Microsoft Word - numero_52_art_07_2686 M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 82 Alternative estimation of effective Young’s Modulus for Lightweight Aggregate Concrete LWAC Meriem Fakhreddine Bouali Department of Civil Engineering, Faculty of Sciences & Technology, University of Mohamad Cherif Messaadia, Souk Ahras, 41000, Algeria m.bouali@univ-soukahras.dz b.meriemfakhreddine@gmail.com, http://orcid.org/0000-0002-6986-980X Abdelkader Hima Department of Electrical Engineering, Faculty of Technology, University of El-Oued, 39000, Algeria Abdelkader-hima@univ-eloued.dz, http://orcid.org/0000-0002-5533-3991 ABSTRACT. The prediction of effective mechanical properties of composite materials using analytical models is of significant practical interest in situations in which tests are impossible, difficult, or costly. Many experimental and numerical works are attempting to predict the elastic properties of Lightweight Aggregate Concrete (LWAC). In order to choose the optimized prediction composite model, the purpose of this paper is to appraise the effective Young’s modulus of LWAC using two-phase composite models. To this effect, results of previous experimental research have used as a platform, upon which, 07 two-phase composite models were applied. The outcomes of this comparative analysis show that not all two-phase analytical models can be directly used for predicting Young’s modulus of LWAC. The Maxwell, Counto1 and Hashin-Hansen models are in close concordance with the experimental Young’s modulus of all LWAC used for comparison in this study (119 values). They were found more appropriate for reasonable prediction of elasticity modules of the LWAC. KEYWORDS. Analytic model; Concrete; Young’s modulus; Lightweight aggregate; Two-phase. Citation: Bouali, M. F., Hima, A. Alternative estimation of effective Young’s Modulus for Lightweight Aggregate Concrete LWAC, Frattura ed Integrità Strutturale, 52 (2020) 82- 97. Received: 15.11.2019 Accepted: 08.01.2020 Published: 01.04.2020 Copyright: © 2020 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION ecently, special attention has been paid to the development of Lightweight Aggregate Concrete (LWAC) 1, 2, 3 which offers many advantages as a building material, including low weight, easier construction and better resistance compared with ordinary concrete. Lightweight Aggregate Concrete (LWAC) primarily improves the thermal and sound insulation properties of buildings next to its basic applications 4. The lightweight concrete are created by substituting the natural aggregates with the lightweight aggregates (LWA), which are classified into two fundamental R https://youtu.be/y01QADxMwDw 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 Vg of the lightweight aggregate varies from 0% (the matrix) to 47.8% and the contrast of the characteristics of the phases Eg/Em (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 Em (Eg  Em) 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. PREDICTION 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 Eg and volume fraction Vg and a continuous phase of the mortar matrix, with a Young’s modulus Em and volume fraction Vm. M M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 84 As explained by Gilormini and Brechert 18, the choice of a model is governed by several parameters including the geometry of the heterogonous medium, the mechanical contrast between the phases (Eg/Em) and the volume fraction of reinforcement (Vg). Therefore, the equivalent homogenous behavior of LWAC depends of the characteristics of the mortar (matrix, phase m) and lightweight aggregate (dispersed phase, phase g). Figure 1: Composite models: (a) Voigt model, (b) Reuss model, (c) Popovics model, (d) Hirsch-Dougill model, (e) Hashin-Hansen model, (f) Maxwell model, (g) Counto1 model, (h) Counto2 model. Voigt model 10, 19: c _ Voigt m m g gE E V E V  . (1) Reuss model 10, 19:   m g c _ Reuss g g m g E E   E E V E E    (2) Popovics model 10, 20:  Voigt Reussc _ Popovics c c1E E E 2   . (3) Hirsch-Dougill model 10, 15, 21: c _ Hirsch c _ Voigt c _ Reuss 1 1 E 2 1 1 E E         (4) Hashin-Hansen model 10, 11, 22:         m g g m g c _ Hashin m m g g m g E E E E V E E E E E E V            . (5) Maxwell model (dispersed phase) 10, 15:         g c _ Maxwell m g g m 1 2V α 1 / α 2 E E 1 V α 1 / α 2 E E                   . (6) Counto1 mod 17, 23:   g c _ Counto1 m m g g g m V E E 1 E V V E E                . (7) Counto2 model 17:   g c _ Counto2 m g g g m V E E 1 E V E E              . (8) Bache and Nepper-Christensen model 15, 24: gm VV c _ Bache m gE E E  (9) M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 85 The models of Voigt (Eq. and Reuss (Eq.2) provide the upper and lower bound of effective properties, respectively. It has been indicated 11, 19 that the upper