双轴应力下非贯通节理岩体压缩损伤本构模型
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摘要
针对目前节理岩体损伤变量定义中大多仅考虑节理长度、倾角等几何性质,而未考虑节理抗剪强度等力学性质的不足,基于断裂力学中的由于单个节理存在引起的附加应变能增量与损伤力学中的损伤应变能释放量相关联的观点,推导出了在双轴应力下含单条非贯通闭合节理岩体的损伤变量计算公式,并根据断裂力学理论对双轴压缩荷载下的单个节理尖端应力强度因子计算方法进行了研究,得出了应力强度因子KⅠ、KⅡ的计算公式;同时考虑多节理间的相互作用,给出了单组单排及单组多排非贯通节理尖端应力强度因子计算公式,由此建立了相应的节理岩体双轴压缩损伤本构模型,并利用该模型进行了相应的算例分析。结果表明:对含单条非贯通闭合节理的岩体而言,当节理倾角小于其内摩擦角时,岩体强度与完整岩石相同,岩体损伤为0,而后随着节理倾角增加,岩体强度、损伤随节理倾角的变化分别呈开口向上及向下的抛物线,当节理倾角约为60°时,岩体损伤最大,强度最低。随着节理长度增加,岩体损伤增加,而随着节理内摩擦角的增加,岩体损伤则减小;对含单组单排非贯通闭合节理的岩体而言,当节理总长度一定时,随着单条节理长度的减小及节理条数的增加,岩体损伤则逐渐减小,但其减小幅度与节理条数并不呈线性关系。
Currently, most definitions of the damage variable for jointed rock mass only use geometrical factors of joints such as the length and dip angle, but cannot consider joint shear strength. Due to this limitation, a new damage variable formulae is firstly deduced to calculate rock mass with a non-persistent closed joint, based on the connection between the increment of additional strain energy caused by the existence of one joint in fracture mechanics and the emission of damaged strain energy in damage mechanics. Secondly, the calculation method of the stress intensity factor(SIF) of a single joint tip under biaxial compression is studied according to fracture mechanics theory, and then the calculation SIF formulae of KⅠ and KⅡ are obtained. Thirdly, the calculation formulae of the tip SIF of a set of one or more-rowed joints are given by considering the interaction among the joints. Finally, a biaxial compression damage constitutive model for the jointed rock mass is developed, which is further employed to analyze an example. It is found that for rock mass with a single non-persistent closed joint, the strength of rock mass is the same as that of the intact rock, and the damage is 0 when the joint dip angle is less than its internal friction angle. Furthermore, with the increase in joint dip angle, the change laws of rock mass strength and the damage with the joint dip angle are parabola with the hatch up and down, respectively. The strength of rock mass is the lowest and its damage is the highest when the joint dip angle is about 60°. With the increase of joint length, the damage of rock mass increases; while with the increase of the internal friction angle of joint, the damage of rock mass decreases. For the rock mass with a set of one-rowed non-persistent closed joint, when the total length of the joint is the same, the damage of rock mass gradually decreases with the decrease of a single joint length and the increase of the joint number, however the relationship between the decrease amplitude and the joint number exhibits nonlinear response.
Currently, most definitions of the damage variable for jointed rock mass only use geometrical factors of joints such as the length and dip angle, but cannot consider joint shear strength. Due to this limitation, a new damage variable formulae is firstly deduced to calculate rock mass with a non-persistent closed joint, based on the connection between the increment of additional strain energy caused by the existence of one joint in fracture mechanics and the emission of damaged strain energy in damage mechanics. Secondly, the calculation method of the stress intensity factor(SIF) of a single joint tip under biaxial compression is studied according to fracture mechanics theory, and then the calculation SIF formulae of KⅠ and KⅡ are obtained. Thirdly, the calculation formulae of the tip SIF of a set of one or more-rowed joints are given by considering the interaction among the joints. Finally, a biaxial compression damage constitutive model for the jointed rock mass is developed, which is further employed to analyze an example. It is found that for rock mass with a single non-persistent closed joint, the strength of rock mass is the same as that of the intact rock, and the damage is 0 when the joint dip angle is less than its internal friction angle. Furthermore, with the increase in joint dip angle, the change laws of rock mass strength and the damage with the joint dip angle are parabola with the hatch up and down, respectively. The strength of rock mass is the lowest and its damage is the highest when the joint dip angle is about 60°. With the increase of joint length, the damage of rock mass increases; while with the increase of the internal friction angle of joint, the damage of rock mass decreases. For the rock mass with a set of one-rowed non-persistent closed joint, when the total length of the joint is the same, the damage of rock mass gradually decreases with the decrease of a single joint length and the increase of the joint number, however the relationship between the decrease amplitude and the joint number exhibits nonlinear response.
