梯度塑性理论及其在地质灾害预测研究中的应用
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摘要
岩石结构稳定性问题是岩土工程实践中迫切需要解决的重要课题之一。文章以地震为例,讨论了地质灾害的局部化特征,介绍了经典弹、塑性理论的某些缺陷及梯度塑性理论的几点优越性:(1)控制方程总是适定的;(2)病态网格依赖性消失;(3)局部化带宽度由材料的内部长度完全确定;(4)可对岩石结构的尺寸效应及失稳回跳进行合理解释和预测;(5)对预测宏观及微观问题均比较有效。介绍了基于梯度塑性理论的岩石变形、破坏及稳定性研究进展。梯度塑性理论可用于研究单轴压缩条件下,岩石试件发生剪切破坏时全程应力-应变曲线、尺寸效应、剪切带倾角尺寸效应及失稳回跳等问题,它们对土木工程及岩土工程均十分重要。若将单轴压缩岩样比拟为矿柱,则该失稳判据即为矿柱岩爆准则。梯度塑性理论可用于研究韧性断层带内部应变、应变率分布规律、断层带错动位移及带内孔隙度分布规律,为韧性断层带定量分析提供了新的手段。此外,该理论还可对直剪试验机———岩样系统不稳定性进行分析,系统失稳可比拟为断层岩爆。发展基于梯度塑性理论尺度律及失稳判据等解析解一方面可加深对岩石变形、破坏的理解;另一方面,还可用来检验数值结果的正确性。
The problem of stability on rock structure is one of particularly important objects in geo-engineering. The characteristics of strain localization of earthquake were discussed firstly. Then,several defects of classical elastoplastic theory were analyzed and advantages of gradient-dependent plasticity were introduced:(1)governing equation is always well posed; (2)pathological mesh dependence vanishes; (3)the size of localization band is determined strictly according to internal length parameter; (4)it is possible for one to explain and predict the size effect and the snap-back behavior and (5) it is valid for macroscopic and microscopic problems. Then,the analytical progress of deformation,failure and instability of rock structure based on gradient-dependent plasticity is discussed. For uniaxial compression quasi-brittle materials subjected to shear failure,gradient-dependent plasticity can be used to investigate the complete stress-strain curve,size effect,size effect of inclination angle of shear band and snap-back instability criterion etc,which are especially important for civil engineering and geotechnical engineering. If the uniaxial compression specimen is seen as the pillar, the instability criterion is that of pillar rock burst. The theory can be used to study the distributed strain, strain rate, porosity and plastic shear displacement in fault band, which presents a new method for quantitative analysis of ductile shear zone. In addition, the stability of the system composed for shear band ("specimen") and elastic rock mass outside the band ("testing machine") can be analyzed based on the theory. Losing stability of the system means that fault rock burst occurs. Developing the analytical solutions for size effect and instability criterion etc. will enrich the understanding of deformation and failure of rock on one hand. On the other hand, the analytical solutions can be used to check the validity of the numerical results. Finally, further objects of research were proposed.
The problem of stability on rock structure is one of particularly important objects in geo-engineering. The characteristics of strain localization of earthquake were discussed firstly. Then,several defects of classical elastoplastic theory were analyzed and advantages of gradient-dependent plasticity were introduced:(1)governing equation is always well posed; (2)pathological mesh dependence vanishes; (3)the size of localization band is determined strictly according to internal length parameter; (4)it is possible for one to explain and predict the size effect and the snap-back behavior and (5) it is valid for macroscopic and microscopic problems. Then,the analytical progress of deformation,failure and instability of rock structure based on gradient-dependent plasticity is discussed. For uniaxial compression quasi-brittle materials subjected to shear failure,gradient-dependent plasticity can be used to investigate the complete stress-strain curve,size effect,size effect of inclination angle of shear band and snap-back instability criterion etc,which are especially important for civil engineering and geotechnical engineering. If the uniaxial compression specimen is seen as the pillar, the instability criterion is that of pillar rock burst. The theory can be used to study the distributed strain, strain rate, porosity and plastic shear displacement in fault band, which presents a new method for quantitative analysis of ductile shear zone. In addition, the stability of the system composed for shear band ("specimen") and elastic rock mass outside the band ("testing machine") can be analyzed based on the theory. Losing stability of the system means that fault rock burst occurs. Developing the analytical solutions for size effect and instability criterion etc. will enrich the understanding of deformation and failure of rock on one hand. On the other hand, the analytical solutions can be used to check the validity of the numerical results. Finally, further objects of research were proposed.
