## Acknowledgments

The authors wish to thank to the Department of Geotechnical Engineering and Geosciences and the Department of Construction Engineering at Technical University of Catalonia for their help and support during the doctorate years of Mr. Galo Valdebenito. This work is inspired in the basic result of that investigation. Likewise, thank to the Faculty of Engineering Sciences and the Department of Research and Development (DID) at Universidad Austral de Chile for their help and support in this publication.

## Preface

Earthquakes can be really destructive. There is no doubt. Recent seismic events have demonstrated the important effects on structures, and especially on bridges. In this sense, cable-stayed bridges are not an exception, although their seismic performance during recent events has been satisfactory. Their inherent condition as part of life-lines makes the seismic design and retrofitting of such structures be seriously considered.

Traditionally, seismic protection strategies have been based on provide enough strength and ductility. In the case of buildings or bridges with adequate supports and degrees of redundancy, that approach can be satisfactory, however, in the case of structures with few degrees of redundancy, or questionable ductility, that scheme could be inadequate, and worse, dangerous, as usually happens with cable-stayed bridges. All traditional modern strategies to design seismic structures are focused on the adequate comprehension of the mechanisms involved, in which ductility can be provided by some elements specially designed for these purposes. In these sense, strategies such as performed-based design or displacement-based design consider that well-designed structures need to dissipate enough energy by hysteresis in order to obtain economic and safe structures.

The incorporation of additional energy dissipation and isolation devices, by means of passive, active, semi-active and hybrid strategies, constitutes without doubt efficient schemes to protect structures controlling or avoiding damage, in which the energy dissipation is guaranteed through the action of external elements specially designed for those purposes. By this way, now it is possible to provide enough strength and energy dissipation capacity at the same time, avoiding damage on important structural elements, with the subsequent guaranty of the functionality, very important on life-lines, even during strong ground motions.

The present work constitutes an approach to the seismic protection of cable-stayed bridges including the incorporation of fluid viscous dampers as additional energy dissipation devices. The idea of the authors is to provide an up-to-date vision of the problem taking into account that long-period structures such as those proposed here, need to be adequately protected against strong motions, and considering that, because of their importance, an elastic behaviour is desirable. Chapter 1 describes the object to study in general terms. Chapter 2 constitutes a state-of-the-art review regarding the seismic behaviour and performance of fluid viscous dampers as external energy dissipation devices. The mechanical behaviour and technological aspects are now introduced with an energetic point of view, in which some practical applications are exposed and discussed. Chapter 3 describes the seismic response of cable-stayed bridges without external seismic protection, considering a parametric analysis in order to study the effects of the stay cable layout, stay spacing and deck level. A complete modal characterization is exposed, followed by a response spectrum analysis for comparative purposes. The effect of variations of the stay forces is analyzed, and finally, a nonlinear step-by-step analysis is performed for the critical structures, considering the velocity dependence of such bridges and the effects of far-fault and near-fault ground motions. The last Chapter exposes the seismic analysis of the selected structures including the incorporation of fluid viscous dampers as passive additional energy dissipation devices. Because of the inherent nonlinear behaviour of the structures and external devices, a mandatory nonlinear direct integration time-history analysis is performed for all the cases, in which parametric analyses are carried out in order to select the best damper parameters, and for the case of both far-fault and near-fault ground motions. In this part, comparative results are exposed with the aim to propose some practical recommendations.

Galo E. Valdebenito
Ángel C. Aparicio
Llavaneras (Barcelona), October 2009.

## Chapter 1. Introduction

1.1 Cable-Stayed Bridges and Seismic Protection

Bridges are without a doubt attractive civil engineering works from a structural point of view. But they are not only exciting as a structure: the project, construction, maintenance, operation as well as functional, aesthetic, economic and political aspects make them extremely interesting constituting a great social event [Maldonado et al, 1998].

Suspension bridges are very interesting and useful structures because they can be used for long-spans, solving many practical problems for which is necessary to cross large distances without intermediate supports. These kinds of structures are a challenge from all points of view, due to the constant increase of the main span length demand, constituting most of the times a human whim or that competitive and insatiable desire to break goals at any price. Cable supported bridges can be divided into suspended and cable-stayed bridges, as can be appreciated in Fig. 1.1.

From a structural point of view, both types of bridges are completely different, since contrary to suspended bridges, in cable-stayed bridges the cables are prestressed. Keeping in mind functional and economical aspects, suspension bridges permit longer spans with more economical results than cable-stayed bridges [Podolny and Scalzi, 1986]. Actually, the longer main spans in cable-stayed bridges reach 900 m, although recent investigations show the feasibility and possibility of building bridges of this kind with main spans exceeding 1000 m. These studies are based on the current high standard technologies and the lightness of superstructures that use orthotropic slabs [Aschrafi, 1998; Nagai et al, 1998].

(a) Cable-Stayed bridge
(b) Suspended bridge
Fig. 1.1 Cable-Supported Bridges

In spite of the relative simplicity of bridges, the recent earthquake events of San Fernando (1971), Loma Prieta (1989), Northridge (1994), Kobe (1995) and Taiwan (1999) have shown that these systems are very vulnerable, mainly those of reinforced concrete. For that reason, is a high-priority to improve the comprehension of this phenomenon, learning from the recent earthquake lessons [Priestley et al, 1996]. These structural systems expose a few degrees of redundancy, and the collapse mechanisms should be known in detail to reach an appropriate performance. Some aspects that should be considered are: degree of redundancy of the system, soil-structure interaction, spatial variability effects, near source effects, geological faults and geotechnical aspects, bridge length effects, vertical component of motion and damping [Valdebenito, 2005]. All these aspects are explained in the references of Ghasemi (1999), Kawashima (2000); Cheung et al (2000) and Calvi (2004).

