A review of the mechanism of frost heave failure in fractured rock masses
TAN Xianjun1，ZHENG Peichao1，2，SU Zhouzhou3，4，JIA Hailiang5，ZHANG Chaoxuan6，ZHOU Yun1，CHEN Weizhong1
(1. State Key Laboratory of Geomechanics and Geotechnical Engineering Safety，Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，Wuhan，Hubei 430071，China；2. University of Chinese Academy of Sciences，Beijing 100049，China；3. State Key Laboratory of Bridge Intelligent and Green Construction，China Railway Major Bridge Engineering Group Co.，Ltd.，Wuhan，Hubei 430034，China；4. China Railway Bridge Science Research Institute Co.，Ltd.，Wuhan，Hubei 430000，China；
5. College of Architecture and Civil Engineering，Xi?an University of Science and Technology，Xi?an，Shaanxi 710054，China；6. Institute of Road and Bridge Engineering，Taizhou University，Taizhou，Zhejiang 318000，China)
Abstract：As cold region engineering expands to higher altitudes and latitudes，the application of fractured rock masses(FRM) in cold region engineering has increased significantly. However，existing theories in frozen soil mechanics are insufficient to address the engineering challenges in these areas. This study investigates the mechanisms of freeze heave(FH) in FRM under low temperatures and freeze-thaw cycles. Through theoretical analysis，laboratory and field experiments，and numerical simulations，the research explores the formation mechanism and failure patterns of FH pressure in FRM. The study finds that FRM exhibit various FH mechanisms，including volumetric expansion，segregated ice，and mixed FH. The semi-elliptical open fissure mixed FH model provides a better description of these mechanisms. FH in FRM is a complex coupling of thermo-hydro-mechanical processes that involve moisture migration，multiphase heat conduction，and crack propagation. Factors such as fissure structure，saturation，sealing properties，freeze mode，ice-rock interactions and phase transitions significantly influence FH pressure and damage. The primary mechanism of damage in FRM is driven by FH pressure promoting the crack propagation，which is significantly influenced by the characteristics of the fissure and rock mass. Moreover，laboratory and field tests show differences in FH behavior，especially concerning freeze-thaw cycles，crack initiation temperature，and water absorption conditions. Future research should focus on micro- and meso-mechanisms，supported by laboratory and field experiments，to investigate moisture migration and ice-rock interactions. The objective is to solve FH pressure，explore the evolution of fracture networks using numerical methods，and develop an adaptive monitoring and decision-support system for predicting FH failure，integrating artificial intelligence and big data.
谭贤君1，郑培超1，2，苏舟舟3，4，贾海梁5，张朝轩6，周 云1，陈卫忠1. 裂隙岩体冻胀破坏机制研究综述[J]. 岩石力学与工程学报, 2025, 44(5): 1065-1088.
TAN Xianjun1，ZHENG Peichao1，2，SU Zhouzhou3，4，JIA Hailiang5，ZHANG Chaoxuan6，ZHOU Yun1，CHEN Weizhong1. A review of the mechanism of frost heave failure in fractured rock masses. , 2025, 44(5): 1065-1088.
[1] 齐吉琳，马 巍. 冻土的力学性质及研究现状[J]. 岩土力学，2010，31(1)：133–143.(QI Jilin，MA Wei. State-of-art of research on mechanical properties of frozen soils[J]. Rock and Soil Mechanics，2010，31(1)：133–143.(in Chinese))
[2] 徐 彬，李 宁，李仲奎，等. 低温液化石油气和液化天然气储库及相关岩石力学研究进展[J]. 岩石力学与工程学报，2013，32(增1)：2 977–2 993.(XU Bin，LI Ning，LI Zhongkui，et al. Lowtemperature LPG and LNG storage caverns and related research review of rock mechanics[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(Supp.1)：2 977–2 993.(in Chinese))
[3] 乔京生，陶龙光，弭尚银. 地铁隧道水平冻结施工地表变形特性的模拟研究[J]. 岩石力学与工程学报，2004，23(15)：2 643–2 646. (QIAO Jingsheng，TAO Longguang，MI Shangyin. Simulation study on deformation characteristics of ground surface in horizontal freezing construction of metro tunnel[J]. Chinese Journal of Rock Mechanics and Engineering，2004，23(15)：2 643–2 646.(in Chinese))
[4] TABER S. Frost heaving[J]. The Journal of Geology，1929，37(6)：428–461.
