Numerical modelling of the friction pendulum system incorporating static friction at breakaway

The increasing use of sliding bearings with curved surfaces, like the Friction Pendulum System® (FPS), to implement the base isolation design in constructions, benefits from the improvement of numerical models able to capture their experimental behavior and enhance the predictive capability of nonlinear response history analyses. An effective implementation of the static, or breakaway, friction of sliding bearings in object-oriented software for structural analysis has not yet been achieved, and the use of dynamic friction only is a common practice in design. The formulation proposed in this study aims at filling the gap, by incorporating in an established numerical framework the change in the coefficient of friction occurring at the transition from the sticking, or pre-sliding phase to the dynamic sliding motion. First, a mathematical formulation is developed in order to address the variability of the coefficient of friction based on experimental data that can be retrieved from laboratory tests on FPS bearings. The proposed “BVNC” formulation accounts for variation in the coefficient of friction with the instantaneous change of axial load and velocity, and with the amount of energy dissipated during cyclic motion; eventually, it incorporates as a new feature the static friction developed at the breakaway and at any temporary sticking between the sliding surfaces when velocity is null. The novel formulation is hence coded in the object-oriented finite element software OpenSees by modifying the standard “SingleFPSimple3d” element which reproduces the behavior of the FPS comprising one concave sliding surface and a spherical articulation. The hysteretic force – displacement characteristics of the FPS in the horizontal direction is mathematically modelled using the theory of plasticity, and two distinct yield thresholds with a trigger condition are introduced to account for either static or dynamic friction. Other features of the model are the variation of dynamic friction with axial load and velocity, and its degradation during cyclic motion. The primary assumptions in the development of the friction model and the verification of the new FPS element are validated in a code-to-code comparison with the standard OpenSees element. A case study relevant to a base-isolated reinforced concrete frame demonstrates the improved prediction capability of the new element over its standard counterpart, such as estimating a +40% increase in superstructure drift and column shear force and a +58% increase in isolators displacement during high intensity, Basic Design earthquakes, and up to a +130% increase in internal forces and deformations of the structure under Serviceability Design earthquakes as a consequence of not-engagement of the FPS during small-to-medium magnitude events.