## 4 Re-Bearing Capacity Characteristics of Damaged Sandstone
### Damaged Sandstone Characteristic Stress and Poisson's Ratio Analysis  
Figure 4 shows the relationship curves between initiation stress \(\sigma\)ci, damage stress \(\sigma\)cd, peak stress \(\sigma\)c, and the unloading point, while Figure 5 shows the relationship curves between Poisson's ratio \(\mu\) and the unloading point. It can be found that, on the whole, there is an obvious decreasing trend of the crack initiation stress, damage stress, and peak stress of the damaged sandstone with the increase in the unloading point. However, before the unloading point of 70%, the peak stress curve experienced a small increase and then decrease, and the peak stresses at 40%, 45%, 50%, and 55% of the unloading point  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Type** & **Unloading Point** & \begin{tabular}{c} \(\sigma_{ci}\) \\ **/MPa** \\ \end{tabular} & \
\begin{tabular}{c} \(\sigma_{cd}\) \\ **/MPa** \\ \end{tabular} &
\begin{tabular}{c} \(\sigma_{c}\) \\ **/MPa** \\ \end{tabular} \\ \hline Single-axis & / & 13.30 & 54.40 & 78.63 \\ \hline Single & 40\% & 10.26 & 50.47 & 78.93 \\  & 45\% & 9.76 & 54.35 & 79.15 \\  & 50\% & 8.93 & 53.70 & 81.16 \\  & 55\% & 9.25 & 53.20 & 79.70 \\  & 60\% & 8.94 & 51.95 & 78.06 \\ Single-axis after & 65\% & 10.54 & 42.36 & 76.01 \\ injury & 70\% & 11.49 & 33.65 & 75.05 \\  & 75\% & 4.21 & 5.63 & 37.65 \\  & 80\% & 1.57 & 2.82 & 5.50 \\  & 85\% & 0.14 & 0.14 & 2.68 \\  & 90\% & 0.08 & 0.08 & 2.14 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristic strengths of sandstone under uniaxial reloading with different peak front unloading point damage.  
were larger than the peak stresses of the intact sandstone. In addition, the peak stresses were comparable to the peak stresses of the intact sandstone only at 60% of the unloading point, indicating that the sandstone had initial damage. The lower peak unloading point compressed the original fracture of the specimen, and the peak stresses appeared to increase instead of decrease. Compared with the intact sandstone, the crack initiation stress \(\sigma\)ci and the damage stress \(\sigma\)cd at different unloading points of the damaged sandstone were reduced. It is noteworthy that the damage stress and crack initiation stress curves completely overlap at 85% and 90% of the unloading point, indicating that the highly damaged specimens have a higher degree of internal crack development and do not go through the crack stable extension stage during the uniaxial reloading process, but directly enter the crack unstable extension stage until damage. From the relationship curve between the Poisson's ratio and the unloading point in Figure 5, it can be seen that, with the increase in the unloading point, the Poisson's ratio is increasing, and at 85% and 90% of the unloading point, the Poisson's ratio is close to 0.5. In elastic mechanics, a Poisson's ratio of 0.5 indicates that the material is incompressible in the elastic stage, i.e., the damaged sandstone at 85% and 90% of the unloading point does not experience an elastic stage in the uniaxial reloading process, which is different from not experiencing a crack stable expansion phase, as mentioned above.