引文
[1]AKIN,MUTLUHAN.Slope stability problems and back analysis in heavily jointed rock mass:A case study from Manisa,Turkey[J].Rock Mechanics and Rock Engineering,2013,46(2):359-371.
[2]WANG TAI-TIEN,HUANG TSAN-HWEI.Anisotropic deformation of a circular tunnel excavated in a rock mass containing sets of ubiquitous joints:Theory analysis and numerical modeling[J].Rock Mechanics and Rock Engineering,2014,47(2):643-657.
[3]袁小清,刘红岩,刘京平.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 Xiao-qing,LIU Hong-yan,LIU Jing-ping.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.
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[7]SWOBODA G,SHEN XP,ROSAS L.Damage model for jointed rock mass and its application to tunneling[J].Computers and Geotechnics,1998,22(3/4):183-203.
[8]郑少河,朱维申.裂隙岩体渗流损伤耦合模型的理论分析[J].岩石力学与工程学报,2001,20(2):156-159.ZHENG Shao-he,ZHU Wei-shen.Theoretical analysis of a coupled seepage-damage model of fractured rock mass[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(2):156-159.
[9]SWOBODA G,YANG Q.An energy-based damage model of geomaterials-Ⅰ,Formulation and numerical results[J].International Journal of Solids and Structures,1999,(36):1719-1734.
[10]LI N,CHEN W,ZHANG P,et al.The mechanical properties and a fatigue-damage model for jointed rock masses subjected to dynamic cyclical loading[J].International Journal of Rock Mechanics&Mining Sciences,2001,38(7):1071-1079.
[11]李世愚,和泰名,尹祥础.岩石断裂力学导论[M].合肥:中国科学技术大学出版社,2010.LI Si-yu,HE Tai-ming,YIN Xiang-chu.Introduction of rock fracture mechanics[M].Hefei:Press of University of Science of Technology of China,2010
[12]楼志文.损伤力学基础[M].西安:西安交通大学出版社,1991.LOU Zhi-wen.Fundamentals of damage mechanics[M].Xi’an:Press of Xi’an Jiaotong University,1991
[13]HUANG C,SUBHASH G,VITTON SJ.A dynamic damage growth model for uniaxial compressive response of rock aggregates[J].Mechanics of Materials,2002,34(5):267-277.
[14]HUANG C,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.
[15]PALIWAL B,RAMESH KT.An interacting micro-crack damage model for failure of brittle materials under compression[J].Journal of the Mechanics and Physics of Solids,2008,56(3):896-923.
[16]LEE S,RAVICHANDRAN G.Crack initiation in brittle solids under multiaxial compression[J].Engineering Fracture Mechanics,2003,70(13):1645-1658.
[17]李建林,哈秋瓴.节理岩体拉剪断裂与强度研究[J].岩石力学与工程学报,1998,17(3):259-266.LI Jian-lin,HA Qiu-ling.A study of tensile-shear crack and strength related to jointed rock mass[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(3):259-266.
[18]范景伟,何江达.含定向闭合断续节理岩体的强度特性[J].岩石力学与工程学报,1992,11(2):190-199.FAN Jing-wei,HE Jiang-da.The strength behavior of rockmasses containing oriented and closed intermittent joints[J].Chinese Journal of Rock Mechanics and Engineering,1992,11(2):190-199.
