# Performance Evaluation of Reinforced Recycled Aggregate Concrete Columns under Cyclic Loadings
## 2 Numerical Modelling
### Validation and Discussion  
As discussed in Section 1, [PERSON] et al. [42] and [PERSON] [43] have conducted cyclic tests on the seismic performance of RRC columns under constant axial load and cyclic lateral reversals. The loading process in the above experiments consisted of a load-controlled phase followed by a displacement-controlled phase. During the first phase, the lateral load was progressively exerted on the specimen with an of increment of, respectively, \(0.20P_{\rm y}\)[42] and 5 kN [43]. After steel yielded, the loading method was switched to the displacement-controlled mode. In both experiments the displacement increment was adopted as \(1.0\Delta_{\rm y}\) (\(\Delta_{\rm y}\) = the displacement at steel yielding). The loop at each drift level was repeated three times until the lateral load resistance dropped below 80% [42] or 70% [43] of the peak load. Figure 2 and Table 1 show the material properties and the geometries of the RRC cantilever-type test columns. Note that to compensate the larger water absorption of RAC, a so-called additional water method (AWM) (see Section 3.1 for detail) for RAC mix proportion was used in the aforementioned cyclic tests. The experimental outcomes from these tests were employed to validate the numerical model developed herein. The failure mode of all the test specimens was solely flexural-dominated failure (see Figure 3).  
Figure 2: Reinforcement and geometry diagram of reported specimens (unit: mm). (**a**) Specimens in [PERSON] et al. [42], and (**b**) specimens in [PERSON] [43].  
Following the modeling approach described previously, the global cyclic response of the specimens in [42, 43] can be calculated. Figure 4 compares the lateral load-displacement hysteresis loops obtained from the experiments and the simulations.  
Figure 3: Flexural failure modes of test specimens. (**a**) NCCC-1 [42]; (**b**) NAC-0.30-40 [43]; (**c**) NAC-0.30-60 [43]; (**d**) NAC-0.30-100 [43]; (**e**) RAC50-0.30-40 [43]; (**f**) RAC50-0.30-60 [43]; (**g**) RAC50-0.30-100 [43]; (**h**) RAC100-0.30-60 [43]; (**i**) RCCC-2 [42]; (**j**) RAC50-0.15-60 [43]; and (**k**) RAC50-0.45-60 [43].  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multirow{2}{*}{\(w_{\mathrm{eff}}\)/\(w_{\mathrm{eff}}\)\(w_{\mathrm{eff  
Figure 4: _Cont._  
The lateral load-carrying capacity and the ductility in Figure 4 were defined as the maximum lateral load (\(P_{\text{u}}\)) and the displacement ductility coefficient (\(\mu\)), respectively. In Table 1, \(P_{\text{u,t}}\) is the experimental ultimate load, \(P_{\text{u,s}}\) is the corresponding numerical ultimate load, and \(\mu_{\text{t}}\) and \(\mu_{\text{s}}\) are the experimental and numerical displacement ductility coefficients, respectively. The value of \(\mu\) is defined as the ratio of the ultimate lateral displacement (denoted as \(\Delta_{0.85}\)) at the load corresponding to 85% of the peak load in the descending backbone curve to the yield lateral displacement (denoted as \(\Delta_{\text{y}}\)) determined based on the energy equivalence principle (see Figure 5).  
\[\mu=\frac{\Delta_{0.85}}{\Delta_{\text{y}}} \tag{5}\]  
Figure 4: Comparison of hysteresis loops between experimental and numerical results. (**a**) Test specimens in [PERSON] et al. (2019), and (**b**) test specimens in [PERSON] (2019).  
Figure 5: Load-displacement backbone curve.  
From Figure 4 and Table 1, it is clear that the predicted hysteresis loops correlated well with the measured ones; the prediction-to-test ratio for the two major seismic performance indexes (\(P_{\rm u}\) and \(\mu\)) was close to unity (\(P_{\rm u,s}/P_{\rm u,t}=1.00\) and \(\mu_{\rm s}/\mu_{\rm t}=0.92\)). It can also be seen that the coefficients of variation on the ultimate lateral load and displacement ductility were small on the whole. Hence, the finite-element model developed can provide an overall faithful tool to estimate the seismic performance of RRC columns.