Π7 Bull Earthquake Eng DOI 10.1007/s10518-009-9172-z ORIGINAL RESEARCH PAPER
Restrain of a seismically isolated bridge by external stoppers Stergios A. Mitoulis · Ioannis A. Tegos
Received: 12 December 2008 / Accepted: 13 December 2009 © Springer Science+Business Media B.V. 2010
Abstract The current design of seismically isolated bridges usually combines the use of bearings and stoppers, as a second line of defence. The stoppers allow the development of the in-service movements of the bridge deck, without transmitting significant loads to the piers and their foundations, while during earthquake they transmit the entire seismic action. Despite the fact that stoppers, which restrain the transverse seismic movements of the deck, are used frequently in seismically isolated bridges, the use of longitudinal stoppers is relatively rare, mainly due to the large in-service constraint movements of bridges. The present paper proposes a new type of external longitudinal stoppers, which are installed in stiff sub-structures-boundaries, aiming at limiting the bridge seismic movements. The parametric investigation, which was conducted in order to identify the seismic efficiency of the external stoppers, showed that the interaction of the bridge with the stiff boundaries can lead to significant reductions in the seismic movements of the bridge. Serviceability is appropriately arranged in the paper by expansion joints and approach slabs. Keywords Bridge · External · Stopper · Seismic · Interaction · Restrain · Displacement · Serviceability
1 Introduction The use of stoppers, usually referred to codes as seismic links (Eurocode 8 Part 2 2005) or restraining devices (NCHRP 12-49 2001), is a very frequent structural measure in current Bridge Engineering, especially in seismically isolated bridges. They are used as a second line of defence as they are designed to reduce the possibility of unseating and to secure
S. A. Mitoulis (B) · I. A. Tegos Laboratory of Reinforced Concrete and Masonry Structures, Aristotle University of Thessaloniki, P.O.Box 482, 54124 Thessaloniki, Greece e-mail:
[email protected] I. A. Tegos e-mail:
[email protected]
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the structural integrity of the bridge under extreme seismic movements (Eurocode 8 Part 2 2005). Furthermore, the stoppers protect the bearings against excessive seismic deflections and therefore have the ability to control the seismic movements of the deck. The stoppers, which are restraining the transverse seismic movements of a box-girder or a prestressed I-beam isolated bridge deck, i.e. the transverse stoppers, are used widely in isolated bridges. However, the implementation of longitudinal stoppers is relatively rare. This is mainly due to the serviceability needs of the deck, which are critical for the longitudinal direction of the bridge. Serviceability requires the free contraction and expansion of the deck, due to the annual thermal cycle (Eurocode 1 Part 1–5 2003; Eurocode 8 Part 1 2005) shrinkage, creep (Arockiasamy and Sivakumar 2005) and prestress (PCI 2005). Therefore adequate clearances, namely expansion joints, between the longitudinal stoppers and the deck are required (Eurocode 8 Part 2 2005). The expansion joints should have variable magnitudes along the deck, because the constraint in-service movements of the deck are also varying along the length of the bridge. Furthermore, the longitudinal stoppers are not expected to be mobilised simultaneously during earthquake, because the piers, on which the stoppers are installed, respond with different longitudinal displacements. Therefore, the conventional design of longitudinal stoppers does not seem to be efficient in controlling the seismic displacements of the bridge. In current Bridge Engineering, the control of the longitudinal displacements is usually based on the increase in the damping of the structure (Kawashima 2004), which leads to the use of high damping bearings and, rarely, viscous dampers (Eurocode 8 Part 2 2005). The aforementioned design of bridges can be characterized as conventional, in the sense that the current codes for the design of bridges (Eurocode 8 Part 1 2005; Eurocode 8 Part 2 2005) cover the use and the modeling of these elements, namely bearings and hydraulic dampers. However, in some cases there are structural solutions which can be implemented in order to change the overall resisting system of the bridge (Saiidi et al. 2001), aiming at controlling its seismic response. For example, in case of integral bridges (Arockiasamy and Sivakumar 2005) the increase in the stiffness of the bridge resisting system, by taking into account the participation of the abutments (Caltrans 1999) and the passive resistance of the backfill soil (Dicleli 2005) usually leads to reductions in the seismic movements of the deck. These reductions are mainly observed in the longitudinal direction of the bridge (Mikami et al. 2008; Mylonakis et al. 1999; Tegos et al. 2005). Such unconventional structural measures can be introduced in order to control large seismic displacements of bridges. In the present study high capacity stoppers are proposed to be installed externally at the bridge, aiming at controlling the seismic displacements of the deck. These unconventional stoppers are proposed to be restrained by stiff boundaries, which can be either an external sub-structure or adjacent structures, such as neighboring tunnels. In fact a semi-connection of the bridge with the tunnels which acts as an additional horizontal support of the deck is introduced. This support is formulated by the extension of the deck’s slab on the backfill soil, which is the so-called continuity slab, and an external stopper. Interstructural connections have also been suggested in the past for buildings in order to prevent undesirable pounding effects (Westermo 1989). The semi-connection proposed in the paper is characterized as unconventional, because the seismic actions are not only enhanced by the conventional resisting elements of the bridge–seismic isolation devices and piers–but also by external elements, which participate strongly during earthquake. The proposal is based on the observation that the geomorphology, which leads to the construction of bridges, often requires the construction of tunnels, which are neighboring with the bridge. It is noted that, in many bridge cases, a longitudinal restrain of the ends of the bridge by monolithic connections would not be possible, as the deck would develop large serviceability
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movements and loads to these connections. Hence, the continuity slab, which is proposed to connect the deck with the external stoppers, would probably fail in tension or compression during the bridge service. The present investigation proposes a semi-connection, as appropriate gaps provide on the one hand the appropriate separation of the deck from the external stiff boundaries and on the other hand, the desirable increase in the seismic participation of the semi-connection. The performance of the proposed semi-connection, in terms of serviceability and earthquake resistance, was estimated by an extensive parametric study, which utilized a seismically isolated bridge of PATHE Motorway. This bridge was considered to be the “reference” bridge. The displacements of the deck were considered to be the critical parameter of the analytical study as they describe the response of the overall bridge system and the seismic actions of the bearings and the piers. The serviceability problems of the resulting unconventional bridge system are also addressed. 2 Description of the “reference” bridge The present study used an I-beam precast and prestressed bridge of P.A.TH.E Motorway, which is located at Skarfeia–Raches territory in Greece, Fig. 1a. This bridge was considered to be the “reference” bridge of the study. The bridge is straight, has five spans and a total length equal to 177.5 m. The end spans have a length equal to 34.75 m, while the three central spans have a length equal to 36.0 m. The deck of the bridge, Fig. 1b, consists of six prestressed and precast beams, precast deck slabs and cast in-situ part of the slab. Its width is equal to 14.2 m. The deck is seated on both the abutments and the piers through low damping rubber bearings. The bearings have a circular cross section with a diameter equal to 500 and 450 mm, while the total thickness of their elastomeric rubber is 110 and 99 mm at the abutments and at the piers correspondingly. The piers, Fig. 1c, are hollow circular sections with external diameter equal to 3.0 m and a web thickness equal to 0.5 m. The piers are founded
tunnel A1
P1 34.75 18.20
P2 36.00 16.50
P3 177.50 36.00
A2
P4 36.00
tunnel
34.75
13.60
15.30
(a) 3.00 14.20
2.00
7.50 1.00
2.30 3.00
2.00
2.50
7.00
3.00
(b)
(c)
(d)
Fig. 1 a Longitudinal section of the “reference” conventional bridge located at Skarfeia–Raches territory of P.A.TH.E Motorway in Greece. The cross section of: b the deck at the mid-span, c the pier and d the longitudinal section of the foundation of P1 , P2 and P3
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on 3 × 3 pile groups, Fig. 1c, which are connected to 7.5 × 7.5 m pile-caps. The diameter of the piles is 1.0 m and their length is 7.0 m for piers P1 , P2 and P3 and 13.0 m for pier P4 . The abutment is a conventional seat-type abutment, which provides the required clearance according to Eurocode 8 (Eurocode 8 Part 2 2005) between the deck slab and its backwall. The abutments restrain the movements of the deck in the transverse direction of the bridge, as capacity design stoppers are installed on them. Stoppers, which restrain the transverse movements of the deck, were also used on the piers. The bridge is founded on a ground type B (Eurocode 8 Part 1 2005) and a design ground acceleration equal to 0.24 g was used in the final design. The importance factor adopted was equal to γI = 1.0, while the behaviour factors were equal to 1 for the longitudinal, the transverse and the vertical direction of the bridge, respectively. The bridge described above was considered to be the conventional system, while the so-called “unconventional” bridge is the same bridge system with the additional equipment of the proposed external stoppers implemented at the tunnels at both ends of the bridge deck.
