爆炸应力波引起地表位移的数值分析
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摘要
将爆孔围岩粉碎区简化为一个圆形孔洞,将半空间表面假定一个半径为无穷大的圆弧,则爆炸应力在粉碎区表面产生向外传播的P波(压缩波),在半空间表面产生散射,而散射波在粉碎区上再次产生散射,如此多次散射,进而引起半空间表面的位移。根据粉碎区周边应力平衡和半空间表面完全自由的边界条件,求得了待定散射系数,并进一步得到了半空间表面的位移的理论解答。最后通过数值计算分析了不同爆炸应力峰值和爆炸源埋深对地表位移的影响,结果表明:(1)在爆炸源埋深和爆孔围岩粉碎区大小等条件都相同的情况下,随着爆炸应力峰值的增大,地表振动位移明显增大,增大的数值基本上与爆炸应力峰值成线性比例;(2)在爆炸应力峰值和爆孔围岩粉碎区大小等条件都相同的情况下,随着爆炸源埋深的增大,地表处水平位移和竖向位移明显减小,但减小的幅度由快变缓。
Crush zone surrounding the blasting hole is simplified as a circular cavity and the half-space surface as an arc with infinite radius,only P waves(compression wave) are assumed to be generated at the crush zone surface,and these P waves propagate outside and would be scattered by the half-space surface and these scattered again by the crush zone surface,and these obvious half-space displacements are generated by these multi-scattering P waves.The stresses at the crush zone surface are assumed as continuous and the half-space surface is free,then the scattering coefficients are determined based on stress conditions,and the theoretical solutions of the half-space surface displacements are obtained.Finally,the influences of different burying depth of blasting source and explosion peak stress on the surface displacement are analyzed,and the results show that:(1) when burying depth of blasting source and size of crush zone keep the same,the half-space surface displacements increase obviously with the blasting peak stress and they have the linear relationship;(2) when blasting peak stress and size of crush zone keep the same,the half-space surface displacements decrease obviously with the burying depth of blasting source,but decrease slowly when burying depth of blasting source exceeds some value.
Crush zone surrounding the blasting hole is simplified as a circular cavity and the half-space surface as an arc with infinite radius,only P waves(compression wave) are assumed to be generated at the crush zone surface,and these P waves propagate outside and would be scattered by the half-space surface and these scattered again by the crush zone surface,and these obvious half-space displacements are generated by these multi-scattering P waves.The stresses at the crush zone surface are assumed as continuous and the half-space surface is free,then the scattering coefficients are determined based on stress conditions,and the theoretical solutions of the half-space surface displacements are obtained.Finally,the influences of different burying depth of blasting source and explosion peak stress on the surface displacement are analyzed,and the results show that:(1) when burying depth of blasting source and size of crush zone keep the same,the half-space surface displacements increase obviously with the blasting peak stress and they have the linear relationship;(2) when blasting peak stress and size of crush zone keep the same,the half-space surface displacements decrease obviously with the burying depth of blasting source,but decrease slowly when burying depth of blasting source exceeds some value.
引文
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[12]夏致晰,缪协兴,茅献彪.爆炸应力波对深埋巷道的作用效应分析[J].河南科学,2004,22(1):88-91.(Xia Zhixi,Miao Xiexing,Mao Xianbiao.Analysis of ground shock wave on deep buried tunnels[J].Henan Science,2004,22(1):88-91.(in Chinese))
[13]Donze F V,Bouchez J,Magnier S A.Modeling frac-tures in rock blasting[J].International Journal of Rock Mechanics and Mining Science,1997,34(8):1152-1163.
[2]李忠献,田力.地下爆炸波作用下基底滑移隔震建筑-土-隧道相互作用的动力分析[J].工程力学,2004,21(6):56-64.(Li Xianzhong,Tian Li.Dynamic interaction analysis of sliding base-isolated building-soil-tunnel subjected to underground explsosion wave[J].Engineering Mechanics,2004,21(6):56-64.(in Chinese))
[3]Feldgun V R,Kochetkov A V,Karinski Y S,et al.Internal blast loading in a buried lined tunnel[J].International Journal of Impact Engineering,2008,35(3):172-183.
[4]高广运,高盟,冯世进.无限弹性介质中隧道内爆炸动力响应的解析解[J].西北地震学报,2008,30(2):124-127.(Gao Guangyun,Gao Meng,Feng Shijin.Analytical solution for the dynamic response of tunnel to an internal explosion in infinite elastic medium[J].Northwestern Seismological Journal,2008,30(2):124-127.(in Chinese))
[5]浦锡锋,张海波,田宙,等.岩石中强爆炸动力学过程数值模拟[J].岩石力学与工程学报,2005,24(增1):5 007-5 012.(Pu Xifeng,Zhang haibo,Tian zhou,et al.Numerical simulation of underground explosion in granite[J].Chinese Journal of Rock Mechanicsand Engineering,2005,24(Supp.1):5007-5012.(in Chinese))
[6]Davis C A,Lee V W,Bardet J P.Transverse response of underground cavities and pipes to incident SV waves[J].Earthquake Engineering and Structural Dynamics,2001,30:383-410.
[7]Lee V W,Karl J.On deformation near a circular under-ground cavity subjected to incident plane P waves[J].European Journal of Earthquake Engineering,1993,7(1):29-36.
[8]Lee V W,Karl J.Diffraction of SV waves by under-ground,circular,cylindrical cavities[J].Soil Dynam-ics and Earthquake Engineering,1991,11:445-456.
[9]Abramowitz M,Stegun,I A.Handbook of mathematical Functions with formulas,graphs,and mathematical ta-bles[M].Dover Publications,Inc.New York,1970.
[10]Senseny P E,Simons D A.Comparison of calculational approaches for structural deformation in jointed rock[J].International Journal of Numerical Analysis Meth-ods in Geomechanics,1994,18(2):327-344.
[11]Low H Y,Hao H.Reliability analysis of direct shear and flexural failure modes of RC slabs under explosive loading[J].Engineering Structures,2002,24(2):189-198.
[12]夏致晰,缪协兴,茅献彪.爆炸应力波对深埋巷道的作用效应分析[J].河南科学,2004,22(1):88-91.(Xia Zhixi,Miao Xiexing,Mao Xianbiao.Analysis of ground shock wave on deep buried tunnels[J].Henan Science,2004,22(1):88-91.(in Chinese))
[13]Donze F V,Bouchez J,Magnier S A.Modeling frac-tures in rock blasting[J].International Journal of Rock Mechanics and Mining Science,1997,34(8):1152-1163.
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