Effects of Strain Amplitude on the Static and Dynamic Nonlinear Deformation of Berea Sandstone

T: A series of carefully controlled static compressive loading and ultrasonic pulse transmission tests on room-dry Berea sandstone were performed to develop a fundamental understanding of the micro-mechanisms that result in nonlinear dynamic and static stress-deformation relationships of granular rocks. Young's modulus and Poisson's ratio were calculated as a function of axial stress from static uniaxial strain and uniaxial stress tests. Dynamic Young's modulus were computed as a function of axial stress from compressional (P) and shear (S) wave velocities measured during the ultrasonic pulse transmission tests. We found that measured dynamic moduli match initial tangent moduli computed from small-strain, small-stress amplitude cycles executed during a static uniaxial strain test. Further, the nonlinear stress dependence of both P-and S-wave velocities can be reproduced from these tangent moduli. These results show that nonlinear static and dynamic properties of a granular rock, such as Berea sandstone, are due to the strain amplitude of the loading, rather than to frequency-dependent dynamic loading effects. By applying appropriate effective medium models based on the micromechanics of microcrack closure and grain elasticity we have related the nonlinear dynamic response of a granular rock to the nonlinear behavior under static loading. Such a relationship between nonlinear static and dynamic properties will be helpful in understanding the nonlinear behavior of granular rocks under high strain amplitude waves.