Dynamic and Static Elastic Properties of Sedimentary Rocks

Understanding the differences between static and dynamic elastic properties of underground rocks is essential for the successful hydraulic fracturing. For heterogeneous porous sedimentary rocks, static elastic properties can differ a lot from dynamic elastic properties even at the same stress level. We investigate the stress dependence of dynamic and static mechanical properties through laboratory measurements and micro-mechanical analysis on sandstone and shale samples. In general, static tests respond to the superpositions of the elastic, viscoelastic, and non-elastic properties along with a stress increment, whereas dynamic tests, with more than two orders of magnitude smaller strain amplitude, only reflect the elastic properties of rocks. As a result, the dynamic modulus is characteristically higher than the static modulus at almost any stress level, whereas the static Poisson’s ratio expresses a lower value at low stress and higher value at high stress in contrast to the dynamic Poisson’s ratio. The experimental results also suggest that intrinsic beddings of the anisotropic shales would have significant impacts on dynamic and static properties. The rock is generally stiffer in the bedding-parallel direction than in the bedding-normal direction. Considering the strong stress dependence of static properties, we propose two ways to determine static elasticity in the stress-strain curves: uniaxial load-unload experiments with a series of minor stress cycles and increasing-amplitude cyclic loading and unloading experiments. The first one offers an easy approach to investigate static properties of the rock matrix without microstructural effects. The second one documents the evolution of static elastic properties in great detail by considering the in-situ stress conditions and emphasizes that there exists a relatively elastic region with similar static properties regardless of the numbers of loaded or unloaded stress cycles. The new approach is more effective than the traditional one, which is limited to the linear elastic region of the loading stress-strain curves.