**4. Conclusion**

The following diagrams contain the hysteretic energy dissipation processes of the following two main opposing mechanisms of the earthquake (devices and piers): the devices in terms of force‐displacement (there is dissipation only in case of dampers and sliders) and the material of the piers, relating to the base section, in terms of moment‐curvature. The area underlying

**Figure 16.** Comparison of energy dissipation (restraint device and section at the base of the pier n.1 – earthquake ULS

The following chart (**Figure 17**) summarises the endeavour performed by the piers during the duration of the earthquake: the same is obtained as the sum of the products of forces at the base of the pier and the displacement at the top of the same pier for each moment of the seismic event. In particular, it is clear how the piers are implicated in the total dissipation process of the seismic energy, partly carried out also by the devices in terms of displacement. Moreover, it can be deduced how the solution with the sliders allows transferring only a reduced portion

**Figure 17.** Bar charts representing energy dissipation in the earthquake expressed by the piers.

the curves is an indicator of the dissipated energy.

of Collapse).

144 Structural Bridge Engineering

of energy to the piers.

The analysis focused on three different retrofit solutions of an existing viaduct, examining the technical aspects relating to the design of dissipation and isolation systems. When it is necessary to operate on existing structures, a special attention and carefully conceived solutions are mandatory. Regarding the actual design of the viaduct in question, the restraints are related to the impossibility of stopping traffic and to intervening by reinforcing the existing piers, respecting limitations imposed by the client regarding safety conditions during the implementation of the works.

## **4.1. General considerations**

All the solutions proposed have been designed and calibrated in order to respect the require‐ ment of not using the plastic reserve of the piers, to contrast the forces induced by the system. The refining has related to the modulation of the operative velocity of the viscous devices, the definition of the curvature of the sliding isolators and the level of the stiffness of the rubber of the elastomeric isolators (as reported in **Charts 1**–**3**). The chart, in **Figure 10**, represents the comparison between the stressing actions and the yield limit of the substructures.
