## 2 Specim Preparation
### Compressibility Analysis of Mudstone and Rock Salt  
From Figure 5, the specimen height variation is linear with the mudstone content under the same mass and stress conditions, and the height of the specimen decreases with the increase of the mudstone content because the mudstone is more compressible than rock salt. The mudstone is porous and composed of clay minerals and other finely divided minerals, so its compressibility is higher than  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Diameter (mm)** & **Height (mm)** & **Mass (g)** & **Density (g-cm\({}^{-3}\))** & **Mudstone Content (\%)** \\ \hline a1 & 25.47 & 47.67 & 51.1576 & 2.106 & 0 \\ b1 & 25.49 & 52.63 & 57.1631 & 2.128 & 0 \\ c1 & 25.61 & 51.17 & 57.1781 & 2.169 & 20 \\ d1 & 25.57 & 50.48 & 57.1842 & 2.206 & 40 \\ e1 & 25.61 & 49.89 & 56.9402 & 2.216 & 50 \\ f1 & 25.57 & 49.23 & 57.0120 & 2.255 & 60 \\ g1 & 25.69 & 48.47 & 56.9275 & 2.266 & 80 \\ h1 & 25.65 & 47.19 & 56.9406 & 2.335 & 100 \\ i1 & 25.39 & 50.01 & 57.2017 & 2.259 & 100 \\ \hline \hline \end{tabular} Note: a1 is made of particles of pure rock salt; b1 is synthetic pure rock salt with a small amount of cement and brine; h1 is synthetic pure mudstone with a small amount of cement and brine; i1 is made of particles of pure mudstone.  
\end{table}
Table 2: Physical parameters of mixed specimens.  
Figure 5: The relationship between the height and the mudstone content of b1-h1.  
rock salt. Now, we compare the compressibility of mudstone and rock salt from the theoretical point of view.  
[PERSON] [24] defined a rock effective compression factor:  
\[c_{p}=\frac{dV_{p}}{V_{p}\cdot dP} \tag{1}\]  
where \(c_{p}\) is rock compression factor, \(V_{P}\) is the rock pore volume and \(P\) is pressure.  
The commonly-used Hall chart curve [25] is shown in Figure 6, and the empirical formula for \(c_{p}-\phi\) is:  
\[c_{p}=\frac{2.59\times 10^{-4}}{\phi^{0.44}} \tag{2}\]  
where \(\phi\) is the porosity of rock.  
When the ordinary single-phase solid material is compressed, the compression factor can be defined by the following equation [26]:  
\[c_{s}=\frac{dV_{s}}{V_{s}\cdot d\sigma_{s}} \tag{3}\]  
Here, \(c_{s}\) is the compression coefficient of rock solid matter in MPa\({}^{-1}\), and \(\sigma_{s}\) is the average of the three principal stresses of the solid matter in MPa.  
In the case of elastic deformation, the compression coefficient for solid matter can be calculated by the following equation [27]:  
\[c_{s}=\frac{3(1-2\
u)}{E_{s}} \tag{4}\]  
where \(\
u\) is [PERSON]'s ratio and \(E_{s}\) is the Young's modulus. Li [26] derived the following relationship for compressibility and porosity:  
\[c_{p}=\frac{\phi}{1-\phi}c_{s} \tag{5}\]  
For a rock of the same material, \(c_{s}\) is roughly a constant, so the compression coefficient of the rock increases as the porosity increases. At the same time, the mineral properties affect the compression coefficient, and the compression coefficient of the rock decreases as the stiffness of the mineral increases, which is partly why mudstone is easier to compress than salt rock.  
Figure 6: The compressibility \(\times\) porosity chart from [PERSON] [25].