## 1 Introduction  
As an important part of large-scale water conservancy projects, the safety of water conveyance tunnels is crucial. In China, increasing development scale and engineering challenges in hydropower are causing the concrete lining of water conveyance tunnels to permeate under high-pressure water. On the one hand, a water head of several hundred meters during tunnel operation will cause the concrete lining to crack, leading to internal water exosmosis [1; 2; 3]. On the other hand, during the emptying period of the tunnel, high-pressure external water in the surrounding rock will permeate the concrete lining in the opposite direction or directly permeate through cracks, leading to external water endosym [4; 5]. Therefore, improving concrete impermeability is important for the safe operation of high-pressure water conveyance tunnels. Concrete is a porous medium composed of cementitious materials, aggregates, and water in certain proportions. External water molecules continuously enter the interior of concrete through convection, diffusion, and the capillary action of these pores. Water molecules under high pressure accelerate permeation into the concrete from the pore channel and change the parameters of the concrete, including the number of micropores, porosity, and pore size [6]. Researchers have found that high-pressure water can change the pore structure of concrete, reduce its strength, and increase its deformation [7; 8; 9; 10]. This process reduces the bearing capacity of the structure. In addition, researchers have studied the effect of high water pressure on concrete cracking [11; 12; 13], finding that high-pressure water accelerates the cracking and failure process of concrete [14; 15; 16]. Therefore, an increasing number of researchers are paying attention to methods for improving concrete impermeability [17; 18; 19; 20]. A common method is to mix additive agents with the concrete substrate to improve its pore structure [21; 22]. Many studies have focused on the influence of the type and content of additive agents on concrete impermeability [23; 24; 25]. These studies have found that moderate additive agents can improve the overall density of concrete [18; 26; 27; 28; 29; 30; 31; 32]. Additive agents inhibit water expansion in the internal pores of the concrete and enhance the strength of the concrete skeleton, thus improving the impermeability of the concrete itself. Additive agents can also reduce porosity and pore size to a certain extent, but they cannot change concrete's inherent hydrophilic properties. Water molecules under high water pressure can still permeate the interior of concrete through these pore channels. By contrast, dense and hydrophobic coatings are more effective in inhibiting the permeation of water molecules [33; 34; 35; 36]. These coatings are polymer materials with no macroscopic pore channels inside, exhibiting excellent hydrophobicity and low permeability. Researchers have developed many hydrophobic coatings suitable for concrete. [PERSON] et al. [37] designed a multi-layer coating with extremely strong hydrophobicity. At the same time, the coating also resists the permeation of chloride ions, with a 92% improvement over untreated concrete. [PERSON] et al. [38] prepared an inexpensive and environmentally friendly fluorine-free superhydrophobic coating based on carbon-based materials, with a water contact angle (WCA) of 156\({}^{\circ}\). [PERSON] et al. [39] modified the surface of concrete with silica sol and developed a hydrophobic coating suitable for high salt environments. In addition, researchers evaluated the impermeability of various coatings on the surface of concrete. [PERSON] et al. [40] studied the interaction between four coatings, namely, sodium acetate, fluoropolymer, silicone resin, and silane, and concrete with different moisture contents. They found that sodium acetate could provide optimal protection for concrete at various moisture contents. [PERSON] et al.