KSCE Journal of Civil Engineering (2013) 17(1):122-132 DOI 10.1007/s12205-013-1063-9
Structural Engineering
www.springer.com/12205
Use of Sliding Multirotational Devices of an Irregular Bridge in a Zone of High Seismicity José M. Jara*, Manuel Jara**, Hugo Hernández***, and Bertha A. Olmos**** Received November 27, 2009/Revised October 22, 2010/Accepted March 26, 2012
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Abstract The 525 meters long Infiernillo II bridge crosses the Infiernillo Dam and it is the first isolated bridge built in Mexico. It is located in the Morelia-Lazaro Cardenas highway that connects the central cities of the country to the Pacific Coast. Arch steel trusses compose the superstructure of the five simple supported spans. The substructure consists of reinforced concrete abutments and piers supported on cylinders and piles. The total cylinder-pier subsystem height is in the range of 46 m to 71 m, causing a strong irregularity in the transverse and longitudinal directions. The bridge was subjected to an assembly of real strong motion movements recorded close to the Pacific Coast in Mexico, site where the most severe earthquakes occur in the country. The study started by evaluating the analytical model with environmental vibration measurements previously taken. Based on the similarity of the results, none adjustment was required for the numerical model. The results show the importance of the isolator dynamic characteristics on the expected seismic behavior of the bridge. Special emphasis is dedicated to analyze the effectiveness of the isolation system for avoiding concentration of strength and displacement ductility demands on an irregular bridge substructure. Keywords: seismic response of irregular bridges, isolated bridges, expected seismic behavior of isolated bridges, multirotational bearings, seismic strong motions ···································································································································································································································
1. Introduction The irregular substructure configuration of a bridge has an important influence in the concentration of pier seismic demands and the expected damages in specific parts of the structure. Strong concentration of force demands in short piers and the influence of superior vibration modes can be significant (Isakovic et al., 2006; Akbari and Maalek, 2010; Maalek et al., 2009). The inclusion of isolators on a bridge makes more flexible the structure and reduces the lateral stiffness differences among the piers if adequate properties of the isolation devices are adopted. Isolation systems have materialized as an effective technique to reduce the seismic response of bridges by uncoupling a structure from damaging effects of earthquakes. Common isolation devices include frictional/sliding bearings, elastomeric bearings, high damping rubbers and lead rubber bearings. Several of these systems are frequently combined with passive energy devices by a need to control the isolator displacements. Experimental studies have shown the feasibility of the use of metallic yielding devices to enhance the energy dissipation capacity of structures with stable hysteretic behavior. The use of base isolation systems
in bridge structures are described by Sarrazín et al. (2005), Jangid (2004), Shen et al. (2004), Jara and Casas (2002) and Savage et al. (1999) among others. Reviews of experimental and analytical studies are provided in Kelly (1993), Skinner, Robinson and Mc Verry (1993), Buckle and Mayes (1990), Kunde and Jangid (2003), Buckle (2000), Soong and Dargush (1997), Soong and Spencer (2002) and Jara et al. (2006). Mexico is geographically located in a high seismic zone and most of the strong earthquakes have epicenters in the vicinity of the Pacific Coast. The subduction process of the Cocos and Rivera plates beneath the North American Plate produces, in average, an earthquake with magnitude M 7.0 every two years. The close location of many urban areas and highways to the origin of the seismic events generated in this source, make attractive the use of base isolation to enhance structural safety against seismic hazards.