[5] EVERETT D H. The thermodynamics of frost damage to porous solids[J]. Transactions of the Faraday Society，1961，57：1 541– 1 551.
[6] HARLAN R L. Analysis of coupled heat-fluid transport in partially frozen soil[J]. Water Resources Research，1973，9(5)：1 314–1 323.
[7] MILLER R D. Freezing and heaving of saturated and unsaturated soils[J]. Highway Research Record，1972，393：1–11.
[8] GILPIN R R. A model of the“liquid-like”layer between ice and a substrate with applications to wire regelation and particle migration[J]. Journal of Colloid and Interface Science，1979，68(2)：235–251.
[9] 曹宏章，刘 石. 饱和颗粒土冻结过程的数值模拟[J]. 工程热物理学报，2007，28(1)：128–130.(CAO Hongzhang，LIU Shi. Numerical simulation of saturated granular soil freezing process[J]. Journal of Engineering Thermophysics，2007，28(1)：128–130.(in Chinese))
[10] KONRAD J M，MORGENSTERN N R. The segregation potential of a freezing soil[J]. Canada Geotechnical Journal，1981，18(4)：482–491.
[11] NIXON J F. Field frost heave predictions using the segregation potential concept[J]. Canadian Geotechnical Journal，1982，19(4)：526–529.
[12] 徐学祖，张立新，王家澄. 土体冻胀发育的几种类型[J]. 冰川冻土，1994，16(4)：301–307.(XU Xuezu，ZHANG Lixin，Wang Jiacheng. Essential types of heave development for soil freezing[J]. Journal of Glaciology and Geocryology，1994，16(4)：301–307.(in Chinese))
[13] TAKASHI T，YAMAMOTO H，OHRAI T，et al. Effect of penetration rate of freezing and confining stress on the frost heave ratio of soil[C]// Proceedings of the 3rd International Conference on Permafrost. [S. l.]：[s. n.]，1978：737–742.
[14] BLANCHARD D，FREMOND M. Soil Frost Heaving and Thaw Settlement[C]// Proceedings of 4th International Symposium on Ground Freezing. Sapporo：[s. n.]，1985：209–216.
[15] GUO L，LI T，NIU Z. Finite element simulation of the couple heat-fluid transfer problem with phase change in frozen soil[C]// Earth and Space 2012：Engineering，Science，Constructionand Operations in Challenging Environments，ASCE. [S. l.]：[s. n.]，2012：867–877.
[16] AKAGAWA S. Experimental study of frozen fringe characteristics[J]. Cold Regions Science and Technology，1988，15(3)：209–223.
[17] WATANABE K，MIZOGUCHI M. Ice configuration near a growing ice lens in a freezing porous medium consisting of micro glass particles[J]. Journal of Crystal Growth，2000，213(1)：135–140.
[18] LOCH J P G，KAY B D. Water redistribution in partially frozen，saturated silt under several temperature gradients and overburden loads[J]. Soil Science Society of America Journal，1978，42(3)：400–406.
[19] 苗天德，郭 力，牛永红，等. 正冻土中水热迁移问题的混合物理论模型[J]. 中国科学(D辑：地球科学)，1999，29(1)：8–14.(MIAO Tiande，GUO Li，NIU Yonghong，et al. A mixture theoretical model for water thermal migration in positive frozen soil[J]. Science China(Series D：Geoscience)，1999，29(1)：8–14.(in Chinese))
[20] FREMOND M，MIKKOLA M. Thermodynamical modelling of freezing soil[C]// Proceedings of 6th International Symposium on Ground Freezing. [S. l.]：[s. n.]，1991：17–24.
