For modeling and interpreting seismic velocity reduction due to loosening in the Excavation Disturbed Zone (EDZ), we have studied the Kuster-Toksoz model (K-T model) which has been widely used as an inclusion model for a cracked rock. The K-T model can represent seismic velocity of a cracked rock based on seismic scattering theory due to cracks within the rock. The K-T model is first described mathematically and then used for calculating P-wave velocity vs. porosity relation in a cracked granitic rock. Assuming the porosity and aspect ratio of the crack, model calculations are compared to actual observations in many tunnels in different types of rocks. These comparisons reveal that seismic velocity reduction strongly depends on porosity and the aspect ratio of the crack in the rock and the rock physics model such as the K-T model can be used for predicting seismic velocity reduction due to loosening in the EDZ.
In site characterization of a planned tunnel route, a seismic refraction survey is commonly performed for designing a tunnel support system through seismic velocities. However a tunnel support pattern determined based on a rock mass classification using seismic velocities obtained a seismic refraction survey before tunnel excavation often significantly differs from that after excavation (Kimura & Ohashi 2002). It has been recognized that the seismic velocity before excavation represents a rock state with confinement and often differs from that after excavation without confinement, especially for a rock with large loosening. Kimura & Ohashi (2002) conducted seismic velocity measurements at many tunnels before and after excavations for studying a rational way of design of the tunnel support pattern considering reduction of seismic velocity due to loosening of a tunnel wall. Figure 1 shows the seismic velocities for various types of rocks before and after excavations they measured. It should be noted that seismic velocity reduction is larger as rock mass quality is higher.
For interpreting the seismic properties of the excavation disturbed zone (EDZ) as above, we have studied rock physics models which have been aggressively used in modeling seismic properties of oil and gas reservoir rocks (Mavko et al. 2009). In this study Kuster-Toksoz model (K-T Model) (Kuster & Toksoz 1976) is applied to represent seismic P-wave velocity of a rock. This model is one of inclusion models, which has been widely employed for modeling a cracked rock. In this paper we first describe how to calculate model parameters following Saito et al. (1983) and then discuss how to model and interpret the EDZ seismic properties.