## 6 Concluding Remarks  
In this study, the feasibility of an XFEM-based multiscale modeling approach was validated using experimental observations of four RC columns subjected to monotonic and hysteretic loadings. The influence of mesostructure variation in concrete on the macroscale behavior of tested RC column specimens was discussed in depth. The main conclusions of this study are as follows:  
1. The simulation results show that ignorance of bond-slip effect in FEM models leads to relatively higher load-bearing capacity and structural stiffness of RC columns. Moreover, the specific position of the main crack in numerical models of RC columns is sensitive to bond-slip effect between concrete and steel bars.
2. The distribution pattern of main cracks in RC columns subjected to cyclic loading can be effectively predicted by XFEM-based two-scale models, which agrees well with the experimental results. Compared with solid element models, the computational efficiency of the XFEM-based two-scale model can be obviously improved with guaranteed simulation accuracy.
3. The influence of ACR on the structural behavior of tested RC column specimens is forecast utilizing the XFEM-based two-scale modeling approach. The numerical results match well with that observed from the experimental study. RC columns subjected to higher ACRs present cracks at lower parts of RC columns, greater structural stiffness and higher load-bearing capacity.  
* The monotonic behavior of RC columns can be simulated using XFEM-based multiscale models with acceptable accuracy. Compared with CDP-based multiscale models, the XFEM-based multiscale models are more efficient in predicting the cracking phenomenon and global structural response of RC columns. However, severer convergence problems also exist in XFEM-based multiscale simulations.  
The XFEM-based multiscale modeling method provides an efficient way for the numerical simulation of the non-linear behavior of RC members due to the advantages of XFEM in the analysis of crack initiation and propagation in concrete. The feasibility of the XFEM-based multiscale modeling method in 3D numerical simulation and the difference between 2D and 3D models will be further investigated in the following studies. Moreover, the experimental measurement of material property for aggregates, the ITZ and mortar utilizing nanoindentation equipment will be the research focus of future work.  
Conceptualization, X.N. and B.X.; Methodology, H.C. and J.W.; Software, H.C. and B.X.; Validation, H.C. and X.N.; Formal Analysis, H.C.; Investigation, J.W.; Resources, B.X.; Data Curation, J.W.; Writing--Original Draft Preparation, H.C.; Writing--Review and Editing, B.X.; Visualization, J.W.; Supervision, Y.-L.M.; Project Administration, X.N. and B.X.; Funding Acquisition, H.C. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 51908320) and China Postdoctoral Science Foundation (Grant No. 2019M650688).  
The authors would like to thank the anonymous reviewers for their constructive comments and suggestions. The opinions expressed in this study are those of the authors and do not necessarily reflect the views of sponsors.  
The authors declare no conflict of interest.