基于受压裂隙开裂准则的损伤模型
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摘要
为了反映岩石内部裂隙对岩石本构关系的影响,建立受裂隙分布及裂隙面摩擦因数共同影响的损伤模型。类比弹簧束模型,定义与开裂裂隙长度有关的损伤模型。基于受压裂隙的开裂准则,对不同应力状态下的开裂裂隙长度范围进行求解,通过概率统计的方法计算开裂裂隙长度的数学期望,将其代入建立的损伤模型中得到损伤变量。利用模型对岩石应力-应变曲线进行计算。研究结果表明:建立的损伤模型能够反映裂隙面摩擦因数与裂隙角度对岩石强度的影响。当摩擦因数为0时,裂隙角度45o对应的岩石强度最小,随着裂隙摩擦因数增大,最小峰值强度对应的裂隙倾角逐渐减小;当裂隙角度一定时,摩擦因数越大,峰值强度越大;数值计算结果与实验结果一致。该模型还能够反映裂隙长度分布对岩石强度的影响。当长裂隙数占比较大时,岩石强度较小;反之,岩石强度较大。计算结果能够反映岩石在塑性阶段的变形特征,该损伤模型具有合理性。
In order to reflect the influence of rock internal fracture on rock constitutive relation, a damage model affected by fracture distribution and friction coefficient of fracture surface was established. Analogous to the spring beam model, a damage model related to the length of cracked fissure was defined. Based on the cracking criterion of the compression fracture, the length range of crack fracture in different stress states was solved, the mathematical expectation of crack length was calculated by probability statistics, and the damage variable was obtained in the damage model. The stress-strain curve of rock was calculated by this model. The results show that the model can reflect the influence of fracture surface friction coefficient and angle on rock strength. When the friction coefficient is 0, the corresponding angle of minimum strength of rock is 45o. With the increase of the friction coefficient, the crack angle corresponding to the minimum peak strength decreases gradually. When the angle is constant, the greater the friction coefficient is, the larger the peak strength is. The calculated results are in agreement with the experimental results. The model can also reflect the effect of crack length distribution on rock strength. When the long crack occupies a larger proportion of the crack, the strength of rock is smaller. When the long crack occupies a smaller proportion, the strength of rock is larger. The calculated results reflect he deformation characteristics of rock at plastic stage, which shows the reliability of the model.
In order to reflect the influence of rock internal fracture on rock constitutive relation, a damage model affected by fracture distribution and friction coefficient of fracture surface was established. Analogous to the spring beam model, a damage model related to the length of cracked fissure was defined. Based on the cracking criterion of the compression fracture, the length range of crack fracture in different stress states was solved, the mathematical expectation of crack length was calculated by probability statistics, and the damage variable was obtained in the damage model. The stress-strain curve of rock was calculated by this model. The results show that the model can reflect the influence of fracture surface friction coefficient and angle on rock strength. When the friction coefficient is 0, the corresponding angle of minimum strength of rock is 45o. With the increase of the friction coefficient, the crack angle corresponding to the minimum peak strength decreases gradually. When the angle is constant, the greater the friction coefficient is, the larger the peak strength is. The calculated results are in agreement with the experimental results. The model can also reflect the effect of crack length distribution on rock strength. When the long crack occupies a larger proportion of the crack, the strength of rock is smaller. When the long crack occupies a smaller proportion, the strength of rock is larger. The calculated results reflect he deformation characteristics of rock at plastic stage, which shows the reliability of the model.
引文
[1]LEMAITRE J.A continuous damage mechanics model for ductile fracture[J].Transactions of the Asme Journal of Engineering Materials&Technology,1985,107(107):83-89.
[2]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):1489-1496.ZHAO Yiqing,LIU Hongyan,LüShuran,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):1489-1496.
[3]袁小清,刘红岩,刘京平,等.基于宏细观损伤耦合的非贯通裂隙岩体本构模型[J].岩土力学,2015,36(10):2804-2814.YUAN Xiaoqing,LIU Hongyan,LIU Jingping,et al.Constitutive model of rock mass with non-persistent joints based on coupling macroscopic and mesoscopic damages[J].Rock and Soil Mechanics,2015,36(10):2804-2814.
