Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis of an Existing Bridge

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1 Journal of Civil Engineering and Architecture 9 (215) doi: / / D DAVID PUBLISHING Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis João Coimbra Sampayo and Carlos Sousa Oliveira Instituto Superior Técnico, Universidade de Lisboa (Superior Technical Institute of Lisbon University), Lisbon 149-1, Portugal Abstract: This paper is dedicated to study of seismic performance of an existing RC (reinforced concrete) bridge localized in a region of moderate seismicity. The bridge has six spans and piers with very different heights, three of which are monolithically connected to deck. To understand roles of different pier sizes in overall behavior, several analyses were carried out in longitudinal direction: (1) linear dynamic approach; (2) non-linear static approach; (3) non-linear dynamic approach. Linear dynamic analysis was made in order to design bridge for ultimate limit state considering largest value of ductility factor. No safety verification was made for or loads. Using non-linear static analyses, sensitivity was performed to check influence of reinforcement quantities of each pier on overall behavior of bridge under Lisbon seismic action. For non-linear dynamic approach, a series of strong motion records compatible with EC-8 spectrum for Lisbon area were generated. The very same combinations of reinforcement quantities were studied. Comparisons between static and dynamic non-linear analysis were made to confirm validity of first one in case under analysis, where period of vibration is quite high. Key words: RC bridge, seismic behavior, linear methods, non-linear methods. 1. Introduction Till mid-fifties of last century, effect of seismic action on structures was represented by static lateral forces with value equivalent to a percent of existing vertical loads. This method was considered not sufficient to characterize seismic behavior and, consequently, or methods based on kinematic and dynamic modeling of structures were developed. Non-linear analyses were recommended after understanding that linear methods by mselves could not represent reality in many instances, even though linear modeling toger with concept of ductility is still in use in majority of design offices. At that time, a set of studies were made in order to study in detail cycle behavior of steel and concrete, and influence of various seismic parameters of seismic action namely PGA (peak ground acceleration), PGV (peak ground velocity), frequency content and duration. Corresponding author: João Coimbra Sampayo, scholar grantee, research fields: earthquake engineering and dynamics. joaocsampayo@gmail.com. In behavior of structure, we should explore ductility, not only to support displacements but mainly energy accumulated in structure. In past Portuguese code [1] and in recent developed EC-8-1 [2], linear methods are recommended toger with use of behavior coefficients. However, with introduction of high capacity computations, it is possible today to analyze more complex structures, giving rise to non-linear static and dynamic studies. In particular, static methods, among which is so-called N2, when applied to regular structures, present results which are quite adequate so y initiate ir exploitation in design (as recommended in EC-8). Neverless, for irregular structures, y do not have capacity to simulate all conditioning constrains. In this paper where an irregular structure with a pier of high stiffness is modeled, this method is tested against a more general method of non-linear dynamic analysis and results are confronted both with non-linear static and with just linear methods. In this way, it is possible to check how far more sophisticated method comes from or methods.

2 636 Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis The bridge has a total length of 44 m with six spans: central two with 1 m, two with 75 m and two connecting to embankments with 45 m. The deck, a monolithically multi-supported beam, has a hollow box-girder of variable height. The three central piers are monolithically connected to deck and are 62., 67.4 and 24.8 m high, respectively. The cross-section of se piers is typicallyy a hollow rectangle reinforced at corners and with variable dimensions in region close to base. The or spans are supported by supporting devices at piers connections and embankments. Fig. 1 presents profile of bridge and geometric characteristics of typical cross-sections. Following initial design, a concrete C4 and steel class A4 were used in this analysis. The main properties of se materials which were used in linear analysis, are presented in Table 1 (values already reduced as in design), while non-linear constitutive relations for those materials are based in Mander [3] for concrete and Manegotto [4] for reinforcement. 2. LDA (Linear Dynamic Analysis) The linear analysis was performed with SAP2 software [5], strictly following original drawings. The deck and piers were modeled with beam elements with a discretization of 3.5 m for Pier 4 and 5 m for all or elements. Piers were built-in at foundation, a solid rock geological complex. In this analysis, all piers were supposed monolithically connected to deck. The concrete Young modulus value is reduced to 5% to consider exteriorr cracking of concrete. Two main modal shapes weree identified in analysis performed on longitudinall and vertical direction only: one associated with longitudinal displacement of deck with a period of T = 1.76 s, and local mode of Pier 3 with a period of T =.33 s. These values were validated by in-situ ambient measurements provoked by vibration of passing cars and vans. The bridge was considered as belonging to importance Class IV (corresponding to an importance factor γ = 1.95) located in a soil Type A [2]. h h h (a) Mid-span section 2-S, 3-S, 4-S and 4-I 2-I and 3-I (b) (c) (d) Fig. 1 Profile of bridge and geometric characteristics of cross-sections: (a) bridge overall; (b) mid-span section; (c) piers superiorr sections; (d) piers inferior sections (units in m). Source: credits by Armando Rito.

