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Hybrid Blast Load Method
To overcome the limitations of existing approaches, the authors present a new approach termed HBL, which can simulate blast loads on structures realistically while preserving the accuracy of the pressure load method (Yi et al. 2007). In this approach, ConWep pressure generated for a specific charge weight is transferred to an air layer near the structural element, as shown in Fig. 1(c). The blast wave front transferred from ConWep propagates through the surrounding air layers. The air mesh interacts with the Lagrangian structure element to apply the load on structural elements. Fig. 5 shows this approach of applying blast loads on structural members.
ConWep basically offers a one-dimensional (1D) pressure varying with standoff distance, and is mapped to a three-dimensional (3D) simulation in this research. Proper arrangement of load (air) segments, i.e., the mapping points, can overcome the air pressure propagation problem in the detonation simulation. In this research, load (air) segments are set for each structural member separately. This approach can reduce the calibration effort significantly while ensuring appropriate representation of the behavior of the structure, such as spalling and exposing of rebars (Yi 2009). Fig. 5 shows an example of a column whose behavior during blast loads has been simulated using the HBL approach.
Fig. 5. Simulation of column under blast wave using proposed approach: (a) column under blast wave load; (b) simulation results
The proposed approach of applying blast loads has advantages of both pressure load (ConWep) and detonation simulation approaches. It produces a correct pressure field with the same arriving time of blast wave as ConWep, as seen from plots in Fig. 4, and can simulate blast wave reflection and diffraction. When simulation involves complex geometry or nonair blast waves, such as interexplosion in a box girder and air pressure near the deck, other experimental data or a program such as BlastX are necessary to calibrate the load effect parameters. In the proposed approach, applied loads can be calibrated by the BlastX program by assuming that when the pressure load is applied on an air layer segment,the pressure of the nearest air element has the same peak as the applied load.
Verification of Blast Load Effects Using LS-DYNA
Generally, the validation of the reliability of a finite-element model is done through comparison of the results with those from experimental ones. However, there are no published test data available on blast load effects on bridges or an element of a bridge. Hence, reliability of the FE model in LS-DYNA for investigating blast load effects has been carried out by considering blast test data on two reinforced concrete beams by Magnusson and Hallgren (2004). Fig. 6(a) shows the elevation and cross-sectional details of two beam models. Table 1 presents the strength properties and tensile reinforcement details for the two beams. In the study by Magnusson and Hallgren (2004), concrete beams were assembled in a test rig, whichwas positioned in the test area of a shock tube (1:631:2m), as shown in Fig. 6(b). Table 2 presents the results fromthe air blast tests
Table 1. Strength Properties of the Two Beams
Table 2. Results from Air Blast Tests
Fig. 6. (a) Dimensions (in millimeters) of tested reinforced concrete beam; (b) experimental setup of the air blast tests
Finite-element models of two beams using solid elements havebeen developed in LS-DYNA. Hourglass control has been applied toavoid zero-energy modes. Given that the simulation time duration is short and blast pressure is very high, gravity loads were neglected in the simulation. The concrete beam is simulated by solid element with the Johnson Holmquist concrete (JHC) material model (MAT_111 in LSDYNA). This model is capable of simulating concrete behavior during loadswhen the material experiences large strains, high strain rates, and high pressures. Steel rebars aremodeled as beamelements with plastic kinematic material (MAT_3 in LS-DYNA), assuming that a perfect bond exists between the concrete and rebar at the shared nodes.