Transient wave propagation in a multi-layered soil with a fluid surface layer: 1D analytical/semi-analytical solutions
Transient wave propagation in a multi-layered soil with a fluid surface layer: 1D analytical/semi-analytical solutions
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具有流体表面层的多层土壤中的瞬态波传播：一维解析/半解析解
DOI：
10.1002/nag.3253
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发表时间：
2021
影响因子：
4
通讯作者：
Ling Daosheng
中科院分区：
文献类型：
--
作者：
Shan Zhendong;Jing Liping;Zhang Lei;Xie Zhinan;Ling Daosheng
本文研究了一维瞬态波在具有流体表层的饱和多层土壤中的传播。基于毕奥理论，采用特征函数展开法、传递矩阵法、状态空间法和精细时步积分法得到了解析/半解析解。对于一种特殊情况（大的动态渗透系数），我们得到了一个解析解。对于一般情况（任意动渗透系数），由于阻尼项的影响，我们开发了一个半解析解，可用于评估动渗透系数较小的沉积物。新推导的解决方案进行了验证与解决方案所获得的拉普拉斯变换和数值逆拉普拉斯变换，这也是这里。新推导的解在时域中以级数形式给出，并且是直接和明确的，使得解易于实现。通过数值算例，分析了动流体渗透系数对模型瞬态响应的影响，这在海洋地震和海洋声学应用中具有重要意义。
This paper studies one‐dimensional transient wave propagation in a saturated multi‐layered soil with a fluid surface layer. Based on Biot theory, the eigenfunction expansion method, the transfer matrix method, the state‐space method, and the precise time step integration method are employed to develop analytical/semi‐analytical solutions. For a special case (large dynamic permeability coefficient), we obtain an analytical solution. For a general case (arbitrary dynamic permeability coefficient), due to the influence of the damping term, we develop a semi‐analytical solution that can be used to evaluate sediment with small dynamic permeability coefficients. The newly derived solutions are verified with solutions obtained by the Laplace transformation and numerical inverse Laplace transformation, which are also presented here. The newly derived solutions are presented in series form in the time domain and are straightforward and explicit so that the solutions are easy to implement. Through numerical examples, we analyse the influences of the dynamic fluid permeability coefficients on the transient response of the model, which is important in marine seismic and ocean acoustics applications.