PSI - Issue 78

Laura Ragni et al. / Procedia Structural Integrity 78 (2026) 2094–2101

2097

3. Numerical simulation 3.1. Numerical model

For the base-isolated building, a simplified model with three parallel components is proposed: a Kelvin model (spring with stiffness k 0 and damper with constant c 0 ), a Maxwell model (spring with stiffness k 1 and damper with constant c 1 ) and a friction model with a constant friction force F fr . The Kelvin and Maxwell models simulate the behavior of High Damping Rubber Bearings (HDRBs), while the friction model represents Lead-Filled Sliding Bearings (LFSBs). This setup captures both short-term and long-term viscous effects of HDRBs: • at low displacement rates, the Maxwell model dominates, leading to low global stiffness (approaching k 0 ) and large lost displacement, which is slowly recovered over time; • at high displacement rates, the damper in the Maxwell model reacts strongly (minimizing lost displacements) and the global stiffness increases to approximately k 0 + k 1 (matching the nominal stiffness of the bearings); • at even higher velocities, damping increases, but stiffness remains constant. The main simplification in the model is assuming linear behaviour of HDRBs. However, as shown later, the simulated results closely match experimental data for this application. In the next section, the model parameters for a single HDRB (Fig. 3a) are first derived from type tests. This model is then used to simulate the response of the base-isolated building (Fig. 3b), including the friction forces from sliders.

Fig. 3. Numerical model of the single HDRB (a) and the mase-isolated building (b)

3.2. Model parameters calibration based on type tests of elastomeric devices During the production of bearings, the European standard on anti-seismic devices (EN 15129:2009) as well as the national seismic code (NTC 2018) prescribe to perform type tests in order to verify that bearings proprieties agree with design prescriptions. Three different kinds of test are required: horizontal cyclic characterization (HCC) tests carried out at a frequency of 0.5 Hz and different displacements, a one side ramp (OSR) test carried out at the design displacement with a velocity of 5 mm/s (that is not mandatory and not performed in some cases) and lateral capacity (LC) tests. In the latter minimum and maximum axial loads are imposed to the bearings together with an increasing horizontal displacement up to a maximum value, then the displacement is then held constant for about 4 minutes before decreasing it. With regard to the single bearing model (Fig. 3a) the following hypotheses have been made to compute the parameters of Maxwell and Kelvin elements: ( i ) the velocity of the HCC test (Fig. 4) is such that the lost displacement is zero and ( ii ) the force recorded at the end of the constant displacement path of the LC test (Fig. 5) is representative of the Kelvin element stiffness (i.e. elastic stiffness). Consequently, the nominal stiffness for seismic applications of a single bearing ( k n,is ) coincides with the equivalent stiffness of the HCC test and can be computed as the sum of the stiffness of the Maxwell and Kelvin elements ( k 1,is + k 0,is ), as reported in the following expression: k n,is = G A is / h is = k 1,is + k 0,is (1)