## 6 Parametric Study and Discussions
### Effect of the Eccentric Distance  
Figure 18 presents the relation between interaction forces \(F_{x}\), \(F_{y}\), \(F_{z}\) and cutting surface width \(B\) under different eccentric distances of 0, 0.1 \(D\), 0.2 \(D\), 0.4 \(D\) and 0.6 \(D\), where \(D=6\) m is the diameter of the shield machine. As shown in Figure 18a, \(F_{x}\) decreases linearly with the increase of eccentric distance; the main reason for this is that the number of cutting tools reduced. The tools on opposite sides of the cutter head have different cutting directions, which cancel each other out. Therefore, the unbalance force of cutter head \(F_{x}\) is usually small. As shown in Figure 18b, \(F_{y}\) generally presents a trend of increasing first and then decreasing and reaches a peak at about 0.3 \(D\)-0.4 \(D\). \(F_{y}\) is affected by both the number of tools and the cutting force angle of the tools. On the one hand, the increase of the eccentric distance causes the cutting force component of the tools in the Y direction to increase, which thereby increases \(F_{y}\). On the other hand, as the eccentric distance increases, the number of tools involved in cutting the pile decreases, which causes \(F_{y}\) to decrease. In engineering practice, the appropriate cutter head rotation direction can be set actively to increase the force applied on the pile, thereby reducing pile settlement and formation disturbance. As shown in Figure 18c, \(F_{z}\) declines overall. \(F_{z}\) decreases rapidly when the centrifugal distance is in the range of 0-0.1 \(D\) and greater than 0.4 \(D\) and changes smoothly when the eccentric distance is in the range of 0.1-0.4 \(D\). The main reason is the change in the number of tools.  
Figure 17: Effect of the cutting surface width \(B\) on the interaction moment: (**a**) \(M_{x}\); (**b**) \(M_{y}\) and (**c**) \(M_{z}\).  
Figure 18: _Cont._Figure 19 presents the relation between interaction forces \(M_{x}\), \(M_{y}\), \(M_{z}\) and cutting surface width \(B\) under different eccentric distances of 0, 0.1 \(D\), 0.2 \(D\), 0.4 \(D\) and 0.6 \(D\). \(M_{x}\) and \(M_{y}\) generally show a similar trend of increasing first and then decreasing, and reaches a peak at about 0.3 \(D\)-0.4 \(D\). They reach the peaks when the eccentric distance is about 0.3 \(D\)-0.4 \(D\). This is the result of the combined effect of the change in the number of tools, the change in the force arm and the moments in different directions. The moments caused by the tools at the opposite sides of the cutter head (upper side and lower side for \(M_{x}\); left side and right side for \(M_{y}\)) have different signs. Notably, the magnitude of \(M_{z}\) is significantly larger than that of \(M_{z}\) and \(M_{z}\). A reason is that the cutting force of tool is usually greater than the penetration force. Another reason is that all of the moments caused by cutting force of tools have the same sign. In addition, with the increase of eccentric distance, \(M_{z}\) declines first, then increases, and decreases to 0 at last. The peak in the ascending interval appears at about 0.3 \(D\)-0.4 \(D\). The main reason for this is the change in the number of tools involved.  
Figure 19: _Cont._  
Figure 18: Effect of the eccentric distance \(e\) on the interaction forces: (**a**) \(F_{x}\); (**b**) \(F_{y}\) and (**c**) \(F_{z}\).