Estimation of grain elasticity properties from ultrasonic measurements on dry granular pack
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The elastic properties of crystalline rocks can be estimated from ultrasonic measurements on the powders of crushed rocks produced by the drilling process. To determine the elastic properties of grains from properties of powder packs, we study the dependence of their ultrasonic wave velocities on pressure. From this dependency, using the Hertz–Mindlin theory, we can calculate the effective ratio of the grain shear modulus to one minus the Poisson ratio. The Hertz–Mindlin theory requires the knowledge of grain coordination number as a function of pressure, which can be obtained using an empirical relation based on published numerical simulations. Previous work has shown that this approach gives an accurate prediction of the effective bulk modulus of glass beads but produces a significant discrepancy for sand. This discrepancy may be attributed to the angularity of sand grains. To overcome this problem, we introduce a shape factor into the empirical relation for the coordination number. This new shape factor allows us to reconcile the rock physics model with laboratory measurements. We show that the shape factor varies from 1 to 2.5 for different grain shape angularity and sorting (grain size distributions). The modified theory allows us to estimate a combination of elasticity parameters of the grains from the measured dependence of P-wave velocity in the pack on the pressure.
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