## 3 Test Results and Analysis
### The Work Done by Cutting Force and the Specific Energy Associated Therewith  
The rock-breaking energy of a cutter is defined as the energy needed by a cutter to break a unit volume of rock (and is expressed by the specific energy). The lower the specific energy, the lower the energy needed to break a unit volume of rock and the more efficient the process [28; 29]. The energy required by the reduced-scale TBM cutter in breaking rocks manifests as the work  
Figure 11: Relationship between the average driving force and the microwave exposure time.  
Figure 12: Relationship between the average rolling force and the microwave exposure time.  
done by the driving force and that done by the rolling force, which can be calculated using Equation (1). The specific energy is calculated using Equations (2) and (3) [28; 29]:  
\[W=FL \tag{1}\]  
\[SE= \frac{W}{\Delta V} \tag{2}\]  
\[\Delta V=\frac{m}{\rho} \tag{3}\]  
where \(W\) is the work done by the cutting force (J); \(F\) denotes the cutting force of the cutter (kN); \(L\) represents the motion distance of the cutter (m); \(SE\) denotes the specific energy (MJ/m\({}^{3}\)); \(\Delta V\) is the volume of rock debris falling off in the rock-breaking process (m\({}^{3}\)); \(m\) stands for the mass of rock debris (kg); \(\rho\) is the density of basalt samples (kg/m\({}^{3}\)).  
Tables 5 and 6 show the work done by the average driving force and average rolling force at different microwave exposure times. Figures 13 and 14 illustrate changes in the work done by the average driving force and that done by the average rolling force of the reduced-scale TBM cutter calculated using Equation (1) with increasing exposure to microwave irradiation. The energy consumed by the work done by the driving force and that done by the rolling force is both linearly reduced with increasing exposure to microwave irradiation. That is, as the increasing exposure to microwave irradiation prolongs, the energy associated with the work done by the driving and rolling forces decreases. After 15 min of microwave irradiation, the work done by the driving and rolling forces separately decrease by 33% and 32%. This indicates that microwave irradiation can reduce the energy consumption of the TBM cutter. In addition, a comparison of energy consumption of the work done by the driving force and that done by the rolling force shows that the energy associated with the driving force is about 0.08% of that associated with the rolling force. This indicates that the energy used by the TBM cutter in breaking rocks is associated mainly with the rolling force. When designing and setting a microwave antenna on the TBM cutter, one can follow the principle of mainly reducing the torque delivered by the TBM cutter.  
Tables 7 and 8 show the specific energy by the average driving force and average rolling force at different microwave exposure times. Figures 15 and 16 show the specific energy of the driving force and rolling force of the reduced-scale TBM cutter calculated using Equations (1)-(3). When cutting the basalt samples, the specific energy of the reduced-scale TBM cutter constantly decreases with increasing exposure to microwave irradiation. The specific energy of the driving force and that of the rolling force both reduce with increasing exposure to microwave irradiation in an exponential manner. After microwave irradiation for 15 min at 2100 W, the specific energy of the driving force and that of the rolling force separately decrease by 53% and 52%. This indicates that, when breaking the same volume of rock, microwave irradiation can gradually reduce the energy consumption of the reduced-scale TBM cutter. The reduction in specific energy suggests that microwave irradiation can improve the energy-utilization rate of the TBM cutter when breaking rocks; that is, the rock-breaking efficiency is improved. Under a fixed microwave power, the longer the exposure to microwave irradiation, the greater the reduction in the specific energy and the greater the promotion of the rock-breaking efficiency of the TBM cutter.