动静组合加载下岩石破坏的应变能密度准则及突变理论分析
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摘要
阐述了岩石在动静组合载荷作用下使用应变能密度定义破坏准则的适用性。分析认为,岩石破坏的应变能密度的临界值与岩石破坏之前的不可逆变形过程和外界条件有关,而不可逆变形过程主要是由于岩石的非弹性变形、损伤和其他内部耗散机制引起的,且反映静水压力的体积变形能在某些应力状态条件下的岩石破坏中是不能忽略的。提出用机械模型来反映动静组合加载下岩石单元体弹性的劣化和非弹性变形的产生以及加载速率的影响,并以机械模型为基础,求出受一维静载岩石在动载作用下破坏应变能密度的临界值。同时,根据静力预加载结构的冲击屈曲突变模型,建立了静加载岩石系统的冲击破坏模型,进一步分析了动静组合加载下岩石的破坏。最后,采用低周疲劳加载方法在Instron电液饲服控制材料试验机上进行了红砂岩中应变率下的动静组合加载破坏试验,对应变能密度准则和突变理论模型进行了验证。结果表明,理论模型与试验结果有较好的一致性。
The applicability of a failure criterion for the strain energy density of rock under static-dynamic loading is proposed. According to the analysis,critical value of strain energy density of rock is mainly determined by preceding irreversible deformation process and current environmental state;and the irreversible deformation is mainly caused by nonelastic deformation,damage and other possible intrinsic dissipative mechanisms of rock in a mechanical system;and volume deformation energy associated with hydrostatic stress effects can not be neglected on some stress states. Using mechanical model to represent the reduction of elasticity,occurrence of inelasticity deformation and effect of loading rate are proposed. On the basis of mechanical model,the critical value of strain energy density of rock under static-dynamic loading is derived. According to the catastrophe model for impact buckling of static-loading structures,a new catastrophe model for impact disturbance fragmentation of a rock system under static loading is established to analyze the rock failure under static-dynamic coupling loading ulteriorly. Finally,by using of the Instron electro-hydraulic and servo-controlled material testing machine and adopting low-cycle-index fatigue loading method,the test of red sandstone failure with medium strain rate under dynamic loading is carried out to verify the strain energy density criterion and catastrophe theory model. There is a good agreement between theoretic and experimental results.
The applicability of a failure criterion for the strain energy density of rock under static-dynamic loading is proposed. According to the analysis,critical value of strain energy density of rock is mainly determined by preceding irreversible deformation process and current environmental state;and the irreversible deformation is mainly caused by nonelastic deformation,damage and other possible intrinsic dissipative mechanisms of rock in a mechanical system;and volume deformation energy associated with hydrostatic stress effects can not be neglected on some stress states. Using mechanical model to represent the reduction of elasticity,occurrence of inelasticity deformation and effect of loading rate are proposed. On the basis of mechanical model,the critical value of strain energy density of rock under static-dynamic loading is derived. According to the catastrophe model for impact buckling of static-loading structures,a new catastrophe model for impact disturbance fragmentation of a rock system under static loading is established to analyze the rock failure under static-dynamic coupling loading ulteriorly. Finally,by using of the Instron electro-hydraulic and servo-controlled material testing machine and adopting low-cycle-index fatigue loading method,the test of red sandstone failure with medium strain rate under dynamic loading is carried out to verify the strain energy density criterion and catastrophe theory model. There is a good agreement between theoretic and experimental results.
引文
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[19] Sai S,Sia N N. Dynamic compressive strength of silicon carbide under uniaxial compression[J]. Materials Science and Engineering,2001,(A317):140–144.
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[21] Sang H C,Yuji O,Katsuhiko K. Strain-rate dependency of the dynamic tensile strength of rock[J]. International Journal of Rock Mechanics and Mining Sciences,2003,(40):763–777.