[21] NEAUPANE KM，YAMABE T，YOSHINAKA R. Simulation of a fully coupled thermo-hydro-mechanical system in freezing and thawing rock[J]. International Journal of Rock Mechanics and Mining Sciences，1999，36(5)：563–580.
[22] 周 扬，周国庆，王义江. 饱和土水热耦合分离冰冻胀模型研究[J]. 岩土工程学报，2010，32(11)：1 746–1 751.(ZHOU Yang，ZHOU Guoqing，WANG Yijiang. Separate ice frost heave model for coupled moisture and heat transfer in saturated soils[J]. Chinese Journal of Geotechnical Engineering，2010，32(11)：1 746–1 751.(in Chinese))
[23] 李 萍，徐学祖，王家澄，等. 利用图象数字化技术分析冻结缘特征[J]. 冰川冻土，1999，21(2)：175–180.(LI Ping，XU Xuzu，WANG Jiacheng，et al. Analyses of characteristics of frozen fringe by using the digital technique of picture[J]. Journal of Glaciology and Geocryology，1999，21(2)：175–180.(in Chinese))
[24] FUKUDA M，NAKAGAWA S. Numerical analysis of frost heaving based upon the coupled heat and water flow model[C]// International Symposium on Ground Freezing. [S. l.]：[s. n.]，1985：109–117.
[25] LOZINSKI M W. Uber die mechanische Verwitterung der Sandsteine im gemassibten Klima. Academie des sciences de cracovie，Bulletin international，classe de science[J]. Mathematiques et Naturelles，1909，1：1–25.
[26] POWERS T C. A working hypothesis for further studies of frost resistance of concrete[J]. Journal of the American Concrete Institute，1945，41(1)：245–272.
[27] MELLOR M. Phase composition of pore water in cold rocks[R]. United States Army Engineers，Cold Regions Research and Engineering Laboratory Report，1970：292.
[28] AKAGAWA S，FUKUDA M. Frost heave mechanism in welded tuff[J]. Permafrost and Periglacial Processes，1991，2(4)：301–309.
[29] WALDER J S，HALLET B. A theoretical model of the fracture of rock during freezing[J]. Geological Society of America Bulletin，1985，96(3)：336–346.
[30] MURTON J B，COUTARD J P，LAUTRIDOU J P，et al. Physical modelling of bedrock brecciation by ice segregation in permafrost[J]. Permafrost and Periglacial Processes，2010，12(3)：255–266.
[31] POWERS T C，HELMUTH R. Theory of volume changes in hardened portland cement paste during freezing[J]. Proceedings of the Highway Research Board，1953，32(5)：285–297.
[32] 贾海梁. 多孔岩石及裂隙岩体冻融损伤机制的理论模型和试验研究[博士学位论文][D]. 武汉：中国地质大学(武汉)，2016.(JIA Hailiang. Theoretical damage models of porous rocks and hard jointed rocks subjected to frost action and further experimental verifications [Ph. D. Thesis][D]. Wuhan：China University of Geosciences(Wuhan)，2016.(in Chinese))
[33] SCHERER G W. Crystallization in pores[J]. Cement and Concrete Research，1999，29(8)：1 347–1 358.
[34] SETZER M J. Micro-ice-lens formation in porous solid[J]. Journal of Colloid and Interface Science，2001，243(1)：193–201.
[35] COUSSY O. Poromechanics of freezing materials[J]. Journal of the Mechanics and Physics of Solids，2005，53(8)：1 689–1 718.
[36] MATSUOKA N. Frost weathering and rockwall erosion in the southeastern Swiss Alps：Long-term(1994–2006) observations[J]. Geomorphology，2008，99(1/4)：353–368.
[37] ISHIKAWA M，KURASHIGE Y，HIRAKAWA K. Analysis of crack movements observed in an alpine bedrock cliff[J]. Earth Surface Processes and Landforms，2004，29(7)：883–891.
[38] VLAHOU I，WORSTER M G. Ice growth in a spherical cavity of a porous medium[J]. Journal of Glaciology，2010，56(196)：271–277(7).
