Effectiveness Evaluation of Seismic Protection Devices for Bridges in the PBEE Framework

556 views

Published on

Seismic protection measures for bridges can be used both for obtaining acceptable performances from new structures that for retrofitting existing ones. With the modern design philosophy based on probabilistic Performance-Based Earthquake Engineering (PBEE) approaches, the engineers are allowed to investigate different design solutions in terms of vulnerability assessment. However, if probabilistic PBEE approaches are nowadays well established and widely studied also for bridges, the topic of using the PBEE frameworks for the evaluation of the effectiveness of seismic protection devices for bridges is not extensively treated in literature.
The first objective of this work is to deal with the problem of assessing the earthquake performance of an highway bridge equipped with different bearing device: the
elastomeric bearings (ERB) and the friction pendulum systems (FPS). The second purpose is to evaluate the efficiency of a structure-dependent IM in case of isolated system. The examined structure is an highway bridge with concrete piers and steel truss deck. A FE model of the bridge is developed by using nonlinear beam-column elements with fiber section and the devices are modeled by specific elements implementing their
nonlinear behavior. The effectiveness of the different retrofitting strategies has been carried out in terms of damage probability. Choosing the example of slight damage, and referring to the curvature ductility as EDP, the probability of damage during a period of 50 years is: 23% for the structure without isolation, 7% for the structure equipped with ERB, and 3% for the structure equipped with FPS isolation.

Published in: Design, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
556
On SlideShare
0
From Embeds
0
Number of Embeds
4
Actions
Shares
0
Downloads
8
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Effectiveness Evaluation of Seismic Protection Devices for Bridges in the PBEE Framework

  1. 1. Effectiveness Evaluation of Seismic Protection Devices for Bridges in the PBEE Framework Paolo Emidio Sebastiani1, Jamie E. Padgett2, Francesco Petrini3*, Franco Bontempi4 1,3,4 Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy 2 Department of Civil and Environmental Engineering, Rice University, Houston, TX, USA *corresponding author. E-mail: francesco.petrini@uniroma1.it ABSTRACT Seismic protection measures for bridges can be used both for obtaining acceptable performances from new structures that for retrofitting existing ones. With the modern design philosophy based on probabilistic Performance-Based Earthquake Engineering (PBEE) approaches, the engineers are allowed to investigate different design solutions in terms of vulnerability assessment. However, if probabilistic PBEE approaches are nowadays well established and widely studied also for bridges, the topic of using the PBEE frameworks for the evaluation of the effectiveness of seismic protection devices for bridges is not extensively treated in literature. The first objective of this work is to deal with the problem of assessing the earthquake performance of an highway bridge equipped with different bearing device: the elastomeric bearings (ERB) and the friction pendulum systems (FPS). The second purpose is to evaluate the efficiency of a structure-dependent IM in case of isolated system. The examined structure is an highway bridge with concrete piers and steel truss deck. A FE model of the bridge is developed by using nonlinear beam-column elements with fiber section and the devices are modeled by specific elements implementing their nonlinear behavior. The effectiveness of the different retrofitting strategies has been carried out in terms of damage probability. Choosing the example of slight damage, and referring to the curvature ductility as EDP, the probability of damage during a period of 50 years is: 23% for the structure without isolation, 7% for the structure equipped with ERB, and 3% for the structure equipped with FPS isolation. KEYWORDS Bridges, PBD, fragility, seismic protection, friction pendulum, elastomeric bearings. 1 INTRODUCTION Earthquake damages in last decades showed the bridges as the most vulnerable elements of the transportation network. In order to mitigate potential damage, bridges with insufficient seismic performance may be seismically retrofitted (Imbsen 2001). At the
