气候变暖下青藏高原冻土路基地温场演化规律研究
|
摘要
冻土物理力学特性与温度密切相关,气候变暖背景下冻土路基地温场的分布和演化规律不仅会影响到路基的静力稳定性,还会影响到其在地震、车辆等动力荷载作用下的响应特征与稳定性。为此,基于现场实测路基坡面温度,系统开展气候变暖背景下青藏高原典型(东西、南北、45°)走向条件下冻土路基地温场分布及演化规律的模拟研究。结果表明,阴阳坡侧浅层土体冻结指数差异较融化指数差异更为显著,东西走向下阴坡冻结指数约为阳坡的2倍,而融化指数约为阳坡的0.83。阴阳坡侧路基本体及活动层季节冻融过程存在明显不同步,东西走向条件下阴坡冻结期(融化期)可较阳坡侧长(短)约1个月。路基修筑后,阴坡一侧路基下部人为上限均有一定的抬升,而阳坡仅南北走向有抬升。此后,在气候变暖及沥青路面吸热效应下,路基人为上限不断下降,最大速率可达20cm/a,且逐步出现融化夹层,其中阳坡融化夹层厚度普遍大于阴坡,差值最大可达2.5m。路基本体季节冻融过程的不同步、人为上限埋深及冻土地温分布的不对称性应在未来青藏高原冻土路基静力、动力稳定性设计和研究中予以考虑。
The physical and mechanical characteristics of frozen soils are closely related to the temperature.The distribution and evolution law of a ground temperature field in a permafrost roadbed under climate warming does not only affect the static stability of embankment,but also affects the response characteristics and stability under dynamic loads such as earthquake and vehi-cle loads.Based on the field-measured temperature of roadbed slope,the distribution and evolution law of the ground temperature field in the permafrost roadbed of the Qinghai—Tibet Plateau under climate warming is systematically simulated in this paper.The results show that the difference of the freezing index of the shallow soil on the sunny-shady slope is more obvious than that of thawing index.The freezing index of the shady slope is about twice that of the sunny slope for the two embankments,while the melting index of the shady slope is about 0.83 times of that of the sunny slope.The seasonal freeze-thaw process of the roadbed body and the active layer at sunny-shady slopes do not correlate.The maximum difference in the freezing-thawing period of the two slopes can be as much as one month for the roadbed in ES orientation.After the roadbed construction,the artificial permafrost table beneath the shady slope has a certain uplift under the three orientations.While beneath the sunny slope,the artificial permafrost table only uplifts for the roadbed in NS orientation.Then,because of the climate warming and the significant heat absorption of asphalt pavement,the artificial permafrost table declines quickly both under the sunny and shady slopes,and the maximum decline rate can reach 20 cm/a.With the decline of the artificial permafrost table,thawed bulb develops within the permafrost subgrade.The thickness of the thawed bulb is greater beneath the sunny slope than beneath the shady slope,with a maximum difference of 2.5 m.The seasonal freezing-thawing process of roadbed body and the artificial permafrost table buried depth and asymmetry of temperature field distribution should be considered in future designs and studies on the static and dynamic stability of the permafrost roadway embankment.
The physical and mechanical characteristics of frozen soils are closely related to the temperature.The distribution and evolution law of a ground temperature field in a permafrost roadbed under climate warming does not only affect the static stability of embankment,but also affects the response characteristics and stability under dynamic loads such as earthquake and vehi-cle loads.Based on the field-measured temperature of roadbed slope,the distribution and evolution law of the ground temperature field in the permafrost roadbed of the Qinghai—Tibet Plateau under climate warming is systematically simulated in this paper.The results show that the difference of the freezing index of the shallow soil on the sunny-shady slope is more obvious than that of thawing index.The freezing index of the shady slope is about twice that of the sunny slope for the two embankments,while the melting index of the shady slope is about 0.83 times of that of the sunny slope.The seasonal freeze-thaw process of the roadbed body and the active layer at sunny-shady slopes do not correlate.The maximum difference in the freezing-thawing period of the two slopes can be as much as one month for the roadbed in ES orientation.After the roadbed construction,the artificial permafrost table beneath the shady slope has a certain uplift under the three orientations.While beneath the sunny slope,the artificial permafrost table only uplifts for the roadbed in NS orientation.Then,because of the climate warming and the significant heat absorption of asphalt pavement,the artificial permafrost table declines quickly both under the sunny and shady slopes,and the maximum decline rate can reach 20 cm/a.With the decline of the artificial permafrost table,thawed bulb develops within the permafrost subgrade.The thickness of the thawed bulb is greater beneath the sunny slope than beneath the shady slope,with a maximum difference of 2.5 m.The seasonal freezing-thawing process of roadbed body and the artificial permafrost table buried depth and asymmetry of temperature field distribution should be considered in future designs and studies on the static and dynamic stability of the permafrost roadway embankment.