The structural analysis of a bridge depends undoubtedly on the structural modelling. Therefore, a well-done modelling is reflected in the degree of accuracy of the results. The vertiginous development of high-performance computers permits to solve more complex and large structures, testing a lot of conditions in a relatively short time. Thus, computing time will depend on the modelling used and the required accuracy for the results. Because of almost all the seismic isolators or energy dissipators experience non-linear behaviour, consideration of non-linear aspects in the analysis of the bridge – energy dissipation system is advisable. In spite of the current computer capacity and better non-linear structural analysis software, it is clear that the time and knowledge level of the designer are two serious limitations of the extensive application of these methodologies [Jara and Casas, 2002]. In fact, sometimes is preferable the use of simplified methods that show sufficiently accurate results in short time. In the case of long-span cable-stayed bridges, the problem is more complex, maybe due to the high non-linear behaviour of those structures, and hence, non-linear analysis becomes an indispensable condition, leaving aside the classical response spectrum analysis or the equivalent static analysis. Thus, a relatively complex structure can be solved by the iterative definition of the stiffness and equivalent damping.

Traditional seismic control strategies are based on the modification of stiffness, mass or geometric properties of the structure, reducing inertial forces and displacements caused by an earthquake. Thus, in the current design is necessary to permit controlled structural damage by the ductility provided, with the aim of avoiding too conservative designs and expensive costs. In other words, in the current philosophy, a structure with energy dissipation capacity is required, more than a resistant structure against all events. Although it is certain that traditional strategies for the seismic protection of bridges have progressed in the last years, for appropriate bridge strength and to assure a satisfactory behaviour for different intensity levels, development of special vibration control devices has given origin to a new path in seismic engineering. In general terms, instead of provide more strength, is more attractive to reduce internal forces and displacements through special isolation systems or energy dissipation devices. This energy distribution means that the seismic energy proceeding from the subsoil is distributed to different structural components and thus significant energy accumulation is avoided.

Amongst the existent control systems on bridges, passive strategies are well accepted because of their low comparative price, simple installation and maintenance as well as their great reliability and better theoretical and technological development [Jara and Casas, 2002]. Active, semi-active and hybrid systems seems to be an excellent strategy for the seismic control of structures, however, a lack of regulations and uncertainty regarding their real performance under strong ground motions are important limitations for their application. Without a doubt, there is a very promising future, mainly with semi-active and hybrid systems because of their incomparable advantages, although now their use is very limited, not been properly tested on real structures with real earthquakes. Thus, the general approach reducing the seismic demand of structures, more than trying to increase their strength or deformation capacity with appropriate criteria, is without a doubt an advantageous seismic protection system. These new seismic control strategies are conceived for the reduction of the seismic demand, and the appropriate application of this approach leads to systems that behave elastically during great earthquakes, on the contrary of a traditional design, where high energy dissipation capacity by controlled damage is needed. Passive control systems convert the kinetic energy of the system into heat, transferring it among different vibration modes. They do not require additional external energy for their operation, constituting their main advantage. In general terms, these systems operate elastically during great earthquakes, permitting structural functionality conditions after the event. Because of their low cost, high efficiency and low maintenance, they are additional seismic protection systems widely used in the world. Passive control systems can be classified as follows (Table 1.1):

Table 1.1 Passive Seismic Control Systems [Adapted from Valdebenito and Aparicio, 2005]
 Base Isolation Energy Dissipators Seismic Connectors Resonant Dampers 1. Rubber Bearings (RB) 1. Metallic Yield Dampers (MD) 1. Shock transmission Units TU) 1. Tuned Mass dampers (TMD) 2. High Damping Rubber Bearings (HDR) 2. Friction Dampers (FD) 2. Displacement Control Devices (DCD) 2. Tuned Liquid Dampers (TLD) 3. Lead Rubber Bearings (LRB) 3. Viscoelastic Dampers (VE) 3. Rigid Connection Devices (RCD) 4. Rubber Bearings with Additional Energy Dissipation 4. Fluid Viscous Dampers (VF) 5. Sliding Bearings (SB) 5. Lead Extrusion Dampers (LED) 6. Shape Memory Alloy (SMA)

Base isolation and dissipation result in decreasing the energy applied to the system and the transformation from energy to heat. This is also designated as energy approach, which especially takes into account the energy character of the seismic event. In the seismic isolation, the structure is separated from the subsoil, automatically limiting the energy that affects the structure, which is considerably reduced. As a result, the natural period is increased, which causes a considerable reduction of the structural acceleration during seismic events. Depending on the installed type of isolator, they do not only guarantee the vertical load transmission but also the restoring capacity during and after a seismic event.

 Fig. 1.2 (a) Energy Dissipation of a Traditional Bridge, (b) Energy Dissipation of a Seismic Isolated Bridge [Adapted from Jara and Casas, 2002] Fig. 1.2 (a) exposes a traditionally designed bridge, in which the seismic energy is dissipated by damage at the plastic zones (plastic hinges). For the above-mentioned, an adequate ductility to dissipate the earthquake energy is required. Fig. 1.2 (b) shows the case of an isolated bridge with rubber bearings. In this situation, inertial forces on the pylon are reduced, and the inelastic energy dissipation during severe earthquakes is achieved by hysteretic deformation of the supports [Jara and Casas, 2002].

