A compressive damage model for a rock considering the microcrack mechanical behavior
-
摘要:
针对目前岩石压缩损伤模型未能很好地同时考虑微裂纹滑移与扩展对岩石总变形的贡献、微裂纹复合扩展准则及岩石损伤程度对被激活裂纹数量影响等不足，基于细观力学对微裂纹在单轴压缩荷载下的滑移及扩展机理展开研究。首先根据微裂纹滑移模型及能量平衡原理，建立了岩石单轴压缩应力应变关系，并认为微裂纹服从Weibull分布模型；进而以应变能密度准则作为微裂隙扩展判据，采用迭代法求解复合型断裂的翼裂纹扩展长度，并获得用翼裂纹扩展长度表示的岩石损伤变量演化方程，由此提出了一个新的岩石单轴压缩损伤模型，并验证了其合理性；最后，采用参数敏感性分析研究了微裂纹长度及摩擦系数和岩石断裂韧度对岩石力学特性的影响。结果表明：由本模型预测得到的岩石单轴压缩峰值强度与试验结果吻合较好，说明了其合理性。同时发现随着微裂纹长度增加及其摩擦系数减小、岩石断裂韧度增加，岩石单轴抗压峰值强度及峰值应变均随之减小。当微裂纹长度由60 μm增加到120 μm时，岩石单轴抗压峰值强度近似线性降低；而当微裂纹摩擦系数由0.5增加到0.8及岩石断裂韧度由0.3 MPa·m1/2增加到0.6 MPa·m1/2时，岩石单轴抗压峰值强度均是先缓慢增加，而后迅速增加。本研究为岩石压缩损伤本构模型的建立提供了一条新的思路，具有重要的理论意义。
Abstract:The contributions of the microcrack sliding and propagation to the rock total deformation, the mixed propagation criterion of the microcrack, and the influence of the rock damage degree on the number of the activated microcracks are not completely considered in the existing rock compressive damage model. Thus, the microcrack sliding and propagation mechanism under uniaxial compression was studied with the mesoscopic mechanics. Firstly, the uniaxial compression stress-strain relationship was developed according to the microcrack sliding model and energy balance which assumed the microcracks being Weibull distribution. Then the mixed fracture propagation length of the wing-crack was solved with the strain energy density criterion as the microcrack propagation criterion and iteration method. The damage evolution equation was obtained with the wing-crack propagation length. A new damage model for the rock under uniaxial compression was proposed and verified. Finally, the parametric sensitivity analysis was adopted to study the effects of the microcrack length, friction coefficient, and rock fracture toughness on the rock mechanical properties. The results show that the rock climax strength from the proposed model is consistent with the corresponding test result, indicating that the proposed model is reasonable. The uniaxial compression climax strength and strain both decrease with the increase of the microcrack length and the decrease of the microcrack friction coefficient. When the microcrack length increases from 60 μm to 120 μm, the uniaxial compression climax strength almost decreases linearly. When the microcrack friction coefficient increases from 0.5 to 0.8 and the rock fracture toughness increases from 0.3 MPa·m1/2 to 0.6 MPa·m1/2, the uniaxial compression climax strength increases slowly and then rapidly. This study provides new insight into the establishment of the rock damage constitutive model under compression.