3 Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis 637 Table 1 Material s properties used in linear analysis. Material E (GPa) f k (MPa) f cd (MPa) C4 A In design of steel bars, behavior factor q = 3. was assumed and bridge was studied for three different zones of increasing seismicity starting from original situation: Azambuja with a lower hazard than Lisbon, Lisbon and Aljezur with a higher hazard. Fig. 2 shows acceleration design spectra (Se) corresponding to se locations [6]. The forces directly obtained from SAP2 were added to ones due to second order effects (MM Ed, N Ed ). The analysis of transversal section is made through a simple model of an equivalent binary moment where group of core-flange supports all bending (F M = M Ed /z) and axial (F N = N Ed /2) forces as shown in Fig. 3. By analyzing efforts in Pier 4, it was possible to determine seismic action in Lisbon, such as one which can exploit better ductility of that pier due to percent of reinforced bars of ρ L = 1.8%. The displacement of deck for this case is δ Ed =.19 m and basal shear V Ed = 12, 893 kn which corresponds to a seismic coefficient β = 8.3%. Table 2 presents design efforts, where I and S represent inferior and superior critical sections of each pier. The piers are designed according to EC-8-2 based on capacity design considering an over-strength factor of γ = The length of critical zone is l h = 4 m for both upper and lower zones. The steel bars are 192Φ32 and 176Φ32, respectively, in lower and upper critical zones. These quantities are distributed to flange and core. In connecting zone, steel percent is reduced until approximately mid height where steel is 3Φ32. Dealing with hollow sections, EC-8-2 [7] does not require confinement, however, in cores a minimum quantity of steel for outer stirrups and four stirrups in inner part in both directions, all Φ12//.1. To warrant an adequate shear safety in connection between cores and webs, an additional T (s) Fig. 2 Design response spectrum. Se (m/s 2 ) z Fig. 3 Model of an equivalent binary. Table 2 Forces demand in critical sections. Demand V E (kn) N Ed (kn) 2-S 1, ,, I 1, , S 9, , I 9, ,932.3 MEd (kn m) 59,,59.2 8, , ,25.85 reinforcement with double stirrups Φ16//.1 in critical zones and Φ12//.1 elsewhere. In or piers, a longitudinal steel of 64Φ25 was applied along alll height. 3. NLSA (Non-linear Static Analysis) Using non-linear software SeismoStruct [8], a static analysis of structure was made for ground motion of Lisbon. To proceed with this software, several adaptations were required to represent cross-sections by fiber areas. The deck was modeled as in SAP2 in such a way to keep two conditions: (1) equal displacement; (2) equal stiffness rotation, at top of piers. To achieve that, elements of deck between piers are considered with same flexuree stiffness as in SAP2. The spans outside and central spans are modeled with rotation springs. The masses associated directly to Piers 2, 3 and 4 are applied as concentrated masses in upper part of each one. The remaining masses are applied at a point N Ed 3 Azambuja Aljezur Lisboa M Ed 4 F c = F M + F N F y = F M F N

