Plastic stress field reconstruction based on stress orientations data

Abstract

This paper presents an investigation of the applicability of the stress trajectories concept and the stress trajectories -slip lines alternations method to geomechanical problems. We extend our approach introduced for the stress analysis of two-dimensional plastic bodies to the problem of the stress reconstruction in plastic regions of the lithosphere. The method is developed for the Cauchy boundary value problem and utilizes the data on principal directions as one of the boundary conditions. For this purpose the first order stress indicators of the World stress map (WSM) project database (release 2008) are utilized in computations. The set of considered boundary conditions is supplemented by the normal derivatives of the stress orientations. Complete formulation of the problem involves a yield condition. Although the general approach is not limited to a specific yield criterion, present calculations are performed for the Mohr-Coulomb criterion. Applications of the method include the stress reconstructions in three regions of the Earth's crust (Swiss Alps, Tibetan plateau and Eastern Anatolia). The continuous boundary conditions are derived by an averaging method applied to the discrete data in immediate vicinity of the starting boundary. Thereafter, for the chosen strength parameters of the Mohr-Coulomb theory (friction angle and cohesion), the unique grids of stress trajectories and slip lines are determined. These fields are further compared against the WSM data available inside the regions. The computations are made for different strength parameters in order to provide the best fit to the data. The results of the analysis are presented as two plane fields: the map of normalized mean stresses and the grid of corresponding trajectories of principal directions. The normalization parameter is unknown (it represents an initial value of the mean stress in a single node of the boundary), which is a consequence of non-uniqueness of the stress reconstruction problem based on the data on stress orientations alone. The reconstructed stress orientations are compared with the observations from the WSM database.