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Traditionally, finite-element analysis of bridges using commonly used software packages such as SAP2000 [Computers and Structures (CSI) 2006] and STAAD Pro (Bentley 2007) is performed by modeling typical members as prismatic members. However, because the geometry details may significantly change the load characteristics during the simulation of blast loads on bridge components,a detailed bridge member shape using FEM modeling is necessary for the simulation of blast effects. In addition, because the failure mechanisms for bridge components under blast load are not well understood, a detailed finite-element model should include as many details on bridge geometry and behavior as possible so that all failure modes can be identified. In this research, solid elements were used for most bridge members, including footing, abutment, pier, bent, bearing, and deck. Stringers and diaphragms were modeled using shell elements. The behavior of each of the bridge components has been investigated separately using available blast test data on bridge components because full-scale blast testing data on the behavior of the bridge are unlikely to be available. A detailed description on the modeling of different components of the bridge is presented in the following
Modeling of Concrete Piers, Pier Bents, and Footing
A finite-element model of a concrete pier has been developed by modeling the concrete core, cover, and steel rebar inpidually, as shown in Fig. 11. Generally, reinforced concrete members are modeled by an equivalent monolithic element that can represent the combined behavior of both concrete and steel during hazards such as earthquakes and wind. However, this type of monolithic element is not appropriate for reinforced concrete members subject to blast loads. This can be demonstrated by modeling a concrete column subject to blast loads by (1) an equivalent monolithic concrete where rebars are replaced by an equivalent concrete and (2) by modeling concrete and steel rebars separately. Simulation results show that the column modeled by the equivalent monolithic model does not undergo significant damages, except for spalling at the concrete surface. For the column with concrete and rebars modeled separately, a plastic hinge forms at the bottom of the column. It has been observed from recent experimental data and actual blast damages to buildings that the results obtained for the second case, i.e., column with concrete and rebars modeled separately, are more reasonable (Magnusson and Hallgren 2004; Krauthammer and Otani 1997).
Fig. 11. Modeling of the pier
In modeling bridge piers in this research, core and cover concrete are modeled as separate layers to include confinement effects of rebars on the core concrete. A longitudinal rebar has been extended into the footing and the bent per as-built drawings. Fixed boundary conditions have been assigned to the bottom of the footing. A detailed modeling of the bridge pier, pier bent, and footing has been done so that the failure mechanism of the pier system can be identified.
Modeling of Stringers and Diaphragms
The framing system of the bridge consists of wide flange girders with depths of 91 and 76 cm, 40.6-cm-high wide flange middle diaphragms, and 45.7-cm-high channel end diaphragms, as described in Table 3. A shell element has been used for modeling all stringers and diaphragms. To simplify the connection near bearing stiffeners, supports were modeled using a block that has an equivalent weight and stiffness.
Modeling of Deck, Abutment, and Bearings
Bridge decks and abutments have been modeled by monolithic concrete representing equivalent behavior of reinforced concretemembers to minimize the number of elements in the FEM model. Bridge decks are discontinuous with a 7.6-cm gap between the spans. Contact functions have been defined to evaluate the possibl impact force caused by the contact between the bridge decks. Fig. 12 shows the FEM models of decks, abutments, and gaps.
Fig. 12. Modeling of deck, abutments, and bearings: (a) gap between decks; (b) gap near the abutment