bound relation of the parallel phase ‘Voigt Model’ might be applied as a first approximation to LWAC when g mE E . However, the relation of the series phase ‘Reuss model’ validates the results of normal weight concrete with g mE E 11, 19. The biphasic models of Popovics (Eq. 3) and Hirsch-Dougill (Eq. 4) originally designed for composites with particles (like concrete) [25], propose elastic modulus of the composite by combining the Voigt and Reuss models. Hirsh 21 derived an equation to express the elastic modulus of concrete in terms of empirical constant, and also provided some experimental results for the elastic modulus of concrete with different aggregates. The model composite spheres was introduced by Hashin 25. This model consists of a gradation of size of spherical particles embedded in a continuous matrix 26. Hansen 19 evolved mathematical models to predict the elastic modulus of composite materials based on the individual elastic modulus and volume portion of the components. From the concentric model, Hashin-Hansen model (Eq. 5) supposes that the Poisson ratios of all phases and the composite are equal (c=m=0.2) 10, 19. The dispersed phase model ‘’Maxwell model’’, Eq. (6), describes concrete as a dispersed phase composite material 10, 11. As a concentric model 10, Zhou et al. 17 indicate that a more realistic Counto1 model (Eq.7) can be considered (Fig. 1g). Another version of Counto’s model (Eq.8) 17 is presented in Fig. 1h. The strength-based Bache and Nepper- Christensen model (Eq. 9), gives a geometric average of component properties in relation to their volume fractions Vm and Vg. This is a mathematical model with no physical meaning 17. Experimental data from published literature In this section, the bibliography data for different Lightweight Aggregate Concrete (LWAC) tested experimentally by De Larrard 7, Yang and Huang 8 and Ke Y et al. 9 are compiled in Tabs. 1, 2 and 3, respectively. The mechanical properties Em, Eg are the Young’s modulus of the matrix (mortar: phase m) and lightweight aggregate (dispersed phase, phase g), respectively. The Young’s modulus of the composite obtained experimentally by De Larrard 7, Yang and Huang 8 and Ke Y et al. 9 are _  exp De LarrardE , _exp YangE and _Eexp Ke respectively. For LWAC test results by De Larrard 7 compiled in Tab. 1, it can be seen that the volume fraction Vg (the volume fraction of the lightweight aggregate) varies from 25.5% to 47.8% and that the contrast of the characteristics of the phases Eg/Em varies between 27.74% and 95% except for four types of concretes for which this ratio exceeds 1 because of a very low value of Em (Eg  Em). In their experimental program Yang and Huang 8 have tested three types of artificial coarse aggregates with Young's modulus of 6.01, 7.97 and 10.48GPa made of cement and fly ash with various combinations through a cold-pelletizing process. Each type of aggregate was mixed with four types of mortar matrices with a Young's modulus of 29.330, 28.130, 26.440 and 24.870GPa. This corresponds to a contrast ratio Eg/Em between the two phases ranging from 20.49% to 42.14%. By supposing a Poisson’s ratio of 0.2, the strength of coarse aggregate was computed from the elastic moduli of the components and the strength of concrete. The rate of lightweight aggregate volume fraction Vg was between 18% and 36%, the diameter of the gold aggregates assumed as spherical for all concretes tested had a d/D ratio in the order of (5/10) mm (Tab. 2). In their study, concrete was considered as a composite material in which coarse aggregate were embedded in a matrix of hardened mortar. In the experimental study of Ke Y et al. 9, five LWAs are used: three expanded clay aggregates (A) of quasi-spherical shape (0/4 650A, 4/10 550A, 4/10 430 A) and two aggregates of expanded shale (S) of irregular shape (4/10 520S, 4/8 750 S). The three used matrices (called M8, M9 and M10) are made of Portland cement mortar CEM I 52.5 and normal sand 0/2 mm. Normal, high performance (HP) and very high performance (VHP) mortar matrices, were utilized for the realization of the concrete specimens tested by Ke Y et al. 9. In their work, the volume fraction of aggregate was 0% (mortar), 12.5%, 25%, 37.5% and 45% with a contrast of the properties varying from 12.26% to 69.61%. The Young’s modulus of the three mortar matrices were experimentally determined as 28.6, 33.2 and 35.4 GPa for M8, M9 and M10, respectively, as seen in Tab. 3 9. They correspond to a normal, HP and VHP matrix, respectively 9. Mechanical properties of the lightweight aggregate are shown in Tab. 4 9. The elastic modulus of LWAC is estimated by utilizing some composite material models _c analE like Popovics, Hirsch- Dougill, Hashin-Hansen, Maxwell, Counto1, Counto2, and Bache and Nepper-Christensen (Eqs.