引文
[1] 王嘉荫.中国地质史料[M].北京:科学出版社,1963.
[2] 丁国瑜,李永善.我国地震活动与地壳现代破裂网络[J].地质学报,1979,(5):22-34.
[3] 王绳祖.亚洲大陆岩石圈多层构造模型和塑性流动网络[J].地质学报,1993,67(1):1-18.
[4] 陶玮,洪汉净,刘培询.中国大陆及邻区强震活动主体地区形成的数值模拟[J].地震学报,2000,22:271-277.
[5] 许绍燮,沈佩文.北京周围地区地震的分布特点与地壳屈曲[J].地震学报,1980,2(2):153-168.
[6] 周硕愚,梅世蓉,施顺英,等.用地壳形变图象动力学研究震源演化复杂过程[J].地壳形变与地震,1997,(17):1-9.
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[8] 赵豫生,陈,王仁.岩石裂纹附近的变形局部化与破坏———激光全息干涉法的应用[J].地球物理学报,1988,31(3):294-304.
[9] 潘一山,袁旭东,章梦涛.岩石失稳破坏的应变梯度模型[J].岩石力学与工程学报,1998,17(增):760-765.
[10] 潘一山,杨小彬.岩石变形破坏局部化的白光数字散斑相关方法研究[J].实验力学,2001,16(2):7-12.
[11] 潘一山,杨小彬.Studyondeformationlocalizationofrockbywhitelightdigitalspecklecorrelationmethod[J].岩土工程学报,2002,24(1):97-100.
[12] 王学滨,潘一山,马谨.FLAC3D在岩石变形局部化数值模拟中的应用[J].辽宁工程技术大学学报,2001,20(4):522-523.
[13] 王学滨,潘一山,丁秀丽,盛谦.平面应变状态下岩石剪切带网络数值模拟研究[J].岩土力学,2002,23(6):717-720.
[14] 潘一山,王学滨,马瑾.地震地质中应变局部化现象及剪切带网络数值模拟研究[A].杨桂通,黄筑平,梁乃刚,等.塑性力学与工程(徐秉业教授七十寿辰庆贺文集)[C].万国学术出版社,世界图书出版公司,2002.
[15] 郑宏,葛修润,李焯芬.脆塑性岩体的分析原理及其应用[J].岩石力学与工程学报,1997,16(2):8-21.
[16] VardoulakisIG,MuhlhausHB.Localrocksurfaceinstabilities[J].IntJ.RockMechMinSci,1984,23,137-144.
[17] BardetJP.Shear bandanalysisinidealizedgranularmaterial[J].JournalofEngineeringMechanics,ASCE,1992,118(2):397-415.
[18] GuC,AnandL.Granularmaterials:constitutiveequationsandstrainlocalization[J].JournaloftheMechanicsandPhysicsofSolids.2000,48,1701-1733.
[19] 李锡夔.非线性计算固体力学的若干问题[J].大连理工大学学报,1995,35(6):783-789.
[20] EllenK,EkkehardR,deBorstR.Ananisotropicgradientdamagemodelforquasi brittlematerials[J].ComputerMethodsinAppliedMechanicsandEngineering.2000,183:87-98.
[21] AskesH,PaminJ.Dispersionanalysisandelement freegalerkinsolutionsofsecond andfourth ordergradientenhanceddamagemodels[J].InternationalJournalforNumericalMethodsinEngineering,2000,49,811-832.
