## 3 Results of Numerical Analysis and Discussion
### Crown Deformation  
In terms of the pipe-jacking method, crown deformation is an essential engineering criterion that can determine the maximum tunnel length while still ensuring stability. According to recommendations by the Japan Tunneling Association (1997), it is dangerous to proceed with a pipe-jacking process when the overcutting area between the concrete pipe and the roof's rock surface is less than 30 mm; therefore, additional measures need to be considered to improve the rock strength around a geologically weak/very weak tunnel. For example, various grouting materials are able to be injected into the surrounding rocks of a roadway at various diameters. Before discussing the application of grouting materials to improve the strength of the surrounding rocks, the effects of the tunnel inclination angles and highwall slopes have to be discussed, shown in Figures 8 and 9. The initial conditions considered here are  
Figure 6: Relationship between tunnel length and failure proximity with different tunnel inclination angles. Figure 7: Relationship between tunnel length and failure proximity under different highwall slopes. the same as that discussed in the previous section. However, we also consider another different condition which is grouting method for improving surrounding rock to assess crown deformation. In practice, the allowable crown deformation typically needs to be less than 20 mm, which is an important factor to consider when ensuring proper working conditions for pipe-jacking technology. Therefore, such practices of tunneling through weak rock or soil require the use of grouting methods to improve the rock quality around the tunnel. As mentioned previously, weak rocks can easily expand, which results in immediate squeezing and a significantly increased resistance force. It is seen in Figure 8 that, in both the circular and rectangular tunnels, the highest roof displacement occurs with larger inclination angles, which is similar to the previous numerical results. The highest displacements for circular and rectangular tunnels are 8.1 mm and 10.5 mm, respectively (when tunnel inclinations reached up to 15\({}^{\circ}\)). The differences in roof displacements are 3.7 mm for the circular tunnel and 4.7 mm for the rectangular tunnel, with inclinations varying from 15\({}^{\circ}\) to 5\({}^{\circ}\). Based on the relationship between the tunnel length and crown deformation/roof displacement presented in Figure 9, roof displacement increased from 4.5 mm to 11.2 mm in the circular tunnel and from 5.9 mm to 14.6 mm in the rectangular tunnel, with the highwall slope becoming steeper. Moreover, the amount of deformation in the figures shows that a circular tunnel is significantly more stable than a rectangular tunnel. However, due to the specific purposes of mining, such as coal haulage, ventilation, material transportation, and worker access, a larger cross-sectional roadway needs to be excavated. It can be  
Figure 8: Effect of tunnel inclination angles on crown deformation. Figure 9: Effect of highwall slopes on crown deformation. summarized that pipe-jacking technology is able to be applied without using a grouting method when the crown deformation being not large (less than 20 mm, as obtained from the numerical analysis). The grouting material was injected into the surrounding rock at four external diameters--4.1 m, 4.6 m, 5.1 m, and 5.6 m--before the tunnel could be extended, as illustrated in Figure 10; the material properties are listed in Table 3.  
Hence, to clarify how much improvement was achieved when using the grouting material, we studied the changes in crown deformation using [PERSON]'s modulus, which decreased by some amount and assumed the worst-case scenario. The tunnel inclination was 5\({}^{\circ}\) for both shapes, and a comparison of the numerical results is presented in Figure 11.  
It is noted that [PERSON]'s modulus is reduced by ten times and that the crown deformation drastically increased from 4.3 mm to 42.6 mm in the circular tunnel.