[39] 刘泉声，黄诗冰，康永水，等. 低温冻结岩体单裂隙冻胀力与数值计算研究[J]. 岩土工程学报，2015，37(9)：1 572–1 580.(LIU Quansheng，HUANG Shibing，KANG Yongshui，et al. Numerical and theoretical studies on frost heaving pressure in a single fracture of frozen rock mass under low temperature[J]. Chinese Journal of Geotechnical Engineering，2015，37(9)：1 572–1 580.(in Chinese))
[40] 刘泉声，黄诗冰，康永水，等. 裂隙冻胀压力及对岩体造成的劣化机制初步研究[J]. 岩土力学，2016，37(6)：1 530–1 542.(LIU Quansheng，HUANG Shibing，KANG Yongshui，et al. Preliminary study of frost heave pressure and its influence on crack and deterioration mechanisms of rock mass[J]. Rock and Soil Mechanics，2016，37(6)：1 530–1 542.(in Chinese))
[41] LIN H，D LEI，YONG R，et al. Analytical and numerical analysis for frost heaving stress distribution within rock joints under freezing and thawing cycles[J]. Environmental Earth Sciences，2020，79(12)：305.
[42] 黄继辉，夏才初，韩常领，等. 考虑围岩不均匀冻胀的寒区隧道冻胀力解析解[J]. 岩石力学与工程学报，2015，24(增2)：3 766– 3 774. (HUANG Jihui，XIA Caichu，HAN Changling，et al. Analytical solution of frost heave force acting on cold-region tunnel liner considering anisotropy frost heave of surrounding rock[J]. Chinese Journal of Rock Mechanics and Engineering，2015，24(Supp.2)： 3 766–3 774.(in Chinese))
[43] BRIDGMAN P W. The liquid and five solid forms under pressure[J]. Proceedings of the American Academy of Arts and Sciences，1912，47：439–558.
[44] WINKLER E M. Frost damage to stone and concrete：geological considerations[J]. Engineering Geology，1968，2(5)：315–323.
[45] MATSUOKA N. Mechanisms of rock breakdown by frost action：an experimental approach[J]. Cold Regions Science and Technology，1990，17(3)：253–270．
[46] HALLET B. Why do freezing rocks break?[J]. Science，2006，314(5 802)：1 092–1 093.
[47] HALL K. Rock temperatures and implications for cold region weathering. I：new data from Viking Valley，Alexander Island，Antarctica[J]. Permafrost and Periglacial Processes，1997，8(1)：69–90.
[48] BATTLE W. Temperature observations in bergschrunds and their relationship to frost shattering[J]. Norwegian Cirque Glaciers 1960，4：83–95.
[49] LAUTRIDOU J P，OZOUF J C. Experimental frost shattering：15 years of research at the centre de Geomorphologie du CNRS[J]. Progress in Physical Geography，1982，6(2)：215–232.
[50] SASS O. Rock moisture fluctuations during freeze-thaw cycles：preliminary results from electrical resistivity measurements[J]. Polar Geography，2004，28：13–31.
[51] SASS O. Rock moisture measurements：techniques，results，and implications for weathering[J]. Earth Surface Processes and Landforms，2005，30(3)：359–374.
[52] GILPIN R R. A model for the prediction of ice lensing and frost heave in soils[J]. Water Resources Research，1980，16(5)：918–930.
[53] HALLET B，WALDER J S，STUBBS C W. Weathering by segregation ice growth in microcracks at sustained subzero temperatures：Verification from an experimental study using acoustic emissions[J]. Permafrost and Periglacial Processes，1991，2(4)：283–300.
[54] 阎锡东，刘红岩，邢闯锋，等. 基于微裂隙变形与扩展的岩石冻融损伤本构模型研究[J]. 岩土力学，2015，36(12)：3 489–3 499. (YAN Xidong，LIU Hongyan，XING Chuangfeng，et al. Constitutive model research on freezing-thawing damage of rock based on deformation and propagation of microcracks[J]. Rock and Soil Mechanics，2015，36(12)：3 489–3 499.(in Chinese))
[55] TAN X，CHEN W，LIU H，et al. A unified model for frost heave pressure in the rock with a penny-shaped fracture during freezing[J]. Cold Regions Science and Technology，2018，153：1–9.
