Study on macro-meso damage model of sandstone with open cracks under the coupling action of freeze-thaw and load#br#
LV Siqing，ZHU Jiebing，WANG Bin，ZHU Yongsuo
(Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources，Changjiang River Scientific Research Institute，Wuhan，Hubei 430010，China)
摘要The evolution law of rock damage at macro and meso scales is the basis for evaluating the degradation process of mechanical properties of frozen rock. In this paper，the calculation method of macroscopic damage variable is proposed based on weighing method from the perspective of the volume of open fractures. Combined with the variation characteristics of rock composition and physical and mechanical properties under long-term freeze-thaw cycles，the difference of open porosity was reasonably corrected，and the meso-damage variables under freeze-thaw action were obtained. Considering the compaction characteristics of initial pores and cracks under load，a calculation model of mesoscopic damage variable under load is established by using statistical damage mechanics. The macro-meso coupling total damage is calculated by the macro-meso total damage calculation method based on Lemaitre strain equivalent hypothesis. According to the extended strain equivalence principle，the total damage constitutive model considering the influence of initial compaction section is constructed. In order to verify the rationality of the model，the prefabricated fractured sandstone samples with dip angles of 0°，30°，45°，60° and 90° and the intact sandstone samples were used to carry out the test of physical and mechanical properties after multiple freeze-thaw cycles. The research results show as follows. When the number of freeze-thaw cycles is small，the freeze-thaw damage variables increase rapidly，and the freeze-thaw damage variables gradually tend to be stable and increase slowly with the increase of the number of cycles. The influence of dip angles of fractures on the expansion of micro-pores and micro-fractures in sandstone rock samples is reflected in the different growth rates of damage variables. The increase rate of freeze-thaw damage variable of rock samples with 45° dip angle is the largest，and the expansion rate of micro-pores and micro-fractures of rock samples with 45° dip angle caused by frost heaving force is the fastest. The damage evolution curve of meso total damage model and macro-meso coupling total damage model tends to be consistent，and the coupling effect of freeze-thaw and load is the main source of damage and deterioration of sandstone samples in this test. The variation trends of macro-meso total damage test values of strains at the peak stresses are similar to those of theoretical calculation values，and the proposed theoretical model can reasonably describe the mechanisms of damage and degradation of fractured sandstone.
Abstract：The evolution law of rock damage at macro and meso scales is the basis for evaluating the degradation process of mechanical properties of frozen rock. In this paper，the calculation method of macroscopic damage variable is proposed based on weighing method from the perspective of the volume of open fractures. Combined with the variation characteristics of rock composition and physical and mechanical properties under long-term freeze-thaw cycles，the difference of open porosity was reasonably corrected，and the meso-damage variables under freeze-thaw action were obtained. Considering the compaction characteristics of initial pores and cracks under load，a calculation model of mesoscopic damage variable under load is established by using statistical damage mechanics. The macro-meso coupling total damage is calculated by the macro-meso total damage calculation method based on Lemaitre strain equivalent hypothesis. According to the extended strain equivalence principle，the total damage constitutive model considering the influence of initial compaction section is constructed. In order to verify the rationality of the model，the prefabricated fractured sandstone samples with dip angles of 0°，30°，45°，60° and 90° and the intact sandstone samples were used to carry out the test of physical and mechanical properties after multiple freeze-thaw cycles. The research results show as follows. When the number of freeze-thaw cycles is small，the freeze-thaw damage variables increase rapidly，and the freeze-thaw damage variables gradually tend to be stable and increase slowly with the increase of the number of cycles. The influence of dip angles of fractures on the expansion of micro-pores and micro-fractures in sandstone rock samples is reflected in the different growth rates of damage variables. The increase rate of freeze-thaw damage variable of rock samples with 45° dip angle is the largest，and the expansion rate of micro-pores and micro-fractures of rock samples with 45° dip angle caused by frost heaving force is the fastest. The damage evolution curve of meso total damage model and macro-meso coupling total damage model tends to be consistent，and the coupling effect of freeze-thaw and load is the main source of damage and deterioration of sandstone samples in this test. The variation trends of macro-meso total damage test values of strains at the peak stresses are similar to those of theoretical calculation values，and the proposed theoretical model can reasonably describe the mechanisms of damage and degradation of fractured sandstone.
