Since the beginning of seismic engineering it has been recognized that the damage potential of an earthquake is due essentially to the unfortunate correspondence between the fundamental periods of vibration of the majority of structures and the frequency content of the seismic input. It is also well known that despite the correspondence of dynamic characteristics of structures and earthquakes, many structures are able to find ways to survive by escaping the frequency range where the earthquake has greatest power, as a result of the period elongation due to accumulated damage.
A second fundamental concept in earthquake-resistant design of structures is evident from an examination of the equation of motion of a linear system: the higher the viscous damping, the lower the forces to be resisted by the structure. Viscous damping is actually a way to dissipate energy, which can also be dissipated through hysteresis, friction, and in general any inelastic response. For a numerical simulation of the seismic response, it has often been found convenient to represent the effects of any kind of inelastic behavior by means of an equivalent viscous damping, creating an equivalent model (or substitute structure).
It is clear from the discussion above that the possibility of artificially increasing both the period of vibration and the energy dissipation capacity of a structure has to be regarded as a very attractive way of improving its seismic resistance. This objective can be pursued as a specific design intention, taking advantage of natural characteristics of the soil-foundation-structure system or making use of specific artificial elements designed to isolate part of the structure from the full intensity of the seismic input and to dissipate a large amount of energy. These elements are often called isolators, dampers, or isolation/dissipation (I/D) devices, in most cases overstating the true case or neglecting important aspects of their response; all these terms will be used
alternatively in the following.
The concepts of isolation and dissipation are particularly interesting for bridges, because of a series of potential advantages related to their specific structural characteristics. In most cases bridges are strategic structures that require a higher degree of protection to ensure their functionality after a seismic event. It can therefore be convenient to concentrate the damage potential into a few mechanical elements that may be easily checked and replaced, if need be. In addition, most of the mass of a bridge is concentrated at the deck level, and decks are usually designed to remain elastic under seismic action. A common structural configuration (particularly in Europe) is made by a continuous deck supported on bearings at the tops of piers.
In this case the bearings themselves can be designed as I/D devices, selecting their stiffness, yield strength, and ultimate elongation capacity as a function of the desired protection and of the seismic intensity expected. This option is particularly common in the case of seismic upgrading of existing structures. Since bridges are usually simple structures from the point of view of the expected structural response, it is easier to conceive an appropriate correction of the stiffness distribution than with more complex structures. I/D devices can therefore be used to correct or regularize the expected response, adding flexibility to stiffer piers, thus avoiding possible undesirable concentration of ductility demand. Also, bridges often have long natural periods, particularly if some nonlinear response is accepted and considered. Large displacements are then already expected and accepted. The addition of IlD devices may thus have little effect on the maximum displacements, nonetheless assuring a higher level of protection to selected structural elements and larger energy dissipation capacity.
Isolation and Dissipation Devices
An isolation system should be able to support a structure while providing additional horizontal flexibility and energy dissipation. The three functions could be concentrated into a single device or could be provided by means of different components; consider, for example, a traditional bridge whose continuous deck lies on polytetraftuoroethylene (PTFE) supports to allow thermal deformations: Its displacements could be restrained by means of hydraulic or hysteretic dampers, which will provide additional energy dissipation (i.e., equivalent damping).
A few parameters have to be considered carefully in the choice of an isolation system, in addition to its general ability of shifting the vibration period and adding damping to the structure, such as:
(a) Laminated-Rubber Bearings
A cylindrical or rectangular block of rubber constitutes the simplest isolator for a bridge superstructure but presents a number of inconveniences, essentially related to its high deformability under vertical loads. The insertion of a number of horizontal steel plates, as with elastomeric bearing pads, solves most problems (see Fig. 1) by increasing the vertical stiffness and improving the stability of the behavior under horizontal load. This kind of bearing shows a substantially linear response, governed essentially by the properties of the rubber. It is therefore unusual to utilize it without some other element able to provide increased damping and stability under non seismic loads, except where the rubber exhibits high natural inherent damping.
