屈服矿柱渐进破坏及应力分布数值模拟
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摘要
采用拉格朗日元法,在矿柱端面上不存在水平方向摩擦力条件下,模拟了屈服矿柱的剪切带图案、渐进破坏特征、水平应力及垂直应力分布及演变。在弹性阶段,煤的本构关系为线弹性。峰值强度后煤的本构模型取为莫尔库仑剪破坏与拉破坏复合的应变软化模型。数值计算结果表明,矿柱具有渐进破坏特征。破坏首先以剪切带的形式发生在矿柱的4个角上。然后,矿柱两帮的剪切带逐渐向矿柱内部发展,形成两套剪切带网络,直到两套网络重叠,并进一步演化。倾斜的剪切带多次穿透矿柱。当矿柱处于峰值强度后,矿柱水平及垂直应力分布曲面已经变得凹凸不平。凹陷、凸起区分别对应剪切带中心及边缘。矿柱中部的水平应力较边缘大。因此,其边缘的强度较中心低。严格地讲,水平及垂直应力的分布不是单调的,呈现锯齿型。其原因是矿柱发生了条带状局部破坏。矿柱承载能力的不均匀性由矿柱水平应力的不均匀性所决定。
Shear strain localization,characteristics of progressive failure,distributions of horizontal and vertical stresses within yield pillars were modeled numerically by FLAC under the condition of smooth ends in horizontal direction.The failure criterion for coal was a composite Mohr-Coulomb criterion with tension cutoff,so linear elastic and strain-softening post-peak constitutive relations was adopted.Numerical simulation shows that failure of pillar in the form of shear bands is progressive from the lateral edges to the center.Shear bands are generated initially in the four corners of the pillar,and then propagate towards the center so that two sets of shear band networks near the lateral edges are formed.Finally,shear band networks overlap and further development is not prohibited.Inclined shear bands intersect the pillar from the top to the base.Surfaces of horizontal and vertical stresses are concavo-convex when the peak strength of pillar is reached.Concave and convex zones correspond to the center and the boundary of shear bands,respectively.Generally,horizontal stress in the center of the pillar is greater than that in the edges so that lower strength is reached in the edges.Strictly speaking,distributions of horizontal and vertical stresses are zigzag and not monotonous,which is due to the zonal shear failure inside the pillar.Non-uniformity of load-bearing capacity of pillar stems is controled by the non-uniformity of horizontal stress distribution.
Shear strain localization,characteristics of progressive failure,distributions of horizontal and vertical stresses within yield pillars were modeled numerically by FLAC under the condition of smooth ends in horizontal direction.The failure criterion for coal was a composite Mohr-Coulomb criterion with tension cutoff,so linear elastic and strain-softening post-peak constitutive relations was adopted.Numerical simulation shows that failure of pillar in the form of shear bands is progressive from the lateral edges to the center.Shear bands are generated initially in the four corners of the pillar,and then propagate towards the center so that two sets of shear band networks near the lateral edges are formed.Finally,shear band networks overlap and further development is not prohibited.Inclined shear bands intersect the pillar from the top to the base.Surfaces of horizontal and vertical stresses are concavo-convex when the peak strength of pillar is reached.Concave and convex zones correspond to the center and the boundary of shear bands,respectively.Generally,horizontal stress in the center of the pillar is greater than that in the edges so that lower strength is reached in the edges.Strictly speaking,distributions of horizontal and vertical stresses are zigzag and not monotonous,which is due to the zonal shear failure inside the pillar.Non-uniformity of load-bearing capacity of pillar stems is controled by the non-uniformity of horizontal stress distribution.
引文
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[2]唐春安,徐小荷.岩石破裂过程失稳的尖点突变模型[J].岩石力学与工程学报.1990,9(2):100-107.
[3]布雷迪BHG,布朗ET.地下采矿岩石力学[M].北京:煤炭工业出版社,1990.
[4]李长洪,蔡美峰,乔兰,等.岩石全应力-应变曲线与岩爆的关系[J].北京科技大学学报,1999,21(6):513-515.
[5]潘岳,张孝伍.狭窄煤柱岩爆的突变理论分析[J].岩石力学与工程学报,2004,11(5):1797-1803.
[6]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.
[7]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):101-105.
[8]王学滨,黄梅,赵扬锋,等.岩样失稳回跳与直剪试验机-岩样系统失稳回跳关系研究[J].岩石力学与工程学报,2004,23(3):379-382.
[9]Wang Xuebin,Yang Xiaobin,Zhang Zhihui,et al.Dynamicanalysis of fault rockburst based on gradient-dependentplasticity and energy criterion[J].Journal of University ofScience and Technology Beijing,2004,11(1):5-9.
[10]Wang Xuebin,Dai Shuhong,Hai Long.Quantitativecalculation of dissipated energy of fault rock burst based ongradient-dependent plasticity[J].Journal of University ofScience and Technology Beijing,2004,11(3):197-201.
[11]Chen Rui,Stimpson B.Simulation of deformation andfracturing in potash yield pillars,Vanscoy,Saskatchewan[J].Can.Geotech.J.,1997,34(2):283-292.
[12]Wang Xuebin.Analysis of progressive failure of pillar andinstability criterion based on gradient-dependent plasticity[J].J.Cent.South Univ.Technol.,2004,11(4):445-450.
[13]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.
[14]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.
[15]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.
[16]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.
[17]王学滨.平面应变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
[18]Wang Xuebin.Strain localization of rock failure and instabilitycriterion of rockburst[A].In:Wang Yajun et al.ed.Progress in Safety Science and Technology[C].Beijing:Science Press,2004,4:244-249.
[19]Wang Xuebin.Numerical simulation of influence of sheardilatancy on deformation characteristics of shear band-elasticbody system[J].J.Coal Sci.&Engrg(China),2004,10(2):1-6.
[20]崔希民,缪协兴.条带煤柱中的应力分析与沉陷曲线形态研究[J].中国矿业大学学报,2000,29(4):392-395.
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