## 1 Introduction  
Tunnels often are constructed using the drilling-blasting method in many eastern Chinese cities. The blasting construction of rock tunnels must inevitably underpass existing buildings and structures such as sewage box culverts and pipelines. When the tunnel constructed using the drilling-blasting method underpasses through the structure of box culverts, the impact caused by rock blasting will damage the box culvert structure adjacent to the tunnel [1]. blasting damage in the construction of tunnels is usually regulated in infrastructure contracts because it can influence the lifecycle cost and qualify for tunneling projects [2]. The most critical issue is how to reasonably determine the safe distance between tunnel and existing box culvert in tunnel blasting construction. The control of explosion-induced crushed and cracked zones is of the utmost importance in the rock explosion design [3]. In numerical simulations of tunnel excavation, rock damage-plasticity models are often used to study the influence of both effects on the evolution of deformation and stress distribution in rock masses [4, 5]. The research on the constitutive models of rock blasting damage is a developing process. The blasting damage model of rock (the GK model) [6] was used to simulate the process of rock blasting. The GK model was improved upon using the definition of crack density distribution with the effect of loading time and damage variables with the fracture probability [7, 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 [9, 10]. The rock tension-compression damage model [11]and tension-compression-shear damage model [12] were developed. The damage process of the surrounding rock under multiple full-face blasts is simulated using rock blast-induced damage model integrating the tensile damage model with the Drucker-Prager yield condition [13]. The rock blasting damage constitutive model coupling the tension-compression weighted damage variable and the classical PLASTIC_ KINEMATIC model was used to investigate the rock damage evolution law in slotting-blasting construction [14]. With the development of computer technology, numerical simulation technology has become one of effective methods to investigate the damage evolution of rock in the process of blasting excavation construction [15; 16; 17; 18; 19; 20]. Surrounding rock damage is controlled by accurately describing rock characteristics such as Young's modulus and Poisson's ratio in tunnel blasting construction [17], and by optimizing charge structures and the number of blast-hole rows [18]. The damage degree of the blasting crushing zone was determined using rock fracture theory [19]. The Johnson-Holmquist-Rock (JHR) damage model is proposed to simulate the failure process of rock under blasting load [20]. Elastoplastic cellular automaton was employed to simulate blasting-induced elastoplastic dynamic responses [21]. Rock explosion is a complex problem because neither the rock characteristics nor the explosion waves could be accurately estimated. A first-order reliability analysis can predict rock blasting damage [22]. Through the use of ANSYS/LS-DYNA to establish a three-dimensional finite element model for slope and tunnel, the minimum safe distance from tunnel face to slope surface was determined according to the first strength theory and a linear statistical relationship between peak particle velocity and rock effective tensile stress [23]. Using the 3D numerical model established by LS-DYNA, the safety vibration velocity threshold of each vulnerable area was calculated based on the maximum tensile stress criterion during the whole process of tunnel blasting excavation [24]. The displacement of surrounding rock in tunnel construction can be predicted or estimated using the artificial neural network [25; 26], numerical analysis, fuzzy logic, and statistical analysis models [26], and the gene expression programming [27].