3 The proposed semi-connection The proposed semi-connection of the bridge with the adjacent tunnels consists of two discrete parts, Fig. 2: (a) the continuity slab and (b) the external stopper, namely the linking-key. In the following paragraph an extensive description of these elements is given. Plan view of the semi-connection
continuity slab U-shaped embedment
external stopper ∆2
contact interface
∆1
Detail of the semi-connection external stopper
continuity slab slide-on slab
∆1
∆2 U-shaped embedment
sliding joint deck
continuity slab longitudinal tslab=40cm stirrups reinforcement
expansion joints
frictionless interface concrete slide-on-slab backwall
abutment
shear transfer interface approach embankment
Lkey
tunnel
tunnel foundation shear key (bx t = 1000cm 250cm) U-shaped embedment Bx By = (1000cm+Δ1+Δ2) 250cm
Fig. 2 The proposed restraining system with the continuity slab and the linking-key. Detail Longitudinal section of the semi-connection and the expansion joints and plan view of the semi-connection
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3.1 The continuity slab This slab is the extension of the deck slab towards the backfill soil. It is characterized as “continuity slab” because it eliminates the conventional expansion joint between the deck and the abutment’s backwall. The continuity slab has the ability to accommodate part of the induced constraint contraction of the deck caused by creep, shrinkage, prestressing and thermal contraction. This is achieved by the in-service allowable cracking of this slab, which is developed with narrow cracks, whose widths are of the order of 0.1–0.2 mm (Eurocode 2 Part 1 2004). The length of the continuity slab was considered to be equal to the common distance between the bridge’s abutment and the tunnel, which is usually almost 20.0 m. The transverse dimension of this slab is equal to the width of the deck, namely 14.20 m. The thickness was selected to be 0.30 m and its longitudinal reinforcement ratio equal to 2%. The selection of the reinforcement ratio is related to serviceability criteria, namely to the maximum allowable tension of the deck slab during the bridge total contraction and while the continuity slab has developed its allowable cracking. This reinforcement ratio leads to a maximum in-service tension of the continuity slab which is not affecting the deck’s serviceability. The results of an extensive serviceability check are given in paragraph 6.1 of the manuscript. Appropriate measures against the undesirable in-service friction between the continuity slab and the approach embankment were also considered, as a concrete slide-on slab is provided between the continuity slab and the backfill. The interface between the two slabs, i.e. the concrete slide-on slab and the continuity slab, is proposed to be smooth in order to reduce, as possible, the undesirable friction effects. The slide-on slab also minimizes the flexural deflections of the continuity slab, which are caused by dead and live vertical loading. Finally, a sliding joint between the continuity slab and the abutment’s backwall of the bridge also minimizes the undesirable friction between these elements. 3.2 The semi-connection As it was underlined in the introduction, the monolithical connection of the bridge with the external stiff boundaries, i.e. with the tunnels, is not always possible, due to the large constraint movements of the long deck. Under this restraint, only a semi-connection of the bridge deck with the external stiff boundaries is possible to accommodate the conflict between the design requirements imposed by serviceability and earthquake resistance. The formulation of the aforementioned semi-connection is accomplished by the provision of appropriate expansion joints, namely gaps, between the continuity slab and the tunnel’s foundation and, more specifically, between the linking-key and the appropriately reformed U-shaped embedment. The semi-connection, see Detail in Fig. 2, is formulated, on the one hand, by the increase in the thickness of the continuity slab and, on the other hand, by the extension of the tunnel’s foundation towards the backfill and the construction of a U-shaped embedment, in which the linking-key is restrained, Fig. 2. The embedment restrains the longitudinal movements of the continuity slab when either gap 1 or 2 is closed. The transverse movements are also restrained, as the linking-key is proposed to be in contact with the U-shaped embedment in the longitudinal direction of the link, see the plan view of the semi-connection in Fig. 2. The linking-key and the continuity slab are reinforced with transverse reinforcement in order to protect these elements against the high shear loading, which is developed due to the seismic interaction of the bridge with the tunnel.
