On the effectiveness of rotational friction hinge damper to control responses of multi-span simply supported bridge to non-uniform ground motions

Abstract

Base isolation techniques have been extensively used to improve the seismic performance of the bridge structures. The decoupling of the bridge decks from the piers and abutments using rubber isolator could result in significant reduction in seismic forces transmitted to the bridge substructures. However, the isolation devices could also increase the deck displacement and thus enhance the possibility of pounding and unseating damage of bridge decks. Moreover, previous investigations have shown that pounding and unseating damages on isolated bridges exacerbate due to the spatial variation in earthquake ground motions. Recent earthquakes revealed that isolation bearing could also be damaged due to the excessive movements of decks during large earthquake events. This study proposes the use of rotational friction hinge dampers to mitigate the damages that could be induced by large displacement of bridge decks, particularly focusing on pounding and unseating damages and bearing damages. The device is capable of providing large hysteretic damping and the cost of installing the devices is relatively economical. This article presents numerical investigations on the effectiveness of these devices on a typical Nepalese simply supported bridge subjected to spatially varying ground motions. The results indicate that rotational friction hinge dampers are very effective in mitigating the relative displacement and pounding force, as well as controlling the bearing deformation and pier drift. It is also revealed that the effectiveness of the device is not significantly affected by small changes in the slip forces; thus, small variations in the optimum slip forces during the lifetime of the bridge do not warrant any adjustment or replacement of the device.

Keywords

pounding rotational friction hinge device simply supported bridges spatially varying ground motions unseating

Introduction

Highway bridges are one of the key components of a transportation network and they carry significant importance in providing emergency services after an earthquake. Past and recent earthquakes, such as 1971 San Fernando earthquake, 1994 Northridge earthquake, 1995 great Hanshin earthquake, 2010 Chile earthquake, and many more, revealed that bridges are vulnerable to large ground shakings. In order to improve the seismic performance of both new and the existing bridges, seismic isolation devices have been widely used since last few decades. Seismic isolation is an innovative seismic-resistant design approach that decouples the bridge superstructure from the substructures, reducing the transmitted forces to the piers and abutments. The incorporation of the seismic isolator introduces flexibility at isolation level. As a result, the displacements of bridge decks increase. Since the adjacent bridge decks/abutments might have different vibration frequencies, and ground motion input at different bridge supports is not exactly the same due to seismic wave propagation, the adjacent bridge decks and abutments usually do not vibrate exactly in phase. This out-of-phase vibration results in the relative displacement responses between bridge decks and between a deck and an abutment that leads to two main problems. First, poundings between the adjacent decks or between a deck and an abutment occur if the closing relative displacement exceeds the provided gap size at bridge expansion joints. Pounding of the adjacent bridge structures could cause damages at the expansion joints and could damage adjoining bearings and piers. It can also amplify the relative displacements and contribute toward unseating of bridge spans (Otsuka et al., 1996). The bridge design codes, such as the Japan Road Association (JRA) (2004), specify that the gap size between bridge segments should be large enough to avoid poundings. However, the sizes of the expansion joints have to be limited to allow the traffic to flow smoothly. Therefore, it is often impossible to avoid pounding between the adjacent bridge components with the conventional expansion joints during large earthquake ground excitations. On the other hand, unseating of the bridge spans occur if the opening relative displacement is larger than the provided seat length. Unseating of a bridge span can lead to complete closure of the bridge. As bridges are key components in transportation networks and essential for providing emergency rescue and relief operation after a major earthquake, it is desirable for bridges to not only avoid collapse but also remain functional immediately after an earthquake. Therefore, it is necessary to mitigate unseating and pounding damages of bridges induced by large relative displacement between the adjacent bridge components.

In addition to pounding and unseating damages, large displacement during an earthquake could also damage isolation bearings. For example, during the Tohoku earthquake, Japan in 2011, bearing rupture was observed in multiple bridges, such as the Tobu viaduct where the rupture was caused possibly due to the interaction of the adjacent bridge components (Takahashi, 2011). The failure of the bearing could result in large residual vertical gaps between the girders (Zhu et al., 2004). According to the design specification of highway bridges in Japan (JRA, 2004), the shear strain in the isolation bearing shall be within 250%. Although several researches have been done in the past on preventing unseating damages in bridges, only limited researches have focused on the damages to the bearing during seismic events. Zhu et al. (2004) using a three-dimensional (3D) model evaluated the serviceability of highway bridge with pounding countermeasures. The authors concluded that bearings to be the weakest link in the bridge and are likely to fail during strong earthquake resulting in permanent vertical gaps that could impede the traffic flow. Bi and Hao (2013) used a detailed 3D model of an isolated bridge and reported that bridge girder could dislocate from the bearing and the dislocated girder could pound against rubber bearing leading to further damages. Only limited studies have focused on the bearing protection devices (Choi et al., 2005; Ghosh et al., 2011; Ozbulut and Hurlebaus, 2011; Wilde et al., 2000). It should be noted that these studies did not consider pounding between the adjacent bridge components that could amplify/reduce the bridge displacement. The performance of bearings during earthquake excitations, especially when pounding between the adjacent bridge decks occurs, is not well studied yet.

