Non-Abutment Component Models

Outside of the abutment, the IAB model includes the superstructure longitudinal and

transverse elements, the approach slabs, the fixed and elastomeric bearings found between the piers and superstructure, the pier columns, and the pier foundations. The locations of these components within the IAB model are presented in Figure 2.9. Many of the non-abutment components, such as the bearings and pier columns, are similar to those considered in Filipov et al. (2013a; 2013b) for use in stub abutment bridges, so the developed constitutive models are unchanged. Refinements have been made to components such as the pier columns and the superstructure in order to better represent an IAB.

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Figure 2.9: Location of non-integral abutment components modeled in an overall IAB model.

2.2.3.1 Superstructure

The bridge superstructure is modeled using the grillage method, which represents the girders, deck, parapets, and transverse diaphragms as beam-column elements in the longitudinal and transverse directions. These elements are illustrated in Figure 2.9. The longitudinal elements represent the composite girder-deck section and are located at the elevation of the centroid of the composite section. The longitudinal elements are spaced according to the girder spacing used in actual bridge designs.

Two transverse elements are defined at different elevations in the superstructure, as presented in Figure 2.10 for the deck and model cross-section. The lower transverse elements are located at the girder-deck composite centroid elevation and represent the diaphragms connecting the girders when steel girders are used. They also represent either the permanent bracing (at non- pier and non-abutment locations) or concrete diaphragms (at pier and abutment locations) when prestressed concrete girders are used. The upper transverse elements are located at the deck centroid’s elevation and represent the deck. The transverse elements are spaced

according to the diaphragm and permanent bracing spacing limits provided in the IDOT Bridge Design Manual (IDOT, 2012a).

Figure 2.10: (a) Diagram of the superstructure cross-section, and (b) Representative model of the superstructure cross-section with masses.

The mass of the superstructure is also accounted for in the model, as indicated by the circles at the nodes in Figure 2.10 (b). The masses along the upper transverse element represent the

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deck and the parapets (only in the exterior nodes, as indicated by the larger circles in those locations). The masses along the lower transverse element represents the mass of the girders.

2.2.3.2 Approach Slabs

The approach slabs are not modeled in detail due to their lack of observed damage in past earthquakes. The important contribution from the approach slabs in the model is the mass of these 30-ft long concrete slabs, which may have significant inertial contributions during

dynamic events. Friction between the approach slab and the soil beneath it is not modeled due to an assumption that the soil has settled and there is negligible contact with the slab (Luo et al., 2016). Only 15-ft of the approach slab and its mass contributions are included, as the other half of the mass is expected to be resisted by the approach-transition slab foundation.

2.2.3.3 Elastomeric Bearings, Side Retainers and Fixed Bearings

Type I elastomeric bearings and their side retainers have been experimentally studied in the past (LaFave et al., 2013b; Steelman et al., 2013; Steelman et al., 2018), and numerical models for use in bridge response analysis have been developed based on the experimentally-observed behavior (Filipov et al., 2013b; LaFave et al., 2013a). These previously-developed numerical models are used to represent Type I bearing behavior in the IAB models as well. Samples of these previously-developed numerical models are provided in Figure 2.11.

Figure 2.11: Sample (a) Type I elastomeric bearing cyclic behavior, and (b) side retainer cyclic behavior.

Low-profile fixed bearings have also been experimentally studied to determine their monotonic static and cyclic loading behavior (LaFave et al., 2013b; Steelman et al., 2014). The experiments demonstrated that the primary fuse in the fixed bearing (the component that will fail first) is the anchor bolts (LaFave et al., 2013b). Given this, the fixed bearing model accounts for the shear behavior of the steel anchor bolts and also the friction occurring between the plate and concrete after the anchor bolts fracture. The behavior of the steel anchor bolts is shown in Figure 2.12.

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Figure 2.12: Sample cyclic low-profile fixed bearing behavior (not including the frictional contribution) for a bearing using 1.25-in. diameter steel anchor bolts.

2.2.3.4 Pier Columns

There is evidence of the possibility of significant damage to bridge pier columns during

earthquake events (Waldin et al., 2012). As such, the four circular pier columns of the IABs are explicitly modeled between the pier cap and pile cap at each pier. The pile caps and pier caps are modeled as rigid since they are much stiffer and stronger than the columns. While the pile and pier caps are modeled as rigid, their masses, along with the column masses, are still accounted for in the IAB model. The distributed plasticity column elements that represent the pier columns are force-based beam-column elements developed by Scott and Fenves (2006). The nonlinear behavior in the plastic hinge region is accounted for by using a fiber model of the column cross section. The section is modeled with 8 wedges split into 10 rings. The 2 exterior rings represent the unconfined concrete, while the inner 8 rings represent the confined concrete in the column. The steel reinforcing bars in the column are found between the confined and unconfined concrete. The parameters and modeling methods used for the pier columns in the IAB models have been taken from Filipov et al. (2013b), who validated them against experiments by Kowalsky et al. (1999).

2.2.3.5 Pier Foundations

The pier foundation model is similar to the abutment foundation model. In both cases, the pile caps are modeled as rigid while the individual piles are explicitly modeled along with p-y and t-z springs to represent the effects of the soil surrounding the piles. Unlike the abutment

foundations, the pier foundations experience relatively smaller bending stresses and comprise of more than one row of piles.

The relatively lower bending stresses in the pier piles when compared to the abutment piles leads to some changes in the model of the pier piles as well. The discretization of the pier piles, in terms of both the element and the cross-section, varies from the abutment piles. The pile elements are discretized such that they only extend 20 ft below the pile, where they are then

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assumed to be fixed. The bottom 10 ft of piles are discretized into (10) 12-in. elastic beam- columns, while the top 10 ft are discretized in (20) 6-in. long nonlinear beam-columns.

Additionally, the nonlinear beam-column elements in the top 10 ft have sections composed of only 30 fibers, as opposed to the 120 fibers used in the abutment piles.

The p-y and t-z springs used in the pier foundations are calculated using the same method described for the abutment foundations. There are slight changes between the p-y and t-z curves in the pier and abutment foundations due to the potential differences in pile size (depending on design) and due to the different pile orientations used between the two locations.