## 1 Introduction  
Tunnel boring machines (TBMs) are efficient, safe machines used for constructing tunnels and are widely used in engineering practice, including the excavation of rock tunnels and underground passages [1]. Cutters, as the teeth of a TBM to excavate soil, play a key role in breaking rocks. However, the wear of the cutter has become a key factor that limits the progress of construction under complex strata conditions, taking extremely hard rocks, for example [2, 3]. Therefore, how to increase the service life and improve the rock-breaking efficiency of the cutter has become a focus of research into TBM excavation of tunnels in hard rock. Scholars have conducted much research into the rock-breaking mechanism of TBM cutters. [PERSON] et al. [4] considered that a cutter rolls over and damages rocks because the stress applied to the rocks exceeds their uniaxial compressive strength. [PERSON] et al. [5] conducted experimental research on rock breakage using a wedged cutter and pointed out that the shear force produced in rocks by vertical force applied by the cutter on the rocks causes rock spalling. [PERSON] [6] believed that rock breakage by a cutter is a result of the joint action of tension and compression effects of blades on rocks. By conducting numerical analysis, [PERSON] et al. [7] found that rock breakage by a cutter is mainly achieved by the shear effect. At AGH University of Science and Technology, laboratory tests were carried out to determine the effect of temperature on cutting resistance and the selected mechanical properties of rock salt. The selected mechanical parameters (compressive, tensile, and shear strength) of rock salt for the same temperature values were compared and described [8; 9]. In the Department of Mining, Dressing and Transport Machines, AGH UST in Krakow, innovative and atypical mining tools were developed as crown picks and asymmetrical mini disk tools, especially for hard and very hard rock mining. A special solution of lubricated holder was also developed for cutting tools, allowing to facilitate and increase the number of pick rotations in the holder and, as a consequence, reducing the wear of the tool [10]. [PERSON] et al. [11] performed numerical analysis to reveal that the rock-breaking process and the formation process of cuttings are the results of the propagation of tensile and shear cracks. Researchers at Central South University (Changsha City, China) [12] developed a linear cutting test bench for disc cutters to study the rock-breaking effect under impact and rolling action of the cutters. A combined abrasion test device was independently developed in the State Key Laboratory of Shield Machine and Boring Technology, which has been used to reveal the mechanism underlying the interaction between rocks and mechanical tools [13; 14]. Microwave heating is instantaneous, integrative, and selective [15; 16; 17]. Microwaves-assisted mechanical rock breakage, as a new rock-breaking method, can reduce tool wear and improve rock-breaking efficiency if rocks are fractured by microwave heating before being cut using a cutter [18; 19; 20]. By using a method integrating physical tests and numerical simulation, [PERSON] et al. [21; 22; 23] explored the conditions for the formation of cracks in rocks under microwave irradiation. [PERSON] et al. [24] studied crack propagation in rocks containing different shapes of minerals under microwave irradiation using a numerical method, and the results show that cracks formed under microwave irradiation are mainly tensile cracks. [PERSON] et al. [25; 26] developed an open test facility for microwave-assisted fracturing of hard rocks, which was used to achieve microwave-induced fracturing of large rock samples and engineering rock mass. They also conducted cutting tests on different rock samples subjected to microwave irradiation using a TBM cutter to investigate the influence of microwave energy on the cutting performance of the TBM cutter.