In order to mitigate the adverse effect of the relative displacement in bridges, different devices have been used. Among them, cable restrainers are the most widely used retrofitting method. However, cable restrainers are only effective to mitigate unseating damages caused by the opening relative displacement but could not directly mitigate pounding impacts caused by the closing relative displacement. Moreover, the commonly used cable restrainers rely primarily on their stiffness to limit the opening relative displacement, which can induce a large tensile force which could result in either failure of restrainers or the connecting element. The large tensile forces transferred to adjoining frame/deck/abutment may also alter the seismic responses of the bridge. To overcome the limitation of cable restrainers, Feng et al. (2000) and Kim et al. (2000) investigated the use of energy dissipating restrainers as passive devices to mitigate the damages at the expansion joint. These studies along with many other studies (Shrestha et al., 2016) reported that energy dissipating devices could be a practical solution to the seismic problem arising on bridges with the expansion joints. Other researchers such as Guo et al. (2009) and Ruangrassamee and Kawashima (2003) investigated the active and semi-active devices such as magneto-rheological (MR) dampers to improve the seismic responses of bridges.

One of the important factors affecting the relative displacement responses between the adjacent bridge components that have been commonly neglected is the spatial variation in seismic ground motions. The spatial variation in the ground motions along the length of an extended bridge is inevitable due to the different arrival times of seismic waves at different locations of a bridge and loss of coherency due to scattering of seismic waves and different soil conditions. Some previous studies, for example, Bi and Hao (2013), Chouw and Hao (2008), Li et al. (2012), and Zanardo et al. (2002), have demonstrated that structural response of the bridges subjected to spatially varying ground motions can be drastically different from that under the usually adopted uniform ground motions. Despite the presented facts, most of the previous studies have either neglected the spatial variability of ground motions by assuming uniform ground motion or only partially considered it by including the wave passage effects (Jankowski et al., 2000) when studying the effectiveness of retrofit devices to mitigate the relative displacement–induced damages. To the best knowledge of the authors, none of the previous studies, apart from the study of Shrestha et al. (2015), has modeled the ground motions’ spatial variability in detail in evaluating the effectiveness of pounding and unseating mitigation devices. Since ground motion spatial variation is inevitable, and it causes significantly different responses between the adjacent bridge components, the study on the retrofit devices to mitigate the relative displacement–induced damages without considering the spatial ground motion variations along the length of the bridge may provide unrealistic results.

In this study, rotational friction hinge damper (RFHD) devices are proposed to mitigate damages in the bridge structures subjected to spatially varying ground motions. These devices have large hysteretic energy dissipation capability at a reasonable cost and are easy to install and maintain. The behavior of the device is nearly unaffected by amplitude, frequency, or the number of the applied loading cycles (Mualla and Belev, 2002). Recently, several friction devices have been tested experimentally and some of these have been implemented in buildings around the world (Mualla and Belev, 2002; Nielsen et al., 2004). However, its efficacy in mitigating the relative displacement–induced damages in the bridge structures has not been explored yet. This study focuses on evaluating the effectiveness of the RFHD on mitigating the relative displacement–induced damages in simply supported bridges caused by spatially varying earthquake ground motions. This study does not focus on comparison of the responses of isolated simply supported bridges to spatially varying ground motions with those subjected to uniform ground motion which could be found elsewhere (Zanardo et al., 2002). It focuses on mitigating the adverse responses of isolated multi-span simply supported bridges subjected to spatially varying ground motions, particularly pounding and unseating damages, as highlighted by Zanardo et al. (2002). The analysis is conducted on a typical Nepalese simply supported bridge with four spans of 25 m each. Extensive numerical analysis is conducted to identify the effectiveness of RFHD on mitigating the damages in the bridge structures. Parametric analyses have been conducted to ascertain the optimum slip force of the RFHD. The investigation also compares the bridge structural responses with two configurations of RFHD.

