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1 This article was downloaded by: [Kwon, Oh-Sung] On: 18 March 2009 Access details: Access Details: [subscription number ] Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Structure and Infrastructure Engineering Publication details, including instructions for authors and subscription information: Fragility analysis of a highway over-crossing bridge with consideration of soilstructure interactions Oh-Sung Kwon a ; Amr S. Elnashai b a Department of Civil, Architectural, Environmental Engineering, Missouri University of Science and Technology, MO, USA b Mid-America Earthquake Center, University of Illinois at Urbana-Champaign, Urbana, IL, USA First Published on: 07 March 2009 To cite this Article Kwon, Oh-Sung and Elnashai, Amr S.(2009)'Fragility analysis of a highway over-crossing bridge with consideration of soil-structure interactions',structure and Infrastructure Engineering, To link to this Article: DOI: / URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 Structure and Infrastructure Engineering 2009, 1 20, ifirst article Fragility analysis of a highway over-crossing bridge with consideration of soil structure interactions Oh-Sung Kwon a * and Amr S. Elnashai b a Department of Civil, Architectural, Environmental Engineering, Missouri University of Science and Technology, 1401 North Pine Street Rolla, MO , USA; b Mid-America Earthquake Center, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, IL 61801, USA (Received 9 October 2007; final version received 3 December 2008) Seismic fragility relationships, including the soil structure interaction (SSI) of a common bridge configuration in central and eastern USA, are derived in this study. Four different modelling methods are adopted to represent abutments and foundations of the bridge, namely, (a) fixed abutments and foundations, (b) lumped springs developed from conventional pile analysis of piles at abutments and foundations, (c) lumped springs developed from three-dimensional finite element (3D FE) analysis of abutments and foundations and (d) 3D FE models. Seismic demand on the bridge components is estimated from inelastic response history analysis of the SSI systems. Finally, fragility curves of the components and bridge system are derived. The four different SSI approaches result in different seismic fragility. The implication of this work is that careful consideration is necessary when selecting an analytical representation of a soil and foundation system to obtain reliable earthquake impact assessment. In addition, it is found that abutment bearings are the most critical components for the studied bridge configuration. Keywords: fragility analysis; soil structure interaction; bridge analysis 1. Introduction Seismic risk assessment is required for estimating social and economic losses from earthquakes and for mitigating the estimated losses. Seismic risk may be characterised by the integration of three components: hazard definition, fragility curves and inventory data. Among these components, fragility curves of structures associate the level of ground motion intensity with structural damage. The derivation of fragility curves requires probabilistic seismic performance analysis of structures. Over the past decade, a considerable number of studies have been conducted on the derivation of seismic fragility curves. Some of the fragility curves were derived based on observed damage from past earthquakes (Orsini 1999, Rossetto and Elnashai 2003), while others were derived from analytical simulations (Mosalam et al. 1997, Chryssanthopoulos et al. 2000, Reinhorn et al. 2001). Fragility curves from observed damage data are the most realistic, but lack generality. These fragility curves also include large uncertainty because the damage assessment is based on subjective observations of field investigators. Moreover, few seismic regions have well-organised structural damage reports that can be used for the derivation of fragility curves. With these limitations in the empirical derivation method, analytical derivation of fragility curves is the most commonly adopted approach. The analytical derivation of seismic fragility curves of structures requires realistic analytical representation of structural components. Up to now, most seismic fragility curves of buildings have been derived based on the assumption that structures are supported on rigid foundations. For seismic fragility curves of bridges, Nielson and DesRoches (2007) assumed that pile foundations could be represented as lumped springs, which is the most commonly adopted approach to model a soil foundation system. Soil, however, is a very complex material with a broad spectrum of properties, including friction, cohesion, dilation/contraction and buildup/dissipation of pore water pressure. In addition, the randomness of material properties is much higher than that of common structural materials. Hence the lumped spring approach may not represent the complexity of soil behaviour, neither is it able to explicitly represent the uncertainties associated with soil properties. The objective of the research presented in this paper is to identify the effect of different soil structure interaction (SSI) analysis approaches on the derived seismic fragility curves. To focus on the effect of different soil and foundation modelling representations, fragility curves of a common bridge configuration found in central and eastern USA are derived, rather than deriving a set of fragility curves for several different structural configurations. *Corresponding author. kwono@mst.edu ISSN print/issn online Ó 2009 Taylor & Francis DOI: /

