单轴拉伸岩样破坏过程及尺寸效应数值模拟
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摘要
由于从实验及理论角度研究岩样单轴拉伸条件下的破坏全过程及尺寸效应难度都很大。因此采用拉格朗日元法来研究这些问题。在峰值强度之前后,岩石材料的本构模型分别取为线弹性及拉破坏线性应变软化模型。为了使拉伸塑性区不出现在试样的端部,在试样的两侧面中部预制了2个凹槽。数值模拟结果表明,全程拉应力-拉应变曲线分为峰前和峰后阶段。在接近峰值的峰前阶段,由于两凹槽附近具有明显的拉应力集中现象,拉伸塑性区最先出现在两凹槽附近。随着轴向拉应变的增加,发生拉伸破坏的单元的数目增加,新发生拉伸破坏的单元越来越接近试样的中心,直到两块拉伸塑性区在应变软化阶段贯通。两凹槽连线上各单元拉应力的分布呈现3个阶段,"澡盆型"("U 型")阶段,"双峰型"("M 型")阶段及"单峰型"("П型")阶段。"澡盆型"阶段对应于全程拉应力-拉应变曲线的弹性阶段。"双峰型"阶段及"单峰型"阶段对应于全程拉应力-拉应变曲线的非弹性阶段(包括峰值强度之前的一小段,即应变硬化阶段及峰后的应变软化阶段)。增加试样高度及降低试样宽度,拉应力-拉应变曲线的软化段变得越来越陡峭,因而试样越容易发生失稳破坏。由于试样宽度较大时,试样内部的单元并非处于单向拉应力状态,因此,增加试样宽度,全程拉应力-拉应变曲线的峰值强度增加。当试样宽度较小时,从出现塑性区,到塑性区贯通所需要的时间步较小,或应变范围较窄。这说明试样的脆性较强,前兆不明显。前兆不明显的脆性破坏对应常见的是洞室岩爆、冲击地压及地震等灾害。
Due to the fact that there is a great deal of experimental and analytical difficulty in investigating the failure process and the size effect of rock specimen in uniaxial tension,in the present paper these problems are modeled numerically by FLAC.In elastic and strain-softening stages,the adopted constitutive relations of rock are linear elastic and linear strain-softening due to tensile failure, respectively.To ensure that elements subjected to tensile failure are localized into a narrow band within the specimen,two null elements at two edges of specimen are prescribed to model two notches.It is found from numerical results that the complete tensile stress-tensile strain curve exhibits pre-peak and post-peak branches.Prior to the peak stress,tensile stress concentration appears near the two notches so that two elements close to the two notches due to tension yield.The number of yielded elements is increased with axial tensile strain and the new plastic elements are even closer to the center of specimen until a horizontal and longer plastic zone is formed.Tensile stress distribution undergoes three distinct stages: upward concave stage,stage of downward concavity with two peaks and stage of downward concavity with one peak.The first stage corresponds to the elastic stage of complete stress-strain curve; however,the latter two stages correspond to the inelastic stage including strain-hardening and strain-softening stages.Softening branch of complete stress-strain curve becomes steeper so that the instability of rock specimen easily occurs as the height of specimen is increased or the width of specimen is decreased.Peak stress of complete stress-strain curve increases with the width of specimen, which is due to the fact that the stress state within the specimen is not a simple uniaxial state of stress for wider specimen.For thinner specimen,the needed time steps form the initial formation of yielded elements to the full development of a pfastic zone are less than those for wider specimen.This reflects that the precursor for thinner specimen is less apparent.Brittle failure without obvious precursor is concerned with seriously natural hazards,such as rockburst and earthquake.
Due to the fact that there is a great deal of experimental and analytical difficulty in investigating the failure process and the size effect of rock specimen in uniaxial tension,in the present paper these problems are modeled numerically by FLAC.In elastic and strain-softening stages,the adopted constitutive relations of rock are linear elastic and linear strain-softening due to tensile failure, respectively.To ensure that elements subjected to tensile failure are localized into a narrow band within the specimen,two null elements at two edges of specimen are prescribed to model two notches.It is found from numerical results that the complete tensile stress-tensile strain curve exhibits pre-peak and post-peak branches.Prior to the peak stress,tensile stress concentration appears near the two notches so that two elements close to the two notches due to tension yield.The number of yielded elements is increased with axial tensile strain and the new plastic elements are even closer to the center of specimen until a horizontal and longer plastic zone is formed.Tensile stress distribution undergoes three distinct stages: upward concave stage,stage of downward concavity with two peaks and stage of downward concavity with one peak.The first stage corresponds to the elastic stage of complete stress-strain curve; however,the latter two stages correspond to the inelastic stage including strain-hardening and strain-softening stages.Softening branch of complete stress-strain curve becomes steeper so that the instability of rock specimen easily occurs as the height of specimen is increased or the width of specimen is decreased.Peak stress of complete stress-strain curve increases with the width of specimen, which is due to the fact that the stress state within the specimen is not a simple uniaxial state of stress for wider specimen.For thinner specimen,the needed time steps form the initial formation of yielded elements to the full development of a pfastic zone are less than those for wider specimen.This reflects that the precursor for thinner specimen is less apparent.Brittle failure without obvious precursor is concerned with seriously natural hazards,such as rockburst and earthquake.