RFHD

In recent years, the friction dampers have found several applications in both steel and concrete buildings for seismic rehabilitations and up-gradation of the existing structures as well as applications in newly constructed structures (Mualla and Belev, 2002). A key point in the use of the friction dampers in seismic protection of the structures is that their response is not affected by frequency and duration of ground motions. However, their mechanical behavior is likely to induce residual displacement that may require some recovering operations after the earthquake event.

In this study, a type of friction damper, RFHD, is used to mitigate the damages arising in the bridge structures due to the relative displacements of the adjacent bridge components. RFHD consists of rigid steel plates connected in rotational hinge, and the plates are separated by several shims of friction pads as seen in Figure 1(a). The moment–rotation behavior in the hinge is elastic-frictional. The hinge connection is meant to increase the amount of relative rotation between the rigid plates, which in turn enhances the energy dissipation in the system. During the seismic events, the distance between the connection points and the angle between the damper plates in the hinge changes due to the induced seismic motion. Upon reaching the frictional resistance of the device in torsion, slip and relative rotation between the damper plates take place, thus dissipating a portion of the kinetic energy of the structure. The sticking and sliding modes of the RFHDs succeed each other until the end of motion (Nielsen et al., 2004).

Figure 1.

(a) Damper details, (b) details of Rhombus shape damper with double hinges, and (c) sectional detail of hinge including friction pads.

In order to investigate the effects of different configurations of the dampers on the bridge responses, two damper configurations as shown in Figure 1(a) and (b) are studied. The damper configurations are referred as V-type and R-type, respectively. The geometrical features of the friction dampers are provided in Figure 1(b). Figure 1(c) shows the details of friction pads at rotational hinge. The friction plate has length L, width W, and thickness t. The angle between the two adjacent plates is α. The slip force of the friction damper is calculated using the relations given by Chen and Hao (2013)

F_{h} = \frac{nM}{\sqrt{L^{2} - {(H / 2)}^{2}}} = \frac{nM}{L \cos (α / 2)}

(1)

where M is the rotational friction resistant moment at each hinge, n is the number of hinges in a device, and L is the effective length of the plate. The included angle is given by $α$ , and the height of the device is H.

The value of rotational friction resistant moment, M, depends on the friction coefficient, the preload, and the frictional area. The friction force is given by

dF = μ dN = μ pds = μ p \times 2 π rdr

(2)

The resistant moment is given by

dM = rdF = 2 π r^{2} μ pdr

(3)

M = \int_{R_{1}}^{R} dM = \int_{R_{1}}^{R} 2 π r^{2} μ pdr = \frac{2}{3} π μ p (R^{3} - {R_{1}}^{3})

(4)

where F is the rotational friction force at each joint, $μ$ is the friction coefficient, p is the preloading provided by the bolts, R₁ is the inner radius of the friction pad, and R is the outer radius of the friction pad as shown in Figure 1(c).

The two ends of a V-type damper can be connected to the pier and deck of the bridge, respectively, as shown in Figure 2 to mitigate the relative displacement response. The connection detail of the R-type damper is presented in Figure 3. As shown, for an R-type damper, the connection is between deck to deck at the intermediate joints. In the figures, only the connection scheme to control the longitudinal bridge motion is presented as this study considers only the longitudinal bridge responses that are responsible for pounding and unseating. The connection scheme could be easily extended to control both the longitudinal and the transverse bridge responses.

Figure 2.

Connection scheme for V-type dampers.

Figure 3.

Connection scheme for R-type dampers.

As presented, the damper has a very simple mechanism that makes it easy to be assembled and installed. The simplicity allows for installing devices with multiple units in order to meet the required frictional resistance. While applying, the dampers should be placed parallel to the longitudinal axis of the bridge to mitigate the relative displacement responses in the longitudinal direction. In addition, a hydraulic lock-up device that allows slow movements such as thermal expansion but transmit the shocks from high-frequency movement such as earthquake could be placed along with the device.

