Seismic fragility assessment of existing Italian overpass bridges

Seismic fragility assessment of existing Italian overpass bridges | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Seismic fragility assessment of existing Italian overpass bridges Marco Gaetani d'Aragona, Antonino Recupero, Andrea Prota This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4412197/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study introduces a three-dimensional refined finite element model that is suitable for dynamic analysis of existing overpass bridges with Multi-Span Simply-Supported scheme. The proposed modeling approach allows to realistically reproduce the bridge behavior under seismic loadings via a proper simulation of the expected behavior and failure modes of each bridge component, as well as their mutual interaction. Two different Limit States, as well as a definition of system-level collapse, are introduced depending on the behavior of the bridge components and the interaction between the superstructure and the substructure. The proposed modeling approach is adopted to generate Limit State fragility curves adopting a stochastic approach based on cloud analysis which entails the use of real recorded ground motions for a reference bridge, designed and constructed in southern Italy in the 1970s. The results show that the proposed simulation approach is suitable to realistically reproduce the complex behavior of this type of bridge providing significant insights into their vulnerability. MSSS concrete bridge overpass finite element model fragility curves Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction The seismic vulnerability of existing RC bridges has become a topic of strong interest for the scientific community due to the strategic role that they play during the emergency management phase. These structures, if they are a part of a strategic roadway network, are indeed required to remain fully operational in the aftermath of natural catastrophes such as earthquakes of moderate to severe intensities to allow the implementation of rescue operations. In Italy, the importance of primary transportation networks recently enforced comprehensive research programs [ 1 ] to investigate several topics related to the seismic assessment and retrofit of bridges, and to propose pre-code European guidelines for the assessment of the existing ones. Further, recent collapses involving existing RC bridges such as the Santo Stefano (1996)[ 2 ], the Petrulla (2014), the Annone (2016), the Osimo (2017) overpasses, the Fossano (2018), and the Polcevera viaduct (2018) [ 3 ], have dramatically spotlighted the needing for a systematic vulnerability reduction program for the whole infrastructural system accelerating the release of specific guidelines for the ”Risk-based classification, safety checks and monitoring of existing bridges” [ 4 ]. The most of Italian bridges were built during the two decades from 1955–1975 due to the roadway network development related to the Italian economic growth ([ 5 ], [ 6 ]), and were primarily designed for gravity loads only. Even when the seismic design was considered, this only consisted of the application of nominal equivalent static forces, equal to a maximum of 10% of the weight in higher seismicity areas, with no consideration of the bridge dynamic properties or the possible ductile behavior. For this reason, their structural performances may result inadequate under severe earthquake motions especially due to the lack of proper seismic detailing. The Italian infrastructure network has been shown highly vulnerable due to design deficiencies, adopted technologies and materials, as well as the lack of appropriate maintenance. Recent earthquakes such as the 2009 L’Aquila [ 7 ], the 2012 Emilia [ 8 ], and the 2015 Central Italy [ 9 ] sequences, only evidenced limited damage to RC bridges that was mainly ascribable to poor maintenance, even for bridges not specifically designed for seismic actions, and only in one case, an RC bridge entirely collapsed probably due to pier failure, again due to lack of maintenance [ 7 ]. However, several studies suggest that, especially in southern Europe [ 10 ], [ 11 ], [ 12 ], [ 13 ], existing bridge infrastructures are characterized by high seismic vulnerability, making the implementation of risk mitigation policies deemed urgent to minimize their potential damage and to mitigate the post-event impact on transportation networks, indirect losses, business disruption or emergency response efforts. In this perspective, the vulnerability assessment of existing bridges, expressed in probabilistic terms for suitable damage states, beyond predicting the damage or usability of the structure during the post-earthquake emergency management phase, can provide important information about the prioritization scheme for retrofit interventions, giving crucial indications regarding the most vulnerable component and the most suitable retrofit strategy to be implemented, especially if fragility curves are available at the component level. Most of the Italian RC bridge stock is composed of a rather uniform structural typology made up of simply-supported spans with prestressed beams, and cast-in-place deck slabs supported by single stem or frame-type piers [ 14 ]. Due to the availability of precast prestressed concrete beam technology, these bridges often adopt as a structural scheme that of the multi-span simply-supported beam or the Gerber scheme. For this reason, this paper specifically refers to Multi-Span Simply-Supported (MSSS) bridges with pre-stressed concrete girders adopting a Niagara-type scheme [ 15 ],which has been widely adopted in the past to realize overpass highway bridges. Past seismic events occurred in high-seismicity zones such as the Loma Prieta (1989) and the Northridge (1994) earthquakes evidenced major deficiencies in MSSS concrete bridges. In fact, the use of statically-determined schemes, much simpler to calculate and adaptable to temperature variation and constraint settlements, has the disadvantage of no redundancy and thus limited plastic capacity thus making this type of bridges highly vulnerable to seismic actions. Typical failure modes for this class of bridges consists in flexure/shear failure of bent beams and columns due to the lack or the presence of limited seismic detailing, abutment failure (e.g., [ 16 ], [ 17 ], [ 18 ]), as well as deck unseating at the abutments, cap-beam, or in-span hinges [ 19 ]. In particular, the presence of expansion joints between adjacent decks at the in-span hinges or between the deck and the abutment can result in deck unseating spans due to the lack of properly designed restrainers to the motion in the transverse direction or considerable impact at the expansion joints due to out-of-phase vibration during earthquakes. Deck unseating, as well as shear and flexural failure of the pier columns, and rotation of the deck, have also been recognized in the past among the most relevant failure modes, especially for bridges with non-negligible skew angles [ 20 ]. To provide a realistic assessment of such a type of bridges, reliable analytical models explicitly simulating the expected behavior and failure modes of single components (e.g., bearings, shear keys, bent and abutment beams and columns, foundation system) as well as the mutual interaction between different bridge parts (e.g., deck-deck and deck-abutment hammering, interaction between deck girders and shear-keys) should be developed. With the aim of developing analytical fragility curves for a typical MSSS concrete bridge, a commonly adopted scheme in the realization of overpass bridges in southern Italy, a refined three-dimensional finite element model has been specifically developed to properly simulate their complex behavior. The model explicitly simulates the behavior of each single bridge component and their mutual interactions, accounting for typical relevant failure modes both at the component and the system level. Fragility curves are developed adopting a cloud-based approach by means of nonlinear time-history analyses performed by employing a suite consisting of 125 real ground motions. Two damage limit states corresponding to usability and collapse prevention are defined, system-level fragility curves are developed for a real RC bridge, designed, and constructed in southern Italy between 1968–1974. Section 2 introduces the geometric and structural features of the MSSS concrete bridge adopted for the generation of the model. Section 3 introduces the Finite Element Model concerning the superstructure (§ 3.1), the substructure (§ 3.2), the modeling of the interaction between these two parts (§ 3.3) and between the substructure and the soil (§ 3.4), along with the adopted loads (§ 3.5) and the solution algorithms (§ 3.5). Section 4 introduces the definition of two Limit States and a system-level collapse. Section 5 introduces the stochastic approach based on the cloud analysis to derive the fragility curves, that are carried out in Section 6. Finally, Section 7 highlights the main conclusions drawn for the considered bridge scheme. 2. Description of the reference bridge One representative RC overpass bridge structure realized in the southern Italy in 1970s is adopted as reference structure to generate the fragility curves for MSSS bridges. The structural scheme consists of MSSS prestressed beams with a Niagara-type scheme for the positioning of in-span hinges, see Fig. 1 (a). The bridge is composed of three spans, where the central span is suspended and connected to the cantilever spans by means of half-joints (Gerber saddles). The total bridge length is 89.0 m, with a central span of 44.0 m and lateral cantilever spans of 22.5m. The length of the suspended spans is 31.0m, while the cantilever part of central span is 6.5m long. The deck (Fig. 1 (b)-(c)) is composed of seven equally spaced I-shaped precast concrete girders and a cast-in-place RC deck. In relevant sections, diaphragms are realized to stiffen the deck cross-section. The cross-section of the girders along the lateral spans is not constant and the height linearly varies from a minimum at the abutment to a maximum at the bents. The bents (Fig. 1 (c)) are constructed as multi-column bents with seven RC columns aligned to the girder axis positions, and a rectangular cross-section linearly reducing from the bottom to the top. The cap beam has trapezoidal cross-section. The height of the bent columns is 6.0m for the upstream bent and 6.6m for the downstream one. The abutments (Fig. 1 (b)) are spill-through type abutments composed of four equally-spaced columns and a cap beam with rectangular cross-section. The rectangular cross-section of abutment columns linearly reduces from the bottom to the top. Both the bents and abutments are supported by two rows of four cast-in-place concrete piles with circular cross-section of 1.0m diameter. Elastomeric bearing pads of different sizes and constant thickness of 0.05m are placed at half-joints, and between the deck and substructure at abutments and bents. At the Gerber saddles four interior shear-keys are placed between interior RC girders, while at bents two rows of six interior shear keys, and the abutment only exterior shear-keys are placed. Finally, in zones corresponding to the abutment, inclined rebars are placed in between the head of girders to realize a Mesnager hinge. Further details can be found in Gaetani d’Aragona et al. [ 21 ] 3. Non-linear Finite Element model A three-dimensional finite element model of the bridge is developed using the OpenSees® platform [ 22 ]. The non-linear finite element model has been developed to reproduce the actual behavior of the overpass by suitable modeling the behavior of its components (i.e., for the substructure: bents, abutments, shear-keys, bearings, foundation system; for the superstructure: deck), and the interaction between the different parts of the bridge (i.e., deck-deck, deck-bent, deck-abutments) and between the substructure and the soil (i.e., soil-structure interaction at the abutments). Both the substructure and the superstructure members are modeled with elements placed in the center of mass, while the connections between different bridge parts (i.e., at bents, abutments, and in-span hinges) and with the soil (i.e., at foundations) are preserved by adopting rigid elements to account for the eccentricity of the member axes and the finite size of elements. An illustration of the model is provided in Fig. 2 . 3.1. Superstructure The bridge superstructure, composed of a cast-in-place concrete deck and I-shaped prestressed concrete girders, is expected to remain elastic during earthquake shakings (e.g.,[ 23 ]). Therefore, the deck is simulated via a three-dimensional “spine” model consisting of a series of equivalent elastic beam-column elements placed along its centroid, and assuming full inertial properties (i.e., uncracked). The cross-section properties of the equivalent beam are calculated adopting appropriate flexural and torsional stiffness values, while the variation of the cross-section along the bridge axis is accounted for during the model generation. To properly reproduce the kinematic of the superstructure in zones where the structure-structure interaction takes place, the full width of the superstructure cross-section is incorporated adopting rigid elements (i.e., at abutments, bents, and in-span hinges). 3.2. Substructure The bridge substructure is composed of abutments and bents. Both the bridge bents and the spill-through abutments consist of a multi-column frame system composed of columns with varying cross-section geometry along the height and a top capbeam. Existing RC members with low transverse reinforcement often show limited ductility due to the premature triggering of brittle failure mechanisms such as shear failure after flexural yielding and/or axial failure. To simulate the flexural behavior of columns while accounting for the possible development of brittle failure modes (i.e., flexure-shear, axial failure), a mixed distributed-lumped modeling strategy in which the flexural behavior is simulated via a distributed approach and the shear/axial behavior via a lumped one is adopted. A schematic layout of the modeling strategy adopted to simulate the behavior of bents is schematized in Fig. 3. The flexural behavior of columns is simulated by adopting a distributed fiber-based approach, which entails the use of displacement-based beam-column elements (dispBeamColumn) with fiber-defined cross-sections. The varying geometry along the column axis is simulated by assigning different cross-sections at specified integration points (Fig. 3(a)). The section is discretized into 40x40 fibers for the core and 20x20 fibers for the cover, while the steel rebars embedded in the concrete cross section are modeled by means of straight layers of equivalent thickness. At the cross-section level, the Concrete04 material is used to simulate the behavior of concrete fibers. The Concrete04 is based on Popovic’s [ 24 ] formulation for compression with unloading and reloading degraded stiffnesses according to Karsan-Jirsa [ 25 ], while it adopts an exponential decay for strength for the tensile behavior. The characterization of the Concrete04 parameters was differentiated for the unconfined and the confined part of the cross-section. The parameters for the unconfined concrete behavior are calculated according to Popovics’s [ 24 ] and Mander et al. [ 26 ] in compression and Belarbi and Hsu [ 27 ] in tension, while the behavior of the confined concrete is modeled assuming the confinement parameters by Mander et al. [ 26 ] and Chang and Mander [ 28 ] depending on the arrangement of both longitudinal and transverse reinforcement. The value of the ultimate concrete compressive strain is set according to Scott et al. [ 29 ]. The mean values adopted for Concrete04 parameters are resumed in Table 1 . The behavior of steel rebars is modeled by means of the Steel02 material, which is an elastic-plastic material with isotropic strain hardening based on the Giuffrè-Menegotto-Pinto formulation ([ 30 ], [ 31 ]). The steel model parameters are presented in Table 2 , where the parameter b st represents the ratio between the post-yield tangent and the initial elastic tangent, and R 0 , R 1 and R 2 , which control the transition from elastic to plastic branches, are set according to Filippou et al. [ 32 ] and Lu and Panagiotou [ 32 ]. Table 1 – Parameters for Concrete04 material model for unconfined concrete f c0 E c e c0 e cu f ct e tu [N/mm 2 ] [N/mm 2 ] [%] [%] [N/mm 2 ] [%] 46.0 35092 0.250 0.301 5.1 0.029 Table 2 – Parameters for Steel02 material model f y E 0 b st R 0 R 1 R 2 [N/mm 2 ] [N/mm 2 ] [-] [-] [-] [-] 450.0 210000 0.01 20.0 0.925 0.150 To explicitly account for the possible development of brittle failures mechanisms in RC members, the “lumped” approach proposed by Elwood [ 33 ] is then employed. This approach consists of placing in series with the fiber-based beam-column element a shear and an axial springs that are associated to “limit-state materials” (i.e., limitCurve Shear and limitCurve Axial). The limit state materials [ 33 ] track the column forces and deformations at each step until the global response of the beam-column element exceeds a predefined limit state surface. When this condition takes place, the element response in terms of strength and stiffness is controlled by the response of the activated nonlinear shear and/or axial springs (Fig. 3(b)). This way, flexural deformations are concentrated in the fiber element, while axial and shear deformations are concentrated in extremity springs. Note that when the column drift exceeds a given threshold value, depending on the associated axial limit state curve, the column axial capacity rapidly decreases until the axial demand exceeds the capacity, leading to convergency issues due to the sudden loss of vertical support. To alleviate convergency issues, a very soft elastic axial spring is thus adopted to connect spring nodes allowing a softer migration of gravity loads to adjacent column elements (Fig. 3(a)). To account for the bar-slip effect, rotational springs with envelopes proposed by Sezen and Setzler [ 34 ] are placed at both the ends of the beam-column elements. Both slip springs and shear-axial springs are placed along the main directions of the bridge (i.e., longitudinal and transverse) to account for the possible activation of brittle failure modes in both directions. For what concerns the capbeams, due to their short lengths, it is expected that members are susceptible of shear failure before flexural yielding (ASCE/SEI 41 − 13 [ 35 ]). Thus, the capbeams are modeled as elastic beam-column elements with shear springs, adopting the envelope proposed by Shen et al. [ 36 ], at both ends to account for possible activation of shear failures. Finally, rigid elements are used to account for the finite size of beam-column joints. Regarding the abutments, it is expected to remain into the elastic range during earthquake shaking given the geometrical and mechanical properties of column and beam members. For this reason, the abutments are modeled by assembling a system of elastic beam-column elements and rigid elements (Fig. 4). 3.3. Interaction at structural joints One of the most challenging issue when analytically reproducing the behavior of existing bridges is the simulation of the interaction between the different bridge parts at structural joints which behavior may significantly affect the seismic response of bridges by defining the amount of force that can be transferred from the deck to the abutments and the bents, or to the remaining part of the deck. Since their failure can result in severe damage (e.g., bridge unseating), the correct modeling of joints is of paramount importance when assessing the vulnerability of existing bridges. In the proposed Finite Element Model, the cyclic nonlinear behavior of joints is approximated in correspondence of discrete contact points along both the longitudinal and the transverse directions by assigning suitable constitutive models (Fig. 5 ) to specific degree of freedoms via ZeroLength or TwonodeLink elements in OpenSees. To alleviate convergency issues caused by the lack of definition of envelopes along any direction, very soft or rigid materials are associated with remaining degrees of freedom depending on whether displacements/rotations are allowed or not. 3.3.1. Unilateral contact Due to the nature of elastomeric bearings, these systems only work under compressive forces while are completely ineffective under tensile ones. In this case, separation between these is allowed unless connection rods are placed to make the two parts of the structure integral. To model this unilateral contact (Fig. 5 (h)), the Elastic No-Tension uniaxial material is assigned to ZeroLength elements in the vertical direction to allow the uplift in zones where this effect can take place (Fig. 4, Fig. 6 ). 