## 1 Introduction
It was concluded that the tensile strength and compressive strength of rocks with different degrees of saturation would be reduced under static and dynamic conditions. Various studies have also explored the dynamic-static combined loading of rocks. [PERSON] et al. [16] investigated the effects of static stress on the propagation of stress waves in red sandstone and found that the shapes of stress waves at the same measurement points varied considerably when axial compression was constant. However, the shapes of stress waves at different measurement points remained basically unchanged under the same axial compression. [PERSON] et al. [17] used a dynamic-static combined SHPB device to explore the energy dissipation characteristics of rocks with various porosities during the impact process. The authors found that the energy dissipation caused by the critical failure of rocks gradually decreases with an increase in porosity. [PERSON] et al. [18] conducted SHPB tests on sandstone under a preloaded axial pressure of 25 MPa and obtained a positive correlation between the crack extension rate and impact pressure. [PERSON] et al. [19] investigated the effects of high water pressure on the deformation characteristics of red sandstone based on a self-developed experimental device and found that the peak stress follows a logarithmic distribution with hydraulic pressure. [PERSON] et al. [20] used an improved dynamic-static combined SHPB test device and concluded that the dynamic failure of coal samples is significantly influenced by water. [PERSON] et al. [21], [PERSON] et al. [22], and [PERSON] et al. [23] thoroughly investigated the mechanical behavior and deformation characteristics of rocks under combined dynamic and static conditions. [PERSON] et al. [24] conducted SHPB tests on shale specimens with circular holes using a combined dynamic and static SHPB device and concluded that the main factor causing initial crack formation is the stress concentration caused by the circular holes. [PERSON] et al. [25] analyzed the energy mechanism of postpeak fractured sandstone under axial compression and found that the energy absorption per unit volume of postpeak fractured sandstone follows a linear functional distribution with an increase in axial static load. [PERSON] et al. [26] used a self-improved SHPB dynamic and static combined loading test apparatus to study the mechanical properties of limestone. The authors concluded that the damage patterns of the rock under different peripheral pressures mainly present tensile damage and compressive shear damage. [PERSON] et al. [27; 28] established a nonlinear dynamic model of combined coal rock under one-dimensional dynamic-static combined loading and investigated its energy dissipation characteristics as well as the stress-wave propagation mechanism. The above scholars studied rocks primarily under conditions considering temperature, water, and kinetic-static combinations, loaded with one or both types of coupling. There is limited research, however, on the dynamic properties of rocks under the combined effects of dynamic and static loading after temperature-water coupling. [PERSON] et al. [29] analyzed the mechanical properties of sandstone under the joint coupling of temperature, stress, and water but only performed static tests. [PERSON] et al. [30] only studied the dynamic properties of sandstone under temperature-water coupling but did not perform relevant tests on the sandstone under a combination of dynamic and static loading. Therefore, to prevent the occurrence of disasters and ensure the safe operation of underground space projects, it is necessary to carry out experimental research on the dynamic mechanics of temperature-water-coupled sandstone under dynamic and static combined loading. The sandstone used in this paper was obtained from the roadway of the Pan Er Coal Mine in Huianan City, Anhui Province, China, based on previous kinetic tests of local sandstone by [PERSON] et al.