引文
[1] 齐庆新.煤的直接单轴拉伸特性的试验研究[J].煤矿开采,2001,(4) :15-18．
[2] 冯涛,潘长良.洞室岩爆机理的层裂屈曲模型[J].中国有色金属学报,2000,10(2) :287-290．
[3] 徐林生.卸荷状态下岩爆岩石力学试验[J].重庆交通学院学报,2003,22(1) :1-4．
[4] 潘长良,唐礼忠,王文星,等.深井硬岩矿山岩爆灾害防治研究[J].湘潭矿业学院学报,2003,18(4) :6-10．
[5] 周小平,张永兴,哈秋舱,等.单轴拉伸条件下细观非均匀性岩石变形局部化分析及其应力.应变全过程研究[J].岩石力学与工程学报,2004,23(1) :1-6．
[6] 柳赋铮.拉伸和拉剪状态下岩石力学性质的研究[J].长江科学院院报,1996,13(3) :35-39．
[7] 金丰年,钱七虎.岩石的单轴拉伸及其本构模型[J].岩土工程学报,1998,20(6) :5-8．
[8] 喻勇,张宗贤,俞洁,等.岩石直接拉伸破坏中的能量耗散及损伤特征[J].岩石力学与工程学报,1998,17(4) :386-392．
[9] 刘西拉,温斌.混凝土单轴拉伸的应变软化行为及描述[J].工程力学,1998,(增):8-18．
[10] Okubo S,Fukui K.Complete stress-strain curves for various rock types in uniaxial tension [J].International Journal of Rock Mechanics and Mining Sciences,1996, 33:549-556．
[11] LI Qing-bin,Ansari F.High-strength concrete in uniaxial tension[J].ACI Materials Journal,2000,97(1) :49-57．
[12] Jansen D C,Shah S P,Rossow E C.Stress-strain results of oncrete from circumferential strain feedback control testing[J].ACI Material Journal,1995,(7,8) :419-428．
[13] Ansari F.Stress-strain response of microcracked concrete in direct tension[J].ACI Material Journal,1987,(9-10) :481-490．
[14] Ba(?)ant Z P,Xiang Y.Size effect in compression fracture:splitting crack band propagation[J].Journal of Engineering Mechanics,ASCE,1997,123(2) :162-172．
[15] Ba(?)ant Z P,Desmorat R.Size effect in fiber or bar pullout with interface softening slip[J].Journal of Engineering Mechanics,1994,120(9) :1945-1962．
[16] de Borst R,Muhlhaus H B,Gradient-dependent plasticity:formulation and algorithmic aspects[J].International Journal for Numerical Methods in Engineering,1992, 35(3) :521-539．
[17] Ba(?)ant Z P,Tabbara M R,Kazemi T et al.Random particle model for fracture of aggregate of fiber composites[J].Journal of Engineering Mechanics,ASCE,1990,116(8) :1686-1705．
[18] Vervuurt A,Schlangen E,Van Mier J M G.Tensile cracking in concrete and sandston:part 1:basic instruments[J].Materials and Structures,1996,29:9-18．
[19] Tang C A,Wang S H,Tham L G,et al.Numerical approach to strength characterization of rock under direct uniaxial tension[A].Second International Symposium on New Development in Rock Mechanics and Rock Engineering[C].Lin Yunmei et al.ed.New Jersey:Rinton Press,2002． 251-258．
[20] 王学滨,潘一山,丁秀丽,等.平面应变岩样局部化变形场数值模拟研究[J].岩石力学与工程学报,2003,22(4) :521-524．
[21] 王学滨,潘一山,盛谦,等.岩石试件端面效应的变形局部化数值模拟研究[J].工程地质学报,2002,10(3) :233-235．
[22] 王学滨,潘一山,盛谦,等.动力应变局部化传播及尺寸效应数值模拟[J].计算力学学报,2002,19(4) :500-503．
[23] 王学滨,潘一山,丁秀丽,等.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．
[24] 王学滨,潘一山,丁秀丽,等.孔隙流体对岩体变形局部化的影响及数值模拟研究[J].地质力学学报,2001,7(2) :139-143．
[25] 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．
[26] 王学滨,李毅.平面应变含缺陷岩样变形破坏全过程数值模拟[J].中国矿业大学学报,2005,34(2) :189-203,217．
[27] 王学滨.平面应变压缩岩样侧向变形特征数值模拟[J].岩土工程学报,2005,27(5) :525-530．