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The semi-connection provides two expansion joints, whose widths, 1 and 2 , see Detail in Fig. 2, accommodate only part of the in-service induced movements of the deck. The procedure followed for the selection of the widths of these gaps is described below under the main objective of the study, which is the increase in the seismic participation of the link and the total earthquake resistance of the bridge. The external stopper described above restrains the movements of the continuity slab and consequently the deck, when the longitudinal seismic displacements of the bridge are greater than the gaps provided between the external stopper and the U-shaped embedment. It is underlined that the minimization of the width of these gaps leads to smaller pounding forces (Jankowski et al. 2000). Furthermore, smaller clearances increase the seismic efficiency of the semi-connection, because the seismic movements of the deck are reduced more effectively according to Tegos et al. (2005). Hence, narrower joints are expected to reduce more effectively the actions and, consequently, the structural cost of the piers (Nutt and Mayes 2000). The conventional bridge design requires expansion joints, whose widths are usually determined according to codes (Eurocode 8 Part 2 2005), which usually take into account the inservice (Purvis 1998) and part of the seismic displacement actions. The reason that leads to smaller expansion joints in current Bridge Engineering is mainly economy. Specifically, the cost of providing a road joint to accommodate large seismic deflections may be prohibitive and usually a compromise is adopted (Gloyd 1996). The reduction in the seismic joints leads to the finding that the contact interaction of the bridge deck with the abutment’s backwall is inevitable during earthquake. Furthermore, the backwall, which interacts with the deck, is usually connected to the stiff wing-walls and this interaction can lead, in some cases, in stability problems of the abutment, namely slumping and rotations (Priestley et al. 1996; Chen and Duan 1999). Therefore, the development of the contact interaction between the bridge deck and the tunnel, which is proposed in the present paper, cannot be considered as an additional design problem. On the contrary, appropriate measures, like the ones described above, can lead to improvements of the serviceability performance, while capacity design checks can control safely the prospected seismic interaction of the external stopper with the tunnel’s foundation. 3.3 Determination of the expansion joints at the semi-connection According to the design procedure described above, the widths of the expansion joints, which separate the linking-key from its embedment, were determined as follows. The effects of creep and shrinkage were taken into account by considering an equivalent uniform thermal contraction of the deck equal to −30◦ C, according to PCI (PCI 2005). This uniform temperature was found to cause a constraint contraction of the deck equal to the one caused by creep and shrinkage. A probabilistic approach was applied according to Eurocode 1 (Eurocode 1 Part 1–5 2003) in order to determine the constraint thermal movements. The procedure was implemented under the main objective of the study, which is the minimization of the widths of the expansion joints, 1 and 2 . Under these design considerations, the deck of the bridge is not being compressed during its maximum thermal expansion (Eurocode 1 Part 1–5 2003), as joint 1 is designed to be always open. Joint 1 remains open even in the first years of the bridge service, and while creep and shrinkage effects, which cause a permanent contraction of the deck, have not been developed yet. More specifically, after the completion of the bridge construction, joint 1 can absorb the maximum constraint thermal expansion (Eurocode 1 Part 1–5 2003), namely a total of +25◦ C bridge uniform temperature. After the first years of the bridge service, and while
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creep and shrinkage effects have almost been completed, part of joint 1 can be closed in order to maximize the seismic participation of the proposed semi-connection. The width of the second joint, 2 , was adjusted by taking into account the maximum movements of the deck due to creep, shrinkage, prestressing and thermal contraction. The determination of 2 is influenced by three discrete design criteria: (a) the control of the maximum allowable tension of the deck, (b) the in-service allowable cracking of the continuity slab and (c) the minimization of the width of the joint, which ensures the desirable seismic participation of the external stopper. The widths of joints 1 and 2 can vary, at the beginning of the seismic event, due to the expansion or the contraction of the deck and due to the permanent contraction of the deck caused by creep, shrinkage and prestressing. The present study considered two different states of the joints at the beginning of the seismic event, which correspond to the two extreme cases: (a) the maximum contraction of the deck, which corresponds to 1 = 4.7 cm, while joint 2 is closed namely 2 = 0 and (b) the maximum expansion of the deck, which corresponds to 1 = 2.5 cm and 2 = 2.2 cm. It is noted that the initial widths of these joints, and while creep and shrinkage effects have not been developed yet are: (a) 1 = 2.2 cm, which covers the total thermal expansion of the deck and (b) 2 = 2.5 cm, which accommodates part of the deck’s constraint contraction due to creep, shrinkage, prestress and thermal contraction. The continuity slab accommodates the rest of the constraint contraction of the deck, as it can absorb a total of 2.4 cm due to its in-service allowable cracking. The aforementioned clearances at the joints can be further reduced because, after the completion of the bridge construction, creep and shrinkage effects have been almost fully developed. A calculation conducted according to Eurocode 2 (Eurocode 2 Part 1 2004) showed that these effects have developed its constraint movements by up to 80%, when the construction of the bridge deck is completed. The aforementioned finding allows further reduction in the width of joint 1 up to 2.5 cm, as the width of 1 is always greater than this value after the completion of the structure. However, the rest of the constraint contraction due to creep and shrinkage effects, which is almost 20% of the total constraint movement, lead to a 0.2×2.7 = 0.6 cm reduction of the desired closure of 1 . Therefore, the total reduction of 1 after the completion of the bridge construction can be up to 2.5–0.6 = 1.9 cm. Finally, 1 can vary between 2.8 and 0.3 cm, while 2 can vary between 0 and 2.2 cm. The aforementioned variations of the joints are referring to the maximum thermal expansion and contraction of the deck, respectively. The modeling of the response of the external stopper finally took into account the average value of the aforementioned variation of each joint, namely 1 was considered to be equal to 1.6 cm and joint 2 was considered to be equal to 1.1 cm, see Detail in Figs. 2 and 5c.
4 Modeling of the analysed bridge systems 4.1 Modeling of the “reference” bridge system The seismically isolated bridge described in paragraph 2 of the paper was modeled and analyzed in two different versions: (a) the conventional bridge model, namely the “reference” bridge, which was validated by the refined analysis, which was conducted for the as-built bridge given in Fig. 1 and (b) the unconventional bridge model, which included the model of the conventional one with the addition of the proposed semi-connections on both ends of the bridge. It is underlined that both models–conventional and unconventional–had the same geometry, namely the same total length, cross sections of the deck and the piers and the same foundation.
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The analysis of both bridge systems allows the use of simplified stick models, which are models with only beam elements. The use of stick models is related to the fact that the results of the dynamic analysis are only depended on the stiffness, the mass and the damping of the bridge system. In Fig. 3 the stick model of the “reference” bridge is given. The deck of the bridge was modeled by 29 frame elements, which have the section properties of the deck, given in Fig. 1b. The deck is supported on both the abutments and piers through elastomeric bearings. These bearings were modeled by link elements corresponding to the total resistance of the six bearings supporting the span of the deck on each pier, see Detail 1 in Fig. 3, and on the abutments. The stiffness of these link elements was calculated according to Naeim and Kelly (1999) model. In Table 1 the values of the total stiffness of the link elements used for the modeling of the six bearings are given. The modeling of the six identical bearings by using only one link element is related to the reduction in the duration of the time-consuming non-linear analysis. Stiff zones were used in order to take into account the distance of the center of gravity of the deck’s cross section from the head of the bearings and also the width of the pier’s head, see Detail 1 in Fig. 3. Constraints over each abutment and each pier were used in order to equalize the transverse displacements of the deck with the corresponding ones of the supporting abutments and piers. These constraints are needed due to the construction of transverse stoppers at the as-built bridge system. The piers were modeled by frame elements and each element had a length equal to 3.0 m. The flexibility of their deep foundations was also taken into account by assigning six spring elements–three translational and three rotational at each pier’s foot. The corresponding stiffness values are given in Table 2. These values were obtained by the geotechnical in-situ tests conducted for the design of the as-built bridge. The Detail in Fig. 3 shows the joint in which the six spring elements are connected with the frame elements of the piers. This point is also the centre of gravity of the pile-cap, which is in accordance with the as-build bridge’s final design assumptions.
