## 1 Introduction  
Although protective design has been mainly considered for military facilities, it has recently been expanded to the data and backup centers that store various types of government and private data that are built underground, and safety designs for electromagnetic pulse (EMP) shielding, blast resistance, fire-weapon resistance, and chemical, biological (bacterial), and radiological (CBR) protection are in process [1, 2]. Mitigation of overpressure inside protective tunnels against external detonations is one of the most recent issues of interest. When blast shock waves generated by an external ground explosion enter a protective tunnel, significant levels of blast overpressures can occur in underground facilities located at considerable distances from the tunnel entrance. This is because the blast waves cannot escape the tunnel while propagating; that is, the blast overpressures decrease with the increase in distance, but they are amplified simultaneously through repeated shock wave reflections from the inside walls of the tunnel [3, 4, 5, 6, 7, 8, 9], thus damaging the internal protective facilities. Accordingly, a protective design for the mitigation of blast overpressures propagating inward from the tunnel entrance is necessary to protect internal underground facilities. A computer center is a representative underground protection facility, and hundreds of blast valves are installed on walls for ventilation and the protection of internal personnel and equipment against blast overpressures [7, 10]. Since the cost of blast valves increasessignificantly depending on the pressure rating, measures to mitigate blast overpressures are required to reduce the construction cost [1; 2]. The incident and reflected overpressures inside a tunnel for external detonation on the ground can be reduced using various methods. Regarding structural materials, it is possible to decrease blast overpressures by installing materials or devices that absorb the blast energy or by inducing the failure of structural components made of materials with lower strength and higher ductility, thereby protecting the primary structural members [11; 12; 13; 14]. An alternative method is to use the geometric shape of the tunnel, which may lead to a more efficient and intuitive overpressure reduction compared to the use of the shock-absorbing materials. [PERSON] and [PERSON] [15] proposed a method to reduce the maximum blast overpressure by diverting some of the blast waves using side chambers arranged along the tunnel. [PERSON] et al. [16] conducted a study to reduce the maximum blast overpressure through numerical analysis by increasing the volume of a certain space inside the tunnel, which was done by placing an expansion chamber on the tunnel path. As such, these mitigating blast overpressures in consideration of the tunnel shape methods can be effective but are somewhat restricted in terms of the detonation conditions and the shape of the structures. Other various methods for mitigation techniques of blast overpressures were reported by [PERSON] et al. [17], who summarized geometric designs for shock attenuation using perforated barriers, baffle plates, vertical barriers, smooth double wall duct tube, and so on. These methods can be selectively used for tunnel design compared to those presented in this study. This study presents a numerical investigation of overpressure mitigation inside protective tunnels subjected to external surface explosions. A method of mitigating internal blast overpressures in protective tunnels using simple geometric techniques of external entrance shape and blast pocket was proposed. A numerical model of a protective tunnel for detonation on the ground was constructed using the commercial computational fluid dynamics (CFD) code Viper::Blast [18]. The tunnel was modeled as a rigid body based on the validation study of [PERSON] et al. [19]. Studies on mesh sensitivity based on the _h-refinement_ strategy [20] and overpressure stability have been performed to demonstrate the reliability of the numerical model.