3 2 O. Kwon and A.S. Elnashai 2. Selection of the reference bridge A highway over-crossing bridge in southern Illinois is selected as representative of the bridge inventory in the region. The bridge is located about 110 km from the New Madrid Fault. Nielson (2005) surveyed the bridge inventory of 11 states within central and southern USA and presented statistics on bridge configurations. The reference bridge selected in this study belongs to the category of multi-span continuous steel girder bridges (MSC), which is the third most common configuration (13%) of the entire bridge inventory after multi-span simply supported concrete girder bridges (MSSC; 19%) and single-span concrete girder bridges (SSC; 14%). Figure 1(a) depicts the location of the bridge alongside a city, Paducah, Kentucky, for which artificial ground motions have been generated by Ferna ndez (2007). The selected bridge consists of three bents and continuous steel girders, as illustrated in Figure 1(b). The deck is supported on fixed bearings at bent 2 and on expansion bearings at bents 1 and 3 and the abutments. Each bent consists of three circular piers supported by a pile cap and 10 steel piles. The piles at bent 2 are battered towards the abutments to resist moments transferred from longitudinal movement of the deck. Each abutment in the reference bridge is supported on six steel piles, two of which are battered towards the bridge. Five boring tests were conducted at the site. The boring test results showed that bedrock is located at an average depth of 4.57 m below the bottom of the pile caps. The soil layers consist predominantly of very stiff to hard clays. 3. Seismic hazards at the bridge site Seismic hazards in central and eastern USA are characterised by infrequent but damaging earthquakes. The moment magnitudes of the New Madrid earthquakes from were estimated to be , which are some of the largest earthquakes in the USA since its settlement by Europeans (USGS 2006). The area affected by the earthquake reached 600,000 km 2. Even though those earthquakes occur infrequently, paleoseismic studies using liquefaction features show that there is evidence of other large, prehistoric earthquakes in mid-america (Green et al. 2005). Due to the infrequent nature of earthquakes within central and eastern USA, ground motion records, especially from large earthquakes, do not exist. Therefore, artificial ground motion records are used in conjunction with ground motion records from other sites. The derived fragility curves are intended to be used for similar bridges in central and eastern USA. Hence, rather than selecting ground motions for a specific site and from a specific type of earthquake scenario, a wide range of ground motions are selected. In this study, a total of 60 ground motions, 30 artificial ground motions and 30 recorded ground motions, are used for the fragility analysis. The artificial ground motions generated for Paducah, Kentucky (Ferna ndez 2007), which is about 60 km from the studied region (Figure 1(a)), are used for this study. The artificial ground motions have been generated for three return periods, 475, 975 and 2475 years. The selection criteria of the recorded motions include magnitude (M * 6.5), distance ( km) and site condition (B). The distance range is broad such that the peak ground acceleration (PGA) of the recorded motion can cover a wide range of seismic intensity required for fragility curve derivation. The list of selected ground motions is presented in Table Analytical model of the reference bridge Bridges may suffer from a number of different failure modes. For the reference bridge, the possible failure modes include unseating of the superstructure in the transverse or longitudinal direction, which was repeatedly observed in past earthquakes, bent failures in the transverse direction and abutment failures in the transverse or longitudinal directions. Bent failures in the longitudinal direction are unlikely to happen for the reference bridge, as the abutments limit the longitudinal movement of the superstructure. The bridge is analysed using four approaches of the SSI to understand the effect of different modelling methods on the fragility curves. The first approach assumes that abutments and pile groups are all fixed (approach 1). The second approach includes lumped springs representing foundations and abutments to account for flexibility and hysteretic energy dissipation (approach 2). The spring properties are estimated based on a method frequently used in practice. The third approach adopts lumped springs estimated from an analysis of a three-dimensional finite element (3D FE) model of the soil foundation system (approach 3). In the fourth approach, multiplatform analyses (Kwon and Elnashai 2008) are conducted to combine 3D FE geotechnical and structural models (approach 4). This approach takes into account the flexibility and nonlinearity of the soil and foundation, with fewer assumptions than the third approach. In all of these approaches, bearings and gaps are modelled in detail as those elements critically affect the bridge response. Table 2 summarises the analytical models used in the four approaches. Details of analytical representations of bridge components are presented in the following sections.

4 Structure and Infrastructure Engineering 3 Figure 1. Reference bridge: (a) location and (b) configuration Bents and steel girders The superstructure of the reference bridge consists of a concrete deck on top of six continuous steel girders. The substructure consists of three piers supported by steel pile foundations. The dimensions and configuration of a typical bent and foundation is presented in Figure 2. The steel girders, decks, cross beams of bents and piers are modelled in ZEUS-NL (Elnashai et al. 2002) using cubic frame elements, as shown in Figure 3. Fibre-based elements are used to model each frame element. In fibre-based frame analysis, it is typically assumed that concrete sections are initially uncracked and bond-slip effects are ignored. Thus, in general, the fibre-based frame analysis tends to show larger initial stiffness than the real structure. When the ground

