The elastic properties of sand strongly depend on the grains’ contact stiffness, which can be increased significantly by solid matter and, depending on frequency, viscous fluid acting as contact cement. To calculate seismic velocities in precompacted fluid-cemented sand, we examine how a small amount of viscous fluid at the grain contacts influences their normal and tangential stiffnesses as a function of effective pressure. Using the Hertz-Mindlin approach and considering oscillatory loading in addition to precompaction of a combination of two elastic spheres, we extend the dry-contact elastic theory by a viscoelastic formulation.

Here, we describe the radial flow of the fluid cement induced by the oscillations of the grains’ surfaces around the direct contact, a process that leads to a complex normal stiffness and stiffness/frequency dispersion. In the resulting combined model, the low-frequency real part of the complex normal stiffness identical is to the original Hertz-Mindlin expression. The magnitude of the dispersion is governed by the amount of viscous cement; magnitude decreases as effective pressure increases. The frequency of the maximum imaginary part of the normal stiffness is determined mainly by cement viscosity and contact geometry. The tangential contact stiffness virtually is not influenced by the viscous fluid.

Comparison of predicted results with data from pulse transmission experiments (500 kHz) on glass beads with two different fluids shows an excellent fit in P-wave velocities (Vp), whereas S-wave velocities (Vs) are systematically overestimated by the model. The experimental results confirm, however, the predicted change with effective pressure in the VP/VS ratio for both examined cases as well as reflect the predicted increase in VP and VS, respectively, between the two cases. This implies that our viscoelastic formulation represents a reasonable way to describe the role of viscous cement in sand.

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