岩土的非线性冻结模型试验和相似准则
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摘要
由于冰的比热和导热系数与水的比热和导热系数具有显著的差异性,因此土的比热和导热系数在冻结过程中是不断变化的。依据常热参数建立起来的温度场相似准则,难以准确反映土体在冻结过程中由热参数非线性引起的温度场演变。该文基于考虑热参数非线性变化的热传导微分方程,采用相似变换法导出了冻土模型试验中温度场的相似准则,并给出了采用原土进行模型试验时原型与模型应满足的相似关系。同时,在考虑第三类边界条件对相似准则影响的基础上,导出了模型土应满足的热物性相似条件。在此基础上,分别利用ABAQUS有限元软件对线性、非线性以及考虑第三类边界条件的原型和模型温度场进行了数值模拟,并对冻结过程中特征点的温度演变过程进行了分析。计算结果表明:建立的非线性导热相似准则能够正确反映原型冻土温度场的演变过程,说明模型土热参数的计算方法是合理的。同时表明,满足第三类边界条件的土体非线性冻结相似准则具有明确的物理意义和更高的实用价值。该研究成果为冻土模型试验中模型土的配制提供了切实合理的参数计算方法,为冻土水-热-力三场耦合模型试验的设计和实施提供了理论基础和技术支持。
The specific heat and thermal conductivity of soil change constantly in a freezing process due to the significant difference in the specific heat and thermal conductivity between ice and water.The similarity criterion of the temperature field,built upon constant thermal parameters,can't accurately describe the evolution of the temperature field caused by nonlinear thermal parameters in a freezing process.Based on the heat conduction differential equation that considers the nonlinear behaviour of thermal parameters,the similarity criterion of temperature field of frozen soil model test was derived.The derivation was conducted by using the similar transformation method.The similarity relation between the prototype and the model was given when the original soil was used for model test.Meanwhile,the similarity conditions of thermophysical properties of the model soil were derived,considering the influence of the third boundary condition on the similarity criterion.On this basis,the temperature fields of the prototype and the model were simulated by ABAQUS,which considers the linearity,nonlinearity and the third boundary condition,and analyzed the temperature evolution of characteristic points in the freezing process.The results show that,the established nonlinear similarity criterion of heat conduction accurately reflects the temperature field development of the prototype frozen soil,and indicate the calculation method of thermal parameters of model soil is reasonable.Meanwhile,the nonlinear freezing similarity criterion that satisfies the third boundary condition has definite physical significance and higher practical values.This study provides a practical and meaningful calculation method for the preparation of model soil in the frozen soil model test.It also provides the theoretical basis and technical support for the design and implementation of temperature-moisture-stress coupling test in frozen soil.
The specific heat and thermal conductivity of soil change constantly in a freezing process due to the significant difference in the specific heat and thermal conductivity between ice and water.The similarity criterion of the temperature field,built upon constant thermal parameters,can't accurately describe the evolution of the temperature field caused by nonlinear thermal parameters in a freezing process.Based on the heat conduction differential equation that considers the nonlinear behaviour of thermal parameters,the similarity criterion of temperature field of frozen soil model test was derived.The derivation was conducted by using the similar transformation method.The similarity relation between the prototype and the model was given when the original soil was used for model test.Meanwhile,the similarity conditions of thermophysical properties of the model soil were derived,considering the influence of the third boundary condition on the similarity criterion.On this basis,the temperature fields of the prototype and the model were simulated by ABAQUS,which considers the linearity,nonlinearity and the third boundary condition,and analyzed the temperature evolution of characteristic points in the freezing process.The results show that,the established nonlinear similarity criterion of heat conduction accurately reflects the temperature field development of the prototype frozen soil,and indicate the calculation method of thermal parameters of model soil is reasonable.Meanwhile,the nonlinear freezing similarity criterion that satisfies the third boundary condition has definite physical significance and higher practical values.This study provides a practical and meaningful calculation method for the preparation of model soil in the frozen soil model test.It also provides the theoretical basis and technical support for the design and implementation of temperature-moisture-stress coupling test in frozen soil.
