## 1 Introduction  
Cracking is one of the most common signs of asphalt pavement deterioration, producing a reduction of the mechanical strength and durability of the road pavement over time [1] affecting driving comfort and safety [2]. Generally, the cracks observed at the pavement surface can be caused by two major mechanisms, the bottom-up cracks and the top-down cracks. The bottom-up cracks are initiated by tensile strains at the bottom of the asphalt layer and the top-down cracks are initiated by surface tensile and shear stresses, environmental effects and ageing [3]. Fortunately, the asphalt mixture is a self-healing material, and if enough energy is applied, original mechanical properties can be partially or nearly totally restored. Such technology can enable an important reduction in the consumption of natural resources, saving aggregates and bitumen that would be used in reconstruction or repair/maintenance actions in the road network. By extending the service life of the current pavement, it may occur an overall reduction of the maintenance interventions, thus saving the corresponding costs and CO\({}_{2}\) emissions, as well as minimizing the traffic disruptions caused by such actions [4]. From a molecular point of view, the self-healing phenomenon is due to the wetting and interdiffusion of material between the two faces of a microcrack to achieve properties of the original material [5]. [PERSON] et al. developed a healing function of asphalt material based on molecular diffusion theory [6]. Healing activation energy was found to be a promising parameter for evaluating self-healing ability as if appreciable energy equal to or greater than the healing activation energy exists at the damage faces, the self-healing reaction will start. Molecular diffusion models can only be used for describing the microcracks healing, as in the case of macro cracks, the molecular interdiffusion cannot occur due to a wider gap between the faces. In this case, the capillary flow healing model can be used to describe the self-healing phenomenon. [PERSON] explained that above a specific temperature, the bitumen behaves as a Newtonian fluid, and can fill the cracks in a sort of capillarity flow [7]. Different types of bitumen exhibit different threshold temperatures for flow, depending on their rheological properties, usually ranging from 30 \({}^{\circ}\)C to 70 \({}^{\circ}\)C. The flow behavior index of the bitumen was found to be appropriate to characterize the threshold for the initial self-healing temperature of the bitumen [8; 9; 10]. The healing capability of asphalt mixtures depends on several internal and external factors [11]. As for the internal factors, bitumen properties have a strong influence on healing capability. Bitumen with lower flow behavior index not only need less energy for starting healing, but also produce better healing levels [10]. At the microscale level, chemical composition has a strong influence on the healing properties of asphalt [12; 13]. [PERSON] et al. demonstrated the influence of the surface energy on the healing capability of bitumen [14]. According to the findings of these authors, the most efficient healers should have relatively lower Lifshitz-van der Waals components and higher acid-base components of surface energy. The amount of bitumen content in the mixture increases the healing capability of asphalt pavement [15]. Some volumetric properties also influence the self-healing properties [16], as well as the type of mixture. [PERSON] et al. found that porous asphalt mixtures heal faster than the dense mixture, and provide better healing levels [10]. Between the external factors, rest time, temperature and damage degree are the most influential [9; 17]. Many researchers have focused on finding the optimal temperature to maximize the healing effect. If the temperature is too low, bitumen cannot flow through the cracks.