Table 1 Stiffness values of the link elements used for the modeling of the six bearings supporting a span of the deck on each pier or abutment, (see Detail 1 in Fig. 3) Translational springs
Kx,tot (KN/m)
Ky,tot (KN/m)
Kz,tot (KN/m)
Bearings on abutments Bearings on piers
9639 8675
9639 8675
3.32. 106 2.99. 106
Rotational springs
KRx,tot (KN/ rad)
KRy,tot (KN/ rad)
KRz,tot (KN/ rad)
Bearings on abutments Bearings on piers
6.06×107 5.46×107
51940 37864
175711 158139
Table 2 Stiffness values of the spring elements used for the modeling of the flexibility of the piers’ foundations, (see Detail 2 in Fig. 3)
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Stiffness value
Pier P1
Pier P2
Pier P3
Pier P4
Kx = (KN/m) Ky = (KN/m)
1.8×106 1.8×106
1.5×106 1.5×106
1.7×106 1.7×106
3.3×106 3.3×106
Kz = (KN/m)
1.2×107
9.9×106
1.1×107
9.5×106
Krx = (KN/ rad)
5.6×107
4.8×107
5.2×107
4.7×107
Kry = (KN/ rad)
5.6×107
4.8×107
5.2×107
4.7×107
Krz = (KN/ rad)
4.0×107
4.0×107
4.0×107
4.0×107
Bull Earthquake Eng Detail 1 1
2
3 4 5
6
1 slab connecting spans
2 deck 3 stiff zone (from bearing's head to deck's center of gravity) 4 link corresponds to 6 bearings 5 stiff zone (width of the pier's head) 6 pier (frame elements) deck (29 frame elements)
z
x
Detail 1 Detail 2
piers
P1
P2
P3
P4
(a) Detail 2 1 Pier Pi (frame element) 2 hinge of Pi 3 stiff zone
Krxi, Kryi, Krzi
Kxi,Kyi Kzi 4 spring elements (foundation's flexibility)
2 3
1
pier's bottom cross section
4
(b) Fig. 3 The model of the as-built conventional bridge. a Detail 1 Longitudinal section of the deck’s seating on the pier through bearings and modeling of the connection with frame and link elements, b Detail 2 The spring elements used for the modeling of the foundation’s flexibility and the possible plastic hinge at the bottom cross section of the pier
The possible plastic hinges of the feet of the piers were also modeled, see Detail 2 in Fig. 3. The required moment-curvature (M − φ) curves were calculated by means of RCCOLA-90 (Kappos 2002). Piers P1 , P2 and P3 have equal longitudinal and transverse reinforcements and consequently the resulting M − θ curves are almost identical for these piers, see Fig. 4. The M − φ curves are kept the same in both directions of the piers, as their reinforcement and cross section are symmetrical in both axis, i.e. longitudinal and transverse. The critical point of the M − θ curve used is the definition of the rotational capacity θpu . This capacity can be estimated by multiplying the plastic curvature by an equivalent plastic hinge length Lpl .
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80 000
My (KNm)
Piers P1, P2, P3
60 000 40 000 20 000 Pier P4
0
0
0.005
0.01
0.015
θ (rad)
continuity slab
Detail
z
deck (28 frame elements) piers
x
(a) P1
P2
P3
P4
Detail multi-linear links transverse restraint
7.10m
Pkey tension of the slab
y
7.10m Kimp ∆2 Cimp ∆ 1
x continuity slab (frame elements) stiff zones
(b)
∆1=1.6cm compression of the slab
5
Kimp=7.2 10 KN/m ux ∆ 2=1.1cm
(c)
Fig. 5 a The model of the unconventional bridge system, b Detail The three multi-linear links used for the modeling of the external stopper (plain view), and c the multi-linear link, which models the response of the semi-connection
The last was calculated according to Priestley et al. (1996). The post-elastic stiffness of the piers was assumed to be equal to 2.0% of the initial elastic one. It is noted that the program used for the analysis, which is SAP 2000 ver. 11.0.3 (Computers and Structures Inc 2007), models the plastic hinges by non-linear rotational spring elements. 4.2 Modeling of the proposed semi-connection The model of the unconventional bridge includes the model of the conventional one with the addition of the proposed continuity slab and the external stopper at both ends of the bridge. The model of the unconventional bridge system is given in Fig. 5a. The proposed semi-connection, given in Fig. 2 consists of two discrete parts: (a) the continuity slab, which is the extension of the deck slab of the bridge onto the backfill and, (b) the linking-key, which consists of a stopper and the U-shaped embedment constructed in the foundation of the tunnel, see the Detail of the semi-connection in Fig. 2. The continuity slab was modeled by frame elements whose cross section had a transverse width equal to 14.2 m and a thickness equal to 0.30 m. The axial resistance of the continuity slab during its tension was determined by the axial stiffness of its longitudinal reinforcements, as this slab develops cracks, which are allowable during the bridge service. These reinforcements on the one hand ensure the required distribution of the slab’s cracks and, on
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the other hand, they control the maximum in-service axial tension of the deck slab. The axial resistance of the continuity slab during its compression was determined by the axial stiffness of a frame element which has the cross section of the continuity slab and a length equal to 20.0 m, which is equal to the distance between the bridge and the tunnel’s foundation. It is noted that the continuity slab is compressed only during earthquake, as joint 1 , given in Fig. 2, is not closing during the maximum thermal expansion of the deck. In paragraph 3.3 the determination of joints 1 and 2 at the semi-connection was extensively discussed. The response of the linking-key was modeled by multi-linear links, which take into account both joints 1 and 2 , Fig. 5b, c. The aforementioned multi-linear links have three discrete branches: (i) a compression branch, which models the case that the deck is moving towards the tunnel during earthquake and 1 is closed, (ii) a tension branch, which models the case that the deck is either drawing away from the tunnel during earthquake or is contracting during service, and 2 is closed and (iii) a constant branch, which models the case that both gaps, 1 and 2 , are open and consequently the bridge and the tunnel are not interacting, namely the resistance of the external stopper is negligible. The stiffness of the compression and tension branches correspond to the stiffness of the contact element, i.e. Kimp , which models the collisions between the continuity slab and the tunnel, see Fig. 5b. The stiffness of this contact element was determined by the axial stiffness of the slab of the deck, which is equal to 7.2 × 105 KN/m, (Anagnostopoulos 2004; Jankowski et al. 2000). The damping, which occurs due to the inelastic collisions of the deck with the foundation of the tunnels, was modeled by an equivalent viscous damper, i.e. Cimp , according to Anagnostopoulos (2004). It is underlined that the foundation of the tunnel was considered to be stiff and, consequently, one joint of each multi-linear link was fixed, while the other one was connected to the continuity slab, see Detail in Fig. 5b. It is noted that three multi-linear link elements were used in order to model the response of each linking-key, see Detail in Fig. 5b. The use of three multi-linear links is mainly related to the possible participation of the linking-key during the transverse seismic response of the bridge. This is due to the fact that the rotations of the continuity slab, about the vertical axis, can lead to the closure of the gaps at the multi-linear link. Therefore, the use of one multilinear link would not be adequate to model this effect. The link elements are connected to the continuity slab by transversely directed stiff zones, see Fig. 5b, which correspond to the in-plane stiffness of the continuity slab. Also, the transverse displacements of the continuity slab were restrained at the linking-key as the last is in contact with the U-shaped embedment, see the plan view of the semi-connection in Fig. 2.
