VULNERABILITY EVALUATION OF COMMON SIMPLE-SUPPORTED BRIDGES

Transcription

1 10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska VULNERABILITY EVALUATION OF COMMON SIMPLE-SUPPORTED BRIDGES M. C. Gòmez-Soberón 1 and I. Soria-Rodríguez 2 ABSTRACT Fragility curves and damage probability matrices, defined by simulation process, of common Mexican highway bridges are presented in this work. Different typologies of bridges, located at the most seismic hazardous zone of Mexico were selected. Local and global damage indices of selected bridges were defined trough nonlinear analyses, fragility curves were elaborated with these values Changes in fragility curves were evaluated when some damage levels are presented in bridge piers. In addition, changes in fragility curves were analyzed when the bridges piers were rehabilitate with steel jackets. Results show the differences of damage probability in various bridge types. For example, a bridge with a continuous box girder and single pier by bent has more probability of damage that a bridge with simple-supported pretested girders and multiple piers by bent. 1 Professor, Dept. of Materials, Universidad Autónoma Metropolitana, México DF, México 2 Graduate Student Researcher, Dept. of Materials, Universidad Autónoma Metropolitana, México DF, México Gómez-Soberón M C, Soria-Rodríguez, I. Vulnerability evaluation of common simple-supported highway bridges. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

2 Vulnerability evaluation of common simple-supported highway bridges M. C. Gómez-Soberón 1 and I. Soria-Rodríguez 2 ABSTRACT Fragility curves and damage probability matrices, defined by simulation process, of common Mexican highway bridges are presented in this work. Different typologies of bridges, located at the most seismic hazardous zone of Mexico were selected. Local and global damage indices of selected bridges were defined trough nonlinear analyses, fragility curves were elaborated with these values Changes in fragility curves were evaluated when some damage levels are presented in bridge piers. In addition, changes in fragility curves were analyzed when the bridges piers were rehabilitate with steel jackets. Results show the differences of damage probability in various bridge types. For example, a bridge with a continuous box girder and single pier by bent has more probability of damage that a bridge with simple-supported pretested girders and multiple piers by bent. Introduction Seismic damages reported after recent earthquakes, once again have demonstrated that bridges are the most vulnerable structures in the highway system. Then, it is important that bridges remain in a full or partial operative condition, and to retrofit them as soon as possible if it is required [1]. For rehabilitation, the structure current conditions have to be determined by characterizing the more susceptible systems and defining the rehabilitation procedures to degraded structures, by means of vulnerability evaluations. The vulnerability in various structures has been defined by different procedures; one of them is the evaluation of damage probability matrices and its continuum relations, the fragility curves. When appropriate analytical tools are accessible, analytical methodologies are an adequate technique to define fragility curves. Among the analytical methodologies, the comparisons between demand and capacity, also defined as damage indices and damage spectrum, could be used. The stochastic methods with Monte Carlo simulations and artificial records are used to define fragility functions, as in the Nasserasadi et al. work [2]. Fragility curves for bridges were defined by Shinozuka [3] and Liao and Loh [4] for systems in China and Taiwan, starting from statistics of reported damages. Recently, fragility curves for bridges in México were proposed by Olmos and Jara [5], with nonlinear static analyses, where piers extreme rotation was defined to characterize damage. Nielson and 1 Professor, Dept. of Materials, Universidad Autónoma Metropolitana, México DF, México 2 Graduate Student Researcher, Dept. of Materials, Universidad Autónoma Metropolitana, México DF, México Gómez-Soberón M C, Soria-Rodríguez, I. Vulnerability evaluation of common simple-supported highway bridges. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