3.3.2. Bearings Bearings are commonly adopted in concrete bridges to decouple the superstructure from the substructure, or in correspondence of in-span hinges to interrupt the superstructure, by allowing sliding between the two parts thus making the superstructure susceptible to large deformations. In this structure, elastomeric bearing pads were adopted. This type of bearing allows to transfer horizontal forces by friction, and it is characterized by sliding behavior that depends on the initial stiffness. Once the friction coefficient is exceeded, the stiffness of the bearing pad rapidly decreases to zero allowing horizontal sliding. Therefore, the behavior of elastomeric pads can be ideally simulated by adopting an elastic perfectly-plastic material [ 37 ]. The initial stiffness of the pad (k pad ) can be calculated according to the following formula: $${k}_{pad}=\frac{GA}{h}$$ 1 Where G is the shear modulus, A is the cross-section area, and h the thickness of the bearing pad. The force corresponding to sliding (F y ) is calculated based on the normal force acting on the bearing pad (N) times the coefficient of friction of the pad (µ): $${F}_{y}=\mu \bullet N$$ 2 The axial force acting on the single bearing is calculated considering the loads from the deck determined starting from the corresponding determinate scheme. Both µ and G play a key role in bearing behavior and consequently, have considerable effects on whole bridge seismic behavior [ 38 ]. The shear modulus of neoprene rubber is strongly influenced by strain demand [ 39 ], and for lateral displacements around 60–100% of the pad thickness decreases to about 1/2 − 1/3 of the initial value[ 40 ] while for higher displacements increases again. The pad shear modulus can be assumed like that of new devices since natural aging of the material (for 30-40yrs service) does not generally produce significant modifications in the elastic shear modulus [ 41 ]. In this study it is considered that the deck at the abutment and bents rested on 5x70x30-cm elastomeric bearing pads (laminated rubber bearings), while at the Gerber saddles on 5x40x65-cm pads. An elastic shear modulus equal to G = 0.9MPa and shear friction coefficient µ = 0.3 [ 42 ] are adopted for the elastomeric bearing pads. To simulate the elastic perfectly-plastic behavior of elastomeric bearing pads (Fig. 5 (a)), steel01 uniaxial material is assigned to ZeroLength elements both in the longitudinal and transverse directions of the bridge. 3.3.3. Shear keys Shear keys provide restraint to the superstructure in the transverse direction under both service and earthquake loads. These are typically designed as sacrificial elements to limit the transmission of horizontal forces to abutment and column bents. Therefore, they are generally expected to fail before the column bents and piles reach their maximum capacity, representing a highly vulnerable bridge component. In the bridge both interior (i.e., at bents and in-span hinges) and exterior (i.e., at abutments) RC shear-keys were inserted to restrain displacements of the bridge superstructure in the transverse direction under service loads and moderate earthquake forces. At the bents two rows of six interior shear-keys are placed between the concrete girders (Fig. 3(a)), while at the in-span hinges four interior shear-keys are placed between interior Gerber saddles (Fig. 6 ). The capacity of the interior shear-keys (F cap ) is calculated according to Megally et al. [ 43 ], and the maximum deformation (D max ), including an initial gap between the shear-key and the girder equal (D gap ) equal to 1.0 inches, at which the capacity of shear keys system drops to zero is set equal to 4.5 inches. According to experimental evidence, the capacity of the shear-key rapidly degrades under reverse load cycles as a function of their aspect ratio. At the abutment, the bridge is provided with exterior non-isolated flexural shear-keys. According to the experimental evidence ([ 43 ], [ 44 ]) and past earthquakes [ 45 ] such a type of shear-key displayed a predominant flexure-shear response, failing due to the formation of plastic hinge in the flexural key, and often resulting in a significant residual lateral displacement for the bridge girders. For shear keys having a predominant flexural behavior, the capacity can be determined using a moment-curvature analysis [ 43 ]- [ 44 ]. The proper simulation of the shear-key elements represents a very complex task due to the necessity of simulating the initial gap between shear-keys and deck girders, as well as due to the convergency issues caused by sharp envelope peaks and to the combination of different materials in series to obtain the final expected envelope. Further, the simulation strategy for interior shear-keys is complicated by the necessity of simulating that damage can be produced by the impact of the two adjacent girders, while for exterior one by the fact that only in one verse (approaching) the shear-key is effective. To this end, the behavior of interior shear-keys is simulated via combination of nonlinear springs placed in series. To simulate the behavior of exterior shear keys (Fig. 3(a)), the Hysteretic Uniaxial Material is assigned to a ZeroLength element in the transverse direction to reproduce the response of the shear-key element (Fig. 5 (c),(d)), while the initial space gap (Fig. 5 (i)) between the shear-key and the deck girders by assigning the Elastic Perfectly-Plastic Gap material to TwonodeLink elements. The adopted assembly of nonlinear springs allows the correct simulation of damage that can be produced by the impact of the two adjacent girders. For exterior shear keys (Fig. 4), the ElasticNoTension Uniaxial material (Fig. 5 (h)) is assigned to the TwonodeLink element to simulate the effectiveness of shear-keys only when the girder is approaching, while in the other direction the contact results ineffective. The initial and post-yield stiffnesses of each spring of the assembly for both interior and exterior shear-keys are composed considering in series behavior to match the expected response of the shear-keys with initial gap. Finally, a MinMax Uniaxial Material is added to remove the shear key element once it is failed (D > D max ) during the response history analysis to reduce convergency issues [ 46 ]. 3.3.4. Seismic Pounding The impact between the deck and abutments or between two deck parts can occur due to out-of-phase motion during seismic shakings, resulting in pounding at the bodies interface. Pounding can result in the crashing of the concrete at the interface, deck unseating, or even damage to different bridge components such as columns, bearings, abutments, and shear keys. Researchers have proposed different contact models to simulate the normal-direction contact force that is generated during seismic pounding. Among the others, Linear, viscoelastic linear, Janikowsky, Hertz-damp, and simplified Hertz-damp contact models have been widely adopted to estimate the contact forces arising during pounding [ 47 ]. In this study, the Impact Material, which is a bilinear approximation of the Hertz model, developed by Muthukumar & DesRoches [ 48 ] is employed. The parameters for the impact model are calibrated to the total expected energy loss during an impact event. The total expected energy loss ( DE ) is expressed by: Where k h is an impact stiffness parameter, n is the Hertz coefficient set equal to 3/2, e is the coefficient of restitution generally assumed in the range 0.6–0.8, and d m is the maximum penetration of the two decks. In this study it is assumed that the maximum penetration d m is equal to 25.4mm ([ 37 ], [ 49 ]) and the yield penetration is taken as d y =0.1 d m ([ 47 ], [ 48 ]). The stiffness parameter of the Hertz model ( k h ) is a function of the elastic properties and geometry of the two colliding bodies and is calculated according to Muthukumar & DesRoches [ 48 ]. For simplicity, to model the collision between two adjacent decks at the (girder) single saddle level, in model parameter calculation, the total mass of the superstructure is simply divided by the number of girders (Gerber saddles). The Impact Material (Fig. 5 (f)) is assigned to ZeroLength elements along the longitudinal direction to simulate the seismic pounding at the abutments (Fig. 4) and at the in-span hinges (Fig. 6 ) 3.3.5. Pinned connections The joints at the abutment are designed to behave as pinned connections (Mesnager hinges). Mesnager hinges connect the abutment to the superstructure by means of crossing hinge rebars consisting of two series of 3f16 inclined reinforcement bars. The behavior of shear reinforcement bars is modeled by employing the force-displacement envelope proposed in FIB43 [ 50 ] based on studies performed by Psycharis and Mouzakis [ 51 ] and Dulácska [ 52 ] for pinned connections realized with Double-sided inclined dowel pin in a skew angle, while hysteretic parameters are those suggested by Simon & Vigh [ 53 ]. In the longitudinal direction the actual inclination of the crossing bars has been considered, while in the transverse direction, the formulation for non-skewed bars has been adopted. Finally, the strength of the pinned connection has been corrected to account for the thickness of the elastomeric pad [ 54 ]. To model the pinned connections (Fig. 5 (e)) at the abutments, the Pinching4 uniaxial material is assigned to ZeroLength elements in both the longitudinal and transverse directions (Fig. 4). 3.4. Soil-structure interaction 3.4.1. Foundation-soil The bents and abutments are founded on pile-supported footings. This system consists of a group of cast-in-place piles connected by a footing capbeam. Several numerical and analytical methods were proposed to simulate the dynamic stiffness and the seismic response of pile foundations accounting for soil-structure interaction. The complex interaction between the pile cap, the piles, and the soil may in fact produce an amplification of the translational motion, increased flexibility of the system, and hysteretic and radiation damping due to the action of the soil [ 55 ]. This study neglects the effect of the soil-structure interaction regarding foundation piles while analyzing the response of the structure and the soil separately. The design philosophy at the time of bridge construction was to provide the foundation system sufficient strength to allow the formation of plastic hinges at the base of the RC columns, thus no significant excursion for the piles into the inelastic range is expected. However, to account for the possible plasticization of piles, their response is simulated by adding translational and rotational nonlinear springs at the interface between the footing capbeam and the pile head. A trilinear force-deformation envelope is adopted to model the nonlinear response of the piles according to the recommendations of Choi [ 56 ]. The backbone parameters for each foundation pile are obtained by multi-linearization of the pile-soil response simulated via the commercial software LPile® adopting as input the on-site soil profile and the geometric and mechanical characteristics of piles. The hysteretic behavior of piles is simulated via the Hysteretic material in OpenSees with the parameters pinchX and pinchY as 0.75 and 0.5 as proposed in Ramanathan [ 57 ]. 3.4.2. Abutment-backfill The spill-through abutment interacts both in the longitudinal and the transverse directions with a large volume of soil, represented by the compacted embankment soil. The participating mass of the embankment may have a critical effect on mode shapes and consequently the dynamic response of the bridge [ 58 ]. Along the transverse direction, due to the small wing-wall length, the embankment contribution in terms of stiffness and mass can be ignored [ 46 ]. In the longitudinal direction, the contribution of the embankment cannot be neglected. Thus, additional participating masses due to embankment soil have been attributed to the abutment nodes, these are calculated by considering an average value of embankment critical length between those determined according to the work of Zhang and Makris [ 59 ] and Werner [ 60 ]. Along the transverse direction, the lateral stiffness and strength of the abutments are provided only by the system of abutment piles and the bent framing system with no interaction with the embankment soil. Along the longitudinal direction, the interaction between the abutment and the embankment soil is simulated by adopting a Winkler-type approach that discretizes the continuous contact between the soil and the structure via a set of “interface elements” (i.e., nonlinear only-compression springs) representing the mobilization of the active and passive limit states in the soil. The piecewise relationship adopted in Marchi et al. [ 55 ], and firstly proposed to simulate earth-retaining diaphragm walls by Becci and Nova [ 61 ] is adopted to characterize the backbone of nonlinear springs (Fig. 5 (b)). The characterization of nonlinear springs depends on the characteristics of the soil and the structure. In particular, the soil resistance (F a (z), F p (z), active and passive, respectively) is expressed as a function of the vertical effective stress (σ’ v (z)), the active (K A ) and passive (K P ) earth pressure coefficients, and the transverse soil section (A i (z)). The earth pressure coefficients depend on the angle of shearing resistance of the soil and the soil-wall friction angle (δ) and are calculated according to Rampello et al. [ 62 ] and Lancellotta [ 63 ] in seismic conditions. The soil-wall friction angle δ is taken equal to 2/3φ’, while K A and K P are determined by considering the seismic intensity during each nonlinear time history analysis. The effect on earth pressure coefficients of the seismic intensity variation during the analysis was neglected and a single value of the seismic coefficients were adopted for each analysis based on the peak ground acceleration of each seismic input, as suggested in Rampello et al. [ 62 ]. The earth stiffness coefficients k a and k p are then determined based on the formulation proposed by Franchin and Pinto [ 64 ] depending on the Young’s Modulus (E 0 (z)), by converting the distribution of the small-strain shear modulus (G 0 (z)) into an equivalent variation the Young’s modulus (assuming a Poisson’s coefficient ν = 0.3), on the active and passive characteristic lengths [ 61 ], and the transverse soil section area A i (z). Since the abutment is a spill-through type (i.e., a framed system), the contact with the abutment soil is not continuous, and the springs are placed only in correspondence of the vertical (i.e., column) and horizontal (i.e., capbeams) abutment elements, thus the transverse soil section area A i (z)=Δz*B d depends on the depth, and on the contact surface. For springs placed in correspondence of the abutment capbeam and foundation beam B d is calculated considering the tributary area corresponding to that spring, while for springs placed in correspondence of columns, B d is set equal to the column width times a coefficient, set equal to 1.2, to account for the quota of back-fill soil participating to the abutment-embankment interaction due to an arching effect. The compression-only shifted non-symmetric elastic-plastic law characterizing these springs depicted in Fig. 5 (b) is obtained by suitably combining in parallel Elastic-Perfectly Plastic Gap materials assigned to ZeroLength elements. The nonlinear springs are pre-loaded to simulate the earth pressure of the soil at rest. The effect of riprap on the spill-through is neglected. 3.5. Loads The self-load masses and loads of the structure are automatically calculated depending on the geometry of the bridge components and lumped in nodes throughout the structure. Additional loads and masses relying on the bridge deck (assumed 450 kg/m 2 for the pavement and 700 kg/m for the railing) are lumped into discrete nodes along the spine element. 3.6. Solution algorithms The accurate representation of the main bridge components to allow a realistic simulation of the complex bridge behavior introduces a major challenge in terms of analysis convergency. In fact, the explicit modeling of components characterized by highly nonlinear behavior (e.g., fiber-based columns, combination of several in-series nonlinear springs), the complex interaction between them, also along different directions, and the complexity introduced by the mass distribution along the deck, may lead to convergency issues, especially when performing nonlinear dynamic analyses. In this context, the use of the implicit integration algorithm TRBDF2 [ 65 ], a composite integration method that uses Implicit Newmark and a three-point-backward Euler scheme alternately in consecutive integration time steps, is one of the most suitable algorithms according to the studies performed by Liang et al.[ 66 ] which analyzed the effect of different implicit and explicit solution algorithms when analyzing the nonlinear dynamic behavior of complex RC bridges, and it has been adopted in this study. To achieve convergency, various nonlinear solvers are consecutively tried for any iteration of an integration time step in OpenSees. According to Liang & Mosalam [ 67 ] the Newton-Raphson with line-search ( algorithm NewtonLineSearch ) is used as initial solver, the order of subsequent other solvers generally has little impact on the convergency, and thus this strategy has been adopted. Finally, the Normal Displacement Increment convergency test ( test NormDispIncr ) is used since it has been demonstrated to be the most suitable for this type of models [ 22 ]. 