基于细观力学脆性岩石剪切特性演化模型研究
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摘要
压缩作用下岩石内部细观裂纹扩展导致岩石产生损伤,其对岩石变形、强度等力学特性有着重要影响;然而,岩石内部裂纹扩展与剪切特性(黏聚力、内摩擦角及剪切应力)动态演化关系很少被研究。基于裂纹扩展机制推出的岩石应力-应变本构模型,并结合摩尔-库仑失效准则,推出了在岩石应力-应变关系峰值应力(对应岩石压缩强度)状态时,本构模型细观力学参数与岩石黏聚力、内摩擦角及剪切强度之间的状态关系。然后,引入岩石应力-应变本构关系塑性变形阶段服从摩尔-库仑屈服准则的力学流动规律,进而将已推出的应力-应变关系峰值状态点所满足的细观力学参数与黏聚力、内摩擦角关系,推广到岩石进入塑性变形后,岩石内部裂纹扩展(或应变)与黏聚力、内摩擦角及剪切应力动态演化的理论关系。随着裂纹扩展或应变增加,黏聚力、内摩擦角及剪切应力先增大,达到一个峰值点后减小,该结果与应力-应变本构曲线变化趋势相对应。通过试验结果验证了所提出理论结果的合理性。并讨论了初始裂纹之间摩擦系数对黏聚力、内摩擦角及剪切应力随裂纹扩展或应变演化规律的影响。
The damage of brittle rock is induced by its microcrack growth which significantly affects the deformation and strength of rocks subjected to the compressive loadings. However, the relationships between microcrack growth and the variable shear properties(cohesion, internal friction angle, and shear stress) are rarely studied. In this study, the relationships between internal friction angle,cohesion, shear strength and micro-parameters at the peak point of stress-strain relationship are proposed, according to the stress-strain relationship triggered by crack growth and the Mohr-Coulomb failure criterion. By introducing the Mohr-Coulomb yield criterion, the theoretical expression is established for dynamic variations of cohesion, internal friction angle and shear stress along with microcrack growth or strain at plastic deformation phase of brittle rocks. Cohesion, internal friction angle, and shear stress firstly increase until to maximum values, and then decrease with the increasing crack growth or axial strain in brittle rocks under compressive loading, which is corresponding to the stress-strain constitutive curves in triaxial compressive tests. Finally, the rationality of the proposed theoretical expression is verified by comparing with the experimental results. Besides, the effects of friction coefficient between microcrack interfaces on the relationships between cohesion, internal friction angle, shear stress and crack growth or axial strain are discussed.
The damage of brittle rock is induced by its microcrack growth which significantly affects the deformation and strength of rocks subjected to the compressive loadings. However, the relationships between microcrack growth and the variable shear properties(cohesion, internal friction angle, and shear stress) are rarely studied. In this study, the relationships between internal friction angle,cohesion, shear strength and micro-parameters at the peak point of stress-strain relationship are proposed, according to the stress-strain relationship triggered by crack growth and the Mohr-Coulomb failure criterion. By introducing the Mohr-Coulomb yield criterion, the theoretical expression is established for dynamic variations of cohesion, internal friction angle and shear stress along with microcrack growth or strain at plastic deformation phase of brittle rocks. Cohesion, internal friction angle, and shear stress firstly increase until to maximum values, and then decrease with the increasing crack growth or axial strain in brittle rocks under compressive loading, which is corresponding to the stress-strain constitutive curves in triaxial compressive tests. Finally, the rationality of the proposed theoretical expression is verified by comparing with the experimental results. Besides, the effects of friction coefficient between microcrack interfaces on the relationships between cohesion, internal friction angle, shear stress and crack growth or axial strain are discussed.
引文
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[13]李鹏飞,赵星光,郭政,等.北山花岗岩在三轴压缩条件下的强度参数演化[J].岩石力学与工程学报,2017,36(7):1599-1610.LI Peng-fei,ZHAO Xing-guang,GUO Zheng,et al.Variation of strength parameters of Beishan granite under triaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(7):1599-1610.
[14]ASHBY M F,SAMMIS C G.The damage mechanics of brittle solids in compression[J].Pure and Applied Geophysics,1990,133(3):489-521.
[15]ZHAO X G,CAI M.A mobilized dilation angle model for rocks[J].International Journal of Rock Mechanics and Mining Sciences,2010,47(3):368-384.