(2)-(9)). M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 86 This Study try to figure out that these composite material models, mentioned above, got reliable prediction abilities for the modulus of elasticity of LWAC. The modulus of elasticity values were predicted utilizing the composite models and then, the predicted results were compared to the experimental results of De Larrard 7, Yang and Huang 8 and Ke Y et al. 9 respectively. Ref. grav. d/D (mm) Vg Eg (GPa) Em (GPa) Eexp_De Larrard (GPa) 8 Argi 16 8 Isol S 8 Leca 7j. 8 Leca 28j. 8 Surex 675 8 Galex 7j. 8 Galex 28j. 9 Schiste 15j. 9 Schiste 28j. 9 Leca 1j. 9 Leca 2j. 9 Leca 7j. 9 Leca 28j. 9 Leca 90j. 9 Surex 1j. 9 Surex 2j. 9 Surex 7j. 9 Surex 28j. 9 Surex 90j. 3 LWC1 Crush 3 LWC1 Crush 3 LWC1 Pellet 3 LWC1 Pellet 3 HSLWC Pel. 3 HSLWC Pel. 1 Liapor 2 Liapor 16 Javron 16 G/S -0.2 16 G/S +0.2 16 EAU + 16 EAU – 4-12 3.15-8 4-10 4-10 6.3-10 3-8 3-8 - - 4-10 4-10 4-10 4-10 4-10 6.3-10 6.3-10 6.3-10 6.3-10 6.3-10 10-20 10-20 5-20 5-20 5-20 5-20 0-16 4-16 4-10 4-10 4-10 4-10 4-10 0.414 0.414 0.414 0.414 0.414 0.425 0.425 0.391 0.391 0.414 0.414 0.414 0.414 0.414 0.414 0.414 0.414 0.414 0.414 0.403 0.403 0.414 0.414 0.255 0.255 0.473 0.432 0.463 0.443 0.478 0.473 0.453 8 13.1 7.6 7.6 16.2 33 33 21 21 8.6 8.6 8.6 8.6 8.6 19 19 19 19 19 13.6 13.6 14 14 14 14 21.5 21.5 16 16 16 16 16 25.2 25.2 23.5 25.2 25.2 20.6 21.9 24.9 25.6 11 15 20 25.2 31 11 15 20 25.2 31 33.2 33.2 32.8 32.8 38.5 38.5 29.7 27.9 23.8 24.6 23.1 26.6 21.1 15.6 19.2 14.1 15.7 21 25.5 25.8 23.9 23.4 10 12 13.9 16 17.8 14.6 17.1 20.6 22.3 22.6 23 24.3 22.7 24.3 27.6 28.3 25.5 24.8 19.7 19.9 19.7 20.9 18.1 Table 1: Characteristics of LWAC tested by De Larrard 7. Ref. grav. d/D (mm) Vg Eg (GPa) Em (GPa) Eexp_Yang (GPa) A3 A4 A5 A6 5-10 0.18 0.24 0.30 0.36 6.01 6.01 6.01 6.01 29.33 28.13 26.44 24.87 23.020 20.600 18.210 15.800 B3 B4 B5 B6 0.18 0.24 0.30 0.36 7.97 7.97 7.97 7.97 29.33 28.13 26.44 24.87 23.790 21.530 19.010 17.220 C3 C4 C5 C6 0.18 0.24 0.30 0.36 10.48 10.48 10.48 10.48 29.33 28.13 26.44 24.87 24.660 22.580 20.320 18.650 Table 2: Characteristics of LWAC tested by Chung-Chia Yang and Ran Huang 8. M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 87 Eexp_Ke E0Ke E0.125Ke E0.250Ke E0.375Ke E0.450Ke M8 0/4 650A 4/10 550A 4/10 430A 4/10 520S 4/8 750S 28.588 23.539 26.157 24.900 25.135 27.367 20.665 21.680 21.391 22.471 26.262 16.743 17.900 17.293 19.428 25.281 15.669 16.606 15.699 18.286 24.324 M9 0/4 650A 4/10 550A 4/10 430A 4/10 520S 4/8 750S 33.183 29.396 29.159 27.568 29.480 31.931 23.712 24.934 23.778 26.521 30.987 19.871 21.358 20.818 22.188 30.146 17.175 19.696 18.935 20.184 29.311 M10 0/4 650A 4/10 550A 4/10 430A 4/10 520S 4/8 750S 35.397 31.147 32.089 30.220 32.783 34.213 26.753 27.991 26.033 27.998 33.845 22.427 23.684 22.296 24.340 32.945 20.346 21.724 20.082 22.024 33.002 Table 3: Characteristics of LWAC tested by Ke Y et al. 9 (GPa). LWA 0/4 650A 4/10 550A 4/10 430A 4/10 520S 4/8 750S Eg 6.870 6.790 4.340 6.490 19.900 Table 4: Mechanical properties of lightweight aggregate tested by Ke Y et al. 9 (GPa). RESULTS AND DISCUSSIONS Comparative analysis omparison between the estimative results of effective elastic modulus of LWAC obtained as a result of calculations of the Eqns. (2-9) and those of experimental data have been presented in Tabs. 5, 6 and 7 respectively. A confrontation of LWAC Young’s modulus between experimental results in 7, 8, 9 and the predictions of 07 composite models material models are shown in Fig. 2, Fig. 3 and Fig. 4 respectively. The differences between the various predictive composite models and the experimental results in 7, 8, 9 have been computed according to the proportion of reinforcement Vg in LWAC. When the volume fraction of aggregates Vg grows, the errors between the predictions and the experimental results increase for all composite material models. Since the weakest component of LWAC is not the cement matrix but the lightweight aggregates, the effect of volume fraction of lightweight aggregate on Young’s modulus of LWAC is very clear. The increase in the volume fraction of lightweight aggregates Vg substantially reduces the Young’s modulus of the LWAC. To compare the experimental and predicted Young’s modulus of LWAC, the error percentage E . is determined using the following expression:   c _ anal exp exp E E E  % 100 E          (10)  E Abs E   , Absolute value of E  It appears for first time that all models are generally suitable for predicting the modulus of elasticity of the LWAC. Tabs. 8-9-10 give the error percentages of the composite material models and experimental results in 7, 8, 9 respectively. In order to choose the models which have good performances, the error percentages below 10% are chosen as desired range and the model’s error percentages below this value are indicated in