引文
[1]马巍,牛富俊,穆彦虎.青藏高原重大冻土工程的基础研究[J].地球科学进展,2012,27(11):1185-1191.MA Wei,NIU Fujun,MU Yanhu.Basic Research on the Major Permafrost Projects in the Qinghai—Tibet Plateau[J].Advances in Earth Science,2012,27(11):1185-1191.
[2]杨成松,何平,程国栋,等.冻土热融下沉研究的现状和进展[J].工程地质学报,2004,12(增刊1):147-150.YANG Chengsong,HE Ping,CHENG Guodong,et al.Current State and Progress of the Study on Thawing Settlement of Frozen Ground[J].Journal of Engineering Geology,2004,12(Supp1):147-150.
[3]胡泽勇,程国栋,谷良雷,等.青藏铁路路基表面太阳总辐射和温度反演方法[J].地球科学进展,2006,21(12):1304-1313.HU Zeyong,CHENG Guodong,GU Lianglei,et al.Calculating Method of Global Radiation and Temperature on the Roadbed Surface of Qinghai—Xizang Railway[J].Advances in Earth Science,2006,21(12):1304-1313.
[4]汪双杰,霍明,周文锦.青藏公路多年冻土路基病害[J].公路,2004(5):22-26.WANG Shuangjie,HUO Ming,ZHOU Wenjin.Subgrade Failure of Qinghai—Tibet Highway in Permafrost Area[J].Highway,2004(5):22-26.
[5]董昶宏,赵相卿.青藏铁路多年冻土区路基变形特征及影响因素分析[J].铁道标准设计,2013(6):5-8.DONG Changhong,ZHAO Xiangqing.Analysis on Subgrade Deformation Features and Influence Factors in Permafrost Regions on Qinghai—Tibet Railway[J].Railway Standard Design,2013(6):5-8.
[6]穆彦虎,马巍,牛富俊,等.青藏铁路多年冻土区普通路基热状况监测分析[J].冰川冻土,2014,36(4):953-961.MU Yanhu,MA Wei,NIU Fujun,et al.Monitoring and Analyzing the Thermal Conditions of Traditional Embankments along the Qinghai—Tibet Railway[J].Journal of Glaciology and Geocryology,2014,36(4):953-961.
[7]丑亚玲,盛煜,马巍.青藏高原多年冻土区铁路路基阴阳坡表面温差的计算[J].岩石力学与工程学报,2007,26(增刊2):4102-4107.CHOU Yaling,SHENG Yu,MA Wei.Calculation of Difference in Temperature Between Sunny Slope and Shady Slope along Railways in Permafrost Regions in Qinghai—Tibet Plateau[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Supp2):4102-4107.
[8]胡达,喻文兵,易鑫,等.青藏工程走廊楚玛尔河高平原地区路基边界温度特征[J].冰川冻土,2016,38(5):1332-1339.HU Da,YU Wenbing,YI Xin,et al.Boundary Temperature Features of the Embankment in Qumar River Region along the Qinghai—Tibet Transportation Engineering Corridor[J].Journal of Glaciology and Geocryology,2016,38(5):1332-1339.
[9]易鑫,喻文兵,陈琳,等.边界条件对多年冻土路基热稳定性的影响分析[J].冰川冻土,2014,36(2):369-375.YI Xin,YU Wenbing,CHEN Lin,et al.Influence of Boundary Conditions on the Thermal Stability of Embankments in Permafrost Regions[J].Journal of Glaciology and Geocryology,2014,36(2):369-375.
[10]丑亚玲,蒋先刚,朱彦鹏.高温多年冻土路基纵向裂缝发育的热-力耦合分析[J].兰州理工大学学报,2014,40(1):123-129.CHOU Yaling,JIANG Xian'gang,ZHU Yanpeng.Thermomechanical Coupled Analysis on the Embankment Longitudinal Crack in Warm Permafrost Regions[J].Journal of Lanzhou University of Technology,2014,40(1):123-129.