[16]MARTIN C D,CHANDLER N A.The progressive fracture of Lac du Bonnet granite[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1994,31(6):643-659.
[17]沈珠江.摩尔-库仑材料的屈服理论[J].水利水运工程学报,1981(2):4-12.SHEN Zhu-jiang.A yield theory for Mohr-Coulomb materials[J].Hydro-Science and Engineering,1981(2):4-12.
[18]赵星光,马利科,苏锐,等.北山深部花岗岩在压缩条件下的破裂演化与强度特性[J].岩石力学与工程学报,2014,33(增刊2):3665-3675.ZHAO Xing-guang,MA Li-ke,SU Rui,et al.Fracture evolution and strength characteristics of Beishan deep granite under compression conditions[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Suppl.2):3665-3675.
[19]左建平,周宏伟,范雄,等.三点弯曲下热处理北山花岗岩的断裂特性研究[J].岩石力学与工程学报,2013,32(12):2422-2430.ZUO Jian-ping,ZHOU Hong-wei,FAN Xiong,et al.Research on fracture behavior of Beishan granite after heat treatment under three-point bending[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(12):2422-2430.
[20]胡少华,陈益峰,周创兵.北山花岗岩渗透特性试验研究与细观力学分析[J].岩石力学与工程学报,2014,33(11):2200-2209.HU Shao-hua,CHEN Yi-feng,ZHOU Chuang-bing.Laboratory test and mesomechanical analysis of permeability variation of Beishan granite[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(11):2200-2209.
[21]ASHBY M F,HALLAM S D.The failure of brittle solids containing small cracks under compressive stress states[J].Acta Metallurgica,1986,34(3):497-510.
[22]OHNAKA M,AKATSU M,MOCHIZUKI H,et al.Aconstitutive law for the shear failure of rock under lithospheric conditions[J].Tectonophysics,1997,277(97):1-27.
[23]周辉,程广坦,朱勇,等.基于三维扫描和三维雕刻技术的岩石结构面原状重构方法及其力学特性[J].岩土力学,2018,39(2):417-425.ZHOU Hui,CHENG Guang-tan,ZHU Yong,et al.A new method to originally reproduce rock structural plane by integrating 3D scanning and 3D carving techniques and mechanical characteristics of reproduced structural planes[J].Rock and Soil Mechanics,2018,39(2):417-425.
[2]孙闯,张树光,贾宝新,等.花岗岩峰后力学特性试验与模型研究[J].岩土工程学报,2015,37(5):847-852.SUN Chuang,ZHANG Shu-guang,JIA Bao-xin,et al.Physical and numerical model tests on post-peak mechanical properties of granite[J].Chinese Journal of Geotechnical Engineering,2015,37(5):847-852.
[3]张春会,郑晓明.岩石应变软化及渗透率演化模型和试验验证[J].岩土工程学报,2016,38(6):1125-1132.ZHANG Chun-hui,ZHENG Xiao-ming.Strain softening and permeability evolution model of loaded rock and experimental verification[J].Chinese Journal of Geotechnical Engineering,2016,38(6):1125-1132.
[4]沈珠江.岩土破损力学:理想脆弹塑性模型[J].岩土工程学报,2003,25(3):253-257.SHEN Zhu-jiang.Breakage mechanics for geological materials:an ideal brittle-elasto-plastic model[J].Chinese Journal of Geotechnical Engineering,2003,25(3):253-257.
[5]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 Wen-gui,ZHANG Sheng,ZHAO Ming-hua.Study on statistical damage constitutive model of rock based on new definition of damage[J].Rock and Soil Mechanics,2006,27(1):41-46.
[6]杨强,陈新,周维垣.岩土材料弹塑性损伤模型及变形局部化分析[J].岩石力学与工程学报,2004,23(21):3577-3583.YANG Qiang,CHEN Xin,ZHOU Wei-yuan.Elasto-plastic damage model for geomaterials and strain localizaion analyses[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(21):3577-3583.
[7]朱其志,刘海旭,王伟,等.北山花岗岩细观损伤力学本构模型研究[J].岩石力学与工程学报,2015,34(3):433-439.ZHU Qi-zhi,LIU Hai-xu,WANG Wei,et al.Amicromechanical constitutive damage model for Beishan granite[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(3):433-439.
[8]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 Xiao-ping,LIU Hong-yan,WANG Zhi-qiao.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.