5 4 O. Kwon and A.S. Elnashai Table 1. Recorded ground motions selected for fragility analysis. Date Earthquake M Station Distance km PGA, g Component 1 Component 2 17 Jan :31 Northridge LA 116th St School Feb :00 San Fernando Castaic Old Ridge Route Oct :05 Loma Prieta Belmont Envirotech Jan :31 Northridge LA Baldwin Hills Nov :27 Trinidad, California Rio Dell Overpass, E Ground Jun :58 Landers Barstow Sep :47 Chi-Chi, Taiwan 7.6 CHY Sep :47 Chi-Chi, Taiwan 7.6 CHY Jun :58 Landers Coolwater Apr :06 Cape Mendocino Eureka Myrtle & West Jan :31 Northridge 6.7 Featherly Park Pk Maint Bldg Oct :05 Loma Prieta Golden Gate Bridge Oct :05 Loma Prieta Golden Gate Bridge Jan :31 Northridge Inglewood Union Oil Jan :31 Northridge 6.7 Beverly Hills Mulhol Jan :31 Northridge LA Obregon Park Jan :31 Northridge LA Obregon Park Jan :31 Northridge Castaic Old Ridge Route Feb :00 San Fernando Pasadena CIT Athenaeum Jul :53 Kern County Santa Barbara Courthouse Oct :05 Loma Prieta SAGO South Surface Apr :06 Cape Mendocino Shelter Cove Airport Apr :06 Cape Mendocino Shelter Cove Airport Sep :47 Chi-Chi, Taiwan 7.6 TCU Sep :47 Chi-Chi, Taiwan 7.6 TCU Sep :47 Chi-Chi, Taiwan 7.6 TCU Sep :47 Chi-Chi, Taiwan 7.6 TCU Sep :47 Chi-Chi, Taiwan 7.6 TCU Jan :31 Northridge LA Univ. Hospital Feb :00 San Fernando Wrightwood 6074 Park Dr Table 2. Analytical models of bridge components for four SSI approaches. Bridge components Approach 1 Approach 2 Approach 3 Approach 4 Bearings Fixed bearings Longitudinal and transverse direction: trilinear model based on the test by Mander et al. (1996) Expansion bearings Longitudinal direction: theoretical derivation of stiffness from geometry in addition to the inclusion of friction based on Mazroi et al. (1983) Transverse direction: trilinear model based on the test by Mander et al. (1996) Bents and decks Fibre-based element in ZEUS-NL (Elnashai et al. 2002) Abutments Fixed Lumped spring using practical approach by Caltrans (2004) and Maroney (1995) Foundations Fixed A single pile analysis using LPile (Ensoft 2005) and consider group effect Lumped spring from FE embankment and abutment model Lumped spring from FE foundation model Multiplatform analysis Multiplatform analysis shaking intensity is large enough to crack concrete sections, however, the fibre-based frame analysis is very reliable, especially for frames with flexural failure Bearings and gap models Two types of bearings are used in the bridge, as in Figure 1(b). The expansion bearings are typical segmental rocker-type units where the radius of bearing surface (r) is larger than half of the bearing height (H/2) between two contacting surfaces. The longitudinal stiffness of this type of bearing increases with the relative displacement between two contacting surfaces. A linearised segment of the nonlinear displacement force relationship is used for response history analyses. In addition to the stiffness from bearing geometry, frictional resistance exists between bearings and bearing plates. Mazroi et al. (1983) tested

6 Structure and Infrastructure Engineering 5 Figure 2. Configuration of typical bents and foundations. the friction of circular bearings in various conditions: clean (as-built) condition, rusted condition and with debris on the bearing surface. Mazroi et al. (1983) determined that a 0.05 coefficient of friction is appropriate when there is debris at the contacting surface between bearings and bearing plates. In this study, the longitudinal stiffness of expansion bearings includes a frictional coefficient of 0.05 consistent with the findings of Mazroi et al. (1983). Figure 4(a) shows the hysteretic behaviour of expansion bearings in the longitudinal direction. Mander et al. (1996) tested bearings taken from existing bridges. Among the several types of tested bearings, the behaviour of low-type bearings is expected to be similar to the transverse response of the reference bridge bearings. The movement at all of these bearings is restrained by pintle pins and pintle holes, which act as shear key connections. The study showed that the behaviour of bearings in the transverse direction is controlled by the contact and separation of pintle pins to bearing plates and bearing plates to anchor bolts. Until the gaps between these elements are closed, constant friction is observed. Then, the resisting force increases with the increase of displacement. Figure 4(b) compares the test result of low-type sliding bearings and the behaviour of the idealised trilinear model. In the absence of further experimental data, the behaviour of fixed bearings in transverse and longitudinal directions and the behaviour of expansion bearings in the transverse direction are assumed to be similar to the transverse direction tests of low-type bearings by Mander et al. (1996). The response of a bridge subjected to earthquake loading can be significantly influenced by the opening and closing of gaps between the deck and abutments. The design drawings of the bridge show that there should be a 38 mm of gap between the deck and abutments at a temperature of 108C. Neglecting the variation of the length of the superstructure with temperature variation, the gaps are modelled as asymmetric springs, such that the spring has no resistance on tensile loading, and they become stiff when the gap closes. The hysteretic behaviour of a gap element used in the bridge model is shown in Figure 4(c) Abutments and foundations Approach 1: fixed foundation assumption It is assumed herein that abutments and foundations are fixed. This approach allows the investigation of the failure modes of a bridge with rigid boundary conditions and compares it to the failure modes of a bridge with flexibility at the supports Approach 2: lumped springs derived from conventional methods The foundation stiffness and strength are evaluated using the pile analysis software LPile (Ensoft Inc.

