## 1 Introduction  
Slotting-blasting is the most critical technology in the construction of rock tunnels using the drilling and blasting method. The methods of applying blasting load and blasting theory affect the engineering application of tunnel blasting numerical simulation results. There are many ways of applying blasting loads in tunnel engineering. In the past, the blasting load was applied by using the attenuation models such as the triangular impact load model or the exponential function one [1]. The effect of blasting loads is simulated by applying load curves on the hole walls [2; 3]. Jones-Wilkins-Lee (JWL) model is a high-energy combustion model. At present, the JWL equation of explosives state is often adopted for the description of detonation products of explosives [4; 5; 6; 7; 8; 9; 10; 11; 12]. The development of rock blasting theory mainly experienced three stages: elastic-plastic theory, fracture mechanics theory and damage mechanics theory. At present, the blasting damage theories represent the development frontier of rock blasting studies [8]. Using the damage mechanics theory of rock can better simulate the formation and development process from microscopic cracks to macroscopic cracks of rock with native defects [13; 14; 15; 16; 17]. Under blasting load, there is the damage phenomenon besides the obvious elastic-plastic deformation for rock. A lot of researchers have studied the problem of rock mass damage caused by blasting and focus on the damage evolution law of rock mass material under blasting load and the mechanism and law of rock mass failure due to crack propagation. The dynamic damage mechanism was firstly introduced by [PERSON] and [PERSON] (1980) to simulate the blasting process, and they proposed an isotropic rock blasting damage model (the GK model) [18]. The blasting damage models were developed using the damage variable defined by the probability of fracture and considering the effect of loading time on the crack density [4; 5]. An elastoplastic blasting damage constitutive model considering rock initial damage was established, and a damage criterion to evaluate the effects of rock blasting damage was proposed [8]. A tension and compression-shear blasting damage model was developed by considering damage patterns of rock mass and the effect of strain rate [9]. Using the numerical simulation technologies of finite element [2; 3; 4; 5; 7; 8; 9; 10; 11; 12; 19], the finite difference [1] and discrete element [6; 7; 10; 19] methods can simulate tunnel blasting and investigate the damage evolution law of rock effectively in tunnel drilling and blasting construction. In addition to numerical simulation methods, other methods such as the dynamic caustics blasting experiments [20] and strain gauge method [21] can also be used to investigate the stress wave propagation during slotting blasting and the effect of explosive stress waves on the crack propagation in the defective medium under slitting blasting loading. At present, rock blasting damage models are rarely used to study tunnel cutting blasting mechanism. Rock is the typical material whose tensile strength and compressive strength are very different. The increment relation of rock stress and strain in the stretched state is different from that in the compressed state. [PERSON] et al. (2016) developed tension and compression-shear damage model to investigate the damage evolution mechanisms of rock in deep tunnels induced by cutting blasting [9]. To fully reflect the contribution of tensile stress damage and compressive stress damage to tunnel cutting blasting, it is necessary to develop a reasonable tension-compression coupling damage model to investigate the damage evolution mechanism caused by rock tunnel cutting blasting. In this paper, we propose a method to calculate the weighted damage degree denoted by the damage weight coefficient calculated by the proportional relation of current principal stresses to measure the coupled effect of tension stress damage and compression stress damage.