多年冻土区隧道传热模型及温度场分布规律
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摘要
针对高温多年冻土区隧道传热模型及温度场分布规律开展深入的理论分析、数值模拟和现场监测研究。首先,基于热传导理论,建立隧道衬砌和围岩径向传热模型,利用叠加原理和拉普拉斯变换法求得寒区隧道衬砌和围岩的温度场理论解;其次,建立洞内空气的传热微分方程,根据能量守恒原理,建立隧道纵向洞内空气与洞壁的气-固耦合传热模型,结合径向温度场理论解,提出多年冻土区隧道衬砌、围岩及洞内空气的三维温度场计算方法,该计算方法可考虑围岩、衬砌、保温层等多层传热介质及隧道沿洞轴线的不同埋深;最后,根据依托工程现场实测数据,反演围岩的热物性参数,并运用推导的隧道纵向传热模型和横向传热模型,分析姜路岭隧道不同冻土区内衬砌和围岩中的温度场分布规律。研究结果表明:在隧道径向,多年冻土和非冻土围岩温度都会随洞内气温的变化而产生波动,距离围岩表面越近,温度振幅越大,且热量在围岩径向传递过程中有一定的滞后性;在隧道纵向,在一年中最冷时刻,隧道衬砌及围岩温度呈"两端低,中间高",此时姜路岭隧道围岩、二衬表面最高温度分别为-2.72℃,-7.80℃;在一年中最热时刻,衬砌温度呈"两端高,中间低",此时姜路岭隧道二衬表面最低温度为1.92℃,但由于受围岩初始地温的影响,围岩表面的温度呈倒V形,最低温度为-1.22℃。
Theoretical analysis, numerical simulation, and field monitoring of a tunnel heat transfer model and the temperature field distribution in a high-temperature permafrost region were carried out. Firstly, based on the theory of heat conduction, the radial heat transfer model of tunnel lining and surrounding rock was established, and the theoretical solution of the temperature field of the tunnel lining and surrounding rock in the cold region was obtained by superposition principle and Laplace transform method. Secondly, the differential equations of heat transfer of air in the tunnel were established. According to the principle of energy conservation, the gas-solid coupled heat transfer model of the air and tunnel wall in the longitudinal tunnel was established. Combined with the theoretical solution of the radial temperature field, a three-dimensional temperature field calculation method for the tunnel lining, surrounding rock, and air in the permafrost region was proposed. The calculation method can take multilayer heat transfer media such as surrounding rock, lining, and insulation layer as well as different burial depths along the tunnel axis into account. Finally, according to the measured data in the field, the thermal physical parameters of surrounding rock were analyzed inversely. Based on the derived tunnel longitudinal and transverse heat transfer models, the temperature field distributions of lining and surrounding rock in different frozen soil areas of the Jiangluling Tunnel were analyzed. Analysis results show that in the radial direction of tunnel, the temperatures of surrounding rocks of permafrost and non-permafrost fluctuate with temperature changes in the tunnel. The closer the tunnel is to the surface of surrounding rocks, the larger the temperature fluctuates, and there is a certain lag in the radial heat transfer process of surrounding rock. Longitudinally, on the coldest day of the year, the temperatures of the tunnel lining and surrounding rock were "low at both ends and high in the middle". At this time, the maximum surface temperature of the surrounding rock of Jiangluling Tunnel is-2.72 ℃, and the maximum surface temperature of the second lining is-7.80 ℃. On the hottest day of the year, the lining temperature was "high at both ends and low in the middle", and the minimum surface temperature of the second lining of Jiangluling Tunnel is 1.92 ℃. The surface temperature of the surrounding rock is an inverted V-shape owing to the influence of the initial ground temperature of the surrounding rock, and the minimum surface temperature of the surrounding rock of the Jiangluling Tunnel is-1.22 ℃.