7 6 O. Kwon and A.S. Elnashai Figure 3. FE model of the bridge and connectivity of structural components. 2005). The nonlinear response of a single pile is obtained from the LPile analysis. The pile group effects are considered using the p-multipliers of Brown and Reese (1985). Figure 5(a) shows the hysteretic behaviour of the pile group. The force developed in an abutment consists of active/passive pressure of soil in addition to the force developed in the pile head. As the soil pressure on abutment walls and the pile resistance at abutment bases act together, the contribution of each may be summed. The contribution of piles supporting abutments is approximated from the LPile analysis. The passive response of abutments is approximated from the full-scale abutment test by Maroney (1995). These two components are combined, as shown in Figure 5(b). In the active longitudinal direction, it is assumed that only piles contribute to the resistance of abutments, while in the passive longitudinal direction, passive soil pressure contributes to the abutment resistance in addition to the contribution of piles. Due to the limited availability of experimental data, the stiffness of an abutment in the transverse direction is assumed to be 50% of the stiffness of an adjacent bent, following the Caltrans design criteria (2004). The stiffness and strength of a pile in the transverse direction is approximated from the LPile analysis. As one can note in this approach, a simplified method inevitably needs several assumptions to define the stiffness and strength of foundations, embankments and abutment systems Approaches 3 and 4: FE foundation model In these approaches, the soil pile foundation systems are modelled in a 3D FE analysis package, OpenSees (McKenna and Fenves 2001), using realistic soil material models. The mesh of the FE model is refined such that the computational cost is affordable with minimal loss of accuracy. A parametric study for foundations supporting bents 1 and 3 showed that the

8 Structure and Infrastructure Engineering 7 Figure 4. Analytical model of bridge components: (a) expansion bearing model in longitudinal direction, (b) low-type bearing behaviour in transverse direction (low-type sliding bearing in transverse direction, Mander et al. (1996)) and (c) hysteretic behaviour of a gap element.

9 8 O. Kwon and A.S. Elnashai Figure 5. Hysteretic behaviour of: (a) a pile group and (b) abutments from approach 2. global load deformation relationships of the soil pile foundation model with a fine mesh of 5510 elements and with a coarse mesh of 1400 elements are very similar. The reduction in analysis time per each time step is significantly reduced by a ratio of 1/20. Similar mesh refinement studies are conducted for the foundations of bent 2 and the embankments. Figure 6 shows the final mesh with the numbers of elements and nodes. Boring log data shows that the soil of the bridge site predominantly consists of stiff to hard clay. Therefore, the subsoil layers are assumed to be pressure-independent material with soil properties of stiff clay proposed by the developer of the soil material model Yang et al. (2005). Due to lack of information on embankment properties, the material properties of the embankments are taken from those of a similar study conducted by the present authors (Kwon and Elnashai 2008). The stiffness and strength of foundations identified from pushover analyses of these models are used in approach 3. In approach 4, these models are combined with a structural model in ZEUS-NL (Elnashai et al. 2002) using the multiplatform analysis framework UI-SimCor (Kwon et al. 2005). 5. Random variables in seismic capacity and demand The seismic demand, structural capacity and structural and geotechnical material properties are considered as random variables. The variation in these random variables is estimated based on the published literature, as well as engineering judgement Concrete strength Barlett and MacGregor (1996) investigated the relationship between the strength of cast-in-place concrete and specified concrete strength. When concrete was 1 year old, the ratios of the average in-place strength to the specified strength were 1.3 and 1.4, for short and long elements, respectively, with a coefficient of variation (COV) of 19%. The variation of strength throughout the structure for a given mean in-place strength depended on the number of members, number of batches and type of construction. In this study, it is assumed that there is no variability of concrete within the structure. The specified concrete strength (or design strength) of the considered structure was 24 MPa. In-place concrete strength is assumed to be 1.40 times larger than the specified strength (33.6 MPa).

