随着寒区工程建设的快速发展，在冻融环境下因裂隙岩体破裂失稳而诱发的地质灾害频发，尤其是在高寒地区，具有环境驱动性强和链式发展的冻融灾害严重威胁着寒区基础工程的安全稳定。本文以寒区裂隙岩体为研究对象，采用室内试验、理论分析和数值计算相结合的研究方法，运用粒子追踪法和热成像技术，构建了冻融裂隙岩体粒子追踪测速试验系统，开展了冻融作用下裂隙岩体水热迁移及相变冻胀特性的试验研究，完成了冻融与荷载联合作用下裂隙岩体特性试验，建立了荷载-冻融联合作用下裂隙岩体力学模型，获得了冻融与荷载联合作用下边缘裂隙周边/前缘处应力-位移解析，研究了冻融与荷载联合作用下裂隙岩体损伤断裂特性，完成的主要研究工作及结论如下：

（1）运用粒子图像追踪原理，进行了裂隙岩体冻融过程的PIV实时追踪实验，实时直观地展现了常规测试方法无法观测的裂隙岩石和裂隙水的水热迁移过程，着重分析了冻融作用下裂隙岩体锋面运动特征、温度场和裂隙水流场变化特征，描述了岩石在水热迁移中冻结锋面移动速度以及温度变化规律。冻融裂隙岩体微水流场受温度变化影响：在冻结过程中，裂隙水流速急剧降低，而随着温度梯度的减弱裂隙水流速度趋于稳定；在融化过程中，裂隙中自由水随着裂隙冰的融化而增多，水流场呈现出明显的温度指向性。当裂隙岩体温度升至常温，粒子运动变得紊乱。所提出的PIV实时追踪测试方法能够实现裂隙水从微流场到宏观冻胀力的冻结全过程的动态描述。

（2）从微观角度研究了裂隙岩体在冻融循环过程中裂隙水相变特征，揭示了水-岩界面上裂隙冰成核→长大→裂隙壁晶核生长的过程及其生长方式和速度变化规律，分析了水-岩界面冰晶生长形态和冻胀力演化规律。阐明了冻融环境下裂隙岩体水热迁移过程和裂隙水相变的机制。探讨了温度梯度对晶核生长速度的影响，并开展了冻融损伤对裂隙岩体冻胀力和前缘应变的影响分析。研究发现：在冻结过程中，冻结锋面由下至上、由外向内呈扇形扩散，直至迁移至裂隙附近；融化过程中，岩体正立面的冻结锋面呈扇形向中下部发展收缩，直至消失。裂隙水相变的冻胀力演化规律可分为7个阶段：孕育阶段、陡升阶段、峰后下降阶段、稳定阶段、二次冻胀阶段、融化阶段以及完全消散阶段。

（3）研制了冻融与荷载联合作用下裂隙岩体损伤试验的压/剪荷载施加装置，完成了冻融受荷裂隙岩体损伤试验，重点分析了裂隙内部温度场、冻胀力及裂隙端部应变的演化规律，探讨了压缩荷载和剪切荷载对裂隙扩展的影响规律，研究了裂隙周边力学行为变化，揭示了冻融循环作用下裂隙岩体的冻胀损伤机制。研究表明：在整个冻融过程中冻胀变形对裂隙端部变形起主导作用；裂隙端部应变在冻融过程中以冻胀张拉为主，冻胀损伤以残余应变的形式不断累积，直至超过岩石强度极限，裂隙端部发生破坏变形。裂隙岩体的变形以冻胀为主，随着冻融循环次数的增加，冻胀损伤不断积累，直至裂隙失稳破坏。剪切荷载对裂隙岩体的冻胀损伤具有促进作用。随着冻融次数的增加，剪切荷载越大，裂隙前缘越早萌发宏观的冻胀−剪切裂纹，更易形成断裂失稳。

（4）考虑裂隙水相变力学演化特征和不同边界条件，提出了裂隙岩体前缘处冻融循环损伤断裂判据，建立了冻融受荷裂隙岩体力学模型，推导了冻融与荷载联合作用下边缘裂隙周边/前缘处应力-位移和裂隙扩展解析方程，求得了冻胀拉力和剪切力作用下Westergaard 应力函数以及应力-位移全场式，对岩体裂隙塑性区边界和岩体裂隙长度扩展进行了解析，与试验结果进行了验证分析。完成了冻胀力作用下岩体裂隙位移计算，揭示了裂隙岩体受荷破坏规律，实现了裂隙岩体力学指标的定量计算，为寒区岩石工程设计和施工提供基础数据。

（5）采用擅长模型缺陷部位网格划分兼具较高连续性检测精度的数值计算软件HyperWorks进行冻融受荷裂隙岩体损伤断裂性能研究，获得了室内试验难以捕捉的前缘处裂隙扩展至破坏的瞬间力场、位移场分布特征，深入探究冻融与荷载作用下裂隙前缘塑性区演化和裂隙扩展长度变化，分析了压/剪荷载作用下裂隙冻融破坏特征，验证了冻融与荷载联合作用下岩体裂隙断裂解析计算的可靠性，定量研究了地层压力、剪切力、冻胀拉力和剪力对前缘裂隙扩展的临界尺度和断裂尺度下限的影响规律，分析了荷载与冻结作用下裂隙表面位移演化规律，为高寒工程灾害防治研究提供科学依据。

With the rapid development of engineering construction in cold regions, geological disasters induced by the instability and failure of fractured rock masses in freeze-thaw environments have become frequent, especially in alpine regions. Freeze-thaw disasters, which are strongly environmentally driven and develop in a chain-like manner, pose a severe threat to the safety and stability of infrastructure projects in cold regions. This paper takes fractured rock masses in cold regions as the research object and adopts a research methodology that combines laboratory experiments, theoretical analysis, and numerical calculations. By utilizing particle tracking and thermal imaging techniques, a particle tracking and velocity measurement experimental system for fractured rock masses under freeze-thaw conditions is established. Innovative experimental research is conducted on the hydrothermal migration and frost heave characteristics of phase change in fractured rock masses under freeze-thaw action. Experiments on the characteristics of fractured rock masses under the combined action of freeze-thaw and loading are completed. A mechanical model for fractured rock masses under the combined action of loading and freeze-thaw is established. Analytical solutions for stress-displacement around/at the edge of fractures under the combined action of freeze-thaw and loading are obtained. The damage and fracture characteristics of fractured rock masses under the combined action of freeze-thaw and loading are investigated. The main research work and conclusions are as follows:

(1)Using the principle of particle image velocimetry (PIV), real-time PIV tracking experiments are conducted on the freeze-thaw process of fractured rock masses. This visually and in real-time presents the hydrothermal migration process of fractured rock and fracture water that cannot be observed by conventional testing methods. The paper focuses on analyzing the characteristics of frontal movement, temperature field, and fracture water flow field changes in fractured rock masses under freeze-thaw action. It describes the movement speed of the freezing front and temperature change laws during hydrothermal migration in rock. The micro-water flow field of fractured rock masses under freeze-thaw conditions is affected by temperature changes: during the freezing process, the flow velocity of fracture water decreases sharply and then stabilizes as the temperature gradient weakens; during the thawing process, free water in the fractures increases as the fracture ice melts, and the water flow field exhibits a clear temperature directionality. When the temperature of the fractured rock mass rises to room temperature, particle movement becomes turbulent. The proposed PIV real-time tracking testing method enables dynamic description of the entire freezing process of fracture water from the micro-flow field to macroscopic frost heave forces.

(2) The phase change characteristics of fracture water in fractured rock masses during freeze-thaw cycles are studied from a microscopic perspective. The process of fracture ice nucleation, growth, and crystal nucleus growth on fracture walls at the water-rock interface, as well as its growth mode and speed change laws, are revealed. The growth morphology of ice crystals at the water-rock interface and the evolution of frost heave forces are analyzed. The mechanisms of hydrothermal migration and fracture water phase change in fractured rock masses in freeze-thaw environments are clarified. The influence of temperature gradients on the growth rate of crystal nuclei is discussed, and an analysis of the impact of freeze-thaw damage on frost heave forces and strain at the leading edge of fractured rock masses is conducted. The study found that during the freezing process, the freezing front spreads in a fan shape from bottom to top and from outside to inside until it migrates near the fracture; during the thawing process, the freezing front on the front face of the rock mass develops and contracts in a fan shape towards the middle and lower parts until it disappears. The evolution of frost heave forces during the phase change of fracture water can be divided into seven stages: an incubation stage, a steep rise stage, a post-peak decline stage, a stable stage, a secondary frost heave stage, a thawing stage, and a complete dissipation stage.

(3) A compression/shear loading application device for damage testing of fractured rock masses under the combined action of freeze-thaw and loading is developed. Damage experiments on fractured rock masses under freeze-thaw and loading conditions are completed. The evolution laws of the internal temperature field, frost heave forces, and strains at the ends of fractures are analyzed with emphasis. The influence laws of compressive and shear loads on fracture propagation are discussed. Changes in the mechanical behavior around fractures are studied, revealing the frost heave damage mechanism of fractured rock masses under freeze-thaw cycles. Research shows that frost heave deformation dominates the deformation at the ends of fractures throughout the freeze-thaw process; strain at the ends of fractures is mainly caused by frost heave tension during freeze-thaw cycles, and frost heave damage accumulates continuously in the form of residual strain until the rock strength limit is exceeded, resulting in damage and deformation at the ends of fractures. The deformation of fractured rock masses is dominated by frost heave. As the number of freeze-thaw cycles increases, frost heave damage accumulates until the fractures become unstable and fail. Shear loads promote frost heave damage in fractured rock masses. As the number of freeze-thaw cycles increases, the greater the shear load, the earlier macroscopic frost heave-shear cracks initiate at the fracture front, making it easier to form fracture instability.

(4) Considering the mechanical evolution characteristics of fracture water phase change and different boundary conditions, a criterion for damage and fracture due to freeze-thaw cycles at the leading edge of fractured rock masses is proposed. A mechanical model for fractured rock masses under freeze-thaw and loading conditions is established. Analytical equations for stress-displacement and fracture propagation around/at the edge of fractures under the combined action of freeze-thaw and loading are derived. The Westergaard stress function and full-field stress-displacement equations under the action of frost heave tensile and shear forces are obtained. The boundaries of the plastic zone and the extension of fracture length in rock masses are analyzed and verified against experimental results. Calculations of fracture displacement in rock masses under frost heave forces are completed, revealing the failure laws of fractured rock masses under loading. Quantitative calculations of mechanical indicators for fractured rock masses are achieved, providing basic data for rock engineering design and construction in cold regions.

(5) HyperWorks, a numerical calculation software that excels in mesh division for model defects and has high continuity detection accuracy, is used to study the damage and fracture properties of fractured rock masses under freeze-thaw and loading conditions. The instantaneous force field and displacement field distribution characteristics at the leading edge, where fractures propagate to failure, which are difficult to capture in laboratory experiments, are obtained. The evolution of the plastic zone at the fracture front and changes in fracture propagation length under the action of freeze-thaw and loading are deeply explored. The freeze-thaw failure characteristics of fractures under compression/shear loads are analyzed. The reliability of analytical calculations for fracture failure in rock masses under the combined action of freeze-thaw and loading is verified. The influence laws of formation pressure, shear force, frost heave tensile force, and shear force on the critical scale of fracture propagation at the leading edge and the lower limit of fracture scale are quantitatively studied. The evolution laws of fracture surface displacement under loading and freezing are analyzed, providing a scientific basis for research on the prevention and control of engineering disasters in alpine regions.

[1]马巍,王大雁. 中国冻土力学研究50a回顾与展望[J]. 岩土工程学报,2012,34(04):625-640.

[2]崔鹏. 中国山地灾害研究进展与未来应关注的科学问题[J]. 地理科学进展,2014,33(02):145-152.