[56] HUANG S，LIU Q，LIU Y，et al. Frost heaving and frost cracking of elliptical cavities (fractures) in low-permeability rock[J]. Engineering Geology，2018，234：1–10.
[57] BOST M，POUYA A. Stress generated by the freeze-thaw process in open cracks of rockwalls：empirical model for tight limestone[J]. Bulletin of Engineering Geology and the Environment，2017，76(4)：1 491–1 505.
[58] TAO S，TANG X，RUTQVIST J，et al. The influence of stress anisotropy and stress shadow on frost cracking in rock[J]. Computers and Geotechnics，2021，133(4)：103967.
[59] ZHANG Q，LIU Y，DAI F. A frost heave pressure model for fractured rocks subjected to repeated freeze-thaw deterioration[J]. Engineering Geology，2024，337：107587.
[60] WETTLAUFER J S，WORSTER M G. Premelting dynamics[J]. Annual Review of Fluid Mechanics，2006，38(1)：427–452.
[61] 高世桥，刘海鹏. 毛细力学[M]. 北京：科学出版社，2010：82–88.(GAO Shiqiao，LIU Haipeng. Capillary mechanics[M]. Beijing：Science Press，2010：82–88.(in Chinese))
[62] REMPEL A W，WETTLAUFER J S，WORSTER M G. Interfacial premelting and the thermomolecular force：thermodynamic buoyancy[J]. Physical Review Letters，2001，87(8)：088501.
[63] DE GENNES P G. Wetting：Statics and dynamics[J]. Reviews of Modern Physics，1985，57(3)：827–863.
[64] 刘泉声，黄诗冰，康永水，等. 低温饱和岩石未冻水含量与冻胀变形模型研究[J]. 岩石力学与工程学报，2016，35(10)：2 000–2 012. (LIU Quansheng，HUANG Shibing，KANG Yongshui，et al. Study of unfrozen water content and frost heave model for saturated rock under low temperature[J]. Chinese Journal of Rock Mechanics and Engineering，2016，35(10)：2 000–2 012.(in Chinese))
[65] MILLER R D. Lens initiation in secondary heaving[C]// Proceedings of the International Symposium on Frost Action in Soils. [S. l.]：[s. n.]，1977：16–18.
[66] ZHENG P，TAN X，JIA H，et al. A unified model for frost wedging in an open fissure under unidirectional freezing[J]. International Journal of Rock Mechanics and Mining Sciences，2024，176：105726.
[67] JIA H，LEITH K，KRAUTBLATTER M. Path-dependent frost-wedging experiments in fractured，low-permeability granite[J]. Permafrost and Periglacial Processes，2017，28(4)：698–709.
[68] 夏才初，王岳嵩，吕志涛，等. 单向冻结条件下裂隙岩体冻胀特性试验[J]. 同济大学学报：自然科学版，2018，47(9)：1 268–1 276. (XIA Caichu，WANG Yuesong，LV Zhitao，et al. Experimental study on frost heaving characteristics of fractured rock mass under unidirectional freezing condition[J]. Journal of Tongji University：Natural Science，2018，47(9)：1 268–1 276.(in Chinese))
[69] 申艳军，杨更社，荣腾龙，等. 低温环境下含表面裂隙硬岩温度场及冻胀演化过程分析[J]. 岩土力学，2016，37(增1)：521–529. (SHEN Yanjun，YANG Gengshe，RONG Tenglong，et al. Analysis of evolution of temperature field and frost heaving in hard rock with surface cracks under low temperature environment[J]. Rock and Soil Mechanics，2016，37(Supp.1)：521–529.(in Chinese))
[70] MATSUOKA N. Direct observation of frost wedging in alpine bedrock[J]. Earth Surface Processes and Landforms，2010，26(6)：601–614.
[71] DAVIDSON G P，NYE J F. A photoelastic study of ice pressure in rock cracks[J]. Cold Regions Science and Technology，1985，11(2)：141–153.
