爆炸应力波引起地表位移的数值分析

Numerical Analysis of Surface Displacements Caused by Blasting Stress Wave

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 sur- face, 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 haff-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.