Base isolation systems and seismic connectors applied to bridges have been properly tested and used for more than 20 years, and there is a lot of documentation and experience regarding to this. In relation to energy dissipation systems, the use of fluid viscous dampers can be the future for the application to large structures such as long-span cable-stayed bridges, mainly due to their high capacity, robustness, and good results of recent investigations.

 Fig. 1.3 Minimized Seismic Energy Penetration by Seismic Isolation and Energy Dissipation It seems that additional damping devices are clearly adequate considering the current high standards and technology, and in conjunction with isolation, produce the best possible seismic protection, mainly if the structural system is not velocity-dependent. On one hand, isolation reduces the spectral acceleration (demand), and on the other hand, fluid viscous dampers dissipate input energy avoiding structural damage (Fig. 1.3). A good state-of-the-art in relation to supplemental energy dissipation can be found in the work of Soong and Spencer (2002).

In the case of cable-stayed bridges, their seismic behaviour has been, in general terms, very satisfactory, maybe due to their great flexibility. In spite of the above-mentioned, comprehension of their behaviour is very complex being appropriate and promising to consider special systems of additional seismic protection. On those structures, these additional systems have been applied basically to control vibrations on cables due to the effect of the wind and rain (rain - wind vibration), to solve aerodynamic problems on unstable and complex structures and for the seismic retrofit of existing bridges. Now, application of these devices for the control of seismic actions begins to be used with more frequency; not only on the cables to mitigate the cable-deck interaction [Macdonald and Georgakis, 2002] but also to isolate the superstructure, as can be appreciated in the recently inaugurated Rion-Antirion Bridge (Fig. 1.4), in the Gulf of Corinthian, Greece [Infanti et al, 2004].

Fig. 1.4 Rion-Antirion Bridge, Greece [from [1] www.aecom.com]]

Design of almost all cable-stayed bridges located at moderate-to-high seismicity zones is more complex than design of conventional bridges. Bridge design regulations and modern previsions have been developed in general terms and for standard bridges, in order to provide safe and economical structures. As general design philosophy, it is accepted the important request of having structural damage but permitting emergency communications for a not frequent severe earthquake. For the new cable-stayed bridges, code previsions cannot be applicable, being necessary the urgent improvement of regulations and general recommendations for the seismic design of these bridges, based on numeric, experimental or full-scale testing investigations. Also, the lack of information about the real performance of these bridges during strong earthquakes increases the uncertainty in terms of an appropriate design [Abdel-Ghaffar, 1991]. In fact, according to Eurocode 8 Part 2 [CEN, 1998b], cable-stayed bridges are classified as special bridges, aspect that implies that these regulations need to be considered only as general recommendations. At the moment, existent regulations with regard to passive systems are limited to seismic isolation and energy dissipation devices, without the incorporation of hybrid, active or semi-active systems. Design specifications for bridges with LRB systems, published by the New Zealand Ministry of Works and Development in 1983, were the first regulations about bridges with special seismic protection based on isolation and energy dissipation systems. Later, in the 90s, official recommendations for the first time in USA [1991, 2000], Italy (1991), Japan (1996), and Europe through Eurocode 8 [CEN, 1998a, 1998b] were published.

1.2 Historical Background

The early stayed bridges used chains or bars for the stays. The advent of various types of structural cables, with their inherent high carrying capacity and ease of installation, led engineers and contractors to replace the chains and bars [Podolny and Scalzi, 1986].

 Fig. 1.5 Löscher-type Timber Bridge [Courtesy of the British Constructional Steelwork Association, Ltd] The concept of a bridge partially suspended only by inclined stays is credited to C.J. Löscher, a carpenter from Fribourg, Switzerland who built a completely timber bridge including stays and tower in 1784, with a span of 32 m. (Fig. 1.5).

Cable-stayed bridges might have become a conventional form of construction had it not been for the bad publicity that followed the collapses of two bridges: the 79 m pedestrian bridge crossing the Tweed River near Dryburgh-Abbey (England) in 1818; and the 78 m long bridge over the Saale River near Nienburg, Germany, in 1824 [Podolny and Scalzi, 1986]. The famous French engineer, Navier, discussed these failures with his colleagues, and his adverse comments are assumed to have condemned the stay-bridge concept to relative obscurity. Whatever the reason, engineers turned to the suspension bridge, which was also emerging, as the preferred type of bridge for river crossings.

The principle of using stays to support a bridge superstructure returned with the works of John Roebling. The Niagara Falls Bridge (Fig. 1.6), the Old St. Clair Bridge in Pittsburgh (USA), the Cincinnati Bridge over the Ohio River (USA) and the Brooklyn Bridge (Fig. 1.7) in New York (USA) are good examples.

 Fig. 1.6 Niagara Falls Bridge [Courtesy of the Niagara Falls Bridge Commission] Fig. 1.7 Brooklyn Bridge [from [2] www.elclubdigital.com]]

It should be noted that the stays used by Roebling in his suspension bridges were used as an addition to the classical suspension bridge with the main catenary cable and its suspenders. During Roebling’s time the suspension bridge concept was suffering with failures resulting from wind forces. He knew that by incorporating the diagonal stays he could minimize the susceptibility of his structures to adverse wind loading. However, it is not clear whether he used the two suspension systems compositely.

