# Advanced Hysteretic Model of a Prototype Seismic Isolation System Made of Polymeric Bearings
## 6 Conclusions  
The paper reports the results of the comprehensive investigation designed to verify the effectiveness of an advanced mathematical model in simulating complex hysteretic behaviour of a prototype base isolation system made of PBs in numerical analysis. High effectiveness of PBs in reducing structural vibrations due to seismic excitations has already been experimentally confirmed during previously conducted shaking table investigation [28]. In the present paper, an advanced hysteretic model was developed to capture mechanical behaviour of PBs in numerical analysis. The effectiveness of the mathematical model was verified by comparing the previously obtained shaking table investigation data (i.e., seismic response of a single-storey and two-storey structure models under various ground motions) with the results of the detailed lumped-parameter analysis. The results obtained from the investigation explicitly confirmed that the proposed mathematical model can be successfully adopted to accurately capture complex mechanical behaviour of PBs in numerical studies. They show that the reduction levels in peak lateral accelerations between numerical \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**Numerically Computed Peak Lateral**} & & \\  & \multicolumn{2}{c}{**Acceleration for the Two-Storey**} & & **Reduction Based** & **Reduction Based on** \\ \cline{2-5}
**Dynamic Excitation** & \multicolumn{2}{c}{**Structure Model (m/s\({}^{2}\))**} & & **on Numerical** & **Shaking Table** \\ \cline{2-5}  & \multicolumn{2}{c}{**Fixed-Base**} & \multicolumn{2}{c}{**Base-Isolated**} & **Analysis (\%)** & **Investigation (\%)**[28] \\ \cline{2-5}
**1940 El Centro earthquake** & & & & \\ NS component, original record & 5.77 & 3.89 & 32.58 & 33.3 \\ with PGA = 3.070 m/s\({}^{2}\) & & & & \\ \hline
**1971 San Fernando earthquake** & & & & \\ Pacomia Dam station, N74\({}^{\circ}\)E & & & & \\ component, scaled record with & 8.45 & 3.77 & 55.38 & 56.8 \\ PGA = 5.688 m/s\({}^{2}\) & & & & \\ \hline
**1989 Loma Prieta earthquake** & & & & \\ Corralitos station, NS & 5.54 & 4.00 & 27.80 & 28.1 \\ PGA = 3.158 m/s\({}^{2}\) & & & & \\ \hline
**194 Northridge earthquake** & & & & \\ Santa Monica station, EW & & & & \\ component, scaled record with & 7.85 & 5.10 & 35.03 & 33.1 \\ PGA = 4.332 m/s\({}^{2}\) & & & & \\ \hline
2002 Polkowice mining tremor & & & & \\ NS component, original record & 2.67 & 2.40 & 10.11 & 12.4 \\ with PGA = 1.634 m/s\({}^{2}\) & & & & \\ \hline \hline \end{tabular} Where: PGA: Peak Ground Acceleration, NS: North-South, EW: East-West.  
\end{table} 
Table 4: Results of the seismic tests for the two-storey structure model. and experimental results are very similar for all ground motions considered in the study. Moreover, relatively low normalized mean square errors were obtained when the whole time-acceleration numerical and experimental records were compared. It has to be also added that the results of the study indicated that the accuracy of the numerical analysis somewhat decreases as the number of DOFs increases. The calibration procedure presented in the current investigation (performed by curve-fitting the general form of the developed mathematical model into the experimentally obtained hysteresis loops) was conducted for the prototype seismic isolation system made of PBs. Nevertheless, the preliminary experimental results obtained from the full-scale PBs, indicate that very similar shape of hysteresis loops can be observed. Therefore, the general form of the proposed mathematical model is expected to be also suitable for different PBs, regardless of their dimensions or scale factors. However, curve-fitting procedure has to be performed to evaluate a new set of function parameters for each specific PB. Further development of the seismic isolation system made of full-scale PBs is to be performed. More studies are necessary to be conducted in order to fully verify the effectives of full-scale multi-dimensional PBs as a base isolation system for real structures.