引文
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[3]付兴,林友新,李宏男.风雨共同作用下高压输电塔的风洞试验及反应分析[J].工程力学,2014,31(1):72-78.Fu Xing,Lin Youxin,Li Hongnan.Wind tunnel test and pesponse analysis of high-voltage transmission tower subjected to combined loads of wind and rain[J].Engineering Mechanics,2014,31(1):72-78.(in Chinese)
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[6]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.Zhu Zhiwu,Ning Jianguo,Ma Wei.Constitutive model and numerical analysis for the coupled problem of water,temperature and stress fields in the process of soil freeze-thaw[J].Engineering Mechanics,2007,24(5):138-144.(in Chinese)
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[8]张涛,杨维好,黄家会,等.管内盐水流动状态对单管冻结温度场影响规律分析[J].煤炭学报,2015,40(9):2057-2064.Zhang Tao,Yang Weihao,Huang Jiahui,et al.Influence law of brine flow state in pipe on single pipe freezing temperature field[J].Journal of China Coal Society,2015,40(9):2057-2064.(in Chinese)
[9]张晨,蔡正银,黄英豪,等.输水渠道冻胀离心模拟试验[J].岩土工程学报,2016,38(1):109-117.Zhang Chen,Cai Zhengyin,Huang Yinghao,et al.Centrifuge modelling of frost-heave of canals[J].Chinese Journal of Geotechnical Engineering,2016,38(1):109-117.(in Chinese)
[10]Yoshikawa K,Overduin P P.Comparing unfrozen water content measurements of frozen soil using recently developed commercial sensors[J].Cold Regions Science and Technology,2005,42(3):250-256.
[11]毛卫南,刘建坤.不同离散化方法在正冻土水热耦合模型中的应用[J].工程力学,2013,30(10):128-132.Mao Weinan,Liu Jiankun.Different discretization method using in coupled water and heat transport model for soil under freezing conditions[J].Engineering Mechanics,2013,30(10):128-132.(in Chinese)
[12]Wen Z,Sheng Y,Ma W,et al.Experimental studies of thermal conductivity of undisturbed permafrost at beiluhe testing site on the tibetan plateau[J].Journal of Glaciology and Geocryology,2005,27(2):182-187.
[13]耿萍,晏启祥,何川,等.隧道水平冻结施工过程的数值模拟[J].工程力学,2010,27(5):122-127.Geng Ping,Yan Qixiang,He Chuan,et al.Numerical simulation of underground construction by horizontal ground freezing method[J].Engineering Mechanics,2010,27(5):122-127.(in Chinese)
[14]Sun K G,Yang P,Qiu W G,et al.Research on the temperature field and the buried depth of drains for tunnels in cold region[J].Journal of Railway Engineering Society,2017,34(4):51-57.
[15]梁波,陈兴冲.青藏铁路的重要意义、技术难点及力学问题[J].工程力学,2004,21(增刊1):139-149.Liang Bo,Chen Xingchong.The significance,the key technical problem and the mechanical problem of Qinghai-Tibetan Railway[J].Engineering Mechanics,2004,21(Suppl 1):139-149.(in Chinese)
[16]Yang P,Ke J M,Wang J G,et al.Numerical simulation of frost heave with coupled water freezing,temperature and stress fields in tunnel excavation[J].Computers and Geotechnics,2006,33(6):330-340.