Theoretical analysis, numerical simulation, and field monitoring of a tunnel heat transfer model and the temperature field distribution in a high-temperature permafrost region were carried out. Firstly, based on the theory of heat conduction, the radial heat transfer model of tunnel lining and surrounding rock was established, and the theoretical solution of the temperature field of the tunnel lining and surrounding rock in the cold region was obtained by superposition principle and Laplace transform method. Secondly, the differential equations of heat transfer of air in the tunnel were established. According to the principle of energy conservation, the gas-solid coupled heat transfer model of the air and tunnel wall in the longitudinal tunnel was established. Combined with the theoretical solution of the radial temperature field, a three-dimensional temperature field calculation method for the tunnel lining, surrounding rock, and air in the permafrost region was proposed. The calculation method can take multilayer heat transfer media such as surrounding rock, lining, and insulation layer as well as different burial depths along the tunnel axis into account. Finally, according to the measured data in the field, the thermal physical parameters of surrounding rock were analyzed inversely. Based on the derived tunnel longitudinal and transverse heat transfer models, the temperature field distributions of lining and surrounding rock in different frozen soil areas of the Jiangluling Tunnel were analyzed. Analysis results show that in the radial direction of tunnel, the temperatures of surrounding rocks of permafrost and non-permafrost fluctuate with temperature changes in the tunnel. The closer the tunnel is to the surface of surrounding rocks, the larger the temperature fluctuates, and there is a certain lag in the radial heat transfer process of surrounding rock. Longitudinally, on the coldest day of the year, the temperatures of the tunnel lining and surrounding rock were "low at both ends and high in the middle". At this time, the maximum surface temperature of the surrounding rock of Jiangluling Tunnel is-2.72 ℃, and the maximum surface temperature of the second lining is-7.80 ℃. On the hottest day of the year, the lining temperature was "high at both ends and low in the middle", and the minimum surface temperature of the second lining of Jiangluling Tunnel is 1.92 ℃. The surface temperature of the surrounding rock is an inverted V-shape owing to the influence of the initial ground temperature of the surrounding rock, and the minimum surface temperature of the surrounding rock of the Jiangluling Tunnel is-1.22 ℃.
引文
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[11] 米隆,赖远明,吴紫汪,等.高原冻土铁路路基温度特性的有限元分析[J].铁道学报,2003,25(2):62-67.MI Long,LAI Yuan-ming,WU Zi-wang,et al.The Finite Element Analysis for Temperature Property of Railway Embankments in Cold Regions[J].Journal of the China Railway Society,2003,25 (2):62-67.
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[14] 陈建勋,昝勇杰.寒冷地区公路隧道防冻隔温层效果现场测试与分析[J].中国公路学报,2001,14(4):75-79.CHEN Jian-xun,ZAN Yong-jie.Field Test and Analysis of Antifreezing Thermal-protective Layer Effect of the Highway Tunnel in Cold Area [J].China Journal of Highway and Transport,2001,14 (4):75-79.
[15] 朱东鹏,袁堃,陈建兵,等.高温多年冻土区公路通风管路基传热特征分析[J].中国公路学报,2015,28(12):69-77.ZHU Dong-peng,YUAN Kun,CHEN Jian-bing,et al.Analysis on Heat Transfer Characteristics of Highway Duct-ventilated Embankment in High Temperature Permafrost Regions [J].China Journal of Highway and Transport,2015,28 (12):69-77.
[16] 夏才初,范东方,李强,等.寒区隧道保温层铺设长度的计算方法[J].同济大学学报:自然科学版,2016,44(9):1363-1370.XIA Cai-chu,FAN Dong-fang,LI Qiang,et al.An Approach for Determining Length of Insulation Layer in Cold Region Tunnel [J].Journal of Tongji University:Natural Science,2016,44 (9):1363-1370.
[17] 徐小涛.鄂拉山隧道保温抗冻及防排水技术研究[D].重庆:重庆交通大学,2013.XU Xiao-tao.Study on Frostance,Anti-freezing and Drainage Technology of the Elashan Tunnel [D].Chongqing:Chongqing Jiaotong University,2013.
[18] 黄继辉,夏才初,韩常领,等.寒区公路隧道冻胀力荷载的分布形式和简化计算方法[J].现代隧道技术,2016,53(5):63-70,91.HUANG Ji-hui,XIA Cai-chu,HAN Chang-ling,et al.Distribution and Simplified Calculation Method of the Frost Heaving Force of Highway Tunnels in Cold Regions [J].Modern Tunnelling Technology,2016,53 (5):63-70,91.
