Advances in Civil Engineering

Volume 2019, Article ID 6873096, 12 pages

https://doi.org/10.1155/2019/6873096

## Seismic Performance Evaluation of a Fully Integral Concrete Bridge with End-Restraining Abutments

^{1}Department of Civil Engineering, Hanbat National University, Yuseong-gu, Daejeon 34158, Republic of Korea^{2}Sunkoo Engineering Co, Ltd., Sunkoo Square 5th Floor, 85 Anyangpangyo-ro, Uiwang-si, Gyeonggi-do 16004, Republic of Korea^{3}Department of Civil Engineering, Konkuk University, 120 Neudong-ro, Gwangjin-gu, Seoul 05029, Republic of Korea^{4}Department of Civil Engineering, Vinh University, 182 Le Duan, Vinh 461010, Vietnam

Correspondence should be addressed to Tae-Hyung Lee; rk.ca.kuknok@eelht

Received 21 September 2018; Revised 2 February 2019; Accepted 26 February 2019; Published 27 March 2019

Academic Editor: Antonio Formisano

Copyright © 2019 Byung H. Choi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A fully integral bridge that is restrained at both ends by the abutments has been proposed to form a monolithic rigid frame structure. Thus, the feasible horizontal force effect due to an earthquake or vehicle braking is mainly prevented by the end-restraining abutments. In a recent study, a fully integral bridge with appropriate end-restraining abutment stiffness was derived for a multispan continuous railroad bridge based on linear elastic behavior. Therefore, this study aims to investigate the nonlinear behavior and seismic capacity of the fully integral bridge and then to assess the appropriate stiffness of the end-restraining abutment to sufficiently resist design earthquake loadings through a rigorous parametric study. The finite element modeling and analyses are performed using OpenSees. In order to obtain the force-deflection curves of the models, nonlinear static pushover analysis is performed. It is confirmed that the fully integral bridge prototype in the study meets the seismic performance criteria specified by Caltrans. The nonlinear static pushover analysis results reveal that, due to the end-restraining effect of the abutment, the lateral displacement of the fully integral bridge is reduced, and the intermediate piers sustain less lateral force and displacement. Then, the sectional member forces are well controlled in the intermediate piers by a proper application of the end-restraining abutments.

#### 1. Introduction

An integral bridge is known as a bridge type that integrates the superstructure and basic substructures. In general, integral bridges are considered as having more economic benefit than a regular bridge because an integral bridge can be constructed without expensive supplemental devices such as expansion joints and bridge bearings [1–8]. Integral abutment bridges (IABs) are commonly used in modern bridge construction, with well over 9,000 IABs in service across the US. Additionally, the integral abutment bridge can be selected as a seismic retrofitting method for existing bridges [9, 10] in addition to the conventional retrofitting techniques [11–13]. In spite of its increasing usage, standard design methods for integral bridges have not been fully established yet that led to the necessity of further research [14–16]. The research study of Far et al. [17] has presented that thermal and seismic loads greatly affect the design of integral abutment bridges due to the integrity of the structure and complex soil-structure-pile interactions. Similarly, there have been studies concerning the seismic behavior of non-IABs [14, 18]. These studies looked into the effects that elastomeric bearings have on energy dissipation, as well as how non-IABs behave as a whole system when subjected to seismic excitation. The studies generally concluded that the bearings, abutment backwall, and pier columns provide a large contribution to an entire bridge’s seismic behavior. Kozak et al. [14] have evaluated an existing integral abutment bridge seismic behavior including all important limit states that could occur in each bridge components. Erhan et al. [19] have demonstrated that integral bridges have superior seismic performance in terms of smaller inelastic structure displacement, rotations, or forces compared to conventional bridges. Additional studies have also considered the individual behavior of the pile-pile cap connection under seismic load and of the girder-abutment connection, both of which are of concern due to the large moments transferred at these locations. Most prior studies concerning the seismic behavior of IABs have not considered the behavior of bridges as a whole, instead focusing on individual components, which may neglect some important interactions between components [14]. Understanding the seismic behavior of bridges is important not only to develop cost-effective designs but also to properly assess existing bridges and their safety immediately after an earthquake. Since there is little experimental data on the seismic response of fully integral bridges, numerical models are essential for understanding structural behavior and ensuring safety in design provisions.

