Constitutive model for predicting dynamic interactions between soil ejecta and structural panels

A constitutive model is developed for the high-rate deformation of an aggregate comprising of mono-sized spherical particles with a view to developing an understanding of dynamic soil–structure interactions in landmine explosions. The constitutive model accounts for two regimes of behaviour. When the particle assembly is widely dispersed (regime I), the contacts between particles are treated as collisions, analogous to those between molecules in a gas or liquid. At high packing densities (regime II) the contacts are semi-permanent and consolidation is dominated by particle deformation and inter-particle friction. Regime I is modelled by extending an approach proposed by Bagnold (1954. Experiments on a gravity-free dispersion of large solid particles in a Newtonian fluid under shear. Proceedings of the Royal Society of London A 225, 49–63) to a general strain history comprising volumetric and deviatoric deformation. For regime II, classical soil mechanics models (such as Drucker–Prager) are employed. The overall model is employed to investigate the one-dimensional impact of sand against a rigid stationary target. The calculations illustrate that, unlike single-particle impact, the momentum transmitted to a rigid target is insensitive to the particle co-efficient of restitution, but strongly dependent on initial density. The constitutive model is also used to examine the spherical expansion of a shell of sand (both dry and water saturated). In line with initial experimental observations, the wet sand is predicted to form clumps while the dry sand fully disperses. The model shows that this clumping of explosively loaded wet sand exerts higher pressures on nearby targets compared to equivalent dry sand explosions.