Qualitative non-destructive testing of concrete-like materials

International audienceIn this paper we explore the capacity of Qualita-tive Inversion Methods to detect macroscopic cracks or a lattice of small cracks in concrete-like materi-als. These materials are difficult to probe since the heterogeneities size inside the medium and the wave-length of classically used sensors are of the same order of magnitude. We shall demonstrate how this diffi-culty can be avoided in the case of macroscopic cracks by using so-called differential measurements and ap-plication of the Linear Sampling Method. For a lat-tice of small cracks we rather propose to construct a macroscopic indicator based on the eigenvalues of a suitable transmission problem. Introduction We are interested in using elastic waves to perform complete non destructive testing of concrete-like ma-terials. The main difficulty in controlling concrete is its heterogeneous nature. Concrete is made of cement paste, water and aggregates. After a drying period, this mixture results in a heterogeneous material. As far as waves propagation is concerned, the main char-acteristics is the difference of celerity between aggre-gates and cement paste, especially as the wavelength and the size of the aggregates are similar, thus, in what follows, we will model concrete as a biphasic material.This concrete-like material has the following properties: the celerity of pressure wave is 5700ms −1 in aggregates and 4300ms −1 in cement paste. Defect Figure 1: Simulated concrete and numerical set-up for direct and inverse proble