# Seismic Assessment and Strengthening of a Load-Bearing Masonry Structure Considering SSI Effects
## 3 Materials and Numerical Modeling  
### FE Models  
The structural composition of the Archaeological Museum of Lemnos comprises a complex system that incorporates both traditional materials and later reinforced concrete additions. Each floor level exhibits different masonry types and construction techniques, which were carefully taken into account in the development of the numerical models. The ground floor is constructed with three-leaf rubble masonry, while two-leaf masonry is used for the interior walls. On the first floor, the exterior walls are also constructed with two-leaf masonry, whereas the interior partitions are made of clay brick masonry. The second floor features a dual construction system: two-leaf masonry integrated with a traditional embedded timber frame system (friggia). Although structurally significant, this system was excluded from direct modelling due to its complexity and the variability in the performance of timber elements, which depends on factors such as age and the quality of joinery. Timber components were, however, included in the model to represent floor joists, ties, and wall plates. Subsequent intervention phases introduced reinforced concrete (RC) elements into the structure, including a floor slab with beams, RC bond beams, and IPE steel beams supporting the second-storey floor. The numerical modeling and structural analysis were performed using SAP2000 [28]. For modeling purposes, the following material and section typologies were identified and assigned geometrical and mechanical properties:  
* Three-leaf rubble masonry (ground floor exterior walls). * Two-leaf rubble masonry (ground floor interior walls and first-floor exterior walls). \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Model 1** & **Model 2** \\ \hline
**Three-leaf rubble masonry** & \multirow{2}{*}{Grout injections} & \multirow{2}{*}{Repointing works} \\ (ground floor) & & \\ \hline
**Two-leaf rubble masonry** & & \\ (1 st and 2 nd floors) & & \\ \hline
**1 st level’s floor** & Double layered timber flooring & 15 cm thick reinforced concrete slab supported \\  & — timber joists & by 35 cm wide horizontal RC beams \\ \hline
**2 nd level’s floor** & Double layered timber flooring & \\  & — timber joists & Triple layered timber flooring—timber joists \\ \hline
**Openings** & - & Demolition of exterior walls to accommodate a \\  & & lift for people with disabilities \\ \hline
**Roof beams** & Wooden tie beams & Reinforced concrete bond beam (senaz) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Repair Methods. * Two-leaf rubble masonry with timber frames (second-floor exterior walls, modeled with adjusted unit weight to reflect embedded timber content). * Clay brick masonry (ground floor and first-floor interior walls). * Steel beams (IPE). * Timber elements (tie beams, floor joists, and roof wall plates). * Reinforced concrete elements (slab with beams, bond beam). Two structural models were simulated to evaluate the seismic behavior of the building (Figure 8):  
Figure 8: FE Models 1 and 2: M1: Ground floor with numbered building elevations (**a**), first floor (**b**) and second floor (**c**); M2: Ground floor (**d**), first floor (**e**) and second floor (**f**). The first model (Model 1 or M1) represents the building with its original structure (wooden floors), assuming that the load-bearing masonry has been strengthened through grout injection. Although constructed at a later phase, the first-floor interior walls are modeled as clay brick masonry, to support the overlying timber joists. The second model (Model 2 or M2) represents the current state of the building (fifth construction phase). In this case, a 20% increase in masonry strength is applied [29] to account for improvements due to repointing works. In both models, masonry is treated as a homogeneous, isotropic material that combines the properties of its constituent materials (stone and mortar).