Phase-field modeling of frost propagation of cracks for rock mass under frost action
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摘要: 寒区岩体冻结时，裂隙水相变成冰体积膨胀，冰-岩相互作用常引起裂隙冻胀扩展。为探索冻结岩体裂隙冻胀扩展的模拟和预测方法并深入认识不同条件下裂隙冻胀扩展规律，引入以弥散化标量场表征裂隙的相场法描述裂隙冻胀扩展，利用等效热膨胀系数法施加裂隙冰相变膨胀，在COMSOL Multiphysics软件平台实现对岩体裂隙冰-岩相互作用力学场控制方程和裂隙冻胀扩展相场演化控制方程的求解。基于冻结岩体冻胀扩展试验，对多种工况下裂隙冻胀扩展进行相场法模拟。模拟所得不同倾角、外荷载作用下单裂隙冻胀扩展，及不同岩桥倾角、裂隙夹角工况时双裂隙冻胀扩展均与试验获得裂隙冻胀扩展形态接近，说明文中建立的相场法模型能够较准确地模拟预测冻结岩体的裂隙冻胀扩展。受外荷载作用时，单裂隙冻胀扩展向荷载作用方向偏转。对不同岩桥倾角的双裂隙，因裂隙之间相互作用，裂隙内尖端冻胀扩展总是向另一条裂隙方向偏转，裂隙外尖端则产生共面冻胀扩展。对不同夹角的双裂隙，平行双裂隙会形成两条独立呈“蝶状”的冻胀扩展裂隙，而具有倾斜交角的双裂隙会形成交于一点的辐射状冻胀扩展裂隙。Abstract: As the rock masses in cold regions freeze, water in cracks turns into ice and expands in volume, and the mechanical interaction between ice and rock may lead to the frost propagation of cracks. To study the prediction method for the frost propagation of cracks and further cognize the laws of the frost propagation under different conditions, the phase-field model which represents cracks in a diffusive way with a scalar field is introduced to simulate the frost propagation, and the method for the equivalent thermal expansion coefficient is utilized to simulate the volume expansion of ice in cracks due to phase transition. Moreover, the governing equations for stress field for ice-rock interaction and the governing equations of phase-field evolution for the frost propagation of cracks are solved through the COMSOL Multiphysics software. Numerical simulations with the phase-field model on the frost propagation are conducted based on a series of frost propagation experiments on the rock masses. The numerical results are similar to the experimental ones for both the frost propagation of a single crack under different dip angles and external loads, and the frost propagation of double cracks under different dip angles of rock bridge and different intersection angles. It is indicated that the phase-field model established can accurately simulate the frost propagation of cracks in the rock masses. Furthermore, when subjected to an external load, the frost propagation of a single crack deflects towards the direction of the load. For the double cracks with different dip angles of rock bridge, the frost propagation of inner tips always deflects towards the adjacent crack due to the interaction of two cracks, while the outer tips propagate approximately along the coplanar direction. For double cracks with different intersection angles, two independent new frost cracks in a butterfly shape will form when the two cracks are parallel to each other, while new frost cracks in a radiation shape will form for the double cracks with an inclined intersection angle.
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Keywords:
- rock mass /
- frost propagation /
- phase-field method /
- single crack /
- double cracks
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图 3 倾角0°应力分布与裂隙冻胀扩展
Figure 3. Stresses and frost propagation of crack with dip angle of 0°
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图 10 外荷载1 MPa工况裂隙冻胀扩展
Figure 10. Frost propagation of crack with external load of 1 MPa
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图 11 竖向外荷载3 MPa工况裂隙冻胀扩展
Figure 11. Frost propagation of crack with vertical load of 3 MPa
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图 12 竖向外荷载6 MPa工况裂隙冻胀扩展
Figure 12. Frost propagation of crack with vertical load of 6 MPa
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[1] 刘泉声, 黄诗冰, 康永水, 等. 裂隙岩体冻融损伤研究进展与思考[J]. 岩石力学与工程学报, 2015, 34(3): 452-471. doi: 10.13722/j.cnki.jrme.2015.03.003 LIU Quansheng, HUANG Shibing, KANG Yongshui, et al. Advance and review on freezing-thawing damage of fractured rock[J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(3): 452-471. (in Chinese) doi: 10.13722/j.cnki.jrme.2015.03.003
[2] DAVIDSON G, NYE J. A photoelastic study of ice pressure in rock cracks[J]. Cold Regions Science and Technology, 1985, 11(2): 141-153. doi: 10.1016/0165-232X(85)90013-8
[3] 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(1): 78-84. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201801011.htm HUANG Shibing, LIU Quansheng, CHENG Aiping, et al. Preliminary experimental study of frost heaving pressure in crack and frost heaving propagation in rock mass under low temperature[J]. Rock and Soil Mechanics, 2018, 39(1): 78-84. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201801011.htm
[4] 乔趁, 王宇, 宋正阳, 等. 饱水裂隙花岗岩周期冻胀力演化特性试验研究[J]. 岩土力学, 2021, 42(8): 2141-2150. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202108010.htm QIAO Chen, WANG Yu, SONG Zhengyang, et al. Experimental study on the evolution characteristics of cyclic frost heaving pressure of saturated fractured granite[J]. Rock and Soil Mechanics, 2021, 42(8): 2141-2150. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202108010.htm
[5] BOST M, POUYA A. Stress generated by the freeze–thaw process in open cracks of rock walls: empirical model for tight limestone[J]. Bulletin of Engineering Geology and the Environment, 2017, 76(4): 1491-1505. doi: 10.1007/s10064-016-0955-6