3 DesRoches [6] adjusted lognormal distribution to limited function, demand and capacity, to define fragility curves in the United States central southeast zones. Karim and Yamazaki [7] defined analytic fragility curves using damage indices of common bridges in Japan. Probabilistic analyses were used by Mackie and Nielson [8] to evaluate the influence in fragility curves for different uncertainties. Also, applying a probabilistic approximation, Zhang et al. [9] defined analytic fragility curves for several bridge configurations, including continuous and simple supported bridges, monolithic and simple supported abutments and structures with or without isolating elements. Using analytical methods, Shinozuka [3] and Padgett and DesRoches [10] defined fragility curves for reinforced bridges. Then, they used fragility curves as tools to ascertain the influence of some rehabilitation techniques, evaluating changes in damage stated probabilities. Related papers indicated that fragility curves for bridges are evaluated using different techniques; in recent years, using mainly nonlinear static and dynamic probabilistic analyses. In México, there are not many works that evaluate fragility curves for common bridges; it is necessary to increment these studies to define a reliable database. The analytical fragility curves for three common highway bridges are defined in this work, considering three initial reinforcing steel percentages, the reinforcement of bridge piers with two options of steel jackets and/or some substructure elements with initial degradation. Bridge models Three types of highway bridge typology in México were selected to define fragility curves. The studied bridges are: a) Motín de Oro bridge. This is a continuous box unicellular girder with single bend and circular section piers. This bridge has three-single RC piers of different length, between 4.11 m and 4.46 m, shown in Fig. 1. The four-span bridge has a total length of m. The pretressed girder has a 10 m transversal and a 1.8 m vertical dimension. The bridge is classified as irregular due to the variation of piers and girder lengths. It had been repaired in 1994 using external and longitudinal pretressed cables, Fig. 1; but the fragility curves were evaluate with the original conditions. b) Second bridge. This bridge has a simple-supported deck with AASTHO girders and multiple-bent circular piers. The girders are simple-supported over bearings, placed above two transversal girders with a length of 9.9 m. The total length of the bridge is m, with five spans of 20.5 m each one, presented in Fig. 2. The substructure has four bents, with six piers by bent with a height of 5 m, a diameter of 1.2 m and 2.32 m of transversal dimension between elements. c) Despeñadero bridge. This is a simple supported bridge, with three spans of m, 26.1 and 25.9 m, with a total length of m, Fig. 3. The superstructure consists of a concrete slab of m cross section, supported over six AASTHO IV girders. Girders are sustained in neoprene bearings of 20 x 40 cm, 4.1 cm height, for fixed bearings and 5.7 cm for movable bearings. It presents frame-type piers, with rectangular-section columns of 160 x 123 cm, and 13 m of height. Columns present a transversal strength with RC horizontal girders of 130 x 130 cm, located almost in the central part of them. There are diaphragms in the superstructure, located in extremes and each third of length.

4 Figure 1. Photograph and general dimensions of Motín de Oro Bridge Figure 2. General dimensions of Second Bridge Figure 3. Despeñadero bridge Bridges were modelled in the SAP 2000 program [11] to define dynamic characteristics. This program was used because it offers more tools to model bridge structures, like the ones to define bearings elements. Fig. 4 shows SAP models of the selected structures. The models were calibrated using experimental works [12]. The first two periods for the bridges were and 0.276; and 0.155; and and s for Motín de Oro, Second and Despeñadero structures, respectively. Bridges were also modelled using Ruaumoko 3D program [13] in order to evaluate damage indices to elaborate fragility curves. Interaction diagrams and moment curvature diagrams for piers, needed as input data for the Ruaumoko program, were defined with external

5 routines. In this work, Takeda model was applied to define constitutive laws of elements. In all the models, superstructure elements were assumed elastic, so damage could be produced only in piers. Ruaumoko models for selected bridges are presented in Fig. 5. Figure 4. SAP models of bridges Figure 5. Ruaumoko 3D models of bridges For Ruamoko 3D models, ductility in columns was defined using the expression proposed by Prietsley and Park [14] where it is assumed that the horizontal earthquake load acts in the center of mass of the system. Then, the columns ductility was evaluated by μ=1+3(φmax/φy-1)(lp/l)(1-0.5lp/l) (1) where L p is the plastic hinge length, L is the distance between the column base and the center of mass of the superstructure, ϕ y and ϕ max are, respectively, the yield and maximum curvature at the column base. Seismic load To define the external action, real accelerograms were selected to simulate artificial records. As bridges are located in one of the most hazardous region of Mexico, the Pacific Coast, real signals were selected from in area seismic stations: Colima, Manzanillo, Caleta de Campos, Scartsa, and Arteaga. From these stations, four earthquakes were chosen in function of PGA and duration values; these earthquakes represent the four seismic scenarios for with fragility curves were

