## 1 Introduction  
With global warming, the deterioration of long-lasting permafrost within the Qinghai-Tibet Plateau region has an impact on the stability of transportation roadbeds [1]. Since the construction of the Qinghai-Tibet Railway, the problem of settlement and deformation of the roadbed has become increasingly serious due to the effects of cyclic loading and climate [2, 3]. Scholars have studied the annual average ground temperature of permafrost along the Qinghai-Tibet Railway, such as the average ground temperature range at different depths and based on that, divided the permafrost regions [4, 5]. Permafrost exhibits a pronounced sensitivity to temperature fluctuations, and as a result, variations in temperature and water content can significantly alter its engineering behavior and performance characteristics [6]. Some scholars studied temperature and moisture content influence on mechanical behavior of permafrost along the Qinghai-Tibet Railway [7, 8]. The construction of transportation projects in permafrost areas inevitably changes the water-heat exchange conditions in the soil, which is also one of the key factors affecting the stability of permafrost, so it is necessary to carry out a research on the influence of temperature and water content on the dynamic characteristics of permafrost roadbeds of Qinghai-Tibet Railway. The problems of frozen soil roadbed stability, mechanical properties, and permanent deformation have always been the hotspots concerned by engineering construction in cold regions [9, 10, 11, 12, 13, 14, 15]. [PERSON] et al. [16] conducted a comprehensive study on the frozen chalk soil of roadbeds in the Qinghai-Tibetan Plateau, utilizing low-temperature cyclic dynamic triaxial testing to unravel the intricate variations in dynamic shear modulus and damping ratio of the frozen soil under various conditions of temperature, water content, compaction, and confining pressure during graded cyclic loading. [PERSON] et al. [17] embarked on a thorough examination of the dynamics of remolded permafrost in the Qinghai-Tibet Engineering Corridor, utilizing dynamic triaxial testing to elucidate the intricate interplay between the damping ratio and dynamic shear modulus ratio of the permafrost under cyclic loading, as modulated by factors such as confining pressure, temperature, water content, and loading frequency. [PERSON] et al. [18] performed triaxial tests on high-salt content frozen powdery clay sourced from the Xinjiang region, delving into its deformation behavior and strength properties across varying confining pressures and temperatures, they assessed the suitability of the refined Duncan-Chang model and the parabolic strength criterion in the context of high-salt permafrost, offering valuable insights into the material's mechanical response. Numerous scholars from both domestic and international realms have embarked on numerical simulation endeavors, aiming to elucidate the intricate mechanical and deformation characteristics exhibited by frozen clay, these studies have provided valuable insights into the material's behavior under various conditions [19; 20; 21]. [PERSON] et al. [22] developed a numerical model to simulate the settlement of the Qinghai-Tibet Railway's permafrost roadbed caused by train vibrations. This model enabled an in-depth analysis of how varying factors, including roadbed height, thickness of ice-rich permafrost, and the site's initial annual average ground temperature, influence the settlement and accumulation of permanent deformation in the multi-year permafrost roadbed. [PERSON] et al. [23] conducted isotropic and shear tests on natural permafrost samples from Alaska to investigate the strength properties of permafrost at different temperatures and perimeter pressures and developed an elasto-plastic model to analyze the mechanical tests of permafrost, which was applied to describe the compressive collapse behavior of permafrost foundations.