen soil, especially the emergence of ice lens, make the research of the frozen soil more complex than the common soil. To prevent and control the phenomenon of frost-heaving and thawing-settlement during freezing and thawing of the soil, sufficient attention should be paid to the coupled mechanism of the moisture-heat-stress fields.
Based on the model of Harlan, this paper synthetically considers the hypothesis of rigid ice and the model of hydrodynamics, and regards the soil as elastic. Most of the earlier scholars treat the ice content as a coupled factor. This paper simplifies the moisture-migration-equation through substituting equivalent water content for ice content, adopts ice-impedance-factors to solve calculation-parameter, uses apparent heat capacity to deal with phase change latent heat, and considers the influence of soil strain on the water content. The model of the coupled moisture-heat-stress field in freezing soil is established.
At the end of this paper, FEM and FDM are employed to solve the coupled equation of the moisture-heat-stress field during the freezing of the saturated soil, simulate the freezing process of soil-pole and frozen bed, and summarize the laws of water-content-distribution and the stress distribution, and the influence of frozen time, temperature boundary on water-content-distribution and the stress distribution. From analysis of the results, the conclusion is drawn that it is effective to protect the stability and the security of buildings in the frozen region through heat preservation and temperature control of the bed.
引文
[1]周幼吾,郭东信,邱国庆,程国栋,李树德.中国冻土[M].北京:科学出版社,2000.
[2]催托维奇HA.冻土力学[M].张长庆,朱元林译.北京:科学出版社,1985.
[3]青藏冻土研究论文集[M].北京:科学出版社,1983.
[4]马巍,吴紫汪.围压作用下冻结砂土微结构变化的电镜分析[J].冰川冻土[J],1995,17(2):152-157.
[5]吴紫汪,何平,张家懿等.围压对冻结粉土在振动荷载作用下蠕变性能的影响[J].冰川冻土,1995,17(supp):20-25.
[6]何平,朱元林等.饱和冻结粉土的动弹模及动强度[J].冰川冻土,1993,15(1):170-174.
[7]李洪升,张小鹏,朱元林等.冻土断裂韧度KIc的测定研究[J].冰川冻土,1995a,17(4):328-333.
[8]徐邵新等.季节冻土区水工建筑物抗冻害技术研究的成就与展望[M].第五届全国冰川冻土学大会论文集(上).兰州:甘肃文化出版社,1996,291-298.
[9]朱林楠,吴紫汪,臧恩穆.冻土退化与道路工程[M].第五届全国冰川冻土学大会论文集[M].兰州:甘肃文化出版社,1996,333-340.
[10]Kay B D,Perfect E.State of the art:heat and mass transfer in freezing soils[C].In:Proc of 5th intemational Symposium on ground freezing,1988,3-21.
[11]Goodrich L E.The influence of snow cover on the ground thermal regime[J].Canadian Geotechnical Journal,1982,19:421-432.
[12]Benoit G R,Mostaghimi S.Modeling soil frost under three tillage system[J].Transactions of the ASAE,1985,28:1499-1505.
[13]Kay B D,Fukuda M,et al.The importance of water migration in the measurements of the thermal conductivity of unsaturated frozen soils[J].Cold region Sci and Tech,1981,5:95-106.
[14]Osterkamp T E.Freezing and thawing of the soils and permafrost containing unfrozen water of brine[J].Water Resources Res,1987,23:2279-2285.
[15]Cary J W.A new method for calculating frost heave incluseing solute effects[J].Water Resources Res,1987,23:1620-1624.
[16]苗天德,郭力,牛永红,张长庆等.正冻土中水热迁移问题的混合物理论模型[J].中国科学,D 辑,1999,29(supp):8-14.
[17]徐学祖,邓友生.冻土中水分迁移的实验研究[M].北京:科学出版社,1991,23.
[18]李述训,陈国栋.冻融土中的水热输运问题[M].兰州:兰州大学出版社,1995,112-118.
[19]#12
[20]王家澄,程国栋等.饱水砂土反复冻融时成冰条件的实验研究[J].冰川冻土,1992,14(2):101-106.
[21]Aboustit B L,Advani S H,Lee J K,Sandhu R S.Finite element evaluation of thermo-elastic consolidation[C].In:Proc US Symp Rock Mech,1998,23~(rd),587-595.
[22]Nourished J,Tsang C F,Witherspoon P A.Coupled thermal-hydraulic-machanical phenomena in saturated fractured porous rocks:numerical approach[J].J Geophy Res,89(B 12):10365-10373
[23]Thomas H R,He Y.Analysis of coupled heat,moisture and air transfer in a deformable unsaturated soil[J].Geotechnique,1995,45(4):677-689.
[24]Gatmiri B.Fully coupled thermal-hydraulic-mechanical behavior of saturated porous media(soils and fractured rocks),new formulation and num-erical approach[J].Final Report CERMES-EDF,1995.
[25]Harlan R L.Analysis of coupled heat-fluid transport in partially frozen soil.Water Resources Res,1973,9:1314-1323
[26]Guymon G,Berg R,Hromadka T.Mathematical model of frost heave and thaw settlemen in pavements[C].CRREL Report 93-2,April,1993.