Previous investigation had showed that the behavior of the friction damper is essentially bilinear (Mualla, 2000; Mualla and Belev, 2002). Due to this behavior, it is quite common to represent a friction damper using rigid plastic link (Mualla and Belev, 2002; Vafai et al., 2001) or elastic perfectly–plastic link in numerical modeling. Bhaskararao and Jangid (2006) studied the response of multiple-degree-of-freedom (MDOF) structures connected using the friction dampers modeled using fictitious springs. The fictitious spring was assumed to having large stiffness during the non-slip mode and zero stiffness during the slip mode. The same concept is utilized here to model the RFHD with a high initial stiffness (k_d) during non-slip mode as shown in Figure 4. The slip takes place whenever the force in the dampers exceeds the slip force $F_{h}$ , which is the limiting force in that friction damper.

Figure 4.

Force–displacement relationship for RFHD.

Bridge model

Bridge description

Figure 5 shows the details of the simply supported bridge considered in this study. The bridge has four spans of 25 m each and the total length is 100 m. These are typical simply supported bridges commonly found in Nepal. The bridge is supported on three piers and two abutments. The piers are of circular geometry with 1.6 m diameter. The total height of the bridge piers from the top of the foundation is 6 m. The bridge deck is slab on girder-type construction with three girders of 2 m depth. The total weight of each 25-m deck is 2.13 MN. The details of the deck and pier-to-deck connections are presented in Figure 6. The deck is supported on elastomeric bearings of area 0.4 m × 0.3 m and thickness of 0.05 m. The piers and abutments are provided with shear keys that inhibit the lateral movement of bridge decks. The abutment is a seating type with back wall of 2 m in height and 7.2 m in width. The length of the seat at the abutment is 0.94 m. All the bridge piers and the abutment rest on a well foundation of diameter of 6 m and depth of 13 m.

Figure 5.

Sectional view of the bridge.

Figure 6.

(a) Bridge geometrical details, (b) hysteretic behavior of elastomeric bearing, and (c) pier reinforcement details.

Numerical modeling

In this study, a two-dimensional (2D) finite element model of the bridge is developed. The geometrical property of the bridge is calculated based on the details of the bridge designs illustrated in Figure 6. The superstructures of an isolated bridge are usually designed to remain elastic under seismic events. Therefore, an elastic beam–column element with the calculated properties is used to model the bridge deck. The piers are modeled using nonlinear beam–column element. Fiber element modeling, also known as discretized-section model for nonlinear analyses, is used in this study to represent nonlinear behavior of the reinforced concrete bridge piers. Reinforced concrete sections are constructed from three materials, namely, unconfined concrete, confined concrete, and reinforcing steel. The unconfined and confined concrete behavior is modeled using the nonlinear concrete model that follows the constitutive relationship proposed by Mander et al. (1988) and the cyclic rules proposed by Martínez-Rueda and Elnashai (1997). The confinement effects provided by the lateral transverse reinforcement are incorporated through the rules proposed in Mander et al. (1988), whereby constant confining pressure is assumed throughout the entire stress–strain range. To represent the behavior of the steel rebars, Menegotto–Pinto steel model (Menegotto and Pinto, 1973) is used. The yield strength of the rebar is 500 MPa, and the elastic modulus, E_s, is 200 GPa. The reinforcement details of the piers are shown in Figure 6(b).

The foundation of the bridge is assumed to be fixed at the top of well foundation. To simplify the problems, interaction between soil and the foundation of the bridge structure is neglected in this study. It is common in engineering practice to use a simplified bilinear model with kinematic hardening rules, as shown in Figure 7(b), to represent the behavior of elastomeric bearings (Naeim and Kelly, 1999). The bilinear model can be completely described by the elastic stiffness, K₁, characteristic strength Q, and post-yielding stiffness K₂. The characteristics strength Q of the bearing is taken as 10% of the weight carried by the bearings. This value has been widely accepted among the bearing designers (Abdel Raheem, 2009; Ali and Abdel-Ghaffar, 1995). The elastic stiffness to post-yielding stiffness ratio, K₂/K₁, is taken as 0.10. The elastic stiffness of the elastomeric bearings is taken as 13.25 MN/m, the post-yielding stiffness is 1.32 MN/m, and the characteristic strength is 98.60 kN.

Pounding between two decks or deck and abutment is modeled using a linear impact spring element with a gap of 25 mm. The stiffness of impact element K_i and the impact force F_i at the impact spring element are expressed as

K_{i} = γ \frac{AE}{L}

(5)

F_{i} = K_{i} \cdot Δ u

(6)

where Δu is the relative closing displacement between the adjoining bridge superstructures beyond the provided gap width. In equation (5), A is the sectional area of the deck, γ is the ratio of the impact spring stiffness to the stiffness of the superstructure, and E is the modulus of elasticity of the deck material. In this study, γ is taken as 2 based on the previous studies on similar bridges (Abdel Raheem, 2009; Ruangrassamee and Kawashima, 2003). The stiffness of the impact spring is calculated to be 7884 MN/m. The abutment of the bridge is modeled using linear spring. The stiffness of abutment spring, K_abut, used in the analysis is 174 MN/m. The abutment springs get activated only in passive direction of the abutment.