6 evaluated. Selected accelerograms were: (S1) first seismic scenario, defined by the accelerograms registered the January 11 th, 1997, with a PGA of 396 cm/s 2 (this is the seismic scenario with the grater PGA); (S2) second seismic scenario, defined by the accelerograms registered the October 12 th, 1995, with a PGA of 227 cm/s 2 ; (S3) third seismic scenario, defined by the accelerograms registered the April 30 th, 1986, with a PGA of 69.2 cm/s 2 (this is the scenario with the smaller PGA); and (S4) four seismic scenario (4), defined by the accelerograms registered the September 19 th, 1985, with a PGA of 140 cm/s 2, this is the record with larger duration of the intense phase. The elastic spectra of the four accelerograms, for a 5% of critical damping and for the horizontal signal with greater PGA, are shown in Fig. 6. As it is observed, the fundamental periods of the selected accelerograms are less than 0.5 s. So, the fundamental periods of two of the selected structures are located in the greater amplitude zone of the spectrum. 11/01/1997 (396 gal) 12/10/1995 (227 gal) 19 /09/1985(140 gal) 30/04/1986( 69.2 gal) Figure 6. Acelerograms and elastic spectrums of the selected signals Elastic and inelastic analyses Fragility curves for selected bridges (Figs. 1 to 3) were obtained by means of nonlinear analyses. In these analyses, the earthquake effect was evaluated using local and global damage indices. Ruaumoko 3D code evaluates different damage index models, but in this work only the expression proposed by Park et al. [15] was used. This damage index is one of the most employed because of their simple evaluation and exhaustive calibration with experimental test. To represent the global damage of the system, Park et al. suggest a combination rule based on the proportional weigh of the local damage index of each damaged element of the bridge. Local (for elements) and global (for a system) damage indices of Park et al. are expressed as (2) (3) where δ m and δ u are respectively the maximum and ultimate strain of the element subjected monotonic load, β is represents the strength loss (β=0.15), E is the hysteretic dissipated energy, F y is the yield load and ID G and ID are the global and local indices.

7 Reinforced options Since the original design of the longitudinal reinforcing steel in columns was not available for Despeñadero bridge; it was determined considering three longitudinal steel percentages: C1, for a design with almost a minimum reinforcing longitudinal steel of ρ=0.005 (for structures of the same typology but designed with obsolete codes); C2, for a normal design of columns with a steel longitudinal percentage of ρ=0.01; and C3, for an extra reinforced elements with a steel longitudinal percentage of ρ=0.02. In this case the recommendations of ACI-318 [16] were used. For Despeñadero bridge columns with a percentage of longitudinal reinforcing steel of ρ=0.01 (case C2) were reinforced with steel jackets, considering two options: 1) steel sections with a thickness of 19 mm, and 2) steel sections with a thickness of 25.4 mm; both represent a compact steel section. To define moment-axial compressive force and moment-curvature curves and the effective stiffness of the reinforced elements, provisions of AISC-2005 [17] for composite sections, specifically for filled elements were applied. Considering this specifications, the effective stiffness of the composite section, EI eff, is EI eff =E s I s + E s I sr +C 3 E c I c C 3 = (A S / A s +A c ) (4) where E s and E c are the modulus of elasticity of steel and concrete, respectively; and I s, I sr and I c are also respectively the moment of inertia of the steel section, reinforcing bars and concrete section. Elements with initial degradation For central pier of the Motín de Oro bridge and extreme piers of Second bridge an initial degradation was considered, taking into account a reduction of 50% of the elements strength. Uncertains Evaluation A probabilistic evaluation of the damage was considered to include the uncertainty of the external load and the mechanical properties of materials. For that, the Monte Carlo simulation technique was employed, using 300 variations of the nonlinear analyses by each seismic phenomenon, bridge, initial longitudinal steel percentage and reinforced options. Table 1 shows the considered random variables with their assumed probabilistic distribution functions and the associated parameters, both taken from the available literature. The inherent uncertainty of the seismic load was defined by means of artificial records, which were generated based on the four previously described scenarios. The number of variations analyses, was defined considering that the mean value of the results is nearly constant when it is close to 300. Fragility Curves In Fig. 7, the fragility curves of some pier elements, the ones with the highest cumulative probability of damage, for the Motín de Oro, Second and Despeñadero bridges are depicted for