5 Parametric study The proposed interlocking of the seismically isolated bridge by the external stoppers was parametrically investigated in order to identify the earthquake resistance efficiency of the restraining system, mainly in terms of percentage reductions in the deck’s displacements. The parameters of the analytical study are related to the design spectrum considered, namely the ground type and the peak ground acceleration. Specifically, the “reference” and the unconventional bridge systems were subjected to artificial accelerogramms that were compatible to ground type A, B and C dependent Eurocode 8 elastic spectra, (Eurocode 8 Part 1 2005) and two different peak ground accelerations, 0.16 and 0.24 g, were considered. The nonlinear dynamic time history analysis used five (5) artificial accelerograms for each different ground type and the maximum values of the calculated displacements were considered. The non-linear response of the resulting bridge systems was analyzed using the FEM code SAP
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2000 ver. 11.0.3 (Computers and Structures Inc 2007). Dynamic non-linear time history analysis was implemented and the average acceleration Newmark (constant) method was chosen (Chopra 1995), as this method is the most robust to be used for the step-by-step dynamic analysis of large complex structural systems. The mass and stiffness proportional damping was chosen and critical damping ratios equal to 5 and 4% were considered for the first and the second period of the analyzed bridge systems according to Aviram et al. (2008). 6 Analytical results and discussion 6.1 Serviceability The serviceability needs of the deck are accommodated by two different structural measures: (a) the use of expansion joints (gaps) at the semi-connection, and (b) the in-service allowable cracking of the continuity slab. The widths of the joints and the in-service cracking of the continuity slab have already been discussed above, see paragraph 3.3. In the present paragraph a check of the in-service loading of the deck is given. The check was deemed to be necessary in order to ensure that the deck can withstand the in-service induced loading, which influences the detailing, namely the thickness and the reinforcement, of the continuity slab. One of the most critical design aspects of the proposed semi-connection is the in-service actions transmitted to the deck by the continuity slab. These actions are mainly tension and the resulting bending, due to the eccentricity of the axial load from the center of gravity of the deck’s cross section. The expansion of the deck is not affecting the serviceability of the proposed semi-connection, neither the serviceability of the deck, as this constraint movement is fully absorbed by expansion joint 1 , see Fig. 2. Therefore, the only longitudinal movements that affect the serviceability of the deck, relatively to the proposed semi-connection, are the movements corresponding to creep, shrinkage and thermal contraction effects. Joint 2 can absorb part of this constraint movement. The rest of the movement is absorbed by the in-service allowable cracking of the continuity slab, as commented in paragraph 3.3 of the paper. In that case, and while the continuity slab is cracked, only its longitudinal reinforcements are resisting to the resulting tension. Hence, the longitudinal reinforcement of the slab controls the maximum tension force, which is transmitted to the deck by the external stopper. If a reinforcement ratio equal to 2.0% and a modulus of elasticity of steel equal to 200 GPa are considered, the total axial stiffness of the longitudinal bars is 8.5 × 105 KN/m. For a constraint movement equal to 2.4 cm, the aforementioned longitudinal reinforcement resists with a total force equal to 20 × 103 KN. The analytical study concluded that the aforementioned axial load and the resulting moment, due to the load’s eccentricity, do not affect the serviceability of the deck. 6.2 Comparison of the dynamic response of the analyzed bridge systems The present study dealt, on the one hand, with the optimization and the serviceability of the proposed semi-connection and, on the other hand, with the comparison of the dynamic response of the conventional and the unconventional bridge system. This comparison was considered to be important as the seismic participation of the external stoppers was expected to modify strongly the dynamic response of the bridge. In Figs. 6 and 7 three important mode shapes and the corresponding participation factors of the conventional and the unconventional bridge system are given. It is noted that the displacements, which are given in order to characterize the mode shapes as longitudinal
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x
0.012 0.018 0.019
y 0.
014
0.021 0.013 0.014
0.013 0.020
T1=1.72s Participation 92%
2nd Mode: Transv. T2=0.85s Participation 82%
10th Mode: Transv. T10=0.20s Participation 7%
Fig. 6 The mode shapes and the participation factors of the conventional bridge system
x y
0.010 0.019 0.020 0.011
1st Mode: Transv. T1=0.66s Participation 77%
0 .0
02
8th Mode: Long. T8=0.22s Participation 5%
0 .0
14
12th Mode: Long. T12=0.17s Participation 63%
Fig. 7 The mode shapes and the participation factors of the unconventional bridge system
or transverse, do not correspond to real modal displacements and they only reflect the relative displacements of the joints of the deck. The model of the unconventional bridge system used multi-linear elements, which do not participate during the modal analysis. The mode shapes in that case resulted by considering linear spring elements instead of non-linear impact elements during the analysis. The stiffness of the spring elements was equal to the stiffness of the impact elements, i.e. Kimp , used for the modeling of the semi-connection. The influence of the gaps, existing between the external stopper and the U-shaped embedment, were not taken into account for the estimation of the values of the linear spring elements, because the response of the unconventional bridge system alters only when the strong interaction of the bridge with the tunnel takes place, namely when the gaps are closed. The comparison between Figs. 6 and 7 shows that the proposed semi-connections of the bridge with the tunnels lead to an increase in the overall stiffness of the system. The period of the first transverse mode shape is up to 22% reduced in the unconventional bridge system, in comparison to the period of the conventional one. Specifically, the first transverse period of the conventional bridge system is 0.85s, see 2nd mode shape in Fig. 6, while the first transverse period of the unconventional bridge system is 0.66 s, see 1st mode shape in Fig. 7. The participation factors are 82 and 77% for the conventional and the unconventional bridge system correspondingly. In the longitudinal direction, the participation of the external stoppers also influences strongly the dynamic response of the bridge. The reduction in the period of the first longitudinal mode is up to 87%. Specifically, the period of the bridge is reduced from 1.72 s, see 1st mode shape in Fig. 6, to 0.22 s, see 8th mode shape in Fig. 7. However, the corresponding structural acceleration of the bridge is reduced, despite the fact that the reduction in the modal period of the bridge usually leads in increases in its spectral acceleration. The spectra illustrated in Fig. 8a, which represent the structural accelerations of the conventional and the unconventional bridge system, show that the acceleration, corresponding to the longitudinal
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30
50
ξ=5%
unconventional bridge
Sa,Y(m/s2)
Sa,x(m/s2)
40
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20
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10
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0 0.0
0.22
1.0
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0.0
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0.2
0.66 0.6
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Period (s)
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0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25