4. Definition of Limit States In this paper, two Limit States are introduced to derive the fragility curves namely Damage Limitation (LS DL ), Collapse Prevention (LS CP ). Limit States are attained either when single or multiple bridge structural components overcome a specific threshold value defined in terms of strength/deformation or at the global level. Finally, the condition triggering the complete Collapse (C) is also introduced. The LS DL is attained when the bridge functionality is compromised in the aftermath of an earthquake and single or multiple components must be repaired or replaced without still representing an actual threat to safety. According to Table 3 , the LS DL is attained when the first condition occurs between the following: (i) failure of the expansion joint at the Gerber saddles due to excessive longitudinal displacements; (ii) failure of the elastomeric pads at the Gerber saddles, bents or abutment, due to excessive deformations in the longitudinal or transverse direction, or failure of the pad in tension; (iii) backfill failure due to excessive displacements of the abutment in the longitudinal direction; (iv) bar buckling or concrete spalling of columns at bents or abutments; (v) first cracking of an interior shear-key; (vi) first yielding of the Mesnager hinge in the longitudinal or transverse direction. The LS CP is attained when the structure results unsafe but is not yet completely collapsed. The LS CP is attained when the first condition occurs between the following: (i) failure of shear key support at Gerber saddles due to the asynchronous movements in the longitudinal direction (i.e., the constraint provided by interior shear keys at the Gerber saddles becomes ineffective due to excessive relative displacements between the cantilever and the Gerber spans of the bridge, corresponding to the thickness of the shear key, t shear key ); (ii) first shear key reaching peak capacity at the Gerber saddles or at the bents; (iii) first shear failure at the bent or abutment beams or piers; (iv) crushing of elastomeric pads at the abutment, bent, or Gerber saddle (adopting a safety factor, γ); (v) first failure of the Mesnager hinge in the longitudinal or transverse direction. The C case is attained when the structure is partially or completely collapsed. It is attained when the first condition occurs between the following: (i) deck unseating at Gerber saddles due to excessive relative displacements in the longitudinal or the transverse direction; (ii) deck unseating at the abutment (i.e., failure of every Mesnager hinge and excessive displacements) along the longitudinal direction; (iii) failure of the Gerber shear key system (i.e., failure of every interior shear key at Gerber saddles or bents); (iv) failure of the abutment shear key system (i.e. every Mesnager hinge and at least one exterior shear key) along the transverse direction; (v) crushing of elastomeric pads at the abutment, bent or Gerber saddle (without considering any safety factor); (vi) Side-sway and (vii) Gravity-load collapse at the bents defined according to Gaetani d’Aragona et al. ([ 68 ], [ 69 ]) or shear failure of all bent capbeams. Table 3 – Definition of Limit States and corresponding threshold values Component (D) Demand parameter (C) Threshold value Damage Limitation (LS SL ) Expansion joint Ds long. Gerber ≥ 50 mm Elastomeric Pad Ds long. Gerber/Bent/Abutment ≥ t Pad Ds transv. Gerber/Bent/Abutment N vert. Pad Gerber/Bent/Abutment ≤ 0 (tension) Backfill Ds long. Abutment ≥ 50 mm RC member Bar buckling/Spalling IDR long. Bent/Abutment Pier depending on geometric and mechanical features of RC members IDR transv. Bent/Abutment Pier First interior Shear-key cracking Ds sk,transv. Gerber/Bent Shear−keys ≥ D cr,interior First yielding of Mesnager hinges Ds MH,long. Abutment ≥ D y,Mesnager,long . Ds MH,transv. Abutment ≥ D y,Mesnager,transv . Collapse Prevention (LS CP ) Ineffective Interior Shear-keys Ds sk,long. Gerber ≥ t shear key First interior Shear-key reaching peak capacity Ds sk,transv. Gerber/Bent ≥ D peak,interior First brittle failure of RC member Beams V d ≥V c Piers IDR ≥IDR F−S ** First crushing of Elastomeric Pad N vert. Pad Gerber/Bent/Abutment ≥ N cap . Pad (g = 1.5) First failure of Mesnager hinges Ds MH,long. Abutment ≥ D ult,Mesnager,long . Ds MH,transv. Abutment ≥ D ult,Mesnager,transv . Collapse (C) Deck unseating at Gerber saddles Ds long. Gerber ≥ t Gerber saddle Ds transv. Gerber ≥ b Gerber saddle Deck unseating at abutment Ds long. Abutment ≥ t Abutment Failure of Gerber Shear-key system Ds sk,transv. Gerber/Bent ≥ D ult,interior Failure of Abutment Shear-key system Ds sk,transv. Abutment ≥ D ult,exterior Crushing of all Elastomeric Pads N vert. Pad Gerber/Bent/Abutment ≥ N cap . Pad (g = 1) Global Collapse (Side-sway collapse / Gravity Load Collapse) *** or shear failure of all capbeams at one Bent *Seviceability Limit State in elastomeric bearing pad is attained for a lateral displacement equal to the thickness of the device, t pad , (45° deformation) [ 70 ] ** For Abutment and Bent Piers Flexure-Shear failure is defined according to the Limit State Material developed by Elwood et al. [ 33 ] depending on the geometric and mechanical characteristics of RC members and Axial Loads. *** Side-sway Collapse and Gravity Load Collapse defined according to ([ 68 ], [ 69 ]). 5. Derivation of fragility curves Fragility curves are generated by adopting a cloud analysis approach in which the seismic demand on the bridge components is estimated via nonlinear time-history analyses performed on the 3D model developed in § 3. The damping ratio was set equal to 4.5% according to observations by Bavirisetty et al. [ 71 ] The suite of ground motions assembled by Manfredi et al. [ 72 ] within the 2019–2021 DPC-ReLUIS Project WP4 “MARS - Seismic Risk Maps” for stiff soil (A/B soil category) is adopted in this study. The suite consists of 125 pairs of real accelerograms specifically assembled for the generation of site-independent damage fragility curves via a Cloud-based approach. The ground motion records cover a wide range of magnitudes ranging from 5.0 to 7.1, with the epicentral distance varying between 4 and 30 km. For each record pair a non-linear time history analysis is performed employing the 3D Finite element model and the peak response of each critical bridge component (e.g., bearing deformations, column drift, abutment deformations) is recorded at each step of the analysis. This allows monitoring the key response parameters representing the demand (D) and the corresponding intensity measure (IM) to determine the parameters for the fragility model. The Peak Ground Acceleration (PGA) is adopted herein as IM since it represents an acceptable compromise between a good correlation with the non-linear seismic response and practical constraints such as the site-independence. In fact, despite many studies focused on IMs that are more suitable for predicting the structural performance, such as the first-mode spectral acceleration ([ 73 ], [ 74 ]), the spectral acceleration averaged over a period range [ 75 ] or vector-valued IMs [ 76 ], [ 77 ], this intensity measure is adopted here since allowing the derivation site-independent fragility curves (i.e., fragility curves irrespective of the hazard characteristic of a specific site). Note that for each record pair, the maximum PGA along the two directions is adopted as IM. The variable adopted to monitor the bridge structural performance is the critical demand-to capacity-ratio (DCR) for a specific Limit State (LS), following denoted as DCR LS [ 78 ]. The DCR LS is defined as the maximum DCR for the components or the mechanisms that lead the system to the onset of a given LS (see Table 3 ). This formulation is particularly useful for cases where various structural components and/or potential failure mechanisms contribute to the attainment of a specific LS. The DCR LS can be defined as follows: $${DCR}_{LS}={max}_{j}^{{N}_{comp}}{max}_{l}^{{N}_{mech}}\frac{{D}_{jl}}{{C}_{jl}\left(LS\right)}$$ 4 where N comp is the number of bridge components which failure can trigger the onset of the LS, N mech is the number of potential failure mechanisms of each component, D jl is the demand evaluated for the j th structural component of the l th mechanism, and C jl (LS) is the Limit State capacity for the j th component of the i th mechanism. In the present study, the fragility functions are derived by adopting a regression-based model proposed in Jalayer et al. [ 79 ] to describe the relationship between DCR LS and the PGA level. The regression probabilistic model is generated by using the results of the NTHAs, performed for each ground motion from the bin, and can be described by the relationship proposed by Cornell et al. [ 80 ] in the log-transformed space: $$\ln {\eta _{DC{R_{LS}}|PGA}}=\ln a+b \cdot \ln PG{A^{}}$$ 5 where η DCRLS|PGA is the median value of the DCR LS given the PGA, and ln a and b regression coefficient that can be computed by performing a linear regression in the log-log space. The dispersion of the probabilistic model is measured via the logarithmic standard deviation: $${\beta _{DC{R_{LS}}|PGA}}=\sqrt {\frac{{{{\sum\nolimits_{{i=1}}^{N} {\left[ {\ln DC{R_{LS,i}} - \left( {a \cdot PGA_{i}^{b}} \right)} \right]} }^2}}}{{N - 2}}}$$ 6 Where DCR LS,i and PGA i are the DCR for the considered LS value obtained for the i th NLTHA and the corresponding PGA value, respectively, and N is the number of ground motions. The fragility curve obtained, based on the results of the Cloud Analysis, represents the probability of reaching or exceeding a specified LS for a given PGA. Under the hypothesis of lognormal distribution for the DCR LS , the fragility curve can be expressed as follows: $$P\left[ {DC{R_{LS}} \geqslant 1|PGA} \right]=\Phi \left[ {\frac{{\ln {\eta _{DC{R_{LS}}|PGA}}}}{{{\beta _{DC{R_{LS|PGA}}}}}}} \right]$$ 7 Where Φ[·] is the standard normal cumulative distribution function and β DCR LS |PGA is logarithmic standard deviations accounting for the uncertainties considered during the analyses (i.e., record-to-record). The ground motion suite considered in this study considers a wide range of seismic intensities. For this reason, a number of records can lead the structure to verge upon collapse (i) according to the definition given in Table 3 for C or (ii) to global dynamic instability (corresponding to the occurrence of very large DCRs) or convergency problems. In this case, the Cloud Analysis can be still carried by partitioning the results into two parts: (1) Non-collapse (NC) cases, corresponding to the analysis cases for which structure does not experience collapse, and (2) Collapse (C) cases, corresponding to analyses for which collapse occurred. In this case, the structural fragility for a prescribed DS can be expanded with respect to NC and C cases by using the Total Probability Theorem [ 68 ]: $$P\left[ {DC{R_{LS}} \geqslant 1|PGA} \right]=P\left[ {DC{R_{LS}} \geqslant 1|PGA,NC} \right] \cdot \left( {1 - P\left[ {C|PGA} \right]} \right)+P\left[ {DC{R_{LS}} \geqslant 1|PGA,C} \right] \cdot P\left[ {C|PGA} \right]$$ 8 In which is the conditional probability that DCR LS is greater or equal than unity given that collapse has not occurred (NC) for a given PGA, and can be expressed in the same manner as for the standard Cloud Analysis (Eq. ( 7 )) and referred to non-collapse cases. The term \(P\left[ {DC{R_{LS}} \geqslant 1|PGA,C} \right]\) is the conditional probability that DCR LS is greater or equal than unity given that collapse occurred (C) for a given PGA. \(P\left[ {DC{R_{LS}} \geqslant 1|PGA,C} \right]=1\) since for Collapse cases the Limit State LS is certainly exceeded. Finally, \(P\left[ {C|PGA} \right]\) is the probability of collapse, which can be predicted via a logistic regression model as a function of the PGA, as follows [ 79 ]: $$P\left[ {C|PGA} \right]=\frac{1}{{1+{e^{ - \left( {{\alpha _0}+{\alpha _1} \cdot \ln \left( {PGA} \right)} \right)}}}}$$ 9 Where α 0 and α 1 are the parameters of the logistic regression model applied to all the analyses, adopting binary values (i.e., 1 or 0 depending on whether collapse occurred or not). In this case, the fragility curve considering collapse is a combination between a lognormal and a logistic regression model. However, it is still possible to represent the fragility curve by adopting an equivalent lognormal distribution. 6. Results Figure 7 (a)-(b) shows in the log-log plane the scatter plot for Cloud Analysis data for the two considered limit states LS DL (a) and LS CP (b) defined according to Table 3 , considering the set of records outlined in Section 5. For a better representation, the upper-bound limit of 20 is assigned to the horizontal DCR LS -axis. For each data point (colored squares), the corresponding record number is also shown. The cyano-colored squares represent the NoC data, while the red-colored squares indicate the C data (i.e., collapse cases defined according to C reported in Table 3 ). The dashed red line DCR LS =1 threshold corresponds to the onset of the considered Limit State. From Fig. 7 (a)-(b) is also possible to infer that the ground motion bin adopted in the Cloud Analysis, originally selected for the fragility assessment of reinforced concrete buildings, not only covers a wide range of PGAs, but also provides numerous data in the range of DCR LS >1 for both considered LSs also covering the entire range of response of the selected bridge. Figure 7 (a)-(b) also reports the conditional dispersion b DCR LS|PGA and the parameters a and b of the regression in Eq. ( 5 ), along with the regression line (dotted gray line), considering only NoC cases. No significant variation was observed in standard deviation (related to record-to-record variability) for different LSs for the reference bridge. Figure 7 (c)-(d) shows the fragility curves calculated considering the Collapse cases (black bold line) along with those obtained considering only NoC data (dotted gray line), calculated with Eq. ( 7 ). According to Eq. ( 8 ), the final fragility curve is obtained by multiplying the fragility curve obtained considering only NoC data times the probability of NoC (= 1-P[C|PGA]) and summed with the P[C|PGA]. For completeness’s sake, the probability of NoC is also depicted in the figures (red dashed line). The explicit consideration of collapse cases leads the fragility curve to shift leftward, indicating a more vulnerable structure. The effect is more pronounced for the LSs corresponding to larger capacities (i.e., LS CP ) Figure 8 depicts the probability of collapse (i.e., the probability of attainment of C) obtained considering Eq. ( 9 ) along with the logistic regression model parameters (α 0 and α 1 ) be predicted using a generalized linear regression with Logit link function on the entire Cloud Analysis data. Note that during the cloud analysis, only 39 records over 125 caused collapse (i.e., lead to C defined according to Table 3 ). Only 10% of records causing collapse had PGA lower than 0.4g, while the most of collapses were attained for PGAs within the range 0.43–1.20g. Table 4 – Lognormal fragility parameters Limit State h [g] b [-] LS DL 0.16 0.38 LS CP 0.20 0.42 C 0.56 0.55 Table 4 summarizes the median (η) and the logarithmic standard deviation (𝛽) of the lognormal fragility curves corresponding to the Damage Limitation (LS DL ), Collapse Prevention (LS CP ) Limit States, and Collapse (C). Note that the lognormal fragility parameters reported in Table 4 are obtained accounting for the probability of collapse according to Eq. ( 8 ), while Fig. 7 (a-d) refers to the sole NoC cases. Even though the final LS fragility curves are a combination between a lognormal and a logistic regression model, the corresponding equivalent lognormal distribution is derived by adopting the method of the moments. Similarly, for Collapse the equivalent lognormal parameters are also reported as an alternative to those of the logistic regression (depicted in Fig. 8 ). Figure 9(a) and (b) show the contribution of different component failures to the attainment of each Limit State with reference to NoC cases. Specifically, Fig. 9(a) and (b) show the number of failures for each component, according to Table 3 , normalized by the number of analyses for which the Collapse did not occur. As can be gathered from Fig. 9(a), referring to LS DL , failure of the elastomeric pads due to traction was never evidenced. In a similar way, the attainment of cracking or spalling of bent piers rarely occurred during the analyses. This result was expected for this type of bridge since the shear keys were designed to restrain lateral displacements under serviceability loads, while they act as a fuse during significant earthquake shakings preventing damage to the substructures. Almost 20–35% of the simulations resulted in the failure of expansion joints and/or the failure of elastomeric pads, while about 20% in the failure of compacted backfill soil. The most of simulations resulted in the damage of components connecting the substructure and the superstructure. More than 40–60% of simulations resulted in the cracking of interior shear-keys, or the yielding of Mesnager hinges. Referring to LS CP , Fig. 9(b), the condition corresponding to the ineffectiveness of shear keys never occurred, since it can only be attained when excessive displacements along the longitudinal axis take place. This condition is not possible for this type of bridge due to the constraint of the deck at the abutments and the possibility of limited relative displacements between its different parts. As for LS DL , brittle failure of piers was not possible due to the limitation of the forces transmitted from the superstructure to the substructure related to the limited capacity of shear keys. Only 5% of simulations evidenced the crushing of elastomeric pads, while for 30–40% of the simulations the attainment of LS CP was ascribable to extensive damage to interior shear keys, or the failure of Mesnager hinges. Figure 9(c) depicts the contribution of different failure modes to the attainment of global Collapse defined according to Table 3 , normalized by the sole Collapse cases. It is worth noting that deck unseating never occurred both in the longitudinal and the transverse direction, neither at the Gerber nor at the abutment. Global collapse neither occurred due to the formation of shear hinges in all the capbeams. Very few simulations (about 5%) evidenced gravity-load collapse at the bents, and about 25% of simulations verged upon collapse due to the crushing of elastomeric pads. Most collapse cases (about 65–80%) are ascribable to a partial failure in which the shear key system at Gerber saddles or at the abutment has no more capacity to sustain lateral loads. In this case, even if deck unseating does not occur, the system does not possess any residual capacity against lateral loads and can be thus considered next to collapse. 7. Conclusions This paper introduces a refined three-dimensional Non-linear Finite Element Model developed in OpenSees® to realistically assess the behavior of Multi-Span Simply-Supported concrete bridges. The proposed model properly simulates the expected behavior and failure modes of bridge components as well as their mutual interactions allowing a realistic simulation of the expected bridge behavior under seismic loads. Two different Limit States, namely Damage Limitation and Collapse Prevention, are introduced depending on the behavior of the single bridge components and the connections between the superstructure and the substructure. Furthermore, the definition of a global Collapse criterion is also introduced to account for the possible failure of the bridge system under seismic loads. By adopting a cloud-based stochastic approach, bridge fragility curves are generated for the selected Limit States, properly introducing for the probability of collapse of the entire system. By employing a suite consisting of 125 real ground motion records, nonlinear time-history analyses are performed, and relevant engineering demand parameters are introduced both at the component and the system level to check the attainment of the prescribed Limit States. It has been found that for the considered bridge typology, the median peak ground acceleration value corresponding to the attainment of Damage Limitation Limit State is 0.16g (with a logarithmic dispersion of 0.38), while the Collapse Prevention occurs for a very close of the ground motion intensity corresponding to 0.2g (and logarithmic dispersion of 0.42). The system-level collapse corresponds instead to a significantly higher value of the peak ground acceleration equal 0.56g (and logarithmic dispersion of 0.55). Further consideration can be drawn based on the analysis of the simulation outcomings. The adopted set of ground motion records, originally proposed to perform cloud analysis for reinforced concrete buildings, is suitable also for the analysis of existing reinforced concrete bridges. In fact, the ground motion set can cover the entire range of structural response, from no damage to complete collapse. Along the longitudinal direction, the relative displacements between the deck and the substructure may be ascribed to the filling of the existing gap between the deck parts, or the motion of the bridge deck along the transverse direction (i.e., related to the rotations of the bridge deck about the vertical axis). The latter is related to the flexibility of the abutment and the bent piers. At the abutment, the presence of a distributed connection system with the deck along both the longitudinal and the transverse directions implies that before the failure of these components, the abutment remains integral to the deck. The spill-through abutment is submerged by the soil and can be subjected to limited displacements along the longitudinal direction (mainly due to the compressibility of the back soil), making thus possible only small additional relative displacements to those along the longitudinal axis. For this reason, the attainment of Damage Limitation and Collapse Prevention Limit States was never triggered by failures related to motion along the longitudinal direction connected to significant displacements (e.g., deck unseating), while only those corresponding to the failure of the connection system are triggered. Along the transverse direction, shear keys act as a sacrificial element not allowing the transmission of significant forces to the substructure. For this reason, the lateral displacement of the bents is generally limited, not allowing the attainment of damage to bent piers or capbeams, or to the foundation. The only failures occurring along the transverse direction are related to the failure of the shear-key system at the Gerber saddles, abutments, or bents. Regarding the elastomeric bearing pads and the Mesnager hinges, due to the limited horizontal displacements allowed, the failure can occur for both the Damage Limitation and Collapse Prevention Limit States. Further, since the vertical component of the ground motion is neglected, because only far-field ground motions are considered, the crushing phenomenon rarely occurred for bearing pads, while the failure for traction never occurred. The Collapse capacity of the bridge system is limited due to the design according to obsolete seismic codes, not accounting for the basic principles of the capacity design, the lack of proper seismic detailing, coupled with a non-statically-determined scheme. Declarations Conflicts of interest The authors have no relevant financial or non-financial interests to disclose. Author contributions MGdA contributed to conceptualization, methodology and model development, visualization, investigation, software, validation, writing—original draft, writing—review and editing. AR contributed to conceptualization, methodology, writing—review and editing, supervision, validation, proofreading. AP contributed to validation and proofreading. 