###### Abstract  
As construction in urban centers increases internationally, many concrete infrastructures are being built at 100 m or more underground, and the influence of groundwater on these facilities is also increasing. Accordingly, the importance of waterproofing and leak-proofing technology for securing long-term durability and safety of underground concrete facilities has been greatly emphasized. The most important required performance of such leak repair technology is to withstand structural behavior and groundwater pressure well. Currently, as a leak repair material for underground concrete facilities, a synthetic rubber-based polymer rubber gel with adhesive flexibility is used internationally. However, quantitative data on how deep the material can perform underground are lacking. In general, the water pressure resistance evaluation of leak repair materials only checks whether it withstands the water pressure of 30 m (0.3 MPa) underground. Therefore, in this study, the toughness of the synthetic rubber polymerized gel (SPRG) leak repair material was calculated using three factors: viscosity, cohesive strength (adhesion strength), and elongation, and an analysis method that can be replaced with water pressure resistance was proposed. In addition, in the correlation between toughness and underground water pressure, it was possible to find out the thickness of the leak repair material used by the underground depth. As a result, it was possible to know the required thickness of the leak repair material according to the depth of the structure to be built underground. today 2022 27 September 20  
to as SPRG) leak repair material has been developed and is being used internationally [7,8]. The biggest reason why SPRG is used as a leak-crack repair material is that it is a non-hardening gel, and it does not break or tear even in cracks and joint behavior, and it has the characteristic of continuously attaching to the wet surface [9,10]. In other words, when high-viscosity SPRG is injected into leaky cracks or gaps in the joint, it has been evaluated because it has excellent resistance to repeated behavior and high pressure. Therefore, it is very important to always maintain high viscosity in order for SPRG to have continuous hydraulic resistance [10,11]. However, for on-site quality control of this material and method, the standard for the appropriate amount of SPRG filling (usage) or the appropriate thickness according to the depth of the underground has not yet been established [12,13]. Therefore, it is necessary to measure the injection amount and thickness of the repair material for leak repair design according to the depth of the underground structure. Therefore, it is necessary to check the correlation between the viscosity of the SPRG and the water pressure resistance, which responds to the behavior of concrete members in cracks or joints, contraction, and expansion due to temperature, and subsidence of the ground. When SPRG is injected along the leak path of cracks and joints, the material repels water while filling the voids. In this state, when the pressure of groundwater acts, the water inflow is blocked by the hydraulic resistance of the SPRG [14,15]. At this time, the water pressure resistance or hydraulic resistance largely depends on the viscosity or cohesiveness (cohesive force) of the SPRG. The higher the viscosity, the greater the cohesive force and hydraulic resistance, and the lower the viscosity, the weaker the cohesive force and hydraulic resistance [16]. Therefore, it is necessary to quantitatively evaluate the correlation with the underground water pressure according to the viscosity or cohesiveness of the SPRG. Therefore, in this study, a theoretical analysis was conducted to confirm the interconnection of viscosity, cohesiveness, toughness, and hydraulic resistance of SPRG. 'Viscosity' is a quantity that indicates the difficulty of fluid flow, and is defined as the degree of stickiness or internal resistance when flowing.