-
-
[1] 邓志颖,范祥,何忠明,等. L形边裂隙单圆孔砂岩单轴压缩力学特性[J]. 吉林大学学报(地球科学版),2023,53(2):541 − 554. [DENG Zhiying,FAN Xiang,HE Zhongming,et al. Uniaxial compressive mechanical properties of sandstone with single circular hole and L-shaped side fissures[J]. Journal of Jilin University (Earth Science Edition),2023,53(2):541 − 554. (in Chinese with English abstract)]
DENG Zhiying, FAN Xiang, HE Zhongming, et al. Uniaxial compressive mechanical properties of sandstone with single circular hole and L-shaped side fissures[J]. Journal of Jilin University (Earth Science Edition), 2023, 53（2）: 541 − 554. （in Chinese with English abstract）
[2] 裂隙岩体循环冻融变形特征及影响因素分析[J]. 地质科技通报, 2021, 40(6):205 − 215. [CUI Shenghua,YANG Qingwen,RUI Xuelian,et al. Effect factors analysis and characteristic of freeze-thaw deformation of fracture rock[J]. Bulletin of Geological Science and Technology, 2021, 40(6):205 − 215. (in Chinese with English abstract)]
CUI Shenghua, YANG Qingwen, RUI Xuelian, et al. Effect factors analysis and characteristic of freeze-thaw deformation of fracture rock[J]. Bulletin of Geological Science and Technology, 2021, 40（6）: 205 − 215. （in Chinese with English abstract）
[3] 刘冬桥,郭允朋,李杰宇,等. 单轴压缩下脆性岩石损伤破坏能量演化规律试验研究[J]. 工程地质学报,2023,31(3):843 − 853. [LIU Dongqiao,GUO Yunpeng,LI Jieyu,et al. Experimental study on damage and failure energy evolution of brittle rocks under uniaxial compression[J]. Journal of Engineering Geology,2023,31(3):843 − 853. (in Chinese with English abstract)]
LIU Dongqiao, GUO Yunpeng, LI Jieyu, et al. Experimental study on damage and failure energy evolution of brittle rocks under uniaxial compression[J]. Journal of Engineering Geology, 2023, 31（3）: 843 − 853. （in Chinese with English abstract）
[4] 封陈晨,李傲,王志亮,等. 锦屏大理岩单轴压缩过程中的微结构演化[J]. 水文地质工程地质,2022,49(6):90 − 96. [FENG Chenchen,LI Ao,WANG Zhiliang,et al. A study of mineral compositions and micro-structure characteristics for the Jinping marble[J]. Hydrogeology & Engineering Geology,2022,49(6):90 − 96. (in Chinese with English abstract)]
FENG Chenchen, LI Ao, WANG Zhiliang, et al. A study of mineral compositions and micro-structure characteristics for the Jinping marble[J]. Hydrogeology & Engineering Geology, 2022, 49（6）: 90 − 96. （in Chinese with English abstract）
[5] 孙钱程,徐晓,丰光亮,等. 长时浸泡红砂岩加/卸荷条件下的剪切特性及细观损伤机理[J]. 水文地质工程地质,2024,51(2):77 − 89. [SUN Qiancheng,XU Xiao,FENG Guangliang,et al. Shear characteristics and mesoscopic damage mechanism of long time soaking red sandstone under loading and unloading conditions[J]. Hydrogeology & Engineering Geology,2024,51(2):77 − 89.(in Chinese with English abstract)]
SUN Qiancheng, XU Xiao, FENG Guangliang, et al. Shear characteristics and mesoscopic damage mechanism of long time soaking red sandstone under loading and unloading conditions[J]. Hydrogeology & Engineering Geology, 2024, 51（2）: 77 − 89.（in Chinese with English abstract）
[6] MENG Qingshan,WU Kai,ZHOU Haoran,et al. Mesoscopic damage evolution of coral reef limestone based on real-time CT scanning[J]. Engineering Geology,2022,307:106781. doi: 10.1016/j.enggeo.2022.106781
[7] 彭志雄,曾亚武. 基于裂纹扩展作用下的岩石损伤力学模型[J]. 东北大学学报(自然科学版),2022,43(12):1784 − 1791. [PENG Zhixiong,ZENG Yawu. Microcrack propagation-based damage mechanics model of rock[J]. Journal of Northeastern University (Natural Science),2022,43(12):1784 − 1791. (in Chinese with English abstract)]
