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Seismic collapse assessment of non-seismically designed circular RC bridge piers retrofitted with FRP composites
Accepted Manuscript Seismic collapse assessment of non-seismically designed circular RC bridge piers retrofitted with FRP composites Anant Parghi, M. Shahria Alam PII: DOI: Reference:
S0263-8223(16)31632-4 http://dx.doi.org/10.1016/j.compstruct.2016.10.094 COST 7920
To appear in:
Composite Structures
Received Date: Accepted Date:
22 August 2016 21 October 2016
Please cite this article as: Parghi, A., Shahria Alam, M., Seismic collapse assessment of non-seismically designed circular RC bridge piers retrofitted with FRP composites, Composite Structures (2016), doi: http://dx.doi.org/ 10.1016/j.compstruct.2016.10.094
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Seismic collapse assessment of non-seismically designed circular RC bridge piers retrofitted
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with FRP composites
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Anant Parghi1 and M. Shahria Alam
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School of Engineering, The University of British Columbia, Kelowna, V1V 1V7 - BC, Canada
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Abstract
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The seismic vulnerability of bridge pier is generally expressed in terms of the fragility curves,
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which reveals the conditional probability that the structural demand due to different levels of
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earthquake intensities exceeding the structural capacity at particular damage state. This research
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represents results of fragility curve development of typical single circular reinforced concrete
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(RC) bridge pier. The different parameters are considered in the analysis which includes the
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strength of concrete, yield strength and amount of longitudinal steel rebar, level of axial load and
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shear span-depth ratio, and carbon fiber reinforced polymer confinement layer. Nonlinear static
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pushover analysis (NSPA), and incremental dynamic analysis is conducted using suits of
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earthquake ground motions with scaled peak ground acceleration (PGA) to investigate the
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nonlinear dynamic behavior of the retrofitted piers. The impact of various parameters is
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evaluated under probability point of view in terms of its influence on the bridge pier fragility
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curve. Considering collapse drift as demand parameters, fragility curves were generated with
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different parameters of non-seismically designed RC circular bridge piers. It was observed that
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the amount of reinforcement, shear span-depth ratio, and level of the axial load could
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significantly affect the collapse fragility curve of the retrofitted bridge piers.
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Keywords: Fiber reinforced polymer; bridge piers; fragility curve; confinement ratio; nonlinear
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analyses; collapse assessment 1
Corresponding Author, Email: [email protected] Tel: +1.250.807.9397, Fax: +1.250.807.9850
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1. Introduction
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Bridges are considered as an important element in highway networks, since they play a critical
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role in the development of country’s economic activity. The bridges can connect cities and
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countries by providing links, render smooth, and quick transportation. In the early development
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of country, measures were adopted to improve transportation safety, accessibility, and economic
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efficiency. Conversely, large numbers of existing reinforced concrete (RC) highway bridges in
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North America were built when the seismic design guidelines were at an early stage of
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development. Moreover, earthquake hazard levels have been recently increased throughout the
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globe, which might affect the seismic performance of existing highway bridges. On one hand,
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truck loads have increased significantly over the years; and the other hand, bridges are restricted
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to their load capacity. Therefore, these structures cannot allow heavier trucks/traffic volume
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without proper strengthening. One option is replacing a deficient structure with a new once;
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while new construction is normally expensive, time consuming and even impractical. For
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instance, for the stoppage of an obsolete but a critical bridge in a busy highway system, the
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replacement of bridge could cause many difficulties. Accordingly, the other alternative of
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strengthening the bridge structures based on the current codes becomes the only possibility under
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certain conditions. For example, strengthening beams and piers is essential to provide much
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desirable load carrying capacity.
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Various rehabilitation methods are available to upgrade the structural performance of
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existing sub-standard bridges. The sub-standard bridge pier can be defined as the bridge piers,
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which are constructed with inadequate lateral ties and longitudinal spliced length reinforcement.
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In the past three decades, concrete and steel plate jacketing has been frequently used for the
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structural strengthening of deficient structures. In such a way, significant improvement in the
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ultimate flexural strength and ductility could be achieved. However, these techniques have many
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problems associated with their use. For example, in the case of concrete jacketing, it is labor
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intensive, time consuming, shrinkage and bonding problem to the substrate concrete. Another
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main drawback is the reduction of available floor-space, since jacketing enriches the cross-
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section dimension, which leads to a substantial mass increase, stiffness modification, and
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consequently modification of the dynamic characteristics of the entire structure. The steel plate
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jacketing needs specialized heavy equipment at the work site. Moreover, high cost and likelihood
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of steel corrosion at the interface of steel and concrete resulting in the bond deterioration are
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considered as problems. Other disadvantages are the difficulty in manipulating heavy steel plates
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in tight construction site, needs scaffolding, and limitation in available plate lengths (which
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required in the case of flexural strengthening of long girders) resulting in the necessity for the
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joints.
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The rapid deterioration of bridge infrastructure and limited funding for maintenance have
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promoted the use of advanced fiber reinforced polymer (FRP) composites as sustainable repair
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and strengthening materials. For the last two decades, a significant research has been focused on
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the application of FRP for the rehabilitation of RC buildings and bridges. Numerous researchers
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have considered FRP as an external reinforcement to upgrade the seismic resistance of the RC
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piers [1], [2], [3], [4]. FRP sheets/strips have been used as retrofitting and rehabilitation materials
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due to their exceptional engineering properties, such as, high strength-to-weight ratio, high
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stiffness with excellent corrosion resistance, low density, long fatigue life. Therefore, they can
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offer a great potential for cost-effective retrofitting method for the concrete structures [5].
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There are several studies, which attempted to explore the feasibility of FRP confinement
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techniques for the seismic retrofit of concrete piers. Some of these studies Elsanadedy and
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Haroun [2], Saadatmanesh et a. [6], Xiao and Ma [7], Chang et al. [8], Han et al. [9] investigated
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the lateral load carrying capacity of RC pier after applying FRP confinement technique. The
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results of these studies have demonstrated that the shear failure could be prevented and
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significant improvement could be obtained in the ductility of the retrofitted piers. Saadatmanesh
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et a. [6] conducted an experimental investigation on the seismic behavior of on 1/5-scaled RC
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pier strengthened with glass fiber reinforced polymer (GFRP) straps. The results showed that the
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seismic resistance of retrofitted piers improves significantly and the longitudinal reinforcement
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are prevented from buckling under lateral cyclic loading. Chang et al. [8] performed pseudo-
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dynamic tests on the as-built and carbon fiber reinforced polymer (CFRP) strengthened
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rectangular RC bridge piers under near-fault ground motions. They found that the seismic
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performance of damaged concrete bridge piers could be effectively improved after retrofitting by
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CFRP. Elsanadedy and Haroun [2] conducted tests on the as-built and FRP composite-wrapped
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scaled models of circular and square RC piers with inadequate lap-spliced length under
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simulated seismic loading. The results demonstrated that the as-built pier suffers from the brittle
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failure due to the bond deterioration of the lap-spliced of longitudinal reinforcement. The circular
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retrofitted piers improved ductility and enhanced seismic performance, while the ductility
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improvement for the square retrofitted pier is limited compared to the as-built pier. Han et al. [9]
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studied the seismic behavior of hollow rectangular bridge piers retrofitted with carbon FRP. The
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results reported that failure modes and damage regions would be changed, and the ductility and
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dissipated energy of the retrofitted piers could improve greatly; however, the lateral load
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capacity did not improve comparatively. Xiao and Ma [7] studied as-built and glass FRP
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composite-wrapped ½-scaled models of circular bridge piers with poor lap splice detailing. They
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reported that the as-built model pier exhibited brittle failure due to bond deterioration of the lap-
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spliced longitudinal reinforcement. The brittle failure was prevented in the repaired and
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retrofitted piers, and dramatic improvement was observed in the ductility and energy dissipation
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capacity of piers.
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In this paper, the seismic vulnerability assessment of non-seismically designed RC bridge
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piers retrofitted with FRP jacketing is conducted. A finite element model of retrofitted and
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unretrofitted circular RC bridge piers are first validated with experimental results and then,
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nonlinear analyses are conducted. The structural response of the retrofitted bridge piers under
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severe seismic events are considerably different compared to regular bridge pier. The paper
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focuses on quantifying the inelastic demand and capacities of FRP retrofitted non-seismically
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designed circular RC bridge piers using nonlinear static pushover analyses (NSPA), and
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incremental dynamic analyses (IDA). The behavior and response of the FRP retrofitted piers are
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investigated using nonlinear analyses by a fiber element model with suitable cyclic constitutive
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laws of FRP-confined concrete. IDA is conducted with finite element numerical models of the
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FRP retrofitted piers to a family of 20 earthquake ground motions scaled with different intensity
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measures (IM). With respect to IM, such as peak ground acceleration (PGA), the maximum
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responses in terms of governing engineering demand parameters (EDP), such as the maximum
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drift or deformation, and ductility demand of the structure are estimated to compare
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performances of retrofitted bridge piers. The results of this study will be useful for the decision
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makers for developing strategies and practices to improve currently used bridge management
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systems.
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2. Design and Geometry of Bridge Pier
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This section briefly explains the design and configuration of different RC bridge piers. The RC
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circular bridge piers are assumed to be located in Vancouver, BC, Canada and is non-seismically
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designed without consideration of the current seismic design guidelines. The diameter of piers is
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fixed to be 400 mm in all the piers. Several parameters affect the design and behavior of the
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bridge piers. The important variables of this parametric study are selected as the compressive
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strength of concrete, f c' , the yield strength, fy, and amount of longitudinal reinforcement, ρl, FRP
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confinement layers, n, axial load, P, and shear span-depth ratio, l/d. Table 1 lists the factors and
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associated values considered in this article. These parameters are selected based on literature
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[10], [11], [12]. For each parameter, two different values (levels) are considered.
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Table 2 shows a summary of the FRP retrofitted piers analyzed in this article. A total of 12
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non-seismically RC circular bridge piers are designed in order to study the effect of different
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parameters on the seismic vulnerability of FRP retrofitted piers. One parameter at a time is
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varied and the others are kept constant. As reported by Parghi and Alam [13], the interaction of
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parameters has an insignificant effect on the response, and therefore, they are not considered in
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this article. The diameter and number of longitudinal bars change for different rebar percentages.
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6mm circular stirrups are used at 250 mm spacing as the lateral reinforcement in all of the piers.
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Figure 1 displays the geometry and reinforcement detailing of the RC pier. In order to ensure that
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the dominant failure mode will be a flexural failure (i.e. avoiding shear failure), and two different
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aspect ratios (4 and 7) are considered.
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3. Numerical Investigation of Bridge Piers
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3.1 Bridge pier model
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The finite element model of the bridge pier is approximated as a continuous 2-D finite element
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frame using the nonlinear analysis program SeismoStruct [14]. Figure 2(a) and Figure 2(b) show
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a typical FRP retrofitted pier and a three-dimensional (3-D) model, respectively. In order to
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consider material nonlinearity, 3-D inelastic displacement-based frame elements has been used
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for modeling the piers. To generate the hysteretic relationship for the circular piers, fiber-based 6
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model is employed. By specifying cross-section pieces along the height of the element, the
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distribution of inelastic deformation and forces are determined. In addition to the fiber elements,
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to capture bond-slip rotations at the pier-footing interface, a nonlinear rotational spring element
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is used in the model. The rotational spring element is defined with a zero-length element in
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SeismoStruct [14]. A rotational spring at the bottom of the pier indicates the longitudinal
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reinforcement pullout from the footing. Its properties was used from Gallardo-Zafra and
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Kawashima [15]. Figure 2(c) characterizes the pier fiber and its sub-section, which is divided
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into cover concrete, core concrete and steel reinforcement. At the numerical integration points,
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each element is characterized by numerous cross-sections where each section is sub-divided into
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a number of fiber under uniaxial state of stress. For concrete compressive strength of 35 MPa,
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the nonlinear variable confinement model proposed by Madas and Elnashai [16], which follows
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the constitutive relationship presented by Mander et al. [17], and the cyclic rules proposed by
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Martinez-Rueda and Elnashai [18] is model implemented in the analyses. For the FRP confined
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concrete, Ferracuti and Savoia [19] model, which follows the constitutive relationship and cyclic
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rules proposed by Mander et al. [17], and Yankelevsky and Reinhardt [20] under compression
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and tension, respectively is used. This model employs Spoelstra and Monti’s [21] model for the
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confining effect of FRP jacket. For the FRP materials, linear elastic behavior up to the rupture
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with zero compressive strength is considered. Menegotto and Pinto [22] steel model with
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Filippou et al. [23] isotropic strain hardening property is adopted as the constitutive model of
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rebar to develop the analytical model. When the pier is jacketed by FRP sheets, the cover
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concrete is considered as the concrete confined by the FRP jacket, while the core concrete is
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considered as the concrete confined by FRP and the transverse reinforcements.
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3.2 Model calibration with experimental results
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In order to calibrate the numerical models, the circular RC pier experimentally studies by
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Kawashima et al. [24] is adopted in this research. The pier specimen has a diameter of 400 mm,
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and an effective height of 1350 mm. The pier is reinforced with 12-15M steel (dia. of 16 mm)
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longitudinal reinforcement ratio of 1.89, and 0.128% transverse steel (dia. of 6 mm), with 300
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mm center to center spacing, and the clear cover of concrete of 35 mm. The confined region,
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where carbon fiber reinforced polymer (CFRP) jackets are applied from the base of the pier, has
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a height of 1000 mm. An axial compressive load of 188.4 kN representing 5% of the axial
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capacity is applied at the top of the pier. The pier is free on top and flexural dominated in the
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reversed cyclic load test. The specified compressive strength of the unconfined concrete, the
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yield strength of longitudinal and transverse reinforcements is considered as 35, 374, and 363
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MPa, respectively. The CFRP retrofitting technique adopted in this paper is adapted from
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Kawashima et al. [24]. The CFRP composites have an initial stiffness, and an ultimate strain of
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266 GPa and 1.63%, respectively.
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Figure 3(a) and Figure 3(b) demonstrate the hysteretic behavior of as-built and CFRP
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retrofitted piers, respectively. In order to validate the numerical model, the CFRP retrofitted pier
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is modelled and analyzed using a finite element program SeismoStruct [14] under the
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displacement-controlled reversed cyclic loading history same as the experimental test [24]. The
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RC cantilever pier is displaced with an increment of 0.5% drift until reaching a maximum drift of
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5%. The numerical model of pier, retrofitted with a single layer of CFRP sheet representing the
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volumetric confinement ratio of 0.11%, is validated with the experimental results [24] . As
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shows in Figure 3(a) and Figure 3(b), the numerical model can capture the experimental response
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[24] in terms of initial and post elastic stiffness, and the ultimate load capacity with a good
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accuracy. Compared to the experimental results, the stiffness and capacity, respectively varies by
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3.5 and 3%.
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4. Nonlinear Static Pushover Analysis and the Flexural Limit States
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According to the performance-based design guidelines, structures are designed based on a
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damage limit state at which the loss of life is prohibited. However, the structure would be out of
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service for a certain time, which could withstand extensive structural and non-structural
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damages. The performance of the bridge pier can be quantified in terms of limit states with
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corresponding strain limits. In order to study the effect of different parameters of retrofitted
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circular bridge piers, four performance criteria have been considered: the displacements (∆) and
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base shear (V) at the onset of first yielding of longitudinal steel (∆y, Vy), first crushing of core
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concrete (∆crush, Vcrush), first buckling of longitudinal steel (∆buck, Vbuck) and first fracture of
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longitudinal steel (∆fract, Vfract) pier. In order to identify the limit states for all combinations of the
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retrofitted piers (Table 2), nonlinear static pushover analyses are conducted. The yielding of
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longitudinal steel reinforcement is assumed to take place at a tensile strain of steel fy/Es. The
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crushing strain of unconfined concrete varies from 0.0025 to 0.006 [25]. Consequently, Paulay
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and Priestley [10] recommended that the crushing strain of confined concrete is much higher and
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changes from 0.015 to 0.05. In the present analysis, the crushing of confined concrete is assumed
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to occur when the concrete compressive strain reaches 0.035. Longitudinal bar buckling and
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fracture are determined according to the equations proposed by Berry and Eberhard [26]. They
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proposed that the onset of bar buckling and fracture are best predicted as functions of the
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effective confinement ratio, ρeff. Buckling and fracture of the longitudinal bar are defined as the
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points when the tensile strain in the extreme tensile steel fibre reaches 0.045 and 0.046,
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respectively [26].
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As depicted in Table 3, and Figure 4 - Figure 9, different parameters affect the flexural
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performance of the FRP retrofitted bridge piers. For instance, as shown in Figure 3 - Figure 8, it
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can be observed that higher values of the parameters can increase the capacity of the piers.
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Yielding, bucking, and fracture of reinforcement, and crushing of core concrete are also
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presented in Figure 4 - Figure 9.
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From Figure 4, it is observed that 35 MPa concrete increases the pier yielding and crushing
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base shear capacities of 14 and 8.3%, respectively; while the buckling and fracture base shear
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capacities decrease by 4.4 and 4.3% compared to 20 MPa concrete. It could be attributed to the
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fact that for the low strength concrete (20 MPa), the FRP confinement is more effective which
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could give a higher deformability compared to the high strength concrete (35 MPa). Thus, low
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strength concrete shows a higher displacement for crushing, buckling, and fracture of the rebar.
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There is no difference in the yield displacement for 20 and 35MPa concrete. The results
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presented in Figure 4 indicate that the stiffness of both piers is quite similar until the yielding of
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the rebar. The results show that the stiffnesses of both piers are quite similar until cracking of the
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concrete. Once the concrete is cracked, the 20 MPa pier exhibits comparatively lower stiffness
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compared to 35 MPa concrete due to a lower modulus of elasticity of the concrete.
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From Figure 5, it can be observed that the yield strength of longitudinal reinforcement
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significantly affects the flexural performance of the FRP retrofitted bridge piers. For the high
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yield strength (400 MPa) reinforcement shows higher yielding, crushing, buckling and fracture
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base shear of 24.3, 27.3, 30.1 and 4.5%, and larger displacement by 28.6, 15.4, 27.3, 6.8, and
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4.7%, respectively compared to the lower yield strength (250 MPa).
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From Figure 6, it is observed that the amount of longitudinal steel considerably affects the
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flexural strength and limit states of the retrofitted bridge piers. For 2.5% longitudinal
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reinforcement ratio, the yielding, crushing, buckling and fracture base shear capacities are
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improved by 44.9, 48.7, 55.8, and 56.1% compared to that of 1% longitudinal steel. For 2.5%
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longitudinal reinforcement ratio, the yielding, buckling, and fracture displacements increase by
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14.3, 9.5, and 9.3%, respectively, but the crushing displacement decreases by 14.3% compared to
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that of 1% longitudinal steel.
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From Figure 7, it can be observed that at 20% axial load, the yielding, crushing, buckling,
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and fracture base shear increases by 41.5, 14.3, 7.4, and 7.2% compared to that of 10% axial
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load. The yielding displacement increases by 14.3% for 20% axial load compared to 10% axial
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load; and crushing, buckling and fracture displacements are almost the same for 20 and 10%
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axial load. The results presented in Figure 7 reveal that the stiffnesses of both piers are quite
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similar. The pier with 10% axial load has a higher deformation compared to 20% axial load pier.
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From Figure 8, it can be observed that the shear span-depth ratio significantly affects the
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flexural performance of the FRP retrofitted bridge piers. For the shear span-depth ratio of 7
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shows 52.6, 44.3, 100.6, and 101.7% lower yielding, crushing, buckling, and fracture base shear
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capacities, respectively compared to those having shear span-depth ratio of 4. For the shear span-
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depth ratio of 7, yielding, crushing, buckling, and fracture displacements increase by 57.1, 64.3,
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67.4 and 65.9%, respectively compared to those for the shear span-depth ratio of 4. According to
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the results presented in Figure 8, the shear span-depth ratio of 4 shows higher stiffness and lower
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deformability compared to the shear span-depth ratio of 7.
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From Figure 9, it can be observed that the FRP-confinement layer does not affect the
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flexural performance of the piers in terms of yielding, crushing, buckling, and fracture base
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shears and displacements. Similar base shear and displacement limit states are observed from 2
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and 3 layers of FRP confinement.
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5. Incremental Dynamic Analysis of Piers
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In order to predict the structural response under lateral load, NSPA is widely used. Conversely,
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during a seismic event the lateral load experienced by the structures is dynamic in nature; hence,
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nonlinear dynamic time history analysis will provide accurate estimation of structural response
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under a seismic load. Luco and Cornell [27] developed incremental dynamic analysis (IDA)
258
method which is well explained in detail in Vamvatsikos and Cornell [28], and Yun et al. [29].
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IDA needs multiple nonlinear dynamic time history analyses of a structural model by scaling sets
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of seismic ground motion records based on adopted intensity measures (IM). Then, regression
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equations of engineering demand parameters (EDP), such as maximum drift at different intensity
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levels will be developed. The suite of different ground motions is properly chosen to cover the
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entire range of the model’s response from elastic to yield, and nonlinear inelastic which leads to
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global dynamic instability of structures. In IDA, different scaling factors should be selected for
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different piers. Here, PGA is selected as IM and the incremental scaling series in IDA ranges
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from 0.1g to 3.0g. Overall, when the maximum top drift of the piers exceeds certain level, it
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experiences dynamic instability with a large deformation or drift. In this article, a “collapse
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point” is considered as the first incidence of such large deformation or drift [28]. Though,
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Konstantinidis and Nikfar [30] reported that increase of an actual ground motion PGA value by
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a scaling factor does not certainly lead to reliable results; however, it will provide a better
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understanding of the behavior of the inelastic system over the range of different intensity
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measures. In portraying the inelastic demand, non-linear behavior in the collapsed state are
273
defined. The collapse results are modeled by developing fragility curves at the collapse limit
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state.
