Diameter-Effect Modelling in Unconfined Steady Non-Ideal Detonations

Since explosives are the source of all energy used for rock blast fragmentation and heave, multidimensional effects in the detonation driving zone become essential to better describe the detonation process. In order to use the explosive as an energy source-information for more realist blasting performance simulations, a simple and effective modelling strategy is desirable. Facing this challenge, an engineering approach to two-dimensional unconfined non-ideal detonation is proposed. Based on the elliptical construction of the shock locus, the model combines the axial cylindrical stick Q1D solution with some additional limiting conditions to determine the sonic edge of the charge. For a given set of rate law parameters and velocity of detonation, a complete axial solution is firstly computed through the Q1D model. From this solution, a vital relationship between the axial shock curvature with the shock shape parameters can be stablished. Once this relationship is found, the problem simply reduces in finding the shock shape parameters subject to the sonic edge condition. As a result of this calculation, the corresponding charge diameter can be found. Consequently, the proposed model can map the diametereffect curve by relating the unconfined velocity of detonation with its corresponding diameter. Finally, because of its low computation cost, the proposed engineering approach can be also used for characterizing the rate law parameters by fitting to data from unconfined detonation experiments