PENG Zhixiong, ZENG Yawu. Microcrack propagation-based damage mechanics model of rock[J]. Journal of Northeastern University （Natural Science）, 2022, 43（12）: 1784 − 1791. （in Chinese with English abstract）
[8] 李晓照,戚承志,邵珠山. 脆性岩石局部细观裂纹成核损伤突变机理研究[J]. 中国科学:技术科学,2021,51(4):480 − 492. [LI Xiaozhao,QI Chengzhi,SHAO Zhushan. Research on mechanisms of the damage catastrophe from localized microcrack nucleation in brittle rocks[J]. Scientia Sinica (Technologica),2021,51(4):480 − 492. (in Chinese with English abstract)] doi: 10.1360/SST-2020-0185
LI Xiaozhao, QI Chengzhi, SHAO Zhushan. Research on mechanisms of the damage catastrophe from localized microcrack nucleation in brittle rocks[J]. Scientia Sinica （Technologica）, 2021, 51（4）: 480 − 492. （in Chinese with English abstract） doi: 10.1360/SST-2020-0185
[9] HUANG Shuling,ZHANG Chuanqing,DING Xiuli. Hardening–softening constitutive model of hard brittle rocks considering dilatant effects and safety evaluation index[J]. Acta Mechanica Solida Sinica,2020,33(1):121 − 140. doi: 10.1007/s10338-019-00108-4
[10] 赵越,司运航,张译丹,等. 水化-冻融耦合条件下大理岩蠕变损伤本构模型[J]. 吉林大学学报(地球科学版),2024,54(1):231 − 241. [ZHAO Yue,SI Yunhang,ZHANG Yidan,et al. Creep damage constitutive model of marble under hydration freeze-thaw coupling[J]. Journal of Jilin University (Earth Science Edition),2024,54(1):231 − 241. (in Chinese with English abstract)]
ZHAO Yue, SI Yunhang, ZHANG Yidan, et al. Creep damage constitutive model of marble under hydration freeze-thaw coupling[J]. Journal of Jilin University （Earth Science Edition）, 2024, 54（1）: 231 − 241. （in Chinese with English abstract）
[11] HUANG Jingqi,ZHAO Mi,DU Xiuli,et al. An elasto-plastic damage model for rocks based on a new nonlinear strength criterion[J]. Rock Mechanics and Rock Engineering,2018,51(5):1413 − 1429. doi: 10.1007/s00603-018-1417-1
[12] BARYAKH A A,TSAYUKOV A A,EVSEEV A V,et al. Mathematical modeling of deformation and failure of salt rock samples[J]. Journal of Mining Science,2021,57(3):370 − 379. doi: 10.1134/S1062739121030029
[13] 刘海峰,宁建国. 冲击荷载作用下混凝土材料的细观本构模型[J]. 爆炸与冲击,2009,29(3):261 − 267. [LIU Haifeng,NING Jianguo. A meso-mechanical constitutive model of concrete subjected to impact loading[J]. Explosion and Shock Waves,2009,29(3):261 − 267. (in Chinese with English abstract)] doi: 10.3321/j.issn:1001-1455.2009.03.007
LIU Haifeng, NING Jianguo. A meso-mechanical constitutive model of concrete subjected to impact loading[J]. Explosion and Shock Waves, 2009, 29（3）: 261 − 267. （in Chinese with English abstract） doi: 10.3321/j.issn:1001-1455.2009.03.007
[14] 张向东,王浩,敬鹏飞. 基于岩石“等效损伤” 探究宏观断裂规律[J]. 中国地质灾害与防治学报,2020,31(3):117 − 125. [ZHANG Xiangdong,WANG Hao,JING Pengfei. Studying the macroscopic fracture rule based on rock “equivalent damage”[J]. The Chinese Journal of Geological Hazard and Control,2020,31(3):117 − 125. (in Chinese with English abstract)]
ZHANG Xiangdong, WANG Hao, JING Pengfei. Studying the macroscopic fracture rule based on rock “equivalent damage”[J]. The Chinese Journal of Geological Hazard and Control, 2020, 31（3）: 117 − 125. （in Chinese with English abstract）
[15] ZHOU H,JIA Y,SHAO J F. A unified elastic–plastic and viscoplastic damage model for quasi-brittle rocks[J]. International Journal of Rock Mechanics and Mining Sciences,2008,45(8):1237 − 1251. doi: 10.1016/j.ijrmms.2008.01.004
[16] GRADY D E,KIPP M E. Continuum modelling of explosive fracture in oil shale[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1980,17(3):147 − 157.