[72] THARP T M. Conditions for crack propagation by frost wedging[J]. Geological Society of America Bulletin，1987，99(1)：94–102.
[73] MATSUOKA N. Microgelivation versus macrogelivation：towards bridging the gap between laboratory and field frost weathering[J]. Permafrost and Periglacial Processes，2001，12(3)：299–313.
[74] ZHANG J，WANG G，LIU H，et al. Characterizing frost heave pressure distribution on rock crack surfaces during freeze-thaw[J]. Engineering Geology，2023，324：107258
[75] LV Z，XIA C，WANG Y，et al. Frost heave and freezing processes of saturated rock with an open crack under different freezing conditions[J]. Frontiers of Structural and Civil Engineering，2020，14：947–960.
[76] 路亚妮，李新平，吴兴宏. 三轴压缩条件下冻融单裂隙岩样裂缝贯通机制[J]. 岩土力学，2014，35(6)：1 579–1 584.(LU Yani，LI Xinping，WU Xinghong. Fracture coalescence mechanism of single flaw rock specimen due to freeze-thaw under triaxial compression[J]. Rock and Soil Mechanics，2014，35(6)：1 579–1 584.(in Chinese))
[77] WANG Y，SUN T，YANG H，et al. Experimental investigation on frost heaving force(FHF) evolution in preflawed rocks exposed to cyclic freeze-thaw conditions[J]. Geofluids，2021，2021(1)：1–12.
[78] 单仁亮，白 瑶，孙鹏飞，等. 裂隙红砂岩冻胀力特性试验研究[J]. 煤炭学报，2019，44(6)：122–132.(SHAN Renliang，BAI Yao，SUN Pengfei，et al．Experimental study on frost heaving pressure properties in fractured red sandstone[J]. Journal of China Coal Society，2019，44(6)：122–132.(in Chinese))
[79] 申艳军，杨更社，王 铭，等. 冻融–周期荷载下单裂隙类砂岩损伤及断裂演化试验分析[J]. 岩石力学与工程学报，2018，37(3)：709–717.(SHEN Yanjun，YANG Gengshe，WANG Ming，et al. Experiments on the damage characteristics and fracture process of single-joint quasi-sandstone under the cyclic freezing-thawing and cyclic loading[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(3)：709–717.(in Chinese))
[80] 李 平，唐旭海，刘泉声，等. 双裂隙类砂岩冻胀断裂特征与强度损失研究[J]. 岩石力学与工程学报，2020，39(1)：115–125.(LI Ping，TANG Xuhai，LIU Quansheng，et al. Experimental study on fracture characteristics and strength loss of intermittent fractured quasi-sandstone under freezing and thawing[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(1)：115–125.(in Chinese))
[81] TANG X，TAO S，LI P，et al. The propagation and interaction of cracks under freeze-thaw cycling in rock-like material[J]. International Journal of Rock Mechanics and Mining Sciences，2022，154：105112.
[82] 乔国文，王运生，杨新龙. 高寒山区岩体冻胀冰劈破坏试验[J]. 山地学报，2014，32(5)：579–586.(QIAO Guowen，WANG Yunsheng，YANG Xinlong. Experiment on rock frost heaving damage of ice splitting in alpine mountain regions[J]. Mountain Research，2014，32(5)：579–586.(in Chinese))
[83] HUANG S，YE Y，CUI X，et al. Theoretical and experimental study of the frost heaving characteristics of the saturated sandstone under low temperature[J]. Cold Regions Science and Technology，2020，174：103036.
[84] 李杰林. 基于核磁共振技术的寒区岩石冻融损伤机制试验研究[博士学位论文][D]. 长沙：中南大学，2012.(LI Jielin. Experiment study on deterioration mechanism of rock under the conditions of freezing-thawing cycles in cold regions based on NMR technology[Ph. D. Thesis][D]. Changsha：Central South University，2012.(in Chinese))
[85] 裴向军，蒙明辉，袁进科，等. 干燥及饱水状态下裂隙岩石冻融特征研究[J]. 岩土力学，2017，38(7)：1 999–2 006.(PEI Xiangjun，MENG Minghui，YUAN Jinke，et al. Freezing-thawing characteristics of fractured rockmass under dry and saturated conditions[J]. Rock and Soil Mechanics，2017，38(7)：1 999–2 006.(in Chinese))
[86] ZHANG G，CHEN G，XU Z，et al. Crack failure characteristics of different rocks under the action of frost heaving of fissure water[J]. Frontiers in Earth Science，2020，8：13.