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Soil Dyn Earthq Eng 5(4). 10.1016/0267-7261(86)90006-0 Nagarajaiah S, Ferrell K (1999) Stability of Elastomeric Seismic Isolation Bearings. J Struct Eng 125(9). 10.1061/(asce)0733-9445(1999)125:9(946) Kato M et al (1997) Aging effect on laminated rubber bearings of Pelham bridge, in 14th International conference on Structural Mechanics in Reactor Technology (SMiRT 14) , Lyon, France Mangalathu S, Soleimani F, Jeon JS (2017) Bridge classes for regional seismic risk assessment: Improving HAZUS models. Eng Struct 148. 10.1016/j.engstruct.2017.07.019 Megally SH, Silva PF, Seible F (2002) Seismic response of sacrificial shear keys in bridge abutments Bozorgzadeh A, Megally S, Restrepo JI, Ashford SA (2006) Capacity Evaluation of Exterior Sacrificial Shear Keys of Bridge Abutments, Journal of Bridge Engineering , vol. 11, no. 5, doi: 10.1061/(asce)1084-0702(2006)11:5(555) Yashinsky M, Oviedo R, Ashford S, Fargier-Gabaldon L, Hube MA (2010) Performance of Highway and Railway Structures During the February 27, 2010 Maule Chile Earthquake. EERI/PEER/FHWA Bridge Team Rep, 9, 1 Amirihormozaki E, Pekcan G, Itani A (2015) Analytical modeling of horizontally curved steel girder highway bridges for seismic analysis. J Earthquake Eng 19(2). 10.1080/13632469.2014.962667 Hughes PJ, Mosqueda G (2020) Evaluation of uniaxial contact models for moat wall pounding simulations. Earthq Eng Struct Dyn 49(12). 10.1002/eqe.3285 Muthukumar S, DesRoches R (2006) A Hertz contact model with non-linear damping for pounding simulation. Earthq Eng Struct Dyn 35(7). 10.1002/eqe.557 Guo A, Shen Y, Bai J, Li H (2017) Application of the endurance time method to the seismic analysis and evaluation of highway bridges considering pounding effects. Eng Struct 131. 10.1016/j.engstruct.2016.11.009 fib (2008) Structural connections for precast concrete buildings Psycharis IN, Mouzakis HP (1970) Shear resistance of pinned connections of precast members to monotonic and cyclic loading. Eng Struct 41. 10.1016/j.engstruct.2012.03.051 Dulacska H, DOWEL ACTION OF REINFORCEMENT CROSSING CRACKS IN CONCRETE (1972) J Am Concr Inst 69(12). 10.14359/11281 Simon J, Vigh LG (2016) Seismic fragility assessment of integral precast multi-span bridges in areas of moderate seismicity. Bull Earthq Eng 14(11). 10.1007/s10518-016-9947-y Kremmyda GD, Fahjan YM, Psycharis IN, Tsoukantas SG (2017) Numerical investigation of the resistance of precast RC pinned beam-to-column connections under shear loading. Earthq Eng Struct Dyn 46(9). 10.1002/eqe.2868 Marchi A, Gallese D, Gorini DN, Franchin P, Callisto L (2023) On the seismic performance of straight integral abutment bridges: From advanced numerical modelling to a practice-oriented analysis method. Earthq Eng Struct Dyn 52(1). 10.1002/eqe.3755 Choi E (2002) Seismic analysis and retrofit of mid-America bridges, no. October, 2002 Ramanathan KN (2012) Next generation seismic fragility curves for California bridges incorporating the evolution in seismic design philosophy. Georgia Tech, Atlanta, Georgia Aviram A, Mackie KR, Stojadinovic B (2008) Effect of abutment modeling on the seismic response of bridge structures. Earthq Eng Eng Vib 7(4). 10.1007/s11803-008-1008-3 Zhang J, Makris N (2002) Kinematic response functions and dynamic stiffnesses of bridge embankments. Earthq Eng Struct Dyn 31(11). 10.1002/eqe.196 Werner SD (1994) Study of Caltrans’ Seismic Evaluation Procedures for Short Bridges, in Proceedings of the 3rd Annual Seismic Research Workshop , Sacramento, California Becci B, Nova R (1987) A method for analysis and design of flexible sheetpiles. Rivista Italiana di Geotecnica 87:33–47 Rampello S, Callisto L, Masini L (2011) La spinta delle terre sulle strutture di sostegno Lancellotta R (2002) Analytical solution of passive earth pressure. Geotechnique 52(8). 10.1680/geot.2002.52.8.617 Franchin P, Pinto PE (2014) Performance-based seismic design of integral abutment bridges. Bull Earthq Eng 12(2). 10.1007/s10518-013-9552-2 Bathe KJ (2007) Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme. Comput Struct 85:7–8. 10.1016/j.compstruc.2006.09.004 Liang X, Mosalam KM, Günay S (2016) Direct Integration Algorithms for Efficient Nonlinear Seismic Response of Reinforced Concrete Highway Bridges. J Bridge Engineering 21(7). 10.1061/(asce)be.1943-5592.0000895 Liang X, Mosalam KM (2016) Performance-based robust nonlinear seismic analysis with application to reinforced concrete highway bridge systems, Berkeley, CA Gaetani d’Aragona M, Polese M, Elwood KJ, Baradaran Shoraka M, Prota A (2017) Aftershock collapse fragility curves for non-ductile RC buildings: a scenario-based assessment. Earthq Eng Struct Dyn 46(13). 10.1002/eqe.2894 Gaetani d’Aragona M, Polese M, Prota A (2022) Stick model for as-built and retrofitted infilled RC frames. Eng Struct 268. 10.1016/j.engstruct.2022.114735 Tortolini P, Marcantonio PR, Petrangeli M, Lupoi A (2001) Criteri per la verifica e la sostituzione degli appoggi in neoprene di viadotti esistenti in zona sismica, in XIV Convegno ANIDIS Bavirisetty R, Vinayagamoorthy M, Duan L (2003) Dynamic analysis. Bridge Engineering: Seismic Des. 10.4324/9780203708712-6 Manfredi V, Masi A, Özcebe AG, Paolucci R, Smerzini C (2022) Selection and spectral matching of recorded ground motions for seismic fragility analyses. Bull Earthq Eng 20(10). 10.1007/s10518-022-01393-0 Shome N, Cornell CA, Bazzurro P, Carballo JE (1998) Earthquakes, records, and nonlinear responses. Earthq Spectra 14(3). 10.1193/1.1586011 Jalayer F, Beck JL, Zareian F (2012) Analyzing the Sufficiency of Alternative Scalar and Vector Intensity Measures of Ground Shaking Based on Information Theory. J Eng Mech 138(3). 10.1061/(asce)em.1943-7889.0000327 Eads L, Miranda E, Lignos DG (2015) Average spectral acceleration as an intensity measure for collapse risk assessment. Earthq Eng Struct Dyn 44(12). 10.1002/eqe.2575 Baker JW, Cornell CA (2008) Vector-valued intensity measures incorporating spectral shape for prediction of structural response. J Earthquake Eng 12(4). 10.1080/13632460701673076 Kohrangi M, Bazzurro P, Vamvatsikos D (2016) Vector and scalar IMs in structural response estimation, Part I: Hazard analysis. Earthq Spectra 32(3). 10.1193/053115EQS080M Jalayer F, Franchin P, Pinto PE (2007) A scalar damage measure for seismic reliability analysis of RC frames. Earthq Eng Struct Dyn 36(13). 10.1002/eqe.704 Jalayer F, Ebrahimian H, Miano A, Manfredi G, Sezen H (2017) Analytical fragility assessment using unscaled ground motion records. Earthq Eng Struct Dyn 46(15). 10.1002/eqe.2922 Cornell CA, Jalayer F, Hamburger RO, Foutch DA (2002) Probabilistic Basis for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guidelines. J Struct Eng 128(4). 10.1061/(asce)0733-9445(2002)128:4(526) Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4412197","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":302783902,"identity":"255e7a86-9694-40e4-8efd-587452f5172c","order_by":0,"name":"Marco Gaetani d'Aragona","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0001-8817-7940","institution":"University of Naples Federico II: Universita degli Studi di Napoli Federico II","correspondingAuthor":true,"prefix":"","firstName":"Marco","middleName":"Gaetani","lastName":"d'Aragona","suffix":""},{"id":302783903,"identity":"49c3b6b0-12c6-4294-b011-8bd77d21d93f","order_by":1,"name":"Antonino Recupero","email":"","orcid":"","institution":"University of Messina: Universita degli Studi di Messina","correspondingAuthor":false,"prefix":"","firstName":"Antonino","middleName":"","lastName":"Recupero","suffix":""},{"id":302783904,"identity":"6cf5f8d3-87ec-4ca4-a17f-29a88ec39073","order_by":2,"name":"Andrea Prota","email":"","orcid":"","institution":"University of Naples Federico II: Universita degli Studi di Napoli Federico II","correspondingAuthor":false,"prefix":"","firstName":"Andrea","middleName":"","lastName":"Prota","suffix":""}],"badges":[],"createdAt":"2024-05-13 09:27:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4412197/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4412197/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":57068702,"identity":"500fbcd5-62a0-4ccf-953e-0fa10acd7125","added_by":"auto","created_at":"2024-05-24 07:41:52","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":68598,"visible":true,"origin":"","legend":"\u003cp\u003eGeneral layout of the overpass bridge: (a) 3D-view of the bridge; (b) frontal view of the Abutment; (c) frontal view of the Bent.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/f1d709510d9cabdc210f88ab.png"},{"id":57069142,"identity":"79ea5095-1e40-4267-b713-e22db6f28aac","added_by":"auto","created_at":"2024-05-24 07:49:52","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":67275,"visible":true,"origin":"","legend":"\u003cp\u003eOpenSees model for bridge components\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/fabb90c5eb93ca751de4f9b1.png"},{"id":57067866,"identity":"066ec1c6-d8b8-4a96-804c-684c7a906265","added_by":"auto","created_at":"2024-05-24 07:33:52","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":43959,"visible":true,"origin":"","legend":"\u003cp\u003eShematic layout for OpenSees model of bents\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/fe0aba0214a9b11a9371a818.png"},{"id":57067865,"identity":"53dafd2f-4f0a-49fa-ac7f-2c2fcfe6718a","added_by":"auto","created_at":"2024-05-24 07:33:52","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":39425,"visible":true,"origin":"","legend":"\u003cp\u003eShematic layout for OpenSees model of Abutments\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/fc278984831412916ce3657a.png"},{"id":57067872,"identity":"581d8bf2-c432-4212-b1c3-dc3287c9dbfb","added_by":"auto","created_at":"2024-05-24 07:33:52","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":26799,"visible":true,"origin":"","legend":"\u003cp\u003eConstitutive models adopted to simulate the connection/interaction between different bridge parts.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/742509f3dabdfbcfae8a671b.png"},{"id":57067870,"identity":"b5d4adc9-f3e1-4b50-8857-904d66937992","added_by":"auto","created_at":"2024-05-24 07:33:52","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":20807,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic layout for OpenSees model of in-span hinge (Gerber saddle)\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/d79c1fc28eec0a37b488172d.png"},{"id":57068704,"identity":"2fbeba20-113b-49a3-a3b9-cfeb2ecbb518","added_by":"auto","created_at":"2024-05-24 07:41:52","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":55240,"visible":true,"origin":"","legend":"\u003cp\u003eCloud Analysis data and regression (a)-(b), fragility curves and probability of observing NoC (c)-(d) for Limit States corresponding to Damage Limitation (a)-(c), and Collapse Prevention (b)-(d).\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/b3a36b93a6d4638a73b86e08.png"},{"id":57067871,"identity":"b70b79d5-464a-42ca-9147-e49fe3eb84a5","added_by":"auto","created_at":"2024-05-24 07:33:52","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":11134,"visible":true,"origin":"","legend":"\u003cp\u003eProbability of collapse\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/97abe82a897f30382d1923bf.png"},{"id":57067873,"identity":"2c543b35-c7ac-441c-85d8-52526915eaa4","added_by":"auto","created_at":"2024-05-24 07:33:52","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":32680,"visible":true,"origin":"","legend":"\u003cp\u003eContribution of different component failures to the attainment of Limit States (a) LS\u003csub\u003eDL\u003c/sub\u003e, (b) LS\u003csub\u003eCP\u003c/sub\u003e, and (c) global collapse C.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/420b342c767523ab976ac03a.png"},{"id":59777199,"identity":"c026c474-3788-4263-b48c-494c04864b03","added_by":"auto","created_at":"2024-07-06 15:21:13","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1138440,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4412197/v1/e1feeef4-125f-4060-ba05-1060f5f302ad.pdf"}],"financialInterests":"","formattedTitle":"Seismic fragility assessment of existing Italian overpass bridges","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe seismic vulnerability of existing RC bridges has become a topic of strong interest for the scientific community due to the strategic role that they play during the emergency management phase. These structures, if they are a part of a strategic roadway network, are indeed required to remain fully operational in the aftermath of natural catastrophes such as earthquakes of moderate to severe intensities to allow the implementation of rescue operations.\u003c/p\u003e \u003cp\u003eIn Italy, the importance of primary transportation networks recently enforced comprehensive research programs [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] to investigate several topics related to the seismic assessment and retrofit of bridges, and to propose pre-code European guidelines for the assessment of the existing ones. Further, recent collapses involving existing RC bridges such as the Santo Stefano (1996)[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], the Petrulla (2014), the Annone (2016), the Osimo (2017) overpasses, the Fossano (2018), and the Polcevera viaduct (2018) [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], have dramatically spotlighted the needing for a systematic vulnerability reduction program for the whole infrastructural system accelerating the release of specific guidelines for the \u0026rdquo;Risk-based classification, safety checks and monitoring of existing bridges\u0026rdquo; [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe most of Italian bridges were built during the two decades from 1955\u0026ndash;1975 due to the roadway network development related to the Italian economic growth ([\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]), and were primarily designed for gravity loads only. Even when the seismic design was considered, this only consisted of the application of nominal equivalent static forces, equal to a maximum of 10% of the weight in higher seismicity areas, with no consideration of the bridge dynamic properties or the possible ductile behavior. For this reason, their structural performances may result inadequate under severe earthquake motions especially due to the lack of proper seismic detailing.\u003c/p\u003e \u003cp\u003eThe Italian infrastructure network has been shown highly vulnerable due to design deficiencies, adopted technologies and materials, as well as the lack of appropriate maintenance. Recent earthquakes such as the 2009 L\u0026rsquo;Aquila [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], the 2012 Emilia [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], and the 2015 Central Italy [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] sequences, only evidenced limited damage to RC bridges that was mainly ascribable to poor maintenance, even for bridges not specifically designed for seismic actions, and only in one case, an RC bridge entirely collapsed probably due to pier failure, again due to lack of maintenance [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. However, several studies suggest that, especially in southern Europe [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], existing bridge infrastructures are characterized by high seismic vulnerability, making the implementation of risk mitigation policies deemed urgent to minimize their potential damage and to mitigate the post-event impact on transportation networks, indirect losses, business disruption or emergency response efforts. In this perspective, the vulnerability assessment of existing bridges, expressed in probabilistic terms for suitable damage states, beyond predicting the damage or usability of the structure during the post-earthquake emergency management phase, can provide important information about the prioritization scheme for retrofit interventions, giving crucial indications regarding the most vulnerable component and the most suitable retrofit strategy to be implemented, especially if fragility curves are available at the component level.\u003c/p\u003e \u003cp\u003eMost of the Italian RC bridge stock is composed of a rather uniform structural typology made up of simply-supported spans with prestressed beams, and cast-in-place deck slabs supported by single stem or frame-type piers [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Due to the availability of precast prestressed concrete beam technology, these bridges often adopt as a structural scheme that of the multi-span simply-supported beam or the Gerber scheme.\u003c/p\u003e \u003cp\u003eFor this reason, this paper specifically refers to Multi-Span Simply-Supported (MSSS) bridges with pre-stressed concrete girders adopting a Niagara-type scheme [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e],which has been widely adopted in the past to realize overpass highway bridges.\u003c/p\u003e \u003cp\u003ePast seismic events occurred in high-seismicity zones such as the Loma Prieta (1989) and the Northridge (1994) earthquakes evidenced major deficiencies in MSSS concrete bridges. In fact, the use of statically-determined schemes, much simpler to calculate and adaptable to temperature variation and constraint settlements, has the disadvantage of no redundancy and thus limited plastic capacity thus making this type of bridges highly vulnerable to seismic actions. Typical failure modes for this class of bridges consists in flexure/shear failure of bent beams and columns due to the lack or the presence of limited seismic detailing, abutment failure (e.g., [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]), as well as deck unseating at the abutments, cap-beam, or in-span hinges [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. In particular, the presence of expansion joints between adjacent decks at the in-span hinges or between the deck and the abutment can result in deck unseating spans due to the lack of properly designed restrainers to the motion in the transverse direction or considerable impact at the expansion joints due to out-of-phase vibration during earthquakes. Deck unseating, as well as shear and flexural failure of the pier columns, and rotation of the deck, have also been recognized in the past among the most relevant failure modes, especially for bridges with non-negligible skew angles [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo provide a realistic assessment of such a type of bridges, reliable analytical models explicitly simulating the expected behavior and failure modes of single components (e.g., bearings, shear keys, bent and abutment beams and columns, foundation system) as well as the mutual interaction between different bridge parts (e.g., deck-deck and deck-abutment hammering, interaction between deck girders and shear-keys) should be developed.