## 1 Introduction  
In order to clearly understand the fracture mechanism of reinforced-concrete (RC) structures, efficient numerical simulation on the whole failure process of RC structures from the initiation of cracks to the final failure at both local and global points of view is meaningful. For extending the simulation accuracy of a traditional finite element method (FEM) in simulating cracks of concrete materials and RC structures, various cracking models for concrete materials have been developed [1; 2]. In particular, the concrete damaged plasticity (CDP) model has been extensively employed to simulate the damage initiation and evolution process in concrete [3; 4], where the damage coefficient is adopted to reflect the degradation of material strength and stiffness of cracked concrete members. However, the concrete is a typical elastic-brittle material, and it changes from a continuum component to a discontinuous body once a crack initiates, which leads to degradation in material strength, structural stiffness and load-carrying capacity of RC members. It is difficult to truly reflect the crack initiation and propagation using damage coefficients. In recent years, the extended FEM (XFEM) has been proposed to describe the discontinuous fields independent of element boundary due to its strong vitality in analyzing discontinuous problems. Utilizing XFEM, the cracking process of the simply supported beam was simulated with preset cracks [5]. [PERSON] et al. [6] also introduced XFEM to the numerical analysis of concrete slabs and beams. In addition, the pinching mechanism of RC columns under cyclic loading has been systematically investigated as well [7]. Moreover, the strain fluctuation and stress redistribution of steel bars and concrete in RC structures subjected to cyclic loadings can be obtained [8]. The opening and closing phenomenon of each crack can be effectively simulated at macro-scale [7; 9]. XFEM has become a popular method to simulate crack propagation problems in concrete [10]. However, it has been recognized that the nonuniformity of concrete at meso-level and the randomness of aggregate distribution in concrete are essential factors leading to the non-linear properties of concrete materials and the stochastic structural behavior at macro-level [11; 12; 13; 14]. Until now, perfect simulation for predicting the local crack evolution and failure patterns of concrete are still challenging since the properties of concrete materials are mainly obtained from material tests at macro-level [1]. At meso-level, concrete is treated as composite material composed of aggregate, mortar, interfacial transition zone (ITZ), initial pores and defects. By means of XFEM, the formation and propagation processes of microfracture in concrete have been studied at meso-level [15], which laid a solid foundation for XFEM-based mesoscale simulation of concrete. The two-scale model composed of beam elements and solid elements or shell elements has been proposed and extensively employed in FEM analysis on RC structures owing to its high computational efficiency [16]. Meanwhile, various kinds of two-scale modeling methods have been successfully applied in the damage and failure analysis of civil structures under earthquakes [16; 17; 18; 19; 20]. Moreover, the mesoscale modeling approach has been successfully applied in the numerical simulation of concrete structures subjected to various loading cases [21; 22; 23]. The feasibility of XFEM-based multiscale models composed of two-scale and mesoscale models needs to be further investigated to provide an efficient way to analyze the structural behavior of RC structures. In this study, the XFEM-based multiscale numerical modeling methodology was developed to investigate both global and local failure behavior of RC columns.