[28] 王学滨,杨梅,潘一山.井眼变形局部化剪切带数值模拟研究[J].钻采工艺,2002,25(2) :17-19．
[29] 王学滨,赵扬锋,代树红,等.地震块体模型的共轭剪切破裂带数值模拟[J].防灾减灾工程学报,2004,24(2) :119-125．
[30] 王学滨.地震前兆特征与岩样剪切应变率异常数值模拟[J].大地测量与地球动力学,2005,25(1) :102-107,122
[31] WANG Xue bin.Strain localization of rock failure and instability criterion of rockburst[A]..Progress in Safety Science and Technology(Vol Ⅳ)[C].Wang Yajun ,et al.ed.Beijing:Science Press,2004． 244-249．
[32] WANG Xue bin.Numerical simulation of influence of shear dilataney on deformation characteristics of shear band-elastic body system[J].Journal of Coal Science & Engineering (China),2004,10(2) :1-6．
[33] 王学滨.三维岩样单轴压缩端面效应及破坏数值模拟[J].四川大学学报(工程科学版),2005,37(2) :28-33．
[34] Pan Yishan,Wang Xuebin,Li Zhonghua.Analysis of the strain softening size effect for rock specimens based on shear strain gradient plasticity theory[J].International Journal of Rock Mechanics and Mining Sciences,2002, 39(6) :801-805．
[35] 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．
[36] 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．
[37] WANG Xue bin,Pan Yishan.Size effect and snap back based on conservation of energy and gradient-dependent plasticity[A].Second International Symposium on New Development in Rock Mechanics and Rock Engineering[C].Lin Yunmei et al.ed .New Jersey:Rinton Press,2002． 89-92．
[38] 李先炜.岩块力学性质[M].北京:煤炭工业出版社,1983．
[39] 杨圣奇,徐卫亚.岩石尺寸效应及其机理研究[A].岩土力学前,2004[C]任青文主编.南京河海大学出版社,2004． 179-193．
[2] 冯涛,潘长良.洞室岩爆机理的层裂屈曲模型[J].中国有色金属学报,2000,10(2) :287-290．
[3] 徐林生.卸荷状态下岩爆岩石力学试验[J].重庆交通学院学报,2003,22(1) :1-4．
[4] 潘长良,唐礼忠,王文星,等.深井硬岩矿山岩爆灾害防治研究[J].湘潭矿业学院学报,2003,18(4) :6-10．
[5] 周小平,张永兴,哈秋舱,等.单轴拉伸条件下细观非均匀性岩石变形局部化分析及其应力.应变全过程研究[J].岩石力学与工程学报,2004,23(1) :1-6．
[6] 柳赋铮.拉伸和拉剪状态下岩石力学性质的研究[J].长江科学院院报,1996,13(3) :35-39．
[7] 金丰年,钱七虎.岩石的单轴拉伸及其本构模型[J].岩土工程学报,1998,20(6) :5-8．
[8] 喻勇,张宗贤,俞洁,等.岩石直接拉伸破坏中的能量耗散及损伤特征[J].岩石力学与工程学报,1998,17(4) :386-392．
[9] 刘西拉,温斌.混凝土单轴拉伸的应变软化行为及描述[J].工程力学,1998,(增):8-18．
[10] Okubo S,Fukui K.Complete stress-strain curves for various rock types in uniaxial tension [J].International Journal of Rock Mechanics and Mining Sciences,1996, 33:549-556．
[11] LI Qing-bin,Ansari F.High-strength concrete in uniaxial tension[J].ACI Materials Journal,2000,97(1) :49-57．
[12] Jansen D C,Shah S P,Rossow E C.Stress-strain results of oncrete from circumferential strain feedback control testing[J].ACI Material Journal,1995,(7,8) :419-428．
[13] Ansari F.Stress-strain response of microcracked concrete in direct tension[J].ACI Material Journal,1987,(9-10) :481-490．
[14] Ba(?)ant Z P,Xiang Y.Size effect in compression fracture:splitting crack band propagation[J].Journal of Engineering Mechanics,ASCE,1997,123(2) :162-172．
[15] Ba(?)ant Z P,Desmorat R.Size effect in fiber or bar pullout with interface softening slip[J].Journal of Engineering Mechanics,1994,120(9) :1945-1962．