Towards the end of the 19th century, the success of these hybrid structures – part suspension, part stayed – resulted in a slowing down of the use of structures supported exclusively by inclined rods. However, it was not until 1899 that the French engineer A. Gislard further advanced the development of stayed bridges by the introduction of a new system of hangers, at the same time economic and sufficiently rigid [Walter, 1999]. The system was characterized by the addition of cables intended to take up the horizontal components of the forces set up by the stays. This arrangement cancels out any compressive forces in the deck and thus avoids deck instability.

 Fig. 1.8 The Bridge over the Donzère Canal, France [photo: J. Kerisel] Surprisingly, the first “modern” cable-stayed bridges were built in concrete by Eduardo Torroja in the 1920s (Tampul aqueduct) and by Albert Caquot in 1952 (Donzère Canal Bridge, Fig. 1.8). However, the real development came from Germany with papers published by Franz Dischinger and with the famous series of steel bridges crossing the river Rhine, as the Oberkassel Bridge, in Düsseldorf, Germany (Fig. 1.9). Fig. 1.9 Oberkassel Bridge, Düsseldorf, Germany Fig. 1.10 Maracaibo Bridge, Venezuela [from en.structurae.de]

The increasing popularity of this new type of structure with German engineers slowly extended to other countries. Thus, the Italian architect R. Morandi designed several cable-stayed bridges in reinforced and prestressed concrete. His most outstanding work is the bridge on Lake Maracaibo, Venezuela, built in 1962 (Fig. 1.10).

The international development of this bridge type began in the 1970s, but a very big step forward took place in the 1990s, when cable-stayed bridges entered the domain of very long spans which was previously reserved for suspension bridges. As examples, the Barrios de Luna Bridge – also called the Fernandez Casado Bridge – in Spain (430 m, 1983, Fig. 1.11); the Yang Pu Bridge in Shangai, China (602 m, 1993, Fig. 1.12); the Normandie Bridge in Le Havre, France (856 m, 1994, Fig. 1.13) and the Tatara Bridge in Japan (890 m, 1998, Fig. 1.14). It is extremely interesting to analyse the progress in the world record for cable-stayed bridges, since it provides keys to understand the evolution of their design (Fig. 1.15).

The recently inaugurated Millau Bridge in the Tarn Valley, France, is one of the world’s famous multi-span cable-stayed bridge, with 342 m main span length and 343 m height for the highest pylon. This also called “bridge over the clouds” is one of the more interesting French engineering works at the present (Fig. 1.16). In the same way, the new Sutong Bridge, in Nantong, China (inaugurated in 2008), is considered the longest cable-stayed bridge of the world, with a main span length of 1088 m, and surpassing the Japanese record reached with the Tatara Bridge (Fig. 1.17).

 Fig. 1.11 Barrios de Luna Bridge, Spain [from en.structurae.de] Fig. 1.12 Yang Pu Bridge, China [photo: M. Virlogeux] Fig. 1.13 Normandie Bridge, France [from fr.structurae.de] Fig. 1.14 Tatara Bridge, Japan [from [3] www.answers.com]]

Fig. 1.15 Evolution of Record Spans for Cable-Stayed Bridges [Virlogeux, 1999]
 Fig. 1.16 Millau Bridge, France Fig. 1.17 Sutong Bridge, Nantong, China

Although the use of energy dissipation devices began as an attempt to control the cable vibration on cable-stayed and suspension bridges, very common on those structures due to the inherent low damping of the cable system, the inclusion of additional seismic protection, with the introduction of passive and active energy dissipation devices, has just begun. In this sense, the use of fluid viscous dampers in the recently inaugurated Rion-Antirion Bridge (Greece) is an exceptional opportunity to test in situ, with a real structure in a high-seismicity zone, those devices (Fig. 1.18). The deck of this multi-span cable-stayed bridge is continuous and fully suspended from four pylons (total length of 2252 meters). Its approach viaducts comprise 228m of concrete deck on the Antirion side and 986m of steel composite deck on the Rion side. The Main Bridge seismic protection system comprises fuse restraints and viscous dampers of dimensions heretofore never built. The same act in parallel, connecting the deck to the pylons. The restrainers of the Rion Antirion Bridge were designed as a rigid link intended to withstand high wind loads up to a pre-determined force. Under the reaction of the design earthquake, fuse restrainers will fail and leave the dampers free to dissipate the earthquake-induced energy acting upon the structure. The Approach Viaducts were seismically isolated utilizing elastomeric isolators and viscous dampers [Infanti et al, 2004].

 Fig. 1.18 Rion-Antirion Viscous Dampers [Courtesy of FIP Industriale, Italy] Another interesting application of passive/active devices is to retrofit existent bridges. After important earthquake events, or adjusting the seismic behaviour of existent structures in accordance with new codes and specifications, many bridges need to be retrofitted. For cable-stayed bridges, it seems to be impractical to reinforce structural members, and it will be more simple and efficient to conduct the bridge retrofit by using isolation systems if the system is proved to be feasible [Lai et al, 2004].

The recent application of active (i.e. hybrid, semi-active) systems on cable-stayed bridges is very limited. Actually, a benchmark structural problem for cable-stayed bridges was defined in order to provide a test bed for the development of strategies for the seismic control of those structures. The problem is based on the new cable-stayed bridge that spans the Mississippi River: the Bill Emerson Memorial Bridge, in Cape Girardeau, Missouri, USA. [Dyke et al, 2002].

 Fig. 1.19 Dongting Lake Bridge, China Real applications of active systems to cable-stayed bridges are limited only to aerodynamic structural control of the stays. In this sense, the recent application of Magnetorheological Dampers on the Dongting Lake Bridge over the Yangtze River in the southern central China (Fig. 1.19) is the first known application of those devices to control the rain-wind vibration. The installation finished in June 2002 [Chen et al, 2003].