[27]Guymon G,Berg R,Hromadka T.A one-dimensinal frost heave model based upon simulation of simultaneous heat and water flux[J].Cold Regions Science and Technology,1980,3(2-3):253-263.
[28]Neil K,Miller R D.Exploration of a rigid ice model of frost heave[J].Water Resources Research,1985,21(3):281-196.
[29]O' Neil K,Miller R D.Numerical solutions for a rigid-ice model of secondary frost heave[C].U S Army Cold Reg Res Engg Lab Rep,82-13.Hanover,Nh,1982,11.
[30]Duquennoi C,Fremond M,Levy M.Modelling of thermal soil behaviour[J].VTT Symposium.1989,895-915.
[31]陈肖柏,刘鸿绪,刘建坤,王雅卿.土的冻结作用与地基[M].北京:科学出版社,2006,46
[32]Anderson D M,Tice A C.Predicting unfrozen water contents in frozen soils from surface area measurements[J].Highway Research Record,1972,(393):12-18
[33]Kujala K.Factors Affecting Frost Susceptibility and Hwaving Pressure in Soils[D].Finland:Unicersity of Oulu,1991.
[34]陈飞熊,宋战平,李宁.基于吸附薄膜理论的正冻土水分驱动力模型探讨[J].力学学报,2006,4(3):1-4
[35]靳德武,牛富俊,陈志新,倪万魁.土体冻融过程中渗流场、应力场、温度场耦合作用机理研究[J].煤田地质与勘探,2003,31(5):40-42
[36]Shen Mu,Ladanyi B.Modelling of coupled heat,moisture and stress field in freezing soil[J].Cold Regions Science and Technology,1987,14:237-246.
[37]吴林高,缪俊发,张瑞,姚迎.渗流力学[M].上海:上海科学技术文献出版社,1996.
[38]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社,1997.
[39]张洪武,关振群,李云鹏,顾元宪.有限元分析与CAE技术基础[M].北京:清华大学出版社,2004,63-67.
[40]刘中良,马重芳,孙旋.相变潜热随温度变化对固-液相变过程的影响[J].太阳能学报,2002,24(1):53-57.
[41]邹进,黄素逸.相变热传导的计算[J].能源技术,2000,1:11-14
[42]许康,张劲军.采用焓法方程计算埋地管道含蜡原油停输温降[J].石油大学学报(自然科学版),29(1):84-88.
[43]朱志武,宁建国,马巍.土体冻融过程中水、热、力三场耦合本构问题及数值分析[J].工程力学,2007,24(5):138-144.
[44]Taylor G.S,Luthin J.N.Model for coupled heat and moisture transfer during soil freezing[J].1978,15(4):548-555.
[45]李洪升,刘增利,梁承姬.冻土水热力耦合作用的数学模型及数值模拟[J].力学学报,2001,33(5):621-627.
[46]臧恩穆,吴紫汪.多年冻土退化与道路工程[M].兰州:兰州大学出版社,1999.
[47]曹宏章,刘石.饱和颗粒正冻土一维刚性冰模型的数值模拟[J].冰川冻土,2007,29(1):32-38.
[2]催托维奇HA.冻土力学[M].张长庆,朱元林译.北京:科学出版社,1985.
[3]青藏冻土研究论文集[M].北京:科学出版社,1983.
[4]马巍,吴紫汪.围压作用下冻结砂土微结构变化的电镜分析[J].冰川冻土[J],1995,17(2):152-157.
[5]吴紫汪,何平,张家懿等.围压对冻结粉土在振动荷载作用下蠕变性能的影响[J].冰川冻土,1995,17(supp):20-25.
[6]何平,朱元林等.饱和冻结粉土的动弹模及动强度[J].冰川冻土,1993,15(1):170-174.
[7]李洪升,张小鹏,朱元林等.冻土断裂韧度KIc的测定研究[J].冰川冻土,1995a,17(4):328-333.
[8]徐邵新等.季节冻土区水工建筑物抗冻害技术研究的成就与展望[M].第五届全国冰川冻土学大会论文集(上).兰州:甘肃文化出版社,1996,291-298.
[9]朱林楠,吴紫汪,臧恩穆.冻土退化与道路工程[M].第五届全国冰川冻土学大会论文集[M].兰州:甘肃文化出版社,1996,333-340.
[10]Kay B D,Perfect E.State of the art:heat and mass transfer in freezing soils[C].In:Proc of 5th intemational Symposium on ground freezing,1988,3-21.
[11]Goodrich L E.The influence of snow cover on the ground thermal regime[J].Canadian Geotechnical Journal,1982,19:421-432.
[12]Benoit G R,Mostaghimi S.Modeling soil frost under three tillage system[J].Transactions of the ASAE,1985,28:1499-1505.
[13]Kay B D,Fukuda M,et al.The importance of water migration in the measurements of the thermal conductivity of unsaturated frozen soils[J].Cold region Sci and Tech,1981,5:95-106.