[3] Di Wu,Long Jin,Yanqiu Leng, et al.A full-scale field experiment to study the hydrothermal behavior of the multilayer asphalt concrete pavement in cold regions[J]. Construction and Building Materials,2021,267.

[4] 王绍令． 青藏公路风火山地区的热融滑塌[J]．冰川冻土,1990,12(1):63-70．

[5] 储飞． 新疆乌尉高速天山段岩石冻融破坏特征及崩塌模式分析[D]．成都:成都理工大学,2014．

[6] 黄勇． 高寒山区岩体冻融力学行为及崩塌机制研究[D]．成都:成都理工大学,2012．

[7] Ke B,Zhou K P,Deng H W,et al. NMR pore structure and dynamic characteristics of sandstone caused by ambient freeze-thaw action[J]. Shock and Vibration, 2017,2017: 1-10.

[8] Qin Y H, Tan K H, Yang H F, et al. The albedo of crushed-rock layers and its implication to cool roadbeds in permafrost regions[J]. Cold Regions Science and Technology, 2016, 128: 32-37.

[9] 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(S2):2977-2993．

[10] Wang T,Zhou G Q,Wang J Z,et al. Stochastic analysis of uncertainty mechanical characteristics for surrounding rock and lining in cold region tunnels[J]. Cold Regions Science and Technology,2018,145:160-168.

[11] 孙广忠. 论“岩体结构控制论”[J]. 工程地质学报,1993,1(1):14-18.

[12] 周维垣. 高等岩石力学[M]. 北京:水利电力出版社,1990:1-3.

[13] 蒋坤,夏才初. 基于不同节理模型的岩体边坡稳定性分析[J]. 同济大学学报(自然科学版),2009,37(11):1440-1445.

[14] 贾海梁,项伟,申艳军,等. 冻融循环作用下岩石疲劳损伤计算中关键问题的讨论[J]. 岩石力学与工程学报,2017,36(2):335-346.

[15] 杨更社，周春华，田应国，等．软岩材料冻融过程中的水热迁移实验研究[J]．煤炭学报，2006，(05)：566-570．

[16] 杨更社，周春华，田应国，等．软岩类材料冻融过程水热迁移的实验研究初探[J]．岩石力学与工程学报，2006，(09)：1765-1770．

[17] 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[D]. 武汉:中国地质大学,2016.

[18] 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.

[19] 赵建军,解明礼,余建乐,等. 冻融作用下含裂隙岩石力学特征及损伤演化规律试验研究[J]. 工程地质学报, 2019, 27(6):1199-1207.

[20] 王永岩,张金龙,张余彪. 单裂隙类岩石强度特性及蠕变模型的实验研究[J]. 科学计算与工程, 2018,18（18）:94-100.

[21] 张平,李宁,贺若兰,等. 动载下3条断续裂隙岩样的裂缝贯通机制[J]. 岩土力学, 2018,2006（9）:1457-1464.

[22] Wong R H C,Law C M,Chau K T,et al. Crack propagation from 3-D surface fractures in PMMA and marble specimens under uniaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences,2004,41(Suppl 1):1-6.

[23] Li Y P,Chen L Z,Wang Y H. Experimental research on pre-cracked marble under compression[J]. International Journal of Solids and Structures,2005,42(9-10):2505-2516.

[24] Park C H,Bobet A. Crack coalescence in specimens with open and closed flaws:A comparison[J]. International Journal of Rock Mechanics and Mining Sciences, 2009,46(5): 819-829.

[25] Mondal S,Olsen K L,Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3-D surface flaw under uniaxial compression[J]. International Journal of Numerical and Analytical Methods in Geomechanics,2019,43（7）:1448-1466.

[26] Gratchev I,Kim D,Yeung C. Strength of rock-like specimens with pre-existing cracks of different length and width[J]. Rock Mechanics and Rock Engineering,2016,46(11):4491-4496.

[27] Shi H,Song L,Zhang H Q,et al. Numerical study on mechanical and failure properties of sandstone based on the power-law distribution of pre-crack length[J]. Geomechanics and Materials,2006,38(1-2):142-159.

[28] Wong R H C,Lin P,Tang C A. Experimental and unmerical study on splitting failure of brittle solids containing single pore under uniaxial compression[J]. Mechanics of Materials,2006,38(1-2):142-159.

[29] Bastola S,Cai M. Investigation of mechanical properties and crack propagation in pre-cracked marbles using lattice-spring-based synthetic rock mass(LS-SRM) modeling approach[J]. Computers and Geotechnics,2019,110:28-43.

[30] Zhu Q Q,Li D Y,Han Z Y,et al. Mechanical properties and fracture evolution of sandstone specimens containing different inclusions under uniaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences,2019,115:33-47.

[31] Lu Z D,Chen C X,Feng X T,et al. Strength failure and crack coalescence behavior of sandstone containing single pre-cut fissure under coupled stress,fluid flow and changing chemical environment（Article）[J]. International Journal of Central South University,2014,21（3）:1176-1183.

[32] Chen B,Xia Z G,et al. Failure characteristics and mechanical mechanism of study on red sandstone with combined defects[J]. Geomechanics and Engineering,2021,24（2）:179-191.

[33] Chen S J,Xia Z G,Feng F,et al. Numerical study on strength and failure characteristics of rock samples with different hole defects[J]. Bulletin of Engineering Geology and the Environment,2021,80(2):1523-1540.

[34] Li H Q,Wong L N Y. Numberical study on coalescence of pre-existing flaw pairs in rock-like material[J]. Rock Mechanics and Rock Engineering,2014,47（6）:2087-2105.

[35] Yang S Q,Yang D S,Jing H W,et al. An experimental study of the fracture coalescence behavior of brittle sandstone specimens containing three fissures[J]. Rock Mechanics and Rock Engineering,2012,45（4）:563-582.

[36] Haeri H,Khaloo A,Marji M F. Fracture analyses of different pre-holed concrete specimens under compression[J]. Acta Mechanica Slinica,2015,31（6）:855-870.

[37] Asadizadeh M,Moosavi M,Hossaini M F. Investigation of mechanical behaviour of non-persistent jointed blocks under uniaxial compression[J]. Geomechanics and Engineering,2018,14（1）:29-42.

