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借助复变函数的保角映射方法将有限长度的空沟映射变换为单位圆,根据空沟四周完全自由的边界条件,运用波动函数展开法得到了空沟对SH波隔离的理论解答。引入位移比值(屏障后某点由入射和散射弹性波产生的总位移与入射弹性波单独产生的位移之比),计算了沟宽0.4 m、沟长分别为3.0 m、4.0 m、5.0 m和6.0 m共4条空沟的位移比值,通过比较发现:随着空沟长度的增加(由3.0 m增加到5.0 m),最佳隔振效果明显提高,区域明显增大;当空沟长度超过一定值(5.0 m)后,最佳隔振效果基本不变,而有效隔振区域由中间向两侧扩展。最后对比了空沟和单排空心管桩的隔振效果,结果表明:空沟的最佳隔振效果高于单排空心管桩,空沟的最佳隔振区域在屏障后靠近屏障的一定区域内,而单排空心管桩的最佳隔振区域在屏障后远离屏障的一定区域内。
Based on the conformal mapping method of complex functions, the finite-length empty-line map is transformed into a unit circle. According to the completely free boundary condition around the empty groove, the theoretical solution to the SH-wave isolation by the empty groove is obtained by the wave function expansion method. The displacement ratio (the ratio of the total displacement generated by incident and scattered elastic waves to the displacement generated by incident elastic waves at a certain point after the barrier) is introduced. The width of the groove is 0.4 m and the groove length is 3.0 m, 4.0 m, 5.0 m and The displacement ratio of four empty gullys is 6.0 m. The comparison shows that with the increase of the length of the gully (from 3.0 m to 5.0 m), the best vibration isolation effect obviously increases and the area increases obviously. When the gully length exceeds a certain value The value of (5.0 m), the best isolation effect is basically the same, while the effective isolation area from the middle to both sides of the expansion. Finally, the vibration isolation effect of the hollow and single-row hollow pipe piles is compared. The results show that the best vibration isolation effect of the empty channel is higher than that of the single-row hollow pipe pile. The best vibration isolation area of the empty channel is close to the barrier after the barrier Of the region, and the best single-row hollow pipe pile vibration isolation area in the barrier away from a certain area.