[19] 汪双杰,王佐,袁堃,等.青藏公路多年冻土地区公路工程地质研究回顾与展望[J].中国公路学报,2015,28(12):1-8,32.WANG Shuang-jie,WANG Zuo,YUAN Kun,et al.Qinghai-Tibet Highway Engineering Geology in Permafrost Regions:Review and Prospect [J].China Journal of Highway and Transport,2015,28 (12):1-8,32.
[20] 汪双杰,陈建兵,金龙,等.基于能量平衡的多年冻土区公路设计理论研究[J].冰川冻土,2014,36(4):782-789.WANG Shuang-jie,CHEN Jian-bing,JIN Long,et al.Design Theory of Highway in Permafrost Regions Based on Energy Balance [J].Journal of Glaciology and Geocryology,2014,36 (4):782-789.
[2] 姚红志,张晓旭,董长松,等.多年冻土区公路隧道保温隔热层铺设方式及材料性能对比分析[J].中国公路学报,2015,28(12):106-113.YAO Hong-zhi,ZHANG Xiao-xu,DONG Chang-song,et al.Comparison Analysis on Heat Insulating Material Property Laying Way of Highway Tunnel in Permafrost Regions [J].China Journal of Highway and Transport,2015,28 (12):106-113.
[3] 周小涵,曾艳华,范磊,等.寒区隧道温度场的时空演化规律及温控措施研究[J].中国铁道科学,2016,37(3):46-52 ZHOU Xiao-han,ZENG Yan-hua,FAN Lei,et al.Temporal-spatial Evolution Laws of Temperature Field in Cold Region Tunnel and Temperature Control Measures [J].China Railway Science,2016,37 (3):46-52.
[4] 何春雄,吴紫汪,朱林楠.祁连山区大坂山隧道围岩的冻融状况分析[J].冰川冻土,2000,22(2):113-120.HE Chun-xiong,WU Zi-wang,ZHU Lin-nan.Analysis of Freeze-thaw Condition in the Surrounding Rock Wall of Dabanshan Tunnel in the Qilian Mountains [J].Journal of Glaciology and Geocryology,2000,22 (2):113-120.
[5] 赖远明.冻土的强度准则和本构关系研究进展[C]//中国力学学会.中国力学大会2015论文集.上海:中国力学学会,2015:1-10.LAI Yuan-ming.Progress in Strength Criteria and Constitutive Relationship of Frozen Soil [C] // Chinese Society of Mechanics.Chinese Mechanics Congress-2015.Shanghai:Chinese Society of Mechanics,2015:1-10.
[6] 张学富,赖远明,喻文兵,等.风火山隧道多年冻土回冻预测分析[J].岩石力学与工程学报,2004,23(24):4170-4178.ZHANG Xue-fu,LAI Yuan-ming,YU Wen-bing,et al.Forecast and Analysis of Refreezing in Fenghuoshan Permafrost Tunnel [J].Chinese Journal of Rock Mechanics and Engineering,2004,23 (24):4170-4178.
[7] 张耀,何树生,李靖波.寒区有隔热层的圆形隧道温度场解析解[J].冰川冻土,2009,31(1):113-118.ZHANG Yao,HE Shu-sheng,LI Jing-bo.Analytic Solutions for Temperature Fields of a Circular Tunnel with Insulation Layer in Cold Region [J].Journal of Glaciology and Geocryology,2009,31 (1):113-118.
[8] 夏才初,范东方,韩常领.寒区隧道不同类型冻土段隔热(保温)层铺设厚度计算方法[J].中国公路学报,2013,26(5):131-139.XIA Cai-chu,FAN Dong-fang,HAN Chang-ling.Piecewise Calculation Method for Insulation Layer Thickness in Cold Region Tunnels [J].China Journal of Highway and Transport,2013,26 (5):131-139.
[9] 夏才初,何佳,范东方.不同冻土区隧道防寒泄水洞的作用和结构型式研究[J].现代隧道技术,2017,54(2):1-8.XIA Cai-chu,HE Jia,FAN Dong-fang.Roles and Structures of Cold-proof Drainage Tunnels for Different Permafrost Tunnels [J].Modern Tunnelling Technology,2017,54 (2):1-8.