## Chapter 2. Fluid Viscous Damping Technology

2.1 General Overview

Structures situated on seismic areas must be designed to resist earthquake ground motions. A fundamental rule regarding the seismic design of structures, express that higher damping implies lower induced seismic forces. For conventional constructions, the induced earthquake energy is dissipated by the structural components of the system designed to resist gravity loads. It is well known that damping level during the elastic seismic behaviour is generally very low, which implies not much dissipated energy. During strong ground motion, energy dissipation can be reached through damage of important structural elements, and considering only the resulting response forces within the structure due to an earthquake leads to massive structural dimensions, stiff structures with enormous local energy accumulation and plastic hinges. This strengthening method combined with usual bearing arrangements permits plastic deformations by way of leading to yield stress and cracks. In this sense, structural repair after an important seismic event is generally very expensive, the structure is set temporarily out of service and sometimes a lot of damaged structures must be demolished [Alvarez, 2004].

General concepts for appropriate protection of structures against earthquakes do not exist, as every structure is quite unique and requires individual considerations. Earthquakes are often interpreted in terms of deformations and acting forces induced upon the structure. As a consequence, there is a tendency to think only about increasing the strength of the structure. Actually, forces and displacements are nothing but a mere manifestation of seismic attacks and do not in fact represent their very essence. An earthquake is actually an energy phenomenon and the forces causing stresses in the structure are the final effect of that event.

In recent years, other strategies have been developed to reduce the seismic response of the structures using additional passive devices. A passive control system may be defined as a system which does not require an external power source for operation and utilizes the motion of the structure to develop the control forces, as a function of the response of the structure at the location of the passive control system, according to Fig. 2.1.

 Fig. 2.1 Block Diagram of Passive Control System [Symans and Constantinou, 1999] A passive control system may be used to increase the energy dissipation capacity of a structure through localized discrete energy dissipation devices located either within a seismic isolation system or over the height of the structure. Such systems may be referred to as supplemental energy dissipation systems [Symans and Constantinou, 1999]

Passive supplemental damping strategies, including base isolation systems, viscoelastic dampers and tuned mass dampers are well understood and are widely accepted by the engineering community as a means for mitigating the effects of dynamic loading on structures. In this sense, energy dissipation systems can be considered as an important passive strategy in which the objective of these devices is to absorb a significant amount of the seismic input energy, thus reducing the demand on the structure by means of the relative motion within the passive devices which, in turn, dissipate energy. In general terms, these devices are not part of the structural system that resists gravity loads, constituting an external system that can be easily replaced after a strong earthquake. Of course, in this case the structural functionality is not affected as well as the stability of the structure, with a low replacement cost of such devices compared with repair or service interruption costs.

Additional damping devices dissipate energy by means of yielding, friction, Viscoelastic action or fluid flow through orifices [Soong and Dargush, 1997; Constantinou, 2003]. In this sense, fluid viscous dampers constitutes one of the well accepted energy dissipation systems by the scientific and engineering community, being considered as additional damping system in this work, as was previously explained and justified. These systems are capable of dissipate an important amount of energy during strong ground motions as well as to control long period displacements. These dampers are basically comprised of a cylinder filled with silicone fluid (oil or paste) and a piston that divides it into two chambers and is free to move in both directions. In case of sudden movements, due to earthquakes or other dynamic actions like braking, wind, etc., lamination of silicone fluid occur through an appropriate hydraulic circuit and leads to energy dissipation. In case of slow displacements, due to structure thermal expansion, such flow is obstructed, so that during normal service the behaviour is substantially rigid, acting like a shock absorber. Because of those advantages, utilization of this technology permits to take full advantage of the strength of structural elements, because it is possible to maximize energy dissipation reaching the maximum level of force that the structure can sustain, without exceeding it. As a consequence, structural elements remain in the elastic field also during high intensity earthquakes.

Actually, manufacture of fluid viscous dampers permits to design such devices for a wide range of specific requirements of velocity and force, constituting a good choice for implementation on new and existing facilities. Those devices are properly tested at specific laboratories, especially when they are applied on important structures or they are required for special conditions. In this sense, manufacturers such as Alga s.P.a. (Milano, Italy); FIP Industriale s.P.a. (Selvazzano, Italy), Taylor Devices, Inc. (New York, USA), Maurer Söhne (München, Germany), Mageba (Bülach, Switzerland) or Nanjing Damper Technology Engineering Co. Ltd (Nanjing, China) design and manufacture a wide variety of such systems.

Today an increasing number of applications of energy dissipation devices on bridges for the control of seismic displacements and energy dissipation is taking place. The more common solution is, probably, the use of linear / non-linear viscous dampers, permitting an adequate control of the displacements avoiding an increase of the structural internal forces and the increase of stiffness for piers and abutments [Jerónimo and Guerreiro, 2002].

The new tendencies regarding the seismic analysis and design of fluid viscous dampers capture the frequency dependence of such devices [Singh et al, 2003]; the earthquake response of non-linear fluid viscous dampers [Peckan et al, 1999; Lin and Chopra, 2002]; the seismic performance and behaviour of these devices during near-field ground motion [Tan et al, 2005; Xu et al, 2007] and the performance-based design of viscous dampers [Kim et al, 2003; Li and Liang, 2007]. A state-of-the-art review can be found in the works of Lee and Taylor (2001) and Symans et al (2008).

