A new damage constitutive model of rock considering microscopic crack growth
LI Shengnan1，XIAO Jun2，LI Yu1，LIU Xinxi2，LIANG Qiao1，CHANG Jin3，LIU Jie1
(1. School of Architectural Engineering，Hunan Institute of Engineering，Xiangtan，Hunan 411104，China；
2. School of Civil Engineering，Changsha University of Science and Technology，Changsha，Hunan 410114，China；
3. School of Naval Architecture，Ocean and Civil Engineering，Shanghai Jiaotong University，Shanghai 200240，China)
Abstract：This paper aims to establish a damage constitutive model that can accurately characterize the mechanical properties of the evolution process of microscopic crack propagation in rocks. Firstly，based on phenomenological theory，the rock mesostructure is generalized into three parts：complete rock micro-elements，crack propagation damage micro-elements and pores. Using the static equilibrium relationship between these three parts，a mesoscopic force model of fractured rock is constructed. Secondly，according to the crack propagation characteristics of rock，a bio-blocking growth model is proposed to characterize the crack propagation length. Based on the geometric damage theory，the quantitative relationship between crack growth length and damage is established，and the damage evolution equation of crack propagation of rock is established. Thirdly，the actual stress of crack propagation damage element is solved by fracture mechanics. Then，by introducing the damage variable of crack propagation and the actual stress of crack propagation damage microelement into the mesostatic equilibrium equation of rock，and considering the influence of nonlinear deformation in the compaction stage of soft rock，a damage constitutive model of rock considering the microscopic crack propagation evolution is established. Finally，a method determining the model parameters is proposed，and the influence of model parameters on the mechanical properties of the rock is discussed. The results show that the model can better characterize the stress-strain characteristics the crack propagation process of rock，which is in good agreement with the test results，and the physical meaning of the model parameters is clear.
[1] 曹文贵，张 超，贺 敏，等．考虑空隙压密阶段特征的岩石应变软化统计损伤模拟方法[J]. 岩土工程学报，2016，38(10)：1 754–1 761. (CAO Wengui，ZHANG Chao，HE Min，et al. Statistical damage simulation method of strain softening deformation process for rocks considering characteristics of void compaction stage[J]. Chinese Journal of Geotechnical Engineering，2016，38(10)：1 754–1 761.(in Chinese))
[2] WU J，FENG M，YU B，et al. Experimental investigation on dilatancy behavior of water-saturated sandstone[J]. International Journal of Mining Science and Technology，2018，28(2)：323–329.
[3] ZHANG Q，ZHANG C，JIANG B，et al. Elastoplastic coupling solution of circular openings in strain-softening rock mass considering pressure-dependent effect[J]. International Journal of Geomechanics，2018，18(1)：04017132.
[4] 梁明纯，苗胜军，蔡美峰，等. 考虑剪胀特性和峰后形态的岩石损伤本构模型[J]. 岩石力学与工程学报，2021，40(12)：2 392–2 401. (LIANG Mingchun，MIAO Shengjun，CAI Meifeng，et al. A damage constitutive model of rock with consideration of dilatation and post-peak shape of the stress-strain cure[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(12)：2 392–2 401.(in Chinese))
[5] 杜修力，黄景琦，金 浏，等. 岩石三维弹塑性损伤本构模型研究[J]. 岩土工程学报，2017，39(6)：978–985.(DU Xiuli，HUANG Jingqi，JIN Liu，et al. Three-dimension elastic-plastic damage constitutive model for intact rock[J]. Chinese Journal of Geotechnical Engineering，2017，39(6)：978–985.(in Chinese))
[6] 祝效华，孙汉文，赵金洲，等．天然气水合物沉积物等效变弹性模量损伤本构模型[J]. 石油学报，2019，40(9)：1 085–1 094.(ZHU Xiaohua，SUN Hanwen，ZHAO Jinzhou，et al. Damage constitutive model of equivalent variable elastic modulus for gas hydrate sediments[J]. Acta Petrolel Sinica，2019，40(9)：1 085–1 094.(in Chinese))
[7] CAO A，JING G，DING Y，et al. Mining-induced static and dynamic loading rate effect on rock damage and acoustic emission characteristic under uniaxial compression[J]. Safety Science，2019，116：86–96.