吕思清，朱杰兵，汪 斌，祝永锁. 冻融荷载耦合作用下含开口裂隙砂岩宏细观损伤模型研究[J]. 岩石力学与工程学报, 2023, 42(5): 1124-1135.
LV Siqing，ZHU Jiebing，WANG Bin，ZHU Yongsuo. Study on macro-meso damage model of sandstone with open cracks under the coupling action of freeze-thaw and load#br#. , 2023, 42(5): 1124-1135.
[1] KRAJCINOVIC D，SILVA M A G. Statistical aspects of the continuous damage theory[J]. International Journal of Solid and Structure，1982，18(7)：551–562.
[2] 曹文贵，方祖烈，唐学军. 岩石损伤软化统计本构模型之研究[J]. 岩石力学与工程学报，1998，17(6)：628–633.(CAO Wengui，FANG Zulie，TANG Xuejun. A study of statistical constitutive model for soft and damage rocks[J]. Chinese Journal of Rock Mechanics and Engineering，1998，17(6)：628–633.(in Chinese))
[3] 徐卫亚，韦立德. 岩石损伤统计本构模型的研究[J]. 岩石力学与工程学报，2002，21(6)：787–791.(XU Weiya，WEI Lide. Study on statistical damage constitutive model of rock[J]. Chinese Journal of Rock Mechanics and Engineering，2002，21(6)：787–791.(in Chinese))
[4] 曹文贵，赵明华，唐学军. 岩石破裂过程的统计损伤模拟研究[J]. 岩土工程学报，2003，25(2)：184–187.(CAO Wengui，ZHAO Minghua，TANG Xuejun. Study on simulation of statistical damage in the full process of rock failure[J]. Chinese Journal of Geotechnical Engineering，2003，25(2)：184–187.(in Chinese))
[5] 杨明辉，赵明华，曹文贵. 岩石损伤软化统计本构模型参数的确定方法[J]. 水利学报，2005，36(3)：345–349.(YANG Minghui，ZHAO Minghua，CAO Wengui. Method for determining the parameters of statistical damage softening constitutive model for rock[J]. Journal of Hydraulic Engineering，2005，36(3)：345–349.(in Chinese))
[6] 曹文贵，莫 瑞，李 翔. 基于正态分布的岩石软硬化损伤统计本构模型及其参数确定方法探讨[J]. 岩土工程学报，2007，29(5)：671–675.(CAO Wengui，MO Rui，LI Xiang. Study on statistical constitutive model and determination of parameters of rock based on normal distribution[J]. Chinese Journal of Geotechnical Engineering，2007，29(5)：671–675.(in Chinese))
[7] WANG Z，LI Y，WANG J G. A damage-softening statistical constitutive model considering rock residual strength[J]. Computers and Geosciences，2007，33(1)：1–9.
[8] 蒋 维，邓 建，李 隐. 基于对数正态分布的岩石损伤本构模型研究[J]. 地下空间与工程学报，2010，6(6)：1 190–1 194.(JIANG Wei，DENG Jian，LI Yin. Study on constitutive model of rock damage based on lognormal distribution[J]. Chinese Journal of Underground Space and Engineering，2010，6(6)：1 190–1 194.(in Chinese))
[9] 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(3)：471–476.(ZHANG Huimei，YANG Gengshe. Research on damage model of rock under coupling action of freeze-thaw and load[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29 (3)：471–476.(in Chinese))
[10] DENG J，GU D. On a statistical damage constitutive model for rock materials[J]. Computers and Geosciences，2011，37(2)：122–128.