The mechanical model of as-built bridge and bridge installed with V-type and R-type RFHD is illustrated in Figure 7(a)–(c), respectively. In the figure, RLinkiL and RLinkiR refer to the rigid link connecting the ith pier with the deck on the left and right sides of the ith pier, respectively, AbutSpr1 is the abutment spring at abutment 1, Br2L refers to the left bearing at Pier 2, and Vtype2L refers to V-type RFHD at the left side of Pier 2. R-type 2 indicates R-type RFHD placed above pier 2.

Figure 7.

Mechanical model of (a) as-built bridge, (b) bridge with V-type dampers, and (c) bridge with R-type dampers at intermediate joints.

Ground motions

The method proposed by Bi and Hao (2012) is used to simulate spatially varying ground motion time histories. The ground motions are simulated to be compatible with the design response spectrum defined in Indian code IS 1893:2002 (2002) for Type III (soft soil) condition normalized to peak ground acceleration (PGA) of 0.65g. The PGA value adopted in this study was determined in recent probabilistic seismic hazard analyses (PSHAs) (Mahajan et al., 2010; Parajuli, 2009; Ram and Wang, 2013) for regions in Nepal and the adjoining areas for rare earthquake events that should be used for designing lifeline bridge structures.

The spatial variation between ground motions recorded at two locations j and k on the ground surface is modeled by a theoretical coherency loss function (Sobczky, 1991)

\begin{matrix} γ_{jk} (i ω) = | γ_{jk} (i ω) | \exp (- i ω d_{jk} \cos α / v_{app}) \\ = \exp (- β ω d_{jk}^{2} / v_{app}) \cdot \exp (- i ω d_{jk} \cos α / v_{app}) \end{matrix}

(7)

where $β$ is a constant reflecting the level of coherency loss, $d_{jk}$ is the distance between the two locations j and k in the wave propagation direction, f is the frequency (Hz), $v_{app}$ is the apparent wave velocity, and $α$ is the seismic wave incident angle. In this study, β = 0.001, and v_app and α are assumed to be 500 m/s and 45°, respectively. The adopted value of β represents the intermediate coherency losses of the spatial ground motions at supports of the bridge. To obtain a relatively unbiased response accounting for the random phase angles of ground motions, five sets of spatial ground motion time histories (referred as GM1–GM5) are simulated independently. The sampling frequency is set to 100 Hz, and the duration of the ground motion is 20.47 s in the simulation. Figure 8 compares the response spectra of the simulated spatial ground motions with the target response spectrum. As shown, the response spectra of the simulated spatial ground motions at the five sites are all compatible with the design response spectrum.

Figure 8.

Comparison of response spectra of simulated ground motions with the design response spectra.

The comparison of the empirical coherency loss function defined by equation (7) between Site 1 and the other sites is presented in Figure 9. A good match can be observed except for $| γ_{15} |$ in the higher frequency range. This is expected since Site 5 is the furthest from Site 1 and the spatial ground motions at these two sites are least correlated. The cross correlation between the spatial motions or the coherency loss decreases with frequency, but the numerically calculated coherency loss between any two spatial ground motion time histories is more than 0.3. This is because the numerically calculated coherency loss has a threshold value of about 0.3–0.4, the value corresponding to the numerically calculated coherency loss between two white noise series as revealed in previous studies, for example Hao et al. (1989).

Figure 9.

Ideal and simulated coherency losses.

