考虑T应力的岩石压剪裂纹起裂机理
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摘要
传统断裂理论在研究岩石压剪裂纹起裂机理时,往往仅考虑裂纹尖端应力场Williams展开式中的r~(1/2)奇异应力项,而忽略了非奇异应力项(T应力)的影响,造成理论预测值与试验结果不符。在对压剪应力下裂纹受力特征进行分析的基础上,将T应力引入传统断裂力学的最大周向应力准则,提出了考虑T应力的修正最大周向应力准则。同时考虑压剪应力下的裂纹应力传递特点,在上述准则中又引入裂纹面法向刚度及切向刚度等变形参数。最终建立了能够同时考虑岩石性质和裂纹几何参数(如裂纹倾角、长度等)、强度参数(裂纹面摩擦系数)及变形参数(裂纹面法向及切向刚度)的最大周向应力准则,更好地反映了岩石压剪裂纹起裂机理。算例表明由该方法计算得到的翼裂纹起裂角与试验结果吻合较好,同时通过参数敏感性分析发现裂纹尖端相对临界尺寸对翼裂纹起裂角的影响最大。
In the studies on the initiation mechanism of cracks of rock in compression and shear, the traditional fracture theory only considers the singular stress(r~(1/2) term) of the elastic stress state near a crack tip in the Williams' series expression, and ignores the effects of the non-singular term(T-stress). It leads to the disagreement between the theoretical predictions and the experimental results. On the basis of analyzing the mechanical behaviors of cracks in compression and shear, the T-stress is introduced into the maximum tangential stress(MTS) criterion of the traditional fracture mechanics, and accordingly the revised MTS criterion is proposed by considering T-stress. Meanwhile, by considering the stress transfer of the cracks in compression and shear, the deformation parameters of cracks, e.g., the crack normal and shear stiffness, are also introduced into the original MTS criterion. Finally, the new MTS criterion is set up to simultaneously consider the properties of rock, the geometrical parameters of cracks(such as dip angle and length), the strength parameters(such as frictional coefficient of crack face), and the deformation parameters(such as crack normal and shear stiffness). Therefore, it can perfectly reflect the initiation mechanism of the cracks of rock in compression and shear. The example indicates that the initiation angle of wing crack obtained from the proposed method agrees well with that obtained from the tests, and it is also found through the sensitivity analysis for the parameters that the relative critical size at the crack tip has the most important influences on the initiation angle of wing crack.
In the studies on the initiation mechanism of cracks of rock in compression and shear, the traditional fracture theory only considers the singular stress(r~(1/2) term) of the elastic stress state near a crack tip in the Williams' series expression, and ignores the effects of the non-singular term(T-stress). It leads to the disagreement between the theoretical predictions and the experimental results. On the basis of analyzing the mechanical behaviors of cracks in compression and shear, the T-stress is introduced into the maximum tangential stress(MTS) criterion of the traditional fracture mechanics, and accordingly the revised MTS criterion is proposed by considering T-stress. Meanwhile, by considering the stress transfer of the cracks in compression and shear, the deformation parameters of cracks, e.g., the crack normal and shear stiffness, are also introduced into the original MTS criterion. Finally, the new MTS criterion is set up to simultaneously consider the properties of rock, the geometrical parameters of cracks(such as dip angle and length), the strength parameters(such as frictional coefficient of crack face), and the deformation parameters(such as crack normal and shear stiffness). Therefore, it can perfectly reflect the initiation mechanism of the cracks of rock in compression and shear. The example indicates that the initiation angle of wing crack obtained from the proposed method agrees well with that obtained from the tests, and it is also found through the sensitivity analysis for the parameters that the relative critical size at the crack tip has the most important influences on the initiation angle of wing crack.
引文
[1]WILLIAMS J G,EWING P D.Fracture in complex stress:the angled crack problem[J].International Journal of Fracture,1972,8(4):416-441.
[2]GUPTA M,ALDERLIESTEN R C,BENEDICTUS R.Areview of T-stress and its effects in fracture mechanics[J].Engineering Fracture Mechanics,2015,134:218-241.