[87] 周科平，李 斌，李杰林，等. 冻融作用下岩石的微观损伤及动态力学特性(英文)[J]. Transactions of Nonferrous Metals Society of China，2015，25(4)：1 254–1 261.(ZHOU Keping，LI Bin，LI Jielin，et al. Microscopic damage and dynamic mechanical properties of rock under freeze-thaw environment(English)[J]. Transactions of Nonferrous Metals Society of China，2015，25(4)：1 254–1 261.(in Chinese))
[88] CHRISTIANSEN H H. Thermal regime of ice-wedge cracking in Adventdalen，Svalbard[J]. Permafrost and Periglacial Processes，2005，16(1)：87–98.
[89] HALES T C，ROERING J J. Climatic controls on frost cracking and implications for the evolution of bedrock landscapes[J]. Journal of Geophysical Research Earth Surface，2007，112(F2).
[90] FAHEY B D，LEFEBURE T H. The freeze-thaw weathering regime at a section of the Niagara escarpment on the Bruce Peninsula，Southern Ontario，Canada[J]. Earth Surface Processes and Landforms，2010，13(4)：293–304.
[91] 陈卫忠，谭贤君，于洪丹，等. 低温及冻融环境下岩体热，水，力特性研究进展与思考[J]. 岩石力学与工程学报，2011，30(7)： 1 318–1 336.(CHEN Weizhong，TAN Xianjun，YU Hongdan，et al. Advance and review on thermos-hydro-mechanical characteristics of rock mass under condition of low temperature and freeze-thaw cycles[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(7)：1 318–1 336.(in Chinese))
[92] WEGMANN M，GUDMUNDSSON G H. Thermally induced temporal strain variations in rock walls observed at subzero temperatures[M]. Berlin Heidelberg：Springer，1999：511–518.
[93] 严 健，何 川，周子寒，等. 寒区裂隙冻岩隧道岩–水–冰力原位测试及冻胀力模型[J]. 土木工程学报，2020，53(增1)：300–305.(YAN Jian，HE Chuan，ZHOU Zihan，et al. Frost heaving force computational model of tunnel with frozen rock containing fissures and rock-hydraulic-ice pressure in situ test in cold region[J]. China Civil Engineering Journal，2020，53(Supp.1)：300–305.(in Chinese))
[94] WU Y，WANG Y，HAIM W，et al. Fracture of rocks in the mountains of Southeast Tibet under hydrothermal conditions at different elevations[J]. Bulletin of Engineering Geology and the Environment，2020，79：4 291–4 308.
[95] AMITRANO D，GRUBER S，GIRARD L. Evidence of frost-cracking inferred from acoustic emissions in a high-alpine rock-wall[J]. Earth and Planetary Science Letters，2012，341：86–93.
[96] MURTON J B，PETERSON R，OZOUF J C. Bedrock fracture by ice segregation in cold regions[J]. Science，2006，314(5 802)：1 127– 1 129.
[97] 徐拴海，李 宁，袁克阔，等. 融化作用下含冰裂隙冻岩强度特性及寒区边坡失稳研究现状[J]. 冰川冻土，2016，38(4)：1 106–1 120.(XU Shuanhai，LI Ning，YUAN Kekuo，et al. Strength behavior of frozen fractured ice-filled rock mass and research status of slope instability during thawing[J]. Journal of Glaciology and Geocryology，2016，38(4)：1 106–1 120.(in Chinese))
[98] 徐拴海，李 宁，王晓东，等. 露天煤矿冻岩边坡饱和砂岩冻融损伤试验与劣化模型研究[J]. 岩石力学与工程学报，2016，35(12)： 2 561–2 571.(XU Shuanhai，LI Ning，WANG Xiaodong，et al. Damage test and degradation model of saturated sandstone due to cyclic freezing and thawing of rock slopes of open-pit coal mine[J]. Chinese Journal of Rock Mechanics and Engineering，2016，35(12)：2 561–2 571.(in Chinese))
[99] DRAEBING D，KRAUTBLATTER M，DIKAU R. Interaction of thermal and mechanical processes in steep permafrost rock walls：A conceptual approach[J]. Geomorphology，2014，226(12)：226–235.