[11] 杨更社，谢定义. 岩体宏观细观损伤的耦合计算分析[C]// 新世纪岩石力学与工程的开拓和发展——中国岩石力学与工程学会第六次学术大会论文集. [S. l.]：[s. n.]，2000：340–342.(YANG Gengshe，XIE Dinyi. Coupling analysis on the macro-damage and meso-damage of rock masses[C]// Development and Development of Rock Mechanics and Engineering in the New Century—Proceedings of the Sixth Academic Conference of Chinese Society of Rock Mechanics and Engineering. [S. l.]：[s. n.]，2000：340–342.(in Chinese))
[12] 张力民，吕淑然，刘红岩. 综合考虑宏细观缺陷的岩体动态损伤本构模型[J]. 爆炸与冲击，2015，35(3)：428–436.(ZHANG Limin，LU Shuran，LIU Hongyan. A dynamic damage constitutive model of rock mass by comprehensively considering macroscopic and mesoscopic flaws[J]. Explosion and Shock Waves，2015，35(3)：428–436.(in Chinese))
[13] 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(8)：1 602–1 611.(YUAN Xiaoqing，LIU Hongyan，LIU Jingping. A damaging model of jointed rock under coupled action of freezing and thawing[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(8)：1 602–1 611.(in Chinese))
[14] 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(2)：100–108.(CHEN Song，QIAO Chunsheng，YE Qing，et al. Composite damage model of joint rock mass under freezing and thawing load[J]. Journal of Harbin Institute of Technology，2019，51(2)：100–108.(in Chinese))
[15] 乔 彤，章 光，胡少华，等. 脆性岩石微裂纹压密段本构模型研究[J]. 中国安全生产科学技术，2017，13(10)：128–135.(QIAO Tong，ZHANG Guang，HU Shaohua，et al. Research on constitutive model of microcrack compaction section in brittle rock[J]. Journal of Safety Science and Technology，2017，13(10)：128–135.(in Chinese))
[16] 马秋峰，秦跃平，周天白，等. 基于颗粒接触理论的岩石压密阶段本构模型[J]. 中南大学学报：自然科学版，2019，50(8)：1 941–1 948. (MA Qiufeng，QIN Yueping，ZHOU Tianbai，et al. Constitutive model of rock compaction stage based on contact theory[J]. Journal of Central South University：Science and Technology，2019，50(8)：1 941–1 948. (in Chinese))
[17] 朱要亮，俞 缙，付晓强，等. 高温损伤后岩石动态损伤本构模型[J]. 长江科学院院报，2022，39(7)：102–109.(ZHU Yaoliang，YU Jin，FU Xiaoqiang，et al. A novel dynamic constitutive model after temperature damage for rock[J]. Journal of Yangtze River Scientific Research Institute，2022，39(7)：102–109.(in Chinese))
[18] 雷 鸣，羽柴公博，福井胜则，等. 压密试验中破碎岩石压密特性的本构方程及数值模拟分析[J]. 岩石力学与工程学报，2011，30(6)：1 258–1 265.(LEI Ming，HASHIBA Kimihiro，FUKUI Katsunori，et al. Constitutive equation and numerical simulation analysis for broken rock behaviors in compaction test[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(6)：1 258–1 265.(in Chinese))
[19] 李修磊，陈洪凯，张金浩. 考虑初始空隙压密的岩石变形全过程本构模型[J]. 西南交通大学学报，2022，57(2)：314–321.(LI Xiulei，CHEN Hongkai，ZHANG Jinhao. Statistical damage model for whole deformation and failure process of rock considering initial void closure[J]. Journal of Southwest Jiaotong University，2022，57(2)：314–321.(in Chinese))
[20] 贾海梁，刘清秉，项 伟，等. 冻融循环作用下饱和砂岩损伤扩展模型研究[J]. 岩石力学与工程学报，2013，32(增2)：3 049–3 055. (JIA Hailiang，LIU Qingbing，XIANG Wei，et al. Damage evolution model of saturated sandstone under freeze-thaw cycles[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(Supp.2)：3 049–3 055.(in Chinese))
[21] 张全胜，杨更社，任建喜. 岩石损伤变量及本构方程的新探讨[J]. 岩石力学与工程学报，2003，22(1)：30–34.(ZHANG Quansheng，YANG Gengshe，REN Jianxi. New study of damage variable and constitutive equation of rock[J]. Chinese Journal of Rock Mechanics and Engineering，2003，22(1)：30–34.(in Chinese))