[38] Mirsalimov V M. Optimal design of shape of a working in cracked rock mass[J]. Geomechanics and Engineering,2021,24（3）:227-235.

[39] HUANG S B,LIU Q S,CHENG A P,et al. A fully coupled thermo-hydro-mechanical model including the determination of coupling parameters for freezing rock[J]. International Journal of Rock Mech Min,2018,103:205-214.

[40] 奚家米,杨更社,董西好. 冻结温度对砂质泥岩力学特性的影响[J]. 长安大学学报(自然科学版),2014,34(04):92-97.

[41] 杨更社,奚家米,李慧军,等. 三向受力条件下冻结岩石力学特性试验研究[J]. 岩石力学与工程学报,2010,29(03):459-464.

[42] 杨更社,魏尧,申艳军,等. 冻结饱和砂岩三轴压缩力学特性及强度预测模型研究[J]. 岩石力学与工程学报,2019,38(04):683-694.

[43] Jinyuan Zhang, Yanjun Shen, Gengshe Yang,et al. Inconsistency of changes in uniaxial compressive strength and P-wave velocity of sandstone after temperature treatments[J]. Journal of Rock Mechanics and Geotechnical Engineering,2021,13:143-153.

[44] Hailiang Jia,Fan Zi,Gengshe Yang,et al. Influence of Pore Water (Ice) Content on the Strength and Deformability of Frozen Argillaceous Siltstone. Rock Mechanics and Rock Engineering[J],2020,53:967-974.

[45] Ting Wang, Qiang Sun, Hailiang Jia, et al. Linking the mechanical properties of frozen sandstone to phase composition of pore water measured by LF-NMR at subzero temperatures.Bulletin of Engineering Geology and the Environment[J],2021,80:4501-4513.

[46] SHEN Y J, WANG Y Z, ZHAO X D, et al. The influence of temperature and moisture content on sandstone thermal conductivity from a case using the artificial ground freezing(AGF) method. Cold Reg Sci Techno,2018,155:149-160.

[47] HUANG S B, LIU Q S, LIU Y Z, et al. Freezing Strain Model for Estimating the Unfrozen Water Content of Saturated Rock under Low Temperature[J]. Int J Geomech, 2018, 18(2).

[48] Hui Liu,Gengshe Yang,Yehui Yun. Investigation of Sandstone Mesostructure Damage Caused by Freeze-Thaw Cycles via CT Image Enhancement Technology[J]. Hindawi Advances in Civil Engineering,2020.

[49] XU J Z, ZHAI C, LIU S M, et al. Investigation of temperature effects from LCO2 with different cycle parameters on the coal pore variation based on infrared thermal imagery and low-field nuclear magnetic resonance[J]. Fuel,2018,215:528-540.

[50] 刘慧,杨更社,贾海梁,等. 裂隙(孔隙)水冻结过程中岩石细观结构变化的实验研究[J]. 岩石力学与工程学报,2016,35(12):2516-2524.

[51] Hailiang Jia, Shun Ding, Fan Zi, et al. Evolution in sandstone pore structures with freeze-thaw cycling and interpretation of damage mechanisms in saturated porous rocks[J]. Catena195, 2020.

[52] CHEN Y L, NI J, JIANG L H, et al. Experimental study on mechanical properties of granite after freeze-thaw cycling[J]. Environ Earth Sci,2014,71(8):3349-3354.

[53] KHANLARI G,SAHAMIEH R Z,ABDILOR Y. The effect of freeze-thaw cycles on physical and mechanical properties of Upper Red Formation sandstones,central part of Iran[J]. Arab J Geosci,2015,8(8):5991-6001.

[54] LIU L L, LIU X Y, LI Z,et al.Experimental Analysis on the Mechanical Properties of Saturated Silty Mudstone under Frozen Conditions[J]. J Test Eval, 2019 ,47(1): 188-202.

[55] YU J, CHEN X, LI H,et al. Effect of Freeze-Thaw Cycles on Mechanical Properties and Permeability of Red Sandstone under Triaxial Compression[J]. J Mt Sci-Engl, 2015, 12(1): 218-231.

[56] Huimei Zhang,Xiangzhen Meng,GengsheYang. A study on mechanical properties and damage model of rock subjected to freeze-thaw cycles and confining pressure[J]. Cold Regions Science and Technology,2020,174.

[57] 张慧梅,杨更社. 冻融岩石损伤劣化及力学特性试验研究[J]. 煤炭学报,2013,38(10):1756-1762.

[58] Zhang Jian,Deng Hongwei,Taheri Abbas,et al. Degradation of physical and mechanical properties of sandstone subjected to freeze-thaw cycles and chemical erosion[J]. Cold Reg Sci Techno,2018,155: 37-46.

[59] Liu Chuanju,Deng Hongwei,Zhao Huatao, et al. Effects of freeze-thaw treatment on the dynamic tensile strength of granite using the Brazilian test[J]. Cold Reg Sci Techno,2018,155: 327-332.

[60] 韩铁林,师俊平,陈蕴生. 砂岩在化学腐蚀和冻融循环共同作用下力学特征劣化的试验研究[J].水利学报,2016,47(05):644-655.

[61] 丁梧秀,徐桃,王鸿毅,等. 水化学溶液及冻融耦合作用下灰岩力学特性试验研究[J]. 岩石力学与工程学报,2015,34(05):979-985.

[62] 陈有亮,王朋,张学伟,等. 花岗岩在化学溶蚀和冻融循环后的力学性能试验研究[J]. 岩土工程学报,2014,36(12):2226-2235.

[63] JIANG H B, MO Z G, HOU X B, et al. Association Rules between the Microstructure and Physical Mechanical Properties of Rock-mass under Coupled Effect of Freeze-thaw Cycles and Large Temperature Difference[J]. Sains Malays[J], 2017, 46(11): 2215-2221.

[64] Jiang Haibao. The Relationship between Mechanical Properties and Gradual Deterioration of Microstructures of Rock Mass Subject to Freeze-thaw Cycles[J]. Earth Sci Res J, 2018, 22(1): 53-57.

