Approche du coefficient de sécurité réel par l'étude de la contrainte moyenne entre deux singularités dans un modèle élémentaire de matériau granulaire cohérent soumis à une compression monoaxiale

Résumé

Dans un modéle comportant deux singularités de même diamètre placées perpendiculairement à la direction d'une sollicitation de compression monoaxiale, dont chaque phase suit les lois de l'élasticité linéaire, l'étude présentée en contraintes planes, propose des relations complétées par une abaque, reliant la contrainte de compression appliquée à la contrainte locale extrême par l'intermédiaire de la contrainte myoenne calculée sur le segment de matrice joignant les centres des singularités. Sur cet axe, les contraintes sont déterminées théoriquement par la méthode des facteurs d'influence, puis expérimentalement en photoélasticité par transmission. Les contraintes moyennes sont calculées en fonction des distances et des grosseurs relatives des singularités, ainsi que des modules d'élasticité des deux phases. La loi de comportement du matériau au seuil de réversibilité fixant la contrainte maximale ultime, la contrainte appliquée ultime est alors connue et fournit le coefficient réel de sécurité dont on dispose.

Summary

Knowledge of the safety factor in the design of a structure in cohesive granular materials (e.g. concrete) is essential. A simple approach taking heterogeneity into account is proposed for obtaining the safety factor in a significant elementary model consisting of a cohesive granular material subjected to unidirectional compression; the results are shown in terms of two-dimensional stress. The average stress between two inclusions (singular features) can easily be measured experimentally and was used as a parameter for measurement of the distance between the stress applied and the field of stress tensors. The material was defined by the ratio of the moduli of elasticity of the binder and the aggregate and by the relative distances from the inclusions. The model had two inclusions of the same diameter aligned perpendicularly to the unidirectional compression applied. Each phase obeyed the laws of linear elasticity. Lorrain's factors of influence method was used as a simple procedure for theoretical calculation of the stresses between the inclusions and justified the elementary model proposed. The method gave results for infinitely rigid inclusions and for holes. Experimental verification was performed using transmission photoelasticity on plane models subjected to unidirectional compression. Stresses were separated by the finite difference method using the isoclinic and isochromatic lines at the apices of a grid. There was good agrement between experimental and theoretical results, making it possible to extend the experimental results to varying ratios of moduli of elasticity between binder and aggregate and enabling, measurements of relative distances between inclusions shorter than the limits of the theoretical study. Finally, formulation of the stress applied is proposed through the average stress between the inclusions; a graph relates the latter to the last local stress whose value is determined by the behaviour law of the material in question. The actual safety factor is thus obtained.