اثر عمق و مورفولوژی ترک های واقعی در سونوگرافی پراکنده در بتن: یک مطالعه شبیه سازی

The aim of the present paper is to simulate the propagation of diffuse ultrasonic energy in concrete in the presence of a real crack. The numerical model is presented and validated by the comparison with experimental data from the literature. Unlike most of the studies which consider a crack as a notch, a realistic crack morphology exhibits partial contacts along its lips. These contacts are modeled in order to study their influence on the diffusion parameters. The feasibility of determining the contact density of the crack is shown, revealing practice implications for non-destructive crack sizing and imaging in concrete.

Cracking is critical for the structural integrity of civil engineering structures, as a consequence of the risks of mechanical failure and loss of impermeability which it can produce. In particular, the latter effect is induced by cracking of the concrete cover located between the surface and the first layer of rebar. This leads to the penetration of aggressive agents into the core of the structure, thus promoting corrosion of the rebar, leading to a degradation of the mechanical properties of the structure. The detection and characterization of such cracks is thus necessary, to allow the remaining lifetime of the structure to be predicted and its maintenance to be optimized. Several difficulties are encountered in the use of acoustic techniques for the characterization of concrete in an industrial context. ISO and ASTM standards [1] and [2] state that ultrasound frequencies in the range between 20 kHz and 150 kHz should be used. The wavelength is thus greater than 3 cm, which does not allow real cracks to be detected efficiently before reaching the rebar located at few centimeter depth. When the frequency is increased, ultrasound measurements become more complex, in particular due to multiple scattering, resulting from the presence of aggregates similar in size to the ultrasound wavelength [3] and [4]. Various authors [5], [6] and [7] have studied the ultrasonic characterization of cracks in concrete. They revealed a change in the waves' time of flight in the presence of a crack with controlled dimensions: a notch, whose walls have no contact points. Analogous results were observed with cracks produced by bending loads [8]. However, these cracks were opened artificially by applying a bending force to the test specimens, thus placing limitations on the accuracy with which they can represent real cracks. A second approach [9], based on the analysis of diffuse ultrasound, was also studied for the purposes of concrete characterization. It shows that the complex propagation of multiple scattered waves in concrete can be simplified into a standard diffusion law. It is founded on the analysis of the ultrasonic energy diffusion by two parameters: the diffusivity D (with dimensions [m]2[s]−1), characteristic of the material's structure, and the dissipation σ (with dimensions [s]−1), which reflects the medium's viscoelastic properties. Anugonda et al. [9] demonstrated the validity of this approach for concrete, both analytically and experimentally. They thus opened up numerous possibilities for the non-destructive characterization of microstructural damage in concrete. Becker et al. [10] thus studied the variation of diffusion parameters as a function of the aggregate diameters, whereas Punurai et al. [11] determined such variations in cement as a function of the quantity of occluded air. Deroo et al. [12] studied the influence of alkali silicate reaction on the diffusion parameters. Diffuse ultrasound was also analyzed in order to characterize cracks in concrete by Ramamoorthy et al. [13]. They showed that the diffusion parameters vary as a function of the length of a notch in concrete. Authors introduced another parameter: the arrival time of maximum energy (ATME). Quiviger et al. [14] confirmed the ability of ATME to characterize the opened portion of a real crack. According to the same authors, the ATME also varies as a function of the length of the closed portion of the crack. The presence of partial contacts along the length of the crack is assumed to be the cause of the observed variations. The aim of the present study is to verify the influence of real crack morphology on the measured diffusion parameters. The morphology of a real crack in concrete and the numerical model are presented. This model is validated by the comparison with experimental data from concrete samples containing controlled notches. A real crack is then introduced by the study of the influence of partial contacts on diffuse ultrasound. Then, the numerical model is applied to the case of real cracks in concrete and compared to experimental data from the literature [14].

The simulation tool and the numerical description of a crack allow a better understanding of diffuse wave's interactions with a real crack. A realistic numerical diffusion model including dissipation is proposed and validated through the use of experimental results from the literature. The simulations reveal the influence of the number of contacts, and their spatial distribution on the measured ATME. A realistic crack morphology is described numerically which makes possible the model to be optimized. It is shown that a linear contact density of 6.5% can explain the experimental variations in ATME, for cracks varying between 1 and 5.5 cm in depth. A more complex distribution could have been used but there is a lack of knowledge about crack morphology to validate such a study. Fig. 1 shows the 3D characteristics of the crack, with varying contact densities between the test specimen's outer surfaces and its center. However it is important to note that Turatsinze et al. produced an image of the crack by slicing the samples. That leads to internal stress release, which can produce openings which are not present in bulk of the samples. In this study, as regard with the symmetric location of the transducers and the position of the cracks, the 2D simulation is accurate. A 3D extension of this simulation is currently being evaluated. It will allow to model non-symmetric samples as well as various transducer locations. However, the main issue concerns the knowledge of the crack morphology in the bulk of the material. Non-destructive 3D observation of the morphology of this type of crack is to be considered in future studies, using X-ray microtomography for example. The complementarity of these data should ultimately allow the 3D crack morphology to be imaged in concrete. The numerical model presented in this paper will also be of interest in future studies dealing with gradual changes in depth. As this simulation method includes the dissipation, it allows to simulate some concrete pathologies such as carbonation by introducing gradual changes of porosity (which mainly drives the dissipation) in the first centimeters of concrete.