This study focuses on the determination of the elastic properties of intensely fractured rocks around tectonic faults. The later are those producing earthquakes, and therefore, quantifying the physical properties of the rocks that host them is of utmost importance to anticipate their rupture behavior during an earthquake. The objective is thus to derive a mathematical compliance modeling of naturally fractured rock mass. This remains a challenge, on the one hand, because the fracture network is dense and complex, and on the other hand because fracturing occurs over a wide range of spatial scales from micro-fractures to largest faults.
A two-stage procedure is applied. The first one was dedicated to elaborate an inferential statistical analysis of the geometric parameters delineating fracture networks: fractal dimension (spatial distribution of masses), length (double power-law), position (exponential distribution) and orientation (mixture of von Mises distribution). The statistical data are extracted from image analysis (Faults R Gems project) in situ Granite Dells in Prescott, Arizona. An algorithm is developed to generate synthetic fracture networks based on the derived statistical laws.
The second stage was devoted to derive the elastic properties of the fractured rock masses. Therefore, their overall mechanical behavior is modeled as a homogenized macroscopic equivalent medium (i.e., a representative volume element (RVE) in which homogeneous mechanical properties can be assumed). A dual boundary integral equation (BIE) formulation using conventional BIE and hyper-singular BIE is applied to model fractures in two-dimensional linear elastic solids. Numerical tests are presented to address questions concerning the stochastic homogenization method as the choice of the RVE size, the number of realizations, the boundary conditions described on the RVE boundaries. This talk will be finished with open questions on the scaling relation between the parent faults and their damage zones.
This is a joint work with Olivier Pantz (LJAD, UCA) in the frame of the DEFIDEF project (P.L. Olivier Pantz) and of the ANR research project FAULTS R GEMS (P.L. Isabelle Manighetti).