## 3 Results and Discussion
### Damage Assessment  
Initially, the impact of amplitude was investigated by subjecting four different loads, namely 5, 6, 7, and 8 m/s, to a loading frequency of 100 Hz. Figure 14 illustrates the structural damage of the tunnel at varying loading amplitudes. At 5 m/s load, the free field PPV is predicted to be 29.1 cm/s with 64 elements cracked, as shown in Figure 14a. The damage in the wall was observed to expand when the loading intensity was increased to 6 and 7 m/s, with estimated PPV values of 34.1 and 39.9 cm/s, respectively. As shown in Figure 14b,c, the number of cracked elements increased to 241 and 466, respectively. At a loading intensity of 8 m/s, the tunnel experienced damage on the left side of the arch foot, resulting in an increase in the number of cracked elements to 1264, as seen in Figure 14d. The PPV was then increased to 45.6 cm/s. This demonstrates that an increase in loading intensity has the potential to cause more damage to the tunnel. Subsequently, an examination was conducted to assess the impact of blast wave frequency on the tunnel damage. A constant predicted free field PPV of 26 cm/s was being investigated for a total of five distant frequencies, namely 10, 21.5, 43, 86, and 100 Hz. It was observed that each frequency load had a distinct tunnel response for the same PPV. Figure 15 illustrates the damage pattern at various loading frequencies. The loading frequency of 100 Hz did not cause any damage. However, when the loading frequency was reduced to 86 Hz, damage was seen on the side wall of the tunnel. Damage increased at 43 and 21.5 Hz loading frequencies, as shown in Figure 15c,d. The 43 Hz load showed damage at the middle-left wall, whereas the 21.5 Hz load predicted damage at the toe of the floor. A load with a frequency of 10 Hz exhibited more damage compared to loads with higher frequencies, as shown in Figure 15e. At the same free field measured PPV, low frequency had a greater potential to damage the tunnel, while high frequency had a lower chance for damage. The location of the damage within the tunnel structure also varied based on the frequency of the blast wave. The study results indicate that the loading intensity and frequency of blast waves significantly affected the extent of tunnel damage. An additional study is being performed to ascertain the threshold at which minor damage leads to the formation of cracks in the concrete tunnel. A comprehensive set of analyses was conducted to examine the damage to the tunnel. The analysis focused on a blast load consisting of 10 distinct amplitudes with five varying frequencies. Figure 16 shows the predicted free field PPV  
Figure 14: Damage prediction at different loading amplitudes: (a) 5 m/s; (b) 6 m/s; (c) 7 m/s; (d) 8 m/s. Figure 15: Damage prediction at different loading frequencies at a constant PPV of 26 cm/s: (a) 100 Hz; (b) 86 Hz; (c) 43 Hz; (d) 21.5 Hz; (e) 10 Hz. First, PPVs were predicted at which no damage had yet occurred. No damage occurred at PPVs of 25.57, 24.34, 20.5, 18.1, and 16.3 cm/s for frequencies of 100, 86, 43, 21.5, and 10 Hz, respectively, as shown in Figure 17. To determine the PPV at which cracks would begin, varying loading amplitudes were applied to various frequencies to define minor damage. At a frequency of 100 Hz, cracks formed at the PPV of 26.57 cm/s, resulting in the cracking of seven elements, as seen in Figure 18a. Cracks formed at the PPVs of 25.3 cm/s and 21.66 cm/s at 86 and 43 Hz frequencies, respectively, and 11 and 13 elements cracked in both frequencies, respectively. These frequency ranges caused damage specifically on the side wall of the tunnel that was directly exposed to the blast wave, as seen in Figure 18a-c. At a loading frequency of 21.5 Hz, it was anticipated that the damage would occur at a velocity of 19.1 cm/s, as shown in Figure 18d, resulting in the formation of nine cracked elements. This damage was specifically seen at the left arch foot of the tunnel. At a frequency of 10 Hz, damage was triggered at a velocity of 17.24 cm/s, resulting in the cracking of 12 elements.