## 1 Introduction  
With the advances in infrastructure construction in China, the number of tunnels constructed is increasing year by year [1; 2; 3; 4; 5]. The shield method has gradually become the mainstream method of tunnel construction, due to advantages which include a high degree of mechanization, high construction efficiency, and the possibility of performing construction with water, and it is widely used for the construction of highways, railways, electric power, urban rail transit, etc. [6; 7; 8]. Disc cutters, as a direct tool used by the shield machine to break up rock and soil, has a crucial impact on the efficiency and safety of the construction of the shield tunnel. The use of an appropriate design for the disc cutter is extremely important in the construction of shield tunnels. There are many factors affecting the rock-breaking efficiency of disc cutters, including the size of the disc cutter, blade width, blade angle, blade fillet, the properties of the rock and soil, etc. [9]. Therefore, to improve the rock-breaking efficiency of the disc cutter, it is necessary to optimize the design according to the factors influencing the rock breaking. Many researchers have studied rock properties and the performance of disc cutters in recent years. In the numerical simulation of rock breaking with disc cutters, the most commonly used rock dynamic computational constitutive model is the HJC (Holmquist-Johnson-Cook) model [10; 11; 12]. The HJC model was originally a constitutive model for simulating concrete taking into consideration the strain rate effects, damage effects, confining pressure effects, crushing effects and compaction effects when subjected to large strains, high strain rates, and high pressure [13; 14]. Since the crushing process of rock is highly consistent with that of concrete, it can also be used to simulate the breaking behaviour of rock. In recent years, many scholars have studied methods for determining the HJC model parameters. Based on the concrete strength calculation formula proposed by the American Concrete Association, [PERSON] and [PERSON] [15] gave a simple method for deriving other basic mechanical parameters in the HJC model from the uniaxial compressive strength, but the limitation of this method is that it does not include the limit surface parameters of the HJC model. [PERSON] et al. [16; 17] enhanced the pressure-shear behaviour of the HJC model and changed the modelling of strain rate sensitivity so that the enhancement factor of strain rate goes to unity for a strain rate of zero. Based on the yield surface theory, [PERSON] et al. [18; 19] established the relationship between the cohesion strength and the parameters of the Mohr-Coulomb criterion and proposed a method for obtaining the limit surface parameters of the HJC model. [PERSON] et al. [20] proposed a method for determining the failure strength parameters and obtained the value of the failure strength parameters. [PERSON] et al. [21] derived the relationship between the cohesion parameter and the cap model parameters based on the plastic yield surface theory. [PERSON] et al. [22] analysed the failure type parameter in the parameters of the HJC model, studied the influence of this parameter on concrete compaction failure, and determined its value range. [PERSON] et al. [23] investigated the previous studies and was able to obtain the strength parameters, state parameters, rate effect parameters, and damage parameters of the HJC model through the analysis and fitting of existing experimental data. In addition, the relevant parameters were revised according to the results of the shield cutting tool cutting concrete test. Since the HJC model was originally used to describe the failure behaviour of concrete, most of the initial parameters are not suitable for rock materials. Therefore, to accurately describe the failure behaviour of rocks, scholars have carried out many studies regarding the determination of the parameters of the HJC model for rocks.