# Dynamic Mechanical Characteristics of Horseshoe Tunnel Subjected to Blasting and Confining Pressure
## 3 Dynamic Response with Different Blast Loading Direction
### Stress Concentration in Partial Damage  
For quantitative analyzing the stress concentration around the tunnel in five specimens, eight key points are selected. The points from the tunnel center are 23 mm radius, and the central angle between two adjacent points is 45\({}^{\circ}\). The name and position of key points are listed in Figure 6.  
The whole dynamic response can be divided into three stages; the first part describes the deformation under the initial stress wave at 20-60 us (see Figure 7). The second part focus on dynamic failure under concentrated stress around the tunnel's free walls at 60-100 us. In the last part, the reflected waveforms the specimen boundary and accelerates the surrounding rock fracturing at 100-140 us.  
Figure 5: Stress field with different loading directions. (**a**) Sidewall, (**b**) Spandrel, (**c**) Vault, (**d**) Corner, (**e**) Bottom floor.  
Figure 7a presents the stress-time curve on the front, up1, up2, up3 and back five points which are located in the upper half of the tunnel. When the initial stress wave arrives at the front surface at 30 \(\upmu\)s, the stress rises up successively, and the stress peaks are lower than 40 MPa. Only elastic deformation is produced under the initial stress wave. Notice that the stress peak on the back point is lower than 10 MPa, which means the initial stress wave has little effect on the deformation along the back surface. The stress concentration is gradually produced in the second part; the stress in the front point exceeds 50 MPa at 63 \(\upmu\)s and then drops to 5 MPa, which indicates is no damage occurred. In the third stage, the reflected waveform from the specimen boundary has a large effect on dynamic damage in the surrounding rock, the stress of the back point rises to 75 MPa, and the irreversible plastic deformation starts accumulating.  
Different from the deformation in the upper half of the tunnel, the stress field is influenced by the corner in the lower half tunnel (Figure 7b). The stress peak of down1 is more than 40 MPa, which is greater than the peak value in the symmetric point up1 at 40 \(\upmu\)s. In the second and third parts, both the stress peaks of down1 and down3 are greater than the peaks in up1 and up3. Especially, the peak of down1 is over 80 MPa, and it is not dropped after 120 \(\upmu\)s; the results indicate that the fractures are mainly formed around the corner position. Meanwhile, the stress of up2 and down2 have similar trends, and the stress concentration is significantly around two corners.  
The stress-time relation along the front and back blasting faces is shown in Figure 8a,b, respectively. The initial stress wave becomes smaller and has little influence on the back surrounding rock at 20-60 \(\upmu\)s. As time increase to 70 \(\upmu\)s, the stress superposition is generated, and stress concentration becomes strong along the front surface and two corners. When the reflected wave from the boundary arrives at the central region, the stress in the back point exceeds the rock strength and causes existing cracks further developing. Note that the stress field around the corners is strong than the symmetric damage zones during the whole response process.  
Figure 6: Eight key points location.  
Figure 7: Dynamic stress in surrounding rock, (**a**) Upper half of tunnel, (**b**) Lower half of tunnel.