Inverse method of identification for three-dimensional subsurface cracks in a half-space

Abstract

A procedure is presented which is well suited for three-dimensional subsurface crack identification in a half-space through the inversion of measured surface displacements. The investigation began with the linear, forward problem of generating contour maps of surface deformation produced by a fracture of known geometry and loading which is embedded in a finite medium. The fundamental solutions for tensile and shear multipoles in a half-space provided an efficient mathematical representation of the three-dimensional fracture. The inverse problem of crack identification centers on the development of a hybrid of the Marquardt–Levenberg algorithm. Initial guesses for the constrained set of search variables were determined heuristically from the correspondences between crack geometry and loading and the resulting uplift at the free surface. Physical measurements of surface deformation were taken for a cube of transparent acrylic polyester in which a fracture was hydraulically pressurized. Displacements induced at the surface of the specimen, which were measured by laser interferometry, had a strong correlation with predictions of the computational model (coupled with a finite element discretization). Numerical tests demonstrate the robustness of the inverse methodology even in the presence of the random and systematic errors corresponding to the experimental interferometric measurements.