[8] 刘新喜，李盛南，徐泽佩，等. 高应力泥质粉砂岩黏弹塑性蠕变模型[J]. 中南大学学报：自然科学版，2019，50(5)：1 210–1 220.(LIU Xinxi，LI Shengnan，XU Zepei，et al. Viscoelastic-plastic creep model of high stress argillaceous siltstone[J]. Journal of Central South University：Science and Technology，2019，50(5)：1 210–1 220.(in Chinese))
[9] 赵阳升. 岩体力学发展的一些回顾与若干未解之百年问题[J]. 岩石力学与工程学报，2021，40(7)：1 297–1 336.(ZHAO Yangsheng. Retrospection on the development of rock mass mechanics and the summary of some unsolved centennial problems[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(7)：1 297–1 336.(in Chinese))
[10] 江 权，冯夏庭，李邵军，等. 高应力下大型硬岩地下洞室群稳定性设计优化的裂化–抑制法及其应用[J]. 岩石力学与工程学报，2019，38(6)：1 081–1 101.(JIANG Quan，FENG Xiating，LI Shaojun，et al. Cracking- restraint design method for large underground caverns with hard rock under high geostress condition and its practical application[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(6)：1 081–1 101.(in Chinese))
[11] 赵怡晴，刘红岩，吕淑然，等. 基于宏观和细观缺陷耦合的节理岩体损伤本构模型[J]. 中南大学学报：自然科学版，2015，46(4)：1 489–1 496.(ZHAO Yiqing，LIU Hongyan，LÜ Shuran，et al. Damage constitutive model of jointed rock mass based on coupling macroscopic and mesoscopic flaws[J]. Journal of Central South University：Science and Technology，2015，46(4)：1 489–1 496.(in Chinese))
[12] 吴贤振，刘建伟，刘祥鑫，等. 岩石声发射振铃累计计数与损伤本构模型的耦合关系探究[J]. 采矿与安全工程学报，2015，32(1)：28–34.(WU Xianzhen，LIU Jianwei，LIU Xiangxin，et al. Study on the coupled relationship between AE accumulative ring-down count and damage constitutive model of rock[J]. Journal of Mining and Safety Engineering，2015，32(1)：28–34.(in Chinese))
[13] 刘新喜，李盛南，徐泽沛，等. 冻融循环作用下炭质页岩蠕变模型研究[J]. 中国公路学报，2019，32(11)：137–145.(LIU Xinxi，LI Shengnan，XU Zepei，et al. Reseach on creep model of carbonaceous shale under freeze-thaw cycle[J]. China Journal of Highway and Transport，2019，32(11)：137–145.(in Chinese))
[14] 李 博，叶鹏进，黄 林，等. 干燥与饱和岩石裂隙受压变形与声发射特性研究[J]. 岩土工程学报，2021，43(12)：2 249–2 257.(LI Bo，YE Pengjin，HUANG Lin，et al. Deformation and acoustic emission characteristics of dry and saturated rock fractures[J]. Chinese Journal of Geotechnical Engineering，2021，43(12)：2 249–2 257.(in Chinese))
[15] 韦立德，徐卫亚，杨春和，等. 具有统计损伤的岩石弹塑性本构模型研究[J]. 岩石力学与工程学报，2004，23(12)：1 971–1 975.(WEI Lide，XU Weiya，YANG Chunhe，et al. Study on elasticplastic constitutive model of rock with statistical damage[J]. Chinese Journal of Rock Mechanics and Engineering，2004，23(12)：1 971–1 975.(in Chinese))
[16] 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))
[17] 温 韬，唐辉明，刘佑荣，等. 影响因子修正的新型岩石损伤统计本构模型[J]. 中国矿业大学学报，2016，45(1)：141–149.(WEN Tao，TANG Huiming，LIU Yourong，et al. Newly modified damage statistical constitutive model of rock based on impact factor[J]. Journal of China University of Mining and Technology，2016，45(1)：141–149.(in Chinese))
[18] 张 超，白 允. 参数型岩石几何损伤模型的构建及其应用研究[J]. 岩土力学，2020，41(12)：3 899–3 909.(ZHANG Chao，BAI Yun. Establishment and application of parametric geometrical damage model of rocks[J]. Rock and Soil Mechanics，2020，41(12)：3 899–3 909.(in Chinese))
[19] ASHBY M F，SAMMIS C G. The damage mechanics of brittle solids in compression[J]. Pure and Applied Geophysics，1990，133(3)：489–521.
