## 1 Introduction
Research has shown that a drill bit equipped with an axe cutter can achieve an instantaneous rate of penetration (ROP) that is up to 35% higher compared to the same input energy applied with other cutter designs [15]. The axe PDC cutter demonstrates a high rate of penetration (ROP) in rock breaking, facilitating easier penetration of hard rocks. This, in turn, helps prevent bit sticking and sliding [16], maintains stable weight on the bit (WOB) during drilling, and enables the bit to maintain a high ROP. Additionally, its simple structure, ease of processing, and relatively mature technology make it an advantageous choice for drilling into hard rock formations. In addition to axe-shaped cutters, new cutter structures have been proposed by some scholars and verified by experiments or numerical simulations. For example, [PERSON] et al. [17] designed a wavy PDC cutter using the mole paw toe as a bionic prototype, and it was found by field experiments that the life and efficiency of PDC bits could be improved by 54% and 230%, respectively, using this cutter, which provided new ideas and methods for the performance improvement of PDC bits. [PERSON] et al. [18] designed a triangular non-planar PDC cutter, numerically simulated its rock-breaking process, and compared it with conventional PDC cutters. They found that the designed cutter was subject to less rock-breaking resistance, was easier to break the rock, and had both good wear resistance and efficiency. [PERSON] et al. [19] studied the rock-breaking characteristics of the triangular prism PDC cutter by numerical simulation and found that this cutter not only has a shearing effect on the rock but also has a crushing effect. The results of field experiments showed that the PDC bit using this cutter requires less torque and penetrates the rock more easily, which helps the bit's stability. The change or optimization of the cutter structure is a more intuitive way to improve the performance of the bit. In addition, the reasonable arrangement of the cutter position on the PDC bit blade can also improve the performance of the drill bit to a great extent. To rationalize the cutter layout, [PERSON] et al. [20] changed the cutter layout by extracting the characteristic curve of the Siberian sheep's horn, which will be applied to the design of the cutter blade of the PDC drill bit. After the study, the probability of load concentration with the changed cutter was greatly reduced, the utilization rate of the cutter was increased to 90%, and the overall life and efficiency of the PDC drill bit were improved. Previous PDC cutters were often arranged in one row on the cutter blade [21], which would lead to wasted space on the cutter blade. Gradually, the cutter layout of some drill bits began to be changed to two or even more rows on one cutter blade [22], which not only rationalized the use of space on the cutter blade but also improved the efficiency and lifetime of PDC drill bits. Even if the cutter structure is not changed, changing the cutter space arrangement can greatly improve the performance of the whole drill bit [12], and these studies mentioned above provide theoretical support for the cutter space layout. A systematic approach is crucial in the investigation of the rock-breaking process associated with PDC bits. Most of the current related studies, using experiments combined with numerical simulations [23], have greatly improved the accuracy of the simulations while reducing the research cost. However, most of the studies treat the rock as a homogeneous model during the numerical simulation, which does not reflect the real scenario of the actual drilling process. In addition, the current studies on PDC cutting tool-related parameters, such as back rake angle [24], depth of cut [25], and speed [26], are conducted in an interval-modified parameter study, which yields experimental results that do not necessarily reflect the true relationship between the parameters and the target variables and thus may lead to inaccurate conclusions.