[14]Osterkamp T E.Freezing and thawing of the soils and permafrost containing unfrozen water of brine[J].Water Resources Res,1987,23:2279-2285.
[15]Cary J W.A new method for calculating frost heave incluseing solute effects[J].Water Resources Res,1987,23:1620-1624.
[16]苗天德,郭力,牛永红,张长庆等.正冻土中水热迁移问题的混合物理论模型[J].中国科学,D 辑,1999,29(supp):8-14.
[17]徐学祖,邓友生.冻土中水分迁移的实验研究[M].北京:科学出版社,1991,23.
[18]李述训,陈国栋.冻融土中的水热输运问题[M].兰州:兰州大学出版社,1995,112-118.
[19]#12
[20]王家澄,程国栋等.饱水砂土反复冻融时成冰条件的实验研究[J].冰川冻土,1992,14(2):101-106.
[21]Aboustit B L,Advani S H,Lee J K,Sandhu R S.Finite element evaluation of thermo-elastic consolidation[C].In:Proc US Symp Rock Mech,1998,23~(rd),587-595.
[22]Nourished J,Tsang C F,Witherspoon P A.Coupled thermal-hydraulic-machanical phenomena in saturated fractured porous rocks:numerical approach[J].J Geophy Res,89(B 12):10365-10373
[23]Thomas H R,He Y.Analysis of coupled heat,moisture and air transfer in a deformable unsaturated soil[J].Geotechnique,1995,45(4):677-689.
[24]Gatmiri B.Fully coupled thermal-hydraulic-mechanical behavior of saturated porous media(soils and fractured rocks),new formulation and num-erical approach[J].Final Report CERMES-EDF,1995.
[25]Harlan R L.Analysis of coupled heat-fluid transport in partially frozen soil.Water Resources Res,1973,9:1314-1323
[26]Guymon G,Berg R,Hromadka T.Mathematical model of frost heave and thaw settlemen in pavements[C].CRREL Report 93-2,April,1993.
[27]Guymon G,Berg R,Hromadka T.A one-dimensinal frost heave model based upon simulation of simultaneous heat and water flux[J].Cold Regions Science and Technology,1980,3(2-3):253-263.
[28]Neil K,Miller R D.Exploration of a rigid ice model of frost heave[J].Water Resources Research,1985,21(3):281-196.
[29]O' Neil K,Miller R D.Numerical solutions for a rigid-ice model of secondary frost heave[C].U S Army Cold Reg Res Engg Lab Rep,82-13.Hanover,Nh,1982,11.
[30]Duquennoi C,Fremond M,Levy M.Modelling of thermal soil behaviour[J].VTT Symposium.1989,895-915.
[31]陈肖柏,刘鸿绪,刘建坤,王雅卿.土的冻结作用与地基[M].北京:科学出版社,2006,46
[32]Anderson D M,Tice A C.Predicting unfrozen water contents in frozen soils from surface area measurements[J].Highway Research Record,1972,(393):12-18
[33]Kujala K.Factors Affecting Frost Susceptibility and Hwaving Pressure in Soils[D].Finland:Unicersity of Oulu,1991.
[34]陈飞熊,宋战平,李宁.基于吸附薄膜理论的正冻土水分驱动力模型探讨[J].力学学报,2006,4(3):1-4
[35]靳德武,牛富俊,陈志新,倪万魁.土体冻融过程中渗流场、应力场、温度场耦合作用机理研究[J].煤田地质与勘探,2003,31(5):40-42
[36]Shen Mu,Ladanyi B.Modelling of coupled heat,moisture and stress field in freezing soil[J].Cold Regions Science and Technology,1987,14:237-246.
[37]吴林高,缪俊发,张瑞,姚迎.渗流力学[M].上海:上海科学技术文献出版社,1996.
[38]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社,1997.
[39]张洪武,关振群,李云鹏,顾元宪.有限元分析与CAE技术基础[M].北京:清华大学出版社,2004,63-67.
[40]刘中良,马重芳,孙旋.相变潜热随温度变化对固-液相变过程的影响[J].太阳能学报,2002,24(1):53-57.
[41]邹进,黄素逸.相变热传导的计算[J].能源技术,2000,1:11-14
[42]许康,张劲军.采用焓法方程计算埋地管道含蜡原油停输温降[J].石油大学学报(自然科学版),29(1):84-88.
[43]朱志武,宁建国,马巍.土体冻融过程中水、热、力三场耦合本构问题及数值分析[J].工程力学,2007,24(5):138-144.
[44]Taylor G.S,Luthin J.N.Model for coupled heat and moisture transfer during soil freezing[J].1978,15(4):548-555.
[45]李洪升,刘增利,梁承姬.冻土水热力耦合作用的数学模型及数值模拟[J].力学学报,2001,33(5):621-627.
[46]臧恩穆,吴紫汪.多年冻土退化与道路工程[M].兰州:兰州大学出版社,1999.
[47]曹宏章,刘石.饱和颗粒正冻土一维刚性冰模型的数值模拟[J].冰川冻土,2007,29(1):32-38.