Results and discussions

Effects of pounding

Prior to assessing the effectiveness of the friction hinge dampers, the effects of seismic pounding on the response of the structure must be understood. It is well-known that seismic pounding results in damaging impact between the adjacent bridge components; however, its effect on the relative opening displacements at the joints of simply supported bridges subjected to non-uniform ground motions has not been well documented. As relative opening displacement may result in unseating damage, it is important to understand the influence of pounding on the relative opening displacement response. To study this, the as-built bridge model with expansion gap of 25 mm and the assumed gap large enough to avoid contact between the adjacent bridge components are analyzed. As shown in Figure 10, without pounding the deck could move beyond the gap size (negative or closing relative displacement more than 25 mm) and the response is more stable for the duration of the earthquake. When pounding occurs, the closing relative movement is limited approximately to 25 mm at each joint as the gap closes. As shown in the figure, peak joint opening displacements at Joint 1 and Joint 2 due to pounding experience an increase of 33% and 250%, respectively. This indicates that the relative joint separations could be amplified by the pounding of the adjacent segments. As a consequence, the unseating displacements (i.e. opening relative displacement between the bridge deck and supporting pier) of the bridge deck, as presented in Figure 11, may increase, which may lead to unseating failure of the bridge deck if the provided seat width is smaller than the unseating displacement.

Figure 10.

Relative displacements between adjacent decks at (a) Joint 1 and (b) Joint 2 with and without pounding.

Figure 11.

Relative displacements between bridge deck and supporting pier at (a) Joint 1, (b) left side of Joint 2, and (c) right side of Joint 2 with and without pounding.

Effectiveness of RFHD

To evaluate the effectiveness of the RFHD in the bridge structures subjected to spatially varying ground motions, the responses of the as-built bridge model and the bridge model with the V-type damper are analyzed and compared. In this section, without losing generality only the case with the total damper slip force of 186 kN, that is, with two dampers with slip force of 93 kN each placed at two outer girders of the deck as shown in Figure 12, is presented. The performance of the bridges is compared in terms of the peak and standard deviation of pounding forces, peak and standard deviation of the relative displacement, residual displacement, bearing deformation, and pier drift.

Figure 12.

Symmetrical placement of dampers at outer bridge girders.

Figure 13 shows the peak pounding forces at five joints of the bridge for the two bridge models, that is, as-built and with the V-type dampers as shown in Figure 2. The middle point represents the mean peak pounding forces while vertical line represents the mean ±1 standard deviation of the peak pounding force at the bridge joints obtained with the five sets of independently simulated spatially varying ground motions. Thus, the tip of the line represents the 84th percentile value of peak pounding force while the bottom end of the line represents the 16th percentile value of the peak pounding force. As shown, the V-type dampers are effective in mitigating peak pounding forces at all the joints of the bridge. Figure 14 compares the peak relative displacement at five joints of the bridges. The V-type dampers are also effective in reducing the peak relative opening of the joints. As shown, the dampers significantly reduce the relative displacement at all the joints except at Joint 4, which has the least relative displacement without the dampers. This is because the dampers are effective only when the relative displacement is relatively large as damping capacity depends on the opening of the joints and have only limited effect if the relative displacement is small as in the case of Joint 4.

Figure 13.

Pounding forces at five joints: (a) as-built bridge and (b) bridge with V-type RFHD.

Figure 14.

Relative displacement at five joints: (a) as-built bridge and (b) bridge with V-type RFHD.

A factor that could limit the application of the friction damper is its mechanical behavior which is likely to induce residual displacement in the structure that could limit the serviceability of the bridge after an earthquake. In order to evaluate the residual deformation that the dampers can induce at the bridge joints, the residual deformations at all joints are measured and compared with the corresponding residual deformations of the as-built bridge model. As shown in Figure 15, residual deformations at the joints are not significantly altered by use of the friction dampers. The residual deformation could widen the gap or completely close the gap; however, the calculated residual deformations are within a limited range (less than 3 cm) for the considered ground motions, thus would not impede the traffic flow.

Figure 15.

Residual displacement at five joints: (a) as-built bridge and (b) bridge with V-type RFHD.

The damper constraints the movement of the bridge deck and this limits the deformation on the bearings. Bearing deformations without the dampers could be large and could result in the failure of the bearings, potentially generating vertical gaps between the two adjacent decks or deck and approach slab. This study verifies the failure of rubber bearing by observing its peak deformation. Although the bridge codes (JRA, 2004) suggest 250% shear strain as the ultimate shear strain limits, the modern isolation bearings can sustain shear strain up to 400% before failure. In this study without losing generality, a failure criterion of shear strain 300% for rubber bearing is adopted as in a previous study (Zhu et al., 2004). Figure 16 shows the peak deformation of the bearing to five sets of the simulated ground motions for two bridge models. As presented, the bearing deformations in as-built bridge model are large and most of the bridge bearing will be damaged due to the earthquake ground motions. Installing the V-type dampers significantly reduces the deformation demand of the bearings and limits the bearing deformations within the permissible limit.

