Relationship Between the Static and Dynamic Bulk Moduli of Argillites

Abstract

Bulk modulus is one of the mechanical properties used in any rock engineering related project. This property can be measured statically, where it is derived from stress–strain data, and dynamically, where it is derived from P- and S-wave velocities. The static bulk modulus is generally different from the corresponding dynamic bulk modulus. As the static bulk modulus is required in computation or modelling of the deformation of the rock when it is stressed hydrostatically, empirical relationships between the static and dynamic bulk moduli are needed to convert the dynamic bulk modulus to static values. In this study, the static and dynamic bulk moduli were measured simultaneously, at effective pressures up to 130 MPa, for dry and fluid-saturated argillites. The samples were collected from four different lithofacies within the upper Naparima Hill Formation, Trinidad. The results show that the dynamic bulk modulus is greater than the static bulk modulus, except for hard lithofacies under dry conditions where the static and dynamic moduli are approximately equal. Under saturated conditions, the porosity plays a key role in increasing the difference between the static and dynamic bulk moduli. A linear relationship with high correlation (R2 greater than 0.85) was established between the static and dynamic bulk moduli, which is dependent on the effective pressure and saturation state.