2. Bridge Description The Infiernillo II Bridge, built between 2000 and 2003, crosses the Balsas River and is part of one of the highways that connect
*Titular Professor, Civil Engineering School, University of Michoacán, Morelia, Michoacán 58000, México (Corresponding Author, E-mail: jmjara70 @gmail. com) **Titular Professor, Civil Engineering School, University of Michoacán, Morelia, Michoacán 58000, México (E-mail:
[email protected]) ***Titular Professor, Civil Engineering School, University of Michoacán, Morelia, Michoacán 58000, México (E-mail:
[email protected]) ****Titular Professor, Civil Engineering School, University of Michoacán, Morelia, Michoacán 58000, México (E-mail:
[email protected]) − 122 −
Use of Sliding Multirotational Devices of an Irregular Bridge in a Zone of High Seismicity
central cities of Mexico to the Pacific Coast. It is located in the kilometer 933+940 and about 100 km from the subduction faults. The bridge superstructure consists in five simple supported 105 meters long spans with a total length of 525 m. The 12 m width deck was built of light-gage steel deck cover with a 18 cm concrete slab depth. The deck is supported on steel girders, spaced at 1.5 m, over floor beams spaced at 6 m. The girders are connected to two Camel Back type steel trusses braced at the top, with a maximum height of 6.5 m. Fig. 1 shows two sights of the bridge and Fig. 2 displays the longitudinal elevation of the structure. The substructure consists in two non-prismatic abutments and four wall type reinforced concrete piers. The piers have a hollow box shape section with plan dimensions of 8.5×3.5 m, 15 m height and thickness of 40 and 60 cm in longitudinal and transverse directions respectively. A hammerhead cap beam, with the dimensions shown in Fig. 3, extends over the total width of the bridge. Shear transverse keys, 70 cm depth, are located at the ends of the cap beam. The piers are supported on two reinforced concrete hollow cylinders (diameter of 8.5 and 10 m) submerged in water. In both ends of the cylinders a solid reinforced concrete cap was built integrally with the cylinders and the piles foundation at the bottom, and the bridge piers at the top. The cylinder’s height is in the range of 21 m to 46 m.
Fig. 3. Bent Cap Beam, Shear Transverse Keys and Steel Bracket Supporters for Isolators
Fig. 4. Isolation and Energy Dissipation Device
2.1 Isolation System The relatively close location of the bridge to the strongest seismic source mechanism of the country and the highly irregular pier stiffness, made desirable the use of an isolation system to improve the expected behavior of the structure when subjected to seismic strong motions. The bridge was projected with bearing isolators of the sliding multirotational type (Fig. 4). These are PTFE (Polytetrafluoroethylene) sliding isolators with a teflon sliding top surface. They are composed by a disc bearing to accommodate rotation when required, mounted on a set of urethane springs, called Mass
Energy Regulators, to provide a restoring force. The bearings dissipate energy through friction and the energy dissipation is then controlled by adjusting the friction force among the plates of the device. The lateral resistance of the bearing is the result of two mechanisms, the friction force and the restoring force generated by compression of the Mass Energy Regulators against the upper plate. An idealized bi-linear hysteresis loop is typically adopted. The designer should provide the following properties to the manufacturer of the isolator: the displacement capacity of the bearing, the seismic and service coefficients of friction, and the size and number of the urethane springs required (Mass Energy Regulators). There are two bearings at each side on the piers and two over each abutment, being a total of 20 devices in the entire bridge (Fig. 5). Previous experimental analyses conducted by the manufacturers showed that bearings have a stable bi-linear hysteretic and non-degradation behavior
Fig. 1. Lateral and Front Views of the Infiernillo II Bridge
Fig. 5 Bearing Positions in Abutments (Left) and in Piers (Right)
Fig. 2. Longitudinal Elevation of the Infiernillo II Bridge Vol. 17, No. 1 / January 2013
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José M. Jara, Manuel Jara, Hugo Hernández, and Bertha A. Olmos
Details about the design procedure used by the structural engineers in charge of the project are not reported in the published papers describing the bridge.
3. Seismic Records
Fig. 6. Idealized Hysteretic Model of the Isolation System
(Muñoz, 2003). According to these results, the isolation system was modeled using a bi-linear hysteretic cycle with the following parameters displayed in Fig. 6: the characteristic strength (Fo), the elastic stiffness (Ke), the yield strength (Fy), the yield displacement (Dy), the post-yielding stiffness (Ki) and the maximum design displacement (Dmax). It should be noted the high elastic stiffness exhibited by the device and the small post-yielding stiffness, of about 1% of the elastic stiffness. Based on the device description given by Muñoz (2003), the design displacement capacity of the device is only 85 mm for a total force of 625 kN.