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5.1 Selection of ground motions
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The properties of seismic ground motion differ in terms of frequency content, peak ground
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acceleration (PGA), and duration. Thus, dynamic time history analyses of structure for one
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ground motion record might not characterize the worst-case scenario. In order to incorporate the
279
uncertainties and variability of ground motion records and their impact on the behavior of bridge
280
piers, a suite of earthquake ground motions is required. Due to limited number of available
281
earthquake records in Vancouver, British Columbia region (western Canada), a suite of 20
282
ground motion histories are obtained from the Applied Technology Council [31] ground motion
283
database. Table 4 shows the characteristics of the un-scaled seismic ground motion records
284
including PGA, peak ground velocity (PGV), epicenter distance (R), and moment magnitude
285
(Mw) of the earthquake. These ground motion records have low to medium values of PGA, R, Mw
286
and PGV, which are in the range of 0.22-0.73g, 8.7-98.2km, 6.5-7.6 and 17-70cm/sec,
287
respectively. It is assumed that these ground motions are considered to be representative of an
288
earthquake motion in Vancouver. In this study, the horizontal components of ground motion
289
records are applied to the pier. The specified magnitude and distance ranges cover the
290
predominant magnitudes and distances for Vancouver.
291
Figure 10(a) shows the acceleration response spectrum of the recorded suits of 20 ground
292
motions with a 5% damping ratio. Figure 10(b) depicts different percentiles of acceleration
293
response spectra with a 5% damping ratio, showing that the selected earthquake ground motions
294
records are well representing the medium to strong intensity earthquake ground motion histories..
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5.2 Incremental dynamic analysis for pier collapse capacity
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For the retrofitted bridge piers, inelastic demands are estimated by conducting IDA. IDA curve is
297
also known as dynamic pushover curve, which is the relationships between IM and EDP. These
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curves are generated using numerous ground motions, and each ground motion records are scaled
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to multiple levels of intensities [28].
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5.3 Dynamic pushover curve
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The incremental dynamic analysis is conducted for all the retrofitted bridge piers using the suite
302
of 20 earthquake ground motion records. Figure 11- Figure 21 show the dynamic pushover curve
303
of total base shear versus top lateral displacement for different compressive strengths of
304
concrete, yield strengths and amount of longitudinal reinforcement, axial loads, shear span-depth
305
ratios, and FRP layers. The dynamic pushover points closely coincide with the static pushover
306
curves before the first yielding of the longitudinal reinforcement. It can be observed from Figure
307
11- Figure 21 that the dynamic pushover curves demonstrate higher base shear values compared
308
to those from the static pushover curves between first yielding and crushing of core concrete.
309
5.4 Incremental dynamic analysis curve
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IDA curve results with all the combinations of parameters are used to identify IM values related
311
to the collapse. Figure 22(a) - Figure 22(l) show the IDA curves of all the retrofitted piers with
312
different adopted parameters (Table 2) and a set of IM values related to the onset of collapse for
313
each ground motions. The overall characteristics of the IDA curves for maximum top drift ratio
314
are different, the initial drift increases gradually with the seismic intensity level. Afterward, the
315
drift increases rapidly when the seismic intensity level reaches a range of 0.2g to 0.4g for all of
316
the piers (Figure 22). According to the results of IDA curves shown in Figure 22(a) - Figure
317
22(l), the non-seismically designed piers show more vulnerability compared to the other bridge
318
piers. Failure modes obtained from the IDA curves at collapse level are summarized in Appendix
319
Table A1.
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6. Collapse Fragility Assessment
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The fragility curves can be produced by using various methods, for instance, an expert opinion,
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damage data observed from field, laboratory testing, based on numerical simulations, or a
323
combination of them [32], [33], [34], [35], [36], [37], [38]. In this research, analytical collapse
324
fragility curves were generated based on IDA results using suits of 20 ground motion records
325
scaled until it causes the collapse of the pier [28]. The analytical fragility curve exhibits
326
advantages compared to other methods. For instance, in the case of analytical fragility curve, the
327
analyst is free to choose the IM , at which analysis is to be conducted, and the number of analysis
328
at each IM [39]. Generally, the fragility curves are mathematical functions which describe the
329
conditional probability that a structure can experience damage by exceeding or reaching a
330
specific level of damage state as a function of demand (drift or ductility), represented by EDP IM
331
(e.g. PGA). In the seismic vulnerability assessment of structure, fragility curves are obtained
332
from IDA [40].. The collapse fragility function gives a probability that a structure would collapse
333
as a function of a specific IM. The collapse fragility assessment can be described using Eq. (1) as
334
a lognormal cumulative distribution function (CDF) reported by [39]. ln ( x θ ) Pc ( C | IM = x ) = Φ β
(1)
335
where Pc(C|IM = x) represents the probability of collapse at a given ground motion with IM = x,
336
Φ(.) is the standard normal CDF, θ is the collapsed median intensity of the fragility function (IM
337
level with 50% probability of collapse not being exceeded), and β is the logarithmic standard
338
deviation. Eq. (1) indicates the assumption of lognormality of the IM values of the ground
339
motions causing the collapse of specific structures [39]. Calibrating Eq. (1) of the pier needs an
340
estimation of θ and β from the IDA results. Figure 23 shows the linear regression models of the
341
median and standard lognormal dispersion for all the combinations of parameters. Table 5 15
342
depicts a summary of the values of linear regression models of the median and standard
343
lognormal dispersion for all the combinations.
344
The probability of collapse can be assessed at a given IM level, x can then be determined as
345
a part of records for which collapse occurs at a level lower than x. Fragility function parameters
346
can be assessed from the regression analyses of their median θ, and dispersion β, values, and by
347
taking the logarithm of each ground motion’s IM value related to the onset of collapse.
348
Based on the obtained collapse mode of IDA results and using fragility curves, the
349
probability of collapse of all the combination of parameters is plotted in Figure 24 - Figure 29. In
350
order to compare the obtained probability of collapse for the combination of different
351
parameters, these curves are plotted together and presented in one figure. In Figure 24 - Figure
352
29, the curve drawn with a black solid line indicates a higher collapse fragility, and the dotted
353
red line shows a lower collapse fragility as obtained by fitting the lognormal distribution to the
354
data. These data are obtained from the IDAs results. It can be observed from the Figure 24 -
355
Figure 29 that the probability of collapse of the lower value has a significant shift to the left and
356
has a smaller PGA for a specific probability of collapse. It leads to an increase in the probability
357
of collapse for a given seismicity. In Figure 24 - Figure 29, SCT represents the median collapse
358
probability.
359
6.1 Effect of compressive strength of concrete on collapse fragility curve
360
Figure 24 shows the effect of concrete compressive strength on the collapse fragility of
361
retrofitted bridge piers based on the maximum collapse drift ratio. The solid black line and the
362
red dotted line represent the probability of collapse with the specified compressive strength of
363
concrete of 35 and 20 MPa, respectively. The fragility curve clearly demonstrates the probability
364
of structural collapse for measuring definite intensity. From Figure 24, it can be observed that the
16
365
difference between fragility curves of 35, and 20 MPa concrete is significant. It is important to
366
note that 35MPa concrete pier is more fragile compared to 20MPa concrete piers. For instance,
367
as shown in Table 6, for the peak ground intensity levels, PGA in the range of 0.5g-2.0g, the
368
relative probability of collapse of 35MPa concrete pier is higher compared to 20MPa concrete
369
pier. 35 MPa concrete pier has higher stiffness that attracts more seismic forces causing more
370
damages to the pier compared to the 20 MPa concrete pier. Since 20 MPa concrete has lower
371
modulus of elasticity compared to 30 MPa concrete, larger strain experienced by the 20 MPa
372
concrete activated the FRP composite confinement and thus, was more effective in resisting
373
seismic forces compared to the 30 MPa concrete at similar drift level. From Figure 24, it can be
374
observed that the 20 MPa concrete pier will have 50% probability of collapse at a PGA value of
375
1.1g whereas the 35 MPa concrete will be able to sustain an earthquake with a PGA of only
376
0.72g to experience similar damage level. In other words, during an earthquake with a PGA of
377
0.72g the probability of collapse of the 20 MPa concrete is only 20% whereas for the 35 MPa
378
concrete it is 50%.
379
6.2 Effect of yield strength of steel reinforcement on collapse fragility
380
Figure 25 shows the effect of yield strength of longitudinal reinforcement on the collapse
381
fragility of retrofitted bridge piers based on maximum collapse drift ratio. The solid black line
382
and the red dotted line indicates the probability of collapse fragility with the yield strength of
383
longitudinal reinforcement of 400, and 250MPa, respectively. The fragility curve clearly
384
demonstrates the probability of structural collapse for measuring definite intensity. From Figure
385
25, it can be observed that the difference between fragility curves of 400, and 250 MPa
386
reinforcements are significant. For example, as shown in Table 6, for the peak ground intensity
387
levels, PGA, in the range of 0.5g-2.0g, the relative probability of collapse for the 400 MPa steel
17
388
RC pier is lower compared to the 250 MPa steel RC pier. For the intensity level of 2.0g, the
389
difference in the collapse probabilities is insignificant. Since both steel has the same modulus of
390
elasticity, the 400 MPa steel experiences yielding at a much larger strain value compared to the
391
250 MPa steel. Hence, the 400 MPa steel gets an added advantage to experience lower damage
392
level at the same ground motion level compared to the 400 MPa steel. From Figure 25, it can be
393
observed that the 400 MPa steel RC pier will have 50% probability of collapse at a PGA value of
394
0.71g whereas the 250 MPa steel RC pier will be able to sustain an earthquake with a PGA of
395
only 0.62g. In other words, during an earthquake with a PGA of 0.62g the probability of collapse
396
of the 400 MPa steel is 40% whereas for the 250 MPa steel it is 50%.
397
6.3 Effect of amount of longitudinal reinforcement on collapse fragility
398
Figure 26 shows the effect of the amount of longitudinal reinforcement on the collapse fragility
399
of retrofitted bridge piers. The solid black line and the red dotted line represents the probability
400
of collapse of the amount of longitudinal reinforcement of 1, and 2.5%, respectively. The
401
fragility curve clearly demonstrates the probability of structural collapse for measuring definite
402
intensity. From Figure 26, it can be observed that the difference between fragility curves with the
403
longitudinal reinforcement of 2.5% is significant compared to 1% reinforcement. Larger amount
404
of rebar increases the stiffness and strength of the pier and hence, it experiences lesser
405
deformation compared to the pier having reduced amount of longitudinal bar. As shown in Table
406
6, for the peak ground intensity levels, PGA, in the range of 0.5g-2.0g, the relative probability of
407
collapse for the 2.5% longitudinal steel is lower compared to 1% longitudinal steel. From Figure
408
26, it can be observed that the 1% longitudinal steel pier will have 50% probability of collapse
409
even at a PGA value of 0.8g whereas the 2.5% steel RC pier will be able to sustain an earthquake
18
410
with a PGA of 1.22g. In other words, during an earthquake with a PGA of 0.8g the probability of
411
collapse of the 1% steel pier is 50% whereas for the 2.5% steel pier it is only 14%.
412
6.4 Effect of axial load on collapse fragility
413
Figure 27 shows the effect of axial load on the collapse fragility of retrofitted bridge piers based
414
on maximum collapse drift ratio. The solid black line and the red dotted line represent the
415
probability of collapse with the axial load ratios of 0.20 and 0.10, respectively. The fragility
416
curves clearly demonstrate the probability of structural collapse. From Figure 27, it can be
417
observed that the difference between fragility curves with the axial load ratios of 0.20 and 0.10 is
418
significant. For example, as shown in Table 6, for PGA values in the range of 0.5g-2.0g, the
419
relative probability of collapse at the axial load of 0.20 is higher compared to 0.10 axial load.
420
From Figure 6.26 it can be observed that the higher axial load pier will have 50% probability of
421
collapse at a PGA value of 0.9g whereas the lower axial load pier will be able to sustain an
422
earthquake with a PGA of 1.31g. In other words, during an earthquake with a PGA of 0.9g the
423
probability of collapse of the higher axial load pier is 50% whereas for the lower axial load pier
424
it is only 16%.
425
6.5 Effect of shear span-depth ratio on collapse fragility
426
Figure 28 shows the effect of shear span-depth ratio on collapse fragility of retrofitted bridge
427
piers. The solid black line and the red dotted line represent probabilities of collapse with the
428
shear span-depth ratios of 4 and 7, respectively. The fragility curves clearly demonstrate the
429
probability of structural collapse. From Figure 28, it can be observed that the difference between
430
fragility curves with shear span-depth ratios of 4 and 7 is not very significant. As shown in Table
431
6, for the peak ground intensity levels, PGA in the range of 0.5g-2.0g, the relative probability of
432
collapse at the shear span-depth ratio of 7 is lower compared to the shear span-depth ratio of
19
433
0.10. From Figure 6.27 it can be observed that the pier with larger shear span-depth ratio will
434
have 50% probability of collapse at a PGA value of 1.16g whereas the pier with lower shear
435
span-depth ratio will be able to sustain an earthquake with a PGA of only 1.24g. In other words,
436
during an earthquake with a PGA of 1.16g the probability of collapse of the larger shear span-
437
depth ratio is 50% whereas for the lower shear span-depth ratio it is 45%.
438
6.6 Effect of confinement on collapse fragility
439
Figure 29 shows the effect of FRP confinement on the collapse fragility of circular RC bridge
440
piers. The solid black line and the red dotted line represent the probabilities of collapse with 2
441
and 3 layers of FRP confinement, respectively. From Figure 29, it can be observed that the
442
difference between fragility curves for 2 and 3 layers of FRP confinement is insignificant at PGA
443
values beyond 1.5g. However, from 0.2g to 1.5g, there are some differences. As shown in Table
444
6, the relative probability of collapse for the 2 FRP confinement layers is higher compared to 3
445
layers of FRP confinement. From Figure 6.28 it can be observed that the 2 layer FRP pier will
446
have 50% probability of collapse at a PGA value of 0.75g whereas the 3 layer FRP pier will be
447
able to sustain an earthquake with a PGA of 0.82g. In other words, during an earthquake with a
448
PGA of 0.75g the probability of collapse of the 3 layer FRP pier is 44% whereas for the 2 layer
449
FRP pier it is 50%
450
The collapse probability difference, ∆, for fragilities of all combination of parameters are
451
reported in a bar chart (see Figure 31 and Figure 32) for four peak ground accelerations of 0.5g,
452
1.0g, 1.5g, and 2.0g. As expected with higher PGA values, the differences in collapse probability
453
gradually decrease.
20
454
6.7 Median peak ground acceleration
455
The median values of the intensity measure, PGA, for a different combination of FRP, retrofitted
456
bridge piers are given in Table 7 and the corresponding bar chart is depicted in Figure 33. The
457
median values of PGA are determined as a level of PGA at which the probability of collapse at
458
each pier reaches 50%. For the same level of collapse probability, lower values of median
459
correspond to the higher probability of collapse, hence it demonstrates that the pier with a lower
460
median value is more fragile compared to other piers. For example, piers with a concrete
461
compressive strength of 35 MPa, a reinforcement yield strength of 250 MPa, a longitudinal
462
reinforcement ratio of 1%, and axial load of 0.20, a shear span-depth ratio of 4, and 2
463
confinement layers have the lowest value of median, respectively, 0.72g, 0.62g, 0.79g, 0.90g,
464
1.16g and 0.78g. It demonstrates that the lowest median values of piers have the inferior
465
performance. It can be noted that the pier with 20MPa concrete gives higher median value of
466
1.1g. As a result, it indicates that the FRP confinement is more effective in 20MPa concrete
467
compared to 35MPa concrete (PGA = 0.72g) in the case of FRP retrofitted piers.
468
The relative difference between the median values of PGA is found to be 10% for 35 and 20
469
MPa concretes. It represents that the 35MPa concrete pier leads to a 10% higher fragility
470
compared to the 20 MPa concrete pier. It is because the FRP confinement is more effective for
471
20MPa concrete compared to the 35MPa concrete. Thus, it is concluded that the deficient pier
472
performance can be improved with FRP.
473
6.8 Performance evaluation of bridge piers
474
Results of IDA curve can be used to evaluate the collapse performance of the RC bridge piers.
475
The collapse median intensity (SCT) obtained from the fragility fitting curves (Figure 25 -Figure
476
30) and the performance of bridge piers can be assessed using collapse margin ratio (CMR) [31].
21
477
The CMR can be expressed at the ratio of the SCT to the design level earthquake intensity (SMT).
478
The CMR ratio is calculated by dividing the SCT by a specific level of SMT, which is equal to
479
0.185g, 0.256g and 0.363g for 10, 5, and 2% probabilities of exceedance in 50 years at the return
480
period of 475, 975 and 2475 years, respectively for Vancouver, British Columbia. Table 8
481
exhibits the CMR values for different combinations of parameters. From Table 8, it can be
482
observed that as the ground motion return period decreases the collapse probability of
483
exceedance increases. For instance, for a pier with a compressive strength of concrete of 35 MPa,
484
the collapse probability value under an earthquake with a return period of 2475 years is 1.98,
485
which is 3.38 and 2.11% lower than a return period of 975 and 475 years, respectively.
486
Observation from Table 8 revealed that, as the earthquake return period increases, its intensity
487
also increases. Hence, the probability of exceeding collapse of a certain pier will increase, which,
488
means that the median collapse spectral acceleration will increase with the increase of
489
earthquake return period. Since the spectral acceleration at maximum considered earthquake will
490
also increase with the increase of earthquake return period, the results presented in Table 8 show
491
the CMR values gradually decrease with increasing return period. For instance, when the yield
492
strength of longitudinal reinforcement increases, the CMR ratio increases from 3.35% to 3.84%
493
at 475 years return period. In the case of increasing compressive strength, the CMR ratio
494
decreases from 5.95% to 3.89% with a return period of 475 years. It is because of the lower
495
strength concrete (20 MPa); the FRP confinement is more effective compared to higher strength
496
(35 MPa) concrete.
497
7. Conclusions
498
The seismic fragility assessment of the bridge can be analyzed using fragility curve, which is a
499
method to estimate the probability of damage of the structure at specific levels of ground motion.
22
500
The piers are the most vulnerable structural element in the bridge structures, which have
501
significant contribution to the failure probability of the bridge system. This article presented the
502
nonlinear static pushover analyses (NSPA) and collapse fragility curves of non-seismically
503
designed RC circular bridge piers located in Vancouver, British Columbia, Canada with a
504
different combination of parameters. Probabilistic seismic demand models were produced using
505
the results obtained from the incremental dynamic analyses (IDA). Considering collapse drift as
506
demand parameter, fragility curves were generated with different parameters of non-seismically
507
designed RC circular bridge piers. It was observed that the amount of reinforcement, shear span-
508
depth ratio, and level of the axial load could significantly affect the collapse fragility curve of the
509
retrofitted bridge piers.
510 511 512
Based on the NSP and results obtained from IDA curves, and collapse fragility curve, the following conclusions can be drawn.
513 514
It can be observed from the NSPA that higher values of parameters could increase the capacity of the piers.
It is observed that 35 MPa concrete increased the pier yield and crushing base shear
515
capacity by 14 and 8.3%, respectively; while the buckling and fracture base shear
516
capacities were decreased by 4.4 and 4.3% compared to 20MPa concrete.
517
For piers with 400 MPa yield strength of longitudinal reinforcements, yielding, crushing,
518
buckling and fracture base shear and displacement capacities increased by 24.3, 27.3,
519
30.1 and 4.5%, and 28.6, 15.4, 27.3, 6.8, and 4.7%, respectively, compared to those of the
520
pier with reinforcements having 250 MPa yield strength.
23
521
For piers with longitudinal reinforcement ratios of 2.5%, the yielding, crushing, buckling
522
and fracture base shear capacities improved by 44.9, 48.7, 55.8, and 56.1% compared to
523
those for 1% longitudinal reinforcement ratios.
524
For piers with longitudinal reinforcement ratios of 2.5%, the yielding, buckling and
525
fracture displacements increased by 14.3, 9.5, and 9.3%, respectively, but the crushing
526
displacement decreased by 14.3% compared to those for 1% longitudinal reinforcement
527
ratios.
528
529 530
It can be observed that at 20% axial load, the yielding, crushing, buckling, and fracture base shear increased by 41.5, 14.3, 7.4, and 7.2% compared to those for 10% axial loads.
The yielding displacement increased by 14.3% for 20% axial load compared to 10% axial
531
load, and crushing, buckling and fracture displacements were almost the same for 20 and
532
10% axial loads.
533
For the shear span-depth ratio of 7, yielding, crushing, buckling, and fracture base shears
534
decreased by 52.6, 44.3, 100.6, and 101.7%, respectively compared to those for 4 shear
535
span-depth ratio.
536
The shear span-depth ratio of 7 resulted in an increase in yielding, crushing, buckling and
537
fracture displacements by 57.1, 64.3, 67.4 and 65.9%, respectively compared to those of
538
4 shear span-depth ratios.
539
540 541 542
The dynamic pushover points closely coincided with the static pushover curves before the first yielding of the longitudinal reinforcement.
The dynamic pushover curved demonstrated higher base shear value compared to f the static pushover curves between first yielding and crushing of core concrete.
24
543
It can be observed that 35 MPa concrete pier is more fragile compared to 20 MPa
544
concrete piers. For PGA values in the range of 0.5g-2.0g, the relative probability of
545
collapse of 35MPa concrete pier is higher (in the range of 74.8-3.2% compared to 20MPa
546
concrete pier).