[16] de Borst R,Muhlhaus H B,Gradient-dependent plasticity:formulation and algorithmic aspects[J].International Journal for Numerical Methods in Engineering,1992, 35(3) :521-539．
[17] Ba(?)ant Z P,Tabbara M R,Kazemi T et al.Random particle model for fracture of aggregate of fiber composites[J].Journal of Engineering Mechanics,ASCE,1990,116(8) :1686-1705．
[18] Vervuurt A,Schlangen E,Van Mier J M G.Tensile cracking in concrete and sandston:part 1:basic instruments[J].Materials and Structures,1996,29:9-18．
[19] Tang C A,Wang S H,Tham L G,et al.Numerical approach to strength characterization of rock under direct uniaxial tension[A].Second International Symposium on New Development in Rock Mechanics and Rock Engineering[C].Lin Yunmei et al.ed.New Jersey:Rinton Press,2002． 251-258．
[20] 王学滨,潘一山,丁秀丽,等.平面应变岩样局部化变形场数值模拟研究[J].岩石力学与工程学报,2003,22(4) :521-524．
[21] 王学滨,潘一山,盛谦,等.岩石试件端面效应的变形局部化数值模拟研究[J].工程地质学报,2002,10(3) :233-235．
[22] 王学滨,潘一山,盛谦,等.动力应变局部化传播及尺寸效应数值模拟[J].计算力学学报,2002,19(4) :500-503．
[23] 王学滨,潘一山,丁秀丽,等.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．
[24] 王学滨,潘一山,丁秀丽,等.孔隙流体对岩体变形局部化的影响及数值模拟研究[J].地质力学学报,2001,7(2) :139-143．
[25] 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．
[26] 王学滨,李毅.平面应变含缺陷岩样变形破坏全过程数值模拟[J].中国矿业大学学报,2005,34(2) :189-203,217．
[27] 王学滨.平面应变压缩岩样侧向变形特征数值模拟[J].岩土工程学报,2005,27(5) :525-530．
[28] 王学滨,杨梅,潘一山.井眼变形局部化剪切带数值模拟研究[J].钻采工艺,2002,25(2) :17-19．
[29] 王学滨,赵扬锋,代树红,等.地震块体模型的共轭剪切破裂带数值模拟[J].防灾减灾工程学报,2004,24(2) :119-125．
[30] 王学滨.地震前兆特征与岩样剪切应变率异常数值模拟[J].大地测量与地球动力学,2005,25(1) :102-107,122
[31] WANG Xue bin.Strain localization of rock failure and instability criterion of rockburst[A]..Progress in Safety Science and Technology(Vol Ⅳ)[C].Wang Yajun ,et al.ed.Beijing:Science Press,2004． 244-249．
[32] WANG Xue bin.Numerical simulation of influence of shear dilataney on deformation characteristics of shear band-elastic body system[J].Journal of Coal Science & Engineering (China),2004,10(2) :1-6．
[33] 王学滨.三维岩样单轴压缩端面效应及破坏数值模拟[J].四川大学学报(工程科学版),2005,37(2) :28-33．
[34] Pan Yishan,Wang Xuebin,Li Zhonghua.Analysis of the strain softening size effect for rock specimens based on shear strain gradient plasticity theory[J].International Journal of Rock Mechanics and Mining Sciences,2002, 39(6) :801-805．
[35] 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．
[36] 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．
[37] WANG Xue bin,Pan Yishan.Size effect and snap back based on conservation of energy and gradient-dependent plasticity[A].Second International Symposium on New Development in Rock Mechanics and Rock Engineering[C].Lin Yunmei et al.ed .New Jersey:Rinton Press,2002． 89-92．
[38] 李先炜.岩块力学性质[M].北京:煤炭工业出版社,1983．
[39] 杨圣奇,徐卫亚.岩石尺寸效应及其机理研究[A].岩土力学前,2004[C]任青文主编.南京河海大学出版社,2004． 179-193．
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