unconventional bridge
0.03m -0.19 conventional bridge
0
5
10
15
20
Transv. displacement (m)
Long. displacement (m)
Fig. 8 The structural accelerations spectra of the conventional and the unconventional bridge deck: a Longitudinal and b transverse direction, (ground type: C, ground acceleration: 0.24 g) 0.15
-0.13
conventional bridge
0.1 0.05 0 -0.05
0.09m
-0.1 -0.15
unconventional bridge
0
5
10
Time (s)
Time (s)
(a)
(b)
15
20
Fig. 9 Comparison of the time histories of the a longitudinal and the b transverse seismic displacements of the deck of the conventional and the unconventional bridge system, (ground type: C, ground acceleration: 0.24 g)
mode shape of the bridge systems, is reduced from 15.7 to 14.6m/s2 . It is noted that the aforementioned reduction refers to the case that both bridge systems are subjected to artificial ground motion that is compatible to Eurocode’s 8 (Eurocode 8 Part 1 2005) elastic spectrum for a ground acceleration equal to 0.24 g and for a ground type C. The spectra of Fig. 8b show that the acceleration, which corresponds to the transverse mode shape of the bridge systems, is increased from 14.8 to 39.2 m/s2 , which means that the proposed semi-connection also affects strongly the structural accelerations in the transverse direction of the bridge. At this point, it was deemed to be necessary to explain how the acceleration response spectra given in Fig. 8a, b were obtained and what they actually represent. An elastic spectrum would not be adequate to describe the non-linear effect of pounding interaction between the deck and the tunnel neither its influence on the response of the bridge. In that case, response spectra with pounding effects are usually introduced (Ruangrassamee and Kawashima 2001). The spectra shown in Fig. 8a represent the structural pseudo-accelerations in the longitudinal direction of the conventional and the unconventional bridge system, for a critical damping ratio equal to 5%. The spectrum, which corresponds to the unconventional bridge system, describes the prospective longitudinal accelerations of the deck for different modal periods of the bridge and takes into account the interaction effects. It is observed that the 1st longitudinal period of the unconventional bridge system (0.22 s) is away from the dominant periods of the response spectrum, namely away from 0.15 or 0.50 s, which would lead to high inertial seismic loads, due to the contact interaction of the deck with the tunnel. Figure 9a, b show the time histories of the displacements of the central joint, specified above, of the deck for the two bridge systems. Figure 9a corresponds to the seismic
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displacements of the deck in the longitudinal direction of the bridge, while Fig. 9b illustrates the corresponding displacements in the transverse direction. The last figures show that the unconventional bridge system responds with smaller displacements in both the longitudinal and the transverse direction. The time histories also show that the overall resisting system of the unconventional bridge becomes stiffer. The above note concerns both directions and is more intense in the longitudinal direction of the bridge. The time histories given in Fig. 9 correspond to an artificial accelerogramm, which is compatible to Eurocode’s 8 (Eurocode 8 Part 1 2005) elastic spectrum for a ground acceleration equal to 0.24 g, and to a ground type C. 6.3 The reductions in the seismic displacements of the analyzed bridge systems The present study is focused on determining the earthquake resistance of the proposed semiconnection. The semi-connection has the ability, on the one hand, to restrain the seismic movements of the bridge, and on the other hand to accommodate the serviceability needs of the bridge deck. The efficiency of the system was mainly assessed by calculating the percentage reductions in the longitudinal and transverse seismic movements of the bridge deck. The reduction in the deck’s seismic movements can be attributed to the energy dissipation that occurs due to the inelastic collisions of the deck with the foundation of the tunnels, (Anagnostopoulos 2004; Jankowski et al. 2000). On the other hand, the interaction of the deck with the stiff foundation of the tunnel also reduces effectively the movements of the bridge deck. This effect has also been reported by Maragakis (1985). His study concluded that the seismic design loading can be appropriately lowered in case the restraint at the abutments is taken into account. Also, Des Roches (2002) and Muthukumar (2002) have found that in general the pounding interaction between a stiff and a flexible structure usually reduces the demand in the flexible one. In the present study the seismically isolated bridge corresponds to the flexible, while the stiff boundaries, i.e. the tunnels, correspond to the stiff structure. The percentage reductions in the deck’s seismic movements, which are expressed by Eq. (1), resulted by comparing the response of the “reference” with the response of the unconventional bridge system. The displacements of the deck were considered to be a critical parameter of the study, as they give a description of the overall system response and are also representative of the seismic actions of the bearings, the piers and the foundations. uE,UNCONV. P.R. = 1 − · 100 (1) uE,CONV. In the above equation, P.R. is the percentage reduction in the movements of the deck, (longitudinal or transverse), uE,UNCONV. is the seismic displacement of the deck of the unconventional bridge and uE,CONV. is the seismic displacement of the deck of the conventional bridge. It can be extracted that if P.R. > 0 then the unconventional bridge system responds with smaller displacements and consequently the proposed restraining system is efficient. Figure 10a shows the variation of the P.R. factor in case both bridge systems are founded in a region with low seismicity, i.e. Seismic Zone I that corresponds to a peak ground acceleration equal to 0.16 g. The horizontal axis corresponds to the deck joints above its sequential supports along the deck, i.e. A1 , P1 , P2 , P3 , P4 and A2 , where Ai is the support of the deck on i-abutment, while Pi is the support of the deck above i-pier. It is observed that the proposed interlocking of the bridge by the external stoppers is able to reduce the longitudinal
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Soil:
A
B
C
80% 60% 40% 20% 0%
ag=0.16g
A1
Joint of the deck over: P1 P2 P3 P4 A2
(a)
50%
P.R. % Reduction in transv. movements u y
P.R. % Reduction in long. movements u x
100%
Soil:
A
B
C
40% 30% 20% 10% 0%
ag=0.16g
A1
Joint of the deck over: P1 P2 P3 P4 A2
(b)
Fig. 10 The percentage reduction (P.R.): a in the longitudinal and b in the transverse movements of the deck of the unconventional bridge system for three different ground types, (ground acceleration: 0.16 g)
