## 3 Brief Introduction to the Physical Test for Limestone Specimens
### Evolution Law of the Permeability Coefficient in the Whole Process of Model Stress-Strain  
The final failure modes of the prefabricated weak surface model (Model 1), prefabricated weak zone model (Model 2), and complete model (Model 3) are shown in Figure 6, and the stress-strain-permeability curves are shown in Figures 7a, 8a and 9a, respectively. Comparison of the post-peak curves in Figure 6a-c with those in Figures 7a, 8a and 9a indicated that when macroscopic shear cracks appeared in Models 1 and 3, the overall stress level decreased, and only the local area underwent high stress, which was due to the existence of some contact points in the shear failure zone. Both models had a certain shear slip after failure. However, the overall stress level of Model 2 did not decrease significantly because, although a shear failure zone formed in the weak area, the rocks on both sides of the failure zone were still intact and could continue to be loaded, and the model did not exhibit interlayer dislocation. Usually, sandstone has large pores high permeability. With axial displacement loading, the pores of sandstone closed. Therefore, the permeability coefficient began decreased slightly from the initial value at first. However, compared with sandstone, limestone has a dense texture, a small permeability coefficient, and almost no water permeability. Therefore, in accordance with the permeability characteristics of limestone, the permeability process of limestone can be divided into the following stages. 1. First stage: With axial displacement loading, some elements were destroyed because the load reached its failure strength. At this time, a micro-fracture occurred and formed a small seepage channel, and the permeability coefficient of the model increased. 2. Second stage: The axial displacement loading continued to increase. When the microcracks reached a certain number, the previous microcracks closed, and the permeability coefficient decreased slightly. 3. Third stage: With the increase in external load stress, failure occurred rapidly, and the cracks interconnected to form a shear failure zone. The penetrating cracks provided a favorable channel for seepage, and the permeability coefficient was greatly improved at this stage. 4. Fourth stage: The shear failure zone was gradually compacted under axial load, and the permeability coefficient decreased. This change in permeability coefficient could be clearly seen in both the experimental results (Figure 4b) and the numerical results. The prefabricated weak zone model (Figure 5b) was not compacted because the intact rock on both sides of the failure zone could continue to withstand the external load, and the decrease in the permeability coefficient was not obvious. \begin{table}
\begin{tabular}{c c c c} \hline  & **Parameter Name** & **Unit** & **Numerical Value** \\ \cline{2-4}
**Parameters of the specimen (m = 2)** & Mean elastic modulus E & MPa & 50,000 \\  & Intensity & MPa & 100 \\  & Poisson ratio \(\mu\) & & 0.25 \\  & Permeability coefficient & m/d & \(1.00\times 10^{-8}\) \\ \hline  & **Parameter Name** & **Unit** & **Numerical Value** \\ \cline{2-4}
**Pad parameters** & Mean elastic modulus E & MPa & 150,000 \\  & Intensity & MPa & 300 \\  & Poisson ratio \(\mu\) & & 0.2 \\  & Permeability coefficient & m/d & \(1\) \\ \hline  & **Parameter Name** & **Unit** & **Numerical Value** \\ \cline{2-4}
**Prefabricated weak surface (weak zone)** & Mean elastic modulus E & MPa & 20,000 \\  & Intensity & MPa & 20 \\  & Poisson ratio \(\mu\) & & 0.25 \\  & Permeability coefficient & m/d & \(1.00\times 10^{-8}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Sample mechanical properties (average value). Figure 6: _Cont_. Figure 6: Numerical results of the cracked mode. (**a**) Whole process curve of load step-stress-permeability coefficient. (**b**) Stress results of the model failure process (MPa). (**c**) Results of water pressure distribution in the model failure process (m). Figure 7: _Cont_. Figure 7: Numerical results of the model with a weak zone.