Figure 1 - Schematic of a beam bending experiment with a) plate or b) cylinder
Figure 2 - Typical results from a beam bending
experiment on a cement paste plate. The plot shows the load (normalized by the intial load) vs. the time.
The funcition R is the hydrodynamic relaxation function, and &PsiVE is the viscoelastic relaxation function
The beam bending (BB) technique consists of monitoring the load necessary to sustain a fixed deflection on a simply supported, submerged, and saturated beam of porous material. When a sudden deflection is imposed on the beam, a pressure gradient forms in the pore fluid with tension below and compression above the neutral axis (Figure 1). In response to this gradient, the pore fluid flows in a manner that restores ambient pressure throughout the pore space.
As the gradient is diminished and the pressure is reduced, the load necessary to sustain the deflection decays (Figure 2). Analysis of the kinetics of this load relaxation permits determination of the transport, elastic, and viscoelastic properties of the porous medium. Details of the theoretical analysis can be found here; Validation of the analytical soloution for the load relaxation with a sample of square cross section can be found here. The BB technique was substantiated through measurements on Vycor glass, an elastic material whose transport properties are known, and on cement paste, a viscoelastic material.