[3]唐世斌,黄润秋,唐春安.T应力对岩石裂纹扩展路径及起裂强度的影响研究[J].岩土力学,2016,37(6):1521-1529,1549.(TANG Shi-bin,HUANG Run-qiu,TANGChun-an.Effect of T-stress on crack growth path in rock and fracture strength[J].Rock and Soil Mechanics,2016,37(6):1521-1529,1549.(in Chinese))
[4]WILLIAMS M L,CALIF P.On the stress distribution at the base of a stationary crack[J].Journal of Applied Mechanics,1957,24(1):109-114.
[5]CHRISTOPHER C J,JAMES M N,PATTERSON E A,et al.Aquantitative evaluation of fatigue crack shielding forces using photoelasticity[J].Engineering Fracture Mechanics,2008,75(14):4190-4199.
[6]COLOMBO C,DU Y,JAMES M N,et al.On crack tip shielding due to plasticity-induced closure during an overload[J].Fatigue Fracture Engineering Material Structure,2010,33(12):766-777.
[7]MATVIENKO Y G.Maximum average tangential stress criterion for prediction of the crack path[J].International Journal of Fracture,2012,176(1):113-118.
[8]SIMTH D J,AYATOLLAHI M R,PAVIER M J.The role of T-stress in brittle fracture for linear elastic materials in mixed-mode loading[J].Fatigue Fracture Engineering Material Structure,2001,24(2):137-150.
[9]LI X F,LIU G L,LEE K Y.Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces[J].International Journal of Fracture,2009,160(1):19-30.
[10]赵彦琳,范勇,朱哲明,等.T应力对闭合裂纹断裂行为的理论和实验研究[J].岩石力学与工程学报,2018,37(6):1340-1349.(ZHAO Yan-lin,FAN Yong,ZHU Zhe-ming,et al.Analytical and experimental study on the effect of T-stress on behavior of closed cracks[J].Chinese Journal of Rock Mechanics and Engineering,2018,37(6):1340-1349.(in Chinese))
[11]FINNIE I,SAITH A.A note on the angled crack problem and the directional stability of cracks[J].International Journal of Fracture,1973,9(4):484-486.
[12]SMITH D J,AYATOLLAHI M R,PAVIER M J.The role of T-stress in brittle fracture for linear elastic materials in mixed-mode loading[J].Fatigue and Fracture of Engineering Materials and Structures,2001,24:137-150.
[13]RASHIDI M M,AYATOLLAHI1 M R,BERTO F.Rock fracture toughness in mode II loading:a theoretical model based on local strain energy density[J].Rock Mechanics and Rock Engineering,2018,51:243-253.
[14]唐世斌,黄润秋,唐春安,等.考虑T应力的最大周向应变断裂准则研究[J].土木工程学报,2016,49(9):87-95.(TANG Shi-bin,HUANG Run-qiu,TANG Chun-an,et al.Study on fracture criterion based on the maximum tangential strain considering the T-stress[J].China Civil Engineering Journal,2016,49(9):87-95.(in Chinese))
[15]PRUDENCIO M,van SINT J M.Strength and failure modes of rock mass models with non-persistent joints[J].International Journal of Rock mechanics&Mining Sciences,2007,46(6):890-902.
[16]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 Shi-yu,HE Tai-ming,YIN Xiang-chu.Introduction of rock fracture mechanics[M].Hefei:University of Science and Technology of China Press,2010.(in Chinese))
[17]LEE H,JEON S.An experimental and numerical study of fracture coalescence in pre-cracked specimens in uniaxial compression[J].International Journal of Solids and Structures,2011,48:979-999.
[18]AYATOLLAHI M R,ALIHA M R M.On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials[J].Engineering Fracture Mechanics,2008,75:4631-4641.
[19]LIU T Y,CAO P,LIN H.Damage and fracture evolution of hydraulic fracturing in compression-shear rock cracks[J].Theoretical and Applied Fracture Mechanics,2014,74:55-63.
[20]WILLIAMS M L,CALIF P.On the stress distribution at the base of a stationary crack[J].Journal of Applied Mechanics,1957,24(1):109-114.
[21]AYATOLLAHI M R,ALIHA M R M.On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials[J].Engineering Fracture Mechanics,2008,75:4631-4641.
[22]BOBET A.The initiation of secondary cracks in compression[J].Engineering Fracture Mechanics,2000,66:187-219.
[2]GUPTA M,ALDERLIESTEN R C,BENEDICTUS R.Areview of T-stress and its effects in fracture mechanics[J].Engineering Fracture Mechanics,2015,134:218-241.