Figure 16.

Peak deformation of bearings: (a) as-built bridge and (b) bridge with V-type RFHD.

Figure 17 compares the peak drift of the three piers of the two bridge models. As shown, applying the V-type dampers results in an increase in the drift of the bridge piers due to the transfer of forces from the superstructure to the pier. However, this does not significantly affect the bridge pier responses as indicated by only the slight increase in the bridge drift because the slip force of the damper is relatively lower and the damper dissipates some of the kinetic energy. Application of the V-type dampers leads to slightly higher forces on the bridge piers; however, this would not significantly reduce the effectiveness of bridge isolation and only slight increase in peak displacement demand would be expected to bridge piers. Despite this undesirable influence on pier responses, the advantages of using the friction dampers to mitigate the relative displacement responses of the bridge superstructures are obvious.

Figure 17.

Comparisons of peak pier drifts: (a) as-built bridge and (b) bridge with V-type RFHD.

Optimum damper slip force

In order to find out the optimum slip force of the dampers to mitigate the relative displacement responses without significantly increasing the pier responses, analyses are carried out with varying slip forces of the dampers. The slip forces of the dampers can be practically controlled by increasing or decreasing bolt pretension and/or by increasing or decreasing the number of friction plates. In this study, five damper slip forces, that is, 93, 186, 280, 373, and 466 kN, are considered to identify the effects of the damper slip force on the bridge response. This represents the normalized damper slip forces, defined as the ratio of slip force over weight of the bridge deck on bearing supports, of 0.09, 0.19, 0.28, 0.38, and 0.47, respectively. In order to investigate the optimum slip force of the dampers, normalized damper slip forces are used to compare the bridge responses.

Figure 18 compares the mean peak pounding forces and mean peak joint opening at five joints of the bridge for five sets of ground motions. As shown, the pounding forces and relative joint opening are significantly reduced due to the application of RFHD. In general, increasing the RFHD slip forces results in reductions in peak pounding forces and joint opening. However, the rate of pounding force and joint opening reduction decreases with higher slip force. When the normalized slip force is larger than 0.28, further increasing the slip force has insignificant effect on the reduction in pounding force and joint opening displacement. This is because, as will be discussed subsequently, the energy dissipated by the dampers reduces with higher slip forces. The reduction in the energy dissipation reduces the effectiveness of the dampers to mitigate pounding forces between the adjacent bridge components.

Figure 18.

Comparison of (a) mean peak pounding forces and (b) mean peak joint opening.

The energy dissipated by the dampers is affected by the damper slip force. Figure 19 presents the comparison of hysteretic responses of a damper, Vtype4R, with normalized damper slip force of 0.09 and 0.47 subjected to GM2. It is observed that the increase in the slip forces could result in a reduction in damper deformation, and in some cases, the device may form an incomplete hysteretic loop, suggesting a reduction in energy dissipation as well as the presence of some residual displacements. Comparison of bearing shear deformation and pier drift demand subjected to GM2 is presented in Figure 20(a). As shown, the bearing deformations of the bridge model without the dampers are large and exceed the ultimate limit state. Placing the dampers with the normalized damper slip forces of 0.09 reduces the bearing deformations; however, the deformations are still large enough to result in bearing failure. Installing the dampers with the normalized damper slip forces of 0.19 or above reduces the shear deformations below the ultimate strain limit of 300%. The higher the normalized slip forces of the dampers, the more the reduction in bearing shear strain. However, when the normalized damper slip force is larger than 0.38, further increase in slip force has insignificant effect on bearing deformation. Figure 20(b) shows that as the normalized slip force is larger than 0.19, further increase in the slip force results in an increase in the peak drift of the bridge piers. This is because large damper slip force reduces the effectiveness of bearing isolation of the bridge deck, and therefore results in more seismic forces being transferred from bridge decks to the piers.

Figure 19.

Comparisons of force–displacement curves of Vtype4R damper with normalized slip force: (a) 0.09 and (b) 0.47, subjected to GM2.

Figure 20.

Comparison of (a) peak bearing deformations and (b) pier drift subjected to GM2.

The above results indicate that increasing the damper slip force is generally beneficial to mitigating the relative displacement responses; however, it would also result in reduction in energy dissipation and larger pier responses. Therefore, a balance needs to be found for a practical application of the dampers for better protection of not only the bridge superstructures (decks) and connection members (bearings) but also the bridge piers. The results presented also suggest that damper effectiveness is not significantly affected by slight variations in the slip force of the dampers. Hence, small variations in optimum slip force over the life of the bridge do not warrant any adjustment or replacement of the friction dampers.

