Scaling the Sand Box - Mechanical (Dis-) Similarities of Granular Materials and Brittle Rock

Abstract

Analog sandbox experiments are an important tool to understand brittle tectonic deformation. To date, most experiments are interpreted kinematically only. With the advent of reliable, small-scale force sensors, however, their dynamic evolution becomes available for analysis, offering new insights into the transient evolution of tectonic systems. Both rock and granular materials show an evolution of strain hardening and weakening during loading in the brittle-plastic regime, but so far, this similarity has only been appreciated qualitatively. As strain weakening is a vital parameter controlling fault reactivation and lifetime, it requires proper scaling. We therefore measured and analyzed two common granular analog model materials (quartz sand and glass microbeads) using ring-shear tests at a range of normal loads typical for analog experiments. We find two different modes of strain weakening as a function of normal load: Strain weakening at normal loads <1 kPa is due to partial loss of extrapolated cohesion, while at normal loads >1 kPa it is controlled by reduction of internal friction, which is consistent with previous measurements in this range. We show that this introduces a scale dependence into the scaling and restricts the possible use of the tested materials to crustal-scale models with a length scaling factor of l(model nature)≈2×10−6. For these we quantitatively compare the model materials’ transient strength evolution to that known from natural rock and the Earth's crust.