10 Structure and Infrastructure Engineering 9 distribution, with a mean value of 201,327 MPa and a COV of 3%. Due to the low level of variability observed, the modulus of elasticity is assumed to be deterministic (201,327 MPa) in this study. The reference bridge was designed with grade 40 steel; thus, the mean steel strength is assumed to be 337 MPa. The steel strength is assumed to follow a normal distribution Soil properties Soil material properties involve more random parameters than concrete or steel. Jones et al. (2002) noted that the COV of undrained shear strength, S u, of clay varies between 22% and 33%. In this study, it is assumed that the COV of S u is 25%. In the same literature, the COVs of shear wave velocity and soil density were reported as 18% (d vs ¼ 0:178) and 9% (d r ¼ 0.09). The shear wave velocity (v s ), density of a soil medium (r), and shear modulus (G) are related by the following equation: G ¼ v 2 s r: ð1þ Taking the logarithm of both sides yields: log G ¼ 2logv s þ log r: ð2þ Assuming that the shear modulus, shear wave velocity and density follow lognormal distributions, the standard deviation of the logarithm of each variable, z, is related by: z 2 G ¼ 22 z 2 v s þ z 2 r ; ð3þ where z. is the standard deviation of the log of.. The standard deviation of a logarithm of a random variable, z, is related to the COV, d, by the following relationship: z 2 ¼ logð1 þ d 2 Þ: ð4þ Figure 6. FE soil pile foundation models: (a) FE model of bents 1 and 3, (b) FE model of bent 2 and (c) FE model of abutment and embankment. This study adopted an assumption of normally distributed concrete strength with a COV of 19% Steel strength Mirza and MacGregor (1979) reported results of tests on grade 40 bars. The mean value and COV of the yield strength were 337 MPa and 11%, respectively. The probability distribution of the modulus of elasticity of grade 40 reinforcing steel followed a normal From Equations (3) and (4), the COV of the shear modulus is estimated to be Note that the randomness of the geotechnical material is much larger than that of engineered material such as steel and concrete. It is anticipated that the shear modulus of soil affects the stiffness of foundations most significantly. As the COV of steel s modulus (3%) is relatively small in comparison with the COV of the shear modulus of soil (38%), a COV of 38% is assumed to define the randomness of the stiffness of lumped soil springs in approaches 2 and Input ground motion The uncertainty in seismic hazard is accounted for by using 60 ground motions. Thirty of the records are from recorded ground motions from sites with soil

11 10 O. Kwon and A.S. Elnashai conditions similar to that of the reference bridge. The remaining 30 records are artificially generated by Ferna ndez (2007) for a site close to the bridge. Table 3 summarises the COVs of random variables used in the geotechnical-structural model. 6. Capacity limit states of bridge components The failure of bearings, bents and abutments are considered in this study. The capacities of these components are estimated from literature reviews, geometry of components, shear strengths and pushover analyses. High COVs are assigned to the capacity limits that do not have clear failure criteria Capacities of bearings The failure mechanisms of fixed and expansion bearings in the transverse direction are expected to be similar to those of the low-type bearings tested by Mander et al. (1996), as all of them are restrained by pintle pins and pintle holes. The tests by Mander et al. (1996) showed that the low-type fixed bearing has constant friction up to a displacement of 3 4 mm. This slippage occurs at interfaces between bearing plates and between bearings and structural elements. After the displacement of 3 4 mm is reached, it is anticipated that the pintle pins, pintle holes or anchor bolts start to be damaged. Thereafter, the serviceability limit state for the transverse displacement is defined as 4 mm for bearings in the transverse direction. After 4 mm of displacement, the bearings begin to develop a high resistance. The damage control limit state is estimated from the shear strength of pintle pins. Each support consists of six bearings that have two pintle pins. Thus, a total of 12 pintle pins transfer lateral forces. Assuming that the pins are made of A992 steel (F y ¼ 345 MPa), the lateral shear capacity of bearings is approximated based on Equation (J4 3) of AISC (2005): F v ¼ 0:6 F y ðaþ ¼ 0:6ð50Þð14:8Þ ¼640 kn; ð5þ where F v, F y and A, are lateral shear capacity, yield strength of pins, and gross sectional area subjected to shear force, respectively. The numerical model in Figure 4(b) reaches the base shear at a displacement of 7 mm. Therefore, the damage control state of the fixed bearings in the transverse direction is defined from the abutment bearings as 7 mm. Experiments by Mander et al. (1996) showed that pintle pins yielded and the bearing started to lose lateral resistance at a displacement of 20 mm. At this displacement, a base shear coefficient of 4 was achieved. In the transverse bearing model in Figure 4(b), a base shear coefficient of 4 is reached at a displacement of 11 mm in the model. Considering the experimental result that the bearing does not develop further resistance after the base shear coefficient of 4, the collapse prevention limit state for the transverse direction is defined as 11 mm. The three limit states in the longitudinal direction for fixed bearings are assumed to be similar to those in the transverse direction. Therefore, limit states of 4, 7 and 11 mm are assumed. The expansion bearings are designed so that they do not incur damage in the longitudinal direction unless bearings are unseated with excess displacement. Thus, it is assumed that the expansion bearings in the longitudinal direction do not contribute to the failure probability of serviceability and the damage control limit state of the bridge system. The collapse of an expansion bearing in the longitudinal direction will occur when the bearings overturn. As the expansion bearing used in the reference bridge rolls, it is assumed that the collapse prevention limit state of expansion bearings in the longitudinal direction is the same as the seat width of the bearing plate, i.e. 230 mm. The mean capacities of bearings are not deterministic. Uncertainties arise from the fact that the capacities are based on experiments whose specimens are not the same as the bearings used in the reference bridge. Even if identical specimens are used, repeated experiments will not provide identical results. Moreover, the numerical model of structural systems is not well-calibrated under high-intensity motion. In addition, existence of vertical ground motion will significantly influence the capacities of bearings. These uncertainties need to be accounted for in a systematic way. Table 3. Random variables in analytical models. Properties COV Reference Concrete strength (MPa) 0.19 Barlett and Macgregor (1996) Steel yield strength (MPa) 0.11 Mirza and MacGregor (1979) Soil unconfined compressive strength 0.25 Jones et al. (2002) Soil shear modulus 0.38 From COV of v s (Romero and Rix 2001) and Stiffness of lumped foundation springs Ground motion recorded motions and 30 artificial motions r (Jones et al. 2002) Fernández (2007)

