# Rock Breaking Performance of TBM Disc Cutter Assisted by High-Pressure Water Jet
## 4 Results and Discussion  
### Mechanics of Rock Broken by the Disc Cutter Couple With a Water Jet  
The mechanics of rock broken by the disc cutter coupled with a water jet were analyzed under the condition that the nozzle is located at the center section of the disc cutter firstly. There is a gap, approximately 0.012 \(\upmu\)m, between the rock and the disc cutter at the initial time in the simulation. When the calculation time is less than 0.23 \(\upmu\)s, the rock is contacted to the water jet only. Therefore, stress of the rock elements is formed by the impacting of the water jet as shown in the stress concentration area in Figure 5. According to the failure criterion, rock will be broken if the maximum principal stress exceeds the rock tensile strength, forming a groove in the rock mass by the impacting of the water jet finally.  
When the calculation time exceeds 0.23 \(\upmu\)s, the rock will be in contact with both the water jet and the disc cutter. Therefore, stress of the rock elements is formed by the water jet coupled with the disc cutter. As shown in Figure 5, the rock in area 1 is broken by the water jet, while the one in area 2 is broken by the disc cutter. Since the groove on the rock mass formed by the impacting of the water jet creates more degree of freedom for rock breaking, the disc cutter can roll and break the rock mass easily.  
In Figure 5, three rock elements (A, B, and C), located in, near, and far from the traverse route of the water jet, respectively, were chosen to study the stress distribution and failure mechanism of the rock. Their maximum principle stress is shown in Figure 6. The rock element fails if its maximum principle stress surpasses 28.5 MPa. Rock element A will fail at 0.0033 s calculation time under the impacting of the water jet, rock element B will fail at 0.0071 s calculation time under the coupled force of the water jet and disc cutter, and rock element C will fail at 0.0125 s calculation time under the rolling force of the disc cutter.  
Figure 5: Rock broken by the disc cutter assisted by a water jet.  
Then, the mechanics of rock broken by the disc cutter couple with a water jet were analyzed under the condition that the nozzle is located beside the center section of the disc cutter. Figure 7 shows that the stress of the rock elements is formed by the water jet coupled with the disc cutter. Rock in area 1, on the moving path of the water jet, will be broken by the water jet, while rock in area 2, on the rolling path of the disc cutter, will be broken by the disc cutter. Rock in area 3, between the water jet and disc cutter, is in the shear stress concentration area, which will be broken by the thrust force of the disc cutter in the form of brittle cracking. The simulation results are consistent with the theoretical analysis results in Section 2 of this paper.  
In Figure 7, another three rock elements (A, B, and C), located in the traverse route of the water jet, between the water jet and disc cutter, and in the rolling route of the disc cutter, were chosen to study the stress distribution and failure mechanism of the rock. Figure 8 shows their maximum principle stress. Rock element A will fail at 0.0085 s calculation time under the impacting of the water jet, while rock element B will fail at 0.0128 s calculation time under the rolling force of the disc cutter. Rock element C will not fail in all calculation times for its maximum principle stress did not exceed the rock tensile strength. However, it has become rock debris under the thrust force of the disc cutter.  
Figure 6: Maximum principle stress of the three rock elements.  
Figure 7: Rock stress formed by the disc cutter and water jet.