8 the selected seismic scenarios. For the Motin de Oro bridge, results are indicated for the left pier. For the Second bridge the fragility curves of the piers were classified, for similitude values, in three groups: external, intermediate and central piers, in transversal direction; central piers fragility curves are the ones indicated in Fig. 7. Table 1. Probabilistic description of the mechanic properties Variable Description Mean CV Distribution f c (KPa) Concrete compressive Normal strength E c (KPa) Concrete elastic modulus Lognormal W c (KN/m 3 ) Concrete specific weight Normal f y (KPa) Steel yield stress Normal f u (KPa) Steel ultimate stress Normal E s (KPa) Steel elastic module Lognormal W s (KN/m 3 ) Steel specific weight Normal Despeñadero Bridge does not suffer damage with anyone of the four seismic scenarios, the results presented in Fig. 7 for a column (the four columns have similar marks) were obtained scaling the accelerograms by a factor of five. For Motin de Oro and Second bridges, results for the S3 seismic scenario was not presented in Fig. 7 because for the majority of the analysis variations, the elements had an elastic behaviour. In this figure, it is observed that the obtained probabilities are similar for the Motín de Oro and Second bridges, when they are subjected to seismic scenario S1. However, for the others seismic scenarios, the probabilities obtained in Second Bridge were lesser, having a minor or equal damage level. Once the damage indices were defined, the global evaluation of structures is accomplished using Eq. 2. With this global damage index, fragility curves of bridges were defined. Fig. 8 presents the fragility curves of the Motín de Oro and Second bridges for the seismic scenario S1. It is observed in this figure that the Motín de Oro Bridge is more vulnerable to this seismic scenario. For these structures, the probabilities of ID G 0.25 is 100%, so at least they have a minor damage for a seismic action similar to the one considered. The Motín de Oro bridge has a probability of 0.38 to have Severe damage (ID G 0.4), while the other structure has a probability of 0.08 for the same scenario. Fragility curves for other longitudinal percentage of reinforcing steel, Cases C1 and C3 were also obtained; it was observed that there are greater probabilities to exceed a specific damage level for bridges with minor reinforced longitudinal steel in columns, as it can be expected. Then, if the structure was designed with a moderate percentage of the longitudinal reinforcing steel, it has moderate probability to suffer mayor damage. Therefore, fragility curves can be used to assess the confidence intervals of a design option. Fragility curves of Motín de Oro bridge and Second bridge were defined when damage is presented in an element or group of elements. For the right pier of Motín de Oro bridge and central piers of Second bridge a strength degradation of 50% was assumed, without changes in the resistance. Fragility curves for bridge elements are presented in Fig. 9. Fragility curves for central piers of Second bridge are not presented (right graphs) because for the majority of variations, the damage indices are lesser than 0.1, so it is impossible to adjust a theoretical

9 probability distribution function S1 S2 S S1 S2 S Motín de Oro Second Depeñadero Figure 7. Fragility curves of the left pier of Motín de Oro, central elements of Second bridges. Seismic scenarios S1, S2 and S Second bridge Motìn de Oro bridge Figure 8. Fragility curves of bridges. Comparing fragility curves for elements with or without previous damage, it is observed that the elements with strength degradation sustain lesser damage, so other more resistant elements assumed the load and have more damage, as it is expected. For Motín de Oro bridge (left curves in Fig. 9), for a minor or equal damage of 0.4 the cumulative probability were of 0.46, 0.64 and 0.83 when damage is not presented, while this probabilities were of 1.0, 0.19 and 0.32 when a previous damage is considered. For the Second bridge similar results were obtained. Changes in cumulative probabilities, for damage greater than 0.4, are up to 44% and 59% for Motín de Oro and Second bridges, respectively. However, the collapse of one pier in the Motín de Oro bridge could represent the collapse of the structure.