  2. 2. same time, through the modern design philosophy based on probabilistic PerformanceBased Earthquake Engineering (PBEE) approaches, the engineers are allowed to investigate different design solutions in terms of vulnerability assessment. However, if probabilistic PBEE approaches are nowadays well established and widely studied for bridges and also extended to other kind of hazards (Ciampoli & Petrini 2012), the use of the PBEE frameworks for the evaluation of the effectiveness of seismic protection devices for bridges is not so extensively treated in literature (Zhang & Huo 2009). This research aims to provide enhanced understanding of the impact of various retrofit strategies on the seismic performance of a bridge through the use of PBEE approach. Two kinds of seismic isolation devices are considered: the elastomeric bearings (ERB) and the friction pendulum system (FPS). The examined structure is an highway bridge with a steel truss deck which is continuous over the concrete piers. Therefore fragility curves are obtained for the bridge equipped with the two above mentioned type of devices, in order to assess the effect of retrofit measures on the seismic performance of bridge under a range of seismic demand levels (Padgett & DesRoches 2009). The comparison of the relative performance of the bridge piers under various retrofit measures in terms of fragility is carried out. Some issues related to the implementation of the PBEE for assessing the effectiveness of the considered isolation devices are highlighted. 2 CASE STUDY, MODELING AND GROUND MOTIONS 2.1 Case study The case study bridge "Mala Rijeka" is one of the most important bridges on the Belgrade - Bar International Line. The bridge was built in 1973 as the highest railway bridge in the World (Worlds Record Lists) and it is a continuous five-span steel frame carried by six piers of which the middle ones have heights ranging from 50 to 137.5 m measured from the foundation interface. The main steel truss bridge structure consists in a continuous girder with a total length L=498.80 m. Static truss height is 12.50 m, and the main beams are not parallel, but are radially spread, in order to adjust to the route line. The bridge longitudinal profile and the deck cross-section are shown in figure 1. 2.2 Ground motion database Current PBEE practice selects ground motions whose intensity (measured by an Intensity Measure or IM) is exceeded with some specified probability at a given site, and whose other properties are also appropriate (as typically determined by probabilistic seismic hazard and disaggregation calculations). For this study two unscaled ground motion sets prepared by N. Jayaram and J. Baker have been selected (peer.berkeley.edu/transportation/). The first set consists of 40 ground motions selected so that their response spectra match the median and log standard deviations predicted for the following scenario: magnitude = 6, source-to-site distance = 25 km. The range of spectral acceleration is between 0 to 0.6 g. The second set (not shown here for sake of brevity), consists of 40 ground motions which similarly are referred to the following
  3. 3. scenario: magnitude= 7, source-to-site distance = 10 km. For both sets it results: Vs30 = 250 m/s, earthquake mechanism = strike slip and the range of Sa is up to 1.5g; response spectra predictions are from the Boore and Atkinson (2008) ground motion model. Figure 1. Bridge longitudinal profile and bridge-deck cross section. 2.3 Bridge column modeling As well known, bridge columns are among the most important components in the seismic design of bridge structures given their role in resisting lateral seismic loads and in transferring vertical loads. The main purpose of this study is to compare two retrofit (or design) methodologies in terms of performance, therefore a simple model of a cantilever column with lumped mass is used to analyze the seismic behaviour of the bridge. The response of the pier III in figure 1 is evaluated via non-linear dynamic analyses run in OpenSees 2.2.2 (McKenna, 1997). The column is modelled with a nonlinear element with fiber-section distributed plasticity. Although the large displacements of the pile can significantly affect the design, as a rough approximation, and just for simplification purposes, the geometric non-linearity is not considered here, with the aim to provide a very first insight on the effects of the different isolation devices. The material properties are assumed as deterministic and are shown in tables 1, 2 and figure 2, where b is the strain-hardening ratio and R is a parameter to control the transition from elastic to plastic branches. According to geotechnical field test the column is assumed to be founded on rock (Radosavljevic & Markovic 1977). The superstructure is idealized as a lumped mass connected to the column top through specific elements implementing nonlinear behavior of the devices: fix restraint in the asbuilt case, the single FPBearing element in case of friction pendulum device and elastomeric Bearing element in case of elastomeric device. The column is 137 m height, with a tube variable section as shown in figure 3. The mass is distributed among the column nodes and the geometry is shown in figure 3. fpc -37050 kN/m2 Table 1. Concrete properties fpcU εc0 εU λ 0.2 fpc -0.0025 -0.01 0.1 ft -0.14 fpc Table 2. Steel properties for rebars fy E b 440000 kN/m2 2.1 E+08 kN/m2 0.01 R 18 Ets ft / 0.002
