Equations and numerical simulation for coupled water and heat transfer in frozen soil
BAI Qing-bo1, LI Xu1, 2, TIAN Ya-hu1, FANG Jian-hong2
1. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China; 2.Qinghai Research and Observation Base, Key Laboratory of Highway Construction & Maintenance Technology in Permafrost Regions, Ministry of Transport, Xining 810001, China
Abstract：Frost heaving and thaw collapsing are the main defects of subgrade in permafrost areas and are highly related to the coupled heat-moisture migration. Based on the water flow theory of unsaturated soil and the heat transfer theory of soil, the differential equations for coupled water and heat transfer are established. The coupled water and heat transfer problem of frozen soil is solved using the secondary development of COMSOL Multi-physics. To verify the method for simulating the heat-moisture coupled process, the freezing and thawing processes of soil columns are simulated, and the results are compared with the measured data from laboratory tests. Finally, a case study is carried out for the subgrade in Maduo county, Qinghai Province, and the characteristics of the coupled heat-moisture migration in permafrost subgrade are analyzed.
白青波, 李旭, 田亚护, 房建宏. 冻土水热耦合方程及数值模拟研究[J]. 岩土工程学报, 2015, 37(zk2): 131-136.
BAI Qing-bo, LI Xu, TIAN Ya-hu, FANG Jian-hong. Equations and numerical simulation for coupled water and heat transfer in frozen soil. Chinese J. Geot. Eng., 2015, 37(zk2): 131-136.
[1] 徐学祖, 王家澄, 张立新. 冻土物理学[M]. 北京: 科学出版社, 2001: 75-98. (XU Xue-zu, WANG Jia-cheng, ZHANG Li-xin. Permafrost physics [M]. Beijing: Science Press, 2001: 75-98. (in Chinese)) [2] 李述训, 程国栋. 冻融土中的水热输运问题[M]. 兰州： 兰州大学出版社, 1995. (LI Shu-xun, CHENG Guo-dong. Problem of heat and moisture transfer in freezing and thawing soils[M]. Lanzhou: Lanzhou University Press, 1995. (in Chinese)) [3] 王铁行, 胡长顺. 多年冻土地区路基温度场和水分迁移场耦合问题研究[J]. 土木工程学报, 2003, 36(12): 93-97. (WANG Tie-xing, HU Chang-shun. Study on the problem of coupled temperature field and moisture migration field of subgrade in permafrost region[J]. China Civil Engineering Journal, 2003, 36(12): 93-97. (in Chinese)) [4] TAYLOR G S, LUTHIN J N. A model for coupled heat and moisture transfer during soil freezing[J]. Canadian Geotechnical Journal, 1978, 15: 548-555. [5] 田亚护, 刘建坤, 钱征宇, 等. 多年冻土区含保温夹层路基温度场的数值模拟[J]. 中国铁道科学, 2002, 23(2): 59-64. (TIAN Ya-hu, LIU Jian-kun, QIAN Zheng-yu, et al. Numerical simulation for temperature field of roadbed on permafrost with insulation[J]. China Railway Science, 2002, 23(2): 59-64. (in Chinese)) [6] 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 Xue-zu, DENG You-sheng. Experimental research of moisture migration in permafrost[M]. Beijing: Science Press, 1991. (in Chinese)) [7] 孙增奎, 王连俊, 魏庆朝, 等. 青藏铁路多年冻土区路基温度场的模拟与预测[J]. 北京交通大学学报, 2004, 28(1): 55-59. (SUN Zeng-kui, WANG Lian-jun, WEI Qing-chao, et al. Simulation and Prediction of temperature field of Qinghai-Tibet railway roadbed on permafrost regions[J]. Journal of Northern Jiaotong University, 2004, 28(1): 55-59. (in Chinese)) [8] 王俊智, 梁四海, 万 力, 等. 高寒地区冻土活动层温度场数值模拟[J]. 人民黄河, 2013, 35(3): 20-23. (WANG Jun-zhi, LIANG Si-hai, WAN Li, et al. Numerical simulation of the thermal regime of permafrost active layer in alpine regions[J]. Yellow River, 2013, 35(3): 20-23. (in Chinese)) [9] 毛雪松, 王秉刚, 胡长顺, 等. 冻土路基水热迁移问题的理论模型及数值模拟[J]. 中外公路, 2006, 26(1): 23-26. (MAO Xue-song, WANG Bing-gang, HU Chang-shun, et al. The theoretical model and numerical simulation of water-heat transfer problems in permafrost roadbed[J]. Journal of China & Foreign Highway, 2006, 26(1): 23-26. (in Chinese)) [10] 陶文铨. 传热学[M]. 西安: 西北工业大学出版社, 2006. (TAO Wen-quan. Heat Transfer[M]. Xi'an: Northwestern Polytechnical University Press, 2006. (in Chinese)) [11] 卢 宁(美), LIKOS William J. 非饱和土力学[M]. 北京: 高等教育出版社, 2012: 269-287. (LU Ning, LIKOS William J. Unsaturated soil mechanics[M]. Beijing: Higher Education Press, 2012: 269-287. (in Chinese)) [12] COMSOL Multiphysics User’s Guide (Version:4.3a)[R]. Stockholm: COMSOL AB, 2012. [13] 曹元兵, 盛 煜, 吴吉春, 等. 上边界条件对多年冻土地温场数值模拟结果的影响分析[J]. 冰川冻土, 2014, 36(4): 802-810. (CAO Yuan-bing, SHENG Yu, WU Ji-chun, et al. Influence of upper boundary conditions on simulated ground temperature field in permafrost regions[J]. Journal of Glaciology and Geocryology, 2014, 36(4): 802-810. (in Chinese)) [14] 吴紫旺. 冻土的温度水分应力及相互作用[M]. 兰州: 兰州大学出版社, 1989: 21-36. (WU Zi-wang. Interaction among Temperature, Moisture and Stress Fields in Frozen Soil[M]. Lanzhou: Lanzhou University Press, 1989: 21-36. (in Chinese)) [15] 毛雪松, 马 骉. 基于水热耦合效应的冻土路基稳定性研究[M]. 北京: 人民交通出版社, 2011: 76-85. (MAO Xue-song, MA Biao. Studies on the stability of permafrost subgrade based on coupled water and heat transfer[M]. Beijing: China Communications Press, 2011: 76-85. (in Chinese))
