## 1 Introduction
Cohesive surfaces were introduced between the interfaces of all triangular elements of the finite element mesh to study the fast crack growth in brittle solids. This generated zigzag crack growth and the obtained results are in accord with experimental observations [13]. The diffuse cohesive interface approach, which is also well-known in the literature, is the so-called zero-thickness cohesive element approach, has been used to predict the structural response of the ultra high-performance fiber-reinforced concrete (UHFFRC) structures enhanced with embedded nanomaterials [14]. Computational modelling of SHC is still in the earlier stages and most of them have used the zero-thickness cohesive element approach. However, that approach has significant drawbacks, such as introducing artificial compliance and mesh dependency [15]. The extended finite element method (XFEM) is a promising, flexible, and powerful discrete crack method, and it allows crack propagation without the requirement for re-meshing; in addition, it has been already implemented into commercial software such as Abaqus [16]. There are a few limitations of the XFEM, which can be found in [17]. These limitations can be classified mainly into two main categories; the first is about the crack propagation near to the element boundary. The second is about enabling the initiation of multiple cracks in the same enrichment zone; for a more detailed explanation refer to [3]. Most of  
Figure 1: Encapsulation-based self-healing using microcapsules. the computational modelling in SHC is focused on studying the fracture mechanism of the microcapsules and the interaction between them and the concrete. The zero-thickness cohesive element approach has been used to model the fracture of the microcapsules and the interaction between the capsules and the concrete [18]. The XFEM and cohesive surface technique have been used to study the fracture mechanism of encapsulation-based self-healing materials [3]. Although the XFEM and the zero-thickness cohesive element approach are based on the cohesive traction-separation law and the fracture energy as a damage criterion, the XFEM has been shown to have high accuracy for modelling fractures in concrete [19]. Another study has employed the XFEM and the zero-thickness cohesive element approach for a configuration consisting of an infinite matrix with an inserted crack and a microcapsule [20]. Since the fracture of the capsules is a critical issue for the healing mechanism, which happens by releasing the healing agent once the capsules are fractured. Therefore, fracture modelling is important, especially for the design of self-healing structures. This is due to the random distribution of the capsules inside the concrete matrix, which can lead to different crack patterns. This random distribution occurs during the mixing process of the concrete, which can lead to capsular clustering. The capsular clustering could be one of the main reasons that generate imperfect bonding between the capsules and the concrete. There are no studies conducted in the literature about the capsular clustering effects within the SHC context. The main novelty of this study is to investigate the effects of capsular clustering on the fracture of encapsulation-based self-healing concrete. In this study, the effects of microcapsule size and clustering on the load-carrying capacity and the probability of fracture or debonding of the microcapsules from the concrete matrix are studied computationally. The computational simulations are performed for 2D modelling of SHC concrete samples with microcapsules loaded under uniaxial tension. The XFEM is used to model the concrete matrix and the microcapsule shell, and the contact surface between them is modelled by the cohesive surface technique. A precrack is not necessary with the XFEM to initiate the crack; however, in this study, an initial precrack was placed at the middle edge of the samples just for comparison purposes when a crack starts to initiate from the same edge.