[11]邓起东,程绍平,马冀,等.青藏高原地震活动特征及当前地震活动形势[J].地球物理学报,2014,57(7):2025-2042.DENG Qidong,CHENG Shaoping,MA Ji,et al.Seismic Activities and Earthquake Potential in the Tibetan Plateau[J].Chinese Journal of Geophysics,2014,57(7):2025-2042.
[12]吴志坚,王兰民,马巍,等.地震荷载作用下冻土的动力学参数试验研究[J].西北地震学报,2003,25(3):210-214.WU Zhijian,WANG Lanmin,MA Wei,et al.Laboratory Study on Dynamics Parameters of Frozen Soil under Seismic Dynamic Loading[J].Northwestern Seismological Journal,2003,25(3):210-214.
[13]王兰民,张冬丽,吴志坚,等.地温对冻土动力特性及其场地地震动参数的影响[J].中国地震,2003,9(19):195-205.WANG Lanmin,Zhang Dongli,WU Zhijian,et al.The Influence of Earth Temperature on Dynamic Characteristics of Frozen Soil and the Parameters of Ground Motion on the Sites of Frozen Soil[J].Earthquake Research in China,2003,9(19):195-205.
[14]陈拓,吴志坚,车爱兰,等.机车动荷载作用下多年冻土区铁路路基动力响应的试验研究[J].地震工程与工程振动,2011,31(1):168-173.CHEN Tuo,WU Zhijian,CHE Ailan,et al.Test Study on Dynamic Responses of Railroad Embankments in Permafrost Regions under Train Dynamic Loading[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(1):168-173.
[15]LI Shuangyang,LAI Yuanming,ZHANG Mingyi,et al.Seismic Analysis of Embankment of Qinghai—Tibet Railway[J].Cold Regions Science and Technology,2009,55(1):151-159.
[16]LI Shuangyang,LAI Yuanming,ZHANG Mingyi,et al.Seasonal Differences in Seismic Responses of Embankment on a Sloping Ground in Permafrost Regions[J].Soil Dynamics and Earthquake Engineering,2015,76:122-135.
[17]汪水银,沙爱民,穆柯,等.地震作用下高原多年冻土区高填方路基动力响应[J].长安大学学报(自然科学版),2017,34(4):68-75.WANG Shuiyin,SHA Aimin,MU Ke,et al.Dynamic Response of High Filled Embankments under Earthquake in Plateau Permafrost Areas[J].Journal of Chang'an University(Natural Science Edition),2017,34(4):68-75.
[18]田亚护,刘建坤,钱征宇,等.多年冻土区含保温夹层路基温度长的数值模拟[J].中国铁道科学,2002,23(2):59-64.TIAN Yahu,LIU Jiankun,QIAN Zhengyu,et al.Numerical Simulation for Temperature Field of Roadbed on Permafrost with Insulation[J].China Railway Science,2002,23(2):59-64.
[19]徐顺国,牟瑞芳,曾晓燕,等.多年冻土区草皮护坡路基温度场的数值模拟[J].路基工程,2006(6):49-51.XU Shunguo,MOU Ruifang,ZENG Xiaoyan,et al.Numerical Simulation of Temperature Field of Turf Side Slope Protection in Permafrost Regions[J].Subgrade Engineering,2006(6):49-51.
[20]朱志武,宋顺成.冻土地区路基温度场数值模拟[J].路基工程,2008(2):18-19.ZHU Zhiwu,SONG Shuncheng.Numerical Simulation of Subgrade Temperature Field in Permafrost Regions[J].Subgrade Engineering,2008(2):18-19.
[21]COMINI G,GUIDICE S Del,LEWIS R W,et al.Finite Element Solution of Nonlinear Heat Conduction Problems with Special Reference to Phase Change[J].Inter J for Numerical Methods in Engineering,1974,8(6):613-624.
[22]郭宽良,孔祥谦,陈善年.计算传热学[M].合肥:中国科学技术大学出版社,1988.GUO Kuanliang,KONG Xiangqian,CHEN Shannian.Computational Heat Transfer[M].Hefei:Press of University of Science and Technology of China,1988.