2.2 Technological Aspects
2.2.1 Historical Background

As with many other types of engineered components, the requirements, needs and available funds from the military allowed rapid design evolution of fluid dampers to satisfy the needs of armed forces. Early fluid damping devices operated by viscous effects, where the operating medium was sheared by vanes or plates within the damper. Designs of this type were mere laboratory curiosities, since the maximum pressure available from shearing a fluid is limited by the onset of cavitation, which generally occurs at between 0.06 N/mm2 and 0.1 N/mm2, depending on the viscosity of the fluid. This operating pressure was so low that for any given output level, a viscous damper was much larger and more costly than other types [Taylor, 1996].

In the late 1800s, applications for dampers arose in the field of artillery, where a high performance device was needed to attenuate the recoil of large cannons. After extensive experimentation, the French Army incorporated a unique (and “top-secret”) fluid damper into the design of their 75 mm gun. These first fluid damper designs used inertial flows, where oil was forced through small orifices at high speeds, in turn generating high damping forces. This allowed the damper to operate at relatively high operating pressures, in the 20 N/mm2 range. The output of those devices was not affected by viscosity changes of the fluid, but rather by the specific mass of the fluid, which changes only slightly with temperature. Thus, the technology of fluid inertial dampers became widespread within the armies and navies of most countries in the 1900 – 1945 period.

During the World War II, the emergence of radar and similar electronic systems required the development of specialized shock isolation techniques. During the Cold War period, the guided missile became the weapon of choice for the military, and the fluid inertial damper was again turned to by the military as the most cost effective way of protecting missiles against both conventional and nuclear weapon detonation. In these cases, transient shock from a miss near weapons detonation can contain free field velocities of 3 to 12 m/s, displacements of up to 2000 mm, and accelerations up to 1000 times gravity. For that reason, extremely high damping forces were needed to attenuate these transient pulses on large structures, and fluid inertial dampers became a preferred solution to these problems [Taylor, 1996].

With the end of the Cold War in the late 80s, much of this fully developed defence technology became available for civilian applications. In this context, demonstration of the benefits of damping technology on structures could take place immediately, using existing dampers and the seismic test facilities available at U.S. university research centres. In this sense, application of fluid viscous dampers as part of seismic energy dissipation systems was experimentally and analytically studied, being validated by extensive testing on one-sixth to one-half scale building and bridge models in the period 1990 – 1993 at the Multidisciplinary Centre for Earthquake Engineering Research (MCEER), located on the campus of the State University of New York at Buffalo in USA. Thus, implementation of fluid viscous damping technology began relatively swiftly, with wind protection usage beginning in 1993, and seismic protection usage beginning in 1995 [Taylor and Duflot, 2002].

2.2.2 General Behaviour

Fluid viscous dampers operate on the principle of fluid flow through orifices. A stainless steel piston travels through chambers that are filled with silicone oil. The silicone oil is inert, non flammable, non toxic and stable for extremely long periods of time. The pressure difference between the two chambers cause silicone oil to flow through an orifice in the piston head and seismic energy is transformed into heat, which dissipates into the atmosphere. This associated temperature increase can be significant, particularly when the damper is subjected to long-duration or large-amplitude motions [Makris 1998; Makris et al, 1998]. Mechanisms are available to compensate for the temperature rise such that the influence on the damper behaviour is relatively minor [Soong and Dargush, 1997]. However, the increase in temperature may be of concern due to the potential for heat-induced damage to the damper seals. In this case, the temperature rise can be reduced by reducing the pressure differential across the piston head (e.g., by employing a damper with a larger piston head) [Makris et al, 1998]. Interestingly, although the damper is called a fluid viscous damper, the fluid typically has a relatively low viscosity (e.g., silicone oil with a kinematic viscosity on the order of 0.001 m2 /s at 20°C). The term fluid viscous damper is associated with the macroscopic behaviour of the damper which is essentially the same as that of an ideal linear or nonlinear viscous dashpot (i.e., the resisting force is directly related to the velocity). Generally, the fluid damper includes a double-ended piston rod (i.e., the piston rod projects outward from both sides of the piston head and exits the damper at both ends of the main cylinder). Such configurations are useful for minimizing the development of restoring forces (stiffness) due to fluid compression [Symans et al, 2008]. The force/velocity relationship for this kind of damper can be characterized as F = C.Vα where F is the output force, V the relative velocity across the damper; C is the damping coefficient and α is a constant exponent which is usually a value between 0.1 and 1.0 for earthquake protection, although at the present time some manufactures begin to apply dampers with very low damping coefficients, typically in the order of 0.02. Fluid viscous dampers can operate over temperature fluctuations ranging from –40°C to +70°C, and they have the unique ability to simultaneously reduce both stress and deflection within a structure subjected to a transient. This is because a fluid viscous damper varies its force only with velocity, which provides a response that is inherently out-of-phase with stresses due to flexing of the structure [Taylor and Duflot, 2002].

Fluid velocity is very high in the piston head so the upstream pressure energy converts almost entirely to kinetic energy. When the fluid subsequently expands into the full volume on the other side of the piston head it slows down and loses its kinetic energy into turbulence. There is very little pressure on the downstream side of the piston head compared with the full pressure on the upstream side of the piston head. This difference in pressures produces a large force that resists the motion of the damper. Viscous dampers, when correctly designed and fabricated, have zero leakage and require no accumulator or external liquid storage device to keep them full of fluid. They have nearly perfect sealing. In a correctly designed and fabricated viscous damper there is nothing to wear out or deteriorate over time so there is no practical limit on expected life. Warranty periods of 35 years are common [Lee and Taylor, 2001]. Fig. 2.2 shows a general view of a fluid viscous damper, and Fig. 2.3 shows fluid viscous dampers for a high-speed railway bridge in Spain.

