An overview of projectile penetration into geological materials, with emphasis on rocks.

Abstract An extensive study was performed of the experimental and analytical aspects of projectile penetration in rocks and soils. The experimental data base is much larger for soils than it is for rocks, in which few instrumented penetration tests have been done. To extrapolate experimental results, several methods of analysis and prediction have been proposed: empirical approaches, such as those of Sandia National Laboratories and the Army's Waterways Experiment Station, analytical methods, such as cavity expansion theories and the differential area force law, and numerical modelling by a variety of techniques, i.e. finite differences, finite elements and discrete elements. This paper contains a comprehensive summary of the features of the various computer programs used for penetration modelling, in many materials and at various speeds, over the past 20 yr. Regarding rock targets, the most significant conclusions to be drawn are: 1. • cracks and joints are ubiquitous in most rocks, and can easily overshadow the intact rock's yield strength in influencing penetration; so, it is clear that appropriate site characterization for penetration estimates must include the geological structure