[65] 许玉娟,周科平,李杰林,等. 冻融岩石核磁共振检测及冻融损伤机制分析[J]. 岩土力学,2012,33(10):3001-3005+3102.

[66] 李杰林,周科平,张亚民,等. 基于核磁共振技术的岩石孔隙结构冻融损伤试验研究[J]. 岩石力学与工程学报,2012,31(06):1208-1214.

[67] 周科平,李杰林,许玉娟,等. 冻融循环条件下岩石核磁共振特性的试验研究[J]. 岩石力学与工程学报,2012,31(04):731-737.

[68] GHOBADI M H, BEYDOKHTI A R T, NIKUDEL MR, et al. The effect of freeze-thaw process on the physical and mechanical properties of tuff[J]. Environ Earth Sci,2016,75(9).

[69] Liu Quansheng,Huang Shibing,Kang Yongshui, et al. A prediction model for uniaxial compressive strength of deteriorated rocks due to freeze-thaw[J]. Cold Reg Sci Techno, 2015, 120: l96-107.

[70] Fu Helin,Zhang Jiabing,Huang, Zhen, et al. A statistical model for predicting the triaxial compressive strength of transversely isotropic rocks subjected to freeze-thaw cycling[J]. Cold Reg Sci Techno,2018, 145: 237-248.

[71] WANG L P, LI N, QI J L, et al. A study on the physical index change and triaxial compression test of intact hard rocksubjected to freeze-thaw cycles[J]. Cold Reg Sci Techno, 2019, 160: 39-47.

[72] Zhang Jiabing,Fu Helin,Huang Zhen,et al. Experimental study on the tensile strength and failure characteristics of transversely isotropic rocks after freeze-thaw cycles[J]. Cold Reg Sci Techno,2019, 163: 68-77.

[73] 唐江涛,裴向军,裴钻,等. 冻融循环作用下岩石的损伤研究[J]. 科学技术与工程,2016,16(27):101-105.

[74] 刘成禹,何满潮,王树仁,等. 花岗岩低温冻融损伤特性的实验研究[J]. 湖南科技大学学报:自然科学版,2005, (1):37-40.

[75] 吴安杰,邓建华,顾乡,等. 冻融循环作用下泥质白云岩力学特性及损伤演化规律研究[J]. 岩土力学,2014,35(11):3065-3072.

[76] 张慧梅,张蒙军,谢祥妙,等. 冻融循环条件下红砂岩物理力学特性试验研究[J]. 太原理工大学学报,2015,46(1):69-74.

[77] YAVUZ H, ALTINDAG R, SARAC S, et al. Estimating the index properties of deteriorated carbonate rocks due to freeze-thaw and thermal shock weathering[J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(5): 767-775.

[78] BAYRAM F. Predicting mechanical strength loss of natural stones after freeze-thaw in cold regions[J]. Cold Regions Science and Technology, 2012, 83(12): 98-102.

[79] KHANLARI G, SAHAMIE R Z, ABDILOR Y. The effect of freeze–thaw cycles on physical and mechanical properties of Upper Red Formation sandstones, central part of Iran[J]. Arabian Journal of Geosciences, 2014, 75(4): 1-13.

[80] 申艳军,杨更社,荣腾龙,等. 岩石冻融循环试验建议性方案探讨[J]. 岩土工程学报,2016,38(10):1775-1782.

[81] Qiang Sun,,Zhihao Dong,Hailiang Jia. Decay of sandstone subjected to a combined action of repeated freezing–thawing and salt crystallization[J]. Bulletin of Engineering Geology and the Environment,2019, 78:5951–5964.

[82] Huang Shibing,Liu Quansheng,Cheng, Aiping,et al. A statistical damage constitutive model under freeze-thaw and loading for rock and its engineering application[J]. Cold Reg Sci Technol,2018,145: 142-150.

[83] WANG Z, ZHU Z D, ZHU S. Thermo-mechanical-water migration coupled plastic constitive model of rock subjected to freeze-thaw[J]. Cold Reg Sci Technol, 2019, 161: 71-80.

[84] LU Y N, LI X P, CHAN A. Damage constitutive model of single flaw sandstone under freeze-thaw and load[J]. Cold Reg Sci Technol, 2019, 159: 20-28.

[85] Qu Dengxing,Li Dengke,Li Xinping. Damage evolution mechanism and constitutive model of freeze-thaw yellow sandstone in acidic environment[J]. Cold Reg Sci Technol,2018,155: 174-183.

[86] 张慧梅,杨更社.冻融与荷载耦合作用下岩石损伤模型的研究[J]. 岩石力学与工程学报,2010,29(03):471-476.

[87] 张慧梅,彭川,杨更社,等. 考虑冻融效应的岩石损伤统计强度准则研究[J]. 中国矿业大学学报,2017,46(05):1066-1072.

[88] 袁小清,刘红岩,刘京平. 冻融荷载耦合作用下节理岩体损伤本构模型[J]. 岩石力学与工程学报,2015,34(08):1602-1611.

[89] 陈松,乔春生,叶青,等. 冻融荷载下节理岩体的复合损伤模型[J]. 哈尔滨工业大学学报,2019,51(02):100-108.

[90] Li Xinping,Qu Dengxing,Luo Yi, et al. Damage evolution model of sandstone under coupled chemical solution and freeze-thaw process[J]. Cold Reg Sci Techno,2019,162: 88-95.

[91] FANG W, JIANG N, LUO X D. Establishment of damage statistical constitutive model of loaded rock and method for determining its parameters under freeze-thaw condition[J]. Cold Reg Sci Technol, 2018, 160: 36-38.

[92] MU J Q, PEI X J, HUANG R Q, et al. Degradation characteristics of shear strength of joints in three rock types due to cyclic freezing and thawing[J]. Cold Reg Sci Technol, 2019, 138: 91-97.

[93] 刘泉声,黄诗冰,康永水,等. 岩体冻融疲劳损伤模型与评价指标研究[J]. 岩石力学与工程学报,2015,34(6):1116-1127.