  4. 4. fy λE0 ft Ets Ep Ets (U, f pcU) (c0 , f pc) E0=2f pc/c0 Figure 2. OpenSees uniaxial materials: Concrete02 and Steel02 Figure 3. Bridge pier details (sizes are in meters). The longitudinal section is rotated of 180° 2.4 Isolation system modeling ERB and FPS are quite common isolation devices. Figure 4 shows the sketches and the correspondent behaviors of these isolators modelled by a bilinear constitutive law. The bilinear model can be completely described by the elastic stiffness k1, characteristic strength fy and post-yielding stiffness k2. Table 3 summarizes the parameters and formulas for bilinear modeling of these two isolation devices. For the FPS, the friction coefficient (m) and sliding surface radius (R) determines the characteristic strength fy and the post-yielding stiffness k2=W/R, where W is the deck weight. The FPS has a very rigid initial stiffness k1 which is taken as 75 times the post-yielding stiffness k2 (Zhang & Huo 2009). For elastomeric bearings, the post-yielding stiffness k2 is determined by the area (A), total thickness (L) and shear modulus (G) of the rubber layers, i.e. k2=GA/L. Figure 4. Bilinear relationship to model the isolation devices
  5. 5. The characteristic strength fy can be obtained by assuming a yielding displacement dy (equal to 6 mm in this paper) and the initial stiffness k1 is taken as 10 times of postyielding stiffness k2 (the value of a in the figure is 0.1). FPS Table 3. Properties of isolation devices initial stiffness k1 strength fy k1=75 k2=160000 kN/m fy=mW= 256.1 kN ERB k1=10 k2=50200 kN/m fy= k1dy =301.2 kN post-yielding stiffness k2 k2=W/R=2134.5 kN/m k2=5020 kN/m 3 SEISMIC DEMAND MODELS The traditional probabilistic seismic demand model (PSDM) offers a relationship between an engineering demand parameter EDP (e.g., column curvature) with one type of ground motion IM or with vector-valued IMs. In both cases, the seismic demands are determined by the parameters of the ground motion and of the structural system, which means that the PSDM is structure specific. Therefore, when the structural design parameters change, new nonlinear time-histories analyses have to be performed. The so called Probabilistic Seismic Demand (PSDA) method utilizes regression analysis to obtain the mean (mIM) and the standard deviation (z) by assuming the logarithmic correlation between median EDP and an appropriately selected IM: where the parameters "a" and "b" are regression coefficients obtained by the nonlinear time history analyses. The remaining variability in ln(EDP) at a given IM is assumed to have a constant variance for all IM range, and the standard deviation can be estimated: 3.1 Engineering demand parameters and intensity measure Object of this work is to focus on simple engineering demand parameters well correlated to the structural damage. For simplicity, two of the most common EDPs are adopted: the curvature ductility at the base of the pier mc and the top displacement ductility dc. In the PBEE procedures the most efficient IM should be chosen on the basis of the relationship between the structural response and the intensity of the seismic action. PGA is one of the most commonly implemented IM. However, especially in case of isolation systems, the PGA could not be the most reliable parameter. In fact the structural response is heavily influenced by the dynamic behavior of the system. For this reason in this study the spectral acceleration Sa(T1) evaluated at the first modal period T1 is adopted. However it is not easy to evaluate a suitable T1 for an isolated system. For instance, in case of base isolation, the T1 of the isolated structure can be evaluated exclusively according to the isolation device properties. On the contrary, when the isolation device is located on the top of the pier and the pier mass is considerable, the stiffness and the mass of the pier can not be neglected. At the same time, as additional modelling issue, the nonlinear
