Analysis of Varying Seismic Velocities in Sands of Different Grain Sizes

Hertz-Mindlin (HM) contact theory provides a model for how the velocity of sound changes through granular materials with respect to porosity, grain coordination number (CN), bulk grain elasticity, grain contact stress, and bulk density. Grain size is not a variable in the Hertz-Mindlin model. Previous experimental studies of varying sand sizes (phi-Wentworth scale) yield results which are difficult to explain using HM alone unless unrealistic estimates for porosity, density and coordination numbers are used. In prior work, lower-than-expected Vp values are attributed to poor sorting. We expect well-sorted sands to show higher Vp values.

Here, we measure Vp in angular to sub-angular sands, sieved into 6 sizes (very fine, fine, coarse, very coarse, very fine sand, and granules). We use an oscilloscope, a pulser (kHz), a sensor-signal amplifier, a polyvinylidene fluoride piezoelectric accelerometer, and two different piezoceramic actuators. We calculate Vp over distances ranging from 0.3 to 2.5 cm and pay special attention to errors derived from distance measurements, actuator type, and pulser voltage.

Velocity estimations use linear best fits to 9 measurements for each grain size. Results show a nearly linear increase in velocity with increasing grain size, as we expect, based on previous studies. For example, in the medium sand grains with actuator described above, the linear best fit velocity is 100 m/s (RMS 0.98) while the best-fit velocity for the granules is 245 m/s (RMS 0.96). In addition, higher angularity in our larger grains may help amplify this trend. We also confirm that better sorting yields overall higher Vp values (e.g., overall 49-261 m/s ) then in a previous study(e.g., 30 115 m/s) where sorting was lower. However, HM implies that in order to keep a reasonable porosity (0.37-0.43) and density (2700 to 3000 kg /m^3), a low CN ( 2), and a low shear modulus (2 GPa) from possible grain cracking are required.