Soil Structure Interaction in Nonlinear Soil

A two-dimensional (2-D) model of a building supported by a semi-circular flexible foundation embedded in nonlinear soil is analyzed. The building, the foundation, and the soil have different physical properties. The model is excited by a half-sine SH wave pulse, which travels toward the foundation. The results show that the spatial distribution of permanent, nonlinear strain in the soil depends upon the incident angle, the amplitude, and the duration of the pulse. If the wave has a large amplitude and a short duration, a nonlinear zone in the soil appears immediately after the reflection from the half-space and is located close to the free surface. This results from interference of the reflected pulse from the free surface and the incoming part of the pulse that still has not reached the free surface. When the wave reaches the foundation, it is divided on two parts—the first part is reflected, and the second part enters the foundation. Further, there is separation of this second part at the foundation-building contact. One part is reflected back, and one part enters the building. After each contact of the part of the wave that enters the building with the foundation-building contact, one part of the wave energy is released back into the soil. This process continues until all of the energy in the building is released back into the soil. The work needed for the development of nonlinear strains spends part of the input wave energy, and thus a smaller amount of energy is available for exciting the building

Dispersion Properties of Explicit Finite Element Methods for Wave Propagation Modelling on Tetrahedral Meshes

We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax–Wendroff time integration scheme. The dispersion properties are obtained semi-analytically using standard Fourier analysis. Based on the dispersion analysis, we give an indication of which method is the most efficient for a given accuracy, how many elements per wavelength are required for a given accuracy, and how sensitive the accuracy of the method is to poorly shaped elements.Applied Geophysics and Petrophysic