# Base Isolation Compared to Capacity Design for Long Corner Periods and Pulse-Type Seismic Records
## 2 Materials and Methods
### Curved Surface Slider as Base Isolator  
Given the particularities of Vrancea seismic source (see also Section 2.2) CSS-Curved Surface Sliders were chosen for the isolation system. The two most important advantages of these sliders are (1) the reduction of the isolator displacement (due to the double curvature) and (2) the high damping of the earthquake-induced movement (due to friction along the curved sliding surface). In this way, the isolator dimensions are reduced to a minimum and reduced dimensions of the isolator supporting structural elements (for example the underground columns) are achieved, making the solution more cost-efficient.  
Base isolation devices need to be designed for the design earthquake (DBE) and their sliding capacity must be checked under maximum expected earthquake (MCE) conditions [35].  
The Romanian Standard for seismic design [18] indicates for the seismic area of Bucharest a design earthquake with return period of 225 years and a maximum expected design ground acceleration of 0.3 g. The characteristics of the isolator devices designed for DBE are shown in Figure 5.  
In Figures 5 and 6, the following terms are used: \(\mu_{\text{opt}}\)--optimum friction, \(d_{\text{bd}}\)--isolator displacement, \(\zeta_{\text{eff}}\)--effective damping, T\({}_{\text{eff}}\)--effective isolation period, T\({}_{\text{iso}}\)--isolation period, R\({}_{\text{eff}}\)--isolator curvature radius, E\({}_{\text{S}}\)--elastic energy reversibly stored in the isolation system, E\({}_{\text{n}}\)--histectic dissipated energy, k\({}_{\text{rest}}\)--restoring stiffness force, N\({}_{\text{S}}\)--gravity load on isolator.  
In the PERFORM 3D software the sliding isolation devices were modelled considering the horizontal force-displacement relations, the restoring stiffness, the displacement capacity and the initial stiffness (until the friction is overrun). The restoring stiffness and displacement capacity result from the isolation device design. The initial stiffness was chosen 100 times larger than the restoring stiffness (to limit the initial displacement, until friction is overrun). As supplementary details, the following sliding isolation device characteristics were considered: the friction coefficient, the radius of the sliding surface and the stiffness for axial compression loads. An earthquake with return period of 475 years and maximum expected horizontal ground acceleration of 0.375 g was considered as the MCE event ([32; 36]). The characteristics of the isolator devices designed for the MCE are shown in Figure 6.  
Because of the building layout (closely spaced columns in some parts of the building) and in order to catch up with the elevator shaft, isolation devices were placed beneath the underground level, on a foundation mat. They directly support a foundation beam girder. This was designed to reduce material consumption for the foundation system.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Mode** & **1** & **2** & **3** & **4** & **5** & **6** \\
**Number** & & & & & & & \\ \hline frequency & & & & & & \\ [Hz] & 1.75 & 2.03 & 2.30 & 5.56 & 7.04 & 8.06 \\ mass ratio & 66\% \(\rightarrow\) & 65\% \(\uparrow\) & 15\% \(\rightarrow\) & 9\%\(\rightarrow\) & 10\%\(\uparrow\) & 6\% \(\uparrow\) \\
[\%] & translation & translation & translation & translation & translation & translation & translation \\
51\% torsion & 2\% torsion & 4\% torsion & 7\% torsion \\ \hline \hline \end{tabular}
\end{table}
Table 2: Eigen modes of over ground structure, ETABS software.  
Figure 5: Design CSS: (**a**) optimization; (**b**) displacement capacity.  
Figure 6: Behaviour CSS for MCE: (**a**) response spectrum; (**b**) displacement capacity.  
Figure 7 shows indicative double curved surface slider dimensions for the analysed structure. Even in large corner period areas such as Bucharest, the double sliding path given by the upper and lower slider curvature provides feasible slider dimensions.