(1. School of Architecture and Civil Engineering，Xi?an University of Science and Technology，Xi?an，Shaanxi 710054，China；
2. School of Mechanics and Civil Engineering，China University of Mining and Technology，Beijing 100083，China)
Abstract：Quasi-sandstone samples in dry and water-saturated states were tested in laboratory to analyze the non-isothermal heat transfer of rocks. The process of phase changes of water to ice leading to the reduction of heat conduction was investigated based on the experimental results. The equations of heat conduction in rock considering the effect of the cyclic freezing and thawing were proposed. The expressions describing the three-step change of temperature for the water-saturated rocks were also put forward and verified with the experiment results. The temperature variation curve of the dry quasi-sandstone samples under cyclic freezing and thawing changes negative exponentially. The rate of temperature change closer to the boundary surface is greater. The rate of temperature change in thawing period is greater than in freezing process. The temperature variation curves of saturated quasi-sandstone samples show three distinctive stages. The temperature changes slower during the process of phase change of water-ice. The rates of the temperature change of the saturated samples appear a bit lower than the dry ones. The structural transformation of water molecules during the process of phase change can be used to explain the phenomenon of reduction of thermal conductivity.
申艳军1，杨更社1，王 铭1，张慧梅1，贾海梁1，荣腾龙2. 冻融循环过程中岩石热传导规律试验及理论分析[J]. 岩石力学与工程学报, 2016, 35(12): 2417-2425.
SHEN Yanjun1，YANG Gengshe1，WANG Ming1，ZHANG Huimei1，JIA Hailiang1，RONG Tenglong2. Experimental and theoretical study on thermal conductivity of rock under cyclic freezing and thawing. , 2016, 35(12): 2417-2425.
[1] 赖远明，吴紫汪，朱元林，等. 寒区隧道温度场、渗流场和应力场耦合问题的非线性分析[J]. 岩土工程学报，1999，21(5)：529–533. (LAI Yuanming，WU Ziwang，ZHU Yuanlin，et al. Nonlinear analyses for the couple problem of temperature，seepage and stress fields in cold region tunnels[J]. Chinese Journal of Geotechnical Engineering，1999，21(5)：529–533.(in Chinese))
[2] 赖远明，张明义，喻文兵，等. 边界条件对碎石层降温效果及机理的影响[J]. 冰川冻土，2005，27(2)：163–168.(LAI Yuanming，ZHANG Mingyi，YU Wenbing，et al. The influence of boundary conditions on the cooling effect and mechanism of ripped rock layers[J]. Journal of Glaciology and Geocryology，2005，27(2)：163–168.(in Chinese))
[3] CHAUDHARY G，LI R. Freezing of water droplets on solid surfaces： An experimental and numerical study[J]. Experimental Thermal and Fluid Science，2014，57(3)：86–93.
[4] COMINI G.，GUIDICE S D，IEWIS R W. Finite element solution of nonlinear heat conduction problems with special reference to phase change[J]. International Journal of Numerical Methods and Engineering，1980，8(6)：613–624.
[5] HOPKE S W. A model for frost heave including overburden[J]. Cold Regions Science and Technology，1980，80(3)：111–127.
[6] ALTS T，HUTTER K. Continuum description of the dynamics and thermodynamics of phase boundaries between ice and water，part I. surface balance laws and their interpretation in terms of three-dimensional balance laws averaged over the phase change boundary layer[J]. Journal of Non-Equilibrium Thermodynamics，1988，13(3)：221–258.
[7] LAI Y M，WU Z W，ZHU Y L，et al. Nonlinear analysis for the coupled problem of temperature，seepage and stress fields in cold-region tunnels[J]. Tunnneling and Underground Space Technology，1988，13(4)：435–440.
[8] AKAGAWA S. Experimental study of frozen fringe characteristics[J]. Cold Regions Science and Technology，1988，15(3)：209–223.
[9] BRONFENBRENER L. The modelling of the freezing process in fine-grained porous media：Application to the frost heave estimation[J]. Cold Regions Science and Technology，2009，56(2/3)：120–134.
[10] TAN X J，CHEN W Z，TIAN H M，et al. Water flow and heat transport including ice/water phase change in porous media：numerical simulation and application[J]. Cold Regions Science and Technology，2011，68(1)：74–84.
[11] LUNARDINI V J. Freezing of soil with phase change occurring over a ?nite temperature difference[C]// Proceedings of the 4th International Offshore Mechanics and Arctic Engineering Symposium. [S.l.]：[s.n.]，1985：102–110.
