**eng. Ștefan Marin, eng. Dan Iancu
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**Summary**

*Introduction*

Seismic isolators are devices with a controlled manufacturing process that are inserted into structural systems to reduce seismic response and increase seismic performance.

When designing structural systeme with base isolation, the variability of the response parameters of the seismic isolators must be considerede in order to obtain the maximum values of the response parameters of the structure.

In the following, the aspects related to the variation of the design parameters of friction pendulum isolators will be presented.

Although the manufacturing process of friction isolators is controlled, for design manufacturers usually provide a nominal (target) value and the extreme values of the confidence range, minimum and maximum. According to SR EN 15129, the variability of the response parameters of the isolators must fall within the range of ±20%.

The friction coefficient of the sliding surface is mainly influenced by the temperature of the moving interface, the moving speed and the pressure on the moving surface.

For a quasi-constant pressure level on the sliding surface the range of variability provided by the manufacturer covers the influence of temperature and speed on the sliding surface.

For applications where a significant variation of the axial force occurs, the variation of the coefficient of friction as a function of the pressure on the sliding surface can only be captured by a μ-N variation curve.

In the design of a base isolated structure with a significant variation of the vertical reaction arises the difficulty of introducing this variability into the design model of the base isolated structure.

**Keywords: base isolation, friction isolators, confidence range**

*References for the dependence of friction with pressure*

Considering that each manufacturer of friction seismic isolators has its own recipe and process of applying the material on the sliding surface, the discrete range of variation or the relationship that defines the dependence of the coefficient of friction on the axial load must be provided by the chosen isolator manufacturer after their predimensioning stage.

The graph below shows the discrete range of variation of the friction coefficient depending on the axial force at which the insulator is loaded. The extreme curves μ_{min} and μ_{max} and the nominal curve for the variation of the coefficient of friction provided by a manufacturer of friction pendulum isolators were plotted in the graph.

The above curves are generated by MAURER and consider an axial force in the group of long-term loads of Nsd=14500kN.

Another manufacturer of seismic devices Freyssinet defines the dependence of the coefficient of friction on the axial force by a relation according to the ratio of the axial force in the long-duration group Nsd to the effective axial force.

Example of friction variation curves with pressure, Freyssinet

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*Modeling of friction pendulum isolators*

In the current modeling of friction pendulum isolators commercial structural software allow modeling with combined spring elements with non-linear variation (curvature dependent), damping and the possibility of decoupling (GAP elements). This type of modeling only allows the consideration of a constant friction coefficient.

In the design process after predimensioning the friction pendulum isolator based on a constant value target friction coefficient it is important for applications with significant vertical force variations in the isolators that the final design of the structure and base isolation system considers the dependence of friction on pressure.

A consistent modeling of the dependence of friction on pressure in a calculation model must be able to correlate the value of the coefficient of friction with the effective axial force at time t for each individual seismic isolator.

From the above representations it can be seen that the modeling of the constant friction coefficient leads to the non-covering evaluation of the response parameters of the isolators and implicitly of the underlying insulated structure.

CSI Analysis Reference Manual, pg. 292

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*The proposed modeling approach*

The aim of the modeling approach was to start from the modeling options available in common (commercial) calculation programs where the friction coefficient is considered constant and to introduce a scaling or filtering method of the axial force to obtain at any time step in the isolator an axial force scaled for the constant friction coefficient, to obtain the μ-N sets from the variation curve.

N(t) the axial force in the isolator, time-varying in amplitude due to the overturning effect of the superstructure, up to the value 0 (uplift).

The principle of the proposed method consists in the introduction of 2 additional “fictitious” non-linear vertical springs, in parallel with the vertical spring that defines the seismic isolator. The role of these two vertical springs is to relieve the isolator of the vertical load, such that the product of the load and the coefficient of friction follows the actual variation curve. Two springs were kept for the purpose of local equilibrium.