[4]刘红岩,王新生,张力民,等.非贯通节理岩体单轴压缩动态损伤本构模型[J].岩土工程学报,2016,38(3):426-436.LIU Hongyan,WANG Xinsheng,ZHANG Limin,et al.Adynamic damage constitutive model for rock mass with non-persistent joints under uniaxial compression[J].Chinese Journal of Geotechnical Engineering,2016,38(3):426-436.
[5]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 softening and damage rocks[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(6):628-633.
[6]曹文贵,张升.基于Mohr-Coulomb准则的岩石损伤统计分析方法研究[J].湖南大学学报(自然科学版),2005,32(1):43-47.CAO Wengui,ZHANG Sheng.Study on the statistical analysis of rock damage based on Mohr-Coulomb criterion[J].Journal of Hunan University(Natural Sciences),2005,32(1):43-47.
[7]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.
[8]ZHU Q Z,SHAO J F.A refined micromechanical damagefriction model with strength prediction for rock-like materials under compression[J].International Journal of Solids&Structures,2015,60/61:75-83.
[9]JIN W,ARSON C.Discrete equivalent wing crack based damage model for brittle solids[J].International Journal of Solids&Structures,2017,s110/111:279-293.
[10]KRAJCINOVIC D,FANELLA D.A micromechanical damage model for concrete[J].Engineering Fracture Mechanics,1986,25(5):585-596.
[11]白卫峰.混凝土损伤机理及饱和混凝土力学性能研究[D].大连:大连理工大学土木工程学院,2008:23-80.BAI Weifeng.Study on damage mechanism of concrete and mechanical properties of saturated concrete[D].Dalian:Dalian University of Technology.School of Civil Engineering,2008:23-80.
[12]李杰,卢朝辉,张其云.混凝土随机损伤本构关系-单轴受压分析[J].同济大学学报,2003,31(5):505-509.LI Jie,LU Zhaohui,ZHANG Qiyun.Random damage constitutive relation of concrete-Uniaxial compression analysis[J].Journal of Tongji University,2003,31(5):505-509.
[13]LI J,REN X D.Stochastic damage model of concrete based on energy equivalent strain[J].International Journal of Solids and Structures,2009,46(11):2407-2419.
[14]LI J,REN X D.Hysteretic deteriorating model for quasi-brittle materials based on micromechanical damage approach[J].International Journal of Non-linear Mechanics,2010,46(1):321-329.
[15]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(s1):3233-3238.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(s1):3233-3238.
[16]李世愚,和泰名,尹祥础.岩石断裂力学[M].北京:科学出版社,2006:15-215.LI Shiyu,HE Taiming,YIN Xiangchu.Rock fracture mechanics[M].Beijing:Science Press,2006:15-215.
[17]张志强.非贯通裂隙岩体破坏细观特征及其宏观力学参数确定方法[D].西安:西安理工大学土木建筑工程学院,2009:52-65.ZHANG Zhiqiang.Mesomechanical failure characteristics and macromechanical parameter estimation of fractured rock mass with nonpenetrative fissures[D].Xi’an:Xi’an University of Technology.School of Civil Engineering and Architechture,2009:52-65.
[18]刘树新,刘长武,韩小刚,等.基于损伤多重分形特征的岩石强度Weibull参数研究[J].岩土工程学报,2011,33(11):1786-1791.LIU Shuxin,LIU Changwu,HAN Xiaogang,et al.Weibull distribution parameters of rock strength based on multi-fractal characteristics of rock damage[J].Chinese Journal of Geotechnical Engineering,2011,33(11):1786-1791.
[19]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 Shuguang,JIA Baoxin,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.
[2]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):1489-1496.ZHAO Yiqing,LIU Hongyan,LüShuran,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):1489-1496.