[22]左宇军,李夕兵,赵国彦.受静载荷作用的岩石动态断裂的突变模型[J].煤炭学报,2004,29(6):654–658.(Zuo Yujun,Li Xibing ,Zhao Guoyan. A catastrophe model for dynamic fracture of static loaded rock[J]. Journal of China Coal Society,2004,29(6):654–658.(in Chinese))
[23]左宇军,李夕兵,马春德,等.动静组合载荷作用下岩石失稳破坏的突变理论模型与试验研究[J].岩石力学与工程学报,2005,24(5):741–746.(Zuo Yujun,Li Xibing,Ma Chunde,et al. Catastrophic model and testing study on failure of static loading rock system under dynamic loading[J]. Chinese Journal of Rock Mechanics and Engineering,2005,24(5):741–746.(in Chinese))
[24]左宇军.动静组合加载下的岩石破坏特性研究[博士学位论文][D].长沙:中南大学,2005.(Zuo Yujun. Study on failure and fragmentation characteristics of rock under static-dynamic coupling loading[Ph. D. Thesis][D]. Changsha:Central South University,2005.(in Chinese)
[25]刘鸿文.材料力学(上册)[M].北京:高等教育出版社,1999.(Liu Hongwen. Mechanics of Materials(I)[M]. Beijing:High Education Press,1999.(in Chinese))
[26]余熙莹.对于第四强度理论的修正[J].广西大学学报(自然科学版),2002,27(增):63–69.(Yu Xiying. The revision of the fourth strength theorem[J]. Journal of Guangxi University(Natural Science),2002,27(Supp.):63–69.(in Chinese))
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[30] Holasut S,Ruiz C. Effect of an impulsive disturbing load on the stability of a statically loaded structure[J]. Int. J. Impact Eng.,1985,3(1):57–73.
[31] Anthony N K. Dynamic buckling of simple two-bar frames using catastrophe theory[J]. International Journal of Nonlinear Mechanics.2002,37:1249–1259.
[32]王德禹,杨桂通.简单弹性结构动力屈曲的突变模型[A].见:现代数学与力学(MMM–4)[C].兰州:兰州大学出版社,1991.275–277.(Wang Deyu,Yang Guitong. A catastrophe model for the dynamic buckling of simple elastic structures[A]. In : Modern Mathematics and Mechanics(MMM –4)[C]. Lanzhou : Lanzhou University Press,1991.275–277.(in Chinese))
[33]王德禹,张善元,杨桂通.静力预加载结构冲击屈曲的突变模型[J].爆炸与冲击,1993,13(3):243–248.(Wang Deyu,Zhang Shanyuan,Yang Guitong. A catastrophe model for the impact buckling of static preloading structures[J]. Explosion and Shock Waves,1993,13(3):243–248.(in Chinese))
[34]金丰年,蒋美蓉,高小玲.基于能量耗散定义损伤变量的方法[J].岩石力学与工程学报,2004,23(12):1976–1980.(Jin Fengnian ,Jiang Meirong,Gao Xiaoling. Defining damage variable based on energy dissipation[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(12):1976–1980.(in Chinese))
[35]余寿文,冯西桥.损伤力学[M].北京:清华大学出版社,1997.(Yu Shouwen,Feng Xiqiao. Damage Mechanics[M]. Beijing:Tsinghua University Press,1997.(in Chinese))
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[2]张玉卓.岩石模糊强度理论及其应用[J].煤炭学报,1994,19(5):451–455.(Zhang Yuzhuo. Fuzzy theory of rock strength and its application [J]. Journal of China Coal Society,1994,19(5):451–455.(in Chinese))
[3]周筑宝,卢楚芬.三轴应力状态下混凝土的一种新强度准则[J].固体力学学报,1999,20(3):272–280.(Zhou Zhubao,Lu Chufen. A new strength criterion of plain concrete under triaxial stresses conditions[J]. Acta Mechanica Solida Sinica,1999,20(3):272–280.(in Chinese))
[4]俞茂宏,昝月稳,范文,等.20世纪岩石强度理论的发展——纪念 Mohr-Coulomb 强度理论100周年[J].岩石力学与工程学报,2000,19(5):545–550.(Yu Maohong,Zan Yuewen,Fan Wen,et al. Advances in strength theory of rock in 20th century—100 years in memory of the Mohr-Coulomb strength theory[J]. Chinese Journal of Rock Mechanics and Engineering,2000,19(5):545–550.(in Chinese))
[5]林皋,王哲.可以考虑压应力球量历史影响的混凝土强度准则[J].土木工程学报,2002,35(5):1–6.(Lin Gao,Wang Zhe. Strength criterion of concrete considering effects of stress spherical tensor history[J]. China Civil Engineering Journal,2002,35(5):1–6.(in Chinese))
[6] Xie H P,Gao F. The mechanics of cracks and a statistical strength theory for rocks[J]. International Journal of Rock Mechanics and Mining Sciences,2000,(37):477–488.