4 638 Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis outside showing identical displacement to displacement of top of piers. Piers cross sections are modeled as an equivalent section that program has in its library. Among possibilities, option was to use an H shape due to large area far from center, keeping in mind that only longitudinal direction of bridge was under study. The equivalent geometry of each section was determined in such a way to warrant same transversal area and same flexure inertia. This can be reached fixing height (h) and web width (w eq ) and changing flange width (b) and thickness (y) of equivalent section as shown in Fig. 4. We should note that plastic behavior of both sections is similar. However, due to large variation of Young modulus along its length, quantity of area of fibers furr located is a factor that may jeopardizee equivalence process of sections once equivalent section presents larger areas of fibers furr located than original section. In order to study sensitivity of distribution of fibers in lateral stiffness, in individual behavior of each pier and state of stress-extension models of longitudinal steel distribution were created. The steel used in each of critical section, four different pier was one obtained with linear model for three piers described above. The name attributed to each case reflexes amount of reinforcement applied as shown in Table 3, being b lowest steel case and A highest. The table also presents reasons for different choices and expected results. The target displacement for each above referred model subjected to seismic loading is computed using N2 approach [9], making use of simplification of system into an equivalent degreee of freedom. The equivalent period T eq is determined equating energy accumulated and ultimate displacement δ u by both original and equivalent system (assuming an elasto-plastic behavior defined by yielding displacement δ y and corresponding base shear V el ). The equivalent mass m eq is associated with masss which actively contributes to fundamental mode shape of bridge in longitudinal direction. That is mass of deck plus masses of piers above ir inflection points. T eq and m eq leads to tangentt rigidity of equivalent system K eq and elastic acceleration S ae e. For flexible structures, targett displacements developed by structure δ ob and by equivalent single degree of freedom δ el are identical. The latter is obtained from ADRS (acceleration displacement response spectrum) as shown in Fig. 5, where S a is acceleration spectrum and S d is displacement spectrum. The coefficient q N2 between total base shear in elastic and in original models reflects ductility capacity of bridge and it increases with increase of stiffness of secondary piers, and mainly with decrease of stiffness of secondary piers. The same statement can be held about value of T eq. As such, decrease of equivalent period is associated with higher stiffnesss and corresponding proximity of a rigid-perfectly plastic behavior, which is an ideal situation as far as energy dissipation is concerned. The plastic factor f pl was introduced to relate ultimate secant rigidity to tangent rigidity (f pl = K ul /K eq ). Lower participation of secondary piers leads to an increase of plastic factor f pl and, consequently, restrain of same displacements s with larger capacity for energy dissipation. Stiffness of Pier 4 does not influence this factor. Table 4 presents in a compact format values obtained for each model. The b.b.a. model is one shorter equivalent period and is sole that presents a target displacement lower w eq /2 h (a) (b) Fig. 4 Determination of equivalent section: (a) original section; (b) equivalent section. b w eq y

5 Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis 639 Table 3 Reinforcement distribution for button section of each pier (units in m). Model Description Piers 2 and 3 Pier 4 b.b.b. Minimum steel in all piers, economically, is most advantageous and one expected to yield in first place. As it should lead to large spectral displacements due to increase of vibrating period, it shows a higher ductility requirement. A.A.b. Steel distribution which causes larger participation in secondary piers. It is studied aiming at determining deformability capacity of Pier 4 which is with very low reinforcement. b.b.a. Steel distribution according to linear model. This distribution leads to a non-linear behavior better matching linear case. So it is used as a model for comparison with or cases. A.A.A. Maximum distribution of steel in all piers. This model tends to exploit, to a lesser extension, ductility capacity to support larger elastic displacements. Besides, as it is more rigid in beginning, it leads to smaller spectral displacements. Table 4 Target displacement, plasticity factor and behavior factor. Model K eq (kn m) δ u (m) V el (kn) δ ob (m) V ob (kn) f pl q N2 b.b.b. 126, , , A.A.b. 16, , , b.b.a. 136, , , A.A.A. 115, , , S a S ae (T eq ) V ced /m eq K eq T c Fig. 5 Determination of target displacement by N2 approach. T eq Equivalent system Original system δ y δ el = δ ob δ u S d than all ors. The difference is lower than 3% which is considered negligible. The stiffness of secondary piers does not influence value of first yield which always occurs in Section 4-I. For this reason, stage of structure is almost exclusively attributed to Pier 4. In next stage, secondary piers with higher stiffness gradually get a higher participation, allowing a considerable increase in structural load capacity. On or hand, models with secondary piers with low reinforcement do not increase capacity in post-yielding stage.

6 64 Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis δ t (m) Fig. 6 Force-displacement of analyzed models where O represents yielding of a section and X representss target displacement δ ob. Fig. 7 Relative stiffness influence in sections curvature M (x1 3 kn m) b.b.a. 4 I 2 b.b.b. 4 S χ (m 1 ) Fig. 8 Moment-curvature of sections. We can see in Fig. 6 that models, where Pier 4 is strongly armed, can support slightly larger displacements in deck. This is due to fact that Pier 4 exerts a great reaction on deck causing smaller curvatures χ, for same top displacement δ 1, as schematically represented in Fig. 7 for Element 2. Looking at Fig. 8, we can see that capacity of cross-sections to take curvatures is much more dependent on amount of reinforcement as already stated by Brito [ 1]. The rupture of sections is always due to exhaustion of deformability capacity in steel. This is due to significant low position of neutral axis, a consequence of low axial reduced load. For target displacement, second steel layer of secondary piers never yield. However, for models with low reinforcement, yielding is attained because elements are subjected to larger curvatures (schematically represented in Fig. 7), by Element 1 in contrast with Element 2. On or hand, for those highly reinforced piers, re is no yielding. In Fig. 9, we can see distribution of axial stressess in upper cross-sections of Piers 2 and 4 for b.b.b. model. The solid lines represent stressess in concretee and dots represent stressess in reinforcement bars. Referring to cross section in Pier 2, we can see that reinforcement bars in compressed flange are still not yielding, implying that Pier 2 still keeps a considerablee capacity for load carrying. Loads acting at critical sections of models b.b.b. and b.b..a., including ir kinematical state, are presented σ c (MPa) Section (m) S Concrete Stress 4 S Concrete Stress 2 S reinforcement stresss 4 S reinforcement stresss σ reinf (MPa) Fig. 9 Stress in concrete (solid line) and in reinforcement bars (dots) superior sections of Piers 2 and 4.