\u003c/p\u003e \u003cp\u003eWith the aim of developing analytical fragility curves for a typical MSSS concrete bridge, a commonly adopted scheme in the realization of overpass bridges in southern Italy, a refined three-dimensional finite element model has been specifically developed to properly simulate their complex behavior. The model explicitly simulates the behavior of each single bridge component and their mutual interactions, accounting for typical relevant failure modes both at the component and the system level. Fragility curves are developed adopting a cloud-based approach by means of nonlinear time-history analyses performed by employing a suite consisting of 125 real ground motions. Two damage limit states corresponding to usability and collapse prevention are defined, system-level fragility curves are developed for a real RC bridge, designed, and constructed in southern Italy between 1968\u0026ndash;1974.\u003c/p\u003e \u003cp\u003eSection 2 introduces the geometric and structural features of the MSSS concrete bridge adopted for the generation of the model. Section 3 introduces the Finite Element Model concerning the superstructure (\u0026sect;\u0026nbsp;3.1), the substructure (\u0026sect;\u0026nbsp;3.2), the modeling of the interaction between these two parts (\u0026sect;\u0026nbsp;3.3) and between the substructure and the soil (\u0026sect;\u0026nbsp;3.4), along with the adopted loads (\u0026sect;\u0026nbsp;3.5) and the solution algorithms (\u0026sect;\u0026nbsp;3.5). Section 4 introduces the definition of two Limit States and a system-level collapse. Section 5 introduces the stochastic approach based on the cloud analysis to derive the fragility curves, that are carried out in Section 6. Finally, Section 7 highlights the main conclusions drawn for the considered bridge scheme.\u003c/p\u003e"},{"header":"2. Description of the reference bridge","content":"\u003cp\u003eOne representative RC overpass bridge structure realized in the southern Italy in 1970s is adopted as reference structure to generate the fragility curves for MSSS bridges.\u003c/p\u003e \u003cp\u003eThe structural scheme consists of MSSS prestressed beams with a Niagara-type scheme for the positioning of in-span hinges, see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a). The bridge is composed of three spans, where the central span is suspended and connected to the cantilever spans by means of half-joints (Gerber saddles). The total bridge length is 89.0 m, with a central span of 44.0 m and lateral cantilever spans of 22.5m. The length of the suspended spans is 31.0m, while the cantilever part of central span is 6.5m long.\u003c/p\u003e \u003cp\u003eThe deck (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b)-(c)) is composed of seven equally spaced I-shaped precast concrete girders and a cast-in-place RC deck. In relevant sections, diaphragms are realized to stiffen the deck cross-section. The cross-section of the girders along the lateral spans is not constant and the height linearly varies from a minimum at the abutment to a maximum at the bents. The bents (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c)) are constructed as multi-column bents with seven RC columns aligned to the girder axis positions, and a rectangular cross-section linearly reducing from the bottom to the top. The cap beam has trapezoidal cross-section. The height of the bent columns is 6.0m for the upstream bent and 6.6m for the downstream one. The abutments (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b)) are spill-through type abutments composed of four equally-spaced columns and a cap beam with rectangular cross-section. The rectangular cross-section of abutment columns linearly reduces from the bottom to the top. Both the bents and abutments are supported by two rows of four cast-in-place concrete piles with circular cross-section of 1.0m diameter.\u003c/p\u003e \u003cp\u003eElastomeric bearing pads of different sizes and constant thickness of 0.05m are placed at half-joints, and between the deck and substructure at abutments and bents. At the Gerber saddles four interior shear-keys are placed between interior RC girders, while at bents two rows of six interior shear keys, and the abutment only exterior shear-keys are placed. Finally, in zones corresponding to the abutment, inclined rebars are placed in between the head of girders to realize a Mesnager hinge. Further details can be found in Gaetani d\u0026rsquo;Aragona et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. Non-linear Finite Element model","content":"\u003cp\u003eA three-dimensional finite element model of the bridge is developed using the OpenSees\u0026reg; platform [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The non-linear finite element model has been developed to reproduce the actual behavior of the overpass by suitable modeling the behavior of its components (i.e., for the substructure: bents, abutments, shear-keys, bearings, foundation system; for the superstructure: deck), and the interaction between the different parts of the bridge (i.e., deck-deck, deck-bent, deck-abutments) and between the substructure and the soil (i.e., soil-structure interaction at the abutments). Both the substructure and the superstructure members are modeled with elements placed in the center of mass, while the connections between different bridge parts (i.e., at bents, abutments, and in-span hinges) and with the soil (i.e., at foundations) are preserved by adopting rigid elements to account for the eccentricity of the member axes and the finite size of elements. An illustration of the model is provided in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Superstructure\u003c/h2\u003e \u003cp\u003eThe bridge superstructure, composed of a cast-in-place concrete deck and I-shaped prestressed concrete girders, is expected to remain elastic during earthquake shakings (e.g.,[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]). Therefore, the deck is simulated via a three-dimensional \u0026ldquo;spine\u0026rdquo; model consisting of a series of equivalent elastic beam-column elements placed along its centroid, and assuming full inertial properties (i.e., uncracked). The cross-section properties of the equivalent beam are calculated adopting appropriate flexural and torsional stiffness values, while the variation of the cross-section along the bridge axis is accounted for during the model generation.\u003c/p\u003e \u003cp\u003eTo properly reproduce the kinematic of the superstructure in zones where the structure-structure interaction takes place, the full width of the superstructure cross-section is incorporated adopting rigid elements (i.e., at abutments, bents, and in-span hinges).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Substructure\u003c/h2\u003e \u003cp\u003eThe bridge substructure is composed of abutments and bents. Both the bridge bents and the spill-through abutments consist of a multi-column frame system composed of columns with varying cross-section geometry along the height and a top capbeam.\u003c/p\u003e \u003cp\u003eExisting RC members with low transverse reinforcement often show limited ductility due to the premature triggering of brittle failure mechanisms such as shear failure after flexural yielding and/or axial failure. To simulate the flexural behavior of columns while accounting for the possible development of brittle failure modes (i.e., flexure-shear, axial failure), a mixed distributed-lumped modeling strategy in which the flexural behavior is simulated via a distributed approach and the shear/axial behavior via a lumped one is adopted.\u003c/p\u003e \u003cp\u003eA schematic layout of the modeling strategy adopted to simulate the behavior of bents is schematized in Fig.\u0026nbsp;3. The flexural behavior of columns is simulated by adopting a distributed fiber-based approach, which entails the use of displacement-based beam-column elements (dispBeamColumn) with fiber-defined cross-sections. The varying geometry along the column axis is simulated by assigning different cross-sections at specified integration points (Fig.\u0026nbsp;3(a)). The section is discretized into 40x40 fibers for the core and 20x20 fibers for the cover, while the steel rebars embedded in the concrete cross section are modeled by means of straight layers of equivalent thickness.\u003c/p\u003e \u003cp\u003eAt the cross-section level, the Concrete04 material is used to simulate the behavior of concrete fibers. The Concrete04 is based on Popovic\u0026rsquo;s [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] formulation for compression with unloading and reloading degraded stiffnesses according to Karsan-Jirsa [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], while it adopts an exponential decay for strength for the tensile behavior. The characterization of the Concrete04 parameters was differentiated for the unconfined and the confined part of the cross-section. The parameters for the unconfined concrete behavior are calculated according to Popovics\u0026rsquo;s [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] and Mander et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] in compression and Belarbi and Hsu [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] in tension, while the behavior of the confined concrete is modeled assuming the confinement parameters by Mander et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] and Chang and Mander [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] depending on the arrangement of both longitudinal and transverse reinforcement. The value of the ultimate concrete compressive strain is set according to Scott et al. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The mean values adopted for Concrete04 parameters are resumed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe behavior of steel rebars is modeled by means of the Steel02 material, which is an elastic-plastic material with isotropic strain hardening based on the Giuffr\u0026egrave;-Menegotto-Pinto formulation ([\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]). The steel model parameters are presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, where the parameter b\u003csub\u003est\u003c/sub\u003e represents the ratio between the post-yield tangent and the initial elastic tangent, and R\u003csub\u003e0\u003c/sub\u003e, R\u003csub\u003e1\u003c/sub\u003e and R\u003csub\u003e2\u003c/sub\u003e, which control the transition from elastic to plastic branches, are set according to Filippou et al. [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] and Lu and Panagiotou [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026ndash; Parameters for Concrete04 material model for unconfined concrete\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ef\u003csub\u003ec0\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eE\u003csub\u003ec\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ee\u003csub\u003ec0\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ee\u003csub\u003ecu\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ef\u003csub\u003ect\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ee\u003csub\u003etu\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[N/mm\u003csup\u003e2\u003c/sup\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[N/mm\u003csup\u003e2\u003c/sup\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[%]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e[%]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[N/mm\u003csup\u003e2\u003c/sup\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e[%]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e46.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35092\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.301\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.029\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026ndash; Parameters for Steel02 material model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ef\u003csub\u003ey\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eE\u003csub\u003e0\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eb\u003csub\u003est\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eR\u003csub\u003e0\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[N/mm\u003csup\u003e2\u003c/sup\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[N/mm\u003csup\u003e2\u003c/sup\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[-]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e[-]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[-]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e[-]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e450.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e210000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.925\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.150\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo explicitly account for the possible development of brittle failures mechanisms in RC members, the \u0026ldquo;lumped\u0026rdquo; approach proposed by Elwood [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] is then employed. This approach consists of placing in series with the fiber-based beam-column element a shear and an axial springs that are associated to \u0026ldquo;limit-state materials\u0026rdquo; (i.e., limitCurve Shear and limitCurve Axial). The limit state materials [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] track the column forces and deformations at each step until the global response of the beam-column element exceeds a predefined limit state surface. When this condition takes place, the element response in terms of strength and stiffness is controlled by the response of the activated nonlinear shear and/or axial springs (Fig.\u0026nbsp;3(b)). This way, flexural deformations are concentrated in the fiber element, while axial and shear deformations are concentrated in extremity springs. Note that when the column drift exceeds a given threshold value, depending on the associated axial limit state curve, the column axial capacity rapidly decreases until the axial demand exceeds the capacity, leading to convergency issues due to the sudden loss of vertical support. To alleviate convergency issues, a very soft elastic axial spring is thus adopted to connect spring nodes allowing a softer migration of gravity loads to adjacent column elements (Fig.\u0026nbsp;3(a)).\u003c/p\u003e \u003cp\u003eTo account for the bar-slip effect, rotational springs with envelopes proposed by Sezen and Setzler [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] are placed at both the ends of the beam-column elements. Both slip springs and shear-axial springs are placed along the main directions of the bridge (i.e., longitudinal and transverse) to account for the possible activation of brittle failure modes in both directions.\u003c/p\u003e \u003cp\u003eFor what concerns the capbeams, due to their short lengths, it is expected that members are susceptible of shear failure before flexural yielding (ASCE/SEI 41\u0026thinsp;\u0026minus;\u0026thinsp;13 [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]). Thus, the capbeams are modeled as elastic beam-column elements with shear springs, adopting the envelope proposed by Shen et al. [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], at both ends to account for possible activation of shear failures. Finally, rigid elements are used to account for the finite size of beam-column joints.\u003c/p\u003e \u003cp\u003eRegarding the abutments, it is expected to remain into the elastic range during earthquake shaking given the geometrical and mechanical properties of column and beam members. For this reason, the abutments are modeled by assembling a system of elastic beam-column elements and rigid elements (Fig.\u0026nbsp;4).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Interaction at structural joints\u003c/h2\u003e \u003cp\u003eOne of the most challenging issue when analytically reproducing the behavior of existing bridges is the simulation of the interaction between the different bridge parts at structural joints which behavior may significantly affect the seismic response of bridges by defining the amount of force that can be transferred from the deck to the abutments and the bents, or to the remaining part of the deck. Since their failure can result in severe damage (e.g., bridge unseating), the correct modeling of joints is of paramount importance when assessing the vulnerability of existing bridges. In the proposed Finite Element Model, the cyclic nonlinear behavior of joints is approximated in correspondence of discrete contact points along both the longitudinal and the transverse directions by assigning suitable constitutive models (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e) to specific degree of freedoms via ZeroLength or TwonodeLink elements in OpenSees. To alleviate convergency issues caused by the lack of definition of envelopes along any direction, very soft or rigid materials are associated with remaining degrees of freedom depending on whether displacements/rotations are allowed or not.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1. Unilateral contact\u003c/h2\u003e \u003cp\u003eDue to the nature of elastomeric bearings, these systems only work under compressive forces while are completely ineffective under tensile ones. In this case, separation between these is allowed unless connection rods are placed to make the two parts of the structure integral. To model this unilateral contact (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e(h)), the Elastic No-Tension uniaxial material is assigned to ZeroLength elements in the vertical direction to allow the uplift in zones where this effect can take place (Fig.\u0026nbsp;4, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2. Bearings\u003c/h2\u003e \u003cp\u003eBearings are commonly adopted in concrete bridges to decouple the superstructure from the substructure, or in correspondence of in-span hinges to interrupt the superstructure, by allowing sliding between the two parts thus making the superstructure susceptible to large deformations. In this structure, elastomeric bearing pads were adopted. This type of bearing allows to transfer horizontal forces by friction, and it is characterized by sliding behavior that depends on the initial stiffness. Once the friction coefficient is exceeded, the stiffness of the bearing pad rapidly decreases to zero allowing horizontal sliding. Therefore, the behavior of elastomeric pads can be ideally simulated by adopting an elastic perfectly-plastic material [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The initial stiffness of the pad (k\u003csub\u003epad\u003c/sub\u003e) can be calculated according to the following formula:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${k}_{pad}=\\frac{GA}{h}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere G is the shear modulus, A is the cross-section area, and h the thickness of the bearing pad. The force corresponding to sliding (F\u003csub\u003ey\u003c/sub\u003e) is calculated based on the normal force acting on the bearing pad (N) times the coefficient of friction of the pad (\u0026micro;):\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${F}_{y}=\\mu \\bullet N$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe axial force acting on the single bearing is calculated considering the loads from the deck determined starting from the corresponding determinate scheme. Both \u0026micro; and G play a key role in bearing behavior and consequently, have considerable effects on whole bridge seismic behavior [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. The shear modulus of neoprene rubber is strongly influenced by strain demand [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], and for lateral displacements around 60\u0026ndash;100% of the pad thickness decreases to about 1/2\u0026thinsp;\u0026minus;\u0026thinsp;1/3 of the initial value[\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] while for higher displacements increases again. The pad shear modulus can be assumed like that of new devices since natural aging of the material (for 30-40yrs service) does not generally produce significant modifications in the elastic shear modulus [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this study it is considered that the deck at the abutment and bents rested on 5x70x30-cm elastomeric bearing pads (laminated rubber bearings), while at the Gerber saddles on 5x40x65-cm pads. An elastic shear modulus equal to G\u0026thinsp;=\u0026thinsp;0.9MPa and shear friction coefficient \u0026micro;\u0026thinsp;=\u0026thinsp;0.3 [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e] are adopted for the elastomeric bearing pads.