# Dynamic Characteristics of Sandstone under Coupled Static-Dynamic Loads after Freeze-Thaw Cycles
## 3 Strength Characteristics of Sandstone under Freeze-Thaw Cycles and Axial Pre-Compression Stresses
### Strength Characteristics of Sandstone at Different Pre-Compression Stresses  
When the pre-compression stress is 0 MPa, 15 MPa, 35 MPa and 55 MPa, the corresponding dynamic stress-strain curves of typical sandstone specimens after treatment of 0, 20, 60, 100 and 140 number of freeze-thaw cycles are presented in Figure 7. The average peak stress and average peak strain under different pre-compression stress and different freeze-thaw cycles are summarized in Table 4.  
Figure 7: _Cont._  
From these graphs, the stress-strain curves at no axial load are observed to go through four stages, namely densification, elasticity, yielding. and failure. When the pre-compression stress is applied, the stress- strain curves show similar characteristics but without the densification stage, indicating that the stress-strain curves are not smooth. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Axial Pre-** \\ **Compression** \\ **Stress (MPa)** \\ \end{tabular} } & \multicolumn{4}{c}{\
\begin{tabular}{c} **Average Peak Stress at Different** \\ **Numbers of Freeze-Thaw Cycles** \\ \end{tabular} } & \multicolumn{4}{c}{
\begin{tabular}{c} **Average Peak Strain at Different** \\ **Numbers of Freeze-Thaw Cycles** \\ \end{tabular} } \\ \cline{2-11}  & **0** & **20** & **60** & **100** & **140** & **0** & **20** & **60** & **100** & **140** \\ \hline
0 & 96.21 & 92.31 & 88.54 & 82.81 & 76.37 & 0.0103 & 0.0106 & 0.011 & 0.0116 & 0.0121 \\
15 & 129.58 & 124.8 & 119.67 & 113.08 & 109.24 & 0.0069 & 0.0072 & 0.0081 & 0.0083 & 0.0084 \\
35 & 119.48 & 116.64 & 112.96 & 110.35 & 105.15 & 0.0062 & 0.0063 & 0.0064 & 0.0067 & 0.0065 \\
55 & 100.11 & 95.95 & 91.29 & 83.80 & 89.41 & 0.0089 & 0.0095 & 0.0100 & 0.0104 & 0.0110 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average peak stress and peak strain at different axial pre-compression load and freeze-thaw cycles. Figure 7: Dynamic stress–strain curves of sandstone under different freeze-thaw cycles and pre-compression stress. internal micro-cracks mainly responsible for the densification stage are closed by the pre-compression load. In this case, there is only three stages of stress-strain curves. The first is the elastic stage where the dynamic stress-strain relationship is nonlinear. This stage shows that with the increase in the pre-compression stress, more micro-cracks in the specimen are generated under dynamic impacts and therefore the slope of the elastic stage decreases gradually. The second is the yielding stage. The compression modulus at this stage is significantly reduced, suggesting that the microcracks in the rock under the action of a stress wave expand rapidly, both in numbers and in sizes, until the peak point is reached. The third is the failure stage or the post-peak behavior where the formation of the macroscopic fractures in the specimen leads to a significant decrease in its bearing capacity. In this stage, when the stress is unloaded to a certain value, the total strain of the specimen will be reduced corresponding to the tail part of the stress-strain curve. With the increase of pre-compression stress and number of freeze-thaw cycles, the rebound trend is increasingly obvious. It can be seen from Figure 7 and Table 4 that when the number of freeze-thaw cycles is the same, the strength of the specimen under dynamic loading is greater than that under static loading, which is mainly due to the strain rate effect. Meanwhile, when the pre-compression stress is consistent, the maximum strain gradually increases. The peak strength and peak strain of the sandstone under different axial pre-compression stresses and different number of freeze-thaw cycles are presented in Figures 8 and 9, respectively. It can be seen from Figure 8 that, under coupling loads, the strength of sandstone is higher than the static strength and its dynamic strength with no pre-compression stress.