[3]唐世斌,黄润秋,唐春安.T应力对岩石裂纹扩展路径及起裂强度的影响研究[J].岩土力学,2016,37(6):1521-1529,1549.(TANG Shi-bin,HUANG Run-qiu,TANGChun-an.Effect of T-stress on crack growth path in rock and fracture strength[J].Rock and Soil Mechanics,2016,37(6):1521-1529,1549.(in Chinese))
[4]WILLIAMS M L,CALIF P.On the stress distribution at the base of a stationary crack[J].Journal of Applied Mechanics,1957,24(1):109-114.
[5]CHRISTOPHER C J,JAMES M N,PATTERSON E A,et al.Aquantitative evaluation of fatigue crack shielding forces using photoelasticity[J].Engineering Fracture Mechanics,2008,75(14):4190-4199.
[6]COLOMBO C,DU Y,JAMES M N,et al.On crack tip shielding due to plasticity-induced closure during an overload[J].Fatigue Fracture Engineering Material Structure,2010,33(12):766-777.
[7]MATVIENKO Y G.Maximum average tangential stress criterion for prediction of the crack path[J].International Journal of Fracture,2012,176(1):113-118.
[8]SIMTH D J,AYATOLLAHI M R,PAVIER M J.The role of T-stress in brittle fracture for linear elastic materials in mixed-mode loading[J].Fatigue Fracture Engineering Material Structure,2001,24(2):137-150.
[9]LI X F,LIU G L,LEE K Y.Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces[J].International Journal of Fracture,2009,160(1):19-30.
[10]赵彦琳,范勇,朱哲明,等.T应力对闭合裂纹断裂行为的理论和实验研究[J].岩石力学与工程学报,2018,37(6):1340-1349.(ZHAO Yan-lin,FAN Yong,ZHU Zhe-ming,et al.Analytical and experimental study on the effect of T-stress on behavior of closed cracks[J].Chinese Journal of Rock Mechanics and Engineering,2018,37(6):1340-1349.(in Chinese))
[11]FINNIE I,SAITH A.A note on the angled crack problem and the directional stability of cracks[J].International Journal of Fracture,1973,9(4):484-486.
[12]SMITH D J,AYATOLLAHI M R,PAVIER M J.The role of T-stress in brittle fracture for linear elastic materials in mixed-mode loading[J].Fatigue and Fracture of Engineering Materials and Structures,2001,24:137-150.
[13]RASHIDI M M,AYATOLLAHI1 M R,BERTO F.Rock fracture toughness in mode II loading:a theoretical model based on local strain energy density[J].Rock Mechanics and Rock Engineering,2018,51:243-253.
[14]唐世斌,黄润秋,唐春安,等.考虑T应力的最大周向应变断裂准则研究[J].土木工程学报,2016,49(9):87-95.(TANG Shi-bin,HUANG Run-qiu,TANG Chun-an,et al.Study on fracture criterion based on the maximum tangential strain considering the T-stress[J].China Civil Engineering Journal,2016,49(9):87-95.(in Chinese))
[15]PRUDENCIO M,van SINT J M.Strength and failure modes of rock mass models with non-persistent joints[J].International Journal of Rock mechanics&Mining Sciences,2007,46(6):890-902.
[16]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 Shi-yu,HE Tai-ming,YIN Xiang-chu.Introduction of rock fracture mechanics[M].Hefei:University of Science and Technology of China Press,2010.(in Chinese))
[17]LEE H,JEON S.An experimental and numerical study of fracture coalescence in pre-cracked specimens in uniaxial compression[J].International Journal of Solids and Structures,2011,48:979-999.
[18]AYATOLLAHI M R,ALIHA M R M.On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials[J].Engineering Fracture Mechanics,2008,75:4631-4641.
[19]LIU T Y,CAO P,LIN H.Damage and fracture evolution of hydraulic fracturing in compression-shear rock cracks[J].Theoretical and Applied Fracture Mechanics,2014,74:55-63.
[20]WILLIAMS M L,CALIF P.On the stress distribution at the base of a stationary crack[J].Journal of Applied Mechanics,1957,24(1):109-114.
[21]AYATOLLAHI M R,ALIHA M R M.On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials[J].Engineering Fracture Mechanics,2008,75:4631-4641.
[22]BOBET A.The initiation of secondary cracks in compression[J].Engineering Fracture Mechanics,2000,66:187-219.
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