bold. Therefore, the models which verified this condition have been underlined. C M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 88 Ref. grav. Eexp_De Larrard Ec_Popovics Ec_Hirsch Ec_Hashin Ec_Maxwell Ec_Counto1 Ec_Counto2 Ec_Bache 8 Argi 16 8 Isol S 8 Leca 7j. 8 Leca 28j. 8 Surex 675 8 Galex 7j. 8 Galex 28j. 9 Schiste 15j. 9 Schiste 28j. 9 Leca 1j. 9 Leca 2j. 9 Leca 7j. 9 Leca 28j. 9 Leca 90j. 9 Surex 1j. 9 Surex 2j. 9 Surex 7j. 9 Surex 28j. 9 Surex 90j. 3 LWC1 Crush 3 LWC1 Crush 3 LWC1 Pellet 3 LWC1 Pellet 3 HSLWC Pel. 3 HSLWC Pel. 1 Liapor 2 Liapor 16 Javron 16 G/S -0.2 16 G/S +0.2 16 EAU + 16 EAU – 15.6 19.2 14.1 15.7 21 25.5 25.8 23.9 23.4 10 12 13.9 16 17.8 14.6 17.1 20.6 22.3 22.6 23 24.3 22.7 24.3 27.6 28.3 25.5 24.8 19.7 19.9 19.7 20.9 18.1 15.71 19.21 14.76 15.39 20.98 25.19 26.09 23.29 23.69 9.93 11.91 14.10 16.17 18.32 13.82 16.54 19.58 22.42 25.30 23.15 23.15 23.05 23.05 29.44 29.44 25.49 24.93 19.80 20.33 19.38 20.92 18.61 15.35 19.16 14.44 14.98 20.97 25.17 26.07 23.29 23.69 9.93 11.89 14.00 15.88 17.69 13.80 16.54 19.58 22.41 25.28 22.95 22.95 22.88 22.88 29.17 29.17 25.49 24.93 19.80 20.32 19.38 20.90 18.61 16.30 19.37 15.29 16.04 21.04 25.09 26.02 23.30 23.70 9.94 11.97 14.33 16.68 19.24 13.73 16.54 19.58 22.43 25.40 23.61 23.61 23.45 23.45 30.31 30.31 25.52 24.94 19.84 20.38 19.41 21.00 18.63 16.98 19.67 15.91 16.76 21.19 25.32 26.20 23.33 23.73 9.96 12.11 14.69 17.31 20.20 13.90 16.57 19.58 22.50 25.63 24.25 24.25 24.04 24.04 31.08 31.08 25.62 25.01 19.96 20.53 19.51 21.21 18.68 16.76 19.57 15.71 16.52 21.14 25.24 26.13 23.32 23.72 9.95 12.06 14.57 17.10 19.88 13.84 16.56 19.58 22.48 25.55 24.05 24.05 23.84 23.84 31.07 31.07 25.58 24.98 19.91 20.47 19.47 21.12 18.66 15.79 19.16 14.82 15.50 20.93 24.96 25.91 23.28 23.67 9.92 11.87 14.08 16.22 18.51 13.63 16.51 19.58 22.39 25.24 23.13 23.13 23.02 23.02 29.38 29.38 25.46 24.90 19.77 20.29 19.35 20.87 18.59 15.67 19.22 14.73 15.34 20.99 25.17 26.07 23.30 23.69 9.93 11.91 14.10 16.15 18.23 13.79 16.54 19.58 22.42 25.31 23.17 23.17 23.06 23.06 29.75 29.75 25.49 24.93 19.80 20.33 19.38 20.92 18.61 Table 5: Modulus of elasticity of LWAC predicted by various composite models compared with the experimental results of De Larrard 7(GPa). Ref. grav. Eexp_Yang Ec_Popovics Ec_Hirsch Ec_Hashin Ec_Maxwell Ec_Counto1 Ec_Counto2 Ec_Bache A3 A4 A5 A6 23.020 20.600 18.210 15.800 21.201 18.879 16.701 14.879 20.471 18.055 15.920 14.190 23.102 20.559 18.039 15.905 23.967 21.501 18.963 16.770 24.121 21.523 18.860 16.570 21.589 19.265 17.018 15.124 22.049 19.422 16.953 14.915 B3 B4 B5 B6 23.790 21.530 19.010 17.220 22.635 20.398 18.248 16.445 22.276 19.987 17.863 16.112 23.848 21.481 19.106 17.095 24.530 22.218 19.820 17.754 24.653 22.236 19.739 17.600 22.709 20.504 18.340 16.515 23.198 20.784 18.451 16.510 C3 C4 C5 C6 24.660 22.580 20.320 18.650 24.047 21.963 19.900 18.166 23.898 21.794 19.746 18.039 24.723 22.568 20.369 18.512 25.214 23.093 20.867 18.960 25.305 23.106 20.810 18.854 23.944 21.900 19.854 18.130 24.370 22.195 20.030 18.221 Table 6: Modulus of elasticity of LWAC predicted by various composite models compared with the experimental results of Yang and Huang 8(GPa). M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 89 Ref. grav. Eexp_Ke Ec_Popovics Ec_Hirsch Ec_Hashin Ec_Maxwell Ec_Counto1 Ec_Counto2 Ec_Bache M8 0/4 650 A 28.588 23.539 20.665 16.743 15.669 28.588 23.182 19.563 16.762 15.308 28.588 22.870 18.903 15.954 14.504 28.588 24.522 20.996 17.908 16.234 28.588 25.101 21.886 18.912 17.233 28.588 25.303 21.886 18.652 16.845 28.588 23.253 19.833 17.044 15.556 28.588 23.921 20.016 16.748 15.050 M8 4/10 550 A 28.588 26.157 21.680 17.900 16.606 28.588 23.132 19.499 16.693 15.237 28.588 22.810 18.820 15.863 14.413 28.588 24.499 20.956 17.857 16.176 28.588 25.084 21.855 18.870 17.185 28.588 25.288 21.855 18.607 16.793 28.588 23.215 19.781 16.984 15.492 28.588 23.886 19.957 16.675 14.971 M8 4/10 430 A 28.588 24.900 21.391 17.293 15.699 28.588 21.195 17.227 14.366 12.906 28.588 20.297 15.597 12.534 11.142 28.588 23.769 19.699 16.216 14.357 28.588 24.561 20.895 17.543 15.667 28.588 24.828 20.895 17.203 15.162 28.588 21.878 18.062 15.041 13.450 28.588 22.586 17.845 14.099 12.240 M8 4/10 520 S 28.588 25.135 22.471 19.428 18.286 28.588 22.939 19.253 16.429 14.967 28.588 22.576 18.499 15.516 14.063 28.588 24.414 20.808 17.662 15.959 28.588 25.022 21.740 18.711 17.002 28.588 25.233 21.740 18.439 16.597 28.588 23.067 19.583 16.756 15.250 28.588 23.752 19.733 16.395 14.669 M8 4/10 750 S 28.588 27.367 26.262 25.281 24.324 28.588 27.305 26.095 24.948 24.286 28.588 27.304 26.091 24.942 24.280 28.588 27.335 26.137 24.988 24.322 28.588 27.396 26.237 25.110 24.448 28.588 27.421 26.237 25.077 24.397 28.588 27.236 26.027 24.895 24.244 28.588 27.322 26.113 24.957 24.288 M9 0/4 650 A 33.183 29.396 