[23]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.XU Xuezu,DENG Yousheng.Experimental Study on Water Transference in Frozen Soil[M].Beijing:Science Press,1991.
[24]丑亚玲.多年冻土区路基阴阳坡效应及纵向裂缝机理研究[D].兰州:中国科学院寒区旱区环境与工程研究所,2008.CHOU Yaling.Study on Shady-Sunny Effect and the Forming Mechanism of the Longitudinal Embankment Crack in Permafrost Region[D].Lanzhou:Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Science,2008.
[25]穆彦虎,李国玉,俞祁浩,等.热管措施作用下锥柱式基础传热过程及冷却降温效果预测研究[J].冰川冻土,2014,36(1):106-117.MU Yanhu,LI Guoyu,YU Qihao,et al.Numerical Simulation of Heat Transfer Process of Cone-cylinder Pipe and Cooling Effects of Thermosiphon along the Qinghai—Tibet DC Interconnection Project[J].Journal of Glaciology and Geocryology,2014,36(1):106-117.
[26]秦大河.中国西部环境演变评估综合报告[M].北京:科学出版社,2002:55-60.QIN Dahe.Comprehensive Report on Environmental Change Assessment in Western China[M].Beijing:Science Press,2002:55-60.
[27]赖远明.构筑物与冻土地基热、力耦合作用的动力学过程[R].兰州:中国科学院寒区旱区环境与工程研究所,2016:60-62.LAI Yuanming.Dynamic Process of Thermal and Mechanical Coupling Between Structures and Frozen Ground[R].Lanzhou:Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Science,2016:60-62.
[28]盛煜,马巍,温智.多年冻土区铁路路基阴阳坡面热状况差异分析[J].岩石力学与工程学报,2005,24(17):3197-3201.SHENG Yu,MA Wei,WEN Zhi,et al.Analysis of Difference in Thermal State Between South Faced Slope and North Faced Slope of Railway Embankment in Permafrost Region[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(17):3197-3201.
[29]WU Qingbai,LIU Yongzhi,Hu Zeyong.The Thermal Effect of Differential Solar Exposure on Embankments along the Qinghai—Tibet Railway[J].Cold Regions Science and Technology,2011,66(1):30-38.
[30]牛富俊,刘明浩,程国栋,等.多年冻土区青藏铁路路基的长期热状况[J].中国科学:地球科学,2015,45(8):1220-1228.NIU Fujun,LIU Minghao,CHENG Guodong,et al.Long Term Thermal Condition of Qinghai—Tibet Railway Embankment in Permafrost Regions[J].Science China:Earth Science,2015,45(8):1220-1228.
[2]杨成松,何平,程国栋,等.冻土热融下沉研究的现状和进展[J].工程地质学报,2004,12(增刊1):147-150.YANG Chengsong,HE Ping,CHENG Guodong,et al.Current State and Progress of the Study on Thawing Settlement of Frozen Ground[J].Journal of Engineering Geology,2004,12(Supp1):147-150.
[3]胡泽勇,程国栋,谷良雷,等.青藏铁路路基表面太阳总辐射和温度反演方法[J].地球科学进展,2006,21(12):1304-1313.HU Zeyong,CHENG Guodong,GU Lianglei,et al.Calculating Method of Global Radiation and Temperature on the Roadbed Surface of Qinghai—Xizang Railway[J].Advances in Earth Science,2006,21(12):1304-1313.
[4]汪双杰,霍明,周文锦.青藏公路多年冻土路基病害[J].公路,2004(5):22-26.WANG Shuangjie,HUO Ming,ZHOU Wenjin.Subgrade Failure of Qinghai—Tibet Highway in Permafrost Area[J].Highway,2004(5):22-26.
[5]董昶宏,赵相卿.青藏铁路多年冻土区路基变形特征及影响因素分析[J].铁道标准设计,2013(6):5-8.DONG Changhong,ZHAO Xiangqing.Analysis on Subgrade Deformation Features and Influence Factors in Permafrost Regions on Qinghai—Tibet Railway[J].Railway Standard Design,2013(6):5-8.
[6]穆彦虎,马巍,牛富俊,等.青藏铁路多年冻土区普通路基热状况监测分析[J].冰川冻土,2014,36(4):953-961.MU Yanhu,MA Wei,NIU Fujun,et al.Monitoring and Analyzing the Thermal Conditions of Traditional Embankments along the Qinghai—Tibet Railway[J].Journal of Glaciology and Geocryology,2014,36(4):953-961.
