## 1 Introduction
When the rubber content was 10%, the change in flexural strength was insignificant, the decrease in bending and tensile modulus was more pronounced, and the seepage resistance improved to float less. When the rubber content was more than 10%, the decrease in flexural strength was greater, and the seepage resistance had a tendency to decrease. Through the Fuller formula to derive the probability of occurrence of each aggregate on any section, the calculation results simulated the aggregate distribution state of each cross-section. Through finite element analysis and comparison with the actual test results, it was found that the specimen damage was due to the pressurization process. The rubber was under less stress, while the concrete around it was under large stress, making the stress distribution uneven and resulting in a concentration of stress, leading to the specimen's destruction [22]. [PERSON] et al. [23] found that regarding the effect of the two factors of mixing and particle size on the various basic mechanical properties of concrete, the particle size factor played a dominant role. The axial compressive stress-strain curve of rubberized concrete with different dosages and particle sizes was studied, and it was found that there was a certain correlation between the stress, strain, and Poisson's ratio of rubberized concrete and rubber dosage and particle size as a whole, but the law was not obvious. In addition, the effects of dosage and particle size on its performance were random, and the law was difficult to determine [24]. The pre-treatment of rubber and then mixing it into the concrete was researched, and it was found that it could reduce the water absorption of concrete and enhance the compressive strength and flexural strength. If the water-cement ratio was higher, the improved performance was better [25]. Rubber of different particle sizes with different substitution amounts were incorporated into concrete, and it was found that the addition of rubber reduced the concrete strength, and the concrete density and modulus of elasticity also decreased with the increase in rubber admixture [26; 27]. Many scholars have conducted a series of studies on static mechanical properties. In engineering, rubberized concrete is commonly used in practical projects [28; 29; 30; 31; 32; 33]. However, with the development of cold regions, related engineering freeze-thaw cycles frequently occur. As well as under the conditions of global climate change, more and more frequent cold wave low temperatures exacerbate the freeze-thaw cycle effect, and the related effect exacerbates the damage to concrete. Rubber blended into concrete can effectively change this situation [1; 34]. Analyzing the gap in physical and mechanical properties between NC and RRC after freeze-thaw cycles in a chloride salt environment, it was found that the RRC mechanical and freeze-thaw properties were optimal when the rubber admixture was 10% [35]. Different rubber powders were added to the concrete, and the concrete had better frost resistance when the rubber powder was 2.5%, and the freeze-thaw damage constitutive model of rubberized concrete was established [36]. Rubber in concrete can play the role of an air-entraining agent, increasing the air content of concrete, and the more rubber mixing, the faster its strength increases on the third and seventh days [37]. A fast-freezing test on rubberized concrete resulted in lighter mass and less density, which resulted in lower compressive strength [38]. For frost resistance of rubber concrete containing different dosages and particle sizes, it was found that as the rubber particle size decreases, the rate of mass loss of concrete decreases, and the higher the modulus of elasticity, the better the frost resistance. As the dosage increases, the rate of mass loss decreases and then increases, and the modulus of elasticity increases and then decreases, and when the rubber dosage is less than 100 L/m\({}^{3}\), the frost resistance is better [39].