Empirical Formula for Dynamic Biot Coefficient of Sandstone Samples from South-West of Poland

Abstract

In this research, two empirical correlations have been introduced to calculate the dynamic Biot coefficients of low-porosity and high-porosity sandstone samples from two open pit mines located in South-West Poland. The experiments were conducted using an acoustic velocity measurement apparatus. Under the undrained condition, firstly, the confining pressure was increased in increments of 200 psi, and the values of pore pressure and dynamic elastic modulus were recorded. This experiment was continued until the Skempton coefficient remained in the range of 0.98–1. Secondly, an experiment on the same sample was conducted under drained conditions, and the corresponding dynamic elastic moduli were calculated. Then, using the calculated dynamic elastic moduli, the dynamic Biot coefficient was determined for each sample under different confining pressure. Finally, two empirical correlations were formulated for each sandstone category. The results demonstrate that, as the confining pressure increases, the Biot coefficient decreases from 0.79 to 0.50 and from 0.84 to 0.45 for low-porosity and high-porosity samples, respectively. Furthermore, as the porosity increases, the sandstone behavior increasingly approaches that of soil. The empirical correlations can be used for sandstone formations with the same porosity in projects where there is not a measurement method for the Biot coefficient.