# Numerical Study of Pressure Attenuation Effect on Tunnel Structures Subjected to Blast Loads
## 1 Introduction  
Tunnels are usually concealed and sheltered by landforms and ground objects to prevent a direct hit from enemy weapons, meaning the transfer of a blast is obstructed and attenuated by orifice plate attenuators, expansion chambers, explosion doors, and tunnel branches.  
Studying the dynamic response of structures subjected to air blast loading has received a lot of attention in the last few decades [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. In terms of studies regarding tunnel explosion protection, in 1992, [PERSON] et al. [11] used a reduced specimen of a steel ammunition storage magazine, with the internal dimensions of 100 \(\times\) 50 \(\times\) 23 cm and loading density of 16.7 kg/m3; detonated 1.9 kg of C-4 explosives inside the specimen; and then discussed the influence of Straight, Elbow, and Dead-End channels on the blast transfer. In 1993, [PERSON] [12] used a round-section of a full-scaled tunnel with a diameter of 3.6 m,and 4000 kg, 2000 kg, and 1000 kg cylindrical RDX explosives in a model scale tunnel with a diameter of 9 cm and cylindrical RDX charge weights of 64, 32, and 16 g. The explosives stand outside the entrance in distances from one to five times the tunnel diameters. The direction is from 0\({}^{\circ}\) (tunnel axis) to 90\({}^{\circ}\) (charge touching the wall) in steps of 30\({}^{\circ}\). The result showed that the blast inside the tunnel attenuated as the distance increased. In 2004, [PERSON] et al. (2013) used a circular tunnel with a diameter of 0.298 m and 54.3 m in length and placed 0.177 kg and 1.77 kg spherical B explosives at the tunnel portal, as well as 60, 30, and 15 cm outside the tunnel portal, in order to perform explosion experiments. The result showed that the blast inside the tunnel attenuated as the distance increased, and the detonation wave impulse inside the tunnel could be regarded as a constant. In the WES (TM 5-855-1, 1998) ([PERSON] et al., 2016) equation, according to the position of the explosive source, explosions outside a tunnel are divided into end-on and side-on. In the EMI equation (TM 5-855-1, 1998) ([PERSON] et al., 2016), the proposed empirical equation can be used to estimate the blast inside a tunnel from an explosion outside the tunnel. As proposed by [PERSON] et al., in 2005 ([PERSON] et al., 2005), the empirical equation can be used for estimating the blast inside a tunnel, as resulted from an explosion outside the tunnel.  
In 2006, [PERSON] et al. (2016) used LS-DYNA software to simulate a strip and a bent channel type ammunition storage magazine and analyzed the internal explosion. The simulation result showed that the bent channel was more effective at attenuating the blast than the strip channel. An appropriate channel design could reduce the lethal area of an explosion inside the ammunition storage magazine. In 2007, [PERSON] and [PERSON] (2007) compiled the protective structure explosion experiment results of [PERSON] et al. from 1965 to 1981. They analyzed the blast transfer attenuation in vertical bar, branch, and mesh tunnels. According to the experimental document review, the aforesaid experiments mainly discussed detonation waves inside the tunnel after an explosion outside the tunnel. This paper discusses the transfer mechanism of a blast resulting from a near-field explosion inside a tunnel. The near-ground and variable tunnel explosion experiments were performed, the numerical simulations and U.S. Force empirical equations were used for analysis and validation, and related empirical equations were established, which are intended to establish a tunnel blast protection evaluation and improvement mechanism to provide a reference for subsequent tunnel building and renovation.