[17]丁德文,罗学波.冻土热工模型实验的理论基础[J].科学通报,1979,24(8):360-364.Ding Dewen,Luo Xuebo.Theoretical basis of thermal model test of frozen soil[J].Chinese Science Bulletin,1979,24(8):360-364.(in Chinese)
[18]徐学祖,王家澄,张立新.冻土物理学[M].北京:科学出版社,2010.Xu Xuezu,Wang Jiacheng,Zhang Lixin.Physics of frozen soil[M].Beijing:Science Press,2010.(in Chinese)
[19]孙立强,任宇晓,闫澍旺,等.人工冻土冻结过程中热-力耦合的数值模拟方法研究[J].岩土工程学报,2015,37(增刊2):137-142.Sun Liqiang,Ren Yuxiao,Yan Shuwang,et al.Numerical simulation method for thermal-stress coupling in artificial freezing process[J].Journal of Geotechnical Engineering,2015,37(Suppl 2):137-142.(in Chinese)
[20]于珊,李顺群,冯慧强.土的导热系数与其干密度、饱和度和温度的关系[J].天津城建大学学报,2015,21(3):172-176.Yu Shan,Li Shunqun,Feng Huiqiang.The relationship between thermal conductivity of soil and its dry density,saturation and temperature[J].Journal of Tianjin Chengjian University,2015,21(3):172-176.(in Chinese)
[21]陈之祥,李顺群,王杏杏,等.热参数对冻土温度场的影响及敏感性分析[J].水利水电技术,2017,48(5):136-141.Chen Zhixiang,Li Shunqun,Wang Xingxing,et al.Analysis on impact and sensitivity of thermal parameters on frozen soil temperature field[J].Water Resources and Hydropower Engineering,2017,48(5):136-141.(in Chinese)
[22]崔广心.相似理论与模型试验[M].徐州:中国矿业大学出版社,1990.Cui Guangxin.Similarity theory and model test[M].Xuzhou:China University of Mining and Technology Press,1990.(in Chinese)
[23]夏锦红,李顺群,夏元友,等.一种考虑显热和潜热双重效应的冻土比热计算方法[J].岩土力学,2017,38(4):973-978.Xia Jinhong,Li Shunqun,Xia Yuanyou,et al.Specific heat of frozen soil considering sensible and latent heat of pore water[J].Rock and Soil Mechanics,2017,38(4):973-978.(in Chinese)
[2]Liao M,Lai Y,Wang C.A strength criterion for frozen sodium sulfate saline soil[J].Canadian Geotechnical Journal,2016,53(7):1176-1185.
[3]付兴,林友新,李宏男.风雨共同作用下高压输电塔的风洞试验及反应分析[J].工程力学,2014,31(1):72-78.Fu Xing,Lin Youxin,Li Hongnan.Wind tunnel test and pesponse analysis of high-voltage transmission tower subjected to combined loads of wind and rain[J].Engineering Mechanics,2014,31(1):72-78.(in Chinese)
[4]Kojima Y,Heitman J L,Flerchinger G N,et al.Sensible heat balance estimates of transient soil ice contents[J].Vadose Zone Journal,2016,15(5):45-57.
[5]武建军,韩天一.饱和正冻土水-热-力耦合作用的数值研究[J].工程力学,2009,26(4):246-251.Wu Jianjun,Han Tianyi.Numerical research on the coupled process of the moisture-heat-stress fields in saturated soil during freezing[J].Engineering Mechanics,2009,26(4):246-251.(in Chinese)
[6]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.Zhu Zhiwu,Ning Jianguo,Ma Wei.Constitutive model and numerical analysis for the coupled problem of water,temperature and stress fields in the process of soil freeze-thaw[J].Engineering Mechanics,2007,24(5):138-144.(in Chinese)
[7]朱林楠,李东庆,郭兴民.无外荷载作用下冻土模型试验的相似分析[J].冰川冻土,1993,15(1):166-169.Zhu Linnan,Li Dongqing,Guo Xingmin.Simulitude analysis of modeling test for chargeless pressure in the freezing-thawing process of soil[J].Journal of Glaciology and Geocryology,1993,15(1):166-169.(in Chinese)
[8]张涛,杨维好,黄家会,等.管内盐水流动状态对单管冻结温度场影响规律分析[J].煤炭学报,2015,40(9):2057-2064.Zhang Tao,Yang Weihao,Huang Jiahui,et al.Influence law of brine flow state in pipe on single pipe freezing temperature field[J].Journal of China Coal Society,2015,40(9):2057-2064.(in Chinese)
[9]张晨,蔡正银,黄英豪,等.输水渠道冻胀离心模拟试验[J].岩土工程学报,2016,38(1):109-117.Zhang Chen,Cai Zhengyin,Huang Yinghao,et al.Centrifuge modelling of frost-heave of canals[J].Chinese Journal of Geotechnical Engineering,2016,38(1):109-117.(in Chinese)
[10]Yoshikawa K,Overduin P P.Comparing unfrozen water content measurements of frozen soil using recently developed commercial sensors[J].Cold Regions Science and Technology,2005,42(3):250-256.