[3]袁小清,刘红岩,刘京平,等.基于宏细观损伤耦合的非贯通裂隙岩体本构模型[J].岩土力学,2015,36(10):2804-2814.YUAN Xiaoqing,LIU Hongyan,LIU Jingping,et al.Constitutive model of rock mass with non-persistent joints based on coupling macroscopic and mesoscopic damages[J].Rock and Soil Mechanics,2015,36(10):2804-2814.
[4]刘红岩,王新生,张力民,等.非贯通节理岩体单轴压缩动态损伤本构模型[J].岩土工程学报,2016,38(3):426-436.LIU Hongyan,WANG Xinsheng,ZHANG Limin,et al.Adynamic damage constitutive model for rock mass with non-persistent joints under uniaxial compression[J].Chinese Journal of Geotechnical Engineering,2016,38(3):426-436.
[5]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 softening and damage rocks[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(6):628-633.
[6]曹文贵,张升.基于Mohr-Coulomb准则的岩石损伤统计分析方法研究[J].湖南大学学报(自然科学版),2005,32(1):43-47.CAO Wengui,ZHANG Sheng.Study on the statistical analysis of rock damage based on Mohr-Coulomb criterion[J].Journal of Hunan University(Natural Sciences),2005,32(1):43-47.
[7]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.
[8]ZHU Q Z,SHAO J F.A refined micromechanical damagefriction model with strength prediction for rock-like materials under compression[J].International Journal of Solids&Structures,2015,60/61:75-83.
[9]JIN W,ARSON C.Discrete equivalent wing crack based damage model for brittle solids[J].International Journal of Solids&Structures,2017,s110/111:279-293.
[10]KRAJCINOVIC D,FANELLA D.A micromechanical damage model for concrete[J].Engineering Fracture Mechanics,1986,25(5):585-596.
[11]白卫峰.混凝土损伤机理及饱和混凝土力学性能研究[D].大连:大连理工大学土木工程学院,2008:23-80.BAI Weifeng.Study on damage mechanism of concrete and mechanical properties of saturated concrete[D].Dalian:Dalian University of Technology.School of Civil Engineering,2008:23-80.
[12]李杰,卢朝辉,张其云.混凝土随机损伤本构关系-单轴受压分析[J].同济大学学报,2003,31(5):505-509.LI Jie,LU Zhaohui,ZHANG Qiyun.Random damage constitutive relation of concrete-Uniaxial compression analysis[J].Journal of Tongji University,2003,31(5):505-509.
[13]LI J,REN X D.Stochastic damage model of concrete based on energy equivalent strain[J].International Journal of Solids and Structures,2009,46(11):2407-2419.
[14]LI J,REN X D.Hysteretic deteriorating model for quasi-brittle materials based on micromechanical damage approach[J].International Journal of Non-linear Mechanics,2010,46(1):321-329.
[15]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(s1):3233-3238.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(s1):3233-3238.
[16]李世愚,和泰名,尹祥础.岩石断裂力学[M].北京:科学出版社,2006:15-215.LI Shiyu,HE Taiming,YIN Xiangchu.Rock fracture mechanics[M].Beijing:Science Press,2006:15-215.
[17]张志强.非贯通裂隙岩体破坏细观特征及其宏观力学参数确定方法[D].西安:西安理工大学土木建筑工程学院,2009:52-65.ZHANG Zhiqiang.Mesomechanical failure characteristics and macromechanical parameter estimation of fractured rock mass with nonpenetrative fissures[D].Xi’an:Xi’an University of Technology.School of Civil Engineering and Architechture,2009:52-65.
[18]刘树新,刘长武,韩小刚,等.基于损伤多重分形特征的岩石强度Weibull参数研究[J].岩土工程学报,2011,33(11):1786-1791.LIU Shuxin,LIU Changwu,HAN Xiaogang,et al.Weibull distribution parameters of rock strength based on multi-fractal characteristics of rock damage[J].Chinese Journal of Geotechnical Engineering,2011,33(11):1786-1791.
[19]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 Shuguang,JIA Baoxin,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.
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