To interpret dynamic and static Young's moduli of soft sedimentary rocks widely distributed in Japan, the sandy shale model of the binary sand/shale mixture model are applied to the measured Young's moduli obtained from velocity logging data for the dynamic modulus and from laboratory mechanical test data for the static modulus. The Young's modulus for the rock is calculated by the Hashin-Strikman lower bound, Hertz-Mindlin contact model and Gassmann's equation. For modelling static Young's modulus, in the Hertz- Mindlin contact model, the shear modulus is calculated by incorporating the mixture of frictional and frictionless grain contacts into the model. The calculated dynamic and static Young's moduli are well consistent with the measured data for three different soft sedimentary rocks. This result demonstrates that the sandy shale model can be used to predict the static moduli required in civil engineering applications from dynamic ones obtained from seismic velocities.
Static and dynamic moduli are terms used to distinguish between the elastic modulus derived from the slope of stress-strain curve in a rock mechanical test (static modulus) and that derived from elastic wave velocity measurements (dynamic modulus). It is well known that there can be large differences between static and dynamic moduli of heterogeneous materials such as porous rocks. Proper understanding and modelling of this difference is especially useful for seismic characterization of a rock mass in rock engineering because seismically derived dynamic elastic modulus can be used for estimating static one of the rock mass. There have been many studies on the relationship between these two moduli of different types of rocks (for example, Fjaer, 2009; Olsen et al., 2008). In this paper, we have studied rock physics models to understand relationship between static and dynamic Young's moduli of soft sedimentary rocks widely distributed in Japan and to predict the static modulus from dynamic one derived by the seismic method.
Many rock physics models have been already proposed and applied to sedimentary rocks, especially sandstones or shaly sandstones, for interpreting seismic velocities measured in and around oil and gas reservoirs (Avseth et al., 2005). A rock physics model called the binary sand/shale mixture model is one of them, which is used to model sandy shale or shaly sandstone consisting of mixtures of sand and shale (or clay) (Marion et al., 1992, Dvorkin et al., 2002) (Figure 1). Takahashi and Tanaka (2009) showed that the sandy shale model of the binary sand/shale mixture model can represent the remarkable features of the soft sedimentary rock that the seismically derived elastic modulus strongly depends on its grain size distribution and the confining pressure.
The static modulus is defined as the modulus at the large strain level, which is usually measured with the laboratory mechanical test and in-situ mechanical tests using a borehole or a tunnel. For a large strain (stress) level, the stress-strain curve has non-linearity, meaning that the elastic modulus changes depending on the strain (stress).
