Deformation of Granular Aggregates: Static and Dynamic Bulk Moduli

Abstract

Sand and glass bead samples were monotonically loaded from 0 to 50 MPa and then monotonically unloaded, all under hydrostatic stress conditions. Sand deformed irreversibly and its porosity loss was permanent. In contrast, the glass bead deformation was almost fully reversible with the initial porosity recovered. During loading, the static bulk modulus in all sand samples increased from 0 to about 0.5 GPa between 0-and 15-MPa stress and remained constant for the remainder of the loading. Such behavior, somewhat unexpected in a granular system, means that sand deforms as a linear elastic body during loading from 15 to 50 MPa. The unloading behavior was very different-the static bulk modulus almost linearly decreased from about 4 GPa at 50 MPa to zero as the stress was reduced. Once again, this behavior was very different from that observed in glass beads, where the static bulk modulus during loading was essentially the same as during unloading and appeared to be a unique function of stress, independent of the direction of its variation. Moreover, the static and dynamic bulk moduli in glass beads, the latter computed from V p , V s , and density measured during the loading/unloading cycle, were very close to each other. In contrast, the dynamic bulk modulus in dry sand exceeded the static modulus during unloading by a factor of 1.5 to 2.0. We used a quantitative theory based on contact mechanics and the concept of stress heterogeneity in particulates to analytically match the observed results.

Rock Physics: Recent History and Advances

“…p instead of the bulk modulus K. The functional form in this theory is the same as that in Gassmann's: Figure 5 shows an example of the results of fluid substitution (pure water) on the elastic properties of high-porosity sand measured in the laboratory [11] at roomdry conditions. Clearly, the pore fluid has a dramatic effect on Poisson's ratio.…”

“…Both Eqs. (11) and (12) were discovered by Archie in 1942 [6] and remain the cornerstone of resistivity interpretation for hydrocarbon saturation in the wellbore. Various modifications of these equations dealing with resistivity interpretation in sediments containing clays and shales are discussed in Mavko et al [1].…”

The Spatiotemporal Evolution of Granular Microslip Precursors to Laboratory Earthquakes

“…This final step is more difficult than it may appear at first glance due to physical and geometric constraints. Since the wave speed in the steel block containing the sensors (∼3,250 m/s) is much larger than that of the fault gouge (∼570 m/s; e.g., Domenico, 1977; Muqtadir et al, 2020), ray theoretical arguments imply that any ray arriving at one of the sensors must have been traveling near vertically in the gouge layer, as the critical angle from gouge to steel is of order 10°. This constraint accentuates the traditional tradeoff between event depth and origin time to the extent that we have essentially zero depth resolution in the gouge.…”

Static and Dynamic Bulk Moduli of Deepwater Reservoir Sands: Influence of Pressure and Fluid Saturation

“…Zimmer [12] applied corrections to the axial strain for the strain gauge hysteresis and the end effects when measuring lab-repacked loose sand samples. Muqtadir et al [34] reported that the radial LVDT gauges in their triaxial testing system failed to track a large displacement when measuring repacked loose sands from Saudi Arabia. Additional corrections are required to obtain reasonable strain data.…”