*2.1. Case Study Description*

The building had four residential floors and an attic. The ceilings on the upper floors were made of wooden beams, while, on the first floor, they were made as arched segmental vaults on steel beams. The floors were 3.2 m high. The staircase was 2.5 m wide and 5.3 m long. The length of the landings was 1.6–1.7 m and the length of the flights was 2.6 m, with a width of 1.2 m. The analyzed stair flights were at an angle of 38◦. The stairs were made of steel and masonry, with arched spans between the landings. The rise of the stair arch had a value of *f* = 1/19 *L*. Figure 5 shows the general view of the arched stair structure under consideration.

**Figure 5.** View of the researched masonry staircase.

The measured dimensions of the bricks were 25 × <sup>12</sup> × 6.5 cm3. The brick and mortar compressive strength was estimated with use of the non-destructive, ultrasonic measurements according to the dependencies described in [107]. The dependency of bricks is shown in Equation (1).

$$f\_{c,brick} = 1.4949 \cdot e^{0.002 \cdot UPV} \text{ (MPa)},\tag{1}$$

where *fc*,*brick* (MPa) is the compressive strength of the brick element and UPV (m/s) is the measured ultrasonic pulse velocity. The dependency of lime–cement mortar is presented in Equation (2).

$$f\_{c,motor} = -5.5 + 0.007671 \cdot LIPV \text{ (MPa)},\tag{2}$$

where *fc*,*mortar* (MPa) is the compressive strength of lime–cement mortar. The results of the tests are presented in Table 1.

**Table 1.** Ultrasonic pulse velocity and calculated compressive strength of tested bricks and mortar.


The compressive strength of the bricks varied in a wide range, from 10.4 to 28.4 MPa with a mean value of 17.6 MPa. The compressive strength of lime–cement mortar varied from 2.1 to 5.4 MPa with a mean value of 4.1 MPa. Due to the large discrepancy found between the strength values of the masonry units and mortar, it was decided to carry out laboratory tests using materials with standard properties. In this respect, a brick class of 25 MPa and a mortar class of 5 MPa were assumed.

#### *2.2. TLS Diagnostic on a Real-Life Structure*

Stair geometry measurements and diagnostics were performed using TLS technology, using a stationary scanner Focus M70 (Faro, Lake Mary, FL, USA) with a single measurement accuracy of 0.2 mm. From the measurements, a point cloud in Autodesk Recap (RCP) format was obtained, which was then verified in CAD software (Version2021, San Rafael, Autodesk, CA, USA). RCP format files store spatially indexed point cloud data that can be processed in applications to view, edit and analyze object geometry. The purpose of the measurements was to analyze the geometry of the masonry arch. The aim of the study was to indicate the geometric irregularities, whose technical condition was visually inspected. After removing the plaster in the selected irregularity areas, the condition of masonry and mortar was evaluated.

The TLS measurements allowed us to determine the exact geometry of the stair flight. Figure 6 shows a general view of the obtained TLS measurement map along with a picture of the geometry of the curved staircase of the building.

**Figure 6.** TLS data acquired from existing building: section view of building (**a**) and geometry measurements for analysis (**b**). The dashed line marks the stair flight which was subjected to further laboratory testing.

Alongside TLS measurements, a visual evaluation of the mortar joints in the stair flights as well as of the treads was performed. Numerous damages and cracks were found. The most important was a crack in the joint on the masonry arch presented in Figure 7.

**Figure 7.** Section of the staircase with visible crack of the arch caused by improper renovation and deterioration of masonry joints.

Incorrectly made support changed the distribution of internal forces in the masonry arch, which was the reason for the whole structural diagnosis. Support should have been put in place for the entire surface of the arch in the form of a centering with an appropriate shape to match the actual geometry of each stair flight arch. Figure 8 shows the output of TLS diagnostics for the run fault of the stair flight.

**Figure 8.** TLS data output for the point damage of the stair flight: section view of the stair flight (**a**) and point of damage (**b**).

The weakest points of the analyzed masonry arch structure were the joints between bricks and mortar. On the basis of the research work carried out, it was decided to reinforce the whole structure of flights and landings with a steel structure fixed from the bottom.
