Mapping KVMB to KV

Program kvKVMBscan.m illustrates the effect of mass ratio between solid frame and a fluid. In Figure 66, the viscosity for water is employed. The most friction results when the masses are equal (not a likely situation given the difference in density of most grains and water). The larger the frame to fluid mass ratio, one would expect the lower the porosity.

Figure 66: Octave program, kvKVMBscan.m, can be run to illustrate the effects which largely depend on porosity. Shown are cases for different mass ratios of solid frame and pore fluid.
\includegraphics[scale=0.7]{FigureQQ}

The reader should note that damping ratio in the KVMB context spans a very different range than the traditional KV damping ratio. This is true despite the fact that the same formula is used for both representations. As explained in Michaels (13), there is a problem in deciding what mass to use in the formula for damping ratio when considering the KVMB case. Recall, damping ratio is given by:

$\displaystyle \delta = \dfrac{D}{2\sqrt{K \cdot M}}$ (52)

where D is damping, K is spring constant, and M is mass. The program uses the combined mass of fluid and frame since most real soils will have permeabilities on the coupled side of the curve.