[7] Aubertin M,Li L,Simon R. A multiaxial stress criterion for short- and long-term strength of isotropic rock media[J]. International Journal of Rock Mechanics and Mining Sciences,2000,(37):1169–1193.
[8] Li Q M. Strain energy density failure criterion[J]. International Journal of Solids and Structures,2001,(38):6997–7013.
[9] Yu M H,Zan Y W,Zhao J,et al. A unified strength criterion for rock material[J]. International Journal of Rock Mechanics and Mining Sciences,2002,(39):975–989.
[10]李夕兵,古德生.岩石冲击动力学[M].长沙:中南工业大学出版社,1994.(Li Xibing,Gu Desheng. Rock Impact Dynamics[M]. Changsha:Central South University of Technology Press,1994.(in Chinese))
[11]李夕兵,陈寿如,古德生.岩石在不同加载波下的动载强度[J].中南矿冶学院学报,1994,25(3):301–304.(Li Xibing,Chen Shouru,Gu Desheng. Dynamic strength of rock under impulse loads with different stress waveforms and durations[J]. Journal of Central South Institute of Mining and Metallurgy,1994,25(3):301–304.(in Chinese))
[12]鞠庆海,吴绵拔.岩石材料三轴压缩动力特性的试验研究[J].岩土工程学报,1993,15(3):73–80.(Ju Qinghai,Wu Mianba. Experimental studies of dynamic characteristic of rocks under triaxial compression[J]. Chinese Journal of Geotechnical Engineering,1993,15(3):73–80.(in Chinese))
[13]戚承志,苗启松,钱七虎.考虑强度–应变率依赖性的岩石弹塑性动力模型[J].世界地震工程,2002,18(3):52–56.(Qi Chengzhi,Miao Qisong , Qian Qihu. Dynamical model of rocks with consideration of strength-strain rate dependence[J]. World Earth- quake Engineering,2002,18(3):52–56.(in Chinese))
[14]戚承志,钱七虎.岩石等脆性材料动力强度依赖应变率的物理机制[J].岩石力学与工程学报,2003,22(2):177–181.(Qi Chengzhi,Qian Qihu. Physical mechanism of dependence of material strength on strain rate for rock-like material[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(2):177–181.(in Chinese))
[15]宋玉普,吕培印,侯景鹏.有侧压混凝土的变速率劈拉强度试验及其破坏准则研究[J].水利学报,2002,(3):1–5.(Song Yupu,Lu Peiyin,Hou Jingpeng. Concrete splitting tensile strength and failure criterion for different loading rate and lateral stress[J]. Journal of Hydraulic Engineering,2002,(3):1–5.(in Chinese))
[16]李海波,赵坚,李俊如,等.花岗岩动三轴抗压强度的裂纹模型研究(I):理论基础[J].岩土力学,2002,23(1):75–80.(Li Haibo,Zhao Jian,Li Junru,et al. Study on dynamic triaxial compressive strength of a granite using sliding crack model(I)t:heory[J]. Rock and Soil Mechanics,2002,23(1):75–80.(in Chinese))
[17]李海波,赵坚,李廷芥,等.花岗岩动三轴抗压强度的裂纹模型研究(II):应用[J].岩土力学,2002,23(3):329–333.(Li Haibo,Zhao Jian,Li Tingjie,et al. Study on dynamic triaxial compressive strength of a granite using sliding crack model(II):application[J]. Rock and Soil Mechanics,2002,23(3):329–333.(in Chinese))
[18] Zhao J. Applicability of Mohr-Coulomb and Hoek-Brown strength criteria to the dynamic strength of brittle rock[J]. International Journal of Rock Mechanics and Mining Sciences,2000,(37):1115–1121.
[19] Sai S,Sia N N. Dynamic compressive strength of silicon carbide under uniaxial compression[J]. Materials Science and Engineering,2001,(A317):140–144.
[20] Li Q M,Meng H. About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test[J]. International Journal of Solids and Structures,2003,(40):343–360.
[21] Sang H C,Yuji O,Katsuhiko K. Strain-rate dependency of the dynamic tensile strength of rock[J]. International Journal of Rock Mechanics and Mining Sciences,2003,(40):763–777.
[22]左宇军,李夕兵,赵国彦.受静载荷作用的岩石动态断裂的突变模型[J].煤炭学报,2004,29(6):654–658.(Zuo Yujun,Li Xibing ,Zhao Guoyan. A catastrophe model for dynamic fracture of static loaded rock[J]. Journal of China Coal Society,2004,29(6):654–658.(in Chinese))
[23]左宇军,李夕兵,马春德,等.动静组合载荷作用下岩石失稳破坏的突变理论模型与试验研究[J].岩石力学与工程学报,2005,24(5):741–746.(Zuo Yujun,Li Xibing,Ma Chunde,et al. Catastrophic model and testing study on failure of static loading rock system under dynamic loading[J]. Chinese Journal of Rock Mechanics and Engineering,2005,24(5):741–746.(in Chinese))
[24]左宇军.动静组合加载下的岩石破坏特性研究[博士学位论文][D].长沙:中南大学,2005.(Zuo Yujun. Study on failure and fragmentation characteristics of rock under static-dynamic coupling loading[Ph. D. Thesis][D]. Changsha:Central South University,2005.(in Chinese)
[25]刘鸿文.材料力学(上册)[M].北京:高等教育出版社,1999.(Liu Hongwen. Mechanics of Materials(I)[M]. Beijing:High Education Press,1999.(in Chinese))
[26]余熙莹.对于第四强度理论的修正[J].广西大学学报(自然科学版),2002,27(增):63–69.(Yu Xiying. The revision of the fourth strength theorem[J]. Journal of Guangxi University(Natural Science),2002,27(Supp.):63–69.(in Chinese))
[27]单仁亮,薛友松,张倩.岩石动态破坏的时效损伤本构模型[J].岩石力学与工程学报,2003,22(11):1771–1776.(Shan Renliang,Xue Yousong,Zhang Qian. Time-dependent damage model of rock under dynamic loading[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(11):1771–1776.(in Chinese))
[28]唐春安.岩石破裂过程中的灾变[M].北京:煤炭工业出版社,1993.(Tang Chun′an. Catastrophe in Rock Unstable Failure[M]. Beijing:China Coal Industry Publishing House,1993.(in Chinese))
[29]江松青,李永池,胡秀章,等.静力预加载环向加筋圆柱壳的轴向流–固冲击屈曲[J].固体力学学报,2000,21(3):189–197.(Jiang Songqing,Li Yongchi,Hu Xiuzhang,et al. Dynamic bucking of statically preloaded ring stiffened cylindrical shells under axial fluid-solid impact loading[J]. Acta Mechanica Solida Sinica,2000,21(3):189–197.(in Chinese))
[30] Holasut S,Ruiz C. Effect of an impulsive disturbing load on the stability of a statically loaded structure[J]. Int. J. Impact Eng.,1985,3(1):57–73.
[31] Anthony N K. Dynamic buckling of simple two-bar frames using catastrophe theory[J]. International Journal of Nonlinear Mechanics.2002,37:1249–1259.
[32]王德禹,杨桂通.简单弹性结构动力屈曲的突变模型[A].见:现代数学与力学(MMM–4)[C].兰州:兰州大学出版社,1991.275–277.(Wang Deyu,Yang Guitong. A catastrophe model for the dynamic buckling of simple elastic structures[A]. In : Modern Mathematics and Mechanics(MMM –4)[C]. Lanzhou : Lanzhou University Press,1991.275–277.(in Chinese))
[33]王德禹,张善元,杨桂通.静力预加载结构冲击屈曲的突变模型[J].爆炸与冲击,1993,13(3):243–248.(Wang Deyu,Zhang Shanyuan,Yang Guitong. A catastrophe model for the impact buckling of static preloading structures[J]. Explosion and Shock Waves,1993,13(3):243–248.(in Chinese))
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