## 1 Introduction  
Metal mine tunneling is often faced with a complex hydrological environment, weak and broken surrounding rock, and other adverse geological conditions, which will bring challenges to tunneling construction and subsequent production safety hazards. If the roadway development process needs to cross the mine rock contact zone or water-rich environment, it usually adopts advanced curtain grouting technology for water-blocking construction to ensure the roadway is safe and smooth digging [1]. An overrun grouting curtain can form an effective water-blocking barrier, improve the strength of the roadway, reduce the risk of water surges, and reduce the deformation capacity of the surrounding rock. Curtain grouting is frequently incorporated into cement slurry water glass to expedite slurry solidification because the dynamic water environment is not conducive to the formation of an effective curtain cement slurry. Additionally, the rheology and plasticity of concrete can be significantly enhanced by the addition of a small amount of water-reducingagent. Due to the significant difference in the mechanical parameters of the ore-rock in the contact zone, the slurry may show different diffusion patterns when it passes through the contact zone of the two rock bodies, which will directly affect the final curtain body water-blocking effect [2]. Moreover, under water-rich conditions, water pressure will make it more difficult for the slurry to form a continuous curtain body. Many researchers have carried out studies on the curtain grouting problem. [PERSON] et al. [1; 2; 3] introduced the grouting design methods and construction procedures, proposed the values of the main grouting parameters and composite materials that are applicable to various flowing water environments, adopted curtain grouting technology for tunnel pre-strengthening, and employed the seepage model to determine the safe thickness of the curtain body under stratigraphic conditions. They also proposed empirical equations between the safe thickness of the curtain body and the BQ. [PERSON] et al. [4] utilized physical probe and borehole exploration methods to identify the tunnel's eroded areas. They then implemented full-section curtain grouting and pipe shed reinforcement measures to significantly reinforce the geotechnical body during construction. Physical detection and drilling exploration methods are employed to identify the erosion area of the tunnel. During the construction process, the geotechnical body is fortified by the installation of a curtain grouting pipe enclosure and other reinforcement measures. [PERSON] [5], [PERSON] [6], and others established a monitoring system and, by observing the development of fractures and the formation of the mechanism, summarized the four mechanisms of local infiltration channel formation. They also proposed a method for evaluating and analyzing the seepage channel. In order to guarantee the safety of mining and the stability of the roadway surrounding the rock, [PERSON] et al. [7] utilize single-row annular curtain grouting to surround the surrounding rock and ore, thereby forming a complete and dense curtain body with specific strength, to address rock damage, fissure development, and other geological issues. [PERSON] et al. [8] employed numerical analysis to simulate the construction process of the curtain grouting section, evaluate the effects of various curtain grouting parameters, select the optimal grouting parameters, and subsequently apply them to the grouting construction. [PERSON] et al. [9; 10] proposed a method of curtain formation and stability (FSC) for overtopping curtain grouting projects. They analyzed the mathematical equations and simplified the model from the engineering problems. The two-phase flow equations of motion proposed by [PERSON] [11], [PERSON] [12], and others can be applied to a variety of porous media and authenticated through numerical simulations. In order to investigate the mechanical properties of the composite rock, [PERSON] et al.