Évaluation des propriétés du béton par des variables réduites

Résumé

Grandeur sans dimension, le nombre Bu=R/v² σ relie les paramètres fondamentaux des essais ultrasoniques du béton: la résistance R, la vitesse de propagation d'une onde longitudinale v et la masse volumique σ. Le nombre Bu est constant pour des bétons de même composition granulaire qui ont des caractéristiques d'hydratation du ciment différentes. Il ne dépend ni du temps ni des conditions de durcissement. Le nombre Bu dépend: 1° de longueurs (comme les dimensions de l'éprouvette et la longuer d'onde) 2° du facteur de macro-structure δ, qui représente la répartition aléatoire des zones faibles dans le matériau et agit seulement sur la résistance. Cette variable réduite est une donnée nécessaire à l'estimation probabiliste de la résistance et peut être calculée par la théorie des milieux poreux.

Summary

The dependence between the strength of concrete R and the sound velocity v, as well as material density σ-can be expressed by a dimensioless number of mechanical similitude Bu=R/v² σ, denoted by the name of the well-known Polish scientist Bronislaw Bukowski, who was working in the field of concrete technology. Instead of strength the elasticity coefficients can be introduced into Bu number, as its theoretical basis is the formula of wave velocity in elastic materials.

The tests carried out on small samples 4/4/16 cm have proved the stability of Bu for the concretes of this kind of structure at various times of hardening and conditions of curing. For the vibrated fine concrete (W/C=0.4) has been found Bu=6.0×10⁻⁴, for cement mortar 1∶3−Bu=5.34×10⁻⁴

The stability of Bukowski's number is a condition of similitude of the macrostructure of concrete and of the way of testing. So Bu depends on two parameters that can be also expressed in the form of dimensionless criteria: the first—grouping the linear dimensions of samples and the wave longitude, the second—determining the macrostrucrure of concrete and expressed by technological data as well as by geometry terms of porous or heterogeneous media.

The attempts to determine a simple functional relationship R—v did not take into account the fact, that R only (not v) depends on the random disposition of the weakest places in material. It has been proved that the dispersion of aggregate grains is subjected to the statistical Poisson's distribution. A joint dimensionless structure coefficient λ as exponent in an exponential reliability function has been deduced. λ number takes into consideration not only the random variations or grain distribution, but also the fluctuations, caused by the conditions of production.