[11]毛卫南,刘建坤.不同离散化方法在正冻土水热耦合模型中的应用[J].工程力学,2013,30(10):128-132.Mao Weinan,Liu Jiankun.Different discretization method using in coupled water and heat transport model for soil under freezing conditions[J].Engineering Mechanics,2013,30(10):128-132.(in Chinese)
[12]Wen Z,Sheng Y,Ma W,et al.Experimental studies of thermal conductivity of undisturbed permafrost at beiluhe testing site on the tibetan plateau[J].Journal of Glaciology and Geocryology,2005,27(2):182-187.
[13]耿萍,晏启祥,何川,等.隧道水平冻结施工过程的数值模拟[J].工程力学,2010,27(5):122-127.Geng Ping,Yan Qixiang,He Chuan,et al.Numerical simulation of underground construction by horizontal ground freezing method[J].Engineering Mechanics,2010,27(5):122-127.(in Chinese)
[14]Sun K G,Yang P,Qiu W G,et al.Research on the temperature field and the buried depth of drains for tunnels in cold region[J].Journal of Railway Engineering Society,2017,34(4):51-57.
[15]梁波,陈兴冲.青藏铁路的重要意义、技术难点及力学问题[J].工程力学,2004,21(增刊1):139-149.Liang Bo,Chen Xingchong.The significance,the key technical problem and the mechanical problem of Qinghai-Tibetan Railway[J].Engineering Mechanics,2004,21(Suppl 1):139-149.(in Chinese)
[16]Yang P,Ke J M,Wang J G,et al.Numerical simulation of frost heave with coupled water freezing,temperature and stress fields in tunnel excavation[J].Computers and Geotechnics,2006,33(6):330-340.
[17]丁德文,罗学波.冻土热工模型实验的理论基础[J].科学通报,1979,24(8):360-364.Ding Dewen,Luo Xuebo.Theoretical basis of thermal model test of frozen soil[J].Chinese Science Bulletin,1979,24(8):360-364.(in Chinese)
[18]徐学祖,王家澄,张立新.冻土物理学[M].北京:科学出版社,2010.Xu Xuezu,Wang Jiacheng,Zhang Lixin.Physics of frozen soil[M].Beijing:Science Press,2010.(in Chinese)
[19]孙立强,任宇晓,闫澍旺,等.人工冻土冻结过程中热-力耦合的数值模拟方法研究[J].岩土工程学报,2015,37(增刊2):137-142.Sun Liqiang,Ren Yuxiao,Yan Shuwang,et al.Numerical simulation method for thermal-stress coupling in artificial freezing process[J].Journal of Geotechnical Engineering,2015,37(Suppl 2):137-142.(in Chinese)
[20]于珊,李顺群,冯慧强.土的导热系数与其干密度、饱和度和温度的关系[J].天津城建大学学报,2015,21(3):172-176.Yu Shan,Li Shunqun,Feng Huiqiang.The relationship between thermal conductivity of soil and its dry density,saturation and temperature[J].Journal of Tianjin Chengjian University,2015,21(3):172-176.(in Chinese)
[21]陈之祥,李顺群,王杏杏,等.热参数对冻土温度场的影响及敏感性分析[J].水利水电技术,2017,48(5):136-141.Chen Zhixiang,Li Shunqun,Wang Xingxing,et al.Analysis on impact and sensitivity of thermal parameters on frozen soil temperature field[J].Water Resources and Hydropower Engineering,2017,48(5):136-141.(in Chinese)
[22]崔广心.相似理论与模型试验[M].徐州:中国矿业大学出版社,1990.Cui Guangxin.Similarity theory and model test[M].Xuzhou:China University of Mining and Technology Press,1990.(in Chinese)
[23]夏锦红,李顺群,夏元友,等.一种考虑显热和潜热双重效应的冻土比热计算方法[J].岩土力学,2017,38(4):973-978.Xia Jinhong,Li Shunqun,Xia Yuanyou,et al.Specific heat of frozen soil considering sensible and latent heat of pore water[J].Rock and Soil Mechanics,2017,38(4):973-978.(in Chinese)
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