[20] 李晓照，邵珠山，戚承志. 岩石裂纹损伤及围压对剪切破坏影响研究[J]. 岩土力学，2019，40(11)：4 249–4 258.(LI Xiaozhao，SHAO Zhushan，QI Chengzhi. Study on rock crack damage and confining pressure effects on shear fracture band[J]. Rock and Soil Mechanics，2019，40(11)：4 249–4 258.(in Chinese))
[21] 曹文贵，张 升，赵明华. 基于新型损伤定义的岩石损伤统计本构模型探讨[J]. 岩土力学，2006，27(1)：41–46.(CAO Wengui，ZHANG Sheng，ZHAO Minghua. Study on statistical damage constitutive model of rock based on new definition of damage[J]. Rock and Soil Mechanics，2006，27(1)：41–46.(in Chinese))
[22] 杨圣奇，徐卫亚，韦立德，等. 单轴压缩下岩石损伤统计本构模型与试验研究[J]. 河海大学学报：自然科学版，2004，(2)：200–203.(YANG Shengqi，XU Weiya，WEI Lide，et al. Statistical constitutive model for rock damage under uniaxial compression and its experimental study[J]. Journal of Hohai University：Natural Science，2004，(2)：200–203.(in Chinese))
[23] 曹文贵，张 超，贺 敏，等. 岩石空隙变化及其变形全过程的统计损伤模拟方法[J]. 湖南大学学报：自然科学版，2017，44(9)：100–106.(CAO Wengui，ZHANG Chao，HE Min，et al. Voids change and statistical damage simulation method of the full deformation process for rocks[J]. Journal of Hunan University：Natural Science，2017，44(9)：100–106.(in Chinese))
[24] 孙梦成，徐卫亚，王苏生，等. 基于最小耗能原理的岩石损伤本构模型研究[J]. 中南大学学报：自然科学版，2018，49(8)：2 067–2 075. (SUN Mengcheng，XU Weiya，WANG Susheng，et al. Study on damage constitutive model of rock based on principle of minimum dissipative energy[J]. Journal of Central South University：Science and Technology，2018，49(8)：2 067–2 075.(in Chinese))
[25] 殷 达，孟庆祥，徐建荣，等. 基于微结构张量的岩石各向异性弹塑性本构及其应用[J]. 岩土工程学报，2020，42(9)：1 751–1 758. (YIN Da，MENG Qingxiang，XU Jianrong，et al. Anisotropic elastoplastic constitutive model based on microstructure tensor and its engineering application[J]. Chinese Journal of Geotechnical Engineering，2020，42(9)：1 751–1 758.(in Chinese))
[26] LI Tingchun，Lianxun LYU，ZHANG Shilin，et al. Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements[J]. Journal of Zhejiang University-Science A(Applied Physics & Engineering)，2015，16(8)：644–655.
[27] 李盛南，刘新喜，李 玉，等. 炭质泥岩渐进破坏过程的变形特性及损伤演化研究[J]. 中国公路学报，2022，35(4)：99–107.(LI Shengnan，LIU Xinxi，LI Yu，et al. Study on deformation characteristics and damage evolution law of progressive failure process of carbonaceous mudstone[J]. China Journal of Highway and Transport，2022，35(4)：99–107.(in Chinese))
[28] LI S N，HUANG Z H，LIANG Q，et al. Evolution mechanism of mesocrack and macrocrack propagation in carbonaceous mudstone under the action of dry-wet cycles[J]. Geofluids，2022，25(2)：56–64.
[29] 刘冬桥，王 焯，张晓云. 岩石应变软化变形特性及损伤本构模型研究[J]. 岩土力学，2017，38(10)：2 901–2 908.(LIU Dongqiao，WANG Zhuo，ZHANG Xiaoyun. Characteristics of strain softening of rocks and its damage constitutive model[J]. Rock and Soil Mechanics，2017，38(10)：2 901–2 908.(in Chinese))
[30] 朱珍德，渠文平，蒋志坚. 岩石细观结构量化试验研究[J]. 岩石力学与工程学报，2007，26(7)：1 313–1 324.(ZHU Zhende，QU Wenping，JIANG Zhijian. Quantitative test study on mesostructure of rock[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(7)：1 313–1 324.(in Chinese))
2023, Vol. 42 
