弹性半空间山体裂纹对弹性波的散射

Scattering of elastic waves by mountain cracks in elastic half space

利用间接边界元法(IBEM),求解了弹性半空间山体裂纹对弹性波的二维散射问题。以含裂纹的半圆山体为例,分析了不同频率弹性波入射下裂纹角度、位置、数量等因素对散射的影响规律,计算了山体表面及两侧地表的位移幅值。研究表明:裂纹的存在对山体表面位移有明显的缩放效应,随着频率的增大,裂纹角度的影响逐渐减小,裂纹数量的影响逐渐增大。P波垂直入射下,山腰处的放大效应最明显,与无裂纹山体相比,在3~5这一频段内山腰处水平位移峰值约放大2倍;SV波垂直入射下,山脚处变化最为明显,最大峰值达到1.8,比无裂纹山体增加近27%。

The indirect boundary element method(IBEM)was used to solve scattering of elastic waves by mountain cracks in elastic half space.Taking a semi-circular mountain with cracks as an example,effects of incident wave frequency,crack angle,crack location and crack number on plane elastic wave scattering were analyzed,anddisplacementamplitudes of the mountain surfaceand the surface on both sides were calculated.Results showed thatcracks have obviousscaling effect on mountain surface displacement;with increase in frequency,effects of crack angle decrease,while effects of crack number increase gradually;when P wave is vertically incident,the amplification effect is the most obvious at the mountainside;compared with the mountain without crack,the peak value of horizontal displacement at the mountainside in the frequency range of 3 to 5 is about 2 times largerthan that in case of the mountain without crack;when SV wave is vertically incident,change at the mountain foot is the most obvious,the maximum peak value reaches 1.8,nearly 27%higher than that in case of the mountain without crack.