12 Structure and Infrastructure Engineering 11 It is certain that results from structural analyses under low-intensity ground motion are more confident than the results under high-intensity ground motion. Therefore, smaller COVs at a low-capacity limit state are adopted than those at a high-capacity limit state. In this regard, Nielson (2005) assumed COVs of 0.25 for lower limit states and 0.5 for upper limit states. In this study, COVs of 0.25, 0.50 and 0.75 are assumed for serviceability limit states, damage control limit states and collapse prevention limit states, respectively. The selection of these COVs is purely based on engineering judgement. More thorough definition of limit states and probabilistic assessment of these limit states remain for future study Capacity limit states of bents The limit states of bents are determined from pushover analyses of a bent in the longitudinal and transverse directions. From static analysis, it is observed that each bent supports approximately 950 kn of dead load. Pushover analyses under an axial load of 950 kn are conducted to estimate limit state thresholds of the bents by applying a displacement at the top of the bents. Three limit states in both directions are defined as drifts at the first yield of steel in tension, achievement of global maximum strength and achievement of core concrete strain of 0.01, for serviceability, damage control and collapse prevention limit states, respectively. The core concrete strain of 0.01 corresponded to 25% loss of core concrete stress, which resulted in a significant reduction in member strength. Based on these criteria, the limit state in the transverse direction is defined as 36 mm (0.6%), 92 mm (1.5%) and 260 mm (4.2%) for the three limit states. In the longitudinal direction, the limit states are defined as 72 mm (1.2%), 124 mm (2.0%) and 500 mm (8.0%). Note that the bent has much larger displacement capacity in the longitudinal direction than in the transverse direction, as it behaves as a cantilever in the longitudinal direction. The estimation of yielding of reinforcement and peak strength can be relatively confidently conducted with fibre-based frame analysis software. Therefore, the COV of bents for serviceability and damage control limit states is assumed to be 0.1. On the contrary, the COV of collapse prevention limit states is assumed as 0.5, as the collapse of a structure cannot be predicted with the same level of confidence Capacities of abutments Abutments can be divided into two general classifications for seismic analysis: monolithic and seat-type abutments. In monolithic abutments, the superstructure of a bridge is monolithically connected to abutments. In seat-type abutments, the forces from the superstructure are transferred through the bearings. Longitudinally, there is a gap between the superstructure and the abutments. The abutments of the reference bridge are seat-type abutments. Abutments can fail due to large deformations in either the transverse or longitudinal directions, or both. In seat-type abutments, the pounding of a superstructure on the back wall of the abutment can break the joint between the abutment and the back wall, imposing extensive, passive pressure on the backfill of the abutments. In the Caltrans procedure (Caltrans 1988, 1989), two values of the acceptable abutment deformations are considered: 25 mm and 61 mm. The first represents the deformation at which the soil pressure reaches its peak value of 369 kpa, and the latter represents the limiting value corresponding to the incipient damage to the abutments. Following the reference, the displacement capacities of abutments are assumed to be 25 and 61 mm for serviceability limit state and damage control limit state, respectively. Padgett and DesRoches (2007) conducted a survey of state department of transportation practitioners for several states. The survey results indicated that collective judgement of practitioners deemed the occurrence of complete failure of abutments from earthquakes to be unlikely. In most seat-type abutments, however, the abutment back wall is designed to resist the soil pressure of filled soil. When a large impact from the superstructure of a bridge is imposed on the back wall, the back wall may fail, which can impose severe disruption on traffic. The displacement limit of the abutment failure in the longitudinal direction is assumed to be the displacement when the shear strength of the abutment back wall is reached. The shear strength of the abutment back wall is approximated as below, based on ACI (2002): V c ¼ p ffiffiffi f 0 c =6bd ¼ pffiffiffiffiffiffiffiffiffi 33:6=6ð12:9Þð0:42Þ ¼5:2MN; ð6þ where b is the assumed length of shear failure and d is the effective thickness of the back wall, as shown in Figure 7. From the FE analysis of the embankment, abutment and supporting pile system in Figure 6(c), a shear strength of 5.2 MN is reached at the abutment displacement of m. Hence, the collapse prevention state of abutment in the longitudinal direction is assumed to be 75 mm. The transverse movement of abutments also disrupts traffic due to the relative displacement between the bridge and abutment, as well as settlement of backfill soil. Without further information about failure criteria in the transverse

