Wave dispersion in fresh and hardened concrete through the prism of gradient elasticity

The determination of the early age concrete properties and the monitoring of their evolution is the key point for an optimized construction with assured high quality. To this direction, the ultrasonic nondestructive testing technique is highly promising since it gives feedback on the mechanical properties and damage condition, allowing for the continuous interrogation of the material. It has experimentally been observed that concrete at both its fresh and hardened state exhibits a significant dispersive behavior concerning longitudinal ultrasonic pulses. Analytically, only few attempts have been made to explain this low-frequency change of phase velocity through the development of enhanced elastic theories. The most commonly used higher order theory is the simple strain gradient elastic theory which takes into account the microstructural effects in heterogeneous media like concrete. These microstructural effects are described by two internal length scale parameters g and h which correspond to the micro-stiffness and micro-inertia, respectively. In the present paper, it is shown that this simplest possible version of the general gradient elastic theory proposed by Mindlin can effectively describe the velocity dispersion of fresh and hardened concrete specimens with various water and sand contents. Moreover, it is here found that micro-inertia is dominant in fresh concrete while, on the other hand, micro-stiffness dominates the hardened concrete, which suggests that gradient elasticity can be successfully applied for the monitoring of the setting process of the above mentioned material. To overcome the fact that the considered strain gradient elastic model cannot attribute geometrical and mechanical properties of the microstructure to the microstiffness and microinertia terms, a non-local lattice model is adopted. Using that model, which reproduces the same differential wave equation as the one dimensional strain gradient elastic model, the derived Mindlin's microstructural coefficients are directly linked to the characteristic size of the microstructure. Finally, using the lattice model, it is made clear that prior knowledge of the dominant microstructural coefficient values accompanied by the mechanical and physical properties of the concrete matrix and aggregates, explicitly provides, among others, the interparticle distance l, the mean diameter of the inclusion as well as a measure of the intensity of nonlocal effects.