Statistical analysis of an experimental compressional sand wedge

The quasi-static deformation of dry sand is widely used as an analogue to the brittle deformation of the upper crust. The quantitative comparison of analogue to natural tectonics, or to mechanical predictions, requires identifying sources of biases and estimating the intrinsic variability of the experimental results. We develop experimental and statistical methods that fulfill these requirements. We consider an initially perfect wedge resting on a flat layer, made of a uniform dry sand in a rectangular glass box. The box is shortened lengthwise by translating one of its end walls towards the other. The lateral walls can remain fixed, or be translated with the moving end wall. Upon shortening, the wedge is thrusted above the flat layer forming classical fore- and backthrusts, as essentially plane-strain, structures. Lifetimes, locations, and dips of all thrusts constitute seven quantifiable output parameters (called observables), in addition to the shortening forces monitored at both end walls during shortening. Up to seventy measurements of each observable were performed in seven final-state cross-sections of ten experiments. A three-step statistical analysis allows us to prove that, first, the observables vary independently, justifying their modeling with independent distributions. Second, the ergodic hypothesis holds, meaning that along strike variations can be used to infer the intrinsic experimental variability. Measurements can thus be repeated on successive cross-sections in each experiment. Third, our data set is free from bias due to friction on the lateral walls, or due to the finite length of the box. We then construct statistical models of each observable using either Gauss or Laplace distributions. For example, forethrusts dip at 38° ± 3.2°, and backthrusts, at 41° ± 3.3°. We finally show how to apply these statistical models to experiments using a different initial geometry. The statistical methods presented here are applicable to experiments with different setups, materials and observables, although the ergodic hypothesis is relevant only to plane-strain experiments.