[10] 乜风鸣,刘德福.多年冻土中隧道泄水洞热动态分析[J].低温建筑技术,2001(3):37-38.NIE Feng-ming,LIU De-fu.The Thermal Dynamic Analysis of Tunnel Drainage Hole in the Perennial Frozen Soil [J].Low Temperature Architecture Technology,2001 (3):37-38.
[11] 米隆,赖远明,吴紫汪,等.高原冻土铁路路基温度特性的有限元分析[J].铁道学报,2003,25(2):62-67.MI Long,LAI Yuan-ming,WU Zi-wang,et al.The Finite Element Analysis for Temperature Property of Railway Embankments in Cold Regions[J].Journal of the China Railway Society,2003,25 (2):62-67.
[12] 刘志春,李文江,朱永全,等.青藏铁路风火山隧道洞内外温度实测与分析[J].铁道标准设计,2004(11):56-58.LIU Zhi-chun,LI Wen-jiang,ZHU Yong-quan,et al.Temperature Measurement and Analysis Inside and Outside Fenghuoshan Tunnel on Qinghai-Tibet Railway [J].Railway Standard Design,2004 (11):56-58.
[13] 陈建勋,罗彦斌.寒冷地区隧道防冻隔温层厚度计算方法[J].交通运输工程学报,2007,7(2):76-79.CHEN Jian-xun,LUO Yan-bin.Calculation Method of Antifreezing Layer Thickness in Cold Region Tunnel [J].Journal of Traffic and Transportation Engineering,2007,7 (2):76-79.
[14] 陈建勋,昝勇杰.寒冷地区公路隧道防冻隔温层效果现场测试与分析[J].中国公路学报,2001,14(4):75-79.CHEN Jian-xun,ZAN Yong-jie.Field Test and Analysis of Antifreezing Thermal-protective Layer Effect of the Highway Tunnel in Cold Area [J].China Journal of Highway and Transport,2001,14 (4):75-79.
[15] 朱东鹏,袁堃,陈建兵,等.高温多年冻土区公路通风管路基传热特征分析[J].中国公路学报,2015,28(12):69-77.ZHU Dong-peng,YUAN Kun,CHEN Jian-bing,et al.Analysis on Heat Transfer Characteristics of Highway Duct-ventilated Embankment in High Temperature Permafrost Regions [J].China Journal of Highway and Transport,2015,28 (12):69-77.
[16] 夏才初,范东方,李强,等.寒区隧道保温层铺设长度的计算方法[J].同济大学学报:自然科学版,2016,44(9):1363-1370.XIA Cai-chu,FAN Dong-fang,LI Qiang,et al.An Approach for Determining Length of Insulation Layer in Cold Region Tunnel [J].Journal of Tongji University:Natural Science,2016,44 (9):1363-1370.
[17] 徐小涛.鄂拉山隧道保温抗冻及防排水技术研究[D].重庆:重庆交通大学,2013.XU Xiao-tao.Study on Frostance,Anti-freezing and Drainage Technology of the Elashan Tunnel [D].Chongqing:Chongqing Jiaotong University,2013.
[18] 黄继辉,夏才初,韩常领,等.寒区公路隧道冻胀力荷载的分布形式和简化计算方法[J].现代隧道技术,2016,53(5):63-70,91.HUANG Ji-hui,XIA Cai-chu,HAN Chang-ling,et al.Distribution and Simplified Calculation Method of the Frost Heaving Force of Highway Tunnels in Cold Regions [J].Modern Tunnelling Technology,2016,53 (5):63-70,91.
[19] 汪双杰,王佐,袁堃,等.青藏公路多年冻土地区公路工程地质研究回顾与展望[J].中国公路学报,2015,28(12):1-8,32.WANG Shuang-jie,WANG Zuo,YUAN Kun,et al.Qinghai-Tibet Highway Engineering Geology in Permafrost Regions:Review and Prospect [J].China Journal of Highway and Transport,2015,28 (12):1-8,32.
[20] 汪双杰,陈建兵,金龙,等.基于能量平衡的多年冻土区公路设计理论研究[J].冰川冻土,2014,36(4):782-789.WANG Shuang-jie,CHEN Jian-bing,JIN Long,et al.Design Theory of Highway in Permafrost Regions Based on Energy Balance [J].Journal of Glaciology and Geocryology,2014,36 (4):782-789.