[22] ZhangHW,SchreflerBA.Gradient dependentplasticitymodelanddynamicstrainlocalizationanalysisofsaturatedandpartiallysaturatedporousmedia:one dimensionalmodel[J].EurJMechA Solids.2000,19,503-524.
[23] deBorstR.Gradient dependentplasticity:formulationandalgorithmicaspects[J].InternationalJournalforSolidsandStructures,1992,35:521-539.
[24] 黄克智,邱信明,姜汉卿.应变梯度理论的新进展(一)———偶应力理论和SG理论[J].机械强度,1999,23(2):81-87.
[25] PeerlingsRHJ,GeersMGD,deBorstR.Acriticalcomparisonofnon localandgradient enhancedsofteningcontinua[J].InternationalJournalforSolidsandStructures,2001,38:7723-7740.
[26] ShuLJ,deBorstR,MuhlhausHB.Wavepropagation,localizationanddispersioninagradientdependentmedium[J].IntJSolidStruct,1993,30:1153-1171.
[27] ShuLJ,deBorstR.Dispersivepropertiesofgradientdependentandrate dependentmedia[J].MechanicsofMaterials,1994,18:131-149.
[28] 潘一山,徐秉业,王明洋.岩石塑性应变梯度与Ⅱ类岩石变形行为研究[J].岩土工程学报,1999,21(4):472-474.
[29] 潘一山,袁旭东,章梦涛.岩石失稳破坏的应变梯度模型[J].岩石力学与工程学报,1998,17(增):760-765.
[30] 潘一山,魏建明.岩石材料应变软化尺寸效应的实验和理论研究[J].岩石力学与工程学报,2002,21(2):152-182.
[31] PanYishan,WangXuebin,LiZhonghua.Analysisofthestrainsofteningsizeeffectforrockspecimentsbasedonshearstraingradientplasticitytheory[J].InternationalJournalofRockMechanicsandMiningSciences,2002,39(6):801-805.
[32] 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):711-714.
[33] WangXuebin,SongWeiyuan,PanYishan.ClassⅡbehaviorofrockorconcretebaseduponshearstraingradientplastictheory[A].EditedbyZhaoGuogang.Proceedingsofthesecondinternationalsymposiumonminingtechnology[C].Beijing:SciencePress,2001,237-241.
[34] 王学滨,潘一山,杨小彬.?
[2] 丁国瑜,李永善.我国地震活动与地壳现代破裂网络[J].地质学报,1979,(5):22-34.
[3] 王绳祖.亚洲大陆岩石圈多层构造模型和塑性流动网络[J].地质学报,1993,67(1):1-18.
[4] 陶玮,洪汉净,刘培询.中国大陆及邻区强震活动主体地区形成的数值模拟[J].地震学报,2000,22:271-277.
[5] 许绍燮,沈佩文.北京周围地区地震的分布特点与地壳屈曲[J].地震学报,1980,2(2):153-168.
[6] 周硕愚,梅世蓉,施顺英,等.用地壳形变图象动力学研究震源演化复杂过程[J].地壳形变与地震,1997,(17):1-9.
[7] 郑捷,姚孝新,陈.岩石变形局部化的实验研究[J].地球物理学报,1982,26(6):554-562.
[8] 赵豫生,陈,王仁.岩石裂纹附近的变形局部化与破坏———激光全息干涉法的应用[J].地球物理学报,1988,31(3):294-304.
[9] 潘一山,袁旭东,章梦涛.岩石失稳破坏的应变梯度模型[J].岩石力学与工程学报,1998,17(增):760-765.
[10] 潘一山,杨小彬.岩石变形破坏局部化的白光数字散斑相关方法研究[J].实验力学,2001,16(2):7-12.
[11] 潘一山,杨小彬.Studyondeformationlocalizationofrockbywhitelightdigitalspecklecorrelationmethod[J].岩土工程学报,2002,24(1):97-100.
[12] 王学滨,潘一山,马谨.FLAC3D在岩石变形局部化数值模拟中的应用[J].辽宁工程技术大学学报,2001,20(4):522-523.