[94] 张慧梅,谢祥妙,彭川,等. 三向应力状态下冻融岩石损伤本构模型[J]. 岩土工程学报,2017,39(8):1444-1452.

[95] 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,2012,33(4):971-978.

[96] 李宁,张平,段庆伟,等. 裂隙岩体的细观动力损伤模型[J]. 岩石力学与工程学报,2002,21(11):1579-1584.

[97] 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.

[98] 李新平,路亚妮,王仰君. 冻融荷载耦合作用下单裂隙岩体损伤模型研究[J]. 岩石力学与工程学报,2013,32(11):2307-2315.

[99] 刘波,刘念,李东阳,等. 含冰软弱面的冻结裂隙红砂岩的强度试验[J]. 煤炭学报,2016,41(4):843-849.

[100] 曾桂军,张明义,李振萍,等. 饱和正冻土水分迁移及冻胀模型研究[J]. 岩土力学,2015,36(04):1085-1092.

[101] 邰博文,刘建坤,李旭,等. 寒区高速铁路路基冻胀数值模型及防冻胀措施[J]. 中国铁道科学,2017,38(03):1-9.

[102] 岑国平,龙小勇,洪刚,等. 青藏高原季冻区砂砾土冻胀特性试验[J]. 哈尔滨工业大学学报,2016,48(03):53-59.

[103] 盛岱超,张升,贺佐跃. 土体冻胀敏感性评价[J]. 岩石力学与工程学报,2014,33(03):594-605.

[104] 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.

[105] WINKLER E M. Frost damage to stone and concrete: geological considerations[J]. Engineering Geology,1968,2(5):315-323.

[106] TABER S. Frost heaving[J]. The Journal of Geology, 1929, 37(5): 428-461.

[107] TABER S. The mechanics of frost heaving[J]. The Journal of Geology, 1930, 38(4): 303-317.

[108] 李宁,程国栋,徐教祖,等. 冻土力学的研究进展与思考[J]. 力学进展,2001,31(1):95-102.

[109] EVERETT D H. The thermodynamics of frost damage to porous solids[J]. Transactions of the Faraday Society, 1961, 57: 1541-1551.

[110] MILLER R D. Freezing and heaving of saturated and unsaturated soils[J]. Highway Research Record, 1972, 393: 1-11.

[111] 赵刚,陶夏新,刘兵. 原状土冻融过程中水分迁移试验研究[J]. 岩土工程学报,2009,31(12):1952-1957.

[112] SASS O. Rock moisture fluctuations during freeze-thaw cycles: preliminary results from electrical resistivity measurements[J]. Polar Geography, 2004, 28(1): 13-31.

[113] 谭贤君,陈卫忠,贾善坡,等. 含相变低温岩体水热藕合模型研究[J]. 岩石力学与工程学报,2008,27(7):1455-1461.

[114] 杨更社. 冻结岩石力学的研究现状与展望分析[J]. 力学与实践,2009,31(6):9-16.

[115] KONRAD J M, DUQENNOI C A. A model for water transport and ice lensing in freezing soil[J]. Water Resources Research, 1993, 29(9): 3109-3124.

[116] KONRAD J M, CAN N R. Segregation potential of freezing soil[J]. Geotech Testing, 1981, 18(4): 482-491.

[117] HALLET B,WALDER J S, STUBBS C. 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.

[118] MATSUOKA N,MURTON J. Frost Weathering:Recent advances and future directions[J]. Permafrost and Periglac. Process,2008,19(1):195-210.

[119] KANG Y S,LIU Q S,HUANG S B. A fully coupled thermo-hydro-mechanical model for rock mass under freezing/thawing condition[J]. Cold Regions Science and Technology, 2013,95(1):19-26.

[120] NEAUPANE K M,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.

[121] 吕志涛,夏才初,李强,等. 单向冻结时开放条件下饱和砂岩冻胀试验及THM耦合冻胀模型[J]. 岩土工程学报,2019,41(08):1435-1444.

[122] 刘泉声,康永水,刘滨,等. 裂隙岩体水-冰相变及低温温度场-渗流场-应力场耦合研究[J]. 岩石力学与工程学报,2011,30(11):2181-2188.

[123] DUCA S,ALONSO E E,SCAVIA C. A permafrost test on intact gneiss rock[J]. International Journal of Rock Mechanics and Mining Sciences,2015,77:142-151.

[124] MURTON J,PETERSON R,OZOUF J. Bedrock fracture by ice segregation in cold regions[J]. Science,2006,314:1127-1129.

[125] AKAGAWA S,FUKUDA M. Frost heave mechanism in welded tuff[J]. Permafrost and Periglacial Processes,1991,2(4):301-309.

[126] HARRIS C,ARENSON L U,CHRISTIANSEN H H,et al. Permafrost and climate in Europe: Monitoring and modeling thermah geomorphological and geotechnical responses[J]. Earth-Science Reviews,2009,92(3):117-171

[127] DERJAGUIN B V,CHURAEV N V. The definition of disjoining pressure and its importance in the equilibrium and flow of thin films[J]. Colloid Journal of the USSR,1976, 38(3):402-410.

[128] DERJAGUIN B V,CHURAEV N V. Flow of nonfreezing water interlayers and frost heaving[J]. Cold Regions Science and Technology,1986,12(1):57-66.

[129] CHURAEV N V,SOBOLEV V D. Disjoining pressure of thin unfreezing water layers between the pore walls and ice in porous bodies[J]. Colloid Journal,2002,64(4):508-511.

[130] DASH J G,FU H,WETTLAUFER J S. The preruelting of ice and its environmental consequences[J]. Reports on Progress in Physics,1995,58(1):115-167.

[131] ROSENBERG R. Why is ice slippery?[J]. Physics Today,2005,58(12):50-55.

[132] DASH J G, REMPEL A W, WETTLAUFER J S. The physics of premelted ice and its geophysical consequences[J]. Reviews of Modern Physics,2006,78(3):695-741.

