饱和多孔介质表面透水性对表面波传播特性影响薄层分析法

Effect of surface permeability of saturated porous media on behaviour of surface waves using thin layer method

饱和半无限体表面透水性会影响表面波(瑞利波和斯通利波)存在及其传播特性。在表面透水情况下,只有瑞利波存在,而在不透水情况,不仅有瑞利波而且还有斯通利波。表面波在工程勘探及声波测试中扮演很重要角色,因此,有必要研究表面透水性对表面波传播特性的影响。采用薄层法,将表面波频率方程根的搜索问题转换成求特征值问题。根据表面波沿深度衰减特性,从一组计算的特征值及特征向量中筛选出与表面波对应特征值、特征向量,由特征值得到表面波频率特性(频散和衰减特性),由特征向量得到孔隙压力、骨架位移随深度变化,进而分析在表面不透水情况下瑞利波和斯通利波影响深度及程度。

Surface permeability of saturated porous half spaces can influence the presence of surface waves, i.e. Rayleigh and/or Stoneley waves, as well as behaviour of these waves. Rayleigh waves exist in the porous half space with permeable surface, while there are both Rayleigh waves and Stoneley waves for the case of the impermeable surface. Rayleigh and Stoneley waves play important roles in engineering prospecting and acoustic testing, respectively. Therefore, it is necessary to investigate effects of the surface permeability on behaviours of these waves. In this paper, the root searching algorithm of the frequency equations of surface waves is transformed into the eigenvalue problem using thin layer method. According to the behaviour of attenuation of the surface waves along depth direction, the eigenvalues and eigenvectors corresponding to the surface waves can be sifted from the calculated ones. The frequency behaviour i.e. dispersion and attenuation can be calculated from the sifted eigenvalues. The variations of the fluid pressure and skeleton displacements with the depth can be obtained from the corresponding eigenvectors. The influence depth and extent of Rayleigh and Stoneley waves are then analyzed based on those variations for the case of the impermeable surface.