[7]丑亚玲,盛煜,马巍.青藏高原多年冻土区铁路路基阴阳坡表面温差的计算[J].岩石力学与工程学报,2007,26(增刊2):4102-4107.CHOU Yaling,SHENG Yu,MA Wei.Calculation of Difference in Temperature Between Sunny Slope and Shady Slope along Railways in Permafrost Regions in Qinghai—Tibet Plateau[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Supp2):4102-4107.
[8]胡达,喻文兵,易鑫,等.青藏工程走廊楚玛尔河高平原地区路基边界温度特征[J].冰川冻土,2016,38(5):1332-1339.HU Da,YU Wenbing,YI Xin,et al.Boundary Temperature Features of the Embankment in Qumar River Region along the Qinghai—Tibet Transportation Engineering Corridor[J].Journal of Glaciology and Geocryology,2016,38(5):1332-1339.
[9]易鑫,喻文兵,陈琳,等.边界条件对多年冻土路基热稳定性的影响分析[J].冰川冻土,2014,36(2):369-375.YI Xin,YU Wenbing,CHEN Lin,et al.Influence of Boundary Conditions on the Thermal Stability of Embankments in Permafrost Regions[J].Journal of Glaciology and Geocryology,2014,36(2):369-375.
[10]丑亚玲,蒋先刚,朱彦鹏.高温多年冻土路基纵向裂缝发育的热-力耦合分析[J].兰州理工大学学报,2014,40(1):123-129.CHOU Yaling,JIANG Xian'gang,ZHU Yanpeng.Thermomechanical Coupled Analysis on the Embankment Longitudinal Crack in Warm Permafrost Regions[J].Journal of Lanzhou University of Technology,2014,40(1):123-129.
[11]邓起东,程绍平,马冀,等.青藏高原地震活动特征及当前地震活动形势[J].地球物理学报,2014,57(7):2025-2042.DENG Qidong,CHENG Shaoping,MA Ji,et al.Seismic Activities and Earthquake Potential in the Tibetan Plateau[J].Chinese Journal of Geophysics,2014,57(7):2025-2042.
[12]吴志坚,王兰民,马巍,等.地震荷载作用下冻土的动力学参数试验研究[J].西北地震学报,2003,25(3):210-214.WU Zhijian,WANG Lanmin,MA Wei,et al.Laboratory Study on Dynamics Parameters of Frozen Soil under Seismic Dynamic Loading[J].Northwestern Seismological Journal,2003,25(3):210-214.
[13]王兰民,张冬丽,吴志坚,等.地温对冻土动力特性及其场地地震动参数的影响[J].中国地震,2003,9(19):195-205.WANG Lanmin,Zhang Dongli,WU Zhijian,et al.The Influence of Earth Temperature on Dynamic Characteristics of Frozen Soil and the Parameters of Ground Motion on the Sites of Frozen Soil[J].Earthquake Research in China,2003,9(19):195-205.
[14]陈拓,吴志坚,车爱兰,等.机车动荷载作用下多年冻土区铁路路基动力响应的试验研究[J].地震工程与工程振动,2011,31(1):168-173.CHEN Tuo,WU Zhijian,CHE Ailan,et al.Test Study on Dynamic Responses of Railroad Embankments in Permafrost Regions under Train Dynamic Loading[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(1):168-173.
[15]LI Shuangyang,LAI Yuanming,ZHANG Mingyi,et al.Seismic Analysis of Embankment of Qinghai—Tibet Railway[J].Cold Regions Science and Technology,2009,55(1):151-159.
[16]LI Shuangyang,LAI Yuanming,ZHANG Mingyi,et al.Seasonal Differences in Seismic Responses of Embankment on a Sloping Ground in Permafrost Regions[J].Soil Dynamics and Earthquake Engineering,2015,76:122-135.
[17]汪水银,沙爱民,穆柯,等.地震作用下高原多年冻土区高填方路基动力响应[J].长安大学学报(自然科学版),2017,34(4):68-75.WANG Shuiyin,SHA Aimin,MU Ke,et al.Dynamic Response of High Filled Embankments under Earthquake in Plateau Permafrost Areas[J].Journal of Chang'an University(Natural Science Edition),2017,34(4):68-75.