Recently, an innovative fully integral bridge system that is restrained at both ends has been proposed to form a monolithic rigid frame structure [18, 20]. The lateral loads (e.g., earthquake load and vehicle braking force) are mainly carried by the end-restraining abutments. Due to such restraining effect, the fully integral bridge is greatly committed to substantially reduce the section properties of the substructure components except for the abutments, which consequently improves the bridge system’s aesthetics, economic efficiency, and seismic performance [21]. In addition, fully integral bridge system eliminates other costly bridge components such as bridge supports, support inspection facilities, and expansion joints while reduces maintenance life-cycle cost due to frequent repair and replacement of bridge components. Thus, it is a low-cost and high-performance bridge system [14, 20–22].

Recently, Choi et al. [21] have provided insights into the load distribution characteristics of a fully integral bridge through a parametric study based on the response spectrum analysis. Their study has shown that the stiffness of the end-restraining abutment has a significant effect on the behavior of intermediate piers. The results show that as the abutment’s stiffness increases, the internal forces (i.e., overturning moment and base shear force) at the piers radically decrease and then converge to a certain level. Finally, a prototype design of a fully integral bridge has been proposed such that lateral forces and displacements of the bridge system are adequately restrained. However, due to the linear elastic assumption and a simplified modeling method used in the study, there is an inevitable limitation lying on the application of the analysis results.

This study aims to investigate the seismic capacity of the fully integral bridge with end-restraining abutments and the variation of the seismic performance along with the sectional stiffness of the abutments considering the nonlinear behavior of the bridges. For doing so, the displacement capacity and the ductility ratio are determined from pushover analyses by referring to the specified performance criteria in Caltrans [23], and the seismic demand is obtained from multimode spectrum analysis based on design specifications [23–25]. The capacity and the demand results are compared to conduct a seismic performance evaluation on the fully integral bridge models. Moreover, a series of parametric numerical analysis has been performed along with the variation of design parameters of the end-restraining abutment. Lastly, the required stiffness for effective end-restraining is examined to accommodate the seismic design requirements. It should be noted that all considerations in this study are in the longitudinal direction only because the effect of end-restraining abutments is expected to enhance the seismic capacity of such bridge in the longitudinal direction. In the transverse direction, the integrated abutment is expected to provide some strength and stiffness to the connected superstructure due to an innate frame action. However, the conventional bridge is usually restrained at abutments in the transverse direction, and in this case, the effect of the integrated abutment to enhance the seismic capacity is not significant.

#### 2. Theoretical Backgrounds

##### 2.1. Force-Displacement Curve and Moment Capacity

The seismic capacity of the entire bridge can be evaluated through global displacement and ductility when the plastic hinge is reached according to Caltrans [23]. This piece of information can be accessed by using the force-displacement curves. In order to obtain the force-displacement curve of a fully integral bridge, nonlinear static pushover analysis is carried out. The following basic steps of pushover analysis are implemented, as follows: (1) the lateral load-deformation behavior of the girder, end-restraining abutment, and intermediate pier sections is determined using moment-curvature (*M*-Φ) analysis, and the results are used to define the finite element model of a fully integral bridge; (2) the pushover analysis is performed along the longitudinal direction, using an increasing monotonic displacement-controlled lateral load pattern, which gives an approximate representation of the relative inertia forces generated at the location of substantial mass, as it reaches its limit of structural stability [23]. It means that each increment pushes the frame, which is the entire integrated bridge system of the study, until the potential collapse mechanism is achieved; (3) the force-displacement curve diagrams are drawn based on the pushover analysis results, where the total applied loads are obtained from the base shear forces and the maximum displacement at a particular location in the top of the entire bridge system; and (4) the bridge ductility and displacement capacity are extracted from the force-displacement curves by applying equation (2). Moreover, the lateral force capacity, *F*_{u}, and the moment capacity, *M*_{u}, are corresponding to Δ_{C}, which is determined at the ultimate state of the bridge system and at the potential collapse of this system after the formation of plastic hinge from the analysis results [23, 26].

