Improved estimation method for dynamic bulk moduli of sandstones subjected to hydrostatic stress.

We designed and modified an experimental method to simultaneously measure the stress-strain (static moduli) and stress dependence of S and P-wave velocities of rocks (sandstone) under hydrostatic pressure by a Hoek’s cell. Dynamic moduli were calculated from the direct measurement of ultrasonic P- and S-wave velocities at a central dominant frequency of 1 MHz, while static moduli was recorded by strain gauges. The hydrostatic pressure was applied with a fixed rate at 1MPa/minute. We observed that the dynamic bulk moduli can be up to 44% higher than the static moduli in sandstones with porosity ranging from 8% to 24%. The results are in agreement with the existing empirical equations for soft rocks. Our experimental results demonstrate that the dynamic bulk’s modulus ranges from 4-13GPa, while the static bulk modulus ranges from 2-11GPa. We measured dynamic Young’s modulus and Poisson’s ratio at four different time periods (before applying the stress, right after the unloading, 20 days, and 60 days after the experiment) to investigate the effect of time on stress relaxation and eventually on the properties of the sandstones. All the samples showed an increase of Young’s modulus right after the stress application and then a gradual decrease of this value over time because of this relaxation; however, most of the samples could not reach the original state due to irreversible deformation at micro-level. Dynamic moduli show greater sensitivity to the irreversible deformations as compared to static moduli (even within the elastic limits). Dynamic moduli of porous material are also more sensitive to the microstructure than the static ones. Independent P and S-wave measurement for this study showed that the estimation of the S-wave velocity from the recorded P-wave velocity is not an accurate procedure and introduces a big error in the final calculation of the dynamic moduli. It also confirmed that by registering an accurate P-wave velocity the UCS (Unconfined Compressive Strength) value can be accurately estimated for sandstones. This demonstrates the great potential of dynamic studies as a non-destructive method to estimate this value for porous materials.