 Fig 2.2 General view of a Fluid Viscous Damper [Courtesy of FIP Industriale s.P.a., Italy] Fig. 2.3 Fluid Viscous Dampers for De Las Piedras-High Speed Railway Bridge, Spain [Courtesy of Maurer Sönhe, Germany]

Fig. 2.4 exposes a schematic of a typical fluid viscous damper showing its elements, which are described next.

 Fig. 2.4 Typical Viscous Damper [Lee and Taylor, 2001] The piston rod is machined from high alloy steel stainless steel and then highly polished. This high polish provides long life for the seal. The piston rod is designed for rigidity as it must resist compression buckling and must not flex under load, which would injure the seal.

The cylinder contains the working fluid and must withstand the pressure loading when the damper operates. Cylinders are usually made from seamless steel tubing and are sometimes machined from steel bars. Proof pressure is generally 1 - 5 times expected internal pressure for the maximum credible seismic event.

Structural applications require a fluid that is fire-resistant, non-toxic, thermally stable and that will not degrade with age. Under current OSHA (Occupational Safety & Health) guidelines this means a flash point of at least 200°F. Silicone fluid is often used as it has a flash point over 650°F and is cosmetically inert, completely non-toxic and one of the most thermally stable fluids available.

The seal must provide a service life of at least 35 years without replacement. As dampers often sit for long periods without use, the seal must not exhibit long-term sticking or allow fluid seepage. The dynamic seal is made from high-strength structural polymer to eliminate sticking or compression set during long periods of inactivity. Acceptable materials include Teflon®, stabilized nylon and members of the acetyl resin family. Dynamic seals made from structural polymers do not age, degrade or cold flow over time.

The piston head attaches to the piston rod and effectively divides the cylinder into two separate pressure chambers. This space between the outside diameter of the piston and in the inside diameter of the cylinder forms the orifice. Very often the piston head is made from a different material than the cylinder to provide thermal compensation. As the temperature rises the annulus between the piston head and the cylinder shrinks to compensate for thinning of the fluid.

The damper shown in Fig. 2.4 uses an internal accumulator to make up for the change in volume as the rod strokes. This accumulator is either a block of closed-cell plastic foam or a movable pressurized piston, or a rubber bladder. The accumulator also accommodates thermal expansion of the silicone fluid.

Viscous dampers add energy dissipation to a structure, which significantly reduces response to earthquakes, blasts, wind gusts and other shock and vibration inputs. A value of 30% of the critical damping ratio is a practical upper limit for combined viscous and structural damping. Around 25% of this is viscous damping and the remaining 5% is structural damping [Lee and Taylor, 2001]. This provides a 50% reduction in structural response compared with the same structure without viscous dampers. Note that the addition of viscous dampers does not change the period of the structure. This is because viscous damping is 90 degrees out of phase with the structural forces. Fig. 2.5 shows a typical plot of base shear against interstorey drift, taken from a laboratory test, according to Lee and Taylor (2001).

 Fig. 2.5 Typical Plot of Base Shear Against Interstorey Drift [Lee and Taylor, 2001] Fig. 2.6 Base Shear Against Interstorey Drift with Added Dampers [Lee and Taylor, 2001]

Note that the hysteresis loop is very flat and thin as there is only 5% damping. Figure 2.6 shows a plot of the same structure with the same input only this time with added viscous damping. Note that interstorey drift is 50% less and that the hysteresis curve is much fuller. In this case, 20% of added linear damping to the structure increased its earthquake resistance compared to that of the same structure without added damping. The area inside the hysteresis loop is the same as in Fig. 2.5. It is theoretically possible to provide enough viscous damping to completely prevent plastic hinging. This provides a totally linear structure. Economically, it is best to retain some plastic hinging as this results in the least overall cost. Viscous dampers still limit interstorey drift sufficiently to provide immediate occupancy after a worst-case event. They also limit and control the degree of plastic hinging and greatly reduce base shear and interstorey shear [Lee and Taylor, 2001]. Only as comparative purpose Table 2.1 shows equivalent damping coefficients for different structures and components. It is clear that an enormous amount of energy can be dissipated with the implementation of seismic dampers, reaching the largest values of dissipated energy. Of course, with those quantities, structural damping in the case of cable-stayed bridges may represent no more than 3% of the additional damping provided by the dampers, that is to say, a negligible amount.

Table 2.1 Comparison of Equivalent Damping Coefficients ξ of Different Structures and Components [Courtesy of Maurer Sönhe, Germany]
 Structural Component Damping ratio (ξ) Steel bridge 0.02 Concrete bridge 0.05 Elastomeric bearing 0.05 – 0.06 High damping rubber bearing 0.16 – 0.19 Lead rubber bearing and friction pendulum 0.30 – 0.40 Fluid viscous dampers Up to 0.60

In terms of the efficiency, the damping coefficient ξ relates to the efficiency η according to:

[Eq. 2.1]

This ends up in a maximum efficiency η = 96% for fluid viscous dampers.

