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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。
The blasting area of surrounding rock is reduced to a circular hole, the surface of the half space is assumed to be an arc of infinite radius, then the explosion stress produces P wave (compressional wave) propagating outwards on the surface of the crushing zone, Resulting in scattering, and scattered waves in the shredding area again produce scattering, so many scattering, and then cause half-space surface displacement. According to the boundary conditions around the crushing zone and the complete freedom of the half-space surface, the to-be-determined scattering coefficient was obtained and the theoretical solution of the displacement of the half-space surface was obtained. Finally, the influence of different explosion stress peaks and explosion depth on surface displacement is analyzed by numerical calculation. The results show that: (1) With the depth of the explosion source and the size of the surrounding rock mass detonating, Explosion stress peak increases, the surface vibration displacement increases significantly, increasing the value of the peak explosive stress is basically a linear ratio; (2) in the explosive stress peak and blasting rock surrounding the size of the crushing area are the same conditions With the increase of the depth of the explosion source, the horizontal and vertical displacements of the ground surface obviously decrease, but the decreasing amplitude decreases from fast to slow.