The shape, plan, and number of bearings are governed by the vertical load to be transmitted: If the maximum horizontal displacement has been assumed, the strength of the bearings is proportional to the bonded area and inversely proportional to the rubber layer thickness, which in turns governs the vertical and torsional stiffness. The total rubber thickness (i.e., the number of layers) influences essentially the maximum allowable lateral displacement and the period of vibration.
b. Lead-Rubber Bearings
The laminated-rubber bearings described in the preceding section present several convenient features, with fundamental drawbacks related to the negligible increase in damping and the high deformability for low static loads. With the insertion of a lead plug (Fig. 2), which provides energy dissipation for seismic response and stiffness for static loads, a single compact device is obtained, able to satisfy most of the requirements for a good isolation system. For these reasons, lead-rubber bearings have been used extensively in practical application to bridge structures.
The reasons why lead is an appropriate material are related to its mechanical properties, which allow a good combination with the characteristics of laminated bearings: low yield shear strength [about 10 MPa (1450 psi)), sufficiently high initial shear stiffness (G approximately equal to 130 MPa (18.8 ksi)], behavior essentially elastic-plastic and good fatigue properties for plastic cycles. Considering the characteristics of rubber it is easy to check that for a lead plug with diameter equal to one-fourth of the diameter of a circular bearing, the initial horizontal stiffness is increased by about 10 times, with obvious advantages under wind and braking loads. The lead responds essentially with elastic-perfectly plastic loops. After yielding, the stiffness is therefore equal to the stiffness of the rubber bearing alone. The global hysteresis loops are therefore almost bilinear, as shown in Fig. 3.
An isolation system should be able to support a structure while providing additional horizontal flexibility and energy dissipation. The three functions could be concentrated into a single device or could be provided by means of different components; consider, for example, a traditional bridge whose continuous deck lies on polytetraftuoroethylene (PTFE) supports to allow thermal deformations: Its displacements could be restrained by means of hydraulic or hysteretic dampers, which will provide additional energy dissipation (i.e., equivalent damping).
A few parameters have to be considered carefully in the choice of an isolation system, in addition to its general ability of shifting the vibration period and adding damping to the structure, such as:
- Deformability under frequent quasistatic load (i.e., initial stiffness)
- Yielding force and displacement
- Ultimate displacement and postultimate behaviour
- Capacity for self-centering after deformation (i.e., restoring force)
- Vertical stiffness
(a) Laminated-Rubber Bearings
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| Figure :1 Laminated-rubber bearing |
The shape, plan, and number of bearings are governed by the vertical load to be transmitted: If the maximum horizontal displacement has been assumed, the strength of the bearings is proportional to the bonded area and inversely proportional to the rubber layer thickness, which in turns governs the vertical and torsional stiffness. The total rubber thickness (i.e., the number of layers) influences essentially the maximum allowable lateral displacement and the period of vibration.
b. Lead-Rubber Bearings
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| Figure :2 Lead-Rubber Bearings |
The reasons why lead is an appropriate material are related to its mechanical properties, which allow a good combination with the characteristics of laminated bearings: low yield shear strength [about 10 MPa (1450 psi)), sufficiently high initial shear stiffness (G approximately equal to 130 MPa (18.8 ksi)], behavior essentially elastic-plastic and good fatigue properties for plastic cycles. Considering the characteristics of rubber it is easy to check that for a lead plug with diameter equal to one-fourth of the diameter of a circular bearing, the initial horizontal stiffness is increased by about 10 times, with obvious advantages under wind and braking loads. The lead responds essentially with elastic-perfectly plastic loops. After yielding, the stiffness is therefore equal to the stiffness of the rubber bearing alone. The global hysteresis loops are therefore almost bilinear, as shown in Fig. 3.
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| Figure :3 Idealized hysteretic loop for a lead-rubber bearing with a lead plug contributing to one-half of the total strength and assuring an initial stiffness equal to 10 times the stiffness of the rubber bearing alone [rubber diameter 650 mm (25.6 in.), lead plug diameter 170 mm (6.7 in.), vertical compression 3150 kN (709 kips), horizontal force frequency 0.9 Hz) |