  6. 6. element for the isolation device is not operative in case of modal analysis, therefore an equivalent model need to be used to calculate the T1 value. The bearing is modeled by a linear spring with a secant equivalent stiffness to approximate the real nonlinear behavior of the device. For comparison purpose, a not-cracked stiffness has been used for the piers, in order to clearly quantify the influence of the isolation on the T1 value. Thus T1 has been evaluated through a linear dynamic analysis. The efficiency of the IM is here evaluated (as usual) on the basis of its correlation with the pertinent EDP. The vibrational periods of the examined bridge column in the three examined configurations are shown in Table 4. Table 4. Dynamic properties after gravity loads application Typology Period of the first mode [s] No isolation T1 = 1.72 FPS T1= 4.20 ERB T1 = 2.90 3.2 Regression results In the as-built case (without isolation), Sa(T1) as IM provides a better correlation than the case when the IM is assumed to be the PGA. No isolation FPS ERB Table 5. Regression parameters EDP INT SLOPE mc 1.67 0.92 PGA dc 1.15 0.81 mc 1.74 0.76 Sa(T1) dc 1.82 0.92 mc 1.75 1.33 PGA dc 1.10 1.12 mc 1.30 0.61 Sa(T1) dc 1.21 0.65 mc 1.83 1.34 PGA dc 1.11 1.14 mc 1.57 0.78 Sa(T1) dc 1.13 0.74 R2 0.54 0.35 0.86 0.92 0.72 0.63 0.58 0.68 0.67 0.63 0.64 0.75 z 0.59 0.77 0.29 0.26 0.58 0.60 0.65 0.56 0.64 0.61 0.67 0.49 The table 5 shows the IM-EDP correlation parameters for all the cases, while in the figure 5 one can see the graphical results in the case without isolation and with m c as EDP. As shown in table 5, when the isolation devices are included in the model, the differences between the dispersion (factors R2 and z) obtained by adopting the two different IMs is not as clear as in the previous case. To this regard, in figure 6 the regression results for the bridge pier equipped with FPS isolation device are also shown. The two dispersions (by assuming either the PGA or the Sa(T1) as IM) are very similar, this indicate that additional studies should be conducted in order to find an IM that is
  7. 7. clearly efficient in both cases of not isolated and isolated structures. Additional comments regarding these aspects are provided in the conclusions. Figure 5. IM-EDP regression results for the bridge pier without isolation. PGA as IM (left), Sa(T1) as IM (right); EDP= curvature ductility at the pier base. Figure 6. IM-EDP regression results for the bridge pierequipped with FPS isolation device. PGA as IM (left), Sa(T1) as IM (right); EDP= curvature ductility at the pier base. 4 FRAGILITY CURVES AND HAZARD 4.1 Damage states The EDPs or functions of EDPs are generally used to derive the damage index (DI) that can be compared with the limit states (LS) correspondent to various damage states (DS) dictated by a capacity model. For simplicity, the DI is chosen as same as the EDP in this study. A number of studies have developed the criteria for the LS and corresponding DS based on damage status of load-carrying capacity. Three damage states DS namely slight, moderate and complete damage are adopted in this study and their concerning limit values are shown in tab. 6. Through a pushover analysis, the slight damage has been associated to the achievement of maximum tensile strength of concrete, while the moderate one to the yielding of the steel rebar. A comparison between the values adopted by Choi et al. (2004) and the ductility factor defined in the EC8 for piers, has allowed us to define also limit values referred to the collapse.
  8. 8. Table 6. Summary of EDPs and corresponding LSs Slight damage DS1 Moderate damage DS2 Cracking Cracking and spalling Curvature ductility mc mc> 1 mc> 2.48 Displacement ductility dc d c> 1 dc> 1.47 EDP Complete damage DS3 Failure mc> 7.44 dc> 4.40 4.2 Fragility results Fragility curves are here developed using a 3D nonlinear time-history analysis for probabilistic seismic demand modeling. Assuming a log-normal distribution of EDP at a given IM, the fragility functions (i.e. the conditional probability of reaching a certain damage state ith for a given IM) can be written as: where F is the standard normal distribution function. Table 7. Fragility parameters (in units of g) for case study for each damage state EDP DS1 DS2 DS3 z z z mIM(g) mIM(g) mIM(g) No isolation FPS ERB mc dc mc dc mc dc 0.103 0.137 0.122 0.156 0.133 0.216 0.299 0.267 0.658 0.565 0.671 0.496 0.337 0.208 0.531 0.281 0.424 0.363 0.299 0.267 0.658 0.565 0.671 0.496 1.408 0.687 3.127 1.517 1.727 1.584 0.299 0.267 0.658 0.565 0.671 0.496 Figure 7. Fragility, with mc as EDP, for as-built (no isolation), FPS and ERB models respectively The fragility curves obtained for the three configurations of no isolation, FPS and ERB are shown in Figure 7, with mc as EDP and Sa(T1) as IM. The mean and dispersion values for all the other cases are summarized in the table 7. 4.3 Hazard and rate of failure For the structure-dependent IM selected, three different hazard curves (Fig. 8) have been evaluated, related to the three periods of vibration as illustrated below (tab. 4). In this study seismic hazard curves for Los Angeles are adopted, and calculated by the OpenSHA software (Field et al. 2003).
