Table 6. Bearing Force under Blast Load
Besides large displacement, structural members may also undergo large strains; structure steel or steel rebars may exhibit plastic strains as high as 20%. The large strain in an element results in extra forces applied on the element because of the P-D effects. Hence, P-D effects must be considered in a numerical model of blast loads on bridges.
Material nonlinearity under blast load can be illustrated using hysteretic behavior of pier concrete.An element in the concrete core at the bottomof the pier is selected, as shown in Fig. 19(a). Figs. 20(a–c) shows the plots of vertical stress versus strain because of blast loads acting on the pier for low, medium, and large levels of blast loads.
Fig. 19. Bottom element of core concrete in the pier
Fig. 20. Stress-strain plots of core concrete element near the bottom of the pier: (a) high load; (b) medium load; (c) low load
It is observed from Fig. 20 that the core concrete material near the pier bottom is elastic under low and medium levels of blast loads. However, the core concrete bursts into large nonlinear strain and then rebounds back when the pier is subject to a high level of blast loads. This figure also shows the high strain-rate effects. The highest concrete stress reaches approximately 27.6 MPa while the concrete compressive strength is 55.2 MPa. Consequently, core concrete undergoes nonlinearity both in tension and compression under the interaction forces from bridge superstructures. Similar to seismic hysteretic behavior, the material is damaged and plastic strain accumulates.
Fig. 21 shows a vertical stress-strain plot of pier concrete facing the blast wave at a point shown in Fig. 19(b). It is observed that the concrete facing air blast waves undergoes compression. Concrete at the location demonstrates predominantly nonlinear behavior during all three levels of blast loads, although strain magnitude is smaller than that in Fig. 20. Fig. 22 shows stress-versus-strain curves for core concrete at the back of the pier, i.e., on the surface that is behind the surface directly exposed to blast loads. It is observed from Fig. 22 that the core concrete shows highly nonlinear behavior for all levels of loading. After the compressive blast load hits the pier surface, the compressive stress wave propagates in concrete material. When the compressive wave propagates to the back surface of the pier, it reflects back as a tensile stress wave, causing tensile strain on the back surface.

Fig. 21. Hysteretic graph of pier concrete element facing the blast wave: (a) high load; (b) medium load; (c) low load
Fig. 22. Hysteretic graphs of core concrete elements of the pier back surface: (a) high load; (b) medium load; (c) low load
The following observations on the behavior of bridge components subject to blast loads can be made from the preceding simulation case:
1. Both local and global damage modes exist in bridges subject to blast loads.
2. The global damage mode for a bridge under blast loads is similar to that for seismic loads. It is in an elastic range during low and medium levels of load and goes into an inelastic range during high levels of blast load.
3. Local damage can lead the core material into nonlinear regions, even under low levels of blast load.
4. The global damage mode, such as a plastic hinge formed in the middle of column, has a bigger energy absorption ability than the local damage mode, such as compressive failure of concrete directly facing the blast wave load.

Conclusion

The objectives of the research presented in this paper have been to (1) propose a new approach called the hybrid blast loadmethod for an accurate application of blast loads on bridge components; (2) present verification of simulation of blast load effects in LS-DYNA; and (3) investigate blast load effects on various bridge components using a high-fidelity model of a three-span reinforced concrete bridge in LSDYNA. Numerical results demonstrate that the proposed approach has advantages of two commonly used methods, produces the correct pressure field with the same arriving time of blast wave as ConWep, and can simulate blastwave reflection and diffraction. Using available blast tests on underreinforced and overreinforced beam models, a detailed verification of simulation of blast load effects using LS-DYNAhas been presented. It has been observed from simulation results that the simulation of blast load effects on reinforced concrete members matches with test results when the element size is approximately 25 mm (1 in.). To investigate blast load effects on highway bridges, a high-fidelity three-dimensional finite-element model of a typical three-span simply supported bridge has been developed. The FEM model of the bridge is in such a detail that it can simulate both global and local failure modes. It is observed from the simulation of a blast approximately 3.048 m (10 ft) from the piers of the bridge that a detailed modeling of rebars is important for the simulation of blast load effects on concrete structures. Blast load effects on the reinforced concrete bridge have been investigated by three levels of blast loads: low, medium, and high. Simulation results show that bridge components such as elastomeric bearings are subjective to excessively high levels of stresses during a high level of blast loads. Extensive simulations have been carried out to identify failure modes andseismic-blast correlations These results have been presented in the companion paper. 公路桥梁英文文献和中文翻译(12):http://www.751com.cn/fanyi/lunwen_13887.html