547
At PGA values from 0.5g to 2.0g, for 400 MPa yield strength, a relatively lower
548
probability of collapse (i.e. in the range of 79.8-4.3%) was observed compared to 250
549
MPa yield strength.
550
At PGAs from 0.5g-2.0g, a relatively lower probability of collapse was observed (i.e. in
551
the range of 83.5-3.2%) for the amount of longitudinal steel of 2.5% is compared to 1%
552
longitudinal steel.
553
At PGAs from 0.5g-2.0g, a relatively higher probability of collapse was observed (i.e. in
554
the range of 74.8-2.7%) for the axial load of 0.20 compared to 0.10 axial load. The higher
555
axial load reduced the deformability.
556
At PGAs from 0.5g-2.0g, a relatively lower probability of collapse was observed (i.e. in
557
the range of 64.8-2.4%) for the shear span-depth ratio of 7 compared to the shear span-
558
depth ratio of 4.
559
At PGAs from 0.5g-2.0g, a relatively higher probability of collapse was observed (i.e. in
560
the range of 77.7-3.4%) for 2 layers of FRP confinement compared to the 3 layers of
561
confinement.
562
Acknowledgements
563
The first author would like to acknowledge the financial support provided by MITACS and
564
POLYRAP Engineered Concrete Solutions, Kelowna, B.C., Canada under the accelerate Ph.D.
565
fellowship award No. IT03809, and Ministry of Human Resources Development (MHRD), Govt.
25
566
of India, New Delhi for the National Oversees Scholarship. The first author is also grateful to S.
567
V. National Institute of Technology (SV NIT), Surat, Govt. of India to grant the study leave for
568
the Ph.D. program at the University of British Columbia (UBC), Canada. The authors are
569
grateful to Dr. Farshad Hedayati Dezfuli of UBC for proof reading of the manuscript. The
570
authors are grateful to Dr. Solomon Tesfamariam from the School of Engineering, UBC for the
571
interpretation of collapse fragility results. . Moreover, the authors would like to thank the
572
unknown referees for their useful remarks and suggestions. The experimental results were
573
provided by Prof. Kazuhiko Kawashima, Professor Emeritus, Department of Civil Engineering,
574
Tokyo Institute of Technology, Japan, and Dr. Richelle G. Zafra, Department of Civil
575
Engineering/Associate Dean, College of Engineering and Agro-Industrial Technology University
576
of the Philippines Los Banos and they are gratefully acknowledged.
577
References
578
[1]
579 580
Saadatmanesh H, Ehsani MR, Jin L. Strength and ductility of concrete columns externally reinforced with fiber composite straps. ACI Struct J 1994;91:434–47.
[2]
Elsanadedy HM, Haroun M. Seismic design criteria for circular lap-spliced reinforced
581
concrete bridge columns retrofitted with fiber-reinforced polymer jackets. ACI Struct J
582
2005;102:354–62.
583
[3]
584 585
containing lap-spliced reinforcing bars. ACI Struct J 2007;104:227–36. [4]
586 587 588
Ghosh KK, Sheikh SA. Seismic upgrade with carbon fiber reinforced polymer of columns
Liu J, Sheikh A G. Glass Fiber-reinforced polymer-reinforced circular columns under simulated seismic loads. ACI Struct J 2013;110:941–51.
[5]
ACI 440.2R. Guide for the design and construction of externally bonded FRP systems for strengthening of concrete structures. ACI Committee 440.2R-08, American Concrete
26
589 590
Institute, Farmington Hills, Detroit, Michigan, USA: 2008. [6]
591 592
with fiber composites. ACI Struct J 1996;93:639–47. [7]
593 594
Saadatmanesh H, Ehsani MR, Jin L. Seismic strengthening of circular bridge pier models
Xiao Y, Ma R. Seismic retrofit of RC circular columns using prefabricated composite jacketing. J Struct Eng, ASCE 1997;123:1357–64.
[8]
Chang SY, Li YF, Loh CH. Experimental study of seismic behaviors of as-built and
595
carbon fiber reinforced plastics repaired reinforced concrete bridge columns. J Bridg Engi
596
ASCE 2004;9:391–402.
597
[9]
Han Q, Wen J, Du X, Jia J. Experimental and numerical studies on seismic behavior of
598
hollow bridge columns retrofitted with carbon fiber reinforced polymer. J Reinf Plast
599
Compo 2014;33:2214–27. doi:10.1177/0731684414557716.
600 601 602 603 604 605 606 607 608 609 610 611
[10] Paulay T, Priestley MJN. Seismic design of reinforced concrete and masonry buildings. New York, USA: John Wiley & Sons Inc; 1992. [11] Hines E, Restrepo JI, Seible F. Force-displacement characterization of wellconfined bridge piers. ACI Struct J 2004;101:537–48. [12] Bae S, Bayrak O. Plastic hinge length of reinforced concrete columns. ACI Struct J 2008;105:290–300. [13] Parghi A, Alam MS. Seismic behavior of deficient reinforced concrete bridge piers confined with FRP–A fractional factorial analysis. Eng Struct 2016;126:531–46. [14] SeismoStruct. A computer program for static and dynamic nonlinear analysis of framed structures, V 7.06 2015:[Online], available from URL:. [15] Gallardo-Zafra R, Kawashima K. Analysis of carbon fiber sheet retrofitted RC bridge piers under lateral cyclic loading. J Earthq Eng 2009;13:129–54.
27
612
[16] Madas P, Elnashai AS. A new passive confinement model for the analysis of concrete
613
structures subjected to cyclic and transient dynamic loading. Earthq Eng Struct Dyn
614
1992;21:409–31.
615 616 617 618 619 620 621 622 623 624
[17] Mander JB, Priestley MJN, Park R. Theoretical stress–strain model for confined concrete. J Struct Eng ASCE 1988;114:1804–26. [18] Martinez-Rueda JE, Elnashai AS. Confined concrete model under cyclic load. Mater Struct 1997;30:139–47. [19] Ferracuti B, Savoia M. Cyclic behavior of CFRP-wrapped piers under axial and flexural loading. Proceeding Int. Conf. Fract., Turin, Italy: 2005. [20] Yankelevsky DZ, Reinhardt HW. Uniaxial behavior of concrete in cyclic tension. Journal of Structural Engineering. J Struct Eng, ASCE 1989;115:166–82. [21] Spoelstra MR, Monti G. FRP-confined concrete model. J Compos Const, ASCE 1999;3:143–50.
625
[22] Menegotto M, Pinto PE. Method of analysis for cyclically loaded R.C. plane frames
626
including changes in geometry and non-elastic behaviour of elements under combined
627
normal force and bending. Symp. Resist. Ultim. Deform. Struct. acted by well-defined
628
repeated loads, Int. Assoc. Bridg. Struct. Eng., Zurich, Switzerland: 1973, p. 15–22.
629
[23] Filippou FC, Popov EP, Bertero V V. Modelling of R/C joints under cyclic excitations. J
630
Struct Eng ASCE 1983;109:2666–84.
631
[24] Kawashima K, Hosotani M, Yoneda K. Carbon fiber sheet retrofit of reinforced concrete
632
bridge piers. Proc. Int. Work. Annu. Commem. Chi-Chi Earthquake, Vol. II-Technical
633
Asp. Natl. Cent. Res. Earthq. Eng. Taipei, Taiwan, ROC, 2000, p. 124–35.
634
[25] MacGregor JG, Wight JK. Reinforced concrete mechanics and design. 4th Editio. New
28
635
Jersey, USA: 4th Edition, Prentice-Hall, Upper Saddle River; 2005.
636
[26] Berry MP, Eberhard MO. Performance modeling strategies for modern reinforced
637
concrete bridge columns. PEER Report 2007/07 Pacific Earthquake Engineering Research
638
Center, College of Engineering, University of California, Berkeley, USA: 2007.
639
[27] Luco N, Cornell CA. Effects of random connection fractures on the demands and
640
reliability for a three-story pre-Northridge (SMRP) structure. Proc sixth US Natl. conf
641
Earthq. eng, Earthq. Eng. Res. Inst., Oakland, California: 1998.
642 643 644 645
[28] Vamvatsikos D, Cornell CA. Incremental dynamic analysis. Earthq Eng Struct Dyn 2002;31:491–514. doi:doi:10.1002/eqe.141. [29] Yun S, Hamburger RO, Cornell C, Foutch DA. Seismic performance evaluation for steel moment frames. J Struct Eng, ASCE 2002;128:534–45.
646
[30] Konstantinidis D, Nikfar F. Seismic response of sliding equipment and contents in base-
647
isolated buildings subjected to broad- band ground motions. Earthq Eng Struct Dyn
648
2015;44:865–87.
649 650
[31] ATC. Quantification of building seismic performance factors. Applied Technology Council, FEMA P695, FEMA, Washington, DC, USA: 2009.
651
[32] Kennedy RP, Ravindra MK. Seismic fragilities for nuclear power plant risk studies. Nucl
652
Eng Des an Int J Devoted to Therm Mech Struct Probl Nucl Energy 1984;79:47–68.
653
[33] Kim SH, Shinozuka M. Development of fragility curves of bridges retrofitted by column
654
jacketing. Probab Eng Mech 2004;19:105–12.
655
[34] Calvi GM, Pinho R, Magenes G, Bommer JJ, Restrepo-Vélez LF, Crowley H.
656
Development of seismic vulnerability assessment methodologies over the past 30 years.
657
ISET J Earthq Technol 2006;43:75–104.
29
658 659 660 661 662 663 664
[35] Villaverde R. Methods to assess the seismic collapse capacity of building structures: state of the art. J Struct Eng, ASCE 2007;133:57–66. [36] Porter K, Kennedy R, Bachman R. Creating fragility functions for performance-based earthquake engineering. Earthq Spectra 2007;23:471–89. [37] Shafei B, Zareian F, Lignos DG. A simplified method for collapse capacity assessment of moment-resisting frame and shear wall structural systems. Eng Struct 2011;33:1107–16. [38] Billah AHMM, Alam MS. Seismic fragility assessment of highway bridges: a state-of-the-
665
art review. Struct Infrastruct Eng 2015;11.
666
doi:https://doi.org/10.1080/15732479.2014.912243.
667 668 669 670
[39] Baker JW. Efficient analytical fragility function fitting using dynamic structural analysis. Earthq Spectra 2015;31:579–99. [40] ATC. Seismic performance assess- ment of buildings: Volume 1 —Methodology. Applied Technology Council, FEMA P-58-1 , FEMA, Washington, DC, USA: 2012.
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List of Figures
674
Figure 1 Specimen geometry and reinforcement detailing used in this study
675
Figure 2 Schematic of section discretization of a typical FRP-confined concrete element
676
Figure 3 Comparison of the force displacement relationship of the numerical and experimental
677
results (A) as-Built pier and (B) CFRP retrofitted pier
678
Figure 4 Results of pushover analysis considering different compressive strength of concrete
679
Figure 5 Results of pushover analysis considering different yield strength of reinforcement
680
Figure 6 Results of pushover analysis considering different longitudinal steel ratio
681
Figure 7 Results of Pushover analysis considering different axial load ratio
682
Figure 8 Results of pushover analysis considering different shear span-depth ratio
683
Figure 9 Results of pushover analysis considering different layer of FRP
684
Figure 10 A suit of 20 earthquake ground motion records (a) Response spectral acceleration (b)
685
percentile of response spectral acceleration of a suit of earthquake ground motion
686
records
687
Figure 11 Results of dynamic and static pushover curve for C-1-35
688
Figure 12 Dynamic and static pushover curve for C-1-20
689
Figure 13 Dynamic and static pushover curve for C-2-400
690
Figure 14 Results Dynamic and static pushover curve for C-2-250
691
Figure 15 Results of dynamic and static pushover curve for C-3-2.5
692
Figure 16 Results of dynamic and static pushover curve for C-3-1
693
Figure 17 Results of dynamic and static pushover curve for C-4-0.20
694
Figure 18 Results of dynamic and static pushover curve for C-4-0.10
695
Figure 19 Results of dynamic and static pushover curve for C-5-7
31
696
Figure 20 Results of dynamic and static pushover curve for C-5-4
697
Figure 21 Results of dynamic and static pushover curve for C-6-2
698
Figure 22 Results of dynamic and static pushover curve for C-6-3
699
Figure 23 IDA results used to identify IM values related with collapse of each ground motions of
700
all the bridge piers retrofitted with FRP
701
Figure 24 Linear regression models for the median and dispersion values from IDA results
702
Figure 25 Effect of concrete strength on collapse fragility
703
Figure 26 Effect of yield strength of longitudinal steel on collapse fragility
704
Figure 27 Effect of amount of longitudinal steel on collapse fragility
705
Figure 28 Effect of axial load on collapse fragility
706
Figure 29 Effect of shear span-depth ratio on collapse fragility
707
Figure 30 Effect of FRP confinement on collapse fragility
708
Figure 31 Collapse probability of the piers at four PGA, 0.5, g, 0.1.0g, 1.5g, and 2.0g
709
Figure 32 Difference between collapse probability of different parameters
710
Figure 33 Bar chart of median values of PGA for the piers with different parameters
711 712 713 714 715 716 717 718
32
719 720
Figure 1 Specimen geometry and reinforcement detailing used in this study
721 722 723 724 725 726 727 728 729 33
730
Deck mass
G
mm 2000 mm
734 735
1600 mm
N6
733
N5
N4
N3 N2
737
N6
Beam element
N5
FRP wraps fiber N4
Beam element
Confined core concrete fiber
N3
Fiber element N2
Zero length Spring element
400 mm
736
N7
N7
2 and 3 Layer of CFRP No FRP
260 mm
732
520 mm
731
400 mm
N1 N1
Reinforcement’s fiber Cover concrete fiber
1150 mm
738 739
(a) Pier schematic
(b) Pier model
(c) Fiber discretization
Figure 2 Schematic of section discretization of a typical FRP-confined concrete element
740 741 742 743 744 745 746 747 748 749 750 751 752
34
150
150
(a) As Built Pier
50 0 -50
-100 -150 -120
753
100 Lateral load (kN)
Lateral load (kN)
100
(b) 0.111mm-CFRP Wrapped Pier
Experimental Numerical -80 -40 0 40 80 Top lateral displacement (mm)
120
50 0 -50
-100 -150 -120
Experimental Numerical -80 -40 0 40 80 Top lateral displacement (mm)
120
754
Figure 3 Comparison of the force displacement relationship of the numerical and experimental
755
results (A) as-Built pier and (B) CFRP retrofitted Pier
756 757 758 759 760 761 762 763 764 765 766 767
35
100 f'c = 35 MPa
Base Shear (kN)
f'c = 20 MPa 75
Yielding Crushing Bucking Fracture
50
25
0 0 768 769
50
100 150 Top Displacement (mm)
200
Figure 4 Results of pushover analysis considering different compressive strength of concrete
770 771 772 773 774 775 776 777 778 779 780 781 782
36
100 fy = 400 Mpa Base Shear (kN)
fy = 250 Mpa 75
Yielding Crushing Bucking Fracture
50
25
0 0 783 784
50
100 150 Top Displacement (mm)
200
Figure 5 Results of pushover analysis considering different yield strength of reinforcement
785 786 787 788 789 790 791 792 793 794
37
795 796
Figure 6 Results of pushover analysis considering different longitudinal steel ratio
797 798 799 800 801 802 803 804 805 806 807 808 809 810
38
811 812
Figure 7 Results of Pushover analysis considering different axial load ratio
813 814 815 816 817 818 819 820 821 822 823 824
39
825 826
Figure 8 Results of pushover analysis considering different shear span-depth ratio
827 828 829 830 831 832 833 834 835 836 837 838
40
839 840
Figure 9 Results of pushover analysis considering different layer of FRP
841 842 843 844 845 846 847 848 849 850 851 852 853 854
41
EQ1 EQ4 EQ7 EQ10 EQ13 EQ16 EQ19
(a)
2.0
EQ2 EQ5 EQ8 EQ11 EQ14 EQ17 EQ20
EQ3 EQ6 EQ9 EQ12 EQ15 EQ18 Mean
1.5
(b)
75 Percentile 50 Percentile
2.0
25 Percentile
1.5
maxi. = 0.73g mini. = 0.22g
1.0
1.0
0.5
0.5
0.0
0.0 0
855
2.5 Spectral Acceleration (g)
Spectral Acceleration (g)
2.5
1
2 3 Period (sec)
4
0
1
2 Period (sec)
3
4
856
Figure 10 A suit of 20 earthquake ground motion records (a) Response spectral acceleration (b)
857
percentile of response spectral acceleration of a suit of earthquake ground motion records
858 859 860 861 862 863 864 865 866
42
160
Base Shear (kN)
C-1-35
Dynamic pushover points Static pushover curve
120
80
40
0 0 867 868
50
100 150 200 Top Displacement (mm)
250
300
Figure 11 Results of dynamic and static pushover curve for C-1-35
869 870 871 872 873 874 875 876 877 878 879 880
43
160
Base Shear (kN)
C-1-20
Dynamic pushover points Static pushover curve
120
80
40
0 0 881 882
50
100 150 200 Top Displacement (mm)
250
300
Figure 12 Dynamic and static pushover curve for C-1-20
883 884 885 886 887 888 889 890 891 892 893 894
44
Base Shear (kN)
160
C-2-400
Dynamic pushover points Static pushover curve
120
80
40
0 0 895 896
50
100 150 200 Top Displacement (mm)
250
300
Figure 13 Dynamic and static pushover curve for C-2-400
897 898 899 900 901 902 903 904 905 906 907 908
45
160
C-2-250
Dynamic pushover points
Base Shear (kN)
Static Pushover curve 120
80
40
0 0 909 910
50
100 150 200 Top Displacement (mm)
250
300
Figure 14 Results Dynamic and static pushover curve for C-2-250
911 912 913 914 915 916 917 918 919 920 921 922 923
46
125
C-3-2.5 Base Shear (kN)
100
Dynamic pushover points Static pushover curve
75 50 25 0 0
924 925
50
100 150 200 Top Displacement (mm)
250
300
Figure 15 Results of dynamic and static pushover curve for C-3-2.5
926 927 928 929 930 931 932 933 934 935 936 937
47
125
Dynamic pushover points
C-3-1
Static pushover curve
Base Shear (kN)
100 75 50 25 0 0 938 939
50
100 150 200 Top Displacement (mm)
250
300
Figure 16 Results of dynamic and static pushover curve for C-3-1
940 941 942 943 944 945 946 947 948 949 950 951 952 953
48
Base Shear (kN)
200
C-4-0.20 Dynamic pushover points Static pushover curve
150
100
50
0 0 954 955
50
100 150 200 Top Displacement (mm)
250
300
Figure 17 Results of dynamic and static pushover curve for C-4-0.20
956 957 958 959 960 961 962 963 964 965 966 967
49
200
Base Shear (kN)
C-4-0.10
Dynamic pushover points Static pushover curve
150
100
50
0 0 968 969
50
100 150 200 Top Displacement (mm)
250
300
Figure 18 Results of dynamic and static pushover curve for C-4-0.10
970 971 972 973 974 975 976 977 978 979 980 981
50
200 Dynamic pushover points
Base Shear (kN)
C-5-7
Static pushover curve
150
100
50
0 0 982 983
50
100 150 200 Top Displacement (mm)
250
300
Figure 19 Results of dynamic and static pushover curve for C-5-7
984 985 986 987 988 989 990 991 992 993 994 995
51
200 Dynamic pushover points
C-5-4 Base Shear (kN)
Static pushover curve 150
100
50
0 0 996 997
50
100 150 200 Top Displacement (mm)
250
300
Figure 20 Results of dynamic and static pushover curve for C-5-4
998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011
52
200 Dynamic pushover points
Base Shear (kN)
C-6-2
Static pushover curve
150
100
50
0 0 1012 1013
50
100 150 200 Top Displacement (mm)
250
300