Effects of damper configuration

To investigate the effectiveness of damper types, responses of bridge model with applications of the V-type and R-type dampers at the different joints are calculated and compared. The results corresponding to five normalized damper slip forces as described above subjected to the five sets of the spatially varying ground motions are compared and discussed. Figure 21(a) and (b) presents the comparisons of the mean peak pounding forces at Joint 3 and mean peak joint opening at Joints 1 and 3 for two damper types with varying normalized damper slip forces, respectively. As shown, the V-type dampers are more effective in mitigating the pounding impact and relative displacement at the joint as it is connected to the bridge piers. The R-type dampers reduce peak opening joint displacement at Joint 3 more effectively than the V-type dampers. However, it should be noted that the peak joint opening at Joint 3 is much smaller compared to that at Joint 1. Figure 21(c) and (d) presents the comparison of shear strain in the bearings and peak drift of three piers with two damper configurations to a set of spatially varying ground motion. The V-type dampers are more effective than the R-type dampers on mitigating bearing deformations; however, it also leads to transfer of large forces to bridge piers resulting in larger deformations. The R-type dampers reduce the pier drift demand as connection is deck to deck and it dissipates some input energy by hysteretic response at the superstructure of the bridge.

Figure 21.

Comparison of (a) mean peak pounding force, (b) mean peak joint opening, (c) bearing shear strain, and (d) pier drift demand for two damper configurations.

From the above results, it can be concluded that in general, the V-type dampers are more effective in reducing pounding and joint opening at the bridge joints. It is to be noted, however, that in the current numerical simulations, in the case of the V-type damper, two friction hinge devices are used at both the sides of each joint connecting the deck to the pier; in the case of the R-type damper, only one friction hinge device with equal slip force as a single V-type unit is used to connect the two adjacent decks. This assumption implies that the force required to make the V-type damper connected joint move is two times of that required to make the R-type damper to move.

The appropriate damper configuration to control the bridge responses thus depends on the responses of the most vulnerable components of the bridge. In the studied bridge, the bearings were weaker components; thus, the V-type dampers that connect the deck to the piers are the appropriate retrofit device as this will lead to reduction in displacement and shearing strains of the bearings. However, more forces are transmitted to the bridge substructures. In case where protection of bridge superstructures from pounding and unseating damages is desired without transfer of additional forces to bridge piers, the R-type dampers are the appropriate selection.

Conclusion

The article presents investigations on the effectiveness of using RFHD to control responses of simply supported bridges subjected to non-uniform ground motions. Five sets of spatially varying ground motions compatible with the design spectrum and empirical coherency loss function along the supports of the bridge are used to simulate realistic relative displacement responses of the bridge. The bridge model is based on a typical Nepalese simply supported bridge. The study found that pounding between the adjacent bridge components could increase relative joint opening, thus enhancing the risk of unseating failures. The results presented in this article suggest that RFHD could be an ideal retrofit device to mitigate the relative displacement–induced damages, such as pounding and unseating damages, abutment back wall deformations, and bearing failure. These devices are capable of reducing the response at the bridge joints by dissipating some of the input energies.

For better mitigation of seismic responses of bridge, the damper with optimum slip force should be provided. Increasing the slip force of the dampers beyond optimum slip force, in general, leads to slight reductions in bridge responses. However, it also increases the pier drift as more forces are transferred to the piers of the bridge. The result presented also shows the effectiveness of the dampers to mitigate the relative displacement–induced damages, such as pounding and unseating, is not significantly affected by small changes in optimum slip force of the dampers. Therefore, small variations on optimum slip forces of the dampers during the life of the bridge do not warrant any adjustment or replacement of the friction dampers.

The V-type dampers are found to be more effective in mitigating pounding and relative opening displacement at the bridge joints. The dampers are also significantly more effective in reducing the deformation demand of the bearings compared to the R-type dampers. However, the V-type dampers could increase the drift demand of the piers because they transfer forces from the superstructure to the bridge piers. The R-type dampers are relatively less effective on mitigating poundings, relative joint displacements, and bearing deformations, but their effectiveness on reducing the piers demands is superior compared to the V-type dampers.

Footnotes

Declaration of Conflicting Interest

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors acknowledge the partial financial support from Australian Research Council (ARC) Linkage Project LP110200906 for carrying out this research.

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