## 2 Experimental Materials and Methods  
### Specimen Preparation  
To investigate the growth behavior of SC-CO\({}_{2}\) induced fractures in hard and soft layered rocks, this research used artificial specimens which had two layers to conduct the SC-CO\({}_{2}\) jet fracturing experiments. As shown in Figure 2, the artificial specimen consisted of artificial sandstone and the casing.  
The artificial sandstone was a cylinder with a diameter of 100 mm and a length of 100 mm. The artificial sandstone had two layers which were made by mixtures consisting of cement, clay minerals, 20-40 mesh natural siliceous and water. As shown in Table 1, two mixtures of different ratios were used to make hard and soft layers, respectively. The lower and upper layers of the artificial stones were continuously poured, to avoid the occurrence of weak structural planes which can affect the fracture propagation. The  
Figure 2: The preparation of specimens. (**a**) A schematic diagram of the cylindrical specimen; (**b**) the completed specimen.  
artificial sandstones were cured over four weeks at a temperature of 25 \({}^{\circ}\)C. Four types of artificial sandstones were made by the mixtures: hard rock, soft rock, hard-soft rock, and soft-hard rock. The mechanical properties of the hard and soft rocks were obtained by the uniaxial compressive strength (UCS) test and direct simple shear (DSS) test listed in Table 2. A hole with a diameter of 6 mm and a length of 50 mm drilled in the center of each artificial sandstone to simulate the perforation. A steel casing plate with a 6 mm diameter hole at center of the casing was stuck to each artificial sandstone by epoxy glue to simulate the wellbore. The thickness and diameter of the casing were 2 mm and 90 mm, respectively, and the thickness of the epoxy resin was 0.5 mm. Two strain gages were stuck to each specimen by super glue, and a layer of polyethylene film was pasted on the surface of the strain gage to prevent external interference. One of the strain gages was 25 mm from the upper surface, and the other was 75 mm from the upper surface. Then, 18 completed specimens were kept in room temperature for one week.  
As shown in Table 3, four groups of specimens were prepared to study the growth behavior of fractures induced by SC-CO\({}_{2}\) jet fracturing in hard and soft layered rocks. Group A was hard rocks, for which the upper and lower layers were hard artificial sandstones; group B was soft rocks, in which the upper and lower layers were soft artificial sandstones; group C was hard-soft rocks, in which the upper layers were hard artificial sandstones, and the lower layers were soft artificial sandstones; group D was soft-hard rocks, in which the upper layers were soft artificial sandstones, and the lower layers were hard artificial sandstones.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Natural Siliceous** & **Cement** & **Clay Minerals** \\ \hline Hard & 56.7\% & 28.3\% & 15\% \\ Soft & 68\% & 17\% & 15\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: The mixtures composition ratio of the hard and soft layers.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Group** & **Upper Layer** & **Lower Layer** & **Specimen NO.** & **Injection Pressure/MPa** \\ \hline \hline \multirow{3}{*}{A} & \multirow{3}{*}{Hard} & \multirow{3}{*}{Hard} & \multirow{3}{*}{A2} & A1 & 35 \\  & & & A2 & 30 \\  & & & A3 & 25 \\  & & & B1 & 25 \\ B & Soft & Soft & B2 & 30 \\  & & & B3 & 35 \\  & & & C1-1 & 25 \\  & & & C1-2 & 25 \\ C & Hard & Soft & C2-1 & 30 \\  & & & C2-2 & 30 \\  & & & C3-1 & 35 \\  & & & C3-2 & 35 \\  & & & D1-1 & 25 \\  & & & D2-1 & 30 \\ D & Soft & Hard