7 Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis 641 Table 5 Loads acting in performance displacements. Model Section M ob (kn m) N ob (KN) V ob (kn) η ob (%) χ ob ( /m) LN ob (%) ε y,ob ( ) ε c,ob ( ) b.b.b. b.b.a. 4-I 88,579-33, , S 79,198-27, S 64,421-26, , I 173,561-34, , S 163,683-28, S 64,48-26,33.6 2, δ t (m) t (s) Original model b.b.b..3 Optimized model b.b.b. Fig. 1 Time-history of deck displacement. in Table 5. Once performance displacements are identical, we observe that not even increase in steel reinforcement in Pier 4 influences efforts and deformations of cross-sections of secondary piers and vice versa. This means that se efforts and deformations of Pier 4 vary quite slightly with amount of reinforcement. 4. NLDA (Non-linear Dynamic Analysis) In this section, a non-linear dynamic analysis of models defined in Section 3 is made in SeismoStruct [8] by applying a set of acceleration time history records. Six records were syntically generated and adjusted to linear spectral shape defined in Section 3. The records are applied at foundation level of three central piers in longitudinal direction. The analysis of response of each one of four models is made for six accelerograms in a total of 24 cases. The basic target configuration used for comparing results is horizontal displacement of deck. Noneless, re is anor important configuration at level of secondary piers. This latter phenomenon is more visible for models with lower reinforcement in se piers. This occurs due to high flexibility of se piers, moving in higher modes, but not constraining overall base configuration. On sequence of a preliminary study of consequences, one concludes that curvatures and extensions in steel in sections along height of piers do not overpass χ = 7 /m and ε y = 25, respectively. Those modes introduce presence of noise in overall hysteretic curves. In order to have a measure of total hysteretic damping coming from non-linear behavior, filtering was applied to system by creating an optimal model with null mass in piers but warranting that total dynamic mass was same. As an illustration, Fig. 1 shows time history of displacements and hysteretic curves for models b.b.b., both optimized and original ones under same accelerogram. The optimized models present similar maximum displacements and similar apparent periods of vibration to values obtained with original models. For this reason, optimized models seem to be good representations of original ones, but without noise. As referred above, an analysis of 24 cases of optimized models is presented below, considering maximum displacements and base shear. The concept of secant period T s is introduced as period of an elastic structure with a secant stiffness obtained from stage force-displacement at maximum. In parallel, apparent period T a is also introduced as value obtained from main periodicity observed in response time history of each run. Table 6 presents average response of all six input

