**2.1. Restraint systems analysis**

It follows a description of the three solutions of seismic protection that will be analysed and compared in the next paragraphs.

For every solution, in order to achieve a monolithic behaviour of the deck during the seismic event, the installation of shock transmitters at the Gerber saddle provides to hinder the relative movements of the box girders. Being a dynamic device, the shock transmitters allow slow displacements (thermal change) and represent a stiff restraint against dynamic actions. The new system remains unchanged in the static stage and becomes unique kinematic chain during the seismic stage.

The restraint systems analysed original scheme, fluid viscous dampers (explained in Section 2.1.1), curved surface sliding isolators (commented in Section 2.1.2) and elastomeric isolators (described in Section 2.1.3) and are outlined in **Figure 5**.

When the viscous damper is indicated, the number following the device type represents the force threshold at which the hydraulic system starts laminating the fluid (**Figures 7** and **8**).






**Figure 7.** Bearing and restraint system.


**Figure 8.** Map legend.

The foundations of the piers and of the abutments are modelled with punctual restraints.

It follows a description of the three solutions of seismic protection that will be analysed and

For every solution, in order to achieve a monolithic behaviour of the deck during the seismic event, the installation of shock transmitters at the Gerber saddle provides to hinder the relative movements of the box girders. Being a dynamic device, the shock transmitters allow slow displacements (thermal change) and represent a stiff restraint against dynamic actions. The new system remains unchanged in the static stage and becomes unique kinematic chain during

The restraint systems analysed original scheme, fluid viscous dampers (explained in Section 2.1.1), curved surface sliding isolators (commented in Section 2.1.2) and elastomeric isolators

When the viscous damper is indicated, the number following the device type represents the force threshold at which the hydraulic system starts laminating the fluid (**Figures 7** and **8**).

**2.1. Restraint systems analysis**

compared in the next paragraphs.

**Figure 7.** Bearing and restraint system.

(described in Section 2.1.3) and are outlined in **Figure 5**.

the seismic stage.

134 Structural Bridge Engineering

#### *2.1.1. Hydraulic dissipation devices*

The system consists of a multidirectional‐encapsulated neoprene support coupled with different types of hydraulic viscous devices. They work at a speed range compatible with those of the target seismic event.

When the system reaches the design velocity that corresponds to a force threshold (following the exponential law at Eq. (2)), the piston starts to laminate the silicone fluid and it allows increasing displacements while the force level, transferred to the substructure, is kept constant.

The oleodynamic‐plastic (OP) devices provide a stiff restraint against static forces but dissipate the seismic energy. It means that they can control the force level transferred to the piers up to a design limit (about 100/150 tons).

The oleodynamic‐thermal‐plastic devices (OTP) permit thermal expansions without remark‐ able resistance; instead, during the seismic stage, they are able to dissipate energy above an imposed strength level (work as an OP for dynamic forces).

The OT(P) devices are able to act as an OP (providing stiffness and dissipating energy) for high‐speed displacements, induced by impulsive forces of dynamic (earthquake) and static (wind and braking) source. They behave like an OTP for low‐speed displacements (tempera‐ ture changes) that are allowed. Its benefit is distributing operation forces, such as braking, on a greater number of piers, reducing the forces of the fixed central device of the train.

The constitutive equation force‐velocity, which characterises them, is non‐linear:

$$F = C \operatorname{v}^a \tag{2}$$

where *C* is the damping constant, *v* is the velocity and α is variable from 0.10 to 0.15, according to the device.

The OT (hydraulic‐thermal) devices, finally, provide for a stiff restraint during the seismic event, acting as a fixed device, while allowing low‐speed displacements in the static stage (thermal expansion).


All the parameters, used in the analysis, are specified in **Chart 1** for each device.

**Chart 1.** Features of the elastomeric isolators used in the analysis. *k*H is the horizontal stiffness, *k*V is the vertical stiff‐ ness, *V* is the maximum vertical load at load combinations including the seismic action and *F* is the maximum vertical load at non‐seismic load combination at ULS.

#### *2.1.2. Curved surface sliding isolators*

The curved surface sliders are sliding isolators based on the working principle of the simple pendulum. In a structure isolated by means of this device, the period of oscillation mainly depends on the radius of curvature of the curved sliding surface and it is almost independent from the mass of the structure.

The energy dissipation is provided by the friction, which develops during the sliding, and the re‐centring capacity is provided by the curvature of the sliding surfaces.

These devices are characterised by two concave surface sliders whose radius of curvature impose the period of oscillation and accommodate for horizontal displacements and rotations. A special thermoplastic material coupled with stainless steel is used on both primary and secondary sliding surfaces to govern the friction.

The material, an ultra‐high molecular weight polyethylene, grants an optimal behaviour in terms of load‐bearing capacity, friction coefficient and consequently energy dissipation, durability and stability to hysteretic displacement cycles. It is used without lubrication on the primary sliding surface, while it is dimpled and lubricated on the secondary one.

The above‐mentioned devices feature a maximum vertical load equal to *N*Ed=2200*t* and allow displacements of ± 150mm, in the load combination that includes the seismic action or foresees a horizontal displacement.



**Chart 2.** Features of the viscous dampers used in the analysis.

The oleodynamic‐thermal‐plastic devices (OTP) permit thermal expansions without remark‐ able resistance; instead, during the seismic stage, they are able to dissipate energy above an

The OT(P) devices are able to act as an OP (providing stiffness and dissipating energy) for high‐speed displacements, induced by impulsive forces of dynamic (earthquake) and static (wind and braking) source. They behave like an OTP for low‐speed displacements (tempera‐ ture changes) that are allowed. Its benefit is distributing operation forces, such as braking, on

where *C* is the damping constant, *v* is the velocity and α is variable from 0.10 to 0.15, according

The OT (hydraulic‐thermal) devices, finally, provide for a stiff restraint during the seismic event, acting as a fixed device, while allowing low‐speed displacements in the static stage

**Chart 1.** Features of the elastomeric isolators used in the analysis. *k*H is the horizontal stiffness, *k*V is the vertical stiff‐ ness, *V* is the maximum vertical load at load combinations including the seismic action and *F* is the maximum vertical

The curved surface sliders are sliding isolators based on the working principle of the simple pendulum. In a structure isolated by means of this device, the period of oscillation mainly

· *<sup>a</sup> F Cv* = (2)

a greater number of piers, reducing the forces of the fixed central device of the train.

The constitutive equation force‐velocity, which characterises them, is non‐linear:

All the parameters, used in the analysis, are specified in **Chart 1** for each device.

imposed strength level (work as an OP for dynamic forces).

to the device.

136 Structural Bridge Engineering

(thermal expansion).

load at non‐seismic load combination at ULS.

*2.1.2. Curved surface sliding isolators*

The value of the minimum dynamic friction coefficient matching with the maximum vertical design load *N*Ed of the isolator is equal to 2.5% and varies with the vertical load, acting on the isolator.

The constitutive equation force‐displacement, which characterises them, is bilinear type:

$$F = F\_0 + k\_r \cdot d = \mu \cdot N\_{\text{Sd}} + (N\_{\text{Sd}} / R) \cdot d \tag{3}$$

where μ is the friction coefficient, *N*Sdis the load acting on the isolator (quasipermanent load), *R* is the equivalent radius of curvature, and *d* is the displacement.

All the parameters, characterising the devices, are specified in **Chart 2** since the vertical load on each support is different, being a continuous deck.