13 12 O. Kwon and A.S. Elnashai direction, the limit state for longitudinal direction is adopted as the limit state for the transverse direction. The COVs of abutment capacity is assumed to be 0.5 for all three limit states, as these are not based on experiments of similar abutment configurations. Table 4 summarises the mean capacities of bridge components and their COVs. 7. Fragility simulation The fragility curves of the reference bridge are derived using the SAC FEMA approach (Cornell et al. 2002). The seismic demand of bridge components and their correlation coefficients are estimated from inelastic nonlinear response history analyses of the reference bridge. As the closed-form estimation of system fragility with various failure modes is not readily achievable, Monte Carlo simulations are employed, based on the distribution of seismic demands of bridge components and their correlation coefficients. Figure 7. back wall. Assumed shear failure mode of the abutment 7.1. Seismic demand of bridge components The intensity measure, I, and seismic demand of structural components, D, are related by the following equation (Cornell et al. 2002): ^D ¼ ai b ; ð7þ where I is the intensity measure and a and b are regression parameters. ^D indicates a median seismic demand. As the relationship between seismic intensity and seismic demand is not deterministic, a term that accounts for uncertainty is introduced into Equation (7): D ¼ ai b e; ð8þ where e is a random variable with a mean of 1. Assuming that e follows a lognormal distribution, logs of both sides yield: ln D ¼ lnðaþþb lnðþþln I ðþ: e ð9þ From nonlinear response history analyses of bridge systems, the seismic demands, D, can be obtained for a given ground motion with an intensity of I. By running regression analysis, the parameters a and b can be determined, such that mean of the residual, 1n(e), is close to zero. The standard deviation of ln(e) is a dispersion of seismic demand of component, b D. The estimated demand parameters of bridge components for the four different SSI approaches are summarised in Table 5 and a qualitative summary of seismic demands are provided in Table 6. Figure 8 presents median demand curves. The following can be observed from the seismic demand assessment of the bridge components using the different SSI approaches. Table 4. Capacity limit states. Properties Serviceability Damage control Collapse prevention Mean COV Mean COV Mean COV Reference Transverse direction Fixed bearing (mm) Mander et al. (1996) Expansion bearing (mm) Mander et al. (1996) Bent deformation (mm) Pushover analysis of bent Abutment movement (mm) Caltrans (1988, 1989) Longitudinal direction Fixed bearing (mm) Mander et al. (1996), geometry of bearing Expansion bearing (mm) N/A N/A N/A N/A Geometry of bearing Bent deformation (mm) Pushover analysis of bent Abutment movement (mm) Caltrans (1988, 1989) and shear strength of back wall

14 Structure and Infrastructure Engineering 13 Table 5. Seismic demands on bridge components. Approach Parameter Abutment (mm) Brg. Abutment (mm) Brg. bent 1, 3 (mm) Brg. bent 2 (mm) Bent (mm) Trans Long Trans Long Trans Long Trans Long Trans Long 1 a N/A N/A b N/A N/A b D N/A N/A a b b D a b b D a b b D Note: The above parameters are evaluated based on the seismic intensity demand relationship in Equation (8). Brg., bearing. Table 6. Qualitative comparison of seismic demand on bridge components. Component Approach 1 Approach 2 Approach 3 Approach 4 Transverse direction Abutment N/A Higher than FE Similar Bearings on abutment Highest at large PGA level Low High Lowest Bearings on bent 1 and 3 Lowest Highest Similar Bearings on bent 2 Lowest Highest High Low Bent Lowest Highest Similar Longitudinal direction Abutment N/A Higher than FE up to 0.7 g Very similar Bearings on abutment Lowest Similar. Distinctively larger than fixed approach Bearings on bent 1 and 3 Lowest Similar. Distinctively larger than fixed approach Bearings on bent 2 Lowest Similar. Distinctively larger than fixed approach Bent Lowest Similar. Distinctively larger than fixed approach Note: Relative seismic demand is qualitatively described as lowest, low, high and highest.. Transverse response, Figures 8(a), (c), (e), (g) and (i): The differences between various SSI approaches are much larger in the transverse direction than in the longitudinal direction. In the transverse direction, the abutment bearings transfer forces, even at low shaking intensity levels. Thus, the characteristics of abutment models directly affect the bridge response. When embankments and abutments are assumed fixed (approach 1), the seismic demand on bearings at abutments is higher than those from other approaches. The seismic demand on other bearings and bents is lower than those from approaches 2, 3 and 4. The fixed abutment assumption (approach 1) tends to limit structural response, but increases demand on the connecting elements, i.e. bearings at abutments, between structure and fixed boundary. The seismic demands from multiplatform simulations (approach 4) and from FE-lumped spring (approach 3) are different, but the differences are not significant. The conventional approach (approach 2), for which foundation properties are estimated from LPile analysis and abutment properties are based on Caltrans (2004), shows significantly different seismic demand from other approaches.. Longitudinal bridge response, Figures 8(b), (d), (f), (h) and (j): The conventional spring (approach 2), FElumped spring approach (approach 3) and multiplatform simulation (approach 4) lead to similar seismic demand for all bearings and bents at low PGA levels. The similarity is attributed to the existence of gaps and expansion bearings on abutments that minimises the interaction between embankments and the bridge. If the bridge

15 14 O. Kwon and A.S. Elnashai Figure 8. Median seismic demand on bridge components: (a) abutment bearing, transverse, (b) abutment bearing, longitudinal, (c) bearing on bent 1 and 3, transverse, (d) bearing on bent 1 and 3, longitudinal, (e) bearing on bent 2, transverse, (f) bearing on bent 2, longitudinal, (g) bents, transverse, (h) bents, longitudinal, (i) abutments, transverse and (j) abutments, longitudinal.

