Boundary reflection in a cylindrical sample examined by a laboratory-scale 3D numerical simulation

Abstract:

For the purpose to understand the time evolution of the wavefield in a cylindrical-shaped small sample, we performed 3D finite difference method simulations of wave propagation in a laboratory-scale. Complicated waveforms with multiple reflections observed in a finite-scaled medium kept us away from the full wave utilization, while wave transmission experiment is a popular technique to estimate the characteristics of a sample. In this study, we utilize a numerical simulation to evaluate the 3D boundary effect of a cylindrical sample, in particular the reflected waves from top/bottom boundaries.

We considered a model including a homogeneous cylindrical sample with a diameter of 50 mm and length of 100 mm which was discretized into two billion grid points. A single force was added on the vertical center of the model sample as a virtual transducer. The simulated wavefield in the sample demonstrated the development of many reflections and conversions of P and S waves at the top/bottom boundaries as well as the side boundary. In addition, Rayleigh waves propagated along sample side surface exposed much large amplitude than the body waves.

To focus on the reflection from the boundaries, we applied absorbing boundary conditions at the top/bottom end of the model sample for reflection inhibition. After subtracting the obtained reflection-free wavefield from the former simulation, the reflected waves at the top/bottom ends were clearly appeared. The visualized wavefield revealed many reflections and conversions of body waves at the top/bottom ends. The Rayleigh waves were developed by conversion from S wave after it reached the boundary, and multi-reflected S waves generated Rayleigh waves one after another propagating to the vertical direction. Laboratory-scale simulation is a good way to estimate the hidden wave propagation process in a sample, and would help to design proper experimental conditions, such as for sample geometry and for observation layout.