## 1 Introduction  
In recent years, with the vigorous development of high-speed train in China, the amplitude, frequency, and number of loadings on the subgrade have greatly increased. This increases the rate of stiffness degradation and accumulation of deformation of the subgrade filling layer, which in turn increases the stress in the underlying ground layer, resulting in excessive settlement or differential settlement [1]. Much research has been conducted on the behavior of sand under cyclic loading using cyclic triaxial tests, with the focus being on the effects of confining pressure, loading amplitude and frequency, over-consolidation ratio, fine particle content, and relative density, etc. [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. [PERSON] and [PERSON] [21] conducted cyclic triaxial tests on sands with different degrees of saturation and found that the damping ratio of saturated sand is greater than that of dry sand and partially saturated sand. [PERSON] et al. [22] studied the relative density on the dynamic pore pressure of tailing sand. It is believed that, for dense tailing sand, the growth rate of dynamic pore pressure decreases with the loading frequency and amplitude. [PERSON] et al. [23] studied the effects of confining pressure, initial shear stress, cyclic stress ratio, and loading frequency on the dynamic strength characteristics of saturated sand in Wenchuan. The authors found that the dynamic strength of saturated sand increases with the increase in confining pressure and loading frequency. Researchers [24; 25; 26; 27; 28; 29; 30] have also studied the dynamic characteristics of materials as pavement subgrade. [PERSON] et al. [31] analyzed the effects of water content, confining pressure and dynamic stress on the dynamic modulus and axial cumulative strain of subgrade coarse-grained materials, and proposed an empirical formula for calculating the dynamic modulus and axial cumulative strain. [PERSON] et al. [32] and [PERSON] et al. [33] studied the effect of frequency on the permanent deformation of coarse-grained fillers in railway subgrade. The authors found that the axial strain development mode is plastic stable type at lower loading frequency, and plastic failure type at higher loading frequency. The degree of permanent deformation and deterioration of the roadbed filler increases as the frequency increases. Research has also been conducted on static and dynamic characteristics of reinforced soils [34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46]. [PERSON] and [PERSON] [47] conducted large dynamic triaxial tests on unreinforced and geotextile reinforced sand. It was found that under cyclic loading, with the inclusion of reinforcement, dynamic modulus did not change much at lower confining pressures, but increased significantly at higher confining pressures. [PERSON] and [PERSON] [48] performed cyclic triaxial tests to study the effect of silt content in geotextile reinforced samples. The results showed that the inclusion of geotextile could decrease the cyclic ductility of dry sand. The sample strength decreased as silt content increase, then decreases once silt content is more than 35%. [PERSON] et al. [49] performed cyclic triaxial tests on saturated sand, and sand reinforced with polymethyl methacrylate horizontal (H) inclusions and horizontal-vertical inclusions. It is found that both unreinforced and reinforced sand showed stiffness softening characteristics under cyclic loading. The inclusion of reinforcement could improve the dynamic modulus of sand. In summary, the existing work on reinforced gravel soils is still limited to the following aspects: (1) The research objects are mainly focused on the dynamic characteristics of unreinforced soils, and the use of large triaxial elements to recycle the reinforced soil. Research on behavior is limited, and there are fewer studies on geogrid-reinforced gravel under high-speed train load.