考虑应变率及应变梯度效应的断层岩爆分析
|
摘要
从理论上研究了考虑应变率效应及微小结构相互影响的断层带-弹性岩石系统的剪切不稳定性。在经典弹-塑性理论的屈服函数中引入应变梯度及考虑应变率效应的函数。将断层岩爆简化为一维动态剪切问题,利用:局部塑性剪应变的对称性;在断层带的边界上,其应变值为零;断层带的宽度由塑性剪切应变取极值来确定等条件,得到了断层带内部的局部塑性剪切应变及局部塑性剪切位移,二者都随应变率的增加而趋于明显增加。同时,还得到了应变软化阶段系统结构响应的理论表达式。令峰后刚度为无穷大,则可得到岩爆发生的临界加载应变率,该参数不仅与岩石材料的本构参数有关,而且还与岩石结构的几何尺寸(即弹性区域的尺寸)有关。应变率增加使断层-弹性岩石系统容易发生失稳回跳。此外,若不考虑应变率效应,则本文的理论结果可以退化为对断层岩爆的静力分析结果。
Dynamic shear instability of fault rockburst is analyzed with considering the effect of strain rate and interaction among microstructures. The second shear strain gradient and the function reflecting the effect of strain rate are introduced into the yield function of classical elastoplastic theory. The fault rockburst is simplified as the one-dimensional dynamic shear problem and shear localization is initiated at the peak shear stress. Symmetry of local plastic shear strain in shear band is considered and in the boundary of the band the strain is zero. In addition,the thickness of band is determined according to the maximum local plastic shear strain. Local plastic shear strain and local plastic shear displacement analytically obtained show that these two local parameters increase with strain rate. Beyond the peak shear stress,the structural response of the system composed of fault band and elastic rock outside the fault is proposed. If the post-peak stiffness of the structural response is infinity,the critical loading strain rate of rockburst can be deduced. Once the critical value is achieved,the rock burst occurs certainty. It is found that the critical parameter is dependent on both constitutive parameters of rock materials and the size of structure. Larger strain rate can lead to snap-back of instability of the system. Besides,if the effect of strain rate is neglected,the static results based on gradient-dependent plasticity by Wang et al. can be obtained by simplifying the present theoretical results.
Dynamic shear instability of fault rockburst is analyzed with considering the effect of strain rate and interaction among microstructures. The second shear strain gradient and the function reflecting the effect of strain rate are introduced into the yield function of classical elastoplastic theory. The fault rockburst is simplified as the one-dimensional dynamic shear problem and shear localization is initiated at the peak shear stress. Symmetry of local plastic shear strain in shear band is considered and in the boundary of the band the strain is zero. In addition,the thickness of band is determined according to the maximum local plastic shear strain. Local plastic shear strain and local plastic shear displacement analytically obtained show that these two local parameters increase with strain rate. Beyond the peak shear stress,the structural response of the system composed of fault band and elastic rock outside the fault is proposed. If the post-peak stiffness of the structural response is infinity,the critical loading strain rate of rockburst can be deduced. Once the critical value is achieved,the rock burst occurs certainty. It is found that the critical parameter is dependent on both constitutive parameters of rock materials and the size of structure. Larger strain rate can lead to snap-back of instability of the system. Besides,if the effect of strain rate is neglected,the static results based on gradient-dependent plasticity by Wang et al. can be obtained by simplifying the present theoretical results.
