Issue 52

M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 83 categories: natural (like pumice, diatomite, volcanic ash, etc.) and manufactured (such as perlite, extended schist, clay, slate, sintered powdered fuel ash (PFA), etc.)  3, 5  . Beside its technical and financial interests, LWAC can be integrated into the demarche of sustainable improvement by utilizing in specific artificial aggregates which are lighter than natural aggregates  6  . The Young’s modulus (elastic modulus) is a very important material property which is measured directly on concrete. Engineers need to know the value of this parameter to conduct any computer simulation of structure. Various experimental works have concerned the study of behavior of LWAC  1, 7, 8, 9, 10, 11, 12  . However from an experimental point of view, this is not always easy. Therefore when the tests are impossible, difficult, costly, or time- consuming, the research about prediction models for the elastic modulus using properly validated composite models is of great practical interest. The aim of the composites materials approach is to develop a model that will enable expression of average properties of the mixtures through properties and volume fractions of its constituents  11  . Diverse explicit models of the literature are utilized. Their application to the prediction of LWAC behaviors shows a wide dissimilarity between the different approaches particularly when the volume fraction of reinforcement is more than 40% and when the contrast between the phases grows  9  . For this purpose and to distinguish the most appropriate two-phase composite model for predicting LWAC's effective modulus of elasticity, the estimation of the Young’s modulus of LWAC using two-phase composite models was applied. Furthermore, an efficient and accurate model is useful to reduce the cost and duration of the experimental mix design studies. In this present work, a large bibliography data for different LWAC tested experimentally and published in the literature are used: De Larrard  7  , Yang and Huang  8  , and Ke Y et al.  9  . For LWAC test results investigated in this study, the volume fraction V g of the lightweight aggregate varies from 0% (the matrix) to 47.8% and the contrast of the characteristics of the phases E g /E m (Young’s modulus of lightweight aggregate and matrix) varies between 0.20% and 95% except for four types of concretes for which this ratio exceeds 1 because of a very low value of E m (E g  E m )  7  . In order to determine the models likely to yield the lowest number of errors; the results of effective Young’s modulus of LWAC obtained by using 07 two-phase composite models were compared with the experimental results obtained by De Larrard  7  , Yang and Huang  8  and Ke Y et al.  9  (119 values) and discussed. Therefore, prediction possibilities using composite material models in determination of modulus of elasticity were sought and some suggestions were made accordingly to a statistical study. P REDICTION OF ELASTIC MODULUS FOR LWAC Two-phase composite models Ore attention has been paid to lightweight aggregate concrete. The weakest component of LWAC is not the cement matrix or the interfacial transition zone (ITZ) but the aggregates. Therefore, the research about prediction model for LWAC’s Young modulus is valuable for the concrete application  6  . Lo and Cui  13  illustrate that the ‘’Wall effect’’ does not exist on the surface of expanded clay aggregates in lightweight concrete by SEM and BSEI imaging, resulting in a better bond and much more slender interfacial zone than the ordinary concrete  14  . So, materials which are produced can be considered a two-phase composite material. The purpose of the composites materials approach is to develop a model that will enable expression of average properties of the mixtures through properties and volume fractions of its constituents  1, 11  . We look for the models to estimate the Young modulus for Lightweight Aggregate Concrete (LWAC) in terms of the properties and volume fractions of its constituents. These include the mortar matrix and the lightweight aggregate as reinforcing material. Before analyzing Lightweight Aggregate Concrete as a composite material, some assumptions must be considered. First, the heterogeneous composite material (LWAC) is considered to be comprised of only two linear-elastic phases (the mortar and the lightweight aggregate). Second, the unit cell is assumed sufficiently large to account for the heterogeneity of the system, and the deferring geometry of the phases. However, it is extremely small so that the composite is described homogeneous on a macro scale  10, 15, 16  . Fig. 1 presents the models for an idealized unit cell of a two-phase composite material  10, 11, 17  . The LWAC comprises a dispersed phase of lightweight aggregate with a Young’s modulus E g and volume fraction V g and a continuous phase of the mortar matrix, with a Young’s modulus E m and volume fraction V m . M