[22] 张慧梅，杨更社. 冻融荷载耦合作用下岩石损伤力学特性[J]. 工程力学，2011，28(5)：161–165.(ZHANG Huimei，YANG Gengshe. Damage mechanical characteristics of rock under freeze-thaw and load coupling[J]. Engineering mechanics，2011，28(5)：161–165.(in Chinese))
[23] 曹文贵，李 翔. 岩石损伤软化统计本构模型及参数确定方法的新探讨[J]. 岩土力学，2008，29(11)：2 952–2 956.(CAO Wengui，LI Xiang. A new discussion on damage softening statistical constitutive model for rocks and method for determining its parameters[J]. Rock and Soil Mechanics，2008，29(11)：2 952–2 956.(in Chinese))
[24] 惠 鑫，马凤山，徐嘉谟，等. 考虑节理裂隙尺寸与方位分布的岩石统计损伤本构模型研究[J]. 岩石力学与工程学报，2017，36(增1)：3 233–3 238.(HUI Xin，MA Fengshan，XU Jiamo，et al. Study on statistical damage constitutive model for rocks considering length and occurrence distribution of joint fissures[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(Supp.1)：3 233–3 238. (in Chinese))
[25] 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)：1 444–1 452.(ZHANG Huimei，XIE Xiangmiao，PENG Chuan，et al. Constitutive model for damage of freeze-thaw rock under three-dimensional stress[J]. Chinese Journal of Geotechnical Engineering，2017，39(8)：1 444–1 452.(in Chinese))
[26] 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(5)：1 066–1 072. (ZHANG Huimei，PENG Chuan，YANG Gengshe，et al. Study of damage statistical strength criterion of rock considering the effect of freezing and thawing[J]. Journal of China University of Mining and Technology，2017，46(5)：1 066–1 072.(in Chinese))
[27] 文志杰，田 雷，蒋宇静，等. 基于应变能密度的非均质岩石损伤本构模型研究[J]. 岩石力学与工程学报，2019，38(7)：1 332–1 343. (WEN Zhijie，TIAN Lei，JIANG Yujing，et al. Research on damage constitutive model of inhomogeneous rocks based on strain energy density[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(7)：1 332–1 343.(in Chinese))
[28] 赵顺利，邓伟杰，路新景，等. 基于自然应变损伤模型的膨胀土冻融损伤分析[J]. 岩土工程学报，2020，42(增1)：127–131.(ZHAO Shunli，DENG Weijie，LU Xinjing，et al. Freeze-thaw damage analysis of expansive soils based on natural strain damage model[J]. Chinese Journal of Geotechnical Engineering，2020，42(Supp.1)：127–131.(in Chinese))
[29] 张慧梅，孟祥振，彭 川，等. 冻融–荷载作用下基于残余强度特征的岩石损伤模型[J]. 煤炭学报，2019，44(11)：3 404–3 411. (ZHANG Huimei，MENG Xiangzhen，PENG Chuan，et al. Rock damage constitutive model based on residual intensity characteristics under freeze-thaw and load[J]. Journal of China Coal Society，2019，44(11)：3 404–3 411.(in Chinese))
[30] HUANG S，LIU Q，CHENG A，et al. A statistical damage constitutive model under freeze-thaw and loading for rock and its engineering application[J]. Cold regions Science and Technology，2018，145：142–150.
[31] FANG W，JIANG N，LUO X. Establishment of damage statistical constitutive model of loaded rock and method for determining its parameters under freeze-thaw condition[J]. Cold Regions Science and Technology，2019，160：31–38.
[32] LU Y，LI X，CHAN A. Damage constitutive model of single flaw sandstone under freeze-thaw and load[J]. Cold Regions Science and Technology，2019，159：20–28.
[33] ZHANG H，MENG X，YANG G. A study on mechanical properties and damage model of rock subjected to freeze-thaw cycles and confining pressure[J]. Cold Regions Science and Technology，2020，174：103056.
2023, Vol. 42 