引文
1潘一山,王来贵,章梦涛等.断层冲击地压发生的理论与实验研究[J].岩石力学与工程学报,1998,17(6):145～151
2蔡美峰,王金安,王双红.玲珑金矿深部开采岩体能量分析与岩爆综合预测[J].岩石力学与工程学报,2001,20(1):37～42
3潘岳,刘英,顾善发.矿井断层冲击地压的折迭突变模型[J].岩石力学与工程学报,2001,20(1):43～48
4王学滨,潘一山,马谨.剪切带-弹性岩体系统的稳定及失稳滑动理论研究[J].岩土工程学报,2002,24(3):360～363
5王学滨,潘一山,马瑾.剪切带内部应变(率)分析及基于能量准则的失稳判据[J].工程力学,2003,20(2):111～115
6唐礼忠,王文星.一种新的岩爆倾向性指标[J].岩石力学与工程学报,2002,21(6):874～878
7谷明成,何发亮,陈成宗.秦岭隧道岩爆的研究[J].岩石力学与工程学报,2002,21(9):1324～1329
8许迎年,徐文胜,王元汉等.岩爆模拟试验及岩爆机理研究[J].岩石力学与工程学报,2002,21(10):1462～1466
9尚嘉兰,沈乐天,赵宇辉等.BukitTimah花岗岩的动态本构关系[J].岩石力学与工程学报,1998,17(6):634～641
10董毓利,谢和平,赵鹏.不同应变率下混凝土受压全过程的实验研究及其本构模型[J].水利学报,1997,(7):72～77
11刘剑飞,胡时胜,胡元育等.花岗岩的动态压缩实验和力学性能研究[J].岩石力学与工程学报,2000,19(5):618～621
12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
13赵坚,李海波.莫尔-库仑和霍克-布朗强度准则用于评估脆性岩石动态强度的适用性[J].岩石力学与工程学报,2003,22(2):171～176
14王学滨,潘一山,盛谦等.岩体假三轴压缩及变形局部化剪切带数值模拟[J].岩土力学,2001,22(3):323～326
15王来贵,潘一山,章梦涛.采掘诱发地震的成因及对策[J].中国安全科学学报,1996,6(3):40～43
16徐思朋,缪协兴.冲击地压的时间效应研究现状[J].矿业安全与环保,2001,28(2):27～29
17杨根地.八一煤矿厚煤层深部水采煤炮的防治[J].水力采煤与管道运输,1997,(2):28～34
18窦林名,何学秋,BernardDrzezls.冲击矿压危险性评价的地音法[J].中国矿业大学学报,2000,29(1):85～88
19王学滨,潘一山,任伟杰.基于应变梯度理论的岩石试件剪切破坏失稳判据及应用[J].岩石力学与工程学报,2003,22(5):747～750
20王学滨,潘一山,杨小彬.准脆性材料试件应变软化尺度效应理论研究[J].岩石力学与工程学报,2003,22(2):188～191
21王学滨,潘一山.剪切带倾角的尺度律与局部化启动跳跃稳定研究[J].岩土力学,2002,23:(4):446～449
22王学滨,潘一山,宋维源.岩石试件尺寸效应的塑性剪切应变梯度模型[J].岩土工程学报,2001,23(6):711～713
23王学滨,潘一山,马瑾.基于应变梯度理论的韧性剪切带理论研究[J].地质力学学报,2002,8(1):79～87
24王学滨,杨梅,潘一山.基于梯度塑性理论的单向拉伸低碳钢试样颈缩分析[J].塑性工程学 报,200 2,9 (3): 55～ 57
2 5W angXuebin,Pa nY ishan. Siz eeffectandsnapback basedonconservationofener gyandgra dient-dependentplasticity[A].I nLinYunmeied.Pro c.ofSecondInter nationalSymposiumonNewDevelopmentinRockMechanicsandRockEngineering[C].NewYork:RintonPress,2002, 89 ～9 2
26P anYishan, Wang Xuebin ,Li Zhon ghua.Anal ysiso ft hestr ainsof teningsi zeeffectfo rrockspecimensbasedonshearstra ingradientplast icitytheory[J].InternationalJournalofRockMechanicsandMiningSciences,2002,39(6): 801～805
27Wa ng Xuebin,S ongWe iyua n,Pan Yishan .ClassII behavio rofrockorconcretebasedup onshearstraing radientplastictheory[A],In:Zha oG uogang ed.ProceedingsofSecondInternationalSymposiumonminingtechno logy[C].Be ijing:SciencePr es s,200 1,237??41
28J oh nsonGR. Fracturecharac teristicsofthreeme tal ssubjectedtovariou sstrains,strainrates,temperaturesandpressures[J].Engi-neeringFractureMechanics,1985,21(1):31～48
