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and Bannister 1997). Figs. 2(a and b) illustrate ConWep pressure directly acting on the surface of a column. This approach is only suitable for the analysis before the failure of the structural surfacebecause of spalling. When structural elements fail during FEM simulation, the eroding technique is used to remove damaged elements or nodes from the structure to avoid element distortion. Because the time-varying pressure generated by ConWep acts directly on the exposed structural surface, it will be lost once the load contact surface (i.e., exposed structural surface) is eroded. On the other hand, blast load continues to act on uneroded elements. Therefore, the simulation in Fig. 2(b) underestimates the damage to the structure because the load is not transmitted to the concrete core after the spalling of the concrete surface. Fig. 3 shows an example of the front plates of a steel box girder under blast load using ADINA (Bathe 2006). At a time instant of 1.07 ms, as shown in Fig. 3(b), parts of the plate elements were eroded under a high blast pressure load. Therefore, the blast load associated with eroded elements for time .1:07 ms vanishes, whereas, in reality, the blast load should have propagated into the box girder and caused more severe load effects. These two examples demonstrate the disadvantages of the pressure load method.
Fig. 1. Application of blast loads on structures: (a) pressure load method; (b) detonation simulation method; (c) hybrid blast load method
Detonation Simulation Method
The detonation simulation approach generates blast loads through the simulation of detonation of high explosives using arbitrary- Lagrangian-Eulerian (ALE) mesh and the *MAT_HIGH_EXPLOSIVE_ BURN control card in LS-DYNA. This method simulates the process of detonation and gives an accurate evaluation of the incident blast wave pressure through the explosive material. It is good for the simulation of the interaction between a structure and close-range blast such as landmine explosions (Wang 2001). However, for blast loads on civil structures where the explosion may occur at a certain standoff distance, blast pressure waves are carried to the column surface using air as a medium. This approach has several advantages over the pressure load method: (1) the blast wave load continues to act on the structure after the structural surface elements erode; (2) it can predict the reflection and diffraction of the blast wave; and (3) this method can account for the mutual interaction between the structure and blast wave. This interactioncannot be ignored when the structural displacement is large under the blast wave load.
Fig. 2. Application of ConWep blast load on concrete surface: (a) ConWep-generated blast load on concrete column; (b) simulation results
Fig. 3. Application of ConWep blast load directly on steel plates
Theoretically, the reflection process can be simulated by setting air mesh and reflecting boundaries using detonation simulation. However, problems arise when air is assumed to be an ideal gas because it is difficult to simulate air under different pressure loads using simple constitutive equations. For example, a blast load of 680 kg (1,500 lb) TNT at a standoff distance of R53m is simulated using the pressure load method and detonation simulation, as shown in Fig. 4(a). It is observed from this figure that although the peak pressure generated by both the pressure load method and the detonation simulation process are identical, the blast wave impulse (i.e., area under the pressure curve) by the detonation simulation approach is much smaller than that by the pressure load method. Fig. 4(b) shows the blast load time history of 680 kg (1,500 lb) TNT at a standoff distance of R515:2m in the same simulation. It is observed that the peak pressure by the detonation simulation method drops to zero very quickly as the standoff distance increases.
Fig. 4. Blast wave pressure time history showing comparisons between different methods (I5impulse): (a) pressure at near point; (b) pressure at far point