Modeling the pressure sensitivity of uncemented sediments using a modified grain contact theory: Incorporating grain relaxation and porosity effects

Abstract

We develop a modified grain contact theory to better describe the pressure-dependent elastic properties of uncemented sediments. The Hertz-Mindlin (HM) theory typically predicts shear moduli that are much higher than observed laboratory measurements, resulting in inaccurate estimates of the dry bulk to shear modulus ratio [Formula: see text]. The HM theory further predicts that the [Formula: see text] ratio is constant with pressure, whereas ultrasonic core measurements typically show an increasing [Formula: see text] ratio as effective pressure decreases. Laboratory data also suggest that the dry bulk and shear moduli variation with effective pressure is greater than the cube-root power law predicted by the HM theory. We introduce two new pressure-dependent calibration parameters to account for the shortcomings in effective medium theory, and we develop a new method to predict pressure-dependent elastic properties. Our calibration parameters agree with the results of published granular dynamics simulations, and they incorporate grain relaxation and porosity effects not included in existing effective medium theories. Our new model provides improved fits to laboratory data when compared with existing models, and it can be used for improved prediction of elastic properties as a function of effective pressure. Our new theory can also be used to model uncemented sediments with values of Poisson’s ratio [Formula: see text], where many existing grain contact and effective medium theories currently fail.