23.712 19.871 17.175 33.183 26.167 21.778 18.468 16.763 33.183 25.636 20.708 17.195 15.512 33.183 28.147 23.821 20.065 18.040 33.183 28.904 24.978 21.363 19.328 33.183 29.166 24.978 21.028 18.829 33.183 26.435 22.283 18.937 17.160 33.183 27.253 22.383 18.384 16.336 M9 4/10 550 A 33.183 29.159 24.934 21.358 19.696 33.183 26.108 21.707 18.394 16.688 33.183 25.562 20.611 17.093 15.410 33.183 28.123 23.780 20.012 17.981 33.183 28.887 24.947 21.320 19.279 33.183 29.151 24.947 20.982 18.776 33.183 26.392 22.228 18.874 17.094 33.183 27.214 22.318 18.303 16.250 M9 4/10 430 A 33.183 27.568 23.778 20.818 18.935 33.183 23.852 19.220 15.934 14.259 33.183 22.477 16.848 13.338 11.782 33.183 27.365 22.485 18.333 16.127 33.183 28.353 23.970 19.975 17.743 33.183 28.684 23.970 19.555 17.121 33.183 24.953 20.430 16.871 15.001 33.183 25.733 19.955 15.475 13.285 M9 4/10 520 S 33.183 29.480 26.521 22.188 20.184 33.183 25.881 21.435 18.113 16.405 33.183 25.274 20.234 16.699 15.021 33.183 28.034 23.627 19.812 17.759 33.183 28.824 24.830 21.158 19.093 33.183 29.095 24.830 20.811 18.577 33.183 26.232 22.020 18.638 16.845 33.183 27.060 22.067 17.996 15.923 M9 4/10 750 S 33.183 31.931 30.987 30.146 29.311 33.183 31.075 29.150 27.371 26.362 33.183 31.069 29.133 27.346 26.335 33.183 31.170 29.276 27.490 26.466 33.183 31.303 29.493 27.749 26.732 33.183 31.355 29.493 27.679 26.626 33.183 30.943 29.031 27.287 26.298 33.183 31.128 29.201 27.393 26.363 M10 0/4 650 A 35.397 31.147 26.753 22.427 20.346 35.397 27.567 22.816 19.271 17.450 35.397 26.907 21.515 17.742 15.953 35.397 29.889 25.176 21.098 18.905 35.397 30.735 26.466 22.541 20.334 35.397 31.026 26.466 22.169 19.781 35.397 27.953 23.452 19.839 17.925 35.397 28.838 23.494 19.141 16.926 M10 4/10 550 A 35.397 32.089 35.397 27.504 35.397 26.826 35.397 29.865 35.397 30.718 35.397 31.011 35.397 27.909 35.397 28.796 M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 90 27.991 23.684 21.724 22.742 19.195 17.373 21.411 17.633 15.847 25.135 21.045 18.845 26.434 22.497 20.285 26.434 22.123 19.727 23.396 19.776 17.858 23.426 19.057 16.837 M10 4/10 430 A 35.397 30.220 26.033 22.296 20.082 35.397 25.099 20.162 16.680 14.904 35.397 23.460 17.394 13.683 12.055 35.397 29.096 23.825 19.351 16.977 35.397 30.180 25.451 21.146 18.742 35.397 30.541 25.451 20.687 18.063 35.397 26.427 21.564 17.748 15.746 35.397 27.229 20.946 16.112 13.766 M10 4/10 520 S 35.397 32.783 27.998 24.340 22.024 35.397 27.261 22.459 18.906 17.085 35.397 26.510 21.007 17.218 15.439 35.397 29.775 24.980 20.843 18.621 35.397 30.654 26.316 22.334 20.098 35.397 30.954 26.316 21.950 19.527 35.397 27.743 23.183 19.536 17.606 35.397 28.634 23.163 18.737 16.498 M10 4/10 750 S 35.397 34.123 33.845 32.945 33.002 35.397 32.858 30.576 28.491 27.317 35.397 32.847 30.546 28.449 27.273 35.397 33.001 30.762 28.665 27.469 35.397 33.176 31.047 29.002 27.815 35.397 33.244 31.047 28.912 27.677 35.397 32.695 30.437 28.398 27.249 35.397 32.938 30.651 28.522 27.316 Table 7: Modulus of elasticity of LWAC predicted by various composite models compared with the experimental results of Ke Y et al. 9(GPa). Figure 2: Confrontation of LWAC Young’s modulus between experimental results in 7 and the predictions of 07 composite material models. Figure 3: Confrontation of LWAC Young’s modulus between experimental results in 8 and the predictions of 07 composite material models. 5 10 15 20 25 30 35 5 10 15 20 25 30 E c_ a n a l (G P a ) Eexp_De Larrard (GPa) Ec_Hashin Ec_Popovics Ec_Hirsch Ec_Bache Ec_Counto2 Ec_Maxwell Ec_Counto1 5 10 15 20 25 30 5 10 15 20 25 30 E c_ a n a l (G P a ) Eexp_Yang (GPa) Ec_Hashin Ec_Popovics Ec_Hirsch Ec_Bache Ec_Counto2 Ec_Maxwell Ec_Counto1 M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 91 Figure 4: Confrontation of LWAC Young’s modulus between experimental results in 9 and the predictions of 07 composite material models. Ref. grav. Popovics Hirsch- Dougill Hashin- Hansen Maxwell Counto1 Counto2 Bache and Nepper- Christensen 8 Argi 16 8 Isol S 8 Leca 7j. 8 Leca 28j. 8 Surex 675 8 Galex 7j. Galex 28j. 9 Schiste 15j. 9 Schiste 28j. 9 Leca 1j. 9 Leca 2j. 9 Leca 7j. 9 Leca 28j. 9 Leca 90j. 9 Surex 1j. 9 Surex 2j. 9 Surex 7j. 9 Surex 28j. 9 Surex 90j. LWC1 Crush 3 LWC1 Crush 3 LWC1 Pellet 3 LWC1 Pellet 3 HSLWC Pel. 3 HSLWC Pel. 1 Liapor 2 Liapor 16 Javron 16 G/S -0.2 16 G/S +0.2 16 EAU + 16 EAU – 0.68 0.05 4.65 -1.98 -0.09 -1.21 1.11 -2.53 1.24 -0.66 -0.76 1.42 1.05 2.93 -5.36 -3.25 -4.95 0.52 11.96 0.66 -4.73 1.54 -5.15 6.65 4.02 -0.03 0.52 0.52 2.16 -1.61 0.09 2.84 -1.62 -0.21 2.40 -4.61 -0.15 -1.28 1.06 -2.53 1.24 -0.67 -0.90 0.70 -0.76 -0.63 -5.48 -3.26 -4.95 0.52 11.87 -0.21 -5.55 0.80 -5.84 5.68 3.06 -0.05 0.51 0.48 2.11 -1.64 -0.01 2.83 4.48 0.89 8.44 2.16 0.18 -1.60 0.84 -2.52 1.27 -0.61 -0.23 3.12 4.27 8.07 -5.96 -3.30 -4.95 0.60 12.37 2.66 -2.83 3.29 -3.51 