8 642 Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis Table 6 Maximum base shear and deck displacement. Model (kn) (m) (s) (s) b.b.b. 12, A.A.b. 14, b.b.a. 19, A.A.A. 2, Table 7 Damping coefficient due to hysteretic behavior. Model n E D (kn m) ξ h ξ b.b.b , A.A.b. 6. 6, b.b.a , A.A.A , Table 8 Values obtained in different analyses made. Analyses DLA NLSA DNLA δ t (m) V (kn) 12,893 18,56 19,94 β , 15, 1, 1, 15, 2, V (kn) 5, δ t (m).2.1 5,.1.2 NLSA NLDA LDA Fig. 11 Capacity curves for different analyses made. accelerograms for each model under study. It should be noted that scatter associated to response values is quite high, attaining in one case value of.29 m for displacement. Neverless, hyposis of equal displacements stands if we consider that maximum difference between maximum displacements in all cases is smaller than 8%. Next, analysis of hysteretic curves is made for each case. To estimate overall area of hysteretic damping dissipation, an envelope of all responses was determined. The area inside envelope represents an upper estimative of maximum energy dissipated per cycle and total energy dissipated is only this one multiplied by number of effective cycles. And a cycle is considered an effective cycle if deck surpasses yielding defined in non-linear static analysis. Damping coefficient due to hysteretic behavior (ξ h ) is given by following equation: ED 2 h n 4π V A summary of damping coefficients from hysteretic phenomena is presented in Table Conclusions The various analyses reported in this paper were made with main objective of deepening knowledge of seismic behavior of a bridge with different pier heights, in which concerns deformation capacity of ir component elements and in factors that may alter that capacity. To achieve this objective, a first linear analysis of an existing bridge was made leading to steel design of critical cross-sections warranting ultimate limit state. Subsequently, a study of sensitivity on amount of steel reinforcement to be used was made. This study, with four different cases, involves non-linear static and dynamic analyses. One of cases, b.b.a., was selected as having same distribution of steel reinforcement of linear case to serve as comparison with or three models. Considering that non-linear dynamic analysis is one that better represents reality, being ors (simpler models) approximations to reality, values obtained with first one are always slightly above ors, causing some perplexity if only simpler models are used. The case under analysis is one deserving a better understanding of entire behavior. In Table 8, it is presented forces and displacement obtained in different analysis made. Fig. 11 shows a comparison of capacity curves derived with various methods referred. The main difference is on capacity curve of linear analysis that max max

9 Seismic Performance of Bridges with Different Pier Heights: Longitudinal Analysis 643 underestimates or ones. As such, it was concluded that behavior coefficient selected for linear analysis based on EC8-2 (q = 3.) is not a good representation for this bridge, once N2 method leads to only half of that value. This suggests this type of bridge be considered as an inverted pendulum as behavior is almost governed by Pier 4. In this sense, it is recommended that behavior coefficient, according to EC8-2, should consider participation of various piers and ir connection type to deck, and not only type of global structural system of bridge. Anor parameter to take into consideration is plasticity factor that may inform on importance of components with less degree of participation. It became clear that curvature capacity of se short piers is very much conditioned by rupture of steel, but ultimate curvature is not much influenced by amount of steel. As far as structural solution is concerned, it can be optimized without touching adopted aestics. The recommendation goes to create a hinge at connection of Pier 4 to deck. This way, it is possible to assure that curvature depends only on top displacement, which, for very flexible structures, does not depend on longitudinal stiffness. The second alteration has something to do with adoption of cross-sections with clear bending dependence with smaller depths at bottom of taller piers. From this study, which only considers seismic load, one can conclude that longitudinal seismic analysis of this type of structures should be made exclusively based on small pier, due to fact that, whatever exploitation of resistance of longer piers, participation of small pier is predominant in overall response. References [1] RSA Regulamento de Segurança e Acções para Estruturas de Edifìcios e Pontes (Code of Safety and Seismic Actions for Buildings and Bridges), Dec 238/83, Imprensa Nacional. (in Portuguese). [2] EN (European Norm). 24. EC-8-1. Eurocode 8: Design of Structures for Earthquake Resistance Part 1: General Rules, Seismic Actions and Rules for Buildings. Reference No. EN :23 E. Brussels: EN. [3] Mander, J. P., Priestley, M. J. N., and Park, R Theoretical Stress-Strain Model for Confined Concrete. ACSE (Americna Society of Civil Engineers) Journal of Structural Engineering 114 (8): [4] Menegotto, M., and Pinto, P. E Method of Analysis for Cyclically Loaded RC Plane Frames Including Changes in Geometry and Non-elastic Behaviour of Elements under Combined Normal Force and Bending. In Proceedings of Symposium on Resisntance and Ultimate Deformability of Structures Acted on by Well Defined Loads, International Association for Bridge and Structural Engineering, [5] Computers and Structures, Inc. 28. Integrated Structural Analysis and Design Software. Berkeley: Computers and Structures, Inc. [6] DNA (National Document Application) Committee for Application of EC-8 to Portugal. DNA. [7] EN. 25. EC-8-2. Design of Structures for Earthquake Resistance Part 2: Bridges, Ref. No. EN :25 E. Brussels: EN. [8] SeismoSoft. 26. SeismoStruct. SeismoSoft. Accessed January 1, [9] Fajfar, P. 2. A Nonlinear Analysis Method for Performance-Based Seismic Design. Earthquake Spectra 16 (3): [1] Brito, A Dimensionamento de Estruturas Subterrâneas de Betão Armado Sujeitas a Acções Sísmicas. Ph.D. sis, Instituto Superior Tecnico. (in Portuguese).