[133] WALDER J, HALLET B. A theoretical model of the fracture of rock during freezing[J]. Geological Society of America Bulletin,1985,96(3):336-346.

[134] VLAHOU I, WORSTER M G. Ice growth in a spherical cavity of a porous medium[J]. Journal of Glaciology,2010,56(196):271-277.

[135] WETTLAUFER J S,WORSTER M G. Premelting dynamics[J]. Annu Review of Fluid Mechanics,2006,38:427-452.

[136] SETZER M J. Development of the micro-ice-lens model[C]// International RILEM Workshop on Frost Resistance of Concrete. [S. 1.]:RILEM Publications SARL,2002: 133-145.

[137] 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(06):1742-1752.

[138] 申艳军,杨更社,荣腾龙,等. 冻融循环作用下单裂隙类砂岩局部化损伤效应及端部断裂特性分析[J]. 岩石力学与工程学报,2017,36(03):562-570.

[139] 夏才初,李强,吕志涛,等. 各向均匀与单向冻结条件下饱和岩石冻胀变形特性对比试验研究[J]. 岩石力学与工程学报,2018,37(02):274-281.

[140] 夏才初,黄继辉,韩常领,等. 寒区隧道岩体冻胀率的取值方法和冻胀敏感性分级[J]. 岩石力学与工程学报,2013,32(09):1876-1885.

[141] 黄诗冰,刘泉声,程爱平,等. 低温岩体裂隙冻胀力与冻胀扩展试验初探[J]. 岩土力学,2018,39(01):78-84.

[142] 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(03):459-467.

[143] 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):2000-2012.

[144] 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(09):1572-1580.

[145] 谷德振. 岩体工程地质力学基础[M]. 北京: 科学出版社, 1979.

[146] 孙玉科, 古讯. 赤平极射投影在岩体工程地质力学中的应用[M]. 北京: 科学出版社,1980.

[147] 王思敬. 赤平极射投影方法及其在岩体工程中的应用[M]. 北京: 科学出版社,1976.

[148] 李泽, 王均星. 基于非线性规划的岩质边坡有限元塑性极限分析下限法研究[J]. 岩石力学与工程学报, 2007(4): 747-753.

[149] 陈炜, 王均星. 节理岩质边坡的块体元塑性极限分析下限法[J]. 岩土工程学报, 2008(2): 272-277.

[150] 沈世伟. 吉林省东南部山区地质环境及边坡稳定性研究[D]. 长春：吉林大学, 2010.

[151] 范刚, 张建经, 付晓. 含泥化夹层顺层和反倾岩质边坡动力响应差异性研究[J]. 岩土工程学报, 2015, 37(4): 692-699.

[152] 黄秋香, 汪家林. 某具有软弱夹层的反倾岩坡变形特征探索[J]. 土木工程学报, 2011, 44(5): 109-114.

[153] 蔡国军, 裴钻. 反倾互层岩质边坡开挖物理模拟试验研究[J]. 水土保持研究, 2007(5):126-130.

[154] 丁秀丽, 付敬, 刘建, 等. 软硬互层边坡岩体的蠕变特性研究及稳定性分析[J]. 岩石力学与工程学报, 2005(19): 12-20.

[155] 左保成, 陈从新, 刘小巍, 等. 反倾岩质边坡破坏机理模型试验研究[J]. 岩石力学与工程学报, 2005(19): 107-113.

[156] 虢柱, 刘小平, 黄赣萍. 岩质边坡稳定性数值模拟及动力响应分析[J]. 公路工程, 2012, 37(5): 23-28.

[157] 舒继森, 才庆祥, 王成龙, 等. 岩石边坡平面滑动时的临界滑面倾角的探讨[J]. 中国矿业大学学报, 2006(4): 437-440.

[158] 王新民, 康虔, 秦健春, 等. 层次分析法-可拓学模型在岩质边坡稳定性安全评价中的应用[J]. 中南大学学报(自然科学版), 2013, 44(6): 2455-2462.

[159] 姚环, 郑振, 简文彬, 等. 公路岩质高边坡稳定性的综合评价研究[J]. 岩土工程学报,2006(5): 558-563.

[160] 李宁, 钱七虎. 岩质高边坡稳定性分析与评价中的四个准则[J]. 岩石力学与工程学报,2010, 29(9): 1754-1759.

[161] 易靖松, 许强, 唐梁, 等. 一个平推式滑坡的典型实例——兼论四川某滑坡的成因机制[J]. 科学技术与工程, 2014, 14(13): 106-111.

[162] 许强, 邓茂林, 李世海, 等. 武隆鸡尾山滑坡形成机理数值模拟研究[J]. 岩土工程学报, 2018, 40(11): 2012-2021.

[163] 穆成林, 裴向军, 黄润秋, 等. 含不连续软弱夹层顺层边坡破坏机制与稳定性分析[J].公路, 2016, 61(7): 50-58.

[164] 郑光, 许强, 常兴旺. 高山峡谷区桥梁基础岸坡稳定性分析评价方法研究[C]//“川藏铁路建设的挑战与对策”2016 学术交流会论文集: 人民交通出版社(China Communications Press), 2016: 629-638.

[165] 杨智翔, 裴向军, 袁进科. 高陡边坡危岩体孤石的稳定性分析[J]. 路基工程, 2017(1):25-29.

[166] 黄润秋, 裴向军, 罗璟. 风载作用下震裂山体崩塌机制及稳定性评价方法[J]. 西南交通大学学报, 2016, 51(5): 958-970.

[167] 李建峰, 万臣, 赵勇. 高寒高海拔地区岩质边坡稳定性评价研究[J]. 重庆交通大学学报(自然科学版), 2015, 34(2): 45-49.

[168] 乔国文, 王运生, 杨新龙. 冻融风化边坡岩体质量评价体系研究[J]. 岩土力学, 2015, 36(2): 515-522.

[169] 王斌, 冯夏庭, 潘鹏志, 等. 物质点法在边坡稳定性评价中的应用研究[J]. 岩石力学与工程学报, 2017, 36(9): 2146-2155.