[100] LAI Y M，WU Z，ZHU Y，et al. Nonlinear analysis for the coupled problem of temperature and seepage fields in cold regions tunnels[J]. Cold Regions Science and Technology，1999，29(1)：89–96.
[101] 谭贤君，陈卫忠，贾善坡，等. 含相变低温岩体水热耦合模型研究[J]. 岩石力学与工程学报，2008，27(7)：1 455–1 461.(TAN Xianjun，CHEN Weizhong，JIA Shanpo，et al. A coupled hydro-thermal model for low temperature rock including phase change[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(7)：1 455–1 461.(in Chinese))
[102] 刘泉声，康永水，刘小燕. 冻结岩体单裂隙应力场分析及热–力耦合模拟[J]. 岩石力学与工程学报，2011，30(2)：217–223.(LIU Quansheng，KANG Yongshui，LIU Xiaoyan. Analysis of stress field and coupled thermos-mechanical simulation of single-fracture freezed rock masses[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(2)：217–223.(in Chinese))
[103] 徐 彬，闫 娜，李 宁，等. 温降对液化石油气储库围岩裂隙开裂影响的数值分析[J]. 岩石力学与工程学报，2011，30(4)：718–726.(XU bin，YAN Na，LI Ning，et al. Numerical analysis of effect of temperature decreasing on crack of chilled LPG unlined storage cavern[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(4)：718–726.(in Chinese))
[104] 刘泉声，康永水，黄 兴，等. 裂隙岩体冻融损伤关键问题及研究状况[J]. 岩土力学，2012，31(4)：971–978.(LIU Quansheng，KANG Yongshui，HUANG Xing，et al. Critical problems of freeze-thaw damage in fractured rock and their research status[J]. Rock and Soil Mechanics，2012，31(4)：971–978.(in Chinese))
[105] 黄诗冰，刘泉声，刘艳章，等. 低温热力耦合下岩体椭圆孔(裂)隙中冻胀力与冻胀开裂特征研究[J]. 岩土工程学报，2018，40(3)：459–467.(HUANG Shibing，LIU Quansheng，LIU Yanzhang，et al. Frost heaving pressure and characteristics of frost cracking in elliptical cavity(crack) of rock mass under coupled thermal-mechanical condition at low temperature[J]. Chinese Journal of Rock Mechanics and Engineering，2018，40(3)：459–467.(in Chinese))
[106] 马 伟，谭贤君，陈卫忠，等. 基于扩展有限元方法的裂隙岩体冻胀力理论与数值研究[J]. 冰川冻土，2020，42(2)：532–539. (MA Wei，TAN Xianjun，CHEN Weizhong，et al. Numerical and theoretical studies on frost heaving pressure in fractured rock mass based on XFEM method[J]. Journal of Glaciology and Geocryology，2020，42(2)：532–539.(in Chinese))
[107] ZHOU Y，TAN X，YANG D，et al. A numerical method to consider the interaction between multiple fractures in frozen rocks based on XFEM[J]. Computers and Geotechnics，2024，169：106240.
[108] SUN L，LIU Q，TAO S，et al. A novel low-temperature thermo-mechanical coupling model for frost cracking simulation using the finite-discrete element method[J]. Computers and Geotechnics，2022，152：105045.
[109] SUN L，TANG X，ABOAYANAH K R，et al. A coupled cryogenic thermo-hydro-mechanical model for frozen medium：Theory and implementation in FDEM[J]. Journal of Rock Mechanics and Geotechnical Engineering，2023，16(11)：4 335–4 353.
2025, Vol. 44 
