Empirical ratio of dynamic to static stiffness for propped artificial fractures under variable normal stress

Abstract

The stiffness coefficient is a key parameter of rock fractures that controls the properties and behavior of a rock mass. According to the displacement discontinuity theory, the dynamic stiffness of rock fractures can be back analyzed using stress wave propagation. This study aims to measure the dynamic stiffness of rock fractures then develop an empirical ratio to describe the relationship between dynamic and static stiffness. Propped artificially fractured shale and granitic rock samples are employed. Mechanical and ultrasonic tests are conducted on two artificial rock fractures during uniaxial loading and unloading. As normal stress changes from 1 MPa to 50 MPa, the average dynamic normal stiffness of shale and granitic rock fractures changes from 330 GPa/m to 1960 GPa/m and from 90 GPa/m to 2320 GPa/m, respectively. For both artificial fractures, the dynamic stiffness is higher than the static stiffness but approaches the static stiffness with increasing normal stress. The ratio of dynamic to static normal stiffness is approximately 2.0 at a normal stress of 15 MPa; this ratio approaches 1.0 with increasing normal stress and varies widely under low normal stress. This study provides a method for evaluating the static or dynamic stiffness of rock fractures, which has important applications for seismic surveys or acoustic logs in the field of geological engineering.