As a summary, the overall characteristics of fluid viscous dampers include:

• During service conditions the device is not pre-tensioned and the fluid is under insignificant pressure
• An extra-low damping exponent, such as those proposed from some manufacturers, provides maximum and well-defined force to a certain limit. No structural damages due to higher damping forces occur even in case the vibration frequency exceeds the expected value.
• With the current technology, velocity ranges from 0.1 mm/sec to 1500 mm/sec or even more can be reached for fluid viscous dampers, which implies wide-variety of applications.
• Maximum response force is given within tenths of second, so structural displacements and vibrations can be more effectively minimized.
• Automatic volume compensation of the fluid caused by temperature changes without pressure increase inside the devices. Any compensation containers are located inside.
• No maintenance works necessarily. Visual inspection can be recommended during the period bridge inspections. Depending on the accumulated displacements and displacement velocities the service life can be reach up to 40 years.
• With the current development, the devices are not prone to leaking
• Range of operating temperatures varies from -40ºC to +70ºC.
• Non-toxic, not inflammable and not ageing fluids are applied.
2.2.3 Application to Bridges

Decks for viaducts and long-span bridges require adequate expansion joints for large displacements under service conditions to absorb the effects of creep and thermal expansion. A common structural layout used in Europe, consists of continuous deck supported by POT devices [Priestley et al, 1996]. By this way, the idea of employing devices with an insignificant response under long-period displacements and at the same time, capable of dissipating much induced seismic energy, was developed.

Some manufacturers differentiate the type of damper according to the motion of the device in the presence of slow displacements. In this case, as for example when thermal expansion occurs, in the OTP type the fluid flows from one chamber to the other with minimum opposition (normally smaller than 10% of the maximum force), while in the OP type such a flow is obstructed, so that during normal service the behaviour is substantially rigid [see the scheme of the typical application of viscous dampers on bridges in Fig. 2.7].

Application of fluid viscous dampers to bridges have been used since middle 90s. Although these devices may be applied to any kind of structures, their application is easier and more effective in bridges. One of the problems in the use of such devices is that the analysis of the dynamic behaviour becomes more elaborated and difficult than the analysis of a bridge with its seismic resistance based on the ductile capacity of the piers [Virtuoso et al, 2000]. Figs. 2.8 and 2.9 show some examples of application of fluid viscous dampers to bridges.

An important aspect to consider is that, if there is some available stiffness and resistance in the connection between the deck and the piers/towers or abutments, it is possible to obtain optimised solutions without inducing significant forces in the structure. That stiffness as the advantage of guaranteeing recentering capability after an earthquake can be used to improve the structure behaviour under other actions [Virtuoso et al, 2000].

Fig. 2.7 Typical Application of Viscous Dampers in Bridges [Courtesy of FIP Industriale s.P.a., Italy]
 Fig. 2.8 Fluid Viscous Dampers at G4-Egnatia Motorway Bridge, Greece [Courtesy of Maurer Sönhe, Germany] Fig. 2.9 850 kN Capacity Damper for the Chun-Su Bridge, South Korea [Courtesy of FIP Industriale s.P.a., Italy]

2.3 Mechanical Behaviour
2.3.1 Energy Approach

An earthquake is an energy phenomenon and therefore this energy character should be considered to achieve the best possible seismic protection for the structure. Without seismic protection system, the seismic energy is entering the structure very concentrated at the fixed axis. By means of shock transmission units the entering energy is distributed to several spots within the structure. In this case the energy input into the structure is still in same magnitude like without those devices, but now the energy is spread over the entire structure in more portions. By implementing additional energy dissipation capability, less energy is entering the structure, with the consequent response mitigation.

The principles of physics that govern the effects of dissipation on the control of dynamic phenomena were studied more than two centuries ago [DAlembert, Traité de Dynamique, 1743]. Nonetheless, their practical application has come about much later and within a much different time-frame in several sectors of engineering. As was previously exposed, the sector that was the first to adopt such damping technology was the military [France, 1897], followed by the automobile industry. In 1956 Housner already suggested an energy-based design of structures. Kato and Akiyama (1975) and Uang and Bertero (1990) made a valuable contribution to the development of the aspects of an energy-based approach, which presently meets with great concensus.

The dynamic equation of a single-degree-of-freedom structure with mass ms damping coefficient cs, stiffness ks and control force u, subject to ground acceleration is:

[Eq. 2.2]

where , and are the displacement, velocity and acceleration responses respectively. The involved parameters are clearly explained in Fig. 2.10, which shows a simplified scheme for a single-degree-of-freedom system. Of course, each term in Eq. 2.2 is a force.

 Fig. 2.10 Complex Bridge Structure Explained with a Simplified Single Oscillation Mass Integrating Eq. 2.2 with respect to x: where each term is now an energy component. Thus, we can define: [Eq. 2.3] [Eq. 2.4]

[Eq. 2.5]

[Eq. 2.6]

[Eq. 2.7]

An energy balance equation can be proposed in terms of the above defined:

[Eq. 2.8]

where:

Ek: Kinetic energy

Ev: Dissipated energy by inherent damping

Ee: Elastic strain energy

Eh: Dissipated energy by additional damping devices

Ei: Induced energy in the structure.

The concept of energy approach (Fig. 2.11) easily explains the energy terms involved in Eq. 2.8. The amount of structural stored energy (Es) has to be as low as possible to avoid damages. Therefore the value of the dissipated energy (Ed) must be great. In the term Eh energy dissipated by hysteretic or plastic deformation may be included; however this part must be kept low, as this way of energy dissipation causes structural yielding and cracks. For that reason, the drastic increase of the value of the energy of additional damping devices is the final opportunity to control the energy balance of the structure.

 Fig. 2.11 Concept of Energy Approach Considering the Energy Exchange Between Structure and Environment

: Stored energy within structure

: Dissipated energy within structure

Thus: