Constraints on friction coefficients by an inverse analysis of sand box thrust dips

We measured the dips of thrusts forming in a uniform sand layer under horizontal shortening by a rigid emerging ramp in conditions of full erosion. Various ramp dips and four types of ramp material were used throughout the 12 experiments. In three experiments, the ramp was shortcut by a less steep thrust forming a spontaneous ramp in the sand. The forward modelling proposed to predict these observations involves (i) computing the total dissipation in the structure by using global force equilibrium and a parameterised kinematic framework including the possibility of shortcut development, and (ii) minimising the total dissipation of mechanical work with respect to the kinematic parameters (i.e., the thrust dips), for which two analytic solutions are found. The inverse problem involves computing probability densities over the parametric space of friction coefficients, including the internal friction angle of the sand, and friction angles of the four materials used on the rigid ramps. Practically, this involves computing a misfit (using the L2 norm) between the observed and predicted thrust dips for every possible value of the friction angles. The resulting probability density provides all the quantitative information that can be retrieved from the experiments in the light of our forward modelling. Ramp friction angles exhibit sharp probability changes at values that trigger the occurrence of shortcuts, thus yielding non-trivial bounds on the ramp friction values that are directly related to the observations of ramp and back thrust geometry. Also, the probability distribution of the internal sand friction, and those of the ramp frictions, is in good agreement with independent measurements. This approach is designed to be applicable to field studies of brittle deformation where geometries are observed and rheological parameters are sought.