movements of the deck by 71–78%. This improvement of the bridge’s seismic response can lead to cost-effective bridge design, as on the one hand the piers’ reinforcement can be reduced and on the other hand, the cost of the rubber bearings is reduced, because smaller heights of the bearings’ elastomer would be adequate for the pre-assumed seismic action. Furthermore, the maintenance cost of the unconventional bridge is expected to be lower, in comparison to the corresponding cost of the conventional one. The last note is related to the elimination of the needed modular expansion joints and to the lower cost of bearings, which would have to be replaced after their service life. Figure 10a also shows that the proposed interlocking system is more efficient in bridges which are founded on soft ground types i.e. C instead of A, as, in that case, the semi-connection has higher efficiency–by up to 5%. Specifically, the movements of the deck of the bridge, which is founded on ground type A, are up to 73% reduced, while the corresponding reduction is 78% in case the bridge is founded on the flexible ground type C. The increased efficiency of the stoppers in bridges, which are founded on soft ground types, can be attributed to the fact that these bridge systems respond with large seismic displacements. Therefore, the semi-connection is participating strongly during earthquake. Figure 10b illustrates the percentage reductions–P.R. factors–for the transverse seismic movements of the deck, in case the peak ground acceleration is equal to 0.16 g. The comparison shows that the external system also contributes in the transverse direction of the bridge as the seismic displacements of the deck are up to 39% reduced. The restraint is more effective over the end piers P1 and P4 , while the desired influence of the external stoppers is reduced over the central piers P2 and P3 . This is attributed to the fact that the continuity slab is acting as a plate during the transverse earthquake motion of the bridge. Therefore, its rotational resistance about vertical axis is mainly causing the reductions in the transverse seismic displacements of the deck. The influence of this rotational restraint, introduced by the continuity slab, is weakening in the central part of the bridge deck. It is noted that the transverse seismic action did not lead in the closure of the gaps at the linking-key. This means that the reductions observed in the transverse seismic movements of the unconventional bridge are only due to the restrain of the continuity slab at the transverse direction of the linking-key, with which it is in contact, see the plan view of the semi-connection in Fig. 2 and the Detail in Fig. 5b. Also, the proposed semi-connection seems to be more efficient in bridges which are founded on stiff ground types, i.e. ground type A instead of C. In Fig. 10b no values are given above the abutments, because the transverse displacements of the deck of both the conventional
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P.R. % Reduction in long. movements u x
100%
Soil:
A
B
C
80% 60% 40% 20% 0%
ag=0.24g
A1
Joint of the deck over: P1 P2 P3 P4 A2
(a)
P.R. % Reduction in transv. movements u y
Bull Earthquake Eng 50%
Soil:
A
B
C
40% 30% 20% 10% 0%
ag=0.24g
A1
Joint of the deck over: P1 P2 P3 P4 A2
(b)
Fig. 11 The percentage reduction (P.R.): a in the longitudinal movements and b in the transverse movements of the deck of the unconventional bridge system for three different ground types, (ground acceleration: 0.24 g)
and the unconventional bridge system are restrained by stoppers. Consequently, the deck is not moving transversely over the abutments. Figure 11a shows the variation of the P.R. factor for the increased seismicity, namely for a ground acceleration equal to 0.24 g. The P.R. factors represent the reduction in the longitudinal movements. The figure shows that the longitudinal movements of the unconventional bridge deck are up to 83% lower than the corresponding ones of the conventional system. Furthermore, it seems that, generally, the efficiency of the proposed interlocking system is increased in soft ground types. Specifically, the corresponding reductions in the longitudinal movements of the deck are up to 83%, instead of 79%, if the unconventional bridge system is founded on the flexible ground type C instead of A. The semi-connection also influences the response of the bridge in the transverse direction, see Fig. 11b, as the restraining effect of the external stoppers leads to a maximum of 39% reduction in the transverse seismic movements of the deck. The comparison between Figs. 10a and 11a leads to the conclusion that, in general, the proposed interlocking system is more efficient in bridges which are founded on areas with high seismicity. Specifically, the longitudinal seismic displacements of the deck are more effectively reduced in case the high ground acceleration is adopted, namely 0.24 g instead of 0.16 g. This can be attributed to the fact that the proposed interlocking system is participating more strongly when the bridge responds with larger displacements. In general, it was found that the higher the seismic action, the more contacts take place in the semi-connection. On the contrary, the efficiency of the system does not seem to be influenced by the level of the seismic action in the transverse direction of the bridge. The comparison between Figs. 10b and 11b shows that the reductions in the displacements are almost the same in both the lower, i.e. 0.16 g, and the higher, i.e. 0.24 g, ground acceleration. The transverse movements of the deck of the unconventional bridge system are not influenced by the non-linear response of the linking-key, as the expansion joints 1 and 2 are not closed during the transverse seismic event. The only factor that seems to alter the transverse response of the unconventional bridge, in comparison to the one of the “reference” bridge, is the restrain of the transverse displacements of the continuity slab at the semi-connection, see the plan view of the semi-connection in Fig. 2 and the Detail in Fig. 5b. This restraint is linear. Therefore, its effectiveness is not influenced by the magnitude of the displacements. It is noted that the displacements were found to be increased by almost the same percentage–almost 50%–in both the conventional and the unconventional bridge system when the ground acceleration is also increased by 50%. Generally, the longitudinal response of the unconventional bridge system seems to be governed by the magnitude of the linking-key’s clearances, i.e. 1 and
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M (KNm)
100000
100000
conventional
M (KNm)
50000 0 -50000
-0.04
0 -50000
unconventional
-100000
Pier P1
conventional
50000
unconventional
-100000
-0.02
0.00 θ (rad)
(a)
0.02
0.04
Pier P4
-0.04
-0.02
0.00 θ (rad)
0.02
0.04
(b)
Fig. 12 Comparison of the resulting moment-rotation (M − θ ) curves of the conventional and the unconventional bridge piers’ bottom cross sections: a pier P1 and b pier P4 , (ground type: C, ground acceleration: 1 g)
2 , while its transverse response seems to be governed by the stiffness of the continuity slab and its transverse restraint at the semi-connection. 6.4 Ductility requirements In the present paragraph, the ductility requirements of the piers of the conventional and the unconventional bridge system are compared. The analytical results showed that the piers of both the conventional and the unconventional bridge system remain elastic, even when the higher seismicity was considered, i.e. 0.24 g, and when the soft ground type was chosen, i.e. ground type C. This seems to comply with the current provision of Eurocode 8 (Eurocode 8 Part 2 2005), which requires that the seismically isolated bridges should remain essentially elastic for the design earthquake. The comparison of the rotations of the piers’ bottom cross section showed that the piers of the unconventional bridge system respond with smaller rotations. This is attributed to the reductions observed in the seismic displacements of the deck. Therefore, the bending actions of the piers are also reduced in the unconventional bridge system. The two bridge alternatives were also subjected to higher seismic actions. According to codes, the bridges are required to avoid collapse in case the seismic action is higher than the design seismic action. Both bridge systems were analyzed for a peak ground acceleration equal to 1g. The study presents the results, namely the M − θ response curves, of the highest and the shortest pier, namely of piers P1 and P4 , respectively. Figure 12a shows the momentrotation (M − θ ) curves of the bottom cross section of pier P1 , while Fig. 12b shows the M − θ curves of pier P4 . Both figures correspond to the response of the bridge in the longitudinal direction. It can be derived that the semi-connection of the bridge with the adjacent tunnels leads in favorable response of the piers, as they were found to remain elastic in the unconventional bridge system. On the contrary, plastic hinges were developed on the piers of the conventional bridge system. The ductility requirements of the bottom cross sections of the piers of the conventional bridge system were calculated and found to be equal to 3.2 for P1 and 2.9 for P4 , in terms of rotations theta (θ ).