##### 2.2. Seismic Performance Criteria

The entire structural system must meet the global displacement criteria and the displacement ductility requirements specified in Caltrans [23]. The bridge system must satisfy the global displacement criteria due to the design earthquake loading, which is expressed aswhere is the entire bridge or the frame displacement capacity when the first ultimate capacity is reached by any plastic hinge in the bridge system and is the displacement demand, due to the earthquake load effects, which can be estimated by multimode spectrum analysis.

According to Caltrans [23], all ductile members in a bridge should satisfy the displacement ductility capacity requirements. Hence in this study, the entire bridge frame corresponds to all ductile members, due to its innate fully integral characteristic. The displacement capacity, , of the entire frame is attributed to its elastic plastic flexibility. The fully integral bridge shall satisfy the displacement ductility capacity, , defined aswhere is the idealized yield displacement of the entire frame at the formation of a plastic hinge.

Each member, including the entire bridge frame, should have a minimum displacement ductility capacity of *μ*_{c} ≥ 3.0, to ensure dependable rotational capacity in the plastic hinge regions, regardless of the displacement demand imparted to that member.

##### 2.3. Multimode Spectrum Analysis

To estimate the displacement demand, Δ_{D}, of the fully integral bridge system, a linear elastic multimode spectrum analysis, utilizing the appropriate response spectrum, should be performed by adopting the methodology specified by Caltrans [23]. In order to capture at least 90% mass participation in the longitudinal direction, the number of degrees of freedom (DOFs) and the number of modes considered in the analysis should be sufficient, which is typically 6 and 30, respectively. Since an earthquake may excite several modes of vibration in a bridge, the elastic response coefficient, *C*_{sm}, should be found for each relevant mode. In multimode spectrum analysis, the structure is analyzed for several sets of seismic forces, each corresponding to the period and mode shape of one of the modes of vibration, and the results are combined using acceptable methods, such as the complete quadratic combination 3 (CQC3) method. Therefore, based on design specifications such as AASHTO LRFD [24], Caltrans [23], and KDS [25], is expressed aswhere is strongly related to the design earthquake return period (i.e., 1,000 years) and to the soil conditions and seismic zone at the site, is the horizontal response spectral acceleration coefficient, and is the period of the *m*th mode vibration of the bridge system. is first obtained and calculated based on equation (4) to determine the design earthquake load, , which is applied as a distributed load along the whole length of the entire frame model:

The design constants *α*, *β*, and *γ* are defined as follows:

Hence, the design earthquake load, , is expressed aswhere is the static load per unit length of the bridge structure and is the static displacement that corresponds to the applied uniformly distributed load, *p*_{o}.

#### 3. Model Description

The prototype bridge in this study is a seven-span prestressed concrete girder bridge with a total length of 227.0 m and a deck width of 10.9 m, as shown in Figure 1. The length of the first and the last span is 26.0 m, while the length of each span in between is 35.0 m. The superstructure and substructure components are integrated and rigidly connected together. The substructure is formed with end-restraining abutments symmetrically placed at both ends and six intermediate piers between them. The end-restraining abutments are designed as hollow rectangular reinforced concrete (RC) member, while the intermediate piers are wall type RC solid member. The heights of the end-restraining abutment and intermediate piers are 10.0 m and 15.0 m, respectively. Since it is a railway bridge, it is also designed in accordance with the Korean National Railroad Agency (KNR) [27]. The cross-sectional configurations and dimensions of the girders are shown in Figure 2, while the end-restraining abutment and intermediate pier are illustrated in Figures 3(a) and 3(b), respectively. Furthermore, the girders are reinforced by prestressed tendons, SWPC 7B, which consist of 7 strands of Φ15.2 mm steel wire that are twisted together and have a yield tensile strength of 1,600 MPa, the ultimate tensile strength of 1,900 MPa, modulus of elasticity of 200,000 MPa, and elongation of 3.5%. The abutments and piers are reinforced with 636-Φ25 mm and 240-Φ29 mm longitudinal steel bars, respectively. The foundation of the end-restraining abutment and intermediate piers are pile cap and three Φ1.5 m drilled piles that are arranged in the direction parallel to the bridge transverse direction. The material properties used in each component will be discussed in the latter sections.