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

A procedure is presented which is well suited for three-dimensional subsurf ace crack identification in a half-space through the inversion of measured surface displacements. The investigation began with the linear, forward pro blem of generating contour maps of surface deformation produced by a fractu re of known geometry and loading which is embedded in a finite medium. The fundamental solutions for tensile and shear multipoles in a half-space prov ided an efficient mathematical representation of the three-dimensional frac ture. The inverse problem of crack identification centers on the developmen t 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 uplif t at the free surface. Physical measurements of surface deformation were ta ken for a cube of transparent acrylic polyester in which a fracture was hyd raulically pressurized. Displacements induced at the surface of the specime n, which were measured by laser interferometry, had a strong correlation wi th predictions of the computational model (coupled with a finite element di scretization). Numerical tests demonstrate the robustness of the inverse me thodology even in the presence of the random and systematic errors correspo nding to the experimental interferometric measurements.