9.82 7.11 0.07 0.57 0.71 2.41 -1.47 0.47 2.91 8.87 2.46 12.87 6.77 0.93 -0.69 1.55 -2.41 1.42 -0.38 0.91 5.68 8.20 13.50 -4.79 -3.08 -4.94 0.91 13.39 5.43 -0.21 5.88 -1.09 12.61 9.82 0.49 0.85 1.34 3.14 -0.94 1.48 3.22 7.42 1.93 11.40 5.24 0.67 -1.03 1.28 -2.44 1.38 -0.46 0.52 4.82 6.90 11.71 -5.22 -3.15 -4.95 0.81 13.04 4.56 -1.03 5.01 -1.90 12.57 9.79 0.30 0.74 1.07 2.86 -1.18 1.04 3.09 1.21 -0.23 5.14 -1.29 -0.33 -2.13 0.43 -2.59 1.16 -0.77 -1.04 1.27 1.36 3.98 -6.64 -3.44 -4.96 0.39 11.67 0.57 -4.81 1.40 -5.28 6.45 3.81 -0.17 0.40 0.34 1.94 -1.77 -0.13 2.72 0.46 0.11 4.44 -2.28 -0.06 -1.30 1.04 -2.53 1.25 -0.66 -0.71 1.45 0.92 2.42 -5.53 -3.26 -4.95 0.54 12.00 0.74 -4.65 1.57 -5.12 7.78 5.11 -0.04 0.52 0.52 2.17 -1.62 0.07 2.84 Table 8: Error percentages of composite models and experimental results in 7 (%). 10 15 20 25 30 35 40 10 15 20 25 30 35 40 E c_ a n a l (G P a ) Eexp_Ke (GPa) Ec_Hashin Ec_Popovics Ec_Hirsch Ec_Bache Ec_Counto2 Ec_Maxwell Ec_Counto1 M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 92 It can be observed from Tab. 8 that: For the Hirsch-Dougill, Popovics, Bache and Nepper-Christensen, Counto2 and Hashin-Hansen models, 31/32 cases lead to E smaller than 10%. All these models give a maximum E for a contrast equal to Eg/Em= 61.29% with a volume fraction of the aggregates Vg = 41.4% (aggregate: 9 Surex 90j.). For the Popovics and Bache and Nepper-Christensen models, 28/32 cases give E smaller than 5% and 3/32 cases give E smaller than 10%. E ranges from –5.53% to 12.00%. For the Hirsch-Dougill and Counto2 models, 27/32 cases give E smaller than 5% and 4/32 cases give E smaller than 10%. E ranges from –5.84% to 11.87%. For the Hashin-Hansen model, 31/32 cases lead to E smaller than 10%. Hence, for 26/32 cases it is smaller than 5%. E ranges from –5.96% to 12.37%. For the Counto1 and Maxwell models, 28/32 cases lead to E smaller than 10%, E ranges from –4.94% to 13.50%. It is clear from these results that the selected models are able to effectively estimate the Young’s modulus of LWAC tested by De Larrard [7] with a max difference E equal to 13.50% (obtained by the Maxwell model) using 32 measurements. Ref. grav. Popovics Hirsch- Dougill Hashin- Hansen Maxwell Counto1 Counto2 Bache and Nepper- Christensen A3 A4 A5 A6 -7.90 -8.36 -8.29 -5.83 -11.07 -12.35 -12.57 -10.19 0.36 -0.20 -0.94 0.66 4.11 4.37 4.13 6.14 4.78 4.48 3.57 4.87 -6.22 -6.48 -6.54 -4.28 -4.22 -5.72 -6.90 -5.60 B3 B4 B5 B6 -4.85 -5.26 -4.01 -4.50 -6.36 -7.17 -6.04 -6.44 0.25 -0.23 0.50 -0.72 3.11 3.20 4.26 3.10 3.63 3.28 3.84 2.21 -4.54 -4.77 -3.53 -4.09 -2.49 -3.47 -2.94 -4.12 C3 C4 C5 C6 -2.49 -2.73 -2.07 -2.59 -3.09 -3.48 -2.82 -3.28 0.26 -0.05 0.24 -0.74 2.25 2.27 2.69 1.66 2.62 2.33 2.41 1.09 -2.90 -3.01 -2.29 -2.79 -1.17 -1.70 -1.42 -2.30 Table 9: Error percentages of composite models and experimental results in 8 (%). Compared with the experimental data of Yang and Huang 8 (Tab. 6, Tab. 9), Bache and Nepper-Christensen, Counto2, Popovics, Hirsch-Dougill, underestimate the measured Young’s modulus. On the other hand, the Maxwell and Counto1 models overestimate the Young’s modulus measured by Yang and Huang [8]. As seen in Tab. 9, for the Hashin-Hansen and Counto1 models, 12/12 cases give E smaller than 5%. E ranges from 0.94% to 4.87%. The Maxwell gives 12/12 cases smaller than 10% and 11/12 smaller than 5%. E ranges from 1.66% to 6.14%. In all composite models, the error percentages differ between 0.05% and 12.57%. It can be seen that the most accurate models are those of Hashin-Hansen, Counto1 and Maxwell which give less errors percentages. The predictions of the LWAC Young’s modulus using the 07 composite material models are compared with experimental data of Ke Y et al. [9] (Tab. 7 and Tab.10) in Fig. 4. All selected composite models appear applicable to predict the Young’s modulus of LWAC tested by Ke Y et al [9]. For the Maxwell model, 50/75 cases give E smaller than 5% and 22/75 cases smaller than 10%. This means that 72/75 cases have E smaller than 10%. This model converges on the experimental values measured by Ke Y et al. [9] with an absolute maximum difference E of 15.72%. For the Counto1 model, 47/75 cases lead to E smaller than 5% and 23/75 smaller than 10%, which gives 70/75 cases with E smaller than 10%, with a maximum difference of 16.14%. For the Hashin-Hansen model, 59/75 cases give E smaller than 10% of which 38/75 cases smaller than 5%. E ranges from 0% to 16.77%. For the Counto2 model, 36/75 cases have E smaller than 10%, of which 27 cases have E smaller than 5%, with the maximum difference of 21.59%. For the Popovics model, 34/75 cases give E smaller than 10% with 25/75 cases smaller than 5%. The maximum E is 25.78%. M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 93 Ref. grav. Popovics Hirsch- Dougill Hashin- Hansen