[19]PRUDENCIO M,VAN SINT JAN M.Strength and failure modes of rock mass models with non-persistent joints[J].International Journal of Rock Mechanics and Mining Sciences,2007,44(6):890-902.
[2]WANG TAI-TIEN,HUANG TSAN-HWEI.Anisotropic deformation of a circular tunnel excavated in a rock mass containing sets of ubiquitous joints:Theory analysis and numerical modeling[J].Rock Mechanics and Rock Engineering,2014,47(2):643-657.
[3]袁小清,刘红岩,刘京平.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 Xiao-qing,LIU Hong-yan,LIU Jing-ping.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]GOODMAN R E,TAYLOR R E,BREKKE T.A model for the mechanics of jointed rock[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1968,94(3):637-659.
[5]DESAI C S,ZAMAN M M,LIGHTNER J G,et al.Thin-layer element for interfaces and joints[J].International Journal for Numerical Methods in Geomechanics,1984,8(1):19-43.
[6]KAWAMOTO T,ICHIKAWA Y,KYOYA T.Deformation and fracturing behavior of discontinuous rock mass and damage mechanics theory[J].International Journal of Numerical Analysis Method in Geomechanics,1988,(12):1-30.
[7]SWOBODA G,SHEN XP,ROSAS L.Damage model for jointed rock mass and its application to tunneling[J].Computers and Geotechnics,1998,22(3/4):183-203.
[8]郑少河,朱维申.裂隙岩体渗流损伤耦合模型的理论分析[J].岩石力学与工程学报,2001,20(2):156-159.ZHENG Shao-he,ZHU Wei-shen.Theoretical analysis of a coupled seepage-damage model of fractured rock mass[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(2):156-159.
[9]SWOBODA G,YANG Q.An energy-based damage model of geomaterials-Ⅰ,Formulation and numerical results[J].International Journal of Solids and Structures,1999,(36):1719-1734.
[10]LI N,CHEN W,ZHANG P,et al.The mechanical properties and a fatigue-damage model for jointed rock masses subjected to dynamic cyclical loading[J].International Journal of Rock Mechanics&Mining Sciences,2001,38(7):1071-1079.
[11]李世愚,和泰名,尹祥础.岩石断裂力学导论[M].合肥:中国科学技术大学出版社,2010.LI Si-yu,HE Tai-ming,YIN Xiang-chu.Introduction of rock fracture mechanics[M].Hefei:Press of University of Science of Technology of China,2010
[12]楼志文.损伤力学基础[M].西安:西安交通大学出版社,1991.LOU Zhi-wen.Fundamentals of damage mechanics[M].Xi’an:Press of Xi’an Jiaotong University,1991
[13]HUANG C,SUBHASH G,VITTON SJ.A dynamic damage growth model for uniaxial compressive response of rock aggregates[J].Mechanics of Materials,2002,34(5):267-277.
[14]HUANG C,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.
[15]PALIWAL B,RAMESH KT.An interacting micro-crack damage model for failure of brittle materials under compression[J].Journal of the Mechanics and Physics of Solids,2008,56(3):896-923.
[16]LEE S,RAVICHANDRAN G.Crack initiation in brittle solids under multiaxial compression[J].Engineering Fracture Mechanics,2003,70(13):1645-1658.
[17]李建林,哈秋瓴.节理岩体拉剪断裂与强度研究[J].岩石力学与工程学报,1998,17(3):259-266.LI Jian-lin,HA Qiu-ling.A study of tensile-shear crack and strength related to jointed rock mass[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(3):259-266.
[18]范景伟,何江达.含定向闭合断续节理岩体的强度特性[J].岩石力学与工程学报,1992,11(2):190-199.FAN Jing-wei,HE Jiang-da.The strength behavior of rockmasses containing oriented and closed intermittent joints[J].Chinese Journal of Rock Mechanics and Engineering,1992,11(2):190-199.
[19]PRUDENCIO M,VAN SINT JAN M.Strength and failure modes of rock mass models with non-persistent joints[J].International Journal of Rock Mechanics and Mining Sciences,2007,44(6):890-902.