Figure 21 Results of dynamic and static pushover curve for C-6-2
1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027
53
200 Dynamic pushover points
Base Shear (kN)
C-6-3
Static pushover curve
150
100
50
0 0 1028 1029
50
100 150 200 Top Displacement (mm)
250
300
Figure 22 Results of dynamic and static pushover curve for C-6-3
1030 1031 1032 1033 1034 1035 1036 1037
54
2.0
2.4
(a) C-1-35
2.0
1.6
1.6
1.2
PGA (g)
PGA (g)
(b) C-1-20
1.2
0.8
0.8 0.4
0.4
0.0
0.0 0
1038 2.0
4 8 12 16 Maximum Drift (%)
20
0
20
2.0
(c) C-2-400
(d) C-2-250
PGA (g)
1.6
PGA (g)
1.6 1.2
1.2
0.8
0.8
0.4
0.4
0.0
0.0 0
1039 3.0
3 6 9 12 Maximum Drift (%)
15
0 2.5
(e) C-3-2.5
2.5
4 8 12 16 Maximum Drift (%)
20
(f) C-3-1
2.0 PGA (g)
PGA (g)
2.0 1.5 1.0
1.5 1.0
0.5
0.5
0.0
0.0 0
1040
5 10 15 Maximum Drift (%)
4 8 12 16 Maximum Drift (%)
20
0
4 8 12 16 Maximum Drift (%)
20
55
3.0
3.0
(g) C-4-0.20
2.5
2.0
2.0
PGA (g)
PGA (g)
2.5
1.5
1.5 1.0
1.0
0.5
0.5
0.0
0.0 0
1041 3.0
4 8 12 16 Maximum Drift (%)
0
20 3.0
(i) C-5-7
2.5
2.5
2.0
2.0
5 10 15 Maximum Drift (%)
20
(j) Col-5-4
PGA (g)
PGA (g)
(h) C-4-0.10
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0 0
1042 3.0
4 8 12 16 Maximum Drift (%)
20
0 3.0
(k) C-6-2
2.5
2.0
2.0
20
(l) C-6-3
PGA (g)
PGA (g)
2.5
4 8 12 16 Maximum Drift (%)
1.5
1.5 1.0
1.0
0.5
0.5
0.0
0.0 0
4 8 12 16 Maximum Drift (%)
20
0
4 8 12 16 Maximum Drift (%)
20
1043 1044 1045
Figure 23 IDA results used to identify IM values related with collapse of each ground motions
1046
of all the bridge piers retrofitted with FRP 56
1.0
1.0
(a) C-1-35
0.5 ln (PGA)
ln (PGA)
0.5 0.0 -0.5 -1.0
-2
-1
1047 1.0
0 X
1
y = 0.4749x + 0.0871 R² = 0.9828 -2
2 1.0
(c) C-2-400
-1
0 X
1
2
(d) C-2-250
0.5 ln (PGA)
ln (PGA)
-0.5
-1.5
0.5 0.0 -0.5 -1.0
-2
-1
1048 1.5
0 X
1
0.0 -0.5 -1.0
y = 0.5335x - 0.3364 R² = 0.9744
-1.5
y = 0.4939x - 0.1327 R² = 0.976
-1.5 -2
2 1.0
(e) C-3-2.5
1.0
-1
0 X
1
2
(f) C-3-1
0.5
0.5
ln (PGA)
ln (PGA)
0.0
-1.0
y = 0.551x - 0.3244 R² = 0.9746
-1.5
0.0 -0.5 -1.0
-2
-1
0 X
1
0.0 -0.5 -1.0
y = 0.4181x + 0.2038 R² = 0.965
-1.5 1049
(b) C-1-20
y = 0.5426x - 0.2411 R² = 0.9852
-1.5 2
-2
-1
0 X
1
2
57
1.0
1.5
(g) C-4-0.20
1.0 ln (PGA)
ln (PGA)
0.5 0.0 -0.5
0.0
-1.0
y = 0.4731x - 0.1056 R² = 0.9756
-1.5 -2
-1
1050 1.5
0 X
1
y = 0.3797x + 0.2686 R² = 0.9807
-1.5 2
-2 1.5
(i) C-5-7
1.0
1.0
0.5
0.5
ln (PGA)
ln (PGA)
0.5
-0.5
-1.0
0.0 -0.5
-1
0 X
1
2
(j) C-5-4
0.0 -0.5
-1.0
-1.0
y = 0.4454x + 0.2098 R² = 0.9829
-1.5 -2 1051
(h) C-4-0.10
-1
0 X
1
y = 0.4184x + 0.1491 R² = 0.9476
-1.5 2
-2
-1
0 X
1
2
58
1.5
(k) C-6-2
1.0
1.0
0.5
0.5
ln (PGA)
ln (PGA)
1.5
0.0 -0.5
0.0 -0.5
-1.0
y = 0.537x - 0.2835 R² = 0.9535
-1.5 -2
1052 1053
(l) C-6-3
-1.0 -1.5
y = 0.4949x - 0.2058 R² = 0.9401
-1
0 1 2 -2 -1 0 1 2 X X Figure 24 Linear regression models for the median and dispersion values from IDA results
1054
Probabilitty of Collapse
1.0 0.8
f'c = 20 MPa f'c = 35 MPa
0.6 SCT
0.4 0.2 0.0 0.0
1055 1056
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 25 Effect of concrete strength on collapse fragility
1057 1058 1059 1060 1061 59
1062 1063
Probabilitty of Collapse
1.0 0.8
fy = 250 MPa fy = 400 MPa
0.6 SCT
0.4 0.2 0.0 0.0
1064 1065
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 26 Effect of yield strength of longitudinal steel on collapse fragility
1066 1067 1068 1069 1070 1071 1072
60
Probabilitty of Collapse
1.0 0.8
ρl = 2.5 % ρl = 1 %
0.6 SCT
0.4 0.2 0.0 0.0
1073 1074
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 27 Effect of amount of longitudinal steel on collapse fragility
1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087
61
Probabilitty of Collapse
1.0 0.8
P = 20 % P = 10 %
0.6 SCT
0.4 0.2 0.0 0.0
1088 1089
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 28 Effect of axial load on collapse fragility
1090 1091 1092 1093 1094 1095 1096
62
Probabilitty of Collapse
1.0 0.8
l/d = 7 l/d = 4
0.6 SCT
0.4 0.2 0.0 0.0
1097 1098
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 29 Effect of shear span-depth ratio on collapse fragility
1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109
63
Probabilitty of Collapse
1.0 0.8
n=2 n=3
0.6 SCT
0.4 0.2 0.0 0.0
1110 1111
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 30 Effect of FRP confinement on collapse fragility
1112 1113 1114 1115 1116 1117 1118
64
Probability of Collpase (%)
1.2
0.5g
1.0g
1.5g
2.0g
1.0 0.8 0.6 0.4 0.2
1119 1120
C-6-3
C-6-2
C-5-4
C-5-7
C-4-0.10
C-4-0.20
C-3-1
C-3-2.5
C-2-250
C-2-400
C-1-20
C-1-35
0.0
Pier-ID Variables Figure 31 Collapse probability of the piers at four PGA, 0.5, g, 0.1.0g, 1.5g, and 2.0g
1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
65
Probability Difference, ∆ (%)
100
f'c
fy
ρl
P
l/d
n
60 20 -20 -60
-100 0.5 1132 1133
1.0 1.5 Peak Ground Acceleration (g)
2.0
Figure 32 Difference between collapse probability of different parameters
1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147
66
1.6
Median Values of PGA at collapse 1.31 1.23
PGA (g)
1.23 1.16
1.10
1.2
0.90
0.8
0.79
0.71
0.72
0.76
0.82
0.62
1148 1149
C-6-3
C-6-2
C-5-4
C-5-7
C-4-0.10
C-4-0.20
C-3-1
C-3-2.5
C-2-250
C-2-400
C-1-20
0.0
C-1-35
0.4
Pier-ID Figure 33 Bar chart of median values of PGA for the piers with different parameters
1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163
67
1164
List of Tables
1165
Table 1 Details of variable parameters considered in this study
1166
Table 2 Details of FRP retrofitted bridge piers
1167
Table 3 Base shear and displacement at different limit states
1168
Table 4 Characteristic of ground motion records used in IDA [31]
1169
Table 5 Median and dispersion values from the results of IDA using regression analysis
1170
Table 6 Collapse probability of different variables at PGAs of 0.5, 1.0, 1.5 and 2.0g
1171
Table 7 Median values of PGA for piers with different parameters
1172
Table 8 Collapse margin ratio (CMR) for collapse safety of piers
1173
Table A1 Failure drift of piers based on IDA results
1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186
68
1187
Table 1 Details of variable parameters considered in this study Modeling factors/parameters Code Values Units ' A 20 35 (MPa) Compressive strength of concrete, ( f c ) Yield strength of steel, (fy) B 250 400 (MPa) Longitudinal steel reinforcement ratio, (ρl) C 1 2.5 (%) Axial load, (P) D 10 20 (%) Shear span-depth ratio, (l/d) E 4 7 -FRP confinement layer, (n) F 2 3 No.
1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 69
Table 2 Details of FRP retrofitted bridge piers
1207
f c'
fy ρl P= ' /A fc g (MPa) (MPa) (%) Compressive C-1-35 35 400 2.5 0.20 ' strength, f c C-1-20 20 400 2.5 0.20 C-2-400 35 400 1 0.20 Yield strength, fy C-2-250 35 250 1 0.20 C-3-2.5 35 400 2.5 0.10 Longitudinal reinforcement, ρl C-3-1 35 400 1 0.10 C-4-0.20 35 400 2.5 0.20 Axial load, P C-4-0.10 35 400 2.5 0.10 C-5-7 35 400 2.5 0.10 Shear span-depth ratio, l/d C-5-4 35 400 2.5 0.10 35 250 2.5 0.20 FRP confinement C-6-2 layer, n C-6-3 35 250 2.5 0.20 Variable
Pier-ID
l/d 2800/400 2800/400 2800/400 2800/400 2800/400 2800/400 1600/400 1600/400 2800/400 1600/400 1600/400 1600/400
n (No.) 3 3 3 3 3 3 3 3 2 2 2 3
1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221
70
Table 3 Base shear and displacement at different limit states
1222
Variable
Pier-ID
Compressive strength
C-1-35 C-1-20 C-2-400 C-2-250 C-3-2.5 C-3-1 C-4-0.20 C-4-0.10 C-5-7 C-5-4 C-6-2
Yield strength Longitudinal reinforcement Axial load Shear spandepth ratio FRP confinement layer
C-6-3
Yielding Base Disp. shear (mm) (kN) 28 63.15 28 55.26 28 63.09 20 47.74 28 58.08 24 31.99 12 133.74 8 94.52 28 56.77 12 119.87 8 97.16 8
97.17
Crushing Base Disp. shear (mm) (kN) 52 74.50 56 68.78 52 74.62 44 54.26 56 71.11 64 36.47 20 138.94 20 129.08 56 69.15 20 124.20 16 107.44 16
105.69
Bucking Base Disp. shear (mm) (kN) 172 60.02 180 63.60 176 57.55 164 40.23 168 66.99 152 29.58 56 138.63 56 133.78 172 65.41 56 131.22 56 102.62 56
103.17
Fracture Base Disp. shear (mm) (kN) 176 59.56 184 63.38 176 57.55 168 38.92 172 66.88 156 29.35 60 138.50 56 133.78 176 65.28 60 131.68 56 102.62 56
103.17
1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 71
Table 4 Characteristic of ground motion records used in IDA [31]
1237
EQ No. Mw Year Earthquake Name 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6.7 7.3 6.7 7.3 7.1 6.9 7.1 6.9 6.5 7.4 6.5 6.5 6.9 6.5 6.9 7.0 7.5 7.6 7.5 7.6
1994 1992 1994 1992 1999 1989 1999 1989 1979 1990 1979 1987 1995 1987 1995 1992 1999 1999 1999 1999
Northridge Landers Northridge Landers Duzce, Turkey Loma Prieta Hector Mine Loma Prieta Imperial Valley Manjil, Iran Imperial Valley Superstition Hills Kobe, Japan Superstition Hills Kobe, Japan Cape Mendocino Kocaeli, Turkey Chi-Chi, Taiwan Kocaeli, Turkey Chi-Chi, Taiwan
Earthquake Recording R PGAmax PGV (cm/s) Station (km) (g) Beverly Hills - Mulhol 13.3 0.42 58.95 Yermo Fire Station 86.0 0.24 52.00 Canyon Country-WLC 26.5 0.41 42.97 Coolwater 82.1 0.28 26.00 Bolu 41.3 0.73 56.44 Capitola 9.80 0.53 35.00 Hector 26.5 0.27 28.56 Gilroy Array #3 31.4 0.56 36.00 Delta 33.7 0.24 26.00 Abbar 40.4 0.51 43.00 El Centro Array #11 29.4 0.36 34.44 El Centro Imp. Co. 35.8 0.36 46.00 Nishi-Akashi 8.70 0.51 37.28 Poe Road (temp) 11.2 0.45 36.00 Shin-Osaka 46.0 0.24 38.00 Rio Dell Overpass 22.7 0.39 44.00 Duzce 98.2 0.31 59.00 CHY101 32.0 0.35 71.00 Arcelik 53.7 0.22 17.69 TCU045 77.5 0.47 37.00
1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248
72
1249
Table 5 Median and dispersion values from the results of IDA using regression analysis Variable Compressive strength
Pier-ID Median (θ) Dispersion (β) C-1-35 -0.32 0.55 C-1-20 0.09 0.47 C-2-400 0.20 0.42 Yield strength C-2-250 -0.24 0.54 C-3-2.5 -0.11 0.47 Longitudinal reinforcement C-3-1 -0.21 0.49 C-4-0.20 0.27 0.38 Axial load C-4-0.10 -0.34 0.53 -0.48 0.59 Shear span-depth C-5-7 ratio C-5-4 0.21 0.45 -0.28 0.54 FRP confinement C-6-2 layer C-6-3 0.15 0.42
R2 0.97 0.98 0.97 0.99 0.98 0.94 0.98 0.97 0.99 0.98 0.95 0.95
1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 73
1266
Table 6 Collapse probability of different variables at PGAs of 0.5, 1.0, 1.5 and 2.0g 0.5g Pc ∆ (%) C-1-35 0.25 Compressive strength C-1-20 0.05 -74.8 C-2-400 0.02 Yield strength C-2-250 0.20 79.8 C-3-2.5 0.11 Longitudinal reinforcement C-3-1 0.16 83.8 C-4-0.20 0.01 Axial load C-4-0.10 0.25 -74.8 0.36 Shear span-depth C-5-7 ratio C-5-4 0.02 64.2 0.22 FRP confinement C-6-2 layer C-6-3 0.02 -77.7 Variable
1267 1268 1269
Pier-ID
1.0g Pc ∆ (%) 0.72 0.43 -27.8 0.31 0.67 32.8 0.59 0.66 33.9 0.24 0.74 -26.4 0.79 0.32 21.0 0.70 0.36 -29.9
1.5g Pc ∆ (%) 0.91 0.75 -9.3 0.69 0.88 11.7 0.86 0.89 10.8 0.64 0.92 -8.2 0.93 0.67 6.8 0.90 0.73 -10.0
2.0g Pc ∆ (%) 0.97 0.90 -3.2 0.88 0.96 4.3 0.95 0.97 3.5 0.87 0.97 -2.7 0.98 0.86 2.4 0.97 0.90 -3.4
Pc: probability of collapse, (- negative sign indicates the reduction in the probability of damage) ∆: relative difference between collapse probabilities of different parameters
1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282
74
1283
Table 7 Median values of PGA for piers with different parameters Variable Compressive strength
Pier-ID C-1-35 C-1-20 C-2-400 Yield strength C-2-250 C-3-2.5 Longitudinal reinforcement C-3-1 C-4-0.20 Axial load C-4-0.10 Shear span-depth C-5-7 ratio C-5-4 FRP confinement C-6-2 layer C-6-3 1284 1285 1286
Pc ∆ 0.72g 1.10g -10 0.71g 0.62g 29 1.23g 0.79g 23 0.90g 1.31g 31 1.23g 1.16g 23 0.76g 0.82g -18
Pc: probability of collapse, ∆: relative difference between collapse probabilities of different parameters
1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 75
1301
Table 8 Collapse margin ratio (CMR) for collapse safety of piers Probability of Exceedance of collapse 10% in 50 years 5% in 50 years 2% in 50 years Compressive C-1-35 3.89 2.81 1.98 strength C-1-20 5.95 4.30 3.03 C-2-400 3.84 2.77 1.96 Yield strength C-2-250 3.35 2.42 1.71 Longitudinal C-3-2.5 6.65 4.80 3.39 reinforcement C-3-1 4.27 3.09 2.18 C-4-0.20 4.86 3.52 2.48 Axial load C-4-0.10 7.08 5.12 3.61 Shear span-depth C-5-7 6.65 4.80 3.39 ratio C-5-4 6.27 4.53 3.20 FRP confinement C-6-2 4.08 2.95 2.08 layer C-6-3 4.43 3.20 2.26 Variable
Pier-ID
1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318
76
1319
Appendix A Table A1 Failure drift of piers based on IDA results
1320 Variables Ground Motion
Northridge Landers Northridge Landers Duzce, Turkey Loma Prieta Hector Mine Loma Prieta Imperial Valley Manjil, Iran Imperial Valley Superstition Hills Kobe, Japan Superstition Hills Kobe, Japan Cape Mendocino Kocaeli, Turkey Chi-Chi, Taiwan Kocaeli, Turkey Chi-Chi, Taiwan
1321 1322
PGA (g) 0.46 0.26 0.86 0.98 0.88 0.58 0.76 2.02 0.53 1.17 0.68 0.68 1.22 1.17 0.46 0.43 0.47 0.39 0.86 1.27
Compressive strength Drift PGA Drift (%) (g) (%) 9.25 1.80 13.92 6.84 0.48 8.67 10.07 1.23 13.98 10.48 1.12 6.67 9.27 1.31 11.09 7.58 0.95 13.92 10.48 1.03 14.38 7.28 2.24 12.67 6.89 0.91 11.62 10.47 1.53 14.12 13.57 1.01 11.67 10.51 1.22 18.84 9.78 2.04 10.73 8.42 1.80 11.21 8.61 0.62 12.22 7.56 0.70 15.37 11.48 0.68 10.55 5.22 0.70 9.50 4.16 0.88 3.07 17.00 1.69 16.41
PGA (g) 0.50 0.26 0.86 1.12 0.95 0.58 0.72 1.57 0.56 0.97 0.63 0.68 1.28 1.19 0.46 0.39 0.45 0.40 1.11 1.18
Yield strength Drift PGA (%) (g) 10.71 0.42 7.37 0.22 12.46 0.66 10.80 0.70 10.26 0.95 7.70 0.69 7.16 0.63 4.80 1.90 8.41 0.46 6.44 0.87 8.60 0.52 10.76 0.58 10.77 1.05 9.73 1.06 8.80 0.42 6.23 0.35 11.18 0.36 7.75 0.32 6.15 1.31 11.21 0.75
Drift (%) 8.81 7.36 8.31 5.87 9.95 6.38 7.29 6.71 7.31 8.49 20.50 9.56 7.97 14.46 7.81 6.49 7.83 8.25 10.54 4.11
Reinforcement ratio PGA Drift PGA Drift (g) (%) (g) (%) 0.99 10.03 0.55 11.49 0.60 5.95 0.35 9.71 1.52 9.84 0.84 10.78 1.18 3.83 0.87 11.01 1.83 9.71 0.95 10.40 1.25 9.15 0.77 9.38 1.27 8.53 0.80 9.26 2.63 8.53 1.82 5.71 0.96 4.63 0.58 9.84 1.94 9.53 1.22 11.64 1.30 7.31 0.65 9.61 0.94 7.85 0.72 11.87 2.04 6.72 2.04 13.92 2.07 6.82 1.19 10.34 0.86 9.21 0.49 9.61 0.80 8.38 0.45 7.48 0.93 8.04 0.50 12.61 0.88 7.11 0.42 10.55 1.10 1.86 1.32 9.48 1.25 3.66 1.13 8.69
Table A1 Cont. Variables Ground Motion
Northridge Landers Northridge Landers Duzce, Turkey Loma Prieta Hector Mine Loma Prieta Imperial Valley Manjil, Iran Imperial Valley Superstition Hills Kobe, Japan Superstition Hills Kobe, Japan Cape Mendocino Kocaeli, Turkey Chi-Chi, Taiwan Kocaeli, Turkey Chi-Chi, Taiwan
Axial load PGA (g) 0.55 0.42 0.59 1.12 1.17 0.93 0.76 2.41 0.89 1.50 1.12 0.63 1.35 1.26 0.64 0.51 0.73 0.82 1.31 1.25
Drift (%) 13.27 7.27 8.55 10.95 10.81 10.01 10.98 13.78 10.59 11.74 9.93 10.68 12.84 10.27 9.80 7.46 10.18 9.90 5.83 11.95
PGA (g) 0.92 0.71 0.96 1.46 1.93 1.40 1.32 2.49 1.18 1.89 1.66 1.06 1.81 1.67 0.71 0.98 1.10 1.19 1.31 1.88
Shear span-depth ratio Drift (%) 19.01 7.41 8.47 9.88 9.56 10.78 10.38 9.75 9.89 14.02 8.71 8.49 13.69 11.63 9.86 10.23 8.61 9.64 3.27 11.54
PGA (g) 0.92 0.60 1.46 1.50 1.72 1.17 1.20 1.65 1.14 2.04 1.33 0.90 2.58 2.27 0.85 0.62 0.87 0.88 1.38 1.53
Drift (%) 15.76 13.28 16.21 9.17 15.58 12.47 13.63 8.16 14.17 15.62 13.65 13.04 16.45 13.89 14.39 8.56 12.28 13.73 4.03 8.01
PGA (g) 0.86 0.71 0.84 1.33 0.80 1.40 1.30 2.91 1.15 0.97 1.67 1.06 0.92 1.60 0.67 0.98 1.01 0.93 2.20 1.74
Drift (%) 15.02 7.42 7.19 8.69 3.22 10.67 10.33 10.93 9.49 3.88 9.59 9.05 4.58 11.63 10.13 12.13 8.07 4.11 9.86 10.02
CFRP layers PGA (g) 0.55 0.38 0.53 1.01 0.95 0.42 0.76 2.49 0.71 1.05 0.85 0.58 1.20 1.40 0.56 0.47 0.37 0.56 1.18 1.03
Drift (%) 13.38 10.31 8.07 11.18 10.86 3.29 12.07 13.36 13.25 6.72 10.50 10.24 12.70 13.83 10.07 8.85 3.41 7.38 4.06 9.08
PGA (g) 0.74 0.38 0.66 1.04 1.06 0.48 0.54 2.69 0.71 1.05 0.85 0.58 1.20 1.40 0.71 0.51 0.64 0.61 1.24 1.10
Drift (%) 13.18 10.14 11.52 11.62 12.92 3.86 6.18 14.92 10.47 6.53 10.23 10.14 12.42 11.83 13.68 10.05 11.41 11.43 4.55 10.72
1323 77
S0263-8223(16)31632-4 http://dx.doi.org/10.1016/j.compstruct.2016.10.094 COST 7920
To appear in:
Composite Structures
Received Date: Accepted Date:
22 August 2016 21 October 2016
Please cite this article as: Parghi, A., Shahria Alam, M., Seismic collapse assessment of non-seismically designed circular RC bridge piers retrofitted with FRP composites, Composite Structures (2016), doi: http://dx.doi.org/ 10.1016/j.compstruct.2016.10.094
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1
Seismic collapse assessment of non-seismically designed circular RC bridge piers retrofitted
2
with FRP composites
3
Anant Parghi1 and M. Shahria Alam
4
School of Engineering, The University of British Columbia, Kelowna, V1V 1V7 - BC, Canada
5
Abstract
6
The seismic vulnerability of bridge pier is generally expressed in terms of the fragility curves,
7
which reveals the conditional probability that the structural demand due to different levels of
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earthquake intensities exceeding the structural capacity at particular damage state. This research
9
represents results of fragility curve development of typical single circular reinforced concrete
10
(RC) bridge pier. The different parameters are considered in the analysis which includes the
11
strength of concrete, yield strength and amount of longitudinal steel rebar, level of axial load and
12
shear span-depth ratio, and carbon fiber reinforced polymer confinement layer. Nonlinear static
13
pushover analysis (NSPA), and incremental dynamic analysis is conducted using suits of
14
earthquake ground motions with scaled peak ground acceleration (PGA) to investigate the
15
nonlinear dynamic behavior of the retrofitted piers. The impact of various parameters is
16
evaluated under probability point of view in terms of its influence on the bridge pier fragility
17
curve. Considering collapse drift as demand parameters, fragility curves were generated with
18
different parameters of non-seismically designed RC circular bridge piers. It was observed that
19
the amount of reinforcement, shear span-depth ratio, and level of the axial load could
20
significantly affect the collapse fragility curve of the retrofitted bridge piers.
