# Seismic Assessment and Strengthening of a Load-Bearing Masonry Structure Considering SSI Effects
## 3 Materials and Numerical Modeling
### Mechanical Properties  
The mechanical properties of all structural elements were calculated according to [1; 23; 26; 27; 29; 30; 31; 32; 33; 34; 35; 36; 37] and they are presented in Tables 2-5.  
alter their dynamic behavior. According to [40], taking SSI into account is particularly important for structures founded on soils with high groundwater levels and high plasticity (PI > 40), typically corresponding to soil categories C or D, for which reduction factors to the shear wave velocity (Vs) and the shear modulus (G) of the soil are recommended.  
For the purposes of the present study, the soil-structure interaction effect was investigated by using formulas [41], which model the foundation-soil system as a discrete system consisting of frequency independent springs, dashpots and masses. More specifically, for each model examined in this study, an additional case was analyzed. In these cases, the fixed supports (as defined in the initial models) (M1 fix, M2 fix) were replaced by link elements with specific mechanical properties (M1 ssi, M2 ssi).  
To apply the aforementioned formulas, the length of the foundation strips was calculated and then divided by the number of masonry joints at the foundation level. The width of the foundation strips is 1.05 m, the calculated length is 0.27 m, so \(\alpha\) = 0.27 m. The shear wave velocity was taken as 150 m/s, the soil density as \(\rho\) = 1900 kg/m\({}^{3}\)[39], and the Poisson's ratio as \(\
u\) = 0.3. Based on these values, the shear modulus G was calculated as 42,750.00 KPa. Applying a reduction coefficient of 0.37 [40], the reduced shear modulus becomes 15,817.50 KPa, corresponding to a reduced shear wave velocity of 91.24 m/s. The values of static stiffness (K) and damping (C) of each link element are presented in Table 6. The soil was assumed to be massless.  
To ascertain the fundamental frequency of the site and evaluate possible resonance effects with the structure of the Archaeological Museum of Lemnos, calculations were conducted utilizing the established soil parameters. With a shear wave velocity of Vs = 150 m/s and presuming a typical soil layer depth of H = 30 m for Category D soils, the fundamental frequency of the soil deposit was computed using the quarter-wavelength approximation: f\({}_{0}\) = Vs/(4H) = 150/(4 \(\times\) 30) = 1.25 Hz. The shear modulus G = 42,750.00 KPa was obtained from the equation G = \(\rho\)Vs\({}^{2}\), where \(\rho\) = 1900 kg/m\({}^{3}\) and Vs = 150 m/s, confirming the relatively soft characteristics of the soil typical of Category D classification. The computed site frequency of 1.25 Hz is within the typical range for historic masonry buildings (0.8-2.0 Hz), indicating potential resonance conditions that could significantly enhance the seismic response. This frequency analysis lays the physical groundwork for understanding why the SSI effects led to increased peak tensile stress and interstorey drift ratios, as the structure-soil system likely underwent dynamic amplification when the building's fundamental frequency neared the site frequency, especially following various strengthening interventions that may have modified the original structural frequency.