An ensemble of eleven accelerograms recorded at stations closely situated to the bridge location was selected. The INPT station is located close to the Infiernillo Dam at 15 km to the Infiernillo Bridge. The other stations are on the Pacific Coast close to the potential seismic sources. In all cases, the earthquake sources of the records are associated to the subduction process in the Pacific Coast where the most severe earthquakes for the bridge are expected to occur. The selected earthquakes have magnitudes in the range of 5.8 to 8.1 aimed at analyzing the seismic behavior of the bridge for service, occasional and rare earthquakes. Table 1 shows the date, magnitude, Peak Ground Acceleration (PGA) and Peak Spectral pseudoacceleration (PSA) of each record. The INES records in the table are again the INPT station events, but scaled to an expected PGA for a 1000 years return period earthquake. Including these two additional scaled events, the bridge was subjected to thirteen seismic records. Figure 7 presents the 5% damped pseudoacceleration response spectra for all the records, classified in three groups: service, occasional and rare earthquakes. The classification is based on
Table 1. Seismic Record Description EQ type
Service
Ocassional
Rare
Seismic record Union9906 Cales8604 Union9412 INPT9912 Cales8509 INPT9906 INPT9705 Union8509 INPT9701 Manza9510 Cales9701 INES9906 INES9705
Earthquake date 21/06/99 30/04/86 10/12/94 29/12/99 19/09/85 21/06/99 25/06/97 19/09/85 11/01/97 10/10/95 11/01/97 21/06/99 25/06/97
Magnitude 5.8 7.0 6.3 5.9 8.1 5.8 5.9 8.1 6.5 7.5 6.9 5.8 5.9
PGA (cm/s2) 73.2 76.5 93.0 103.4 140.8 205.3 221.1 148.3 282.4 387.1 396.2 420.0 420.0
PSA (cm/s2) 268 223 299 267 339 643 517 505 1374 1407 1040 1081 983
MSD (cm) 0.86 3.26 1.33 0.87 13.72 1.73 2.31 19.94 4.13 22.13 7.25 2.91 4.39
Fig. 7. Pseudoacceleration Response Spectra of the Selected Records: (a) Service Earthquakes, (b) Occasional Earthquakes, (c) Rare Earthquakes − 124 −
KSCE Journal of Civil Engineering
Use of Sliding Multirotational Devices of an Irregular Bridge in a Zone of High Seismicity
the seismic hazard analysis developed by Jara (2008), using the Peak Spectral Pseudoacceleration (PSA) as a measure of intensity. The first sixth records of Table 1 correspond to the service earthquakes, with a PSA in the range of 223 to 339 cm/s2. The occasional earthquakes are the next three records whose PSA is in the range of 505 to 643 cm/s2. The rare earthquake group includes the last five records of Table 1 for a PSA between 983 and 1,407 cm/s2. The frequency content of all records is in the range of high frequencies making the isolation an appealing strategy for reducing seismic demands.
