دانلود رایگان مقاله انگلیسی ماتریس های سفتی برای لایه های خاک ناهمسانگرد و مایع با کاربرد در دینامیک خاک - الزویر 2018

ABSTRACT

In this study, we introduce and discuss features and improvements of the well-established stiffness matrix method that is used in simulation of wave propagation in layered media. More specifically, we present stiffness matrices for an acoustic layer and a vertically transverse isotropic (VTI) viscoelastic soil layer. Combining these stiffness matrices enables a straightforward technique for modeling of acousto-elastic wave propagation in layered infinite media. In addition, we propose a technique to simulate discontinuity seismic sources, which was not used earlier in the context of the stiffness matrix method. Finally, we propose a framework to derive a key parameter of the absorbing boundary domain technique Perfectly Matched Layer (PML). Numerical examples are presented in order to help understanding the features and improvements discussed in the study from the fields of geophysics and soil dynamics. It is believed that the features and improvements discussed herein will make the application of the stiffness matrix method even wider and more flexible.

Summary and conclusion

In this study, we introduce and discuss features and improvements of the stiffness matrix method developed in [1] that may enhance the applicability and flexibility of the method. Several numerical examples are provided to support the improvements and features. First, we introduce the acoustic layer stiffness matrices by means of three different formulations in terms of vertical displacement, velocity potential and nodal pressure, respectively. The latter two are easy for implementing air-gun source, while the first one is straightforward to apply a vertical disk load on seabed or within the water layer. Secondly, the soil stiffness matrices for the vertically transverse isotropic (VTI) layer are derived for both P-SV and SH wave modes. The structure of the VTI soil layer stiffness matrices is constructed in the same fashion as for the isotropic soil layer and such that the stiffness matrix for the isotropic case can be recovered by setting the anisotropy factors equal to 1. Thirdly, in order to simulate wave motions subjected to injected (air) volume or dislocation/slip at the interface of two layers, we formulate a technique where the displacement discontinuity can be implemented. Finally, by means of the continuum stiffness matrices we derive the key parameter of PML (thickness, hPML) that can be used in discrete numerical approaches (e.g. FEM, FDM, TLM). We also discuss how the continuum PML can be useful for the contour integration over the complex wavenumber domain, eliminating the need for the branch-cut integral, in the context of the wavenumber integration from the wavenumber to spatial domain.