Multi scale probabilistic analysis of the elastic modulus of concrete using digital image processing -

Abstract

In the design of concrete structures, knowledge of the materials properties is required to conduct a proper, safe, and economical design. Young’s modulus of concrete, denoted as (E), is in particular a key mechanical parameter utilized by engineers in the design and analysis of concrete structures. Design codes provide the engineers with relationships to estimate the elastic modulus of concrete of different strengths; these formulas relate (E) to its 28 day compressive strength. However, concrete is a highly heterogeneous material and extensive research shows that its mechanical properties are effected by the properties of its constituents. Several researchers provided composite models that relate the elastic modulus of concrete to the elastic modulus and volumetric fractions of aggregate, mortar, and interfacial zone (ITZ). However, these models interpret concrete as a homogeneous medium and use deterministic values for the elastic properties of the input variables (aggregate, mortar, and ITZ); thus, neglecting the effects of the spatial distribution of aggregates and the natural variation in the elastic properties of the input variables on the elastic modulus estimation. This study presents a probabilistic framework for estimating the modulus of elasticity of concrete while taking into consideration the uncertainties associated with the mix constituents and their spatial distribution. The variability of the characteristic of the mix constituents, i.e. elastic modulus and Poisson’s ratio, is quantified by experimentally testing cylindrical core specimens of limestone and mortar. The tested specimens originate from different local sources for the case of the limestone and correspond to different mix design proportions for the mortar. This is specifically done to capture the possible range of variability for the input parameters. The spatial distribution of the aggregates and the volumetric fractions are captured by utilizing digital image correlation techniques to process scanned images of sections