  9. 9. Figure 8. Hazard curves:Los Angeles, CA Table 8 -T-year probabilities of damages EDP PTf1 PTf2 PTf3 mc 2.34E-01 1.35E-02 3.87E-05 No isolation dc 1.31E-01 4.95E-02 9.30E-04 mc 3.63E-02 4.33E-04 1.31E-07 FPS dc 1.37E-02 2.13E-03 1.32E-06 mc 6.95E-02 3.35E-03 1.73E-05 ERB dc 1.10E-02 1.98E-03 2.50E-06 The seismic fragility can be convolved with the seismic hazard in order to assess the annual probability PAi of exceeding the ith damage state: where H(a) is the hazard curve that quantifies the annual probability of exceeding a specific level of IM at a site. Additionally, it is possible to evaluate the T-year probability PTfi of exceeding the damage state ith, estimated as: Assuming a T=50 years period, the probabilities of exceeding the different damage states are shown in tab.8. 5 CONCLUSIONS A comparison of the relative performance of the bridge piers under various retrofit measures in terms of fragility and probability of damage is carried out. The adoption of a structure-dependent IM, namely Sa(T1), poses some issues since the first period of vibration T1 changes in the different examined retrofitting strategies. Therefore a direct comparison of the fragility curves obtained for different retrofitting strategies on a single chart is not allowed. Sa(T1) results to be more efficient than the PGA when the isolation is not present, however this result can not be extended to the case with isolation. An explanation of that can be found in the uncertainty which affects the evaluation of a suitable T1 for the case of high pier with isolated deck. As already mentioned, the isolation device is located on the top of the pier, and also the mass of the pier is
  10. 10. considerable with respect to the mass of the deck portion relying on it. Thus a linear equivalent model has been developed to take into account the whole system: pier, device and deck. Moreover, due to the choice of using a structure-dependent IM, also the seismic hazard has been evaluated case by case for the three examined structural configurations. In terms of damage probability, choosing the example of slight damage and referring to the curvature ductility as EDP, the probability of damage during a period of 50 years is: 23% for the structure without isolation, 7% for the structure equipped with ERB, and 3% for the structure equipped with FPS isolation. 6 ACKNOWLEDGEMENTS This work was partially supported by StroNGERs.r.l. from the fund “FILAS - POR FESR LAZIO 2007/2013 - Support for the research spin-off”. 7 REFERENCES Choi, E., DesRoches R., Nielson B. (2004) “Seismic fragility of typical bridges in moderate seismic zones”. EngStruct 2004;26:187 Ciampoli, M., Petrini, F. (2012) “Performance-Based Aeolian Risk assessment and reduction for tall buildings” Probabilistic Engineering Mechanics, 28, 75–84. DOI:10.1016/j.probengmech.2011.08.013 Field, E.H., Jordan, T.H., Cornell, C.A. (2003) “OpenSHA: A Developing CommunityModeling Environment for Seismic Hazard Analysis”.Seismological Research Letters, 74, no. 4, p. 406-419 Imbsen, R.A. (2001) “Use of isolation for seismic retrofitting bridges”. Journal of Bridge Engineering ASCE, 6(6), 425-438 McKenna, F. (1997).“Object-Oriented Finite Element Programming: Frameworks for Analysis, Algorithms, and Parallel Computing”. Ph.D. Thesis, Department of Civil and Environmental Engineering, University of California, Berkeley, USA Padgett, J.E. DesRoches, R. (2009) “Retrofitted bridge fragility analysis of typical classes of multispan bridges”. Earthquake Spectra, 25(1), 117–41 Radosavljevic, Z.,Markovic, O. (1977) “Some Foundation Stability Problems of the Railway Bridge over the Mala Rijeka”. Rock Mechanics 9, 55-64 Wang, Z., Padgett, J.E, Dueñas-Osorio L. (2013) “Toward a uniform risk design philosophy: Quantification of uncertainties for highway bridge portfolios”. Proceedings of 7th National Seismic Conference on Bridges & Highways, Oakland, CA, USA, May 20-22, 2013 Zhang, J., Huo, Y.(2009) “Evaluating effectiveness and optimum design of isolation devices for highway bridges using the fragility function method”. Engineering Structures, 31, 1648-1660

×