Mechanical properties of quartz sand and gypsum powder (plaster) mixtures: 25implications for laboratory model analoguesfor the Earth’s upper crust

Abstract

Granular materials are a useful analogue for the Earth’s crust in laboratory models of deformation. Constraining their mechanical properties is critical for such model’s scaling and interpretation. Much information exists about monomineralic granular materials, such as quartz sand, but the mechanical characteristics of bimineralic mixtures, such as commonly-used quartz sand mixed with gypsum powder (i.e. plaster), are largely unconstrained. We used several mechanical tests (density, tensile, extension, shear) to constrain the failure envelope of various sand-plaster mixtures. We then fitted linear Coulomb and parabolic Griffith failure criteria to obtain cohesions and friction coefficients. Tests of the effects of emplacement technique, compaction and humidity demonstrated that the most reproducible rheology is given by oven-drying, pouring and mechanically compacting sand-plaster mixtures into their experimentation container. As plaster content increases, the tensile strength of dry sand-plaster mixtures increases from near zero (pure quartz sand) to 166±24 Pa (pure plaster). The cohesion increases from near zero to 250±21 Pa. The friction coefficient varies from 0.54±0.08 (sand) to 0.96±0.08 (20 weight% plaster). The mechanical behaviour of the resulting mixtures shifts at 20-35 weight% plaster from brittle Coulomb failure along a linear failure criterion, to more complex brittle-ductile Coulomb-Griffith failure along a non-linear failure criterion. With increasing plaster content, the brittle-ductile transition occurs at decreasing depth within a pile of sand-plaster mixture. We infer that the identified transitions in mechanical behaviour with increasing plaster content relate to (1) increasing porosities, (2) increasing grain size distributions, and (3) a decrease in sand-sand grain contacts and corresponding increase in gypsum-gypsum grain contacts. The presented characterisation enables a more quantitative scaling of the mechanical behaviour of sand-plaster mixtures, including of their tensile strength. Sand-plaster mixtures can thereby realistically simulate brittle-ductile properties of the Earth’s crust in scaled laboratory models.