## 3 Flat-Jack Test Methodology  
The flat-jack test is used to assess the normal stress acting on a specific cross-section of a structural member. The procedure involves making a cut perpendicular to the outer surface of the element. If the element is under compression, the internal force causes the edges of the resultant slot to close. A displacement transducer (e.g., a mechanical strain gage) measures the change in distance between pairs of gage points placed at either side of the cut line. The flat jack is then inserted into the slot and connected to a hydraulic pump. The oil pressure inside the flat jack is gradually increased until the initial pre-cut distance between the gage points is restored. Finally, the stress acting perpendicularly to the cut section is determined based on the internal pressure of the flat jack measured using a manometer and corrected for two calibration factors introduced to account for the stiffness of the flat jack (\(K_{m}\)) and the effective contact area (\(K_{a}\)) between the flat jack and the inner surface of the slot. In more detail, the test procedure is summarized in the following steps, illustrated in Figure 2:  
* Step 1: Preparation of the test area. The cut line is marked on the surface of the element to be investigated, and metal gage points are aligned and bonded above and below the marked line. For masonry, both standards [29; 30] recommend a distance between each pair of gage points between 0.3 and 0.6 times the primary dimension \"L\" of the flat jack (Figure 3). Each row of gage points thus formed shall be equally spaced above and below the cut line. * Step 2: Baseline measurements (\"zero readings\"). Once the adhesive has cured, initial baseline measurements of the distance between each pair of gage points are taken using a mechanical extensometer. * Step 3: Execution of the cut. A precise cut is made along the marked line using a circular saw. The plan geometry of the slot shall be similar to that of the flat jack being used. Slots for circular and semi-rectangular flat jacks are cut using circular saws of sufficient radius to provide the depth required. Slots for rectangular flat jacks may be formed by drilling overlapping holes (stitch drilling) and subsequently using a drill to remove the material and produce a slot of desired dimensions with smooth upper and lower surfaces. Figure 1: Flat-jack test performed in situ on a post-tensioned T-beam, adapted from reference [29]; (**a**) cross-section of the T-beam illustrating the position of the flat jack; (**b**) bottom view of the beam, showing the cut slot for the flat jack and the gage points across the slot; and (**c**) a picture of the test, with the flat jack inserted in the slot, where the oil pipe for pressurizing the flat jack is also visible on its left. * Step 4: Post-cut measurements (\"post-cut readings\"). Assuming that the investigated element is under compression, after the cut the edges of the slot will move closer together. A second set of measurements is taken to record the change in distance between each pair of gage points. * Step 5: Insertion of the flat jack. The flat jack is carefully inserted and packed tightly into the cut slot. * Step 6: Pre-seating of the flat jack. To ensure proper positioning, an initial pressure of half the estimated maximum pressure is applied and then released. * Step 7: Gradual pressurization and displacement monitoring. The pressure inside the flat-jack device is increased by steps, while the change in distance between each pair of gage points is measured. * Step 8: Achievement of the target distance. The test is stopped when the distance between the pairs of gage points is returned (within a certain tolerance) to the baseline (pre-cut) value. The pressure in the flat jack is recorded. * Step 9: Flat-jack removal and restoration. The flat jack is depressurized and removed from the slot (tools may be required to facilitate the extraction). Finally, the slot is filled with a high strength mortar to restore the integrity.