# Structural Performance of Highway Bridges under Given Foundation Settlements

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2 B. Two Bridge Models Example 1 (EX1) is a 3-span posttensioned cast-in-place concrete box girder bridge with a mid-span of 150 feet and 100 feet on each side span, as shown in Figure 1(a). There are two piers and two abutments in EX1. Example 2 (EX2) is a 2- span concrete box girder bridge with a typical span of 150 feet. There are one pier and two abutments in EX2. In both examples, the bridge piers are 30 feet tall, with 6 feet in diameter. A commercial FE code, CSI-Bridge [7] is used to model and analyze the bridges. In the two examples, the following general conditions are assumed: The concrete strength is 4 ksi. (b) Example 2 (EX2): A Two-Span Bridge The bases of the piers are considered as fully fixed, and the abutments are assumed to be roller-supported. The foundation or pier settlements are defined at the bases of the piers. An integral cap beam is adopted for all the bridges. The piers are modeled with three-dimensional (3D) frame elements, and the girder slabs are modelled using 3D shell elements. An overlay of 20 psf is considered. Traffic barriers are used on each side of the bridge girders, and the distributed weight is 1.2 klf. C. Bridge Evaluation Matrix Various bridge design cases are examined using FE simulations to provide a basis for evaluating the settlements and corresponding bridge girder stresses. Table 1 lists the bridge evaluation matrix defined in this study. Four bridge girder horizontal curve radii and five bridge skew angles are selected. Bridges and settlements are evaluated based on the following parameters: (a) Example 1 (EX1): A Three-Span Bridge (c) Cross Section of the Concrete Box Girders Figure 1. Two Examples: Posttensioned Concrete Bridges 1. Horizontal Curve Radii: the four different bridge girder curve radii considered are 250 feet, 500 feet, 1000 feet, and infinite radius, respectively. The last case represents a straight bridge. The 3-span bridges in Example 1 with various horizontal curve radii are illustrated in Figure Skew Angles: To study the effects of bridge skew angles on bridge girder settlement stresses, five different bridge skew angles are considered in this study, namely 0, 15, 30, 45, and 60. These are shown in Figure Settlement Cases: Bridge pier settlement cases, including both one-pier settlement and two-pier settlement, are considered in the FE simulations. Figure 4 shows the simulation setups for both one-pier settlement and twopier settlement. The settlements are defined at the bottom of the piers, as seen in Figure 4, representing the foundation settlement below one pier, or simultaneous settlements underneath two piers. The magnitude of pier settlements is denoted as Δs, as shown in Figure 4. For Example 2, only one-pier settlement is possible. For both one-pier settlement and two-pier settlement, two different pier settlement magnitudes are considered in this study, namely 0.5 inch and 1.0 inch. The consideration of a settlement of 0.5 inch is to verify the bridge FE analysis results obtained using 1.0 inch as the pier settlement. For the rest of the paper, only the FE analysis results based on the one-inch settlement are presented.

3 Table 1. Bridge Evaluation Matrix Curve Radius (ft) Skew Angle (Degree) Pier Settlement (in) , Infinity (b) Skew Angle = 30 Degrees (a) Radius = 250 feet (c) Skew Angle = 45 Degrees (b) Radius = 500 feet (d) Skew Angle = 60 Degrees Figure 3. Example 1: 3-Span Bridges with Various Skew Angles (EX1) (c) Radius = 1,000 feet (d) Radius = Infinite (straight bridge) (a) Example 1: One-Pier Settlement Figure 2. Example 1: 3-Span Bridges with Various Radii (EX1) (b) Example 2: One-Pier Settlement (a) Skew Angle = 15 Degrees

4 (c) Example 2: Two-Pier Settlement Figure 4. Pier Settlement Cases (c) Example 2: Two-Pier Settlement Figure 5. Bridge Girder Deformed Shapes (Dead Load + Settlement) III. RESULTS AND DISCUSSION A. Bridge Deformation and Stress Plots The deformed shapes of the bridge girders for the two examples under both dead load and pier settlements are plotted in Figure 5. As expected the dead load deformation is dominant in both examples, where the maximum girder deformation is found at mid-span between the piers, and piers and abutments. For Example 2, the deformed shapes for onepier settlement and two-pier settlement cases are similar. Figure 6 shows the bridge girder stress contour plots under both dead load and pier settlements for the two examples. It is found that the girder stress induced by pier settlements has maximum (tension) and minimum (compression) values at the pier supports. (a) Example 1: One-Pier Settlement (b) Example 2: One-Pier Settlement (a) Example 1: One-Pier Settlement (b) Example 2: One-Pier Settlement (c) Example 2: Two-Pier Settlement Figure 6. Bridge Girder Stress Contour Plots (Dead Load + Settlement)

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