## 1 Introduction  
Tunnel Boring Machines (TBM) are widely utilized in underground construction due to their superior safety and efficiency compared to traditional tunneling methods [1; 2; 3]. At present, there are many projects using TBM construction internationally, but due to complex global geological conditions, the excavation efficiency of TBMs varies within different geological conditions. For example, low-strength rock can cause instability in tunnel excavation, while high-strength rock can lead to a low penetration rate. TBMs primarily operate by using the disc cutter on the cutter head to interface with the rock, and its substantial thrust and torque enable the cutter to effectively excavate the rock [4; 5]. Generally, a good rock-breaking performance of the disc cutter directly determines the tunnelling efficiency of the TBM. Therefore, the rock-breaking characteristics of disc cutters have attracted great attention from researchers around the world. The cutting parameters and structural parameters of the disc cutter are the most important factors affecting the rock-cutter interaction behavior [6; 7]. Among them, the structural parameters of the disc cutter are mainly affected by the cross-sectional shape of the cutter. Thus, selectingan appropriate blade shape for the cutter according to the specific rock formations can significantly enhance the TBM's construction efficiency [8; 9]. Consequently, research on the blade shape of the cutter has received considerable attention among scholars, as it has the potential to improve TBM performance. Currently, the flat-blade cutter is widely used and has been the focus of extensive research, as shown in Figure 1a. [PERSON] et al. [10] studied the rock-breaking characteristics of the flat-blade cutter with the assistance of pre-cutting grooves, and studied the rock-breaking load and the distribution of the internal stress of the rock under experimental and simulation conditions. [PERSON] et al. [11] conducted a numerical simulation of press in rock breaking with different edge widths of the flat-blade cutter to investigate its impact on rock-breaking efficiency. [PERSON] et al. [12] used discrete elements to analyze the cutting characteristics of the flat-blade cutter under coupled strata, identifying the laws of rock-breaking load and efficiency. Additionally, [PERSON] et al. [13] examined different cutting sequences of the flat-blade cutter using discrete elements and established a rotary cutting model with various arrangements of multiple cutters to study the mechanical response characteristics. [PERSON] et al. [14] investigated the cutter force and cutter wear with the discrete element method. [PERSON] et al. [15] conducted linear cutting tests with small flat-blade cutters and tried to use the testing results to predict the TBM performance. [PERSON] et al. [16] proposed a new method to decide the cutting geometry of the flat-blade cutter based on cutting experiments and simulations. [PERSON] et al. [17] optimized the cutter spacing of the flat-blade cutters considering the joint with the distinct element method. In TBM engineering, the flat-blade cutter is prone to overload due to its large contact area with rocks under hard rock conditions, resulting in significant deformation or even the failure of the flat-blade cutter. In response to these limitations, the arcing-blade cutter was developed as a modification of the flat-blade cutter, as shown in Figure 1b. Due to its structural characteristics, the contact area of the arcing-blade cutter with rocks is small, providing a significant advantage in load reduction. There is also a small amount of research on the arcing-blade cutter. [PERSON] et al. [18] used PFC3D to establish a rotational cutting model of the arcing-blade cutter and simulate its rock-breaking process. [PERSON] et al. [19] simulated the dynamic indentation process of the arcing-blade cutter and analyzed the change in rock-breaking load under different peripheral pressures. Furthermore, [PERSON] et al.