4. Structural Models 4.1 Dynamic Properties of the Cylinders The first analysis was focused on the dynamic properties of the cylinders. These elements were discretized by the use of 12816 solid eight-node finite elements that have six quadrilateral faces and three translational degrees of freedom at each of its connected joints (see upper detail in Fig. 8). The solid element in SAP2000 includes nine incompatible bending modes that improve the bending behavior of the element (CSI, 2006). The model was calibrated with the results of the ambient and forced vibration tests described by Muñoz (2003). These tests were conducted during the construction process of the bridge with the aim to determine the dynamic properties of the cylinders. Table 2 presents the results of the ambient vibration measurements. The modal properties of the cylinders were initially evaluated neglecting the mass of water added to the element. When considering the effect of the added water mass in the cylinders, the fundamental period of the element increased by 19%. The added mass water effect was considered according to the Eurocode
regulation (Eq. (1)) as: m a = ρπ R
2
(1)
where ma is the added mass water, ρ is the water density and R is the radius of the transverse section of the element. With this consideration, the cylinder dynamic properties obtained from the analytical model were well approximated to the results obtained by the ambient vibration measurements, as it can be seen in Tables 2 and 3. 4.2 Ambient Vibration Measurements of the Bridge A series of ambient vibration tests were conducted by a team of researchers of the University of Michoacan. The modal parameters of interest were the longitudinal and transverse frequencies of the bridge and the vertical frequency of the deck. The instruments used for the ambient vibration studies were a Kinemetrics K2 recording console with 12 channels, nine force balanced unidirectional sensors and one Episensor triaxial force balanced instrument. Fig. 9 shows the recording equipment and the sensors before the measurements were taken. The ambient response tests of the system recorded 100 samples per second taken in sets of 15 minutes each. The modal identification of the bridge was evaluated by the use of the frequency Table 2. Dynamic Properties of Cylinders Obtained with Ambient Vibration Tests Cylinder 2 3 4 5
Longitudinal 0.357 0.584 0.598 0.250
Period (s) Transverse 0.333 0.595 0.617 0.250
Vertical 0.044 0.061 0.063 0.045
Table 3. Dynamic Properties of Cylinders obtained with the Analytical Model Cylinder
Fig. 8. Finite Element Model of Cylinders for Calibrating its Dynamic Properties
2 3 4 5
Longitudinal 0.367 0.607 0.643 0.219
Fig. 9. Equipment used and Sensor Arrangement Vol. 17, No. 1 / January 2013
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Period (s) Transverse 0.367 0.607 0.643 0.219
Vertical 0.057 0.081 0.083 0.044
José M. Jara, Manuel Jara, Hugo Hernández, and Bertha A. Olmos
domain decomposition technique (Bendat, 1993). This approach performs an approximate decomposition of the structure into an independent set of single degree of freedom system for each mode. Figure 10 shows the average amplitude spectra in the three orthogonal directions of the recorded data (Hernández et al., 2005). The periods associated to the peak spectral amplitudes are 2.7, 2.45 and 0.9 s for the transverse, longitudinal and vertical directions respectively. 4.3 Three Dimensional Model of the Bridge Several structural models of the bridge with different levels of complexity were analyzed. The models were created using the SAP2000 software (CSI, 2006) considering linear and non-linear elements. In all cases, the truss members were represented by frame type elements with geometrical properties obtained from the structural project and construction drawings of the bridge. The deck, piers and cylinders were modeled with solid finite elements, and the mass water was added to the cylinders as it was explained above. The isolation system was modeled using link elements with bilinear hysteretic properties. They have coupled plasticity properties for shear deformations and the remaining four deformations (axial, and rotation about its three local axis) have linear effective stiffnesses. The modal analysis of the 3D model gave the analytical frequencies and mode shapes that were compared with those obtained through ambient vibration measurements. The fundamental period of the bridge in the transverse direction was 2.52 s, that was 93% of the transverse period identified by the ambient vibration tests. The first longitudinal period obtained is 2.42 s, practically the same as the experimental one. The vertical mode had a period of 0.88 s, 98% of the experimental one. Based on
the accuracy of the results, none adjustment was required for the numerical model. Once the model was calibrated, it was of interest to determine the changes that the bridge would have in its dynamics properties if it were supported over traditional bearings. In the same highway, near to the Infiernillo II bridge location, there are other bridges with very similar span lengths and the same type of superstructure. One of them is the Pizandaran bridge composed by two Camel Back type steel trusses braced at the top and it is supported on Tetron GG pot unidirectional bearings. An analytical model of the Infiernillo II bridge supported on this type of bearings was created. The results show that the fundamental period of the non-isolated bridge is only reduced by an amount of 20% (Galvan, 2008). The small changes in dynamic properties of both structures can be attributed to the inherent high period of the non-isolated bridge as a consequence of the substructure flexibility.
