Figure.1 Pressure maximum of the blast wave The expansion law of the explosive product can be simplified to the polytropic index equation of state [1]. PV const γ = (1) Pis the pressure of the explosive product; V is the volume of the unit quality; γis the polytropic index, related to the component and density of the explosive product, γenlarges when the density value increase. AUTODYN is precise in explosions analysis for its BLAST boundary conditions. In this research, 2kg TNT exploding 2m above the bridge is simulated by AUTODYN [4]. 2.2 Fragment characteristics A large amount fragments are produced when explosion take place, these fragments with high speed will penetrate the bridges. Mott formula is the most widely used to calculate the fragments’ quality [1]. 0.5 1.5 0 0.5 0 0 ( ) (1 ) 2 i i t M Kt t d d m μ + + ＝ (2) 2 pm μ = (3) tm is the payload quality(kg ); pm is the fragment average quality(kg ); 0t is the thickness of the cartridge case(m); id is the internal diameter of the cartridge case(m)；Kis the explosive material factor( 1 2 3 2 kg m ). Gurney formula considering cylindrical payload is used to calculate the fragments’ initial speed [1]. 0 2 1 0.5 t t C m v E C m = + (4) 0v is the initial speed of the fragments( 1 m s− g ); Cis the quality of the explosive materials ( 3 kg m− g );
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