Maxwell Counto1 Counto2 Bache and Nepper- Christensen M8 0/4 650 A 0.00 4.18 1.60 6.96 3.61 0.00 -2.84 -8.53 -4.71 -7.43 0.00 1.52 5.33 0.12 2.31 0.00 6.63 5.91 12.96 9.98 0.00 7.49 5.91 11.40 7.50 0.00 1.21 4.03 1.80 0.72 0.00 1.62 -3.14 0.03 -3.95 M8 4/10 550 A 0.00 6.34 3.34 0.24 2.59 0.00 -12.80 -13.19 -11.38 -13.21 0.00 11.56 10.06 6.74 8.25 0.00 4.10 0.81 5.42 3.49 0.00 3.32 0.81 3.95 1.13 0.00 11.25 8.76 5.12 6.71 0.00 -8.68 -7.95 -6.84 -9.85 M8 4/10 430 A 0.00 4.54 7.91 6.23 8.55 0.00 -18.49 -27.09 -27.52 -29.03 0.00 14.88 19.47 16.93 17.79 0.00 1.36 2.32 1.45 0.20 0.00 0.29 2.32 0.52 3.42 0.00 12.14 15.56 13.02 14.33 0.00 -9.29 -16.58 -18.47 -22.04 M8 4/10 520 S 0.00 2.87 7.40 9.09 12.72 0.00 -10.18 -17.68 -20.14 -23.09 0.00 8.74 14.32 15.44 18.15 0.00 0.45 3.25 3.69 7.02 0.00 0.39 3.25 5.09 9.24 0.00 8.23 12.85 13.75 16.60 0.00 -5.50 -12.18 -15.61 -19.78 M8 4/10 750 S 0.00 0.12 0.48 1.16 0.01 0.00 -0.23 -0.65 -1.34 -0.18 0.00 0.23 0.63 1.32 0.16 0.00 0.11 0.09 0.68 0.51 0.00 0.20 0.09 0.81 0.30 0.00 0.48 0.90 1.53 0.33 0.00 -0.16 -0.57 -1.28 -0.15 M9 0/4 650 A 0.00 4.25 0.46 0.98 5.04 0.00 -12.79 -12.67 -13.46 -9.68 0.00 10.99 8.16 7.06 2.40 0.00 1.67 5.34 7.51 12.54 0.00 0.78 5.34 5.82 9.63 0.00 10.07 6.03 4.70 0.09 0.00 -7.29 -5.60 -7.49 -4.89 M9 4/10 550 A 0.00 3.55 4.63 6.30 8.71 0.00 -12.34 -17.34 -19.97 -21.76 0.00 10.46 12.94 13.88 15.27 0.00 0.93 0.05 0.18 2.12 0.00 0.03 0.05 1.76 4.67 0.00 9.49 10.85 11.63 13.21 0.00 -6.67 -10.49 -14.30 -17.50 M9 4/10 430 A 0.00 0.74 5.44 11.94 14.83 0.00 -18.47 -29.14 -35.93 -37.78 0.00 13.48 19.17 23.46 24.69 0.00 2.85 0.81 4.05 6.29 0.00 4.05 0.81 6.07 9.58 0.00 9.48 14.08 18.96 20.77 0.00 -6.66 -16.08 -25.67 -29.84 M9 4/10 520 S 0.00 4.90 10.91 10.71 11.97 0.00 -14.27 -23.71 -24.74 -25.54 0.00 12.21 19.18 18.37 18.68 0.00 2.23 6.38 4.64 5.36 0.00 1.31 6.38 6.21 7.92 0.00 11.02 16.97 16.00 16.50 0.00 -8.21 -16.79 -18.90 -21.07 M9 4/10 750 S 0.00 2.38 5.52 8.81 9.71 0.00 -2.70 -5.98 -9.29 -10.15 0.00 2.68 5.93 9.21 10.06 0.00 1.97 4.82 7.95 8.80 0.00 1.80 4.82 8.18 9.16 0.00 3.09 6.31 9.48 10.28 0.00 -2.51 -5.76 -9.13 -10.06 M10 0/4 650 A 0.00 4.04 5.89 5.92 7.08 0.00 -13.61 -19.58 -20.89 -21.59 0.00 11.50 14.71 14.07 14.24 0.00 1.32 1.07 0.51 0.06 0.00 0.39 1.07 1.15 2.78 0.00 10.26 12.34 11.54 11.90 0.00 -7.41 -12.18 14.65 -16.81 M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 94 M10 4/10 550 A 0.00 6.93 10.20 11.14 13.25 0.00 -16.40 -23.51 -25.55 -27.05 0.00 14.29 18.75 18.95 20.03 0.00 4.27 5.56 5.01 6.63 0.00 3.36 5.56 6.59 9.19 0.00 13.03 16.42 16.50 17.80 0.00 -10.26 -16.31 -19.54 -22.49 M10 4/10 430 A 0.00 3.72 8.48 13.21 15.46 0.00 -22.37 -33.18 -38.63 -39.97 0.00 16.94 22.55 25.19 25.78 0.00 0.13 2.24 5.16 6.67 0.00 1.06 2.24 7.22 10.05 0.00 12.55 17.16 20.40 21.59 0.00 -9.90 -19.54 -27.73 -31.45 M10 4/10 520 S 0.00 9.18 10.78 14.37 15.45 0.00 -19.13 -24.97 -29.26 -29.90 0.00 16.85 19.78 22.32 22.42 0.00 6.49 6.01 8.24 8.74 0.00 5.58 6.01 9.82 11.34 0.00 15.37 17.20 19.74 20.06 0.00 -12.66 -17.27 -23.02 -25.09 M10 4/10 750 S 0.00 3.29 9.11 12.99 16.77 0.00 -3.74 -9.75 -13.65 -17.36 0.00 3.71 9.66 13.52 17.22 0.00 2.77 8.27 11.97 15.72 0.00 2.57 8.27 12.24 16.14 0.00 4.18 10.07 13.80 17.43 0.00 -3.47 -9.44 -13.43 -17.23 Table 10: Error percentages of composite models and experimental results in 9 (%). The Bache and Nepper-Christensen and Hirsch-Dougill models underestimate the Young’s modulus of LWAC measured in [3]. Bache and Nepper-Christensen model, 43/75 cases give E smaller than 10% and E ranges from 31.45% to 1.62%. For the Hirsch-Dougill model, 29/75 cases give E smaller than 10% with 23 cases smaller than 5%. It can be seen by examining Fig. 4 that the most accurate models are those of Maxwell, Counto1 and Hashin-Hansen which give less errors percentages (Fig. 4 and Tab. 10). Statistical analysis In order to confirm what has been announced previously and distinguish the most suitable model for predicting the effective elasticity modulus of the LWAC, a global statistical study was carried out on all the experimental values of the three researchers (119 measures). To this effect, the mean values and standard deviation for all composite models used in this study and experimental data are calculated as seen in Tab. 10. Popovics Hirsch- Dougill Hashin- Hansen Maxwell Counto1 Counto2 Bache and Nepper- Christensen Mean Values Standard deviation -6.90 8.24 -9.66 11.14 -2.72 5.72 0.29 5.27 -0.23 5.32 -5.94 7.12 -6.42 8.46 Table 10: Mean values and standard deviation of composite models and all experimental data in 7, 8, 9. Fig. 5 shows the normal distribution approximation of error percentage for all 07 composite analytical models. Every estimator has a pick on the mean value and a standard deviation presented by a tight or wide curve. As expected, the Maxwell, Counto1 and