## 4 Experimental Program
### Flat-Jack Calibration  
Before conducting the tests, the flat jacks were calibrated following the guidance of ASTM ASTM (1986) to determine the conversion factor \(K_{m}\). The calibration setup is illustrated in Figure 7 and included the flat jack, the hydraulic pump, and the manometer that were used in the laboratory tests. \begin{table}
\begin{tabular}{c c c c c} \hline
**Test** & **Flat Jack** & **Cut Slot Area** & **Flat-Jack Area** & \(K_{a}\) \\ \hline  & & **[cm\({}^{2}\)]** & **[cm\({}^{2}\)]** & **[-]** \\ \hline M1A & 25 cm & 95.19 & 85.94 & 0.90 \\ M1B & 33 cm & 290.12 & 290.12 & 1.00 \\ M2A & 25 cm & 85.94 & 85.94 & 1.00 \\ M3A & 25 cm & 88.84 & 85.94 & 0.97 \\ M4A & 25 cm & 88.00 & 85.94 & 0.98 \\ M4B & 33 cm & 304.72 & 290.12 & 0.95 \\ \hline \end{tabular}
\end{table} 
Table 2: Correction factors \(K_{a}\) for flat-jack tests. The compression machine used for the calibration included two rigid steel plates, with plan dimensions of 46 \(\times\) 30 cm, covering the devices being calibrated. To ensure proper alignment with the load axis, the coordinates of the centroid of the two flat jacks were calculated using the AutoCAD 2023 software program [33] (Figure 8). Each flat jack was then positioned on the lower plate of the compression machine so that the maximum offset of the centroid with respect to the load axis was less than 6 mm of the machine's load axis. Two load cells with different capacities were used depending on the type of flat jack. The load cell used for the 25 cm flat jack had a capacity of 75 kN, while for the 33 cm flat jack, a 500 kN load cell was employed. Steel shims were inserted between the two rigid plates to simulate different cut slot openings. Spacers measuring 4 mm and 5 mm in thickness were used, corresponding to the actual cut widths measured after the cutting. The flat jack was positioned inside the machine and connected with hoses to the manually operated hydraulic pump. Calibration was performed as follows:  
1. The internal pressure of the flat jack was incrementally increased using the hydraulic pump until the desired pressure level was reached, as indicated on the manometer. The pressure steps began at 5 Bar, followed by 10 Bar, and then increased in 10 Bar increments up to 90 Bar. 2. At each step the pressure was maintained constant for approximately 30 s, and the corresponding force was recorded by the load cell. Figure 8: (a) Centroid coordinates of flat jack A. (b) Centroid coordinates of flat jack B.  
Figure 7: On the right, the compression machine used for the flat-jack calibration, and on the left, the manual hydraulic pump with its manometer and the control panel to record the readings from the load cell. Once the final pressure step was reached and the corresponding force was recorded, the flat jack was fully depressurized. The whole procedure was repeated for both flat jacks and both gap widths (4 mm and 5 mm), performing each time three cycles of pressurization. For each instrument, the pressure readings at the third cycle were similar to the ones at the second cycle but noticeably different from those at the first cycle, when the flat jack had not yet fully settled. Then, the conversion factor \(K_{m}\) was derived as recommended in [30] based on the readings taken at the third cycle:  
\[K_{m}=P_{machine}/P_{flatjack}, \tag{2}\]  
where  
* \(P_{machine}\) [MPa] is the contact pressure that the flat jack applies to the plates of the machine. It is calculated dividing the load recorded from the load cell by the nominal flat-jack area. * \(P_{flatjack}\) [MPa] is pressure inside the flat jack read by the manometer. Figure 9 illustrates the results of the calibration procedure, reporting the conversion factor \(K_{m}\) as a function of the pressure inside the flat jack read on the manometer for both devices. The plots reveal a nonlinear behavior common to both flat jacks, with lower \(K_{m}\) values at low pressure. As the flat-jack pressure increased, \(K_{m}\) also increased and became proportional to \(P_{flatjack}\) above 50 Bar.