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For the beam B100, it has been observed that the midpoint deflection of the beam at failure during the test matches with that from the FE simulation of a beam model with 3,632 elements, each with a mesh size of 27.4mm. Fig. 7 shows the simulation of beam B100 subject to blast loads at different time instants. It is observed fromthis figure that (1) spalling of the beamoccurs at the time instant t52:4 s; (2) tensile concrete in the region of the maximum moment cracks at the instant t53:75 s; failure in the beamis initiated by yielding of the steel while the strains in the concrete are relatively low, with cracks propagating up to the compression region; (3) longitudinal rebars are severed at the instant t55:1 ms; and (4) finally, at time t55:2ms, concrete in the compression zone is completely crushed following the severance of rebars, leading to a complete failure of the beam. The final stage of failure, i.e., crushing of concrete following severance of rebars, is similar to the ductile failure of the balanced-reinforced beam observed during the experiment byMagnusson and Hallgren (2004).
Fig. 7. Effects of blast loads on proper-reinforced beam B100 in Table 2: (a) t52:4 ms; (b) t53:75 ms; (c) t55:1ms; (d) t55:2ms
Similar to the B100 beam, it has been observed from simulation results for the beam B40 that the midpoint deflections of the FE model of the beamat failure is almost in close range to the experimental value of 17.5 mm (0.689 in.) for a mesh size of 28.4 mm (1.12 in.). Fig. 8 shows the simulation of this overreinforced beam B40 subject to blast loads. In this beam, failure is initiated by crushing of the concrete followed by a sudden disintegration of the compression zone while the
stress in the relatively large area of steel has not reached its yield point. This brittle failure behavior of the beam B40 in the finite-element model is also similar to that observed during blast tests byMagnusson and Hallgren (2004).
Fig. 8. Effects of blast loads on overreinforced beam B40 in Table 2:（a）t53:62 ms; (b) t54:58 ms
Results presented previously show that the finite-element model of reinforced concrete elements in LS-DYNA can be used to investigate the effects of blast loads reliably, considering the fact that the modes of failure of two beams were similar to those observed during blast tests when FE models were calibrated for the mesh size based on test results. To ensure the reliability of the simulation of blast load effects on bridge components, the bridge components using a mesh size of 25.4 mm (1 in.) will be modeled.
Bridge Modeling
Hypothetic Target Bridge
The effect of blast loads on bridge components has been investigated by developing a finite-element model of a typical three-span bridge.Fig. 9 shows the plan and elevation of this hypothetical three-span noncontinuous bridge. Table 3 also shows key parameters of the bridge configurations.Anoncontinuous bridge was selected to avoid complex progressive collapse mechanisms due to high bridge system redundancy.
Fig. 9. Plan and elevation of the typical bridge
Table 3. Parameters of the Typical Hypothetical Bridge
Fig. 10 shows rebar detailing in the piers and bents. It has been observed that longitudinal rebars from piers go into bents as well as into footings.Table 3 shows the cross-section properties of stringers in the bridge. Another key element of the bridge is the bearing that defines the boundary condition between the piers and stringers. Although the as-built bridge has different types of bearings, elastomeric bearings were used in this research because they are used extensively to replace old bearings during seismic rehabilitation of bridges
Fig. 10. Rebar detailing: (a) pier section; (b) bent section
Modeling of Bridge Members
A detailed model of the bridge has been developed using LS-DYNA. For finite-element simulation of the bridge, an explicit solver in LSDYNA has been used to handle a large number of elements. The ALE mesh was utilized to consider both the fluid behavior of explosives and nonlinear constitutive material properties of bridge structures. Because large deformations occur in bridge member elements subjected to blast loads, the element eroding technique is used to avoid severe element distortions during the simulation of blast load effects.