Relating Permeability to Damping KVMB

If porosity information is available, it can be combined with stiffness and damping results (viscoelastic, KV) under an alternative constitutive model (KVMB) to estimate permeablility. This would not be absolute, but rather relative permeablility (hydraulic conductivity, units of meters/second). The theory is found in Michaels (2006).

While the constitutive model is structured on highly simplified assumptions, it captures the behavior of granular soils saturated with water or other fluids when shaken by S-waves. Inertial damping resulting from shaking is predicted to peak at some hydraulic conductivity. Damping decreases on one side of the peak due to pore sizes being too small to permit significant relative motion between the frame and fluids. On the other side of the peak, damping decreases because the pores are so large that fluid moves easily with respect to the frame.

There are four octave programs provided with BSU that may be used with the KVMB soil model. Note, the intention is that this model is only valid in the context of granular soils under the assumption of inertial damping and laminar flow. The first three are forward problems, the 4th listed below is an inversion program.

Figure 34: kdKVMBscan.m: Plots Kelvin-Voigt damping ratio vs. hydraulic conductivity for user provided porosity and frquency of shaking. Here, porosity is 30% and frequencies are 10 and 50 Hz. Left of the peak is coupled motion (small pores, fluid largely moves with frame). Right of the peak is uncoupled motion (large pores).
\includegraphics[scale=0.7]{FigurekdKVMB.pdf}

Figure 35: fqKVMBscan.m: Plots Kelvin-Voigt damping ratio vs. frequency fo user defined porosity and hydraulic conductivities. Here, porosity set at 0.25, two different cases of hydraulic conductivity $K_d = .01~~ K_d=.001~~ m/s $ .
\includegraphics[scale=0.7]{FigurefqKVMB.pdf}



Subsections