21
Keywords: Fiber reinforced polymer; bridge piers; fragility curve; confinement ratio; nonlinear
22
analyses; collapse assessment 1
Corresponding Author, Email: [email protected] Tel: +1.250.807.9397, Fax: +1.250.807.9850
1
23
1. Introduction
24
Bridges are considered as an important element in highway networks, since they play a critical
25
role in the development of country’s economic activity. The bridges can connect cities and
26
countries by providing links, render smooth, and quick transportation. In the early development
27
of country, measures were adopted to improve transportation safety, accessibility, and economic
28
efficiency. Conversely, large numbers of existing reinforced concrete (RC) highway bridges in
29
North America were built when the seismic design guidelines were at an early stage of
30
development. Moreover, earthquake hazard levels have been recently increased throughout the
31
globe, which might affect the seismic performance of existing highway bridges. On one hand,
32
truck loads have increased significantly over the years; and the other hand, bridges are restricted
33
to their load capacity. Therefore, these structures cannot allow heavier trucks/traffic volume
34
without proper strengthening. One option is replacing a deficient structure with a new once;
35
while new construction is normally expensive, time consuming and even impractical. For
36
instance, for the stoppage of an obsolete but a critical bridge in a busy highway system, the
37
replacement of bridge could cause many difficulties. Accordingly, the other alternative of
38
strengthening the bridge structures based on the current codes becomes the only possibility under
39
certain conditions. For example, strengthening beams and piers is essential to provide much
40
desirable load carrying capacity.
41
Various rehabilitation methods are available to upgrade the structural performance of
42
existing sub-standard bridges. The sub-standard bridge pier can be defined as the bridge piers,
43
which are constructed with inadequate lateral ties and longitudinal spliced length reinforcement.
44
In the past three decades, concrete and steel plate jacketing has been frequently used for the
45
structural strengthening of deficient structures. In such a way, significant improvement in the
2
46
ultimate flexural strength and ductility could be achieved. However, these techniques have many
47
problems associated with their use. For example, in the case of concrete jacketing, it is labor
48
intensive, time consuming, shrinkage and bonding problem to the substrate concrete. Another
49
main drawback is the reduction of available floor-space, since jacketing enriches the cross-
50
section dimension, which leads to a substantial mass increase, stiffness modification, and
51
consequently modification of the dynamic characteristics of the entire structure. The steel plate
52
jacketing needs specialized heavy equipment at the work site. Moreover, high cost and likelihood
53
of steel corrosion at the interface of steel and concrete resulting in the bond deterioration are
54
considered as problems. Other disadvantages are the difficulty in manipulating heavy steel plates
55
in tight construction site, needs scaffolding, and limitation in available plate lengths (which
56
required in the case of flexural strengthening of long girders) resulting in the necessity for the
57
joints.
58
The rapid deterioration of bridge infrastructure and limited funding for maintenance have
59
promoted the use of advanced fiber reinforced polymer (FRP) composites as sustainable repair
60
and strengthening materials. For the last two decades, a significant research has been focused on
61
the application of FRP for the rehabilitation of RC buildings and bridges. Numerous researchers
62
have considered FRP as an external reinforcement to upgrade the seismic resistance of the RC
63
piers [1], [2], [3], [4]. FRP sheets/strips have been used as retrofitting and rehabilitation materials
64
due to their exceptional engineering properties, such as, high strength-to-weight ratio, high
65
stiffness with excellent corrosion resistance, low density, long fatigue life. Therefore, they can
66
offer a great potential for cost-effective retrofitting method for the concrete structures [5].
67
There are several studies, which attempted to explore the feasibility of FRP confinement
68
techniques for the seismic retrofit of concrete piers. Some of these studies Elsanadedy and
3
69
Haroun [2], Saadatmanesh et a. [6], Xiao and Ma [7], Chang et al. [8], Han et al. [9] investigated
70
the lateral load carrying capacity of RC pier after applying FRP confinement technique. The
71
results of these studies have demonstrated that the shear failure could be prevented and
72
significant improvement could be obtained in the ductility of the retrofitted piers. Saadatmanesh
73
et a. [6] conducted an experimental investigation on the seismic behavior of on 1/5-scaled RC
74
pier strengthened with glass fiber reinforced polymer (GFRP) straps. The results showed that the
75
seismic resistance of retrofitted piers improves significantly and the longitudinal reinforcement
76
are prevented from buckling under lateral cyclic loading. Chang et al. [8] performed pseudo-
77
dynamic tests on the as-built and carbon fiber reinforced polymer (CFRP) strengthened
78
rectangular RC bridge piers under near-fault ground motions. They found that the seismic
79
performance of damaged concrete bridge piers could be effectively improved after retrofitting by
80
CFRP. Elsanadedy and Haroun [2] conducted tests on the as-built and FRP composite-wrapped
81
scaled models of circular and square RC piers with inadequate lap-spliced length under
82
simulated seismic loading. The results demonstrated that the as-built pier suffers from the brittle
83
failure due to the bond deterioration of the lap-spliced of longitudinal reinforcement. The circular
84
retrofitted piers improved ductility and enhanced seismic performance, while the ductility
85
improvement for the square retrofitted pier is limited compared to the as-built pier. Han et al. [9]
86
studied the seismic behavior of hollow rectangular bridge piers retrofitted with carbon FRP. The
87
results reported that failure modes and damage regions would be changed, and the ductility and
88
dissipated energy of the retrofitted piers could improve greatly; however, the lateral load
89
capacity did not improve comparatively. Xiao and Ma [7] studied as-built and glass FRP
90
composite-wrapped ½-scaled models of circular bridge piers with poor lap splice detailing. They
91
reported that the as-built model pier exhibited brittle failure due to bond deterioration of the lap-
4
92
spliced longitudinal reinforcement. The brittle failure was prevented in the repaired and
93
retrofitted piers, and dramatic improvement was observed in the ductility and energy dissipation
94
capacity of piers.
95
In this paper, the seismic vulnerability assessment of non-seismically designed RC bridge
96
piers retrofitted with FRP jacketing is conducted. A finite element model of retrofitted and
97
unretrofitted circular RC bridge piers are first validated with experimental results and then,
98
nonlinear analyses are conducted. The structural response of the retrofitted bridge piers under
99
severe seismic events are considerably different compared to regular bridge pier. The paper
100
focuses on quantifying the inelastic demand and capacities of FRP retrofitted non-seismically
101
designed circular RC bridge piers using nonlinear static pushover analyses (NSPA), and
102
incremental dynamic analyses (IDA). The behavior and response of the FRP retrofitted piers are
103
investigated using nonlinear analyses by a fiber element model with suitable cyclic constitutive
104
laws of FRP-confined concrete. IDA is conducted with finite element numerical models of the
105
FRP retrofitted piers to a family of 20 earthquake ground motions scaled with different intensity
106
measures (IM). With respect to IM, such as peak ground acceleration (PGA), the maximum
107
responses in terms of governing engineering demand parameters (EDP), such as the maximum
108
drift or deformation, and ductility demand of the structure are estimated to compare
109
performances of retrofitted bridge piers. The results of this study will be useful for the decision
110
makers for developing strategies and practices to improve currently used bridge management
111
systems.
112
2. Design and Geometry of Bridge Pier
113
This section briefly explains the design and configuration of different RC bridge piers. The RC
114
circular bridge piers are assumed to be located in Vancouver, BC, Canada and is non-seismically
5
115
designed without consideration of the current seismic design guidelines. The diameter of piers is
116
fixed to be 400 mm in all the piers. Several parameters affect the design and behavior of the
117
bridge piers. The important variables of this parametric study are selected as the compressive
118
strength of concrete, f c' , the yield strength, fy, and amount of longitudinal reinforcement, ρl, FRP
119
confinement layers, n, axial load, P, and shear span-depth ratio, l/d. Table 1 lists the factors and
120
associated values considered in this article. These parameters are selected based on literature
121
[10], [11], [12]. For each parameter, two different values (levels) are considered.
122
Table 2 shows a summary of the FRP retrofitted piers analyzed in this article. A total of 12
123
non-seismically RC circular bridge piers are designed in order to study the effect of different
124
parameters on the seismic vulnerability of FRP retrofitted piers. One parameter at a time is
125
varied and the others are kept constant. As reported by Parghi and Alam [13], the interaction of
126
parameters has an insignificant effect on the response, and therefore, they are not considered in
127
this article. The diameter and number of longitudinal bars change for different rebar percentages.
128
6mm circular stirrups are used at 250 mm spacing as the lateral reinforcement in all of the piers.
129
Figure 1 displays the geometry and reinforcement detailing of the RC pier. In order to ensure that
130
the dominant failure mode will be a flexural failure (i.e. avoiding shear failure), and two different
131
aspect ratios (4 and 7) are considered.
132
3. Numerical Investigation of Bridge Piers
133
3.1 Bridge pier model
134
The finite element model of the bridge pier is approximated as a continuous 2-D finite element
135
frame using the nonlinear analysis program SeismoStruct [14]. Figure 2(a) and Figure 2(b) show
136
a typical FRP retrofitted pier and a three-dimensional (3-D) model, respectively. In order to
137
consider material nonlinearity, 3-D inelastic displacement-based frame elements has been used
138
for modeling the piers. To generate the hysteretic relationship for the circular piers, fiber-based 6
139
model is employed. By specifying cross-section pieces along the height of the element, the
140
distribution of inelastic deformation and forces are determined. In addition to the fiber elements,
141
to capture bond-slip rotations at the pier-footing interface, a nonlinear rotational spring element
142
is used in the model. The rotational spring element is defined with a zero-length element in
143
SeismoStruct [14]. A rotational spring at the bottom of the pier indicates the longitudinal
144
reinforcement pullout from the footing. Its properties was used from Gallardo-Zafra and
145
Kawashima [15]. Figure 2(c) characterizes the pier fiber and its sub-section, which is divided
146
into cover concrete, core concrete and steel reinforcement. At the numerical integration points,
147
each element is characterized by numerous cross-sections where each section is sub-divided into
148
a number of fiber under uniaxial state of stress. For concrete compressive strength of 35 MPa,
149
the nonlinear variable confinement model proposed by Madas and Elnashai [16], which follows
150
the constitutive relationship presented by Mander et al. [17], and the cyclic rules proposed by
151
Martinez-Rueda and Elnashai [18] is model implemented in the analyses. For the FRP confined
152
concrete, Ferracuti and Savoia [19] model, which follows the constitutive relationship and cyclic
153
rules proposed by Mander et al. [17], and Yankelevsky and Reinhardt [20] under compression
154
and tension, respectively is used. This model employs Spoelstra and Monti’s [21] model for the
155
confining effect of FRP jacket. For the FRP materials, linear elastic behavior up to the rupture
156
with zero compressive strength is considered. Menegotto and Pinto [22] steel model with
157
Filippou et al. [23] isotropic strain hardening property is adopted as the constitutive model of
158
rebar to develop the analytical model. When the pier is jacketed by FRP sheets, the cover
159
concrete is considered as the concrete confined by the FRP jacket, while the core concrete is
160
considered as the concrete confined by FRP and the transverse reinforcements.
7
161
3.2 Model calibration with experimental results
162
In order to calibrate the numerical models, the circular RC pier experimentally studies by
163
Kawashima et al. [24] is adopted in this research. The pier specimen has a diameter of 400 mm,
164
and an effective height of 1350 mm. The pier is reinforced with 12-15M steel (dia. of 16 mm)
165
longitudinal reinforcement ratio of 1.89, and 0.128% transverse steel (dia. of 6 mm), with 300
166
mm center to center spacing, and the clear cover of concrete of 35 mm. The confined region,
167
where carbon fiber reinforced polymer (CFRP) jackets are applied from the base of the pier, has
168
a height of 1000 mm. An axial compressive load of 188.4 kN representing 5% of the axial
169
capacity is applied at the top of the pier. The pier is free on top and flexural dominated in the
170
reversed cyclic load test. The specified compressive strength of the unconfined concrete, the
171
yield strength of longitudinal and transverse reinforcements is considered as 35, 374, and 363
172
MPa, respectively. The CFRP retrofitting technique adopted in this paper is adapted from
173
Kawashima et al. [24]. The CFRP composites have an initial stiffness, and an ultimate strain of
174
266 GPa and 1.63%, respectively.
175
Figure 3(a) and Figure 3(b) demonstrate the hysteretic behavior of as-built and CFRP
176
retrofitted piers, respectively. In order to validate the numerical model, the CFRP retrofitted pier
177
is modelled and analyzed using a finite element program SeismoStruct [14] under the
178
displacement-controlled reversed cyclic loading history same as the experimental test [24]. The
179
RC cantilever pier is displaced with an increment of 0.5% drift until reaching a maximum drift of
180
5%. The numerical model of pier, retrofitted with a single layer of CFRP sheet representing the
181
volumetric confinement ratio of 0.11%, is validated with the experimental results [24] . As
182
shows in Figure 3(a) and Figure 3(b), the numerical model can capture the experimental response
183
[24] in terms of initial and post elastic stiffness, and the ultimate load capacity with a good
8
184
accuracy. Compared to the experimental results, the stiffness and capacity, respectively varies by
185
3.5 and 3%.
186
4. Nonlinear Static Pushover Analysis and the Flexural Limit States
187
According to the performance-based design guidelines, structures are designed based on a
188
damage limit state at which the loss of life is prohibited. However, the structure would be out of
189
service for a certain time, which could withstand extensive structural and non-structural
190
damages. The performance of the bridge pier can be quantified in terms of limit states with
191
corresponding strain limits. In order to study the effect of different parameters of retrofitted
192
circular bridge piers, four performance criteria have been considered: the displacements (∆) and
193
base shear (V) at the onset of first yielding of longitudinal steel (∆y, Vy), first crushing of core
194
concrete (∆crush, Vcrush), first buckling of longitudinal steel (∆buck, Vbuck) and first fracture of
195
longitudinal steel (∆fract, Vfract) pier. In order to identify the limit states for all combinations of the
196
retrofitted piers (Table 2), nonlinear static pushover analyses are conducted. The yielding of
197
longitudinal steel reinforcement is assumed to take place at a tensile strain of steel fy/Es. The
198
crushing strain of unconfined concrete varies from 0.0025 to 0.006 [25]. Consequently, Paulay
199
and Priestley [10] recommended that the crushing strain of confined concrete is much higher and
200
changes from 0.015 to 0.05. In the present analysis, the crushing of confined concrete is assumed
201
to occur when the concrete compressive strain reaches 0.035. Longitudinal bar buckling and
202
fracture are determined according to the equations proposed by Berry and Eberhard [26]. They
203
proposed that the onset of bar buckling and fracture are best predicted as functions of the
204
effective confinement ratio, ρeff. Buckling and fracture of the longitudinal bar are defined as the
205
points when the tensile strain in the extreme tensile steel fibre reaches 0.045 and 0.046,
206
respectively [26].
9
207
As depicted in Table 3, and Figure 4 - Figure 9, different parameters affect the flexural
208
performance of the FRP retrofitted bridge piers. For instance, as shown in Figure 3 - Figure 8, it
209
can be observed that higher values of the parameters can increase the capacity of the piers.
210
Yielding, bucking, and fracture of reinforcement, and crushing of core concrete are also
211
presented in Figure 4 - Figure 9.
212
From Figure 4, it is observed that 35 MPa concrete increases the pier yielding and crushing
213
base shear capacities of 14 and 8.3%, respectively; while the buckling and fracture base shear
214
capacities decrease by 4.4 and 4.3% compared to 20 MPa concrete. It could be attributed to the
215
fact that for the low strength concrete (20 MPa), the FRP confinement is more effective which
216
could give a higher deformability compared to the high strength concrete (35 MPa). Thus, low
217
strength concrete shows a higher displacement for crushing, buckling, and fracture of the rebar.
218
There is no difference in the yield displacement for 20 and 35MPa concrete. The results
219
presented in Figure 4 indicate that the stiffness of both piers is quite similar until the yielding of
220
the rebar. The results show that the stiffnesses of both piers are quite similar until cracking of the
221
concrete. Once the concrete is cracked, the 20 MPa pier exhibits comparatively lower stiffness
222
compared to 35 MPa concrete due to a lower modulus of elasticity of the concrete.
223
From Figure 5, it can be observed that the yield strength of longitudinal reinforcement
224
significantly affects the flexural performance of the FRP retrofitted bridge piers. For the high
225
yield strength (400 MPa) reinforcement shows higher yielding, crushing, buckling and fracture
226
base shear of 24.3, 27.3, 30.1 and 4.5%, and larger displacement by 28.6, 15.4, 27.3, 6.8, and
227
4.7%, respectively compared to the lower yield strength (250 MPa).
228
From Figure 6, it is observed that the amount of longitudinal steel considerably affects the
229
flexural strength and limit states of the retrofitted bridge piers. For 2.5% longitudinal
10
230
reinforcement ratio, the yielding, crushing, buckling and fracture base shear capacities are
231
improved by 44.9, 48.7, 55.8, and 56.1% compared to that of 1% longitudinal steel. For 2.5%
232
longitudinal reinforcement ratio, the yielding, buckling, and fracture displacements increase by
233
14.3, 9.5, and 9.3%, respectively, but the crushing displacement decreases by 14.3% compared to
234
that of 1% longitudinal steel.
235
From Figure 7, it can be observed that at 20% axial load, the yielding, crushing, buckling,
236
and fracture base shear increases by 41.5, 14.3, 7.4, and 7.2% compared to that of 10% axial
237
load. The yielding displacement increases by 14.3% for 20% axial load compared to 10% axial
238
load; and crushing, buckling and fracture displacements are almost the same for 20 and 10%
239
axial load. The results presented in Figure 7 reveal that the stiffnesses of both piers are quite
240
similar. The pier with 10% axial load has a higher deformation compared to 20% axial load pier.
241
From Figure 8, it can be observed that the shear span-depth ratio significantly affects the
242
flexural performance of the FRP retrofitted bridge piers. For the shear span-depth ratio of 7
243
shows 52.6, 44.3, 100.6, and 101.7% lower yielding, crushing, buckling, and fracture base shear
244
capacities, respectively compared to those having shear span-depth ratio of 4. For the shear span-
245
depth ratio of 7, yielding, crushing, buckling, and fracture displacements increase by 57.1, 64.3,
246
67.4 and 65.9%, respectively compared to those for the shear span-depth ratio of 4. According to
247
the results presented in Figure 8, the shear span-depth ratio of 4 shows higher stiffness and lower
248
deformability compared to the shear span-depth ratio of 7.
249
From Figure 9, it can be observed that the FRP-confinement layer does not affect the
250
flexural performance of the piers in terms of yielding, crushing, buckling, and fracture base
251
shears and displacements. Similar base shear and displacement limit states are observed from 2
252
and 3 layers of FRP confinement.
11
253
5. Incremental Dynamic Analysis of Piers
254
In order to predict the structural response under lateral load, NSPA is widely used. Conversely,
255
during a seismic event the lateral load experienced by the structures is dynamic in nature; hence,
256
nonlinear dynamic time history analysis will provide accurate estimation of structural response
257
under a seismic load. Luco and Cornell [27] developed incremental dynamic analysis (IDA)
258
method which is well explained in detail in Vamvatsikos and Cornell [28], and Yun et al. [29].
259
IDA needs multiple nonlinear dynamic time history analyses of a structural model by scaling sets
260
of seismic ground motion records based on adopted intensity measures (IM). Then, regression
261
equations of engineering demand parameters (EDP), such as maximum drift at different intensity
262
levels will be developed. The suite of different ground motions is properly chosen to cover the
263
entire range of the model’s response from elastic to yield, and nonlinear inelastic which leads to
264
global dynamic instability of structures. In IDA, different scaling factors should be selected for
265
different piers. Here, PGA is selected as IM and the incremental scaling series in IDA ranges
266
from 0.1g to 3.0g. Overall, when the maximum top drift of the piers exceeds certain level, it
267
experiences dynamic instability with a large deformation or drift. In this article, a “collapse
268
point” is considered as the first incidence of such large deformation or drift [28]. Though,
269
Konstantinidis and Nikfar [30] reported that increase of an actual ground motion PGA value by
270
a scaling factor does not certainly lead to reliable results; however, it will provide a better
271
understanding of the behavior of the inelastic system over the range of different intensity
272
measures. In portraying the inelastic demand, non-linear behavior in the collapsed state are
273
defined. The collapse results are modeled by developing fragility curves at the collapse limit
274
state.
