## 3 Results and Discussion
### The Axial Compressive Performance of AN-LAC
#### 3.5.2 The Elastic Modulus of AN-LAC  
The axial compressive stress-strain curves of AN-LAC are shown in Figure 10. The elastic modulus, which is an important index to evaluate the deformation performance of concrete, was obtained through Equations (11) and (12) according to the calculation method of LWAC. Meanwhile, the specific values are shown in Table 6 and fc is axial compressive strength referring to the peak stress of the stress-strain curve. The elastic modulus of AN-LAC-3 and AN-LAC-6 were the lowest in the single-particle size and combined-particle size gradation groups, respectively:  
\[E_{\text{c}}=\frac{F_{\text{a}}-F_{0}}{A}\times\frac{L}{\Delta n} \tag{11}\]  
\[\Delta n=\varepsilon_{\text{a}}-\varepsilon_{0} \tag{12}\]  
where \(E_{\text{c}}\) is the elastic modulus of AN-LAC (MPa); A is the area of the specimen under axial compression (mm\({}^{2}\)); \(F_{\text{a}}\) and \(F_{0}\) are the load values corresponding to the stress of \(0.4f_{\text{c}}\) and \(0.5\) MPa of concrete, respectively (N); L is the original height of the specimen; \(\Delta n\) is the deformation value when the specimen is loaded from \(F_{0}\) to \(F_{\text{a}}\) (mm); and \(\varepsilon_{\text{a}}\) and \(\varepsilon_{0}\) are the deformation values of concrete after reaching the load of \(F_{\text{a}}\) and \(F_{0}\), respectively (mm). Figure 10: Stress–strain curve of AN-LAC: (**a**) single-particle size gradation groups; (**b**) combined-particle size gradation groups. Figure 9: Typical destruction of specimens: (**a**) AN-LAC-1; (**b**) AN-LAC-2; (**c**) AN-LAC-3; (**d**) AN-LAC-4; (**e**) AN-LAC-5; (**f**) AN-LAC-6; (**g**) AN-LAC-7. In addition, the elastic modulus of OPC concrete was related to cubic compressive strength according to the prediction models of GB 50010-2010 [43] and CEB-FIP Model Code 1990 [36]. Meanwhile, based on the elastic modulus models of JGJ 51-2002 [44], ACI 318-11 [45], [PERSON] et al. [46] and [PERSON] et al. [47], the elastic modulus of LWAC was related to strength (including cubic and axial compressive strength) and dry apparent density. Because the apparent density of AN-LAC was between that of OPC concrete and LWAC, the elastic modulus prediction models mentioned above were used for calculation and then compared with the experimental data, as shown in Figure 11. It could be seen that the prediction results of the prediction model of LWAC were closer to the experimental data than that of OPC concrete. It was due to the fact that the elastic modulus prediction model of LWAC not only considered the strength but also incorporated the apparent density of concrete, leading to its better accuracy of predicted results. It should be noted that the specific surface area of NSLA was different due to its various particle sizes, which played an important role in the apparent density of concrete. Therefore, according to the model of JGJ 51-2002 and the effect of the specific surface area of NSLA on the apparent density of concrete, Equation (13) was established by fitting the data to predict the elastic modulus of AN-LAC:  
\[E_{\text{c}}=1.887(\frac{6}{r})^{-0.08611}\rho f_{\text{cu}}^{0.5} \tag{13}\]  
where \(r\) is the average particle size of NSLA (mm), \(\rho\) is the dry apparent density of concrete (kg/m\({}^{3}\)) and \(f_{\text{cu}}\) is the compressive strength of concrete (MPa). Meanwhile, the predicted results of the modified model exhibited an excellent correlation. The difference between the modified model and prediction models of LWAC, as well as the error bars of each model, are shown in Figure 12. It was clear that the accuracy of the predicted results of the modified model was better and its error bar was relatively short.