Modeling the Pressure Sensitivity of Uncemented Sediments Using a Modified Effective Medium Theory

We present a modified effective medium theory to better describe the pressure-dependent elastic properties of uncemented sediments. Hertz-Mindlin theory typically predicts shear moduli that are higher than observed laboratory measurements, resulting in inaccurate estimates of the dry bulk to shear modulus ratio (Kdry/Gdry). Hertz-Mindlin theory further predicts that the Kdry/Gdry ratio is constant with pressure, whereas ultrasonic core measurements show increasing Kdry/Gdry ratio as effective pressure decreases. Laboratory data also suggest that dry bulk and shear moduli vary with effective pressure stronger than the cube-root power law predicted by Hertz-Mindlin theory. We introduce two new pressure-dependent calibration parameters to account for the shortcomings in effective medium theory, and present a new method to predict pressure-dependent elastic properties. Our calibration parameters agree with results of published granular dynamics simulations, and incorporate grain relaxation and porosity effects not included in existing effective medium theories. Our new model provides improved fits to laboratory data when compared to existing models, and can be used for improved prediction of elastic properties as a function of effective pressure. Our theory can also be used to model uncemented sediments with values of Poisson's ratio > 0.25, where a number of existing effective medium theories currently fail.