Stochastic mechanical analysis of the stress field in a 3D thrust fold

Knowledge of the in-situ stress state is a key factor for any subsurface site characterization and for safe underground geotechnical exploitations. Despite the huge progress in estimating the stress field, understanding the state of stress is still a tedious and challenging endeavor due to incomplete data and sparse information. Moreover, the cost of performing stress measurements is quite elevated while the procedure is delicate and time consuming. Thus, the importance of utilizing geomechanical models for a wider stress evaluation.

We conduct a sensitivity analysis of the stress field with respect to rheological parameters in a kilometric scale thrust fold using a 3D numerical implementation of the theory of Limit Analysis (LA). LA searches for the exact loading force at the onset of failure by bounding it through optimization using a kinematic (upper bound) and a static (lower bound) approach. Elastic parameters are not required, and we only adopt the Coulomb failure criterion characterized by a friction angle and a cohesion.

The 3D geological prototype created, is inspired from the north eastern Jura setting, northern Switzerland, and corresponds to the lateral termination of a partially buried fault cored anticline. It is formed by five material layers with different Coulomb parameters and two different décollement levels. We perform a parametric study by varying the friction angle of the bulk materials, the faults and the shallow décollement.

Our simulations, show various stress distribution patterns depending on the uncertainties related to fault and decollement friction angles. This implies different model behaviors and distinct rupture geometries. However, we identify in particular a stress shielded layer presenting low stress values independently of the parametric variations. Comparing our results with a 2D approach consolidates our findings and highlights the importance of 3D modeling. Finally, we perform a stress analysis of several boreholes taken at various locations. We represent each borehole by an average stress profile with its respective standard deviation. In doing so, we are transforming the parametric variations into stress logs reflecting our uncertainties. This process reveals in particular a counter-intuitive vertical stress decrease with depth near activated blind faults. We argue that this observation is related to material uplift in a compression regime and is only possible for a restricted blind fault.

The aim of this study is to evaluate the possibility of performing real stress data inversion in order to both predict stresses away from the measurements, and determine ranges of compatible rock parameters.