## 5 Conclusions  
This paper takes sandstone rock samples as the research object and conducts mechanical experiments on the rock samples at different strain rates. By analyzing the strength characteristics, deformation characteristics, failure characteristics, energy characteristics and damage characteristics of the rock samples, the damage and failure mechanisms of the rock samples under different strain rates were further revealed. The conclusions obtained are as follows:  
1. The strain rate has a significant influence on the mechanical behavior of rock samples. Both the peak stress and the elastic modulus show a monotonically increasing trend with the increase in the strain rate. When the strain rate increased from 1 mm/min to 3 mm/min, the growth ratios of the peak stress and the elastic modulus were the largest, increasing by 71.1% and 147.4%, respectively. The peak strain, however, shows a monotonically decreasing law with the increase in the strain rate, presenting an evolution trend opposite to the peak stress and elastic modulus. The particle size distribution of the destroyed rock blocks varies under different strain rates. Under a low strain rate, large-sized complete rock blocks of the rock samples dominate, while rock samples with a high strain rate retain more small-sized fragmented rock blocks. This difference stems from the variation of secondary crack propagation characteristics. 2. Rocks exhibit phased energy transformation characteristics during the loading process. In the early stage of loading, the axial stress prompts the closure of the primary fissures. The increase in dissipated strain energy with strain mainly results from the frictional  
Figure 8: Relationship between damage quantity and strain: (**a**) 1 mm/min; (**b**) 3 mm/min; (**c**) 5 mm/min; (**d**) 7 mm/min. slip of the fissures and the fragmentation of minerals. Entering the middle stage of loading, the residual fissures are compacting and maintaining the continuous increase in the dissipated strain energy, but the energy-dominated mechanism undergoes a transformation. The accelerated bifurcation propagation of secondary cracks in the later stage of loading exacerbated the accumulation of the dissipated strain energy, but the elastic energy storage still dominated. When the secondary crack expands to the critical length, the elastic strain energy is suddenly released, causing macroscopic brittle failure of the rock sample. The energy is dissipated in the forms of crack propagation, clastic kinetic energy, and acoustic emission. 3. With the increase in the loading stress, secondary cracks preferentially select the propagation path and slowly expand along the clay-quartz interface. The elastic strain energy is slowly released in the form of frictional heat, eventually forming a penetrating main crack that extends along the boundary of the quartz crystal, resulting in the failure of the rock sample along the crystal. At a high strain rate, the energy transfer mechanism changes, the stress relaxation ability of the clay is suppressed, and the energy is forced to transfer to the quartz crystal. Driven by the high elastic strain energy, the tip of the secondary crack rapidly breaks through the energy threshold of the mineral interface and directly penetrates the internal lattice structure of the quartz crystal, resulting in the transgranular failure of the rock sample. 4. Judging from \(R^{2}\) and \(RMSE\), the constitutive model of energy damage constructed in this paper is reasonable. With the increase in the strain rate, the fitting degree among rock samples with different strain rates gradually increases, and all are greater than 0.908. This model can not only accurately characterize the nonlinear hardening characteristics of the rock sample in the compaction stage under different strain rates, but also respond well to the strength and deformation laws of the rock sample.