\u003c/p\u003e \u003cp\u003eTo simulate the elastic perfectly-plastic behavior of elastomeric bearing pads (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a)), steel01 uniaxial material is assigned to ZeroLength elements both in the longitudinal and transverse directions of the bridge.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.3.3. Shear keys\u003c/h2\u003e \u003cp\u003eShear keys provide restraint to the superstructure in the transverse direction under both service and earthquake loads. These are typically designed as sacrificial elements to limit the transmission of horizontal forces to abutment and column bents. Therefore, they are generally expected to fail before the column bents and piles reach their maximum capacity, representing a highly vulnerable bridge component.\u003c/p\u003e \u003cp\u003eIn the bridge both interior (i.e., at bents and in-span hinges) and exterior (i.e., at abutments) RC shear-keys were inserted to restrain displacements of the bridge superstructure in the transverse direction under service loads and moderate earthquake forces. At the bents two rows of six interior shear-keys are placed between the concrete girders (Fig.\u0026nbsp;3(a)), while at the in-span hinges four interior shear-keys are placed between interior Gerber saddles (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe capacity of the interior shear-keys (F\u003csub\u003ecap\u003c/sub\u003e) is calculated according to Megally et al. [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], and the maximum deformation (D\u003csub\u003emax\u003c/sub\u003e), including an initial gap between the shear-key and the girder equal (D\u003csub\u003egap\u003c/sub\u003e) equal to 1.0 inches, at which the capacity of shear keys system drops to zero is set equal to 4.5 inches. According to experimental evidence, the capacity of the shear-key rapidly degrades under reverse load cycles as a function of their aspect ratio.\u003c/p\u003e \u003cp\u003eAt the abutment, the bridge is provided with exterior non-isolated flexural shear-keys. According to the experimental evidence ([\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]) and past earthquakes [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e] such a type of shear-key displayed a predominant flexure-shear response, failing due to the formation of plastic hinge in the flexural key, and often resulting in a significant residual lateral displacement for the bridge girders. For shear keys having a predominant flexural behavior, the capacity can be determined using a moment-curvature analysis [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]- [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe proper simulation of the shear-key elements represents a very complex task due to the necessity of simulating the initial gap between shear-keys and deck girders, as well as due to the convergency issues caused by sharp envelope peaks and to the combination of different materials in series to obtain the final expected envelope. Further, the simulation strategy for interior shear-keys is complicated by the necessity of simulating that damage can be produced by the impact of the two adjacent girders, while for exterior one by the fact that only in one verse (approaching) the shear-key is effective.\u003c/p\u003e \u003cp\u003eTo this end, the behavior of interior shear-keys is simulated via combination of nonlinear springs placed in series. To simulate the behavior of exterior shear keys (Fig.\u0026nbsp;3(a)), the Hysteretic Uniaxial Material is assigned to a ZeroLength element in the transverse direction to reproduce the response of the shear-key element (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e(c),(d)), while the initial space gap (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e(i)) between the shear-key and the deck girders by assigning the Elastic Perfectly-Plastic Gap material to TwonodeLink elements. The adopted assembly of nonlinear springs allows the correct simulation of damage that can be produced by the impact of the two adjacent girders. For exterior shear keys (Fig.\u0026nbsp;4), the ElasticNoTension Uniaxial material (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e(h)) is assigned to the TwonodeLink element to simulate the effectiveness of shear-keys only when the girder is approaching, while in the other direction the contact results ineffective.\u003c/p\u003e \u003cp\u003eThe initial and post-yield stiffnesses of each spring of the assembly for both interior and exterior shear-keys are composed considering in series behavior to match the expected response of the shear-keys with initial gap. Finally, a MinMax Uniaxial Material is added to remove the shear key element once it is failed (D\u0026thinsp;\u0026gt;\u0026thinsp;D\u003csub\u003emax\u003c/sub\u003e) during the response history analysis to reduce convergency issues [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e3.3.4. Seismic Pounding\u003c/h2\u003e \u003cp\u003eThe impact between the deck and abutments or between two deck parts can occur due to out-of-phase motion during seismic shakings, resulting in pounding at the bodies interface. Pounding can result in the crashing of the concrete at the interface, deck unseating, or even damage to different bridge components such as columns, bearings, abutments, and shear keys.\u003c/p\u003e \u003cp\u003eResearchers have proposed different contact models to simulate the normal-direction contact force that is generated during seismic pounding. Among the others, Linear, viscoelastic linear, Janikowsky, Hertz-damp, and simplified Hertz-damp contact models have been widely adopted to estimate the contact forces arising during pounding [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this study, the Impact Material, which is a bilinear approximation of the Hertz model, developed by Muthukumar \u0026amp; DesRoches [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e] is employed. The parameters for the impact model are calibrated to the total expected energy loss during an impact event. The total expected energy loss (\u003cem\u003eDE\u003c/em\u003e) is expressed by:\u003c/p\u003e \u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"398\" height=\"56\"\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e is an impact stiffness parameter, \u003cem\u003en\u003c/em\u003e is the Hertz coefficient set equal to 3/2, \u003cem\u003ee\u003c/em\u003e is the coefficient of restitution generally assumed in the range 0.6\u0026ndash;0.8, and \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e is the maximum penetration of the two decks. In this study it is assumed that the maximum penetration \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e is equal to 25.4mm ([\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]) and the yield penetration is taken as \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e=0.1\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e ([\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e], [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]). The stiffness parameter of the Hertz model (\u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e) is a function of the elastic properties and geometry of the two colliding bodies and is calculated according to Muthukumar \u0026amp; DesRoches [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. For simplicity, to model the collision between two adjacent decks at the (girder) single saddle level, in model parameter calculation, the total mass of the superstructure is simply divided by the number of girders (Gerber saddles).\u003c/p\u003e \u003cp\u003eThe Impact Material (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e(f)) is assigned to ZeroLength elements along the longitudinal direction to simulate the seismic pounding at the abutments (Fig.\u0026nbsp;4) and at the in-span hinges (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e6\u003c/span\u003e)\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.3.5. Pinned connections\u003c/h2\u003e \u003cp\u003eThe joints at the abutment are designed to behave as pinned connections (Mesnager hinges). Mesnager hinges connect the abutment to the superstructure by means of crossing hinge rebars consisting of two series of 3f16 inclined reinforcement bars.\u003c/p\u003e \u003cp\u003eThe behavior of shear reinforcement bars is modeled by employing the force-displacement envelope proposed in FIB43 [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e] based on studies performed by Psycharis and Mouzakis [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e] and Dul\u0026aacute;cska [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e] for pinned connections realized with Double-sided inclined dowel pin in a skew angle, while hysteretic parameters are those suggested by Simon \u0026amp; Vigh [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]. In the longitudinal direction the actual inclination of the crossing bars has been considered, while in the transverse direction, the formulation for non-skewed bars has been adopted. Finally, the strength of the pinned connection has been corrected to account for the thickness of the elastomeric pad [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo model the pinned connections (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e(e)) at the abutments, the Pinching4 uniaxial material is assigned to ZeroLength elements in both the longitudinal and transverse directions (Fig.\u0026nbsp;4).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Soil-structure interaction\u003c/h2\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.4.1. Foundation-soil\u003c/h2\u003e \u003cp\u003eThe bents and abutments are founded on pile-supported footings. This system consists of a group of cast-in-place piles connected by a footing capbeam. Several numerical and analytical methods were proposed to simulate the dynamic stiffness and the seismic response of pile foundations accounting for soil-structure interaction. The complex interaction between the pile cap, the piles, and the soil may in fact produce an amplification of the translational motion, increased flexibility of the system, and hysteretic and radiation damping due to the action of the soil [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e]. This study neglects the effect of the soil-structure interaction regarding foundation piles while analyzing the response of the structure and the soil separately.\u003c/p\u003e \u003cp\u003eThe design philosophy at the time of bridge construction was to provide the foundation system sufficient strength to allow the formation of plastic hinges at the base of the RC columns, thus no significant excursion for the piles into the inelastic range is expected. However, to account for the possible plasticization of piles, their response is simulated by adding translational and rotational nonlinear springs at the interface between the footing capbeam and the pile head. A trilinear force-deformation envelope is adopted to model the nonlinear response of the piles according to the recommendations of Choi [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. The backbone parameters for each foundation pile are obtained by multi-linearization of the pile-soil response simulated via the commercial software LPile\u0026reg; adopting as input the on-site soil profile and the geometric and mechanical characteristics of piles. The hysteretic behavior of piles is simulated via the Hysteretic material in OpenSees with the parameters pinchX and pinchY as 0.75 and 0.5 as proposed in Ramanathan [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e3.4.2. Abutment-backfill\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe spill-through abutment interacts both in the longitudinal and the transverse directions with a large volume of soil, represented by the compacted embankment soil.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe participating mass of the embankment may have a critical effect on mode shapes and consequently the dynamic response of the bridge [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e]. Along the transverse direction, due to the small wing-wall length, the embankment contribution in terms of stiffness and mass can be ignored [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. In the longitudinal direction, the contribution of the embankment cannot be neglected. Thus, additional participating masses due to embankment soil have been attributed to the abutment nodes, these are calculated by considering an average value of embankment critical length between those determined according to the work of Zhang and Makris [\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e] and Werner [\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAlong the transverse direction, the lateral stiffness and strength of the abutments are provided only by the system of abutment piles and the bent framing system with no interaction with the embankment soil. Along the longitudinal direction, the interaction between the abutment and the embankment soil is simulated by adopting a Winkler-type approach that discretizes the continuous contact between the soil and the structure via a set of \u0026ldquo;interface elements\u0026rdquo; (i.e., nonlinear only-compression springs) representing the mobilization of the active and passive limit states in the soil. The piecewise relationship adopted in Marchi et al. [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e], and firstly proposed to simulate earth-retaining diaphragm walls by Becci and Nova [\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e] is adopted to characterize the backbone of nonlinear springs (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b)). The characterization of nonlinear springs depends on the characteristics of the soil and the structure. In particular, the soil resistance (F\u003csub\u003ea\u003c/sub\u003e(z), F\u003csub\u003ep\u003c/sub\u003e(z), active and passive, respectively) is expressed as a function of the vertical effective stress (σ\u0026rsquo;\u003csub\u003ev\u003c/sub\u003e(z)), the active (K\u003csub\u003eA\u003c/sub\u003e) and passive (K\u003csub\u003eP\u003c/sub\u003e) earth pressure coefficients, and the transverse soil section (A\u003csub\u003ei\u003c/sub\u003e(z)). The earth pressure coefficients depend on the angle of shearing resistance of the soil and the soil-wall friction angle (δ) and are calculated according to Rampello et al. [\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e] and Lancellotta [\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e] in seismic conditions. The soil-wall friction angle δ is taken equal to 2/3φ\u0026rsquo;, while K\u003csub\u003eA\u003c/sub\u003e and K\u003csub\u003eP\u003c/sub\u003e are determined by considering the seismic intensity during each nonlinear time history analysis. The effect on earth pressure coefficients of the seismic intensity variation during the analysis was neglected and a single value of the seismic coefficients were adopted for each analysis based on the peak ground acceleration of each seismic input, as suggested in Rampello et al. [\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e]. The earth stiffness coefficients k\u003csub\u003ea\u003c/sub\u003e and k\u003csub\u003ep\u003c/sub\u003e are then determined based on the formulation proposed by Franchin and Pinto [\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e] depending on the Young\u0026rsquo;s Modulus (E\u003csub\u003e0\u003c/sub\u003e(z)), by converting the distribution of the small-strain shear modulus (G\u003csub\u003e0\u003c/sub\u003e(z)) into an equivalent variation the Young\u0026rsquo;s modulus (assuming a Poisson\u0026rsquo;s coefficient ν\u0026thinsp;=\u0026thinsp;0.3), on the active and passive characteristic lengths [\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e], and the transverse soil section area A\u003csub\u003ei\u003c/sub\u003e(z).\u003c/p\u003e \u003cp\u003eSince the abutment is a spill-through type (i.e., a framed system), the contact with the abutment soil is not continuous, and the springs are placed only in correspondence of the vertical (i.e., column) and horizontal (i.e., capbeams) abutment elements, thus the transverse soil section area A\u003csub\u003ei\u003c/sub\u003e(z)=Δz*B\u003csub\u003ed\u003c/sub\u003e depends on the depth, and on the contact surface. For springs placed in correspondence of the abutment capbeam and foundation beam B\u003csub\u003ed\u003c/sub\u003e is calculated considering the tributary area corresponding to that spring, while for springs placed in correspondence of columns, B\u003csub\u003ed\u003c/sub\u003e is set equal to the column width times a coefficient, set equal to 1.2, to account for the quota of back-fill soil participating to the abutment-embankment interaction due to an arching effect.\u003c/p\u003e \u003cp\u003eThe compression-only shifted non-symmetric elastic-plastic law characterizing these springs depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b) is obtained by suitably combining in parallel Elastic-Perfectly Plastic Gap materials assigned to ZeroLength elements. The nonlinear springs are pre-loaded to simulate the earth pressure of the soil at rest. The effect of riprap on the spill-through is neglected.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.5. Loads\u003c/h2\u003e \u003cp\u003eThe self-load masses and loads of the structure are automatically calculated depending on the geometry of the bridge components and lumped in nodes throughout the structure. Additional loads and masses relying on the bridge deck (assumed 450 kg/m\u003csup\u003e2\u003c/sup\u003e for the pavement and 700 kg/m for the railing) are lumped into discrete nodes along the spine element.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.6. Solution algorithms\u003c/h2\u003e \u003cp\u003eThe accurate representation of the main bridge components to allow a realistic simulation of the complex bridge behavior introduces a major challenge in terms of analysis convergency. In fact, the explicit modeling of components characterized by highly nonlinear behavior (e.g., fiber-based columns, combination of several in-series nonlinear springs), the complex interaction between them, also along different directions, and the complexity introduced by the mass distribution along the deck, may lead to convergency issues, especially when performing nonlinear dynamic analyses.\u003c/p\u003e \u003cp\u003eIn this context, the use of the implicit integration algorithm \u003cem\u003eTRBDF2\u003c/em\u003e [\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e], a composite integration method that uses Implicit Newmark and a three-point-backward Euler scheme alternately in consecutive integration time steps, is one of the most suitable algorithms according to the studies performed by Liang et al.