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The bridge structure model is put into an air mesh so that the blast air wave load can be transferred to the structure. Hence, an air ALE mesh, as shown in Fig. 16(g), is created by setting the reflecting boundary condition at the bottom of the air block to simulate the reflected blast waves from the ground. Other air block surfaces have nonreflecting boundary conditions.
Hourglass Effect
In the simulation of high-strain rate problems by the explicit method, small damping is usually added into the system to avoid a numerical problem called hourglass due to one-point integration (Hallquist 2006). Undesirable hourglass modes tend to have periods that are typically much shorter than the periods of the structural response, and they are often observed to be oscillatory. The hourglassing technique helps to avoid all numerical stability problems caused by zero-energy modes.
Gravity Loads and Dynamic Relaxation
Gravity loads are applied as a body force and are important for the simulation of blast load effects on structures (Krauthammer and Otani 1997). In the simulation using the explicit solver, all the loads, including gravity loads, are applied as dynamic loads. As a result, the effects of the gravity loads also undergo dynamic magnification. This undesirable dynamic effect is removed by dynamic relaxation, which essentially creates a critically damped dynamic system to attenuate the dynamic effects quickly. As a result, using dynamic relaxation, undesirable dynamic effects are eliminated after a simulation time equal to the structural natural period. During the application of blast loads on the bridge, dynamic relaxation is applied to the case of gravity load only in the beginning. Once dynamic effects of gravity loads are neutralized, blast loads are applied afterremoving the dynamic relaxation condition. Hence, bridge component stresses in dynamic relaxation act as the initial condition for the blast load analysis. The duration of simulation during dynamic relaxation is not included in the simulation time of blast loads, i.e., t50 at the instant of the application of the blast loads. The effect of dynamic relaxation is illustrated using stress time history in Fig. 17 at the midspan of the stringer system in the three-span bridge. Considering the weights of nonstructural elements and live loads, the gravity load would cause approximately 65 MPa of initial stress in the girder flange. This value has been verified using a simpler FEM model in SAP2000.Without dynamic relaxation, it is observed from Fig. 17(a) that although initial stress is 0, it varies between 0 and 3.4 MPa during 100 ms of simulation time. On the other hand, the stress is constant at around 65 MPa using dynamic relaxation. The simulation of blast load effects is also different with andwithout dynamic relaxation, as shown in Fig. 17(b). It is observed that stresses in the flange of the stringers at the midspan without dynamic relaxation are almost 40% higher than those using dynamic relaxation.
Fig. 17. Effects of dynamic relaxation: (a) dead load only; (b) blast load
Contacts
In the blast load simulation on bridge components, after shared nodes get eroded, considering extra contacts between different bridge members and fragments is needed. For example, a pier that has been sheared away from the footing under a lateral blast wave load would pierce into the footing without any counterforce from the footing if no contact element is defined between the pier and the footing, as shown in Fig. 18. Similarly, defining contact between the deck/stringer, stringer/bent, bearing/bent, and bent/pier is also needed.
Fig. 18. Pier piercing into footing because of lack of contact definition in simulation
Blast Load Performance of Bridge Components
Bearing Behavior under Blast Load
The unconventional uplift load due to blast can cause severe damage to bridge components. Table 6 presents bridge-bearing force ranges under blast load. It shows that the bearing compressive force has been increased 2–5 times of the service load, and the bearing experiences tensile failure under high blast load. Bridge Piers under Blast Load Simulation of blast loads on bridges is a highly nonlinear problem because of both geometric and material nonlinearities. Structural components undergo large displacement during a blast loading event. Shear displacement of a pier could be several inches at failure. Midspan deflection of a stringer system can reach 1=30 of the span length. Contact and eroding techniques are helpful in dealing with a large displacement problem during blast loads on highway bridges.