## 1 Introduction  
Asphalt concrete is widely used for pavement construction throughout the world. During its service life, the asphalt concrete ages due to environmental effects including oxidation, UV light irradiation and moisture damage, which make it become stiffer with time and gradually lose its original properties [1; 2; 3; 4]. As a result, ageing of asphalt leads to an increase of stiffness and brittleness which make it prone to premature failures like cracking and raveling [5]. Although the phenomenon of ageing deteriorates the performance of asphalt pavement, an asphalt rejuvenator, including industrial rejuvenator and oil [5; 6], can be used to reverse this process by restoring the lost properties of aged asphalt, i.e., stiffness and self-healing capacity [7]. The asphalt rejuvenator has been successfully used in asphalt recycling [8] and surface course rejuvenation [9]. However, the surface course rejuvenation allows the asphalt rejuvenator to reach no more than 2 cm of the pavement structure, which means microcracks inside the pavement cannot be healed. Moreover, all these procedures require onsite construction work which leads to traffic restrictions, use of fresh materials and an increase of CO\({}_{2}\) emission [10]. As an emerging self-healing technology in asphalt pavement, the capsule healing method provides a solution to the ageing problem, thus prolong the service life of asphalt pavement [5]. Researchers have shown that the inclusion of encapsulated asphalt rejuvenator in an asphalt mix is a promising method to improve the self-healing capacity in asphalt pavement [5]. The intention of the embedded capsules is to deliver encapsulated healing agent into the asphalt pavement, when a crack occurs, the healing agent is released into the microcrack, wets the crack surfaces, diffuses into the aged bitumen, and softens the aged binder, allowing it to flow and eventually heal the crack [10]. The concept of using embedded capsules was first reported by [PERSON] et al. [11]. [PERSON]'s self-healing concept has been applied to many other materials, including asphalt. Research has been carried out to explore effective rejuvenator delivery system for asphalt pavement, and some encapsulation methods have been investigated, such as epoxy capsules [12] and Melamine-formaldehyde (MMF) capsules [13]. Recently, alginate, a low-cost and environmentally friendly biopolymer that is largely stored in brown algae, has been used as an encapsulation material for asphalt rejuvenator to achieve self-healing in asphalt pavement [14; 15; 16; 17]. As an anionic polysaccharide, alginate cross-polymerizes when exposed to a solution containing divalent cations such as Ca\({}^{2+}\)[18]. [PERSON] et al. [15] successfully used compartmented alginate fibers to encapsulate rejuvenator and proved the effectiveness of this self-healing system on micro-crack healing. However, the rejuvenator content in the alginate fiber compartments was very limited. To improve this situation, [PERSON] et al. [16] developed a more efficient rejuvenator delivery system using calcium alginate capsules. The prepared capsules had the rejuvenator content of 56% by volume. These capsules were proved to be able to survive during the asphalt production process and showed a significant healing effect on asphalt mastic samples. The previous research demonstrated that alginate is a positive material for rejuvenator encapsulation thus application in self-healing asphalt [16]. However, the healing mechanism of this capsule healing system relies on the properties of the capsules. A change in diameter, microstructure or rejuvenator content of calcium alginate capsules would result in different thermal and mechanical properties, which largely affect the healing capacity of this capsule healing system. Thus, an optimization of this healing system is needed. The main objective of this research is to optimize the calcium alginate capsules for the application in self-healing asphalt.