[\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e] which analyzed the effect of different implicit and explicit solution algorithms when analyzing the nonlinear dynamic behavior of complex RC bridges, and it has been adopted in this study.\u003c/p\u003e \u003cp\u003eTo achieve convergency, various nonlinear solvers are consecutively tried for any iteration of an integration time step in OpenSees. According to Liang \u0026amp; Mosalam [\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e] the Newton-Raphson with line-search (\u003cem\u003ealgorithm NewtonLineSearch\u003c/em\u003e) is used as initial solver, the order of subsequent other solvers generally has little impact on the convergency, and thus this strategy has been adopted. Finally, the Normal Displacement Increment convergency test (\u003cem\u003etest NormDispIncr\u003c/em\u003e) is used since it has been demonstrated to be the most suitable for this type of models [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Definition of Limit States","content":"\u003cp\u003eIn this paper, two Limit States are introduced to derive the fragility curves namely Damage Limitation (LS\u003csub\u003eDL\u003c/sub\u003e), Collapse Prevention (LS\u003csub\u003eCP\u003c/sub\u003e). Limit States are attained either when single or multiple bridge structural components overcome a specific threshold value defined in terms of strength/deformation or at the global level. Finally, the condition triggering the complete Collapse (C) is also introduced.\u003c/p\u003e \u003cp\u003eThe LS\u003csub\u003eDL\u003c/sub\u003e is attained when the bridge functionality is compromised in the aftermath of an earthquake and single or multiple components must be repaired or replaced without still representing an actual threat to safety. According to Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the LS\u003csub\u003eDL\u003c/sub\u003e is attained when the first condition occurs between the following: (i) failure of the expansion joint at the Gerber saddles due to excessive longitudinal displacements; (ii) failure of the elastomeric pads at the Gerber saddles, bents or abutment, due to excessive deformations in the longitudinal or transverse direction, or failure of the pad in tension; (iii) backfill failure due to excessive displacements of the abutment in the longitudinal direction; (iv) bar buckling or concrete spalling of columns at bents or abutments; (v) first cracking of an interior shear-key; (vi) first yielding of the Mesnager hinge in the longitudinal or transverse direction.\u003c/p\u003e \u003cp\u003eThe LS\u003csub\u003eCP\u003c/sub\u003e is attained when the structure results unsafe but is not yet completely collapsed. The LS\u003csub\u003eCP\u003c/sub\u003e is attained when the first condition occurs between the following: (i) failure of shear key support at Gerber saddles due to the asynchronous movements in the longitudinal direction (i.e., the constraint provided by interior shear keys at the Gerber saddles becomes ineffective due to excessive relative displacements between the cantilever and the Gerber spans of the bridge, corresponding to the thickness of the shear key, t\u003csub\u003eshear key\u003c/sub\u003e); (ii) first shear key reaching peak capacity at the Gerber saddles or at the bents; (iii) first shear failure at the bent or abutment beams or piers; (iv) crushing of elastomeric pads at the abutment, bent, or Gerber saddle (adopting a safety factor, γ); (v) first failure of the Mesnager hinge in the longitudinal or transverse direction.\u003c/p\u003e \u003cp\u003eThe C case is attained when the structure is partially or completely collapsed. It is attained when the first condition occurs between the following: (i) deck unseating at Gerber saddles due to excessive relative displacements in the longitudinal or the transverse direction; (ii) deck unseating at the abutment (i.e., failure of every Mesnager hinge and excessive displacements) along the longitudinal direction; (iii) failure of the Gerber shear key system (i.e., failure of every interior shear key at Gerber saddles or bents); (iv) failure of the abutment shear key system (i.e. every Mesnager hinge and at least one exterior shear key) along the transverse direction; (v) crushing of elastomeric pads at the abutment, bent or Gerber saddle (without considering any safety factor); (vi) Side-sway and (vii) Gravity-load collapse at the bents defined according to Gaetani d\u0026rsquo;Aragona et al. ([\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e], [\u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e]) or shear failure of all bent capbeams.\u003c/p\u003e \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003e\u0026ndash; Definition of Limit States and corresponding threshold values\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" style=\"width: 11.0019%;\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eComponent\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e(D) Demand parameter\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e(C) Threshold value\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"10\" style=\"width: 11.0019%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDamage Limitation (LS\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eSL\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eExpansion joint\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003elong.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eGerber\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge;\u0026thinsp;50 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eElastomeric Pad\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003elong.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eGerber/Bent/Abutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; t\u003csub\u003ePad\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003etransv.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eGerber/Bent/Abutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003evert.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003ePad\u003c/em\u003e \u003cem\u003eGerber/Bent/Abutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026le;\u0026thinsp;0 (tension)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eBackfill\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003elong.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eAbutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge;\u0026thinsp;50 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eRC member Bar buckling/Spalling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eIDR\u003c/em\u003e\u003csub\u003e\u003cem\u003elong.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eBent/Abutment Pier\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003edepending on geometric and mechanical features of RC members\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eIDR\u003c/em\u003e\u003csub\u003e\u003cem\u003etransv.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eBent/Abutment Pier\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eFirst interior Shear-key cracking\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003esk,transv.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eGerber/Bent Shear\u0026minus;keys\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; D\u003csub\u003ecr,interior\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eFirst yielding of Mesnager hinges\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003eMH,long.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eAbutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; D\u003csub\u003ey,Mesnager,long\u003c/sub\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003eMH,transv.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eAbutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; D\u003csub\u003ey,Mesnager,transv\u003c/sub\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"7\" style=\"width: 11.0019%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCollapse Prevention (LS\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eCP\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eIneffective Interior Shear-keys\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003esk,long.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eGerber\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; t\u003csub\u003eshear key\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eFirst interior Shear-key reaching peak capacity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003esk,transv.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eGerber/Bent\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; D\u003csub\u003epeak,interior\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eFirst brittle failure of RC member\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\n \u003cp\u003eBeams\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003eV\u003csub\u003ed\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge;V\u003csub\u003ec\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\n \u003cp\u003ePiers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003eIDR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge;IDR\u003csub\u003eF\u0026minus;S\u003c/sub\u003e\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eFirst crushing of Elastomeric Pad\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003evert.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003ePad\u003c/em\u003e \u003cem\u003eGerber/Bent/Abutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; N\u003csub\u003ecap\u003c/sub\u003e.\u003csup\u003ePad\u003c/sup\u003e (g\u0026thinsp;=\u0026thinsp;1.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eFirst failure of Mesnager hinges\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003eMH,long.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eAbutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; D\u003csub\u003eult,Mesnager,long\u003c/sub\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003eMH,transv.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eAbutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; D\u003csub\u003eult,Mesnager,transv\u003c/sub\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"7\" style=\"width: 11.0019%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCollapse (C)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eDeck unseating at Gerber saddles\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003elong.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eGerber\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; t\u003csub\u003eGerber saddle\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003etransv.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eGerber\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; b\u003csub\u003eGerber saddle\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eDeck unseating at abutment\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003elong.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eAbutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; t\u003csub\u003eAbutment\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eFailure of Gerber Shear-key system\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003esk,transv.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eGerber/Bent\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; D\u003csub\u003eult,interior\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eFailure of Abutment Shear-key system\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eDs\u003c/em\u003e\u003csub\u003e\u003cem\u003esk,transv.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003eAbutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; D\u003csub\u003eult,exterior\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 17.0938%;\"\u003e\n \u003cp\u003eCrushing of all Elastomeric Pads\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.5462%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 18.094%;\"\u003e\n \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003evert.\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003ePad\u003c/em\u003e \u003cem\u003eGerber/Bent/Abutment\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 21.1854%;\"\u003e\n \u003cp\u003e\u0026ge; N\u003csub\u003ecap\u003c/sub\u003e.\u003csup\u003ePad\u003c/sup\u003e (g\u0026thinsp;=\u0026thinsp;1)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"4\" style=\"width: 60.9193%;\"\u003e\n \u003cp\u003eGlobal Collapse (Side-sway collapse / Gravity Load Collapse) ***\u003c/p\u003e\n \u003cp\u003eor shear failure of all capbeams at one Bent\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"5\" style=\"width: 71.9212%;\"\u003e\n \u003cp\u003e*Seviceability Limit State in elastomeric bearing pad is attained for a lateral displacement equal to the thickness of the device, t\u003csub\u003epad\u003c/sub\u003e, (45\u0026deg; deformation) [\u003cspan class=\"CitationRef\"\u003e70\u003c/span\u003e]\u003c/p\u003e\n \u003cp\u003e** For Abutment and Bent Piers Flexure-Shear failure is defined according to the Limit State Material developed by Elwood et al. [\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e] depending on the geometric and mechanical characteristics of RC members and Axial Loads.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"5\" style=\"width: 71.9212%;\"\u003e\n \u003cp\u003e*** Side-sway Collapse and Gravity Load Collapse defined according to ([\u003cspan class=\"CitationRef\"\u003e68\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e69\u003c/span\u003e]).\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"5. Derivation of fragility curves","content":"\u003cp\u003eFragility curves are generated by adopting a cloud analysis approach in which the seismic demand on the bridge components is estimated via nonlinear time-history analyses performed on the 3D model developed in \u0026sect;\u0026nbsp;3. The damping ratio was set equal to 4.5% according to observations by Bavirisetty et al. [\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eThe suite of ground motions assembled by Manfredi et al. [\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e] within the 2019\u0026ndash;2021 DPC-ReLUIS Project WP4 \u0026ldquo;MARS - Seismic Risk Maps\u0026rdquo; for stiff soil (A/B soil category) is adopted in this study. The suite consists of 125 pairs of real accelerograms specifically assembled for the generation of site-independent damage fragility curves via a Cloud-based approach. The ground motion records cover a wide range of magnitudes ranging from 5.0 to 7.1, with the epicentral distance varying between 4 and 30 km.\u003c/p\u003e \u003cp\u003eFor each record pair a non-linear time history analysis is performed employing the 3D Finite element model and the peak response of each critical bridge component (e.g., bearing deformations, column drift, abutment deformations) is recorded at each step of the analysis. This allows monitoring the key response parameters representing the demand (D) and the corresponding intensity measure (IM) to determine the parameters for the fragility model.\u003c/p\u003e \u003cp\u003eThe Peak Ground Acceleration (PGA) is adopted herein as IM since it represents an acceptable compromise between a good correlation with the non-linear seismic response and practical constraints such as the site-independence. In fact, despite many studies focused on IMs that are more suitable for predicting the structural performance, such as the first-mode spectral acceleration ([\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e], [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e]), the spectral acceleration averaged over a period range [\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e] or vector-valued IMs [\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e], [\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e], this intensity measure is adopted here since allowing the derivation site-independent fragility curves (i.e., fragility curves irrespective of the hazard characteristic of a specific site). Note that for each record pair, the maximum PGA along the two directions is adopted as IM.\u003c/p\u003e \u003cp\u003eThe variable adopted to monitor the bridge structural performance is the critical demand-to capacity-ratio (DCR) for a specific Limit State (LS), following denoted as DCR\u003csub\u003eLS\u003c/sub\u003e [\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e]. The DCR\u003csub\u003eLS\u003c/sub\u003e is defined as the maximum DCR for the components or the mechanisms that lead the system to the onset of a given LS (see Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). This formulation is particularly useful for cases where various structural components and/or potential failure mechanisms contribute to the attainment of a specific LS. The DCR\u003csub\u003eLS\u003c/sub\u003e can be defined as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${DCR}_{LS}={max}_{j}^{{N}_{comp}}{max}_{l}^{{N}_{mech}}\\frac{{D}_{jl}}{{C}_{jl}\\left(LS\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere N\u003csub\u003ecomp\u003c/sub\u003e is the number of bridge components which failure can trigger the onset of the LS, N\u003csub\u003emech\u003c/sub\u003e is the number of potential failure mechanisms of each component, \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ejl\u003c/em\u003e\u003c/sub\u003e is the demand evaluated for the \u003cem\u003ej\u003c/em\u003e\u003csup\u003e\u003cem\u003eth\u003c/em\u003e\u003c/sup\u003e structural component of the \u003cem\u003el\u003c/em\u003e\u003csup\u003e\u003cem\u003eth\u003c/em\u003e\u003c/sup\u003e mechanism, and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ejl\u003c/em\u003e\u003c/sub\u003e(LS) is the Limit State capacity for the \u003cem\u003ej\u003c/em\u003e\u003csup\u003e\u003cem\u003eth\u003c/em\u003e\u003c/sup\u003e component of the \u003cem\u003ei\u003c/em\u003e\u003csup\u003e\u003cem\u003eth\u003c/em\u003e\u003c/sup\u003e mechanism.\u003c/p\u003e \u003cp\u003eIn the present study, the fragility functions are derived by adopting a regression-based model proposed in Jalayer et al. [\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e] to describe the relationship between DCR\u003csub\u003eLS\u003c/sub\u003e and the PGA level. The regression probabilistic model is generated by using the results of the NTHAs, performed for each ground motion from the bin, and can be described by the relationship proposed by Cornell et al. [\u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e80\u003c/span\u003e] in the log-transformed space:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\ln {\\eta _{DC{R_{LS}}|PGA}}=\\ln a+b \\cdot \\ln PG{A^{}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere η\u003csub\u003eDCRLS|PGA\u003c/sub\u003e is the median value of the DCR\u003csub\u003eLS\u003c/sub\u003e given the PGA, and \u003cem\u003eln\u003c/em\u003e a and b regression coefficient that can be computed by performing a linear regression in the log-log space. The dispersion of the probabilistic model is measured via the logarithmic standard deviation:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${\\beta _{DC{R_{LS}}|PGA}}=\\sqrt {\\frac{{{{\\sum\\nolimits_{{i=1}}^{N} {\\left[ {\\ln DC{R_{LS,i}} - \\left( {a \\cdot PGA_{i}^{b}} \\right)} \\right]} }^2}}}{{N - 2}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere DCR\u003csub\u003eLS,i\u003c/sub\u003e and PGA\u003csub\u003ei\u003c/sub\u003e are the DCR for the considered LS value obtained for the i\u003csup\u003eth\u003c/sup\u003e NLTHA and the corresponding PGA value, respectively, and N is the number of ground motions.\u003c/p\u003e \u003cp\u003eThe fragility curve obtained, based on the results of the Cloud Analysis, represents the probability of reaching or exceeding a specified LS for a given PGA. Under the hypothesis of lognormal distribution for the DCR\u003csub\u003eLS\u003c/sub\u003e, the fragility curve can be expressed as follows:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$P\\left[ {DC{R_{LS}} \\geqslant 1|PGA} \\right]=\\Phi \\left[ {\\frac{{\\ln {\\eta _{DC{R_{LS}}|PGA}}}}{{{\\beta _{DC{R_{LS|PGA}}}}}}} \\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere Φ[\u0026middot;] is the standard normal cumulative distribution function and β\u003csub\u003eDCR\u003cem\u003eLS\u003c/em\u003e|PGA\u003c/sub\u003e is logarithmic standard deviations accounting for the uncertainties considered during the analyses (i.e., record-to-record).