2蔡美峰,王金安,王双红.玲珑金矿深部开采岩体能量分析与岩爆综合预测[J].岩石力学与工程学报,2001,20(1):37～42
3潘岳,刘英,顾善发.矿井断层冲击地压的折迭突变模型[J].岩石力学与工程学报,2001,20(1):43～48
4王学滨,潘一山,马谨.剪切带-弹性岩体系统的稳定及失稳滑动理论研究[J].岩土工程学报,2002,24(3):360～363
5王学滨,潘一山,马瑾.剪切带内部应变(率)分析及基于能量准则的失稳判据[J].工程力学,2003,20(2):111～115
6唐礼忠,王文星.一种新的岩爆倾向性指标[J].岩石力学与工程学报,2002,21(6):874～878
7谷明成,何发亮,陈成宗.秦岭隧道岩爆的研究[J].岩石力学与工程学报,2002,21(9):1324～1329
8许迎年,徐文胜,王元汉等.岩爆模拟试验及岩爆机理研究[J].岩石力学与工程学报,2002,21(10):1462～1466
9尚嘉兰,沈乐天,赵宇辉等.BukitTimah花岗岩的动态本构关系[J].岩石力学与工程学报,1998,17(6):634～641
10董毓利,谢和平,赵鹏.不同应变率下混凝土受压全过程的实验研究及其本构模型[J].水利学报,1997,(7):72～77
11刘剑飞,胡时胜,胡元育等.花岗岩的动态压缩实验和力学性能研究[J].岩石力学与工程学报,2000,19(5):618～621
12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
13赵坚,李海波.莫尔-库仑和霍克-布朗强度准则用于评估脆性岩石动态强度的适用性[J].岩石力学与工程学报,2003,22(2):171～176
14王学滨,潘一山,盛谦等.岩体假三轴压缩及变形局部化剪切带数值模拟[J].岩土力学,2001,22(3):323～326
15王来贵,潘一山,章梦涛.采掘诱发地震的成因及对策[J].中国安全科学学报,1996,6(3):40～43
16徐思朋,缪协兴.冲击地压的时间效应研究现状[J].矿业安全与环保,2001,28(2):27～29
17杨根地.八一煤矿厚煤层深部水采煤炮的防治[J].水力采煤与管道运输,1997,(2):28～34
18窦林名,何学秋,BernardDrzezls.冲击矿压危险性评价的地音法[J].中国矿业大学学报,2000,29(1):85～88
19王学滨,潘一山,任伟杰.基于应变梯度理论的岩石试件剪切破坏失稳判据及应用[J].岩石力学与工程学报,2003,22(5):747～750
20王学滨,潘一山,杨小彬.准脆性材料试件应变软化尺度效应理论研究[J].岩石力学与工程学报,2003,22(2):188～191
21王学滨,潘一山.剪切带倾角的尺度律与局部化启动跳跃稳定研究[J].岩土力学,2002,23:(4):446～449
22王学滨,潘一山,宋维源.岩石试件尺寸效应的塑性剪切应变梯度模型[J].岩土工程学报,2001,23(6):711～713
23王学滨,潘一山,马瑾.基于应变梯度理论的韧性剪切带理论研究[J].地质力学学报,2002,8(1):79～87
24王学滨,杨梅,潘一山.基于梯度塑性理论的单向拉伸低碳钢试样颈缩分析[J].塑性工程学 报,200 2,9 (3): 55～ 57
2 5W angXuebin,Pa nY ishan. Siz eeffectandsnapback basedonconservationofener gyandgra dient-dependentplasticity[A].I nLinYunmeied.Pro c.ofSecondInter nationalSymposiumonNewDevelopmentinRockMechanicsandRockEngineering[C].NewYork:RintonPress,2002, 89 ～9 2
26P anYishan, Wang Xuebin ,Li Zhon ghua.Anal ysiso ft hestr ainsof teningsi zeeffectfo rrockspecimensbasedonshearstra ingradientplast icitytheory[J].InternationalJournalofRockMechanicsandMiningSciences,2002,39(6): 801～805
27Wa ng Xuebin,S ongWe iyua n,Pan Yishan .ClassII behavio rofrockorconcretebasedup onshearstraing radientplastictheory[A],In:Zha oG uogang ed.ProceedingsofSecondInternationalSymposiumonminingtechno logy[C].Be ijing:SciencePr es s,200 1,237??41
28J oh nsonGR. Fracturecharac teristicsofthreeme tal ssubjectedtovariou sstrains,strainrates,temperaturesandpressures[J].Engi-neeringFractureMechanics,1985,21(1):31～48
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心