单轴压缩荷载下非贯通闭合节理岩体损伤本构模型
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摘要
目前损伤力学已被认为是研究节理岩体力学行为的有效工具,但是在目前的节理岩体损伤变量定义中大多仅考虑节理几何特征而未考虑节理内摩擦角等力学参数,这显然不能很好地反映节理岩体的力学特征。为此,拟推导出一个能够综合考虑节理几何及力学参数的损伤变量(张量),并由此建立单轴压缩荷载下岩体损伤本构模型。首先,基于断裂力学的由于单个节理存在引起的附加应变能增量与损伤力学的损伤应变能释放量相关联的观点,推导出了含非贯通节理岩体的损伤变量计算公式;其次,根据断裂力学理论对单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多排非贯通节理应力强度因子计算公式。最后,利用该模型对含单条非贯通节理的岩体在单轴压缩荷载作用下的峰值强度及损伤变量进行了分析计算。结果表明,当节理倾角小于其内摩擦角时,岩体强度与完整岩石相同,岩体损伤为零,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。
Now damage mechanics is regarded to be an effective tool to study the mechanical behavior of jointed rock mass. However, the joint geometrical characteristic is only considered in the definition of most current jointed rock mass damage variables without considering the joint mechanical parameters such as joint internal friction angle, which obviously cannot reflect the mechanical property of jointed rock mass. So, a damage variable(tensor) comprehensively considering the joint geometrical and mechanical parameters is deduced, from which a damage constitutive model for rock mass under uniaxial compression load is set up. Therefore, the damage variable calculation formula of the rock mass with a non-persistent joint is firstly deduced based on the connection of 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 of a single joint under uniaxial compression is studied according to fracture mechanics theory, and the calculation formulas of the stress intensity factor KⅠ and KⅡ are obtained. Finally, this model is adopted to calculate the climax strength and damage variable of rock mass with a single non-persistent joint under uniaxial compression load. The results show that the rock mass strength is the same as that of the intact rock and the damage is zero when the joint dip is less than its internal friction angle. Then with increase in joint dip, the change laws of rock mass strength and damage with the joint dip are parabola with the hatch up and down respectively. And the rock mass strength is least and its damage is largest when the joint dip is about 60°. With increase in joint length, the rock mass damage increases, while with increase in joint internal friction angle, the rock mass damage decreases.
Now damage mechanics is regarded to be an effective tool to study the mechanical behavior of jointed rock mass. However, the joint geometrical characteristic is only considered in the definition of most current jointed rock mass damage variables without considering the joint mechanical parameters such as joint internal friction angle, which obviously cannot reflect the mechanical property of jointed rock mass. So, a damage variable(tensor) comprehensively considering the joint geometrical and mechanical parameters is deduced, from which a damage constitutive model for rock mass under uniaxial compression load is set up. Therefore, the damage variable calculation formula of the rock mass with a non-persistent joint is firstly deduced based on the connection of 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 of a single joint under uniaxial compression is studied according to fracture mechanics theory, and the calculation formulas of the stress intensity factor KⅠ and KⅡ are obtained. Finally, this model is adopted to calculate the climax strength and damage variable of rock mass with a single non-persistent joint under uniaxial compression load. The results show that the rock mass strength is the same as that of the intact rock and the damage is zero when the joint dip is less than its internal friction angle. Then with increase in joint dip, the change laws of rock mass strength and damage with the joint dip are parabola with the hatch up and down respectively. And the rock mass strength is least and its damage is largest when the joint dip is about 60°. With increase in joint length, the rock mass damage increases, while with increase in joint internal friction angle, the rock mass damage decreases.
引文
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[10]楼志文.损伤力学基础[M].西安:西安交通大学出版社,1991.
[11]HUANG C,SUBHASH G,VITTON S J.A dynamic damage growth model for uniaxial compressive response of rock aggregates[J].Mechanics of Materials,2002,34(5):267–277.
[12]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.
[13]刘鸿文.材料力学Ⅰ:第四版[M].北京:高等教育出版社,2004.
[14]LEE S,RAVICHANDRAN G.Crack initiation in brittle solids under multiaxial compression[J].Engineering Fracture Mechanics,2003,70(13):1645–1658.
[15]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 Jianlin,HA Qiulin.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.
[16]PRUDENCIO M,van SINT J 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]张吉宏,刘红岩.综合考虑宏微观复合损伤的节理岩体本构模型[J].煤田地质与勘探,2013,41(6):49–52.ZHANG Jihong,LIU Hongyan.Constitutive model of jointed rock mass by combining macroscopic and microcopic composite damage[J].Coal Geology&Exploration,2013,41(6):49–52.
[3]GOODMAN R E,TAYLOR R E,BREKKE T.A model for the mechanics of jointed rock[J].ASCE Journal of the Soil Mechanics and Foundations Division,1968,94(3):637–659.
[4]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.
[5]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):1–30.
[6]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 Shaohe,ZHU Weishen.Theory analysizing of the jointed rock fluid and damage coupling model[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(2):156–159.
[7]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(9):1719–1734.
[8]陈文玲,李宁.含非贯通裂隙岩体介质的损伤模型[J].岩土工程学报,2000,22(4):430–434.CHEN Wenling,LI Ning.Damage model of the rock mass medium with intermittent cracks[J].Chinese Journal of Geotechnical Engineering,2000,22(4):430–434.
[9]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,2010:89–98.
[10]楼志文.损伤力学基础[M].西安:西安交通大学出版社,1991.
[11]HUANG C,SUBHASH G,VITTON S J.A dynamic damage growth model for uniaxial compressive response of rock aggregates[J].Mechanics of Materials,2002,34(5):267–277.
[12]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.
[13]刘鸿文.材料力学Ⅰ:第四版[M].北京:高等教育出版社,2004.
[14]LEE S,RAVICHANDRAN G.Crack initiation in brittle solids under multiaxial compression[J].Engineering Fracture Mechanics,2003,70(13):1645–1658.
[15]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 Jianlin,HA Qiulin.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.
[16]PRUDENCIO M,van SINT J 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.