16 Structure and Infrastructure Engineering 15 Figure 8. (Continued). is constructed with monolithic abutments, the different SSI approaches may result in different longitudinal seismic responses. The fixed base approach (approach 1) clearly shows different demand for all structural components, as shown in Figures 8(b), (d), (f) and (h). In general, assuming a fixed boundary in the longitudinal direction underestimates demand on components. The seismic demand on abutments is very similar for the FE soil spring approach (approach 3) and multiplatform simulation (approach 4). For structural components, the rate of demand increase tends to decline with increasing PGA, as demonstrated in Figures 8(b), (d), (f) and (h). On the contrary, the rate of demand increase on abutments tends to increase, as shown in Figure 8(j). At low seismic intensity, the demand on structural components is nearly proportional to the input motion intensity. At a certain PGA level, the superstructure starts to contact the abutments, which limits structural response and activates abutment response. The seismic demand on bearings of bent 2 is very low, as shown in Figure 8(f). Due to a high axial force, the bearings exhibit high frictional resistance, which prevents relative movement of the top and bottom plates of bearings.

17 16 O. Kwon and A.S. Elnashai The seismic demand, D, of bridge components in Table 5 can be combined with the component capacity, C, in Table 4 to estimate component fragility: B lnð ^D= ^CÞ C P½C < DjPGA ¼ xš ¼F@ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia b 2 D=S a þ b 2 C 0 1 ð10þ where ^C and ^D are the median values of demand C and D respectively. b C and b D/Sa are dispersion of the capacity C, and dispersion demand, D, for a given seismic intensity, S a. System fragility cannot be directly evaluated from component fragility in Equation (10). For the evaluation of system fragility, a method proposed by Nielson and DesRoches (2007) is adopted, which will be briefly introduced in the following section System fragility curves This study adopts the method proposed by Nielson (2005) to evaluate system fragility from component fragilities. Failure probabilities of components from Equation (10) cannot be directly converted to the failure probability of the bridge system, as component failure probabilities are correlated with each other. For instance, seismic demands on bearings subjected to a longitudinal ground motion can be highly correlated with the seismic demands on bents subjected to the same ground motion. Hence, it is not straightforward to combine the failure probabilities of components to estimate the failure probability of the system. To address this issue, Nielson (2005) proposed a method in which Monte Carlo simulations were used. In the approach, statistical distribution parameters, including the covariance matrix of demands on bridge components, were evaluated from response history analyses. These statistical parameters were used to randomly generate a large number of component demands. Similarly, component capacities were also randomly generated, assuming that the seismic component capacities are independent with respect to each other. These randomly generated demands and capacities were used to evaluate system fragility. In this approach, it was assumed that failure of any component leads to failure of the bridge system. For further information, reference is made to Nielson (2005). To use the fragility curves for regional seismic damage estimation, it is necessary to represent the fragility curves in a functional form. As the fragility curves of bridge components are based on a lognormal distribution, the system fragility curves are most likely to fit well into lognormal cumulative distribution functions. To determine the lognormal parameters of system fragility curves, regression analysis is conducted for the numerically estimated fragility points. Table 7 summarises the system fragility curves in terms of the median (m) and standard deviation (s) in log space. Figure 9 shows fragility curves from a multiplatform simulation. In all limit states, the abutment bearings in the transverse direction are the most vulnerable component. For the serviceability and the damage control limit states, the abutment and bent in the transverse direction and the abutment and bent in the longitudinal direction contribute to the system failure. For the collapse prevention limit state, bents do not contribute to the failure probability due to their large displacement capacity. As the limit state of expansion bearings in the longitudinal direction is defined only for collapse prevention system conditions, those components contribute to the system failure probability. As a brief application example of seismic fragility curves, the failure probability of the bridge is estimated, based on the seismic hazard of the site. The United States Geological Survey (USGS) recommends the seismic hazard of the bridge site to be 0.19, 0.38 and 0.87g for 10%, 5% and 2% probabilities of exceedance (PE) in 50 years. Figure 9 shows the seismic hazards overlapped with failure probabilities. System failure probabilities for each seismic hazard level are Table 7. Regression analysis results of proposed fragility curves. SSI approach Fixed Lumped spring conventional method Limit state LS1 LS2 LS3 LS1 LS2 LS3 m s SSI approach Lumped spring from FE model Multiplatform analysis Limit state LS1 LS2 LS3 LS1 LS2 LS3 m s Note: m and s are log(g) where g is gravity acceleration.