[6] LÜ Zhitao, XIA Caichu, WANG Yuesong, 等. Frost heave and freezing processes of saturated rock with an open crack under different freezing conditions[J]. 结构与土木工程前沿, 2020, 14(4): 947-960. https://www.cnki.com.cn/Article/CJFDTOTAL-PGJX202310015.htm LÜ Zhitao, XIA Caichu, WANG Yuesong, 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(4): 947-960. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-PGJX202310015.htm
[7] 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. doi: 10.1002/ppp.1950
[8] 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. doi: 10.1016/j.coldregions.2018.04.016
[9] 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): 1572-1580. doi: 10.11779/CJGE201509003 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): 1572-1580. (in Chinese) doi: 10.11779/CJGE201509003
[10] 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): 1530-1542. doi: 10.16285/j.rsm.2016.06.002 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): 1530-1542. (in Chinese) doi: 10.16285/j.rsm.2016.06.002
[11] HUANG S, LIU Y, GUO Y, et al. Strength and failure characteristics of rock-like material containing single crack under freeze-thaw and uniaxial compression[J]. Cold Regions Science and Technology, 2019, 162: 1-10. doi: 10.1016/j.coldregions.2019.03.013
[12] WANG Y, FENG W, WANG H, et al. Rock bridge fracturing characteristics in granite induced by freeze-thaw and uniaxial deformation revealed by AE monitoring and post-test CT scanning[J]. Cold Regions Science and Technology, 2020, 177: 103115. doi: 10.1016/j.coldregions.2020.103115
[13] 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. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX202001012.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX202001012.htm
[14] THARP T. Conditions for crack propagation by frost wedging[J]. Bulletin of the Geological Society of America, 1987, 99(1): 94-102. doi: 10.1130/0016-7606(1987)99<94:CFCPBF>2.0.CO;2
[15] 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. doi: 10.1016/j.enggeo.2017.12.024
[16] 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. doi: 10.11779/CJGE201803009 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 Geotechnical Engineering, 2018, 40(3): 459-467. (in Chinese) doi: 10.11779/CJGE201803009
[17] ZHOU Y. Numerical simulation of fracture propagation in freezing rocks using the extended finite element method (XFEM)[J]. International Journal of Rock Mechanics and Mining Sciences, 2021, 148: 104963. doi: 10.1016/j.ijrmms.2021.104963
[18] 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: 103967. doi: 10.1016/j.compgeo.2020.103967
[19] MIEHE C, HOFACKER M, WELSCHINGER F. A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(45-48): 2765-2778.
[20] ZHOU S, ZHUANG X, ZHU H, et al. Phase field modelling of crack propagation, branching and coalescence in rocks[J]. Theoretical and Applied Fracture Mechanics, 2018, 96: 174-192.
[21] ZHOU S, ZHUANG X, RABCZUK T. A phase-field modeling approach of fracture propagation in poroelastic media[J]. Engineering Geology, 2018, 240: 189-203.
[22] 刘嘉, 薛熠, 高峰, 等. 层理页岩水力裂缝扩展规律的相场法研究[J]. 岩土工程学报, 2022, 44(3): 464-473. doi: 10.11779/CJGE202203008 LIU Jia, XUE Yi, GAO Feng, et al. Propagation of hydraulic fractures in bedded shale based on phase-field method[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(3): 464-473. (in Chinese) doi: 10.11779/CJGE202203008
[23] ZHOU S, ZHUANG X, RABCZUK T. Phase field method for quasi-static hydro-fracture in porous media under stress boundary condition considering the effect of initial stress field[J]. Theoretical and Applied Fracture Mechanics, 2020, 107: 102523.
[24] SWEIDAN A, HEIDER Y, MARKERT B. A unified water/ice kinematics approach for phase-field thermo-hydro- mechanical modeling of frost action in porous media[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 372: 113358.
[25] BORDEN M, VERHOOSEL C, SCOTT M, et al. A phase-field description of dynamic brittle fracture[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 217: 77-95.
[26] 丁遂栋. 断裂力学[M]. 北京: 机械工业出版社, 1997. DING Suidong. Fracture Mechanics[M]. Beijing: China Machine Press, 1997. (in Chinese)
[27] 吴家龙. 弹性力学[M]. 2版. 北京: 高等教育出版社, 2011. WU Jialong. Elasticity[M]. 2nd ed. Beijing: Higher Education Press, 2011. (in Chinese)
[28] MIEHE C, WELSCHINGER F, HOFACKER M. Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations[J]. International Journal for Numerical Methods in Engineering, 2010, 83(10): 1273-1311.
[29] 刘艳章, 郭赟林, 黄诗冰, 等. 冻融作用下裂隙类砂岩断裂特征与强度损失研究[J]. 岩土力学, 2018, 39(增刊2): 62-71. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX2018S2010.htm LIU Yanzhang, GUO Yunlin, HUANG Shibing, et al. Study of fracture characteristics and strength loss of crack quasi-sandstone under freeze-thaw cycles[J]. Rock and Soil Mechanics, 2018, 39(S2): 62-71. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX2018S2010.htm
[30] 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.
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