7 Conclusions In the present paper unconventional external stoppers were proposed to be used aiming at limiting the seismic movements of an isolated bridge. The external stoppers are proposed to be installed in stiff and rigid external boundaries, which can be either external sub-structures
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or, in case existing, in adjacent tunnels. The proposed system consists of: (a) a continuity slab, which is the extension of the deck slab of the bridge on the backfill soil and (b) a semi-connection, which offers the restraint of the continuity slab by the external stoppers. The efficiency of the semi-connection was parametrically investigated and assessed, mainly by calculating the percentage reductions in the seismic displacements of the deck. The serviceability problems were also addressed. The resulting bridge deck is continuous and consequently the maintenance cost of the bridge is expected to be reduced. The study came up to the following conclusions: • The proposed semi-connection is possible to accommodate the serviceability requirements of the bridge deck, through the in-service allowable cracking of the continuity slab and the provision of appropriate clearances at the expansion joints (gaps). The minimization of the widths of these joints leads to increased seismic participation of the external stoppers and to a more efficient enhancement of the seismic response of the bridge. • The dynamic characteristics of the unconventional bridge system were found to be strongly influenced by the external stoppers, mainly in the longitudinal direction. This is due to the seismic interaction effects, which take place at the semi-connection. The longitudinal modal period of the bridge is decreased up to 87%. In the transverse direction, the dynamic system of the bridge is not strongly influenced, as the main structural measure, which influences this direction, is the restrain of the transverse movement of the continuity slab at the semi-connection. The linking-key was found to be inactive during the transverse seismic event, which means that the gaps were not closed, not even in case the high ground acceleration and when the soft ground type was considered. • The strong seismic participation of the external stoppers leads in significant reductions in the seismic displacements of the unconventional bridge system, mainly in the longitudinal direction. Specifically, the external stoppers are possible to reduce the longitudinal seismic movements of the deck by 71 to 78%. The system was found to be generally more efficient in bridge structures which respond with large seismic displacements. The conclusion is attributed to the increase in the seismic participation of the semi-connection. Therefore, bridges which are founded on soft ground types and bridges built on areas with high seismicity can efficiently develop the proposed technique. • In the transverse direction of the bridge, the seismic movements of the deck are reduced up to 39%. The displacements are more effectively restrained over the end piers, while the desired influence of the system was found to be reduced over the central piers. The transverse seismic displacements of the deck of the unconventional bridge system and the resulting rotations of the continuity slab do not seem to activate the semi-connection. It follows that the gaps remain open during the transverse seismic event. The last observation seems to justify the almost constant efficiency of the interlocking system when the seismic action is increased by 50% (from 0.16 to 0.24 g), as the transverse seismic displacements of both the conventional and the unconventional bridge system are also increased by almost 50%. It seems that the efficiency of the external stoppers is not affected by the level of the seismic action in the transverse direction of the bridge. • Generally, the alteration in the longitudinal response of the unconventional bridge system seems to be governed by the magnitude of the gaps existing between the external stopper and the U-shaped embedment, while its transverse response seems to be governed by the stiffness of the continuity slab and its transverse restraint at the semi-connection. • The piers of both the conventional and the unconventional bridge system remain elastic for a ground acceleration equal to 0.24 g. The analysis of both bridge systems for a more intense earthquake, i.e. for a ground acceleration equal to 1 g, showed that the proposed
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semi-connection of the bridge with the stiff boundaries leads to favorable response of the piers of the unconventional bridge system. In that case the piers remain elastic, while the conventional bridge system would require the development of plastic hinges in its piers, in order to withstand the high seismic action. • The use of the external stoppers seems to be attractive for future design of bridges with flexible resisting systems, i.e. for isolated bridges. The study needs a complement with analysis of more bridge structures, as the length of the bridge and the height of the piers were not included in the parametric study, and they are considered to be of great importance as far as the seismic efficiency of the proposed semi-connection is concerned.
References Anagnostopoulos SA (2004) Equivalent viscous damping for modeling inelastic impacts in earthquake pounding problems. Earthquake Eng Struct Dyn 33(8):897–902 Arockiasamy M, Sivakumar M (2005) Design implications of creep and shrinkage in integral abutment bridges. ACI Spec Publ 227:85–106 Aviram A, Mackie KR, Stojadinovic B (2008) PEER 2008/03 Guidelines for nonlinear analysis of bridge structures in california Caltrans (1999) Seismic design criteria 1.1. California Department of Transportation, Sacramento Chen W-F, Duan L (1999) Bridge engineering handbook chapter 34. CRC Press, Boca Raton, FL Chopra AK (1995) Dynamics of structures Theory and applications to earthquake engineering. Prentice Hall, Englewood Cliffs, NJ Computers and Structures Inc (2007) SAP 2000 nonlinear version 1.1.03 user’s reference manual. Berkeley, California Des Roches R, Muthukumar S (2002) Effect of pounding and restrainers on seismic response of multiple-frame bridges. J Struct Eng 128(7):860–869 Dicleli M (2005) Integral abutment-backfill behavior on sand soil-pushover analysis approach. J Bridg Eng 10(3):354–364 EN 1991-1-5:2003 (2003) Eurocode 1: actions on structures–Part 1–5: general actions–thermal actions EN 1992-1:2004 (2004) Eurocode 2: design of concrete structures–Part 1: general rules and rules for buildings EN 1998-1:2005 (2005) Eurocode 8: design of structures for earthquake resistance Part 1: general rules, seismic actions and rules for buildings EN 1998-2:2005 (2005) Eurocode 8: design of structures for earthquake resistance, Part 2: bridges Gloyd SC (1996) Seismic movement at bridge abutments, SP 164-15. ACI Int Spec Publ, 164:273–288 Jankowski R, Wilde K, Fujino Y (2000) Reduction of pounding effects in elevated bridges during earthquakes. Earthquake Eng Struct Dyn 29(2):195–212 Kappos AJ (2002) RCCOLA-90: a microcomputer program for the analysis of the inelastic response of reinforced concrete sections. Department of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece Kawashima K (2004) Seismic isolation of highway bridges. J Jpn Association Earthquake Eng, 4(3)(special issue) Maragakis E (1985) A model for the rigid body motions of skew bridges, California Institute of Technology, Report No EERL 85-02. Mikami T, Unjoh S, Kondoh M (2008) The effect of abutments as displacement limiting measure on seismic performance of bridges, Available via DIALOG. www.pwri.go.jp/eng/ujnr/tc/g/pdf/19/4-1mikami.pdf Muthukumar S (2003) A contact element approach with hysteresis damping for the analysis and design of pounding in bridges. PhD Thesis, Georgia Institute of Technology. Accessed 21 Nov 2008 Mylonakis G, Simeonov VK, Reinhorn AM, Buckle IG (1999) Implications of spatial variation of ground motion on the seismic response of bridges: case study. ACI Int Spec Publ SP-187, pp 299–327 Naeim F, Kelly JM (1999) Design of seismic isolated structures from theory to practice. Wiley, New York NCHRP 12-49 (2001) Comprehensive specification for the seismic design of bridges, revised LRFD design specifications, (seismic provisions), 3rd draft of specifications and commentary Nutt RV, Mayes RL (2000) Comparison of typical bridge columns seismically designed with and without abutment participation using AASHTO division I-A and proposed AASHTO LRFD provisions, task F3-1(a)
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Bull Earthquake Eng PCI (2005) Precast, prestressed concrete bridges, the high performance solution, comprehensive bridge design manual, available via DIALOG. www.pci.org/publications/bridge Accessed: 21 Nov 2008 Priestley MJN, Seible F, Calvi GM (1996) Seismic design and retrofit of bridges chapter 1. Wiley, New York Purvis PER (1998) NCHRP 319, bridge deck joint performance, a synthesis of highway practice, project 20–5 (Topic 30–08) Ruangrassamee A, Kawashima K (2001) Relative displacement response spectra with pounding effect. Earthquake Eng Struct Dyn 30(10):1511–1538 Saiidi SM, Moore RT, Itani A (2001) Seismic performance of reinforced concrete bridges with unconventional configurations. ACI Struct J 98(5):717–726 Tegos I, Sextos A, Mitoulis S, Tsitotas M (2005) Contribution to the improvement of the seismic performance of integral bridges. In: Proceedings of the 4th european workshop on the seismic behaviour of irregular and complex structures, Thessaloniki, Greece Westermo BD (1989) The dynamics of interstructural connection to prevent pounding. Earthquake Eng Struct Dyn 18(5):687–699
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