\u003c/p\u003e \u003cp\u003eThe ground motion suite considered in this study considers a wide range of seismic intensities. For this reason, a number of records can lead the structure to verge upon collapse (i) according to the definition given in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e for C or (ii) to global dynamic instability (corresponding to the occurrence of very large DCRs) or convergency problems. In this case, the Cloud Analysis can be still carried by partitioning the results into two parts: (1) Non-collapse (NC) cases, corresponding to the analysis cases for which structure does not experience collapse, and (2) Collapse (C) cases, corresponding to analyses for which collapse occurred. In this case, the structural fragility for a prescribed DS can be expanded with respect to NC and C cases by using the Total Probability Theorem [\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e]:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$P\\left[ {DC{R_{LS}} \\geqslant 1|PGA} \\right]=P\\left[ {DC{R_{LS}} \\geqslant 1|PGA,NC} \\right] \\cdot \\left( {1 - P\\left[ {C|PGA} \\right]} \\right)+P\\left[ {DC{R_{LS}} \\geqslant 1|PGA,C} \\right] \\cdot P\\left[ {C|PGA} \\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn which is the conditional probability that DCR\u003csub\u003eLS\u003c/sub\u003e is greater or equal than unity given that collapse has not occurred (NC) for a given PGA, and can be expressed in the same manner as for the standard Cloud Analysis (Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e7\u003c/span\u003e)) and referred to non-collapse cases. The term \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P\\left[ {DC{R_{LS}} \\geqslant 1|PGA,C} \\right]\\)\u003c/span\u003e\u003c/span\u003eis the conditional probability that DCR\u003csub\u003eLS\u003c/sub\u003e is greater or equal than unity given that collapse occurred (C) for a given PGA. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P\\left[ {DC{R_{LS}} \\geqslant 1|PGA,C} \\right]=1\\)\u003c/span\u003e\u003c/span\u003esince for Collapse cases the Limit State LS is certainly exceeded. Finally, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P\\left[ {C|PGA} \\right]\\)\u003c/span\u003e\u003c/span\u003eis the probability of collapse, which can be predicted via a logistic regression model as a function of the PGA, as follows [\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e]:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$P\\left[ {C|PGA} \\right]=\\frac{1}{{1+{e^{ - \\left( {{\\alpha _0}+{\\alpha _1} \\cdot \\ln \\left( {PGA} \\right)} \\right)}}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere α\u003csub\u003e0\u003c/sub\u003e and α\u003csub\u003e1\u003c/sub\u003e are the parameters of the logistic regression model applied to all the analyses, adopting binary values (i.e., 1 or 0 depending on whether collapse occurred or not).\u003c/p\u003e \u003cp\u003eIn this case, the fragility curve considering collapse is a combination between a lognormal and a logistic regression model. However, it is still possible to represent the fragility curve by adopting an equivalent lognormal distribution.\u003c/p\u003e"},{"header":"6. Results","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e (a)-(b) shows in the log-log plane the scatter plot for Cloud Analysis data for the two considered limit states LS\u003csub\u003eDL\u003c/sub\u003e (a) and LS\u003csub\u003eCP\u003c/sub\u003e (b) defined according to Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, considering the set of records outlined in Section 5. For a better representation, the upper-bound limit of 20 is assigned to the horizontal DCR\u003csub\u003eLS\u003c/sub\u003e-axis. For each data point (colored squares), the corresponding record number is also shown. The cyano-colored squares represent the NoC data, while the red-colored squares indicate the C data (i.e., collapse cases defined according to C reported in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The dashed red line DCR\u003csub\u003eLS\u003c/sub\u003e=1 threshold corresponds to the onset of the considered Limit State. From Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e (a)-(b) is also possible to infer that the ground motion bin adopted in the Cloud Analysis, originally selected for the fragility assessment of reinforced concrete buildings, not only covers a wide range of PGAs, but also provides numerous data in the range of DCR\u003csub\u003eLS\u003c/sub\u003e\u0026gt;1 for both considered LSs also covering the entire range of response of the selected bridge. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e (a)-(b) also reports the conditional dispersion \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eDCR LS|PGA\u003c/em\u003e\u003c/sub\u003e and the parameters \u003cem\u003ea\u003c/em\u003e and \u003cem\u003eb\u003c/em\u003e of the regression in Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e5\u003c/span\u003e), along with the regression line (dotted gray line), considering only NoC cases. No significant variation was observed in standard deviation (related to record-to-record variability) for different LSs for the reference bridge.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e (c)-(d) shows the fragility curves calculated considering the Collapse cases (black bold line) along with those obtained considering only NoC data (dotted gray line), calculated with Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e7\u003c/span\u003e). According to Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e8\u003c/span\u003e), the final fragility curve is obtained by multiplying the fragility curve obtained considering only NoC data times the probability of NoC (=\u0026thinsp;1-P[C|PGA]) and summed with the P[C|PGA]. For completeness\u0026rsquo;s sake, the probability of NoC is also depicted in the figures (red dashed line). The explicit consideration of collapse cases leads the fragility curve to shift leftward, indicating a more vulnerable structure. The effect is more pronounced for the LSs corresponding to larger capacities (i.e., LS\u003csub\u003eCP\u003c/sub\u003e)\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e8\u003c/span\u003e depicts the probability of collapse (i.e., the probability of attainment of C) obtained considering Eq.\u0026nbsp;(\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e9\u003c/span\u003e) along with the logistic regression model parameters (α\u003csub\u003e0\u003c/sub\u003e and α\u003csub\u003e1\u003c/sub\u003e) be predicted using a generalized linear regression with Logit link function on the entire Cloud Analysis data. Note that during the cloud analysis, only 39 records over 125 caused collapse (i.e., lead to C defined according to Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Only 10% of records causing collapse had PGA lower than 0.4g, while the most of collapses were attained for PGAs within the range 0.43\u0026ndash;1.20g.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026ndash; Lognormal fragility parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLimit State\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eh [g]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eb [-]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLS\u003csub\u003eDL\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLS\u003csub\u003eCP\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e summarizes the median (η) and the logarithmic standard deviation (\u0026#120573;) of the lognormal fragility curves corresponding to the Damage Limitation (LS\u003csub\u003eDL\u003c/sub\u003e), Collapse Prevention (LS\u003csub\u003eCP\u003c/sub\u003e) Limit States, and Collapse (C). Note that the lognormal fragility parameters reported in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e are obtained accounting for the probability of collapse according to Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e8\u003c/span\u003e), while Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a-d) refers to the sole NoC cases. Even though the final LS fragility curves are a combination between a lognormal and a logistic regression model, the corresponding equivalent lognormal distribution is derived by adopting the method of the moments. Similarly, for Collapse the equivalent lognormal parameters are also reported as an alternative to those of the logistic regression (depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFigure 9(a) and (b) show the contribution of different component failures to the attainment of each Limit State with reference to NoC cases. Specifically, Fig.\u0026nbsp;9(a) and (b) show the number of failures for each component, according to Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, normalized by the number of analyses for which the Collapse did not occur. As can be gathered from Fig.\u0026nbsp;9(a), referring to LS\u003csub\u003eDL\u003c/sub\u003e, failure of the elastomeric pads due to traction was never evidenced. In a similar way, the attainment of cracking or spalling of bent piers rarely occurred during the analyses. This result was expected for this type of bridge since the shear keys were designed to restrain lateral displacements under serviceability loads, while they act as a fuse during significant earthquake shakings preventing damage to the substructures. Almost 20\u0026ndash;35% of the simulations resulted in the failure of expansion joints and/or the failure of elastomeric pads, while about 20% in the failure of compacted backfill soil. The most of simulations resulted in the damage of components connecting the substructure and the superstructure. More than 40\u0026ndash;60% of simulations resulted in the cracking of interior shear-keys, or the yielding of Mesnager hinges.\u003c/p\u003e \u003cp\u003eReferring to LS\u003csub\u003eCP\u003c/sub\u003e, Fig.\u0026nbsp;9(b), the condition corresponding to the ineffectiveness of shear keys never occurred, since it can only be attained when excessive displacements along the longitudinal axis take place. This condition is not possible for this type of bridge due to the constraint of the deck at the abutments and the possibility of limited relative displacements between its different parts. As for LS\u003csub\u003eDL\u003c/sub\u003e, brittle failure of piers was not possible due to the limitation of the forces transmitted from the superstructure to the substructure related to the limited capacity of shear keys. Only 5% of simulations evidenced the crushing of elastomeric pads, while for 30\u0026ndash;40% of the simulations the attainment of LS\u003csub\u003eCP\u003c/sub\u003e was ascribable to extensive damage to interior shear keys, or the failure of Mesnager hinges.\u003c/p\u003e \u003cp\u003eFigure 9(c) depicts the contribution of different failure modes to the attainment of global Collapse defined according to Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, normalized by the sole Collapse cases. It is worth noting that deck unseating never occurred both in the longitudinal and the transverse direction, neither at the Gerber nor at the abutment. Global collapse neither occurred due to the formation of shear hinges in all the capbeams. Very few simulations (about 5%) evidenced gravity-load collapse at the bents, and about 25% of simulations verged upon collapse due to the crushing of elastomeric pads. Most collapse cases (about 65\u0026ndash;80%) are ascribable to a partial failure in which the shear key system at Gerber saddles or at the abutment has no more capacity to sustain lateral loads. In this case, even if deck unseating does not occur, the system does not possess any residual capacity against lateral loads and can be thus considered next to collapse.\u003c/p\u003e"},{"header":"7. Conclusions","content":"\u003cp\u003eThis paper introduces a refined three-dimensional Non-linear Finite Element Model developed in OpenSees\u0026reg; to realistically assess the behavior of Multi-Span Simply-Supported concrete bridges. The proposed model properly simulates the expected behavior and failure modes of bridge components as well as their mutual interactions allowing a realistic simulation of the expected bridge behavior under seismic loads.\u003c/p\u003e \u003cp\u003eTwo different Limit States, namely Damage Limitation and Collapse Prevention, are introduced depending on the behavior of the single bridge components and the connections between the superstructure and the substructure. Furthermore, the definition of a global Collapse criterion is also introduced to account for the possible failure of the bridge system under seismic loads.\u003c/p\u003e \u003cp\u003eBy adopting a cloud-based stochastic approach, bridge fragility curves are generated for the selected Limit States, properly introducing for the probability of collapse of the entire system. By employing a suite consisting of 125 real ground motion records, nonlinear time-history analyses are performed, and relevant engineering demand parameters are introduced both at the component and the system level to check the attainment of the prescribed Limit States.\u003c/p\u003e \u003cp\u003eIt has been found that for the considered bridge typology, the median peak ground acceleration value corresponding to the attainment of Damage Limitation Limit State is 0.16g (with a logarithmic dispersion of 0.38), while the Collapse Prevention occurs for a very close of the ground motion intensity corresponding to 0.2g (and logarithmic dispersion of 0.42). The system-level collapse corresponds instead to a significantly higher value of the peak ground acceleration equal 0.56g (and logarithmic dispersion of 0.55).\u003c/p\u003e \u003cp\u003eFurther consideration can be drawn based on the analysis of the simulation outcomings.\u003c/p\u003e \u003cp\u003eThe adopted set of ground motion records, originally proposed to perform cloud analysis for reinforced concrete buildings, is suitable also for the analysis of existing reinforced concrete bridges. In fact, the ground motion set can cover the entire range of structural response, from no damage to complete collapse.\u003c/p\u003e \u003cp\u003eAlong the longitudinal direction, the relative displacements between the deck and the substructure may be ascribed to the filling of the existing gap between the deck parts, or the motion of the bridge deck along the transverse direction (i.e., related to the rotations of the bridge deck about the vertical axis). The latter is related to the flexibility of the abutment and the bent piers. At the abutment, the presence of a distributed connection system with the deck along both the longitudinal and the transverse directions implies that before the failure of these components, the abutment remains integral to the deck. The spill-through abutment is submerged by the soil and can be subjected to limited displacements along the longitudinal direction (mainly due to the compressibility of the back soil), making thus possible only small additional relative displacements to those along the longitudinal axis. For this reason, the attainment of Damage Limitation and Collapse Prevention Limit States was never triggered by failures related to motion along the longitudinal direction connected to significant displacements (e.g., deck unseating), while only those corresponding to the failure of the connection system are triggered.\u003c/p\u003e \u003cp\u003eAlong the transverse direction, shear keys act as a sacrificial element not allowing the transmission of significant forces to the substructure. For this reason, the lateral displacement of the bents is generally limited, not allowing the attainment of damage to bent piers or capbeams, or to the foundation. The only failures occurring along the transverse direction are related to the failure of the shear-key system at the Gerber saddles, abutments, or bents.\u003c/p\u003e \u003cp\u003eRegarding the elastomeric bearing pads and the Mesnager hinges, due to the limited horizontal displacements allowed, the failure can occur for both the Damage Limitation and Collapse Prevention Limit States. Further, since the vertical component of the ground motion is neglected, because only far-field ground motions are considered, the crushing phenomenon rarely occurred for bearing pads, while the failure for traction never occurred.\u003c/p\u003e \u003cp\u003eThe Collapse capacity of the bridge system is limited due to the design according to obsolete seismic codes, not accounting for the basic principles of the capacity design, the lack of proper seismic detailing, coupled with a non-statically-determined scheme.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eConflicts of interest\u003c/strong\u003e \u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor contributions\u003c/h2\u003e \u003cp\u003eMGdA contributed to conceptualization, methodology and model development, visualization, investigation, software, validation, writing\u0026mdash;original draft, writing\u0026mdash;review and editing. AR contributed to conceptualization, methodology, writing\u0026mdash;review and editing, supervision, validation, proofreading. AP contributed to validation and proofreading. All authors read and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThe studies presented here were carried out as part of the activities envisaged by the Agreement between the High Council of Public Works (CSLLPP) and the ReLUIS Consortium (Work Package 4) implementing Ministerial Decree 578/2020 and Ministerial Decree 240/2022. The contents of this paper represent the authors\u0026rsquo; ideas and do not necessarily correspond to the official opinion and policies of CSLLPP. 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J Struct Eng 128(4). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1061/(asce)0733-9445(2002)128:4(526)\u003c/span\u003e\u003cspan address=\"10.1061/(asce)0733-9445(2002)128:4(526)\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"MSSS concrete bridge, overpass, finite element model, fragility curves","lastPublishedDoi":"10.21203/rs.3.rs-4412197/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4412197/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study introduces a three-dimensional refined finite element model that is suitable for dynamic analysis of existing overpass bridges with Multi-Span Simply-Supported scheme. The proposed modeling approach allows to realistically reproduce the bridge behavior under seismic loadings via a proper simulation of the expected behavior and failure modes of each bridge component, as well as their mutual interaction. Two different Limit States, as well as a definition of system-level collapse, are introduced depending on the behavior of the bridge components and the interaction between the superstructure and the substructure. The proposed modeling approach is adopted to generate Limit State fragility curves adopting a stochastic approach based on cloud analysis which entails the use of real recorded ground motions for a reference bridge, designed and constructed in southern Italy in the 1970s. The results show that the proposed simulation approach is suitable to realistically reproduce the complex behavior of this type of bridge providing significant insights into their vulnerability.\u003c/p\u003e","manuscriptTitle":"Seismic fragility assessment of existing Italian overpass bridges","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-24 07:33:47","doi":"10.21203/rs.3.rs-4412197/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"eb96f9b6-3b94-4b74-9693-7719f4b7739d","owner":[],"postedDate":"May 24th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-07-06T15:13:05+00:00","versionOfRecord":[],"versionCreatedAt":"2024-05-24 07:33:47","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4412197","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4412197","identity":"rs-4412197","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}