[17] PEI Xiangjun,CUI Shenghua,ZHU Ling,et al. Quantitative investigation on localized deformation process of rocks by uniaxial test and digital image correlation[J]. Environmental Earth Sciences,2023,82(11):267. doi: 10.1007/s12665-023-10939-7
[18] WANG Susheng,ZHAO Lunyang,ZHANG Wanlu. An enhanced constitutive model for quasi-brittle rocks with localized damage[J]. Acta Geotechnica,2022,17(11):5223 − 5238. doi: 10.1007/s11440-022-01677-4
[19] 赵程,鲍冲,田加深,等. 基于应变局部化的双裂纹岩样贯通模式及强度试验研究[J]. 岩石力学与工程学报,2015,34(11):2309 − 2318. [ZHAO Cheng,BAO Chong,TIAN Jiashen,et al. Experimental study of coalescence mode of cracks and strength of rock with double flaws based on strain localization[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(11):2309 − 2318. (in Chinese with English abstract)]
ZHAO Cheng, BAO Chong, TIAN Jiashen, et al. Experimental study of coalescence mode of cracks and strength of rock with double flaws based on strain localization[J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34（11）: 2309 − 2318. （in Chinese with English abstract）
[20] ROSTÁSY F S,WEIΒ R,WIEDEMANN G. Changes of pore structure of cement mortars due to temperature[J]. Cement and Concrete Research,1980,10(2):157 − 164. doi: 10.1016/0008-8846(80)90072-1
[21] 刘红岩,赵雨霞. 冻融循环下隧道围岩冻胀力理论计算[J]. 中南大学学报(自然科学版),2020,51(4):1049 − 1058. [LIU Hongyan,ZHAO Yuxia. Theoretical calculation of frost heaving pressure in tunnel surrounding rock during freeze-thaw cycles[J]. Journal of Central South University (Science and Technology),2020,51(4):1049 − 1058. (in Chinese with English abstract)]
LIU Hongyan, ZHAO Yuxia. Theoretical calculation of frost heaving pressure in tunnel surrounding rock during freeze-thaw cycles[J]. Journal of Central South University （Science and Technology）, 2020, 51（4）: 1049 − 1058. （in Chinese with English abstract）
[22] 周小平,张永兴,哈秋聆,等. 压应力状态下细观非均匀性岩石的损伤局部化和应力应变关系分析[J]. 应用数学和力学,2004,25(9):951 − 957. [ZHOU Xiaoping,ZHANG Yongxing,HA Qiuling,et al. Analysis of the localization of damage and the complete stress-strain relation for mesoscopic heterogeneous rock under uniaxial tensile loading[J]. Applied Mathematics and Mechanics,2004,25(9):951 − 957. (in Chinese with English abstract)]
ZHOU Xiaoping, ZHANG Yongxing, HA Qiuling, et al. Analysis of the localization of damage and the complete stress-strain relation for mesoscopic heterogeneous rock under uniaxial tensile loading[J]. Applied Mathematics and Mechanics, 2004, 25（9）: 951 − 957. （in Chinese with English abstract）
[23] ZHANG Yanbo,YAO Xulong,LIANG Peng,et al. Fracture evolution and localization effect of damage in rock based on wave velocity imaging technology[J]. Journal of Central South University,2021,28(9):2752 − 2769. doi: 10.1007/s11771-021-4806-7
[24] 许江,王晓震,张倩文,等. 不同含水状态凝灰岩损伤演化试验研究[J]. 采矿与安全工程学报,2021,38(6):1189 − 1197. [XU Jiang,WANG Xiaozhen,ZHANG Qianwen,et al. Experimental study on damage evolution of tuff under different moisture states[J]. Journal of Mining & Safety Engineering,2021,38(6):1189 − 1197. (in Chinese with English abstract)]
XU Jiang, WANG Xiaozhen, ZHANG Qianwen, et al. Experimental study on damage evolution of tuff under different moisture states[J]. Journal of Mining & Safety Engineering, 2021, 38（6）: 1189 − 1197. （in Chinese with English abstract）
[25] BRACE W F,BOMBOLAKIS E G. A note on brittle crack growth in compression[J]. Journal of Geophysical Research,1963,68(12):3709 − 3713. doi: 10.1029/JZ068i012p03709