12
275
5.1 Selection of ground motions
276
The properties of seismic ground motion differ in terms of frequency content, peak ground
277
acceleration (PGA), and duration. Thus, dynamic time history analyses of structure for one
278
ground motion record might not characterize the worst-case scenario. In order to incorporate the
279
uncertainties and variability of ground motion records and their impact on the behavior of bridge
280
piers, a suite of earthquake ground motions is required. Due to limited number of available
281
earthquake records in Vancouver, British Columbia region (western Canada), a suite of 20
282
ground motion histories are obtained from the Applied Technology Council [31] ground motion
283
database. Table 4 shows the characteristics of the un-scaled seismic ground motion records
284
including PGA, peak ground velocity (PGV), epicenter distance (R), and moment magnitude
285
(Mw) of the earthquake. These ground motion records have low to medium values of PGA, R, Mw
286
and PGV, which are in the range of 0.22-0.73g, 8.7-98.2km, 6.5-7.6 and 17-70cm/sec,
287
respectively. It is assumed that these ground motions are considered to be representative of an
288
earthquake motion in Vancouver. In this study, the horizontal components of ground motion
289
records are applied to the pier. The specified magnitude and distance ranges cover the
290
predominant magnitudes and distances for Vancouver.
291
Figure 10(a) shows the acceleration response spectrum of the recorded suits of 20 ground
292
motions with a 5% damping ratio. Figure 10(b) depicts different percentiles of acceleration
293
response spectra with a 5% damping ratio, showing that the selected earthquake ground motions
294
records are well representing the medium to strong intensity earthquake ground motion histories..
295
5.2 Incremental dynamic analysis for pier collapse capacity
296
For the retrofitted bridge piers, inelastic demands are estimated by conducting IDA. IDA curve is
297
also known as dynamic pushover curve, which is the relationships between IM and EDP. These
13
298
curves are generated using numerous ground motions, and each ground motion records are scaled
299
to multiple levels of intensities [28].
300
5.3 Dynamic pushover curve
301
The incremental dynamic analysis is conducted for all the retrofitted bridge piers using the suite
302
of 20 earthquake ground motion records. Figure 11- Figure 21 show the dynamic pushover curve
303
of total base shear versus top lateral displacement for different compressive strengths of
304
concrete, yield strengths and amount of longitudinal reinforcement, axial loads, shear span-depth
305
ratios, and FRP layers. The dynamic pushover points closely coincide with the static pushover
306
curves before the first yielding of the longitudinal reinforcement. It can be observed from Figure
307
11- Figure 21 that the dynamic pushover curves demonstrate higher base shear values compared
308
to those from the static pushover curves between first yielding and crushing of core concrete.
309
5.4 Incremental dynamic analysis curve
310
IDA curve results with all the combinations of parameters are used to identify IM values related
311
to the collapse. Figure 22(a) - Figure 22(l) show the IDA curves of all the retrofitted piers with
312
different adopted parameters (Table 2) and a set of IM values related to the onset of collapse for
313
each ground motions. The overall characteristics of the IDA curves for maximum top drift ratio
314
are different, the initial drift increases gradually with the seismic intensity level. Afterward, the
315
drift increases rapidly when the seismic intensity level reaches a range of 0.2g to 0.4g for all of
316
the piers (Figure 22). According to the results of IDA curves shown in Figure 22(a) - Figure
317
22(l), the non-seismically designed piers show more vulnerability compared to the other bridge
318
piers. Failure modes obtained from the IDA curves at collapse level are summarized in Appendix
319
Table A1.
14
320
6. Collapse Fragility Assessment
321
The fragility curves can be produced by using various methods, for instance, an expert opinion,
322
damage data observed from field, laboratory testing, based on numerical simulations, or a
323
combination of them [32], [33], [34], [35], [36], [37], [38]. In this research, analytical collapse
324
fragility curves were generated based on IDA results using suits of 20 ground motion records
325
scaled until it causes the collapse of the pier [28]. The analytical fragility curve exhibits
326
advantages compared to other methods. For instance, in the case of analytical fragility curve, the
327
analyst is free to choose the IM , at which analysis is to be conducted, and the number of analysis
328
at each IM [39]. Generally, the fragility curves are mathematical functions which describe the
329
conditional probability that a structure can experience damage by exceeding or reaching a
330
specific level of damage state as a function of demand (drift or ductility), represented by EDP IM
331
(e.g. PGA). In the seismic vulnerability assessment of structure, fragility curves are obtained
332
from IDA [40].. The collapse fragility function gives a probability that a structure would collapse
333
as a function of a specific IM. The collapse fragility assessment can be described using Eq. (1) as
334
a lognormal cumulative distribution function (CDF) reported by [39]. ln ( x θ ) Pc ( C | IM = x ) = Φ β
(1)
335
where Pc(C|IM = x) represents the probability of collapse at a given ground motion with IM = x,
336
Φ(.) is the standard normal CDF, θ is the collapsed median intensity of the fragility function (IM
337
level with 50% probability of collapse not being exceeded), and β is the logarithmic standard
338
deviation. Eq. (1) indicates the assumption of lognormality of the IM values of the ground
339
motions causing the collapse of specific structures [39]. Calibrating Eq. (1) of the pier needs an
340
estimation of θ and β from the IDA results. Figure 23 shows the linear regression models of the
341
median and standard lognormal dispersion for all the combinations of parameters. Table 5 15
342
depicts a summary of the values of linear regression models of the median and standard
343
lognormal dispersion for all the combinations.
344
The probability of collapse can be assessed at a given IM level, x can then be determined as
345
a part of records for which collapse occurs at a level lower than x. Fragility function parameters
346
can be assessed from the regression analyses of their median θ, and dispersion β, values, and by
347
taking the logarithm of each ground motion’s IM value related to the onset of collapse.
348
Based on the obtained collapse mode of IDA results and using fragility curves, the
349
probability of collapse of all the combination of parameters is plotted in Figure 24 - Figure 29. In
350
order to compare the obtained probability of collapse for the combination of different
351
parameters, these curves are plotted together and presented in one figure. In Figure 24 - Figure
352
29, the curve drawn with a black solid line indicates a higher collapse fragility, and the dotted
353
red line shows a lower collapse fragility as obtained by fitting the lognormal distribution to the
354
data. These data are obtained from the IDAs results. It can be observed from the Figure 24 -
355
Figure 29 that the probability of collapse of the lower value has a significant shift to the left and
356
has a smaller PGA for a specific probability of collapse. It leads to an increase in the probability
357
of collapse for a given seismicity. In Figure 24 - Figure 29, SCT represents the median collapse
358
probability.
359
6.1 Effect of compressive strength of concrete on collapse fragility curve
360
Figure 24 shows the effect of concrete compressive strength on the collapse fragility of
361
retrofitted bridge piers based on the maximum collapse drift ratio. The solid black line and the
362
red dotted line represent the probability of collapse with the specified compressive strength of
363
concrete of 35 and 20 MPa, respectively. The fragility curve clearly demonstrates the probability
364
of structural collapse for measuring definite intensity. From Figure 24, it can be observed that the
16
365
difference between fragility curves of 35, and 20 MPa concrete is significant. It is important to
366
note that 35MPa concrete pier is more fragile compared to 20MPa concrete piers. For instance,
367
as shown in Table 6, for the peak ground intensity levels, PGA in the range of 0.5g-2.0g, the
368
relative probability of collapse of 35MPa concrete pier is higher compared to 20MPa concrete
369
pier. 35 MPa concrete pier has higher stiffness that attracts more seismic forces causing more
370
damages to the pier compared to the 20 MPa concrete pier. Since 20 MPa concrete has lower
371
modulus of elasticity compared to 30 MPa concrete, larger strain experienced by the 20 MPa
372
concrete activated the FRP composite confinement and thus, was more effective in resisting
373
seismic forces compared to the 30 MPa concrete at similar drift level. From Figure 24, it can be
374
observed that the 20 MPa concrete pier will have 50% probability of collapse at a PGA value of
375
1.1g whereas the 35 MPa concrete will be able to sustain an earthquake with a PGA of only
376
0.72g to experience similar damage level. In other words, during an earthquake with a PGA of
377
0.72g the probability of collapse of the 20 MPa concrete is only 20% whereas for the 35 MPa
378
concrete it is 50%.
379
6.2 Effect of yield strength of steel reinforcement on collapse fragility
380
Figure 25 shows the effect of yield strength of longitudinal reinforcement on the collapse
381
fragility of retrofitted bridge piers based on maximum collapse drift ratio. The solid black line
382
and the red dotted line indicates the probability of collapse fragility with the yield strength of
383
longitudinal reinforcement of 400, and 250MPa, respectively. The fragility curve clearly
384
demonstrates the probability of structural collapse for measuring definite intensity. From Figure
385
25, it can be observed that the difference between fragility curves of 400, and 250 MPa
386
reinforcements are significant. For example, as shown in Table 6, for the peak ground intensity
387
levels, PGA, in the range of 0.5g-2.0g, the relative probability of collapse for the 400 MPa steel
17
388
RC pier is lower compared to the 250 MPa steel RC pier. For the intensity level of 2.0g, the
389
difference in the collapse probabilities is insignificant. Since both steel has the same modulus of
390
elasticity, the 400 MPa steel experiences yielding at a much larger strain value compared to the
391
250 MPa steel. Hence, the 400 MPa steel gets an added advantage to experience lower damage
392
level at the same ground motion level compared to the 400 MPa steel. From Figure 25, it can be
393
observed that the 400 MPa steel RC pier will have 50% probability of collapse at a PGA value of
394
0.71g whereas the 250 MPa steel RC pier will be able to sustain an earthquake with a PGA of
395
only 0.62g. In other words, during an earthquake with a PGA of 0.62g the probability of collapse
396
of the 400 MPa steel is 40% whereas for the 250 MPa steel it is 50%.
397
6.3 Effect of amount of longitudinal reinforcement on collapse fragility
398
Figure 26 shows the effect of the amount of longitudinal reinforcement on the collapse fragility
399
of retrofitted bridge piers. The solid black line and the red dotted line represents the probability
400
of collapse of the amount of longitudinal reinforcement of 1, and 2.5%, respectively. The
401
fragility curve clearly demonstrates the probability of structural collapse for measuring definite
402
intensity. From Figure 26, it can be observed that the difference between fragility curves with the
403
longitudinal reinforcement of 2.5% is significant compared to 1% reinforcement. Larger amount
404
of rebar increases the stiffness and strength of the pier and hence, it experiences lesser
405
deformation compared to the pier having reduced amount of longitudinal bar. As shown in Table
406
6, for the peak ground intensity levels, PGA, in the range of 0.5g-2.0g, the relative probability of
407
collapse for the 2.5% longitudinal steel is lower compared to 1% longitudinal steel. From Figure
408
26, it can be observed that the 1% longitudinal steel pier will have 50% probability of collapse
409
even at a PGA value of 0.8g whereas the 2.5% steel RC pier will be able to sustain an earthquake
18
410
with a PGA of 1.22g. In other words, during an earthquake with a PGA of 0.8g the probability of
411
collapse of the 1% steel pier is 50% whereas for the 2.5% steel pier it is only 14%.
412
6.4 Effect of axial load on collapse fragility
413
Figure 27 shows the effect of axial load on the collapse fragility of retrofitted bridge piers based
414
on maximum collapse drift ratio. The solid black line and the red dotted line represent the
415
probability of collapse with the axial load ratios of 0.20 and 0.10, respectively. The fragility
416
curves clearly demonstrate the probability of structural collapse. From Figure 27, it can be
417
observed that the difference between fragility curves with the axial load ratios of 0.20 and 0.10 is
418
significant. For example, as shown in Table 6, for PGA values in the range of 0.5g-2.0g, the
419
relative probability of collapse at the axial load of 0.20 is higher compared to 0.10 axial load.
420
From Figure 6.26 it can be observed that the higher axial load pier will have 50% probability of
421
collapse at a PGA value of 0.9g whereas the lower axial load pier will be able to sustain an
422
earthquake with a PGA of 1.31g. In other words, during an earthquake with a PGA of 0.9g the
423
probability of collapse of the higher axial load pier is 50% whereas for the lower axial load pier
424
it is only 16%.
425
6.5 Effect of shear span-depth ratio on collapse fragility
426
Figure 28 shows the effect of shear span-depth ratio on collapse fragility of retrofitted bridge
427
piers. The solid black line and the red dotted line represent probabilities of collapse with the
428
shear span-depth ratios of 4 and 7, respectively. The fragility curves clearly demonstrate the
429
probability of structural collapse. From Figure 28, it can be observed that the difference between
430
fragility curves with shear span-depth ratios of 4 and 7 is not very significant. As shown in Table
431
6, for the peak ground intensity levels, PGA in the range of 0.5g-2.0g, the relative probability of
432
collapse at the shear span-depth ratio of 7 is lower compared to the shear span-depth ratio of
19
433
0.10. From Figure 6.27 it can be observed that the pier with larger shear span-depth ratio will
434
have 50% probability of collapse at a PGA value of 1.16g whereas the pier with lower shear
435
span-depth ratio will be able to sustain an earthquake with a PGA of only 1.24g. In other words,
436
during an earthquake with a PGA of 1.16g the probability of collapse of the larger shear span-
437
depth ratio is 50% whereas for the lower shear span-depth ratio it is 45%.
438
6.6 Effect of confinement on collapse fragility
439
Figure 29 shows the effect of FRP confinement on the collapse fragility of circular RC bridge
440
piers. The solid black line and the red dotted line represent the probabilities of collapse with 2
441
and 3 layers of FRP confinement, respectively. From Figure 29, it can be observed that the
442
difference between fragility curves for 2 and 3 layers of FRP confinement is insignificant at PGA
443
values beyond 1.5g. However, from 0.2g to 1.5g, there are some differences. As shown in Table
444
6, the relative probability of collapse for the 2 FRP confinement layers is higher compared to 3
445
layers of FRP confinement. From Figure 6.28 it can be observed that the 2 layer FRP pier will
446
have 50% probability of collapse at a PGA value of 0.75g whereas the 3 layer FRP pier will be
447
able to sustain an earthquake with a PGA of 0.82g. In other words, during an earthquake with a
448
PGA of 0.75g the probability of collapse of the 3 layer FRP pier is 44% whereas for the 2 layer
449
FRP pier it is 50%
450
The collapse probability difference, ∆, for fragilities of all combination of parameters are
451
reported in a bar chart (see Figure 31 and Figure 32) for four peak ground accelerations of 0.5g,
452
1.0g, 1.5g, and 2.0g. As expected with higher PGA values, the differences in collapse probability
453
gradually decrease.
20
454
6.7 Median peak ground acceleration
455
The median values of the intensity measure, PGA, for a different combination of FRP, retrofitted
456
bridge piers are given in Table 7 and the corresponding bar chart is depicted in Figure 33. The
457
median values of PGA are determined as a level of PGA at which the probability of collapse at
458
each pier reaches 50%. For the same level of collapse probability, lower values of median
459
correspond to the higher probability of collapse, hence it demonstrates that the pier with a lower
460
median value is more fragile compared to other piers. For example, piers with a concrete
461
compressive strength of 35 MPa, a reinforcement yield strength of 250 MPa, a longitudinal
462
reinforcement ratio of 1%, and axial load of 0.20, a shear span-depth ratio of 4, and 2
463
confinement layers have the lowest value of median, respectively, 0.72g, 0.62g, 0.79g, 0.90g,
464
1.16g and 0.78g. It demonstrates that the lowest median values of piers have the inferior
465
performance. It can be noted that the pier with 20MPa concrete gives higher median value of
466
1.1g. As a result, it indicates that the FRP confinement is more effective in 20MPa concrete
467
compared to 35MPa concrete (PGA = 0.72g) in the case of FRP retrofitted piers.
468
The relative difference between the median values of PGA is found to be 10% for 35 and 20
469
MPa concretes. It represents that the 35MPa concrete pier leads to a 10% higher fragility
470
compared to the 20 MPa concrete pier. It is because the FRP confinement is more effective for
471
20MPa concrete compared to the 35MPa concrete. Thus, it is concluded that the deficient pier
472
performance can be improved with FRP.
473
6.8 Performance evaluation of bridge piers
474
Results of IDA curve can be used to evaluate the collapse performance of the RC bridge piers.
475
The collapse median intensity (SCT) obtained from the fragility fitting curves (Figure 25 -Figure
476
30) and the performance of bridge piers can be assessed using collapse margin ratio (CMR) [31].
21
477
The CMR can be expressed at the ratio of the SCT to the design level earthquake intensity (SMT).
478
The CMR ratio is calculated by dividing the SCT by a specific level of SMT, which is equal to
479
0.185g, 0.256g and 0.363g for 10, 5, and 2% probabilities of exceedance in 50 years at the return
480
period of 475, 975 and 2475 years, respectively for Vancouver, British Columbia. Table 8
481
exhibits the CMR values for different combinations of parameters. From Table 8, it can be
482
observed that as the ground motion return period decreases the collapse probability of
483
exceedance increases. For instance, for a pier with a compressive strength of concrete of 35 MPa,
484
the collapse probability value under an earthquake with a return period of 2475 years is 1.98,
485
which is 3.38 and 2.11% lower than a return period of 975 and 475 years, respectively.
486
Observation from Table 8 revealed that, as the earthquake return period increases, its intensity
487
also increases. Hence, the probability of exceeding collapse of a certain pier will increase, which,
488
means that the median collapse spectral acceleration will increase with the increase of
489
earthquake return period. Since the spectral acceleration at maximum considered earthquake will
490
also increase with the increase of earthquake return period, the results presented in Table 8 show
491
the CMR values gradually decrease with increasing return period. For instance, when the yield
492
strength of longitudinal reinforcement increases, the CMR ratio increases from 3.35% to 3.84%
493
at 475 years return period. In the case of increasing compressive strength, the CMR ratio
494
decreases from 5.95% to 3.89% with a return period of 475 years. It is because of the lower
495
strength concrete (20 MPa); the FRP confinement is more effective compared to higher strength
496
(35 MPa) concrete.
497
7. Conclusions
498
The seismic fragility assessment of the bridge can be analyzed using fragility curve, which is a
499
method to estimate the probability of damage of the structure at specific levels of ground motion.
22
500
The piers are the most vulnerable structural element in the bridge structures, which have
501
significant contribution to the failure probability of the bridge system. This article presented the
502
nonlinear static pushover analyses (NSPA) and collapse fragility curves of non-seismically
503
designed RC circular bridge piers located in Vancouver, British Columbia, Canada with a
504
different combination of parameters. Probabilistic seismic demand models were produced using
505
the results obtained from the incremental dynamic analyses (IDA). Considering collapse drift as
506
demand parameter, fragility curves were generated with different parameters of non-seismically
507
designed RC circular bridge piers. It was observed that the amount of reinforcement, shear span-
508
depth ratio, and level of the axial load could significantly affect the collapse fragility curve of the
509
retrofitted bridge piers.
510 511 512
Based on the NSP and results obtained from IDA curves, and collapse fragility curve, the following conclusions can be drawn.
513 514
It can be observed from the NSPA that higher values of parameters could increase the capacity of the piers.
It is observed that 35 MPa concrete increased the pier yield and crushing base shear
515
capacity by 14 and 8.3%, respectively; while the buckling and fracture base shear
516
capacities were decreased by 4.4 and 4.3% compared to 20MPa concrete.
517
For piers with 400 MPa yield strength of longitudinal reinforcements, yielding, crushing,
518
buckling and fracture base shear and displacement capacities increased by 24.3, 27.3,
519
30.1 and 4.5%, and 28.6, 15.4, 27.3, 6.8, and 4.7%, respectively, compared to those of the
520
pier with reinforcements having 250 MPa yield strength.
23
521
For piers with longitudinal reinforcement ratios of 2.5%, the yielding, crushing, buckling
522
and fracture base shear capacities improved by 44.9, 48.7, 55.8, and 56.1% compared to
523
those for 1% longitudinal reinforcement ratios.
524
For piers with longitudinal reinforcement ratios of 2.5%, the yielding, buckling and
525
fracture displacements increased by 14.3, 9.5, and 9.3%, respectively, but the crushing
526
displacement decreased by 14.3% compared to those for 1% longitudinal reinforcement
527
ratios.
528
529 530
It can be observed that at 20% axial load, the yielding, crushing, buckling, and fracture base shear increased by 41.5, 14.3, 7.4, and 7.2% compared to those for 10% axial loads.
The yielding displacement increased by 14.3% for 20% axial load compared to 10% axial
531
load, and crushing, buckling and fracture displacements were almost the same for 20 and
532
10% axial loads.
533
For the shear span-depth ratio of 7, yielding, crushing, buckling, and fracture base shears
534
decreased by 52.6, 44.3, 100.6, and 101.7%, respectively compared to those for 4 shear
535
span-depth ratio.
536
The shear span-depth ratio of 7 resulted in an increase in yielding, crushing, buckling and
537
fracture displacements by 57.1, 64.3, 67.4 and 65.9%, respectively compared to those of
538
4 shear span-depth ratios.
539
540 541 542
The dynamic pushover points closely coincided with the static pushover curves before the first yielding of the longitudinal reinforcement.
The dynamic pushover curved demonstrated higher base shear value compared to f the static pushover curves between first yielding and crushing of core concrete.
