## 1 Introduction  
The rate of pressure coming from the mine roof is a key factor affecting the stability of the surrounding rock. In actual mining, the advancement speed of the working face, the dynamic adjustment of mining stress, and the disturbance of adjacent working faces may all lead to changes in the rate of roof pressure [1]. Especially in deep mining or under complex geological conditions, the non-uniformity and suddenness of roof compression increase sharply, which is prone to induce disasters such as roof failure, rib spalling, and rockburst [2,3]. Therefore, conducting research on the stability of surrounding rock under different pressure rates has significant practical significance and broad application prospects. To explore the influence of strain rate on the mechanical properties of rocks, scholars at home and abroad have conducted a large number of studies on the strength, deformation, and energy evolution characteristics of rocks and achieved remarkable results [4, 5, 6, 7, 8]. [PERSON] [9] found that the loading rate can change mechanical properties of rock. [PERSON] et al. [10] believe that the increase in damage will weaken the strength of the rock. [PERSON] et al. [11] found through sandstone mechanics experiments that an increase in the loading rate would increase the failure strength and elastic modulus of the rock samples. At low rates, microcracks propagate along the weak surface, while at high rates, severe damage is caused. Similar laws were verified in the prefabricated fractured shale experiments of [PERSON] et al. [12], where the peak load decreased with the maximum displacement as the rate increased. [PERSON] et al. [13]'s research shows that the loading rate mainly regulates the morphology of the fracture zone. An increase in the loading rate significantly extends the length of the fracture zone, but the shape tends to narrow. [PERSON] et al. [14] revealed from the energy perspective that the total strain energy, elastic strain energy, and dissipated strain energy of brittle granite all increase with the increase in the loading rate. However, an increase in the loading rate will intensify the degree of damage and failure of the rock samples. The cyclic loading experiments of [PERSON] et al. [15] confirmed that a high loading rate would enhance the stress memory effect of rocks and inhibit the development of acoustic emission activities. [PERSON] et al. [16] studied the deformation and failure characteristics of shale under different loading rates. The study found that a high loading rate would lead to severe rock damage, but the cracks were relatively simple. However, a low loading rate will lead to complex crack damage, that is, a low loading rate is conducive to the formation of more broken rock blocks in the shale matrix. In terms of sandstone experiments, [PERSON] et al. [17] found that the difference in loading rates directly led to the differentiation of failure modes, and the degree of damage increased with the increase in the loading rates. [PERSON] et al. [18] conducted mechanical tests on rocks at different loading and unloading rates with the aid of a true triaxial loading device. The research finds that with the increase in the unloading rate of the horizontal principal stress, the total elastic strain energy at failure gradually decreases, while the total dissipated energy gradually increases. For special materials, [PERSON] and [PERSON] [19] found that the mass loss rate of high-water-content materials decreased with the increase in the loading speed, and showed significant rate sensitivity. [PERSON] et al. [20]'s research on prefabricated fractured rocks shows that their strength is always lower than that of intact rock masses, but both the peak strength and elastic modulus increase positively with the increase in the loading rate, and based on this, a constitutive model is established.