[13] 王学滨,潘一山,丁秀丽,盛谦.平面应变状态下岩石剪切带网络数值模拟研究[J].岩土力学,2002,23(6):717-720.
[14] 潘一山,王学滨,马瑾.地震地质中应变局部化现象及剪切带网络数值模拟研究[A].杨桂通,黄筑平,梁乃刚,等.塑性力学与工程(徐秉业教授七十寿辰庆贺文集)[C].万国学术出版社,世界图书出版公司,2002.
[15] 郑宏,葛修润,李焯芬.脆塑性岩体的分析原理及其应用[J].岩石力学与工程学报,1997,16(2):8-21.
[16] VardoulakisIG,MuhlhausHB.Localrocksurfaceinstabilities[J].IntJ.RockMechMinSci,1984,23,137-144.
[17] BardetJP.Shear bandanalysisinidealizedgranularmaterial[J].JournalofEngineeringMechanics,ASCE,1992,118(2):397-415.
[18] GuC,AnandL.Granularmaterials:constitutiveequationsandstrainlocalization[J].JournaloftheMechanicsandPhysicsofSolids.2000,48,1701-1733.
[19] 李锡夔.非线性计算固体力学的若干问题[J].大连理工大学学报,1995,35(6):783-789.
[20] EllenK,EkkehardR,deBorstR.Ananisotropicgradientdamagemodelforquasi brittlematerials[J].ComputerMethodsinAppliedMechanicsandEngineering.2000,183:87-98.
[21] AskesH,PaminJ.Dispersionanalysisandelement freegalerkinsolutionsofsecond andfourth ordergradientenhanceddamagemodels[J].InternationalJournalforNumericalMethodsinEngineering,2000,49,811-832.
[22] ZhangHW,SchreflerBA.Gradient dependentplasticitymodelanddynamicstrainlocalizationanalysisofsaturatedandpartiallysaturatedporousmedia:one dimensionalmodel[J].EurJMechA Solids.2000,19,503-524.
[23] deBorstR.Gradient dependentplasticity:formulationandalgorithmicaspects[J].InternationalJournalforSolidsandStructures,1992,35:521-539.
[24] 黄克智,邱信明,姜汉卿.应变梯度理论的新进展(一)———偶应力理论和SG理论[J].机械强度,1999,23(2):81-87.
[25] PeerlingsRHJ,GeersMGD,deBorstR.Acriticalcomparisonofnon localandgradient enhancedsofteningcontinua[J].InternationalJournalforSolidsandStructures,2001,38:7723-7740.
[26] ShuLJ,deBorstR,MuhlhausHB.Wavepropagation,localizationanddispersioninagradientdependentmedium[J].IntJSolidStruct,1993,30:1153-1171.
[27] ShuLJ,deBorstR.Dispersivepropertiesofgradientdependentandrate dependentmedia[J].MechanicsofMaterials,1994,18:131-149.
[28] 潘一山,徐秉业,王明洋.岩石塑性应变梯度与Ⅱ类岩石变形行为研究[J].岩土工程学报,1999,21(4):472-474.
[29] 潘一山,袁旭东,章梦涛.岩石失稳破坏的应变梯度模型[J].岩石力学与工程学报,1998,17(增):760-765.
[30] 潘一山,魏建明.岩石材料应变软化尺寸效应的实验和理论研究[J].岩石力学与工程学报,2002,21(2):152-182.
[31] PanYishan,WangXuebin,LiZhonghua.Analysisofthestrainsofteningsizeeffectforrockspecimentsbasedonshearstraingradientplasticitytheory[J].InternationalJournalofRockMechanicsandMiningSciences,2002,39(6):801-805.
[32] 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):711-714.
[33] WangXuebin,SongWeiyuan,PanYishan.ClassⅡbehaviorofrockorconcretebaseduponshearstraingradientplastictheory[A].EditedbyZhaoGuogang.Proceedingsofthesecondinternationalsymposiumonminingtechnology[C].Beijing:SciencePress,2001,237-241.
[34] 王学滨,潘一山,杨小彬.?
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