# The Shear Behavior of the Curved Interface in Polyurethane-Concrete Composite Structures
## 1 Introduction  
Public infrastructure constructions such as highways, bridges, tunnels, railways, and pipelines are burgeoning. Due to varying traffic conditions, complex service environments, and extended service lifetimes, these infrastructures face numerous concealed defects that impact their structural safety. To address the concealed defects in engineering structures, scholars have proposed polyurethane grouting trenchless repair technology. This technology has been successfully applied in waterproofing, leakage sealing, and other concealed defect prevention in crucial engineering structures such as roads, airport pavements, dams, and tunnels [1; 2; 3; 4; 5]. The enhancement of structural toughness is significantly influenced by the interface between polyurethane materials and various engineering structures. [PERSON] et al. [6] conducted direct shear tests to examine the effects of vertical stress and shear rate on parameters such as shear stress, shear displacement, shear modulus, and shear strength at the interfaces of polyurethane-geotextile and polyurethane-sand. The results showed that, as shear displacement increased, the interface exhibited shear softening behavior. Shear rate had a limited effect on both shear strength and shear modulus. [PERSON] et al. [7] investigated the shear behavior between polyurethane anchor bodies and silty soil, analyzing how anchor diameter, density, and length affect shear strength, as well as the distribution and variation in shear stress under different anchor body lengths. The results indicated that bond strength increased with higher anchor density but decreased with longer anchors and larger pore sizes. [PERSON] et al. [8] explored factors including soil moisture content, normal stress, interface type, polyurethane density, and forming method on interface shear strength through direct shear tests. The results revealed that steel-polymer interfaces exhibited brittle failure. Interface shear strength was closely related to polymer density, normal stress, and soil moisture content. [PERSON] et al. [9] compared epoxy resin and polyurethane for cement and chemical grouting. Their impact on the shear behavior of rock joints was evaluated via direct shear tests. The results showed that grouted samples had higher maximum and residual shear strengths than ungrouted joints. Grouting improved cohesion but reduced friction angles. Cement grouting exhibited brittle behavior, while chemical grouting showed greater ductility. [PERSON] et al. [10] studied the mechanical behavior of polyurethane injection grouting materials containing bentonite using direct shear tests and DIC technology, proposing concepts of equivalent internal friction angle and equivalent cohesion for the polymer-bentonite interface. The results indicated that the shear strength of the polymer-bentonite interface was higher than that of pure bentonite. Increases in normal stress and polymer density enhanced shear strength, while higher bentonite moisture reduced it. Interface failures mainly occurred within the bentonite or at the polymer-bentonite boundary. [PERSON] et al. [11] investigated the influence of interface roughness and density on the shear behavior of polyurethane with pavement materials through shear, splitting, and tensile tests, and established an interface strength model. The results showed that polyurethane formed dense interfacial films, with film thickness increasing with density. Failure modes included breaks along polyurethane boundaries, substrate edges, and interface nodes. Regarding the interfacial mechanical properties between polyurethane materials and concrete, [PERSON] et al. [12] conducted cyclic compression tests on composite structures of concrete and polyurethane materials, finding that the influence of injection thickness, stress ratio, void shape, and density on fatigue performance decreased in that order. [PERSON] et al.