Non-linear softening and relaxation in rocks and geomaterials: a laboratory perspective

In rocks and other consolidated geomaterials, static or dynamic excitation leads to a fast softening of the material, followed by a slower healing process in which the material recovers all or part of its initial stiffness as a logarithmic function of time. This requires us to exit the framework of time-independent elastic properties, linear or not, and investigate non-classical, non-linear elastic behavior and its time dependency. Softening and healing phenomena can be observed during seismic events in affected infrastructure as well as in the subsurface. Since the transient material changes are not restricted to elastic parameters but also affect hydraulic and electric parameters as well as material strength documented for instance by long lasting changes in landslide rates it is of major interest to characterize the softening and recovery phases. To characterize this behavior in a controlled environment, we perform experiments on Bentheim sandstone in a Materials Testing System triaxial cell with pore pressure and confining pressure control. Our sample is subjected to various static loading cycles in both dry and water-saturated conditions, while an active acoustic measurement setup allows us to monitor minute P-wave velocity changes, which can then be directly tied to dynamic elastic modulus changes. Our transducer array allows us to observe the dynamic softening as well as the recovery processes in the sample during repeated loading phases of various time lengths. Observations indicate high spatial, frequency and lapse-time sensitivity of the observed velocity changes, indicating a rich landscape of concurrent effects and physical phenomena affecting our sample during these simple experiments. To investigate the spatial and directional dependency of the velocity changes, we restrict the analysis to direct and reflected ballistic waves. Our observations indicate that, while stress-induced classical effects are clearly anisotropic as expected, the non-classical effects do not exhibit significant anisotropy. This allows us to rule out a number of physical phenomena as the cause for the non-classical effects. Most importantly, we conclude that the microscopic structures responsible for the reversible softening and healing processes are different from the cracks that induce the anisotropic acousto-elastic effect.