5. Seismic Performance 5.1 Pier Displacements Concentration of ductility demands in the stiffer elements and the adequacy of the seat length are concern issues in a simple supported bridge with an expected out of phase seismic response movement, typically presented in piers with irregular configuration. The bridge has a strong irregularity in the transverse and longitudinal directions as a result of the difference in piers’ heights. Pier 4 is 54% taller than the adjoining pier number 5, as it is shown in Table 4. The stiffness of the cylinder-pier subsystem is 63 kN/mm for support 5 and 41 kN/mm for support 4. As it is expected, the isolators leaded to a more uniform stiffness distribution. If the isolator flexibility is added, the stiffness of the cylinder-pier-isolator subsystem for the support 5 moves toward the stiffness of subsystem of pier 4 and the differences among pier lateral stiffness are strongly reduced, especially when the isolator works in the inelastic range of behavior. In order to assess the influence that the isolators have in the dynamic response, the bridge was subjected to all the seismic records described in Table 1. Fig. 11 shows the top displacement of two adjoining piers (3 and 4) for rare (manza9510 record) and occasional (union8509 record) earthquakes, in the longitudinal and transverse directions. In phase movement was expected in these piers, because of the height and stiffness similarities. Fig. 11 confirms the expectations for all the excitations, particularly in the longitudinal direction where displacements were almost the same. In spite of the synchronous movement, the top pier displacements of pier 4 were about 20% larger than those of pier 3 for the transverse direction. The maximum transverse displaceTable 4. Total Substructure Height Pier
Fig. 10. Average Amplitude Fourier Spectra: (a) Transverse Direction, (b) Longitudinal Direction, (c) Vertical Direction − 126 −
2 3 4 5
Cylinder H (m) 34.13 48.63 50.13 25.43
Pier with cap beam H (m) 20.62 20.62 20.62 20.62
Total height H (m) 54.75 69.25 70.75 46.05
KSCE Journal of Civil Engineering
Use of Sliding Multirotational Devices of an Irregular Bridge in a Zone of High Seismicity
Fig. 11. Top Displacements of Piers 3 and 4 subjected to Manza9510 and Union8509 Records: (a) Longitudinal Direction, (b) Transverse Direction
ment of pier 4 was of 94 mm, whereas the maximum displacement of pier 3 was of 79 mm (piers’ drifts of 0.0013 and 0.0011, respectively). In contrast, piers 4 and 5 have very different heights but similar stiffness as a consequence of the added flexibility through the isolator system. It was also observed a synchronous movement in the longitudinal direction for these adjacent piers (Fig. 12), but the displacements of pier 4 were more than twice the displacements of pier 5. In the transverse direction, there was an out of phase movement of the piers with huge differences at the top pier
displacements, e.g., for the Manzanillo record, the top pier displacements in piers 4 and 5 were of 94 mm and 16 mm, respectively (piers’ drifts of 0.0013 and 0.00034). These results suggest that the use of different properties of the isolation system in longitudinal and transverse direction might improve the response of the bridge. Figure 13 shows the displacements at the top of the piers 2 and 3 for the transverse direction. The pier displacements were out of phase, and again the taller pier experience much larger displacements than the shorter one. The same pattern observed in Figs.
