Experimental validation of a velocity discontinuity model for prediction of the seismic and static shear stiffness of rock joints

The stiffness estimation of rough joint is of great significance in rock engineering problems. In general, the value of stiffness measured by seismic wave propagation gives the upper boundary value, while the stiffness determined by static measurements provides the lower boundary value. Several experimental studies on mated fractures quantified this difference in stiffness and revealed that seismic stiffness is two to eight times larger than static stiffness. However, the underlying physical mechanisms responsible for this discrepancy are still poorly understood. In the study presented in this paper, the difference between seismic and static shear stiffnesses was attributed to the strain-level and rate effects. A velocity discontinuity model, composed of the Hooke, modified Saint Venant, and Newton elements, was developed and used for interpretation of experimentally collected shear waves transmitted through a rock joint. The small-strain stiffness defined by the model was relevant to the wave energy dissipation at high frequencies, providing an approximate value of joint seismic stiffness. The rate-independent stiffness of this model was associated with joint responses at low frequencies, providing an estimation of the static stiffness. Thus, the joint stiffness determined by this model is not a constant in the frequency domain. The stiffness value is smaller at low frequencies than at high frequencies, achieving a better prediction about the wave attenuation at a rough joint compared with a displacement discontinuity model. The developed joint model in this study enables estimation of both the seismic and static stiffnesses of rough joints by simple shear wave transmission experiments and thereby contributes some new understanding of strain rate effects.