[170] 何平,程国栋,朱元林. 土体冻结过程中的热质迁移研究进展[J]. 冰川冻土,2001,23（1）:92-98.

[171] R.D.Miller. Freezing and heaving of saturated and unsaturated soils[J]. Highway Research,1972,393:1-11.

[172] 李萍,徐学祖,陈峰峰. 冻结缘和冻胀模型的研究现状与进展[J]. 冰川冻土,2000,22（1）:90-95.

[173] R.L.Harlan. Analysis of coupled heat-fluid transport in partially frozen soil[J]. Water Research,1973,9:1314-1323.

[174] F.Ling. Z.Zeng. and L.X.Zhang. The effect of the construction of revetment in the side of embankment[A]. in Ground Freezing 2000 [C]. 2000.Rotterdam:Balkema.

[175] M.Sheppard,B.Kay. and J.Loch. Development and testing of a computer model for heat and mass flow in freezing soils[A]. in The 3rd International Conference on Permafrost[C].1978.

[176] G.S.Taylor and J.N.Luthin. A model for coupled heat and moisture transfer during soil freezing[J]. 1978,15:548-555.

[177] P.E.Jansson and S.Halldin. Model for annual water and energy flow in a layered soil[A]. in Comparasion of Frost and Energy Exchange Models[C]. 1979.

[178] M.Fukuda. Experimental studies of coupled heat and moisture transfer in soils during freezing[R]. Institute of Low Temperature Science,1982,Hokkaido University:Sapporo.Japan:35-91.

[179] M.Fukuda and S.Nakagawa. Numerical analysis of frost heaving based upon the coupled heat and water flow model[A]. in 4th International Symposium on Ground Freezing[C],1985.Sapporo.Japan.

[180] O’Neil.K. and R.D.Miller. Exploration a rigid-ice of frost heave[J]. Water Resources Research,1985,21:281-296.

[181] Holden.J.T.,D.Piper and R.H.Jones. A mathematical model of frost heave in granular materials[A]. in 4th International Conference on Permafrost[C].Washing.D.C.,National Academy Press,1983.

[182] Piper.D.,J.T.Holden and R.H.Jones. A mathematical model of frost heave in granular materials[A]. in 5th International Conference on Permafrost[C].Norway:Tapir Publication,1983.

[183] Fremond.M. and M.Mikkola. Thermomechanical modelling of freezing soil[A]. in Ground Freezing 91. Proceedings of the 6th International Symposium on Ground Freezing Days[C]. Balkema:Rotterdam,1991.

[184] Mikkola.M. and J.Hartikainen. Computational aspects of soil freezing problem[A]. in Fifth World Congress on Computatinal Mechanics[C]. Vienna.Austria,2002.

[185] Mikkola.M. and J.Hartikainen. Mathematical model of soil freezing and its numerical implementation[J]. International Journal for numerical methods in engineering,2001 ,52:543-557.

[186] 苗天德,郭力,牛永红,等. 正冻土中水热迁移问题的混合外力论模型[J]. 中国科学（D辑）,1999,29（增刊1）:8-14.

[187] 牛永红. 含相变混合物理论与正冻土本构问题[D]. 兰州大学:兰州,2001.

[188] 陈沙,岳中琦,谭国焕. 基于数字图像的非均质岩土工程材料的数值分析方法[J]. 岩土工程学报,2005,27（8）:957-963.

[189] Tsang Y.W. The effect of tortuosity on fluid flow through a single fracture. Water Resources Research 1984,20(9):1209-15.

[190] Pyrak-Nolte L.J.,Morris JP. Single fractures under normal stress: the relation between fracture specific stiffness and fluid flow. International Journal of Rock Mechanics and Mining Sciences 2000,37(1-2):245-62.

[191] Wang Zhongmei. Mesoscopic Failure Behavior of Strip Footing on Geosynthetic-Reinforced Granular Soil Foundations Using PIV Technology[J]. Sustainability,2022,14(24) :16583-16583.

[192] Ikegaya N. et al. Applications of wide-ranging PIV measurements for various turbulent statistics in artificial atmospheric turbulent flow in a wind tunnel[J]. Building and Environment,2022,225

[193] Salehi Saeed and Nilsson Håkan. Effects of uncertainties in positioning of PIV plane on validation of CFD results of a high-head Francis turbine model[J]. Renewable Energy,2022,193 :57-75.

[194] 许联锋,陈 刚,李建中,等. 粒子图像测速技术研究进展[J]. 力学进展,2003,(04):533-540.

[195] 申艳军，杨更社，王铭.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.

[196] Yang Gengshe,Liu Chong,Liu hui.Analysis and research on experimental process of water thermal

migration of freeze-thaw cracked rock based on particle tracking method and thermal imaging technology[J].Sustainability,2023,2(17).

[197] Yen,Y.C.,”Free convection heat transfer characteristics in a melt water layer”,ASME.Journal of Heat Transfer,1980,Vol.100:550-556.

[198] 斋藤杉夫,“水的过冷度对结冰影响的研究”,日本冷冻协会论文集,1990.（3）:213-223.

[199] 池鲤鲋悟,“过冷水在传热面上结冰时不均匀质核的生成”,日本冷冻协会论文集,1995,(1):115-122.

[200] 贾海梁, 赵思琪, 丁顺, 等. 含水裂隙冻融过程中冻胀力演化及影响因素研究[J]. 岩石力学与工程学报, 2022, 41(09): 1832-1845.

[201] 张江伟, 李小军, 迟明杰, 等. 滑坡灾害的成因机制及其特征分析[J]. 自然灾害学报,2015, 24(06): 42-49.

[202] 张慧梅，刘向东. 断裂力学[M]. 徐州：中国矿业大学出版社，2018.1.

[203] 中国航空研究院. 应力强度因子手册[M]. 北京：科学出版社，1981.3.

[204] 蔡美峰, 何满潮, 刘东燕. 岩石力学与工程[M]. 北京: 科学出版社, 2002.

[205] 梁博. 寒区高陡岩质边坡冻融损伤失稳机制研究[博士学位论文][D]. 西安科技大学(西安)，2024.