[9]李晓照,邵珠山.脆性岩石渐进及蠕变失效特性宏细观力学模型研究[J].岩土工程学报,2016,38(8):1391-1398.LI Xiao-zhao,SHAO Zhu-shan.Macro-micro mechanical model for progressive and creep failure of brittle rock[J].Chinese Journal of Geotechnical Engineering,2016,38(8):1391-1398.
[10]邵珠山,李晓照.基于细观力学的脆性岩石长期蠕变失效研究[J].岩石力学与工程学报,2016,35(增刊1):2644-2652.SHAO Zhu-shan,LI Xiao-zhao.Research on long-term creep failure of brittle rock based on micromechanics[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(Suppl.1):2644-2652.
[11]徐涛,于世海,王述红,等.岩石细观损伤演化与损伤局部化的数值研究[J].东北大学学报(自然科学版),2005,26(2):160-163.XU Tao,YU Shi-hai,WANG Shu-hong,et al.Numerical investigation on mesoscopic damage evolution and localization behaviors of rock[J].Journal of Northeastern University(Natural Science),2005,26(2):160-163.
[12]于德海,彭建兵,王旭东.岩石材料局部化渐进剪切破坏特性及模型分析[J].北京工业大学学报,2013,39(1):38-43.YU De-hai,PENG Jian-bing,WANG Xu-dong.Model analysis on localized progressive failure of rock material[J].Journal of Beijing University of Technology,2013,39(1):38-43.
[13]李鹏飞,赵星光,郭政,等.北山花岗岩在三轴压缩条件下的强度参数演化[J].岩石力学与工程学报,2017,36(7):1599-1610.LI Peng-fei,ZHAO Xing-guang,GUO Zheng,et al.Variation of strength parameters of Beishan granite under triaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(7):1599-1610.
[14]ASHBY M F,SAMMIS C G.The damage mechanics of brittle solids in compression[J].Pure and Applied Geophysics,1990,133(3):489-521.
[15]ZHAO X G,CAI M.A mobilized dilation angle model for rocks[J].International Journal of Rock Mechanics and Mining Sciences,2010,47(3):368-384.
[16]MARTIN C D,CHANDLER N A.The progressive fracture of Lac du Bonnet granite[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1994,31(6):643-659.
[17]沈珠江.摩尔-库仑材料的屈服理论[J].水利水运工程学报,1981(2):4-12.SHEN Zhu-jiang.A yield theory for Mohr-Coulomb materials[J].Hydro-Science and Engineering,1981(2):4-12.
[18]赵星光,马利科,苏锐,等.北山深部花岗岩在压缩条件下的破裂演化与强度特性[J].岩石力学与工程学报,2014,33(增刊2):3665-3675.ZHAO Xing-guang,MA Li-ke,SU Rui,et al.Fracture evolution and strength characteristics of Beishan deep granite under compression conditions[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Suppl.2):3665-3675.
[19]左建平,周宏伟,范雄,等.三点弯曲下热处理北山花岗岩的断裂特性研究[J].岩石力学与工程学报,2013,32(12):2422-2430.ZUO Jian-ping,ZHOU Hong-wei,FAN Xiong,et al.Research on fracture behavior of Beishan granite after heat treatment under three-point bending[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(12):2422-2430.
[20]胡少华,陈益峰,周创兵.北山花岗岩渗透特性试验研究与细观力学分析[J].岩石力学与工程学报,2014,33(11):2200-2209.HU Shao-hua,CHEN Yi-feng,ZHOU Chuang-bing.Laboratory test and mesomechanical analysis of permeability variation of Beishan granite[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(11):2200-2209.
[21]ASHBY M F,HALLAM S D.The failure of brittle solids containing small cracks under compressive stress states[J].Acta Metallurgica,1986,34(3):497-510.
[22]OHNAKA M,AKATSU M,MOCHIZUKI H,et al.Aconstitutive law for the shear failure of rock under lithospheric conditions[J].Tectonophysics,1997,277(97):1-27.
[23]周辉,程广坦,朱勇,等.基于三维扫描和三维雕刻技术的岩石结构面原状重构方法及其力学特性[J].岩土力学,2018,39(2):417-425.ZHOU Hui,CHENG Guang-tan,ZHU Yong,et al.A new method to originally reproduce rock structural plane by integrating 3D scanning and 3D carving techniques and mechanical characteristics of reproduced structural planes[J].Rock and Soil Mechanics,2018,39(2):417-425.