10 Figure 9. Fragility curves of elements of bridges with previous damage. S1 scenario For the two steel jacket conditions of reinforcement of columns of Despeñadero bridge, sections with thickness of 25.4 mm and 19 mm, the structure does not present damage. Steel jacket with a thickness of 25.4 mm are associated with a compact section, while the section with a thickness of 19 mm is the minor dimension for a compact section. Others retrofitted options have to be analyzed to define change percentages of damage indices. Conclusions Fragility curves of three common highway bridges are defined for different longitudinal reinforcing steel percentages, for four seismic scenarios, and for elements with previous degradation. In addition, two reinforcement options with steel jackets were used for the bridge columns. Results show that: In the Motín de Oro Bridge, the most and the less earthquake-vulnerable piers were the extreme ones. The most vulnerable elements for Second bridge where the central piers, while for Depeñadero bridge, the four columns have similar results. Bridges have elastic behaviour for some variations of a specific seismic scenario, so fragility curves were not possible to be estimated. Using fragility curves, more vulnerable elements and systems were characterized When one pier or group of piers has or have previous strength degradation, these elements support lesser load but the other substructure elements have more probability of damage. Second Bridge has greater percentage of damage probability than in Motín de Oro Bridge, but a collapse in a pier of the previous bridge type could cause the structure collapse. Fragility curves of the systems are similar with or without previous damage. For C1 reinforcing steel percentage (ρ=0.005), most of local and global damages are near to 1.0. So, old structures, with minimum reinforcing steel percentage could sustain important damage. Comparing the damage indices for C2 (ρ=0.01) and C3 (ρ=0.02) cases (percentages of reinforcing bars in columns) of Despeñadero bridge, it is observed that C2 case has greater damage that C3 case. Then, a more precise design could limit an extensive damage.

11 Starting from the C2 columns design case, reinforcing of this elements were proposed, considering two options of steel jackets. Then, steel sections with a thickness of 25.4 mm and 19 mm were proposed, both represent a steel compact section. For both options, minor damage, less than 0.1, were defined. Using fragility curves, we can introduce a probability evaluation of the behavior of the reinforced bridge elements. Fragility curves can be used as decision tools to define inspection period of time for different elements and bridge typologies Other retrofitted options should be studied considering concrete and fibers jackets. References 1. Shinozuka, M. Effect of seismic retrofit of bridges on transportations networks. Earthquake Engineering and Engineering Vibrations, 2003; 2 (2). 2. Nasserasadi, K, M Ghafory-Ashtiany, S Eshghi, M. R. Zolfaghari. Developing seismic fragility functions of structures by stochastic approach. Asian Journal of Civil Engineering, 2009; 10 (2): Shinozuka, M. Development of bridge fragility curves, Proceedings, US-Italia in Seismic Evaluation and Reinforcing, MCEER, Multidisciplinary Center on Earthquake Engineering, 1998; Liao W and C. Loh, Preliminary study on the fragility curves for highway bridges in Taiwan, Journal of the Chinese Institute of Engineering, 2004; 27 (3): Olmos, B. M. Jara Curvas de fragilidad de desplazamiento de puentes con subestructura tipo marco, XVIII Congreso Nacional de Ingeniería Sísmica, México, In Spanish. 6. Nielson B G and R. DesRoches, Analytical seismic fragility curves for typical bridges in the central and Southeastern United States, Earthquake Spectra, 2007; 23 (3): Karim K R and F. Yamazaki, Comparison of empirical and analytical fragility curves for RC bridges in Japan, 8th ASCE Special Conference on Probabilistic Mechanics and Structural Reliability, Mackie, K R, B. G. Nielson, Uncertainty quantification in analytical bridge fragility curves, Lifeline Earthquake in a Multi-hazard Environment, ASCE, 2009; Zhang, J Y, S. Huo, J. Brandenberg, P. Kashighadi, Effects of structural characterization on fragility functions of bridges subjected to seismic shaking and lateral spreading, Earthquake Engineering and Engineering Vibrations, 2008; 7 (4): , DOI: /s Padgett, J E, R DesRoches. Methodology for the development of analytical fragility curves for retrofitted bridges, Earthquake Engineering and Structural Dynamics, 2008, (37): DOI: /eqe.801m. 11. SAP 2000, Advanced 14.1, integrated solution for structural analyses and design, Computer and Structures INC. 12. Jara, J, M. (2010) Personal communication 13. Carr, A J. Ruaumoko 3D, Inelastic dynamic analyses, Civil Engineering Department, University of Canterbury, Priestley, M J y Y J Park. Strength and ductility of concrete bridge columns under seismic loading, ACI Structural Journal, Technical Paper, Title No. 84-S8, Park, Y. J. y A. H. Ang (1985) Mechanistic seismic damage model for reinforced concrete, Journal of Structural Division (ASCE), Vol. 111, No. 4, pp ACI-318, Building Code Requirements for Reinforced Concrete (ACI ) and Commentary, American Concrete Institute, Detroit Michigan, AISC, Specifications for Structural Steel Buildings, Chapter 1, Design of composite members. American Institute of Steel Constructions, Inc