24
543
It can be observed that 35 MPa concrete pier is more fragile compared to 20 MPa
544
concrete piers. For PGA values in the range of 0.5g-2.0g, the relative probability of
545
collapse of 35MPa concrete pier is higher (in the range of 74.8-3.2% compared to 20MPa
546
concrete pier).
547
At PGA values from 0.5g to 2.0g, for 400 MPa yield strength, a relatively lower
548
probability of collapse (i.e. in the range of 79.8-4.3%) was observed compared to 250
549
MPa yield strength.
550
At PGAs from 0.5g-2.0g, a relatively lower probability of collapse was observed (i.e. in
551
the range of 83.5-3.2%) for the amount of longitudinal steel of 2.5% is compared to 1%
552
longitudinal steel.
553
At PGAs from 0.5g-2.0g, a relatively higher probability of collapse was observed (i.e. in
554
the range of 74.8-2.7%) for the axial load of 0.20 compared to 0.10 axial load. The higher
555
axial load reduced the deformability.
556
At PGAs from 0.5g-2.0g, a relatively lower probability of collapse was observed (i.e. in
557
the range of 64.8-2.4%) for the shear span-depth ratio of 7 compared to the shear span-
558
depth ratio of 4.
559
At PGAs from 0.5g-2.0g, a relatively higher probability of collapse was observed (i.e. in
560
the range of 77.7-3.4%) for 2 layers of FRP confinement compared to the 3 layers of
561
confinement.
562
Acknowledgements
563
The first author would like to acknowledge the financial support provided by MITACS and
564
POLYRAP Engineered Concrete Solutions, Kelowna, B.C., Canada under the accelerate Ph.D.
565
fellowship award No. IT03809, and Ministry of Human Resources Development (MHRD), Govt.
25
566
of India, New Delhi for the National Oversees Scholarship. The first author is also grateful to S.
567
V. National Institute of Technology (SV NIT), Surat, Govt. of India to grant the study leave for
568
the Ph.D. program at the University of British Columbia (UBC), Canada. The authors are
569
grateful to Dr. Farshad Hedayati Dezfuli of UBC for proof reading of the manuscript. The
570
authors are grateful to Dr. Solomon Tesfamariam from the School of Engineering, UBC for the
571
interpretation of collapse fragility results. . Moreover, the authors would like to thank the
572
unknown referees for their useful remarks and suggestions. The experimental results were
573
provided by Prof. Kazuhiko Kawashima, Professor Emeritus, Department of Civil Engineering,
574
Tokyo Institute of Technology, Japan, and Dr. Richelle G. Zafra, Department of Civil
575
Engineering/Associate Dean, College of Engineering and Agro-Industrial Technology University
576
of the Philippines Los Banos and they are gratefully acknowledged.
577
References
578
[1]
579 580
Saadatmanesh H, Ehsani MR, Jin L. Strength and ductility of concrete columns externally reinforced with fiber composite straps. ACI Struct J 1994;91:434–47.
[2]
Elsanadedy HM, Haroun M. Seismic design criteria for circular lap-spliced reinforced
581
concrete bridge columns retrofitted with fiber-reinforced polymer jackets. ACI Struct J
582
2005;102:354–62.
583
[3]
584 585
containing lap-spliced reinforcing bars. ACI Struct J 2007;104:227–36. [4]
586 587 588
Ghosh KK, Sheikh SA. Seismic upgrade with carbon fiber reinforced polymer of columns
Liu J, Sheikh A G. Glass Fiber-reinforced polymer-reinforced circular columns under simulated seismic loads. ACI Struct J 2013;110:941–51.
[5]
ACI 440.2R. Guide for the design and construction of externally bonded FRP systems for strengthening of concrete structures. ACI Committee 440.2R-08, American Concrete
26
589 590
Institute, Farmington Hills, Detroit, Michigan, USA: 2008. [6]
591 592
with fiber composites. ACI Struct J 1996;93:639–47. [7]
593 594
Saadatmanesh H, Ehsani MR, Jin L. Seismic strengthening of circular bridge pier models
Xiao Y, Ma R. Seismic retrofit of RC circular columns using prefabricated composite jacketing. J Struct Eng, ASCE 1997;123:1357–64.
[8]
Chang SY, Li YF, Loh CH. Experimental study of seismic behaviors of as-built and
595
carbon fiber reinforced plastics repaired reinforced concrete bridge columns. J Bridg Engi
596
ASCE 2004;9:391–402.
597
[9]
Han Q, Wen J, Du X, Jia J. Experimental and numerical studies on seismic behavior of
598
hollow bridge columns retrofitted with carbon fiber reinforced polymer. J Reinf Plast
599
Compo 2014;33:2214–27. doi:10.1177/0731684414557716.
600 601 602 603 604 605 606 607 608 609 610 611
[10] Paulay T, Priestley MJN. Seismic design of reinforced concrete and masonry buildings. New York, USA: John Wiley & Sons Inc; 1992. [11] Hines E, Restrepo JI, Seible F. Force-displacement characterization of wellconfined bridge piers. ACI Struct J 2004;101:537–48. [12] Bae S, Bayrak O. Plastic hinge length of reinforced concrete columns. ACI Struct J 2008;105:290–300. [13] Parghi A, Alam MS. Seismic behavior of deficient reinforced concrete bridge piers confined with FRP–A fractional factorial analysis. Eng Struct 2016;126:531–46. [14] SeismoStruct. A computer program for static and dynamic nonlinear analysis of framed structures, V 7.06 2015:[Online], available from URL:
27
612
[16] Madas P, Elnashai AS. A new passive confinement model for the analysis of concrete
613
structures subjected to cyclic and transient dynamic loading. Earthq Eng Struct Dyn
614
1992;21:409–31.
615 616 617 618 619 620 621 622 623 624
[17] Mander JB, Priestley MJN, Park R. Theoretical stress–strain model for confined concrete. J Struct Eng ASCE 1988;114:1804–26. [18] Martinez-Rueda JE, Elnashai AS. Confined concrete model under cyclic load. Mater Struct 1997;30:139–47. [19] Ferracuti B, Savoia M. Cyclic behavior of CFRP-wrapped piers under axial and flexural loading. Proceeding Int. Conf. Fract., Turin, Italy: 2005. [20] Yankelevsky DZ, Reinhardt HW. Uniaxial behavior of concrete in cyclic tension. Journal of Structural Engineering. J Struct Eng, ASCE 1989;115:166–82. [21] Spoelstra MR, Monti G. FRP-confined concrete model. J Compos Const, ASCE 1999;3:143–50.
625
[22] Menegotto M, Pinto PE. Method of analysis for cyclically loaded R.C. plane frames
626
including changes in geometry and non-elastic behaviour of elements under combined
627
normal force and bending. Symp. Resist. Ultim. Deform. Struct. acted by well-defined
628
repeated loads, Int. Assoc. Bridg. Struct. Eng., Zurich, Switzerland: 1973, p. 15–22.
629
[23] Filippou FC, Popov EP, Bertero V V. Modelling of R/C joints under cyclic excitations. J
630
Struct Eng ASCE 1983;109:2666–84.
631
[24] Kawashima K, Hosotani M, Yoneda K. Carbon fiber sheet retrofit of reinforced concrete
632
bridge piers. Proc. Int. Work. Annu. Commem. Chi-Chi Earthquake, Vol. II-Technical
633
Asp. Natl. Cent. Res. Earthq. Eng. Taipei, Taiwan, ROC, 2000, p. 124–35.
634
[25] MacGregor JG, Wight JK. Reinforced concrete mechanics and design. 4th Editio. New
28
635
Jersey, USA: 4th Edition, Prentice-Hall, Upper Saddle River; 2005.
636
[26] Berry MP, Eberhard MO. Performance modeling strategies for modern reinforced
637
concrete bridge columns. PEER Report 2007/07 Pacific Earthquake Engineering Research
638
Center, College of Engineering, University of California, Berkeley, USA: 2007.
639
[27] Luco N, Cornell CA. Effects of random connection fractures on the demands and
640
reliability for a three-story pre-Northridge (SMRP) structure. Proc sixth US Natl. conf
641
Earthq. eng, Earthq. Eng. Res. Inst., Oakland, California: 1998.
642 643 644 645
[28] Vamvatsikos D, Cornell CA. Incremental dynamic analysis. Earthq Eng Struct Dyn 2002;31:491–514. doi:doi:10.1002/eqe.141. [29] Yun S, Hamburger RO, Cornell C, Foutch DA. Seismic performance evaluation for steel moment frames. J Struct Eng, ASCE 2002;128:534–45.
646
[30] Konstantinidis D, Nikfar F. Seismic response of sliding equipment and contents in base-
647
isolated buildings subjected to broad- band ground motions. Earthq Eng Struct Dyn
648
2015;44:865–87.
649 650
[31] ATC. Quantification of building seismic performance factors. Applied Technology Council, FEMA P695, FEMA, Washington, DC, USA: 2009.
651
[32] Kennedy RP, Ravindra MK. Seismic fragilities for nuclear power plant risk studies. Nucl
652
Eng Des an Int J Devoted to Therm Mech Struct Probl Nucl Energy 1984;79:47–68.
653
[33] Kim SH, Shinozuka M. Development of fragility curves of bridges retrofitted by column
654
jacketing. Probab Eng Mech 2004;19:105–12.
655
[34] Calvi GM, Pinho R, Magenes G, Bommer JJ, Restrepo-Vélez LF, Crowley H.
656
Development of seismic vulnerability assessment methodologies over the past 30 years.
657
ISET J Earthq Technol 2006;43:75–104.
29
658 659 660 661 662 663 664
[35] Villaverde R. Methods to assess the seismic collapse capacity of building structures: state of the art. J Struct Eng, ASCE 2007;133:57–66. [36] Porter K, Kennedy R, Bachman R. Creating fragility functions for performance-based earthquake engineering. Earthq Spectra 2007;23:471–89. [37] Shafei B, Zareian F, Lignos DG. A simplified method for collapse capacity assessment of moment-resisting frame and shear wall structural systems. Eng Struct 2011;33:1107–16. [38] Billah AHMM, Alam MS. Seismic fragility assessment of highway bridges: a state-of-the-
665
art review. Struct Infrastruct Eng 2015;11.
666
doi:https://doi.org/10.1080/15732479.2014.912243.
667 668 669 670
[39] Baker JW. Efficient analytical fragility function fitting using dynamic structural analysis. Earthq Spectra 2015;31:579–99. [40] ATC. Seismic performance assess- ment of buildings: Volume 1 —Methodology. Applied Technology Council, FEMA P-58-1 , FEMA, Washington, DC, USA: 2012.
671 672
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673
List of Figures
674
Figure 1 Specimen geometry and reinforcement detailing used in this study
675
Figure 2 Schematic of section discretization of a typical FRP-confined concrete element
676
Figure 3 Comparison of the force displacement relationship of the numerical and experimental
677
results (A) as-Built pier and (B) CFRP retrofitted pier
678
Figure 4 Results of pushover analysis considering different compressive strength of concrete
679
Figure 5 Results of pushover analysis considering different yield strength of reinforcement
680
Figure 6 Results of pushover analysis considering different longitudinal steel ratio
681
Figure 7 Results of Pushover analysis considering different axial load ratio
682
Figure 8 Results of pushover analysis considering different shear span-depth ratio
683
Figure 9 Results of pushover analysis considering different layer of FRP
684
Figure 10 A suit of 20 earthquake ground motion records (a) Response spectral acceleration (b)
685
percentile of response spectral acceleration of a suit of earthquake ground motion
686
records
687
Figure 11 Results of dynamic and static pushover curve for C-1-35
688
Figure 12 Dynamic and static pushover curve for C-1-20
689
Figure 13 Dynamic and static pushover curve for C-2-400
690
Figure 14 Results Dynamic and static pushover curve for C-2-250
691
Figure 15 Results of dynamic and static pushover curve for C-3-2.5
692
Figure 16 Results of dynamic and static pushover curve for C-3-1
693
Figure 17 Results of dynamic and static pushover curve for C-4-0.20
694
Figure 18 Results of dynamic and static pushover curve for C-4-0.10
695
Figure 19 Results of dynamic and static pushover curve for C-5-7
31
696
Figure 20 Results of dynamic and static pushover curve for C-5-4
697
Figure 21 Results of dynamic and static pushover curve for C-6-2
698
Figure 22 Results of dynamic and static pushover curve for C-6-3
699
Figure 23 IDA results used to identify IM values related with collapse of each ground motions of
700
all the bridge piers retrofitted with FRP
701
Figure 24 Linear regression models for the median and dispersion values from IDA results
702
Figure 25 Effect of concrete strength on collapse fragility
703
Figure 26 Effect of yield strength of longitudinal steel on collapse fragility
704
Figure 27 Effect of amount of longitudinal steel on collapse fragility
705
Figure 28 Effect of axial load on collapse fragility
706
Figure 29 Effect of shear span-depth ratio on collapse fragility
707
Figure 30 Effect of FRP confinement on collapse fragility
708
Figure 31 Collapse probability of the piers at four PGA, 0.5, g, 0.1.0g, 1.5g, and 2.0g
709
Figure 32 Difference between collapse probability of different parameters
710
Figure 33 Bar chart of median values of PGA for the piers with different parameters
711 712 713 714 715 716 717 718
32
719 720
Figure 1 Specimen geometry and reinforcement detailing used in this study
721 722 723 724 725 726 727 728 729 33
730
Deck mass
G
mm 2000 mm
734 735
1600 mm
N6
733
N5
N4
N3 N2
737
N6
Beam element
N5
FRP wraps fiber N4
Beam element
Confined core concrete fiber
N3
Fiber element N2
Zero length Spring element
400 mm
736
N7
N7
2 and 3 Layer of CFRP No FRP
260 mm
732
520 mm
731
400 mm
N1 N1
Reinforcement’s fiber Cover concrete fiber
1150 mm
738 739
(a) Pier schematic
(b) Pier model
(c) Fiber discretization
Figure 2 Schematic of section discretization of a typical FRP-confined concrete element
740 741 742 743 744 745 746 747 748 749 750 751 752
34
150
150
(a) As Built Pier
50 0 -50
-100 -150 -120
753
100 Lateral load (kN)
Lateral load (kN)
100
(b) 0.111mm-CFRP Wrapped Pier
Experimental Numerical -80 -40 0 40 80 Top lateral displacement (mm)
120
50 0 -50
-100 -150 -120
Experimental Numerical -80 -40 0 40 80 Top lateral displacement (mm)
120
754
Figure 3 Comparison of the force displacement relationship of the numerical and experimental
755
results (A) as-Built pier and (B) CFRP retrofitted Pier
756 757 758 759 760 761 762 763 764 765 766 767
35
100 f'c = 35 MPa
Base Shear (kN)
f'c = 20 MPa 75
Yielding Crushing Bucking Fracture
50
25
0 0 768 769
50
100 150 Top Displacement (mm)
200
Figure 4 Results of pushover analysis considering different compressive strength of concrete
770 771 772 773 774 775 776 777 778 779 780 781 782
36
100 fy = 400 Mpa Base Shear (kN)
fy = 250 Mpa 75
Yielding Crushing Bucking Fracture
50
25
0 0 783 784
50
100 150 Top Displacement (mm)
200
Figure 5 Results of pushover analysis considering different yield strength of reinforcement
785 786 787 788 789 790 791 792 793 794
37
795 796
Figure 6 Results of pushover analysis considering different longitudinal steel ratio
797 798 799 800 801 802 803 804 805 806 807 808 809 810
38
811 812
Figure 7 Results of Pushover analysis considering different axial load ratio
813 814 815 816 817 818 819 820 821 822 823 824
39
825 826
Figure 8 Results of pushover analysis considering different shear span-depth ratio
827 828 829 830 831 832 833 834 835 836 837 838
40
839 840
Figure 9 Results of pushover analysis considering different layer of FRP
841 842 843 844 845 846 847 848 849 850 851 852 853 854
41
EQ1 EQ4 EQ7 EQ10 EQ13 EQ16 EQ19
(a)
2.0
EQ2 EQ5 EQ8 EQ11 EQ14 EQ17 EQ20
EQ3 EQ6 EQ9 EQ12 EQ15 EQ18 Mean
1.5
(b)
75 Percentile 50 Percentile
2.0
25 Percentile
1.5
maxi. = 0.73g mini. = 0.22g
1.0
1.0
0.5
0.5
0.0
0.0 0
855
2.5 Spectral Acceleration (g)
Spectral Acceleration (g)
2.5
1
2 3 Period (sec)
4
0
1
2 Period (sec)
3
4
856
Figure 10 A suit of 20 earthquake ground motion records (a) Response spectral acceleration (b)
857
percentile of response spectral acceleration of a suit of earthquake ground motion records
858 859 860 861 862 863 864 865 866
42
160
Base Shear (kN)
C-1-35
Dynamic pushover points Static pushover curve
120
80
40
0 0 867 868
50
100 150 200 Top Displacement (mm)
250
300
Figure 11 Results of dynamic and static pushover curve for C-1-35
869 870 871 872 873 874 875 876 877 878 879 880
43
160
Base Shear (kN)
C-1-20
Dynamic pushover points Static pushover curve
120
80
40
0 0 881 882
50
100 150 200 Top Displacement (mm)
250
300
Figure 12 Dynamic and static pushover curve for C-1-20
883 884 885 886 887 888 889 890 891 892 893 894
44
Base Shear (kN)
160
C-2-400
Dynamic pushover points Static pushover curve
120
80
40
0 0 895 896
50
100 150 200 Top Displacement (mm)
250
300
Figure 13 Dynamic and static pushover curve for C-2-400
897 898 899 900 901 902 903 904 905 906 907 908
45
160
C-2-250
Dynamic pushover points
Base Shear (kN)
Static Pushover curve 120
80
40
0 0 909 910
50
100 150 200 Top Displacement (mm)
250
300
Figure 14 Results Dynamic and static pushover curve for C-2-250
911 912 913 914 915 916 917 918 919 920 921 922 923
46
125
C-3-2.5 Base Shear (kN)
100
Dynamic pushover points Static pushover curve
75 50 25 0 0
924 925
50
100 150 200 Top Displacement (mm)
250
300
Figure 15 Results of dynamic and static pushover curve for C-3-2.5
926 927 928 929 930 931 932 933 934 935 936 937
47
125
Dynamic pushover points
C-3-1
Static pushover curve
Base Shear (kN)
100 75 50 25 0 0 938 939
50
100 150 200 Top Displacement (mm)
250
300
Figure 16 Results of dynamic and static pushover curve for C-3-1
940 941 942 943 944 945 946 947 948 949 950 951 952 953
48
Base Shear (kN)
200
