Crack stiffness from crack wave velocities

Abstract

We estimate crack stiffness by analyzing crack wave velocities. We measured crack waves which propagated along an artificial subsurface fracture in Higashi‐Hachimantai Hot Dry Rock model field, Iwate prefecture, Japan. The artificial subsurface fracture was created at a depth of about 370 m by hydraulic fracturing. We controlled contact conditions of the fracture surfaces by hydraulic pressurization. A time‐frequency representation technique, the pseudo‐Wigner distribution, is applied to determine the travel time of the crack wave. The crack wave shows dispersion; low frequency components below 100 Hz have lower velocities. We compare velocity data obtained in the field crack‐wave measurement to those calculated in a simple fracture model in which dimensionless crack stiffness reflects a degree of contact of the asperity on the fracture surfaces. Slope of the dispersion estimated from the field data agrees with that of the theoretical curves. We estimate the dimensionless crack stiffness is 0.001 to 0.005 from this comparison. This dimensionless crack stiffness, 0.001, means that crack stiffness on propagation path of the crack waves is 74 GPa/m.