# Predicting the [PERSON]'s Modulus of Concrete Using a Particle-Based Movable Cellular Automata Method
## 4 Comparison the MCA Results with Experiments
### Comparison with Lightweight Expanded Clay Aggregate Concrete  
Subsequent simulations were based on the experimental results of concrete containing Lightweight Expanded Clay Aggregate (LECA) provided in [83]. Static modulus of elasticity tests were conducted using an MTS Landmark 250 series for cylinders with dimensions of 100 \(\times\) 200 mm according to the directives in ASTM C469. The concretes examined in that studies contained crushed limestone as fine aggregate and three types of LECA: coarse, with a density of 0.81 g/cm\({}^{3}\); medium-coarse, with a density of 1.1 g/cm\({}^{3}\); and fine LECA, with a density of 1.81 g/cm\({}^{3}\). Thirteen different mixtures were tested, three of which contained significant amounts of fly ash; these were omitted from the numerical simulations reported in this study. The remaining concretes contained LECA in equal volume (12% of each type of LECA, or 13.5% of coarse and medium-coarse LECA). None of the mixtures differed in the volume of coarse or medium-coarse LECA; thus, it was not possible to numerically determine separate Young's moduli  
Figure 6: Results of numerical simulations for concretes containing basaltic aggregates in comparison with experimental data from [72] and the European standard defining Young’s modulus based on compressive strength [82]. for these types of LECA. Therefore, coarse and medium-coarse LECA were treated as one material in our numerical simulations. An additional justification for this approach is the similar properties of medium-coarse and coarse LECA, which have nearly the same water absorption along with similar specific gravity and particle size distribution. On the other hand, fine LECA has significantly different properties, with double the specific gravity, half the water absorption capacity, and a different particle size distribution. In Table 6, the volume of limestone, total volume of coarse and medium-coarse LECA (reported as the volume of coarse LECA), and volume of fine LECA are presented. In [83], the authors tested CEM I 42.5 R-type Portland cement produced in accordance with the European standard [74]. Static modulus of elasticity tests were conducted according to the directives in ASTM C469 [65]. The mixtures labeled as Mix 3 and Mix 5 in [83] were excluded from our numerical simulations due to segregation observed in the samples. In the case of Mix 3, this segregation was caused by an excessive amount of superplasticizer with a high water content, while in the case of Mix 5 it was due to an excessive amount of water. Information about the elastic modulus is provided in [83] for moist and oven-dry samples at day 28. In this study, we employed the data for oven-dry samples. The elastic moduli of crushed limestone, coarse LECA, and fine LECA were simultaneously estimated in numerical simulations of three selected mixtures: Mix 7, Mix 8, and Mix 10. The results indicated the elastic modulus of crushed limestone to be 40 GPa, while coarse LECA was estimated at 200 MPa and fine LECA at 3 GPa. These values were employed in the numerical simulations of all eight mixtures. The results of the numerical simulations are provided in Table 6, including the mean Young's modulus and the standard deviation calculated from twenty samples of each mixture. A comparison with experimental values provided the following values of statistical coefficients: coefficient of determination (\(R^{2}\)) = 0.86, MSE = 0.81 GPa\({}^{2}\), MAE = 0.76 GPa, fractional bias (FB) = \(-\)0.047, and fractional error (FE) = 0.056. Figure 7 compares the results of our numerical simulations with the experimental results and European EN 1992-1-1 standard [82] defining Young's modulus based on compressive strength. According to the European standard [82], estimated values of the elastic modulus for Lightweight Aggregate Concrete (LWAC) can be obtained by multiplying the values for normal-density concrete by the coefficient \(\eta_{E}=(\rho/2200)^{2}\), where \(\rho\) denotes the oven-dry density.