C-4-0.20 Dynamic pushover points Static pushover curve
150
100
50
0 0 954 955
50
100 150 200 Top Displacement (mm)
250
300
Figure 17 Results of dynamic and static pushover curve for C-4-0.20
956 957 958 959 960 961 962 963 964 965 966 967
49
200
Base Shear (kN)
C-4-0.10
Dynamic pushover points Static pushover curve
150
100
50
0 0 968 969
50
100 150 200 Top Displacement (mm)
250
300
Figure 18 Results of dynamic and static pushover curve for C-4-0.10
970 971 972 973 974 975 976 977 978 979 980 981
50
200 Dynamic pushover points
Base Shear (kN)
C-5-7
Static pushover curve
150
100
50
0 0 982 983
50
100 150 200 Top Displacement (mm)
250
300
Figure 19 Results of dynamic and static pushover curve for C-5-7
984 985 986 987 988 989 990 991 992 993 994 995
51
200 Dynamic pushover points
C-5-4 Base Shear (kN)
Static pushover curve 150
100
50
0 0 996 997
50
100 150 200 Top Displacement (mm)
250
300
Figure 20 Results of dynamic and static pushover curve for C-5-4
998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011
52
200 Dynamic pushover points
Base Shear (kN)
C-6-2
Static pushover curve
150
100
50
0 0 1012 1013
50
100 150 200 Top Displacement (mm)
250
300
Figure 21 Results of dynamic and static pushover curve for C-6-2
1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027
53
200 Dynamic pushover points
Base Shear (kN)
C-6-3
Static pushover curve
150
100
50
0 0 1028 1029
50
100 150 200 Top Displacement (mm)
250
300
Figure 22 Results of dynamic and static pushover curve for C-6-3
1030 1031 1032 1033 1034 1035 1036 1037
54
2.0
2.4
(a) C-1-35
2.0
1.6
1.6
1.2
PGA (g)
PGA (g)
(b) C-1-20
1.2
0.8
0.8 0.4
0.4
0.0
0.0 0
1038 2.0
4 8 12 16 Maximum Drift (%)
20
0
20
2.0
(c) C-2-400
(d) C-2-250
PGA (g)
1.6
PGA (g)
1.6 1.2
1.2
0.8
0.8
0.4
0.4
0.0
0.0 0
1039 3.0
3 6 9 12 Maximum Drift (%)
15
0 2.5
(e) C-3-2.5
2.5
4 8 12 16 Maximum Drift (%)
20
(f) C-3-1
2.0 PGA (g)
PGA (g)
2.0 1.5 1.0
1.5 1.0
0.5
0.5
0.0
0.0 0
1040
5 10 15 Maximum Drift (%)
4 8 12 16 Maximum Drift (%)
20
0
4 8 12 16 Maximum Drift (%)
20
55
3.0
3.0
(g) C-4-0.20
2.5
2.0
2.0
PGA (g)
PGA (g)
2.5
1.5
1.5 1.0
1.0
0.5
0.5
0.0
0.0 0
1041 3.0
4 8 12 16 Maximum Drift (%)
0
20 3.0
(i) C-5-7
2.5
2.5
2.0
2.0
5 10 15 Maximum Drift (%)
20
(j) Col-5-4
PGA (g)
PGA (g)
(h) C-4-0.10
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0 0
1042 3.0
4 8 12 16 Maximum Drift (%)
20
0 3.0
(k) C-6-2
2.5
2.0
2.0
20
(l) C-6-3
PGA (g)
PGA (g)
2.5
4 8 12 16 Maximum Drift (%)
1.5
1.5 1.0
1.0
0.5
0.5
0.0
0.0 0
4 8 12 16 Maximum Drift (%)
20
0
4 8 12 16 Maximum Drift (%)
20
1043 1044 1045
Figure 23 IDA results used to identify IM values related with collapse of each ground motions
1046
of all the bridge piers retrofitted with FRP 56
1.0
1.0
(a) C-1-35
0.5 ln (PGA)
ln (PGA)
0.5 0.0 -0.5 -1.0
-2
-1
1047 1.0
0 X
1
y = 0.4749x + 0.0871 R² = 0.9828 -2
2 1.0
(c) C-2-400
-1
0 X
1
2
(d) C-2-250
0.5 ln (PGA)
ln (PGA)
-0.5
-1.5
0.5 0.0 -0.5 -1.0
-2
-1
1048 1.5
0 X
1
0.0 -0.5 -1.0
y = 0.5335x - 0.3364 R² = 0.9744
-1.5
y = 0.4939x - 0.1327 R² = 0.976
-1.5 -2
2 1.0
(e) C-3-2.5
1.0
-1
0 X
1
2
(f) C-3-1
0.5
0.5
ln (PGA)
ln (PGA)
0.0
-1.0
y = 0.551x - 0.3244 R² = 0.9746
-1.5
0.0 -0.5 -1.0
-2
-1
0 X
1
0.0 -0.5 -1.0
y = 0.4181x + 0.2038 R² = 0.965
-1.5 1049
(b) C-1-20
y = 0.5426x - 0.2411 R² = 0.9852
-1.5 2
-2
-1
0 X
1
2
57
1.0
1.5
(g) C-4-0.20
1.0 ln (PGA)
ln (PGA)
0.5 0.0 -0.5
0.0
-1.0
y = 0.4731x - 0.1056 R² = 0.9756
-1.5 -2
-1
1050 1.5
0 X
1
y = 0.3797x + 0.2686 R² = 0.9807
-1.5 2
-2 1.5
(i) C-5-7
1.0
1.0
0.5
0.5
ln (PGA)
ln (PGA)
0.5
-0.5
-1.0
0.0 -0.5
-1
0 X
1
2
(j) C-5-4
0.0 -0.5
-1.0
-1.0
y = 0.4454x + 0.2098 R² = 0.9829
-1.5 -2 1051
(h) C-4-0.10
-1
0 X
1
y = 0.4184x + 0.1491 R² = 0.9476
-1.5 2
-2
-1
0 X
1
2
58
1.5
(k) C-6-2
1.0
1.0
0.5
0.5
ln (PGA)
ln (PGA)
1.5
0.0 -0.5
0.0 -0.5
-1.0
y = 0.537x - 0.2835 R² = 0.9535
-1.5 -2
1052 1053
(l) C-6-3
-1.0 -1.5
y = 0.4949x - 0.2058 R² = 0.9401
-1
0 1 2 -2 -1 0 1 2 X X Figure 24 Linear regression models for the median and dispersion values from IDA results
1054
Probabilitty of Collapse
1.0 0.8
f'c = 20 MPa f'c = 35 MPa
0.6 SCT
0.4 0.2 0.0 0.0
1055 1056
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 25 Effect of concrete strength on collapse fragility
1057 1058 1059 1060 1061 59
1062 1063
Probabilitty of Collapse
1.0 0.8
fy = 250 MPa fy = 400 MPa
0.6 SCT
0.4 0.2 0.0 0.0
1064 1065
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 26 Effect of yield strength of longitudinal steel on collapse fragility
1066 1067 1068 1069 1070 1071 1072
60
Probabilitty of Collapse
1.0 0.8
ρl = 2.5 % ρl = 1 %
0.6 SCT
0.4 0.2 0.0 0.0
1073 1074
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 27 Effect of amount of longitudinal steel on collapse fragility
1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087
61
Probabilitty of Collapse
1.0 0.8
P = 20 % P = 10 %
0.6 SCT
0.4 0.2 0.0 0.0
1088 1089
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 28 Effect of axial load on collapse fragility
1090 1091 1092 1093 1094 1095 1096
62
Probabilitty of Collapse
1.0 0.8
l/d = 7 l/d = 4
0.6 SCT
0.4 0.2 0.0 0.0
1097 1098
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 29 Effect of shear span-depth ratio on collapse fragility
1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109
63
Probabilitty of Collapse
1.0 0.8
n=2 n=3
0.6 SCT
0.4 0.2 0.0 0.0
1110 1111
0.5
1.0 1.5 2.0 Peak Ground Acceleration (g)
2.5
3.0
Figure 30 Effect of FRP confinement on collapse fragility
1112 1113 1114 1115 1116 1117 1118
64
Probability of Collpase (%)
1.2
0.5g
1.0g
1.5g
2.0g
1.0 0.8 0.6 0.4 0.2
1119 1120
C-6-3
C-6-2
C-5-4
C-5-7
C-4-0.10
C-4-0.20
C-3-1
C-3-2.5
C-2-250
C-2-400
C-1-20
C-1-35
0.0
Pier-ID Variables Figure 31 Collapse probability of the piers at four PGA, 0.5, g, 0.1.0g, 1.5g, and 2.0g
1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131
65
Probability Difference, ∆ (%)
100
f'c
fy
ρl
P
l/d
n
60 20 -20 -60
-100 0.5 1132 1133
1.0 1.5 Peak Ground Acceleration (g)
2.0
Figure 32 Difference between collapse probability of different parameters
1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147
66
1.6
Median Values of PGA at collapse 1.31 1.23
PGA (g)
1.23 1.16
1.10
1.2
0.90
0.8
0.79
0.71
0.72
0.76
0.82
0.62
1148 1149
C-6-3
C-6-2
C-5-4
C-5-7
C-4-0.10
C-4-0.20
C-3-1
C-3-2.5
C-2-250
C-2-400
C-1-20
0.0
C-1-35
0.4
Pier-ID Figure 33 Bar chart of median values of PGA for the piers with different parameters
1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163
67
1164
List of Tables
1165
Table 1 Details of variable parameters considered in this study
1166
Table 2 Details of FRP retrofitted bridge piers
1167
Table 3 Base shear and displacement at different limit states
1168
Table 4 Characteristic of ground motion records used in IDA [31]
1169
Table 5 Median and dispersion values from the results of IDA using regression analysis
1170
Table 6 Collapse probability of different variables at PGAs of 0.5, 1.0, 1.5 and 2.0g
1171
Table 7 Median values of PGA for piers with different parameters
1172
Table 8 Collapse margin ratio (CMR) for collapse safety of piers
1173
Table A1 Failure drift of piers based on IDA results
1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186
68
1187
Table 1 Details of variable parameters considered in this study Modeling factors/parameters Code Values Units ' A 20 35 (MPa) Compressive strength of concrete, ( f c ) Yield strength of steel, (fy) B 250 400 (MPa) Longitudinal steel reinforcement ratio, (ρl) C 1 2.5 (%) Axial load, (P) D 10 20 (%) Shear span-depth ratio, (l/d) E 4 7 -FRP confinement layer, (n) F 2 3 No.
1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 69
Table 2 Details of FRP retrofitted bridge piers
1207
f c'
fy ρl P= ' /A fc g (MPa) (MPa) (%) Compressive C-1-35 35 400 2.5 0.20 ' strength, f c C-1-20 20 400 2.5 0.20 C-2-400 35 400 1 0.20 Yield strength, fy C-2-250 35 250 1 0.20 C-3-2.5 35 400 2.5 0.10 Longitudinal reinforcement, ρl C-3-1 35 400 1 0.10 C-4-0.20 35 400 2.5 0.20 Axial load, P C-4-0.10 35 400 2.5 0.10 C-5-7 35 400 2.5 0.10 Shear span-depth ratio, l/d C-5-4 35 400 2.5 0.10 35 250 2.5 0.20 FRP confinement C-6-2 layer, n C-6-3 35 250 2.5 0.20 Variable
Pier-ID
l/d 2800/400 2800/400 2800/400 2800/400 2800/400 2800/400 1600/400 1600/400 2800/400 1600/400 1600/400 1600/400
n (No.) 3 3 3 3 3 3 3 3 2 2 2 3
1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221
70
Table 3 Base shear and displacement at different limit states
1222
Variable
Pier-ID
Compressive strength
C-1-35 C-1-20 C-2-400 C-2-250 C-3-2.5 C-3-1 C-4-0.20 C-4-0.10 C-5-7 C-5-4 C-6-2
Yield strength Longitudinal reinforcement Axial load Shear spandepth ratio FRP confinement layer
C-6-3
Yielding Base Disp. shear (mm) (kN) 28 63.15 28 55.26 28 63.09 20 47.74 28 58.08 24 31.99 12 133.74 8 94.52 28 56.77 12 119.87 8 97.16 8
97.17
Crushing Base Disp. shear (mm) (kN) 52 74.50 56 68.78 52 74.62 44 54.26 56 71.11 64 36.47 20 138.94 20 129.08 56 69.15 20 124.20 16 107.44 16
105.69
Bucking Base Disp. shear (mm) (kN) 172 60.02 180 63.60 176 57.55 164 40.23 168 66.99 152 29.58 56 138.63 56 133.78 172 65.41 56 131.22 56 102.62 56
103.17
Fracture Base Disp. shear (mm) (kN) 176 59.56 184 63.38 176 57.55 168 38.92 172 66.88 156 29.35 60 138.50 56 133.78 176 65.28 60 131.68 56 102.62 56
103.17
1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 71
Table 4 Characteristic of ground motion records used in IDA [31]
1237
EQ No. Mw Year Earthquake Name 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6.7 7.3 6.7 7.3 7.1 6.9 7.1 6.9 6.5 7.4 6.5 6.5 6.9 6.5 6.9 7.0 7.5 7.6 7.5 7.6
1994 1992 1994 1992 1999 1989 1999 1989 1979 1990 1979 1987 1995 1987 1995 1992 1999 1999 1999 1999
Northridge Landers Northridge Landers Duzce, Turkey Loma Prieta Hector Mine Loma Prieta Imperial Valley Manjil, Iran Imperial Valley Superstition Hills Kobe, Japan Superstition Hills Kobe, Japan Cape Mendocino Kocaeli, Turkey Chi-Chi, Taiwan Kocaeli, Turkey Chi-Chi, Taiwan
Earthquake Recording R PGAmax PGV (cm/s) Station (km) (g) Beverly Hills - Mulhol 13.3 0.42 58.95 Yermo Fire Station 86.0 0.24 52.00 Canyon Country-WLC 26.5 0.41 42.97 Coolwater 82.1 0.28 26.00 Bolu 41.3 0.73 56.44 Capitola 9.80 0.53 35.00 Hector 26.5 0.27 28.56 Gilroy Array #3 31.4 0.56 36.00 Delta 33.7 0.24 26.00 Abbar 40.4 0.51 43.00 El Centro Array #11 29.4 0.36 34.44 El Centro Imp. Co. 35.8 0.36 46.00 Nishi-Akashi 8.70 0.51 37.28 Poe Road (temp) 11.2 0.45 36.00 Shin-Osaka 46.0 0.24 38.00 Rio Dell Overpass 22.7 0.39 44.00 Duzce 98.2 0.31 59.00 CHY101 32.0 0.35 71.00 Arcelik 53.7 0.22 17.69 TCU045 77.5 0.47 37.00
1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248
72
1249
Table 5 Median and dispersion values from the results of IDA using regression analysis Variable Compressive strength
Pier-ID Median (θ) Dispersion (β) C-1-35 -0.32 0.55 C-1-20 0.09 0.47 C-2-400 0.20 0.42 Yield strength C-2-250 -0.24 0.54 C-3-2.5 -0.11 0.47 Longitudinal reinforcement C-3-1 -0.21 0.49 C-4-0.20 0.27 0.38 Axial load C-4-0.10 -0.34 0.53 -0.48 0.59 Shear span-depth C-5-7 ratio C-5-4 0.21 0.45 -0.28 0.54 FRP confinement C-6-2 layer C-6-3 0.15 0.42
R2 0.97 0.98 0.97 0.99 0.98 0.94 0.98 0.97 0.99 0.98 0.95 0.95
1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 73
1266
Table 6 Collapse probability of different variables at PGAs of 0.5, 1.0, 1.5 and 2.0g 0.5g Pc ∆ (%) C-1-35 0.25 Compressive strength C-1-20 0.05 -74.8 C-2-400 0.02 Yield strength C-2-250 0.20 79.8 C-3-2.5 0.11 Longitudinal reinforcement C-3-1 0.16 83.8 C-4-0.20 0.01 Axial load C-4-0.10 0.25 -74.8 0.36 Shear span-depth C-5-7 ratio C-5-4 0.02 64.2 0.22 FRP confinement C-6-2 layer C-6-3 0.02 -77.7 Variable
1267 1268 1269
Pier-ID
1.0g Pc ∆ (%) 0.72 0.43 -27.8 0.31 0.67 32.8 0.59 0.66 33.9 0.24 0.74 -26.4 0.79 0.32 21.0 0.70 0.36 -29.9
1.5g Pc ∆ (%) 0.91 0.75 -9.3 0.69 0.88 11.7 0.86 0.89 10.8 0.64 0.92 -8.2 0.93 0.67 6.8 0.90 0.73 -10.0
2.0g Pc ∆ (%) 0.97 0.90 -3.2 0.88 0.96 4.3 0.95 0.97 3.5 0.87 0.97 -2.7 0.98 0.86 2.4 0.97 0.90 -3.4
Pc: probability of collapse, (- negative sign indicates the reduction in the probability of damage) ∆: relative difference between collapse probabilities of different parameters
1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282
74
1283
Table 7 Median values of PGA for piers with different parameters Variable Compressive strength
Pier-ID C-1-35 C-1-20 C-2-400 Yield strength C-2-250 C-3-2.5 Longitudinal reinforcement C-3-1 C-4-0.20 Axial load C-4-0.10 Shear span-depth C-5-7 ratio C-5-4 FRP confinement C-6-2 layer C-6-3 1284 1285 1286
Pc ∆ 0.72g 1.10g -10 0.71g 0.62g 29 1.23g 0.79g 23 0.90g 1.31g 31 1.23g 1.16g 23 0.76g 0.82g -18
Pc: probability of collapse, ∆: relative difference between collapse probabilities of different parameters
1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 75
1301
Table 8 Collapse margin ratio (CMR) for collapse safety of piers Probability of Exceedance of collapse 10% in 50 years 5% in 50 years 2% in 50 years Compressive C-1-35 3.89 2.81 1.98 strength C-1-20 5.95 4.30 3.03 C-2-400 3.84 2.77 1.96 Yield strength C-2-250 3.35 2.42 1.71 Longitudinal C-3-2.5 6.65 4.80 3.39 reinforcement C-3-1 4.27 3.09 2.18 C-4-0.20 4.86 3.52 2.48 Axial load C-4-0.10 7.08 5.12 3.61 Shear span-depth C-5-7 6.65 4.80 3.39 ratio C-5-4 6.27 4.53 3.20 FRP confinement C-6-2 4.08 2.95 2.08 layer C-6-3 4.43 3.20 2.26 Variable
Pier-ID
1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318
76
1319
Appendix A Table A1 Failure drift of piers based on IDA results
1320 Variables Ground Motion
Northridge Landers Northridge Landers Duzce, Turkey Loma Prieta Hector Mine Loma Prieta Imperial Valley Manjil, Iran Imperial Valley Superstition Hills Kobe, Japan Superstition Hills Kobe, Japan Cape Mendocino Kocaeli, Turkey Chi-Chi, Taiwan Kocaeli, Turkey Chi-Chi, Taiwan
1321 1322
PGA (g) 0.46 0.26 0.86 0.98 0.88 0.58 0.76 2.02 0.53 1.17 0.68 0.68 1.22 1.17 0.46 0.43 0.47 0.39 0.86 1.27
Compressive strength Drift PGA Drift (%) (g) (%) 9.25 1.80 13.92 6.84 0.48 8.67 10.07 1.23 13.98 10.48 1.12 6.67 9.27 1.31 11.09 7.58 0.95 13.92 10.48 1.03 14.38 7.28 2.24 12.67 6.89 0.91 11.62 10.47 1.53 14.12 13.57 1.01 11.67 10.51 1.22 18.84 9.78 2.04 10.73 8.42 1.80 11.21 8.61 0.62 12.22 7.56 0.70 15.37 11.48 0.68 10.55 5.22 0.70 9.50 4.16 0.88 3.07 17.00 1.69 16.41
PGA (g) 0.50 0.26 0.86 1.12 0.95 0.58 0.72 1.57 0.56 0.97 0.63 0.68 1.28 1.19 0.46 0.39 0.45 0.40 1.11 1.18
Yield strength Drift PGA (%) (g) 10.71 0.42 7.37 0.22 12.46 0.66 10.80 0.70 10.26 0.95 7.70 0.69 7.16 0.63 4.80 1.90 8.41 0.46 6.44 0.87 8.60 0.52 10.76 0.58 10.77 1.05 9.73 1.06 8.80 0.42 6.23 0.35 11.18 0.36 7.75 0.32 6.15 1.31 11.21 0.75
Drift (%) 8.81 7.36 8.31 5.87 9.95 6.38 7.29 6.71 7.31 8.49 20.50 9.56 7.97 14.46 7.81 6.49 7.83 8.25 10.54 4.11
Reinforcement ratio PGA Drift PGA Drift (g) (%) (g) (%) 0.99 10.03 0.55 11.49 0.60 5.95 0.35 9.71 1.52 9.84 0.84 10.78 1.18 3.83 0.87 11.01 1.83 9.71 0.95 10.40 1.25 9.15 0.77 9.38 1.27 8.53 0.80 9.26 2.63 8.53 1.82 5.71 0.96 4.63 0.58 9.84 1.94 9.53 1.22 11.64 1.30 7.31 0.65 9.61 0.94 7.85 0.72 11.87 2.04 6.72 2.04 13.92 2.07 6.82 1.19 10.34 0.86 9.21 0.49 9.61 0.80 8.38 0.45 7.48 0.93 8.04 0.50 12.61 0.88 7.11 0.42 10.55 1.10 1.86 1.32 9.48 1.25 3.66 1.13 8.69
Table A1 Cont. Variables Ground Motion
Northridge Landers Northridge Landers Duzce, Turkey Loma Prieta Hector Mine Loma Prieta Imperial Valley Manjil, Iran Imperial Valley Superstition Hills Kobe, Japan Superstition Hills Kobe, Japan Cape Mendocino Kocaeli, Turkey Chi-Chi, Taiwan Kocaeli, Turkey Chi-Chi, Taiwan
Axial load PGA (g) 0.55 0.42 0.59 1.12 1.17 0.93 0.76 2.41 0.89 1.50 1.12 0.63 1.35 1.26 0.64 0.51 0.73 0.82 1.31 1.25
Drift (%) 13.27 7.27 8.55 10.95 10.81 10.01 10.98 13.78 10.59 11.74 9.93 10.68 12.84 10.27 9.80 7.46 10.18 9.90 5.83 11.95
PGA (g) 0.92 0.71 0.96 1.46 1.93 1.40 1.32 2.49 1.18 1.89 1.66 1.06 1.81 1.67 0.71 0.98 1.10 1.19 1.31 1.88
Shear span-depth ratio Drift (%) 19.01 7.41 8.47 9.88 9.56 10.78 10.38 9.75 9.89 14.02 8.71 8.49 13.69 11.63 9.86 10.23 8.61 9.64 3.27 11.54
PGA (g) 0.92 0.60 1.46 1.50 1.72 1.17 1.20 1.65 1.14 2.04 1.33 0.90 2.58 2.27 0.85 0.62 0.87 0.88 1.38 1.53
Drift (%) 15.76 13.28 16.21 9.17 15.58 12.47 13.63 8.16 14.17 15.62 13.65 13.04 16.45 13.89 14.39 8.56 12.28 13.73 4.03 8.01
PGA (g) 0.86 0.71 0.84 1.33 0.80 1.40 1.30 2.91 1.15 0.97 1.67 1.06 0.92 1.60 0.67 0.98 1.01 0.93 2.20 1.74
Drift (%) 15.02 7.42 7.19 8.69 3.22 10.67 10.33 10.93 9.49 3.88 9.59 9.05 4.58 11.63 10.13 12.13 8.07 4.11 9.86 10.02
CFRP layers PGA (g) 0.55 0.38 0.53 1.01 0.95 0.42 0.76 2.49 0.71 1.05 0.85 0.58 1.20 1.40 0.56 0.47 0.37 0.56 1.18 1.03
Drift (%) 13.38 10.31 8.07 11.18 10.86 3.29 12.07 13.36 13.25 6.72 10.50 10.24 12.70 13.83 10.07 8.85 3.41 7.38 4.06 9.08
PGA (g) 0.74 0.38 0.66 1.04 1.06 0.48 0.54 2.69 0.71 1.05 0.85 0.58 1.20 1.40 0.71 0.51 0.64 0.61 1.24 1.10
Drift (%) 13.18 10.14 11.52 11.62 12.92 3.86 6.18 14.92 10.47 6.53 10.23 10.14 12.42 11.83 13.68 10.05 11.41 11.43 4.55 10.72
1323 77