Fig. 12. Top Displacements of Piers 4 and 5 subjected to Manza9510 and Union8509 Records: (a) Longitudinal Direction, (b) Transverse Direction Vol. 17, No. 1 / January 2013
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José M. Jara, Manuel Jara, Hugo Hernández, and Bertha A. Olmos
Fig. 13. Top Displacements of Piers 2 and 3 for Manza9510 and Union8509 Records
11 and 12 was presented for the longitudinal displacement time histories. It can be concluded that at the top of the piers the displacements are quite different in both directions and a regular structural response was not accomplished. The abutments were considered fixed as a result of the soil conditions; however, all the isolators used in the bridge have the same geometrical and mechanical properties. As a consequence, the stiffness of the abutment-isolator subsystem is larger than the stiffness of the intermediate subsystem supports. The central spans are more flexible and they present larger displacements than those obtained at the end spans, as Fig. 14 shows. In order to balance the stiffness of all the supports (at the end and intermediate locations), the isolators on the abutments should be more flexible than the isolators on the piers. One of the initial assumptions adopted in all the analyses conducted was that the substructure remains elastic and the isolators were the only elements behaving non-linearly. Looking at the previous figures, the pier displacement demands, when the bridge is subjected to one of the strongest accelerograms used (Manzanillo record), were in the range of 33 mm (pier 5) to 79 mm (pier 4) in the longitudinal direction, and in the range of 15 mm (pier 5) to 94 mm (pier 4) in the transverse direction. To evaluate the assumption of pier linear behavior, the moment curvature relationships of these elements were calculated. According to these curves, the yield displacements (∆y) of the piers were in the range of 84 mm (pier 5) to 150 mm (pier 4). Consequently, the maximum displacement demands in both direction of pier 5 were 0.39 ∆y and 0.18 ∆y, and 0.53 ∆y and 0.63
Fig. 14. Deformed Shape of the Bridge in the Transverse Direction for Union8509 Record
∆y in pier 4, confirming the adequacy of the assumption. 5.2 Base Shear Distribution One of the purposes of implementing an isolation system is to regulate the dynamic structural response by making the stiffness of the bearing-pier elements similar and avoiding the concentration of ductility demands at particular locations of the structure. According to the analysis results, this objective was not fully achieved, in spite of the stiffness similarity between the cylinderpier-isolator subsystems. Contrary to expectations, the taller piers experienced the maximum shear force demands and the ductility demand was much greater in pier 4 than in pier 5. Fig. 15 shows the base shear time histories for piers 4 and 5 when the bridge was subjected to the rare and occasional earthquakes (Manzanillo and Union records). As it can be observed, there was an out of phase force distribution in the transverse direction of both piers, and the taller one experienced considerable larger shear forces than those of the shorter pier. Because of the larger displacement demands at pier 4 and the similar stiffness in all subsystems, the maximum shear force and flexural moment demands corresponded to the tallest pier. In the longitudinal direction, the maximum shear force also took place in the tallest pier, particularly for the Union record. 5.3 Collision of Adjacent Decks To study the possible impact effect between two adjacent spans during the action of a seismic event, a nonlinear contact element (gap) was used. This element takes into account the effect of a potential collision when a convergence movement between adjacent decks takes place. The possibility of a collision between two adjacent spans can be estimated by means of the relative displacement time histories. As an example, Fig. 16 shows the time history of the relative displacements between the decks 1-2 (pier 2), 2-3 (pier 3), 3-4 (pier 4) and 4-5 (pier 5) in the longitudinal direction, when the bridge was subjected to the manza9510 record. The steel element located at the center of the expansion joint (Fig. 17), considerably reduces the 150 mm existent gap length, where the roadways could freely move without having a collision, to a value of about 80 mm. Therefore, the reference line in the plots displayed in Fig. 16, is the effective gap size of the expansion joint between the decks (80 mm). The origin of the vertical axis is the gap width, consequently, if at any time the relative displacement in the figure reaches negative values, the
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KSCE Journal of Civil Engineering
Use of Sliding Multirotational Devices of an Irregular Bridge in a Zone of High Seismicity
Fig. 15. Base Shear Forces in Piers 4 and 5. Manzanillo Record (a and b) and Union Record (c and d): (a) Longitudinal, (b) Transverse, (c) Longitudinal, (d) Transverse
Fig. 16. Time History of Relative Displacements between Adjacent Deck Spans subjected to Manza9510 Record
span decks would collide between them. The maximum relative displacement demands for all the records are displayed in Table 5. All the relative displacements obtained for service, occasional and rare earthquakes were smaller than 80 mm with the exception of the Manza9510 record, with a relative displacement demand of 89.8 mm, presenting a slightly larger value than the existent free gap. Deck collision was produced in a very small time interval producing a marginal redistribution of forces between the piers.