[26] LIU Taoying,CAO Ping,LIN Hang. Damage and fracture evolution of hydraulic fracturing in compression-shear rock cracks[J]. Theoretical and Applied Fracture Mechanics,2014,74:55 − 63. doi: 10.1016/j.tafmec.2014.06.013
[27] LI Zhihao,XIONG Ziming,CHEN Haoxiang,et al. Analysis of stress-strain relationship of brittle rock containing microcracks under water pressure[J]. Bulletin of Engineering Geology and the Environment,2020,79(4):1909 − 1918. doi: 10.1007/s10064-019-01660-6
[28] NEMAT-NASSER S,OBATA M. A microcrack model of dilatancy in brittle materials[J]. Journal of Applied Mechanics,1988,55(1):24. doi: 10.1115/1.3173647
[29] LIU H Y,SU T M. A dynamic damage constitutive model for a rock mass with non-persistent joints under uniaxial compression[J]. Mechanics Research Communications,2016,77:12 − 20. doi: 10.1016/j.mechrescom.2016.08.006
[30] ASHBY M F,HALLAM (NÉE COOKSLEY) S D. The failure of brittle solids containing small cracks under compressive stress states[J]. Acta Metallurgica,1986,34(3):497 − 510. doi: 10.1016/0001-6160(86)90086-6
[31] HUANG Chengyi,SUBHASH G. Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids[J]. Journal of the Mechanics and Physics of Solids,2003,51(6):1089 − 1105. doi: 10.1016/S0022-5096(03)00002-4
[32] RASHIDI M M,AYATOLLAHI M R,BERTO F. Mixed mode fracture analysis using generalized averaged strain energy density criterion for linear elastic materials[J]. International Journal of Solids and Structures,2017,120:137 − 145. doi: 10.1016/j.ijsolstr.2017.04.035
[33] SIH G C. Strain-energy-density factor applied to mixed mode crack problems[J]. International Journal of Fracture,1974,10(3):305 − 321. doi: 10.1007/BF00035493
[34] 李文洲,司林坡,卢志国,等. 煤单轴压缩起裂强度确定及其关键因素影响分析[J]. 煤炭学报,2021,46(增刊2):670 − 680. [LI Wenzhou,SI Linpo,LU Zhiguo,et al. Determination of coal cracking initiation strength under uniaxial compression and analysis of its key factors[J]. Journal of China Coal Society,2021,46(Sup 2):670 − 680. (in Chinese with English abstract)]
LI Wenzhou, SI Linpo, LU Zhiguo, et al. Determination of coal cracking initiation strength under uniaxial compression and analysis of its key factors[J]. Journal of China Coal Society, 2021, 46（Sup 2）: 670 − 680. （in Chinese with English abstract）
[35] 杨艳,赵莹,刘红岩. 单轴压缩下岩石动态细观损伤本构模型[J]. 矿业研究与开发,2017,37(4):72 − 79. [YANG Yan,ZHAO Ying,LIU Hongyan. A dynamic microscopic damage constitutive model for rocks under uniaxial compression[J]. Mining Research and Development,2017,37(4):72 − 79. (in Chinese with English abstract)]
YANG Yan, ZHAO Ying, LIU Hongyan. A dynamic microscopic damage constitutive model for rocks under uniaxial compression[J]. Mining Research and Development, 2017, 37（4）: 72 − 79. （in Chinese with English abstract）
[36] 袁小平,刘红岩,王志乔. 考虑微裂纹相互作用的岩石细观力学弹塑性损伤模型研究[J]. 固体力学学报,2012,33(6):592 − 602. [YUAN Xiaoping,LIU Hongyan,WANG Zhiqiao. An interacting crack-mechanics based model for elastoplastic damage model of brittle materials under compression[J]. Chinese Journal of Solid Mechanics,2012,33(6):592 − 602. (in Chinese with English abstract)]
YUAN Xiaoping, LIU Hongyan, WANG Zhiqiao. An interacting crack-mechanics based model for elastoplastic damage model of brittle materials under compression[J]. Chinese Journal of Solid Mechanics, 2012, 33（6）: 592 − 602. （in Chinese with English abstract）
-
下载:
图(6)
计量
- 文章访问数: 90
- PDF下载数: 37
- 施引文献: 0