Octave program KD4kvmb.m can be used to invert values of stiffness and damping to hydraulic conductivity. For example, in a down-hole shear wave transmission survey, one can measure body wave dispersion and amplitude decay with distance to obtain values for stiffness and damping. The procedure to invert velocity dispersion and amplitude decay is detailed in Michaels (10). The result of the inversion are two coefficients of the viscoelastic 1D wave equation (beam divergence is corrected for in the process). The wave equation is a 3rd order PDE:
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Are these predictions accurate? No, of course not. But they are a starting point in estimating hydraulic conductivity from shear wave measurements. While the predicted behaviors are likely correct in terms of how real soils behave, real soils are far more complex, pore spaces are not cylindrical tubes, and fluid flow is not always laminar. In the context of granular soils, these tools may be helpful in mapping soil units, their permeabilities, and predicting levels of damping that might occur when exposed to seismic waves.
pm 2018-04-08