层状地基中表面波有效相速度

Effective phase velocity of surface waves in layered soil media

在表面波互谱分析方法中,考虑表面波高阶模态及振源对表面波传播影响对提高土层剖面参数计算精度是很重要的。为了研究高阶模态及振源对表面波有效相速度影响,基于薄层刚度矩阵方法,给出了弹性层状地基中表面波水平向及竖直向有效相速度一般解析表达式以及远场渐近表达式,并从能量的角度分析高频、低频有效相速度发展趋势。几种典型层状地基中有效相速度的计算表明:在剪切波速随深度递增的分层中,远场有效相速度随频率变化曲线趋近基阶模态频散曲线;在剪切波速随深度无规律变化分层中,高阶模态影响较大,水平向与竖直向有效相速度有较大的不同;在远场,高频有效相速度趋近表层介质瑞利波相速度。结果显示在高模态及振源影响下表面波有效相速度不仅与频率有关,而且与传播距离有关。

In spectral analysis of surface waves, it is very important to consider the effects of higher modes and the source on propagation of surface waves so as to improve the accuracy of calculated soil profile parameters. In order to investigate the effects of higher modes and the source on the effective velocity of surface waves, the analytical expressions of effective phase velocity of horizontal and vertical vibrations as well as the approximate expressions in the far field are derived for horizontally layered elastic media by the thin layer stiffness matrix method. The tendency of the effective phase velocity at both low and high frequencies is analyzed by the rates of energy transmission through layers. Variations of the effective phase velocity with frequency at different positions are obtained for three typical layered systems. The results show that for profiles with shear velocity increasing with depth, the curve of the effective phase velocity versus frequency in the far field approaches to the dispersion of the fundamental mode; for profiles with shear velocity varying irregularly with depth, higher modes have a strong influence on the propagation of surface waves and the effective phase velocities of horizontal and vertical motions are quite different; the effective phase velocities at high frequencies in the far field are approximate to the Rayleigh wave velocity of the first layer. The results indicate that influenced by higher modes and the source, the effective phase velocity is related to frequency as well as the distance from the source.