[18]田亚护,刘建坤,钱征宇,等.多年冻土区含保温夹层路基温度长的数值模拟[J].中国铁道科学,2002,23(2):59-64.TIAN Yahu,LIU Jiankun,QIAN Zhengyu,et al.Numerical Simulation for Temperature Field of Roadbed on Permafrost with Insulation[J].China Railway Science,2002,23(2):59-64.
[19]徐顺国,牟瑞芳,曾晓燕,等.多年冻土区草皮护坡路基温度场的数值模拟[J].路基工程,2006(6):49-51.XU Shunguo,MOU Ruifang,ZENG Xiaoyan,et al.Numerical Simulation of Temperature Field of Turf Side Slope Protection in Permafrost Regions[J].Subgrade Engineering,2006(6):49-51.
[20]朱志武,宋顺成.冻土地区路基温度场数值模拟[J].路基工程,2008(2):18-19.ZHU Zhiwu,SONG Shuncheng.Numerical Simulation of Subgrade Temperature Field in Permafrost Regions[J].Subgrade Engineering,2008(2):18-19.
[21]COMINI G,GUIDICE S Del,LEWIS R W,et al.Finite Element Solution of Nonlinear Heat Conduction Problems with Special Reference to Phase Change[J].Inter J for Numerical Methods in Engineering,1974,8(6):613-624.
[22]郭宽良,孔祥谦,陈善年.计算传热学[M].合肥:中国科学技术大学出版社,1988.GUO Kuanliang,KONG Xiangqian,CHEN Shannian.Computational Heat Transfer[M].Hefei:Press of University of Science and Technology of China,1988.
[23]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.XU Xuezu,DENG Yousheng.Experimental Study on Water Transference in Frozen Soil[M].Beijing:Science Press,1991.
[24]丑亚玲.多年冻土区路基阴阳坡效应及纵向裂缝机理研究[D].兰州:中国科学院寒区旱区环境与工程研究所,2008.CHOU Yaling.Study on Shady-Sunny Effect and the Forming Mechanism of the Longitudinal Embankment Crack in Permafrost Region[D].Lanzhou:Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Science,2008.
[25]穆彦虎,李国玉,俞祁浩,等.热管措施作用下锥柱式基础传热过程及冷却降温效果预测研究[J].冰川冻土,2014,36(1):106-117.MU Yanhu,LI Guoyu,YU Qihao,et al.Numerical Simulation of Heat Transfer Process of Cone-cylinder Pipe and Cooling Effects of Thermosiphon along the Qinghai—Tibet DC Interconnection Project[J].Journal of Glaciology and Geocryology,2014,36(1):106-117.
[26]秦大河.中国西部环境演变评估综合报告[M].北京:科学出版社,2002:55-60.QIN Dahe.Comprehensive Report on Environmental Change Assessment in Western China[M].Beijing:Science Press,2002:55-60.
[27]赖远明.构筑物与冻土地基热、力耦合作用的动力学过程[R].兰州:中国科学院寒区旱区环境与工程研究所,2016:60-62.LAI Yuanming.Dynamic Process of Thermal and Mechanical Coupling Between Structures and Frozen Ground[R].Lanzhou:Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Science,2016:60-62.
[28]盛煜,马巍,温智.多年冻土区铁路路基阴阳坡面热状况差异分析[J].岩石力学与工程学报,2005,24(17):3197-3201.SHENG Yu,MA Wei,WEN Zhi,et al.Analysis of Difference in Thermal State Between South Faced Slope and North Faced Slope of Railway Embankment in Permafrost Region[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(17):3197-3201.
[29]WU Qingbai,LIU Yongzhi,Hu Zeyong.The Thermal Effect of Differential Solar Exposure on Embankments along the Qinghai—Tibet Railway[J].Cold Regions Science and Technology,2011,66(1):30-38.
[30]牛富俊,刘明浩,程国栋,等.多年冻土区青藏铁路路基的长期热状况[J].中国科学:地球科学,2015,45(8):1220-1228.NIU Fujun,LIU Minghao,CHENG Guodong,et al.Long Term Thermal Condition of Qinghai—Tibet Railway Embankment in Permafrost Regions[J].Science China:Earth Science,2015,45(8):1220-1228.