[12] LUNARDINI V J. Effect of convective heat transfer on thawing of frozen soil[C]// Proceedings of the Seventh International Conference on Permafrost. Yellowknife，Canada：[s.n.]，1998：689–695.
[13] ALAN W. Premelting dynamics in a continuum model of frost heave[J]. Journal of Fluid Mechanics，2004，498：227–244.
[14] MCKENZIE J M，VOSS C I，SIEGEL D I. Groundwater ?ow with energy transport and water-ice phase change：numerical simulations，benchmarks，and application to freezing in peat bogs[J]. Advanced Water Resource，2007，30(4)：966–983.
[15] 谭贤君，余祥宏，陈卫忠，等. 岩土介质在冻融过程中的温度场研究及工程应用[J]. 岩石力学与工程学报，2012，31(增1)：2 867–2 874.(TAN Xianjun，YU Xianghong，CHEN Weizhong，et al. Study of temperature field in process of freezing-thawing in geotechnical medium and its application[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(Supp.1)：2 867–2 874.(in Chinese))
[16] 邴 慧，马 巍. 盐渍土冻结温度的试验研究[J]. 冰川冻土，2011，33(5)：1 106–1 113.(BING Hui，MA Wei. Experimental study on freezing point of saline soil[J]. Journal of Glaciology and Geocryology，2011，33(5)：1 106–1 113.(in Chinese))
[17] 周家作，谭 龙，韦昌富，等. 土的冻结温度与过冷温度试验研究[J]. 岩土力学，2015，36(3)：777–785.(ZHOU Jiazuo，TAN Long，WEI Changfu，et al. Experimental research on freezing temperature and super-cooling temperature of soil[J]. Chinese Journal of Geotechnical Engineering，2015，36(3)：777–785.(in Chinese))
[18] 张 婷，杨 平. 不同因素对浅表土冻结温度的影响[J]. 南京林业大学学报：自然科学版，2009，33(4)：132–134.(ZHANG Ting，YANG Ping. Effect of different factors on the freezing temperature of shallow top soil[J]. Journal of Nanjing Forestry University：Natural Science，2009，33(4)：132–134.(in Chinese))
[19] VITEL M，ROUABHI A，TIJANI M，et al. Modeling heat transfer between a freeze pipe and the surrounding ground during artificial ground freezing activities[J]. Computers and Geotechnics，2015，63：99–111.
[20] 蔡海兵，荣传新. 考虑相变潜热的冻结温度场非线性分析[J]. 低温建筑技术，2009，128(2)：43–45.(CAI Haibing，RONG Chuanxin. Considering phase change latent heat of freezing temperature field of nonlinear analysis[J]. Low Temperature Architecture Technology，2009，128(2)：43–45.(in Chinese))
[21] 蒋斌松，沈春儒，冯 强. 外壁恒温条件下单管冻结温度场解析计算[J]. 煤炭学报，2010，35(6)：923–927.(JIANG Binsong，SHEN Chunru，FENG Qiang. Analytical formulation of temperature field of single freezing pipe with constant outer surface temperature[J]. Journal of China Coal Society，2010，35(6)：923–927.(in Chinese))
[22] 杨更社，张全胜，蒲毅彬. 冻结温度对岩石细观损伤扩展特性影响研究初探[J]. 岩土力学，2004，25(9)：1 409–1 412.(YANG Gengshe，ZHANG Quansheng，PU Yibin. Preliminary study on meso-damage propagation characteristics of rock under condition of freezing temperature[J]. Chinese Journal of Geotechnical Engineering，2004，25(9)：1 409–1 412.(in Chinese))
[23] 申艳军，荣腾龙，杨更社，等. 类砂岩相似材料配合比方案试验研究[J]. 水利水电科技进展，2016，36(4)：75–79.(SHEN Yanjun，RONG Tenglong，YANG Gengshe，et al. Experimental study on the ratio of quasi-sandstone similar material[J]. Advances in Science and Technology of Water Resources，2016，36(4)：75–79.(in Chinese))
[24] SUN C Q，XI Z，FU X，et al. Density and phonon-stiffness anomalies of water and ice in the full temperature range[J]. Journal of Physical Chemistry Letters，2013，4(19)：3 238–3 244.
[25] ZHANG X，SUN P，YAN T，et al. Water's phase diagram：From the notion of thermodynamics to hydrogen-bond cooperatively[J]. Progress in Solid State Chemistry，2015，43(4)：71–81.
[26] 胡汉平. 热传导理论[M]. 合肥：中国科学技术大学出版社，2010：261–265.(HU Hanping. Thermal conductivity theory[M] Hefei： University of Science and Technology of China Press，2010：261–265.(in Chinese))
2016, Vol. 35 
