## 5 Multiscale Simulation on RC Column under Monotonic Loading  
### Comparison of Failure Modes  
The tested specimen subjected to monotonic loading was numbered as C4. The dimension and steel arrangement of specimen C4 were identical to that of C1, as detailed in Section 2. The ACR of C4 was also set to 0.08. The failure pattern of C4 is presented in Figure 14. Four cracks were clearly observed in the tested specimen C4, and the main crack was about 8 cm above the column foot. Severe concrete crushing occurred at the compressive side of column foot. In this section, the tested specimen C4 is constructed using the CDP model and XFEM method-based multiscale simulation strategies, respectively. Figure 15 shows the tensile and compressive damage distribution patterns simulated using CDP-based multiscale models. It can be seen that the failure morphology at the tensile side and compressive crush basically agree well with that in experimental observations of the tested specimen C4. However, it is quite difficult to identify the main crack with the maximum width according to the tensile damage distribution presented in Figure 15. Moreover, it can be observed that the specific position of the element exhibiting tensile and compressive damage is different in multiscale models constructed with various mesoscale concrete samples, which denotes that local failure of RC columns is sensitive to the mesostructure variation of concrete. Figure 14: Failure pattern of C4. Figure 15: Damage pattern in CDP-based multiscale models. Figure 16a-e show the comparison of crack patterns of different XFEM-based multiscale models subjected to monotonic loadings. For comparison, the solid element segments of XFEM-based two-scale models are constructed using homogeneous concrete material, and the corresponding crack patterns are presented in Figure 16f. Similar to the simulation results in Figure 15, the location and propagation direction of cracks simulated with XFEM-based multiscale models also change with the aggregate distribution of concrete at meso-level. Since the material strength of the ITZ is the weakest, the initial crack forms inside the ITZ and propagates along the outline of the aggregates. Figure 16a-c are the crack patterns of multiscale models where numerical concrete has identical aggregate geometry but different distribution patterns, which indicates that the local position, length or even the extending direction of cracks are different due to the random distribution of aggregates. Meanwhile, the crack patterns in Figure 16d-e show that the geometric shape of aggregates also leads to a difference in the local crack patterns of RC columns. In contrast, the positions of prominent cracks in Figure 16c,d are closer to that of tested specimen C4 subjected to monotonic loading. The position of the main crack in Figure 16e corresponding to the multiscale model established with elliptical aggregates is obviously higher than that of practical experimental observations. The cracking morphology in a two-scale model shown in Figure 16f matches the best of that of tested specimen C4. However, the effect of random aggregate distribution on local behavior cannot be revealed using homogeneous material assumptions. Figure 16: Crack pattern in XFEM-based multiscale models. Comparatively, the CDP-based multiscale models with polygonal aggregate samples match the best of the experimental results. Therefore, three sets of polygonal aggregate sample were established for XFEM-based multiscale models, and the corresponding load-displacement curves are illustrated in Figure 17b. It can be seen that the simulation results meet the test results at the ascending branch well. Moreover, the structural stiffness can be accurately predicted. However, the simulation encounters severe convergence problems. The convergence problems can be alleviated while using elliptical and circular aggregates in numerical concrete models, as shown in Figure 17c.