Hashin-Hansen composite models provide a good prediction of experimental Young’s modulus of all LWAC tested by De Larrard 7, Yang and Huang 8 and Ke Y et al. 9 (119 values) with a maximum volume fraction of aggregates Vg equal to 49.37%. It is clear from curves of Fig. 5 that the best curves that fit experimental data are respectively Maxwell, Counto1 and Hashin-Hansen models because the mean values are closest to zero than others. It is also important to notice that the standard deviation of both models (Maxwell 5.27, Counto1 5.32 and Hashin-Hansen 5.72) are tight which indicates that there is a high concentration of estimated values around of zero. M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 95 Figure 5: Error percentage distribution approximation to normal statistic low of each composite material model. CONCLUSION he modulus of elasticity is a very important mechanical parameter, its determination sometimes involves impossible, difficult or costly tests, the alternative use of the biphasic laws in these cases appears very interesting but the choice of a model and not another remains a question which requires a precise examination and strongly depends on the type of materials chosen. In order to choose the optimized prediction composite model for Lightweight Aggregate Concrete, the purpose of this paper was to appraise the effective Young’s modulus of LWAC using two-phase composite models. From the obtained numerical predictions, as confronted to existing experimental data and analytical results, the main findings are summarized below: When the Young’s modulus of lightweight aggregates Eg is much less than the Young’s modulus of the mortar matrix in the lightweight aggregate concrete Em, Hirsch-Dougill models remain distant from experimental results and cannot be applied to predict the modulus of elasticity of LWAC. Using Popovics, Counto2 and Bache-Nepper Christensen composite models may not always produce accurate results. For 119 experimental values of Young’s modulus for LWAC, the Maxwell, Counto1 and Hashin-Hansen seem the most reasonable for this purpose. The Maxwell model takes into account in the calculation of the effective elastic modulus of the contrast between the two phases (the mortar matrix and the light aggregates) represented by the coefficient  (Eg/Em) which made it possible to simulate the materials well and offered consequently more precise results if compared with other models. Thus, the precision of this prediction model demonstrates its effectiveness and potential application as a model for Lightweight Aggregate Concrete. The Maxwell model remains close from the experimental values with a man value error equal to 0.29 and a standard deviation equal to 5.27. In addition the Counto1 and Hashin-Hansen models provide a good prediction of T M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 96 experimental Young’s modulus of all LWAC tested by De Larrard 7, Yang and Huang 8 and Ke Y et al. 9 (119 values) with a maximum volume fraction of aggregates Vg equal to 49.37%. In conclusion, it can be suggested that additional studies about investigation for predicting modulus of elasticity of LWAC, may contribute to confirm the reliability and the accuracy of Maxwell, Counto1 and Hashin-Hansen models. NOMENCLATURE E : Young’s modulus gE : Young’s modulus of lightweight aggregate (dispersed phase) mE : Young’s modulus of matrix (mortar) gV : Volume fraction of aggregate (dispersed phase) mV : Volume fraction of matrix (mortar) cE : Young’s modulus of composite c _ VoigtE : Young’s modulus of composite using Voigt model (upper bound) c _ ReussE : Young’s modulus of composite using Reuss model (lower bound) c _ HashinE : Young’s modulus of composite using Hashin-Hansen model c _ HirschE : Young’s modulus of composite using Hirsch-Dougill model c _ PopovicsE : Young’s modulus of composite using Popovics model c _ MaxwellE : Young’s modulus of composite using Maxwell model : Empirical factor c _ Counto1E : Young’s modulus of composite using Counto1 model c _ Counto 2E : Young’s modulus composite using Counto2 model c _ BacheE : Young’s modus of composite using Bache and Nepper-Christensen model Deexp Larrard E : Young’s modulus of LWAC tested by De Larrard and Le Roy (1995) exp _ YangE : Young’s modulus of LWAC tested by Yang and Huang (1998) exp _ KeE : Young’s modulus of LWAC tested by Ke Y et al (2010) c : Poisson’s ratio of composite m : Poisson’s ratio of matrix (mortar) g : Poisson’s ratio of aggregate (dispersed phase) d: Smallest diameter of aggregates in concrete D: Largest diameter of aggregates in concrete c _ analE : Young’s modulus predicted from analytic model E : Error percentage E : Absolute value of error percentage REFERENCES [1] Muhammad Riaz, A. and Bing, C. 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