Fig. 17. Expansion Joint used on the Infiernillo II Bridge Vol. 17, No. 1 / January 2013
5.4 Deck – Shear Keys Interaction It is also important to study the displacement demands at the deck level in transverse direction to evaluate a potential contact − 129 −
José M. Jara, Manuel Jara, Hugo Hernández, and Bertha A. Olmos
Table 5. Maximum Longitudinal Relative Displacements between Adjacent Decks Seismic Record Union9906 Cales8604 Union9412 INPT9912 Cales8509 INPT99906 INPT9705
Displacement (mm) 3.1 7.5 1.2 2.9 38.1 6.3 8.4
Seismic record Union8509 INPT9701 Manza9510 Cales9701 INES9906 INES9705
Displacement (mm) 41.3 5.9 89.8 19.3 5.5 12.9
2
N = ( 305 + 2.5L + 10H ) ( 1 + 0.000125S )
Table 6. Maximum Relative Transverse Displacements of the Deck Seismic record Union9906 Cales8604 Union9412 INPT9912 Cales8509 INPT9906 INPT9705 Union8509 INPT9701 Manza9510 Cales9701 INES9906 INES9705
Pier 2 (mm) 3.9 6.0 2.4 2.3 35.5 4.9 6.9 34.2 8.0 70.4 11.7 7.4 12.2
Pier 3 (mm) 4.0 12.9 3.1 3.0 60.7 6.6 13.8 70.5 21.0 118.6 28.9 12.9 21.9
Pier 4 (mm) 3.4 10.9 2.8 2.2 56.0 5.9 12.1 66.0 18.8 110.9 26.3 11.8 19.1
length. According to AASHTO (2002) regulations, the minimum seat length is:
Pier 5 (mm) 3.6 5.5 2.7 2.5 34.9 4.7 7.4 33.3 8.0 69.0 12.0 7.9 12.0
(2)
N is the minimum seat length in mm, L is the span length in meters, S is the skew in degrees and H is the pier height in meters. According to expression (2), the minimum seat length for the Infiernillo II bridge is N=1270 mm and the existent seat length in the bridge is about 2000 mm. The maximum longitudinal displacement demand obtained in the analyses of all records was about 200 mm and does not represent a risk for losing the seat length of the bridge.
6. Isolation System Response
interaction with the seismic shear keys. It must be pointed out that destruction of the seismic shear keys is a common type of failure presented during different seismic events in Mexico. Table 6 shows the transverse deck displacement demands for all the seismic records. The existent gap between the superstructure elements and the seismic shear keys is about 150 mm, which is wide enough to avoid any impact between the superstructure and the shear keys. It should be noted that the gap between the deck and the transverse shear keys was almost twice the design displacement of the isolator, Dmax = 85 mm (Fig. 6). 5.5 Seat Length A typical bridge failure presented all over the world during the action of strong seismic motions is the superstructure loss of seat
Figure 18 shows a typical hysteretic behavior of the isolation system for a service and rare type earthquakes. In spite of the quite different PGA values in both records, the isolator displacement demands obtained with the service type record were only duplicated when the bridge was subjected to the rare type record. Table 7 presents the maximum isolator displacements obtained at each of the bridge supports. It is remarkable the similar isolator displacement demands on piers and the comparable displacement demands on both abutments. In most of the cases, the isolator displacement demands were smaller in abutments than in piers. This behavior can be attributed to the difference in stiffness between abutments and piers. Isolators are usually designed with enough stiffness to avoid excessive displacements under service conditions, as it is the case for wind, service earthquakes, longitudinal forces induced by the vehicles and others. Nevertheless, the extremely low yield displacement of the isolators (Dy = 0.8 mm) was exceeded for occasional and even for service earthquakes, as Table 7 shows. The maximum displacement demands were attained with the Manza9510, Union8509 and Cales8509 records. It is also remarkable the large displacement demands imposed by the manza9510 record, exceeding the isolator´s design displacements in all piers. It is interesting to observe that the displacements caused by a service earthquake record (Cales8509) were larger than the displacements produced by a rare earthquake record (INPT9701). Other similar results can be observed in Table 7. This behavior could be attributed to the use of PSA as the seismic measure
Fig. 18. Hysteretic Behavior of the Isolation System (Cales8604 Record (Left) and manza9510 Record (Right)) − 130 −
KSCE Journal of Civil Engineering
Use of Sliding Multirotational Devices of an Irregular Bridge in a Zone of High Seismicity
Table 7. Maximum Longitudinal Displacements on the Isolation System Record Union9906 Cales8604 Union9412 INPT9912 Cales8509 INPT9906 INPT9705 Union8509 INPT9701 Manza9510 Cales9701 INES9906 INES9705
Maximum displacement (mm) Abutment Abutment Pier 2 Pier 3 Pier 4 Pier 5 6 1 4.7 4.3 3.4 3.3 4.4 4.6 8.9 11.0 10.6 10.2 11.8 8.3 3.0 2.8 3.2 3.1 3.0 3.1 1.6 3.2 3.1 3.1 3.2 1.3 45.1 55.1 53.2 51.8 57.7 40.8 4.3 7.4 6.1 6.0 7.7 4.4 8.9 10.1 8.5 8.4 10.4 9.12 45.1 57.7 57.1 55.5 61.1 39.6 13.0 11.5 12.1 11.8 12.4 12.2 79.1 101.8 92.3 90.4 106.0 78.4 17.5 25.1 24.3 24.0 25.3 16.7 10.9 10.5 9.0 8.8 11.3 10.0 17.3 19.8 16.5 16.1 20.5 16.6
The extremely low yield displacement of the isolators (Dy = 0.8 mm) was exceeded not only for occasional or rare earthquakes but for service type records. Seat lengths and the gap between the deck and the shear keys of the bridge were adequate; further, it is not likely that the occurrence of the maximum expected seismic strong motion in the future could derive in a stability problem of the bridge. The longitudinal displacement demands on the expansion joints where evaluated to determine the possibility of collision between adjacent spans of the superstructure and potential shear force redistribution between supports. The only collision occurred during the displacement time history of the Manzanillo record, and has only a slight effect on the force distribution demands in the structural elements because the displacement exceeded the gap dimension at only one time step of all the time history. The displacement demands of other records showed that the possibility of contact between adjacent spans was almost negligible.
Acknowledgements intensity for the earthquake classification instead of the Maximum Spectral Displacement (MSD). Table 1 shows that seismic records with small or moderate PGA can have large spectral displacements (Cales8509 and Union8509 records).
7. Conclusions The seismic performance of an important isolated bridge located in a zone of high seismicity was analyzed. The numerical model was calibrated using ambient and forced vibration measurements taken during the early stage of construction and ambient vibration tests at the end of the construction process. Based on the similarity of the results, none adjustment was required for the numerical model. The bridge was subjected to a family of acceleration records grouped by the PSA, leading to the following conclusions: The cylinder dynamic properties obtained from the finite element model were well approximated to the results obtained by ambient vibration measurements, when it was considered the added water mass in the model. The fundamental periods of the complete structure experimentally obtained were also reasonably predicted with the numerical model. In spite of the slightly increase of the isolated structure period (in about 20%), a better stiffness and force redistribution on piers was achieved, reducing the potential concentration of ductility demands. Due to the fixed support condition at the abutments, it would be desirable that the isolators on these elements were more flexible than the isolators on piers in order to balance the stiffness for all supports, which could eventually improve the effectiveness of the isolators. The isolator design displacement was exceeded when the bridge was subjected to the Manzanillo record of the rare earthquake group. However, if the mean displacement value of these events were selected as the displacement demand, the design displacement of the isolation system would be then appropriate. Vol. 17, No. 1 / January 2013
The support of the National Council for Science and Technology, SEP-2004-C01-47314, and the Scientific Research Coordination of the University of Michoacan are greatly acknowledged. In addition, the collaboration of Ivan Aguilar Ruiz is also appreciated.
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