A PHYSICAL MODEL STUDY OF SCATTERING OF WAVES BY ALIGNED CRACKS: COMPARISON BETWEEN EXPERIMENT AND THEORY¹

Abstract

An approximation to plane‐wave propagation through a composite material is examined using a physical model with oriented but randomly distributed penny‐shaped rubber inclusions within an isotropic epoxy resin matrix. A pulse transmission method is used to determine velocities of shear and compressional waves as a function of angle of incidence and crack density. The experimental and theoretical results of Hudson were compared and limitations within the crack parameters used in this study have been determined. Results from both polarized shear waves (S1, S2) compare favourably with the theory for a composite with up to 7% crack density, but theory and experiment diverge at higher crack densities. On the other hand, compressional‐wave velocities at low crack densities (1% and 3%) compare favourably with the theory. It is also shown that the velocity ratio Vp/Vs for two extreme cases, i.e. propagation normal and parallel to the cracks, as a function of crack density and porosity, has a strong directional dependence.

Experimental study on the effect of fracture scale on seismic wave characteristics

“…In our study, we used the equivalent parameter method, which is usually used to study the effect of fracture parameters on seismic wave propagation. The method in laboratory is that low-velocity disks are inserted into base material to simulate the fractured medium (Ass'ad et al, 1992;1993;Rathore et al, 1995;Wei, 2004), which accords with the actual fracture distribution as well as the Hudson's fractured medium theory. Prior studies were mainly on the qualitative or quantitative analysis of shear wave anisotropy, but the quantitative observation of fracture scale, especially for primary waves has been lacking.…”

Effects of fractures on seismic-wave velocity and attenuation

“…A group velocity should be plotted against the group angle. However, in the experiment conducted by Ass'ad et al (1992Ass'ad et al ( , 1993, the authors contended that the maximum differences between the directions of phase and group velocities were lo", 8" and 7" for 10 per cent crack density (highest), which correspond to velocity differences of 1.6 per cent, 1.0 per cent and 0.5 per cent for P, SH and SV waves respectively. These differences become much smaller for smaller crack densities, so using the phase angle rather than the group angle does not pose any serious threat to the analysis.…”

“…The computed velocities with their standard deviations are listed for compressional and shear waves for different angles and crack densities in tabular form in Ass'ad et al (1993). These results are compared with outputs from the Hudson (1981) and MDD models.…”

Comparison of experimental velocity measurements with theoretical results in a solid‐solid composite material

“…When a two-phase medium is constructed of a solid matrix with solid inclusions, most studies address cracked solids with aligned penny-shaped inclusions, so that the medium becomes anisotropic (Hudson, 1981;Hudson and Knopoff, 1989;Sayers and Kachanov, 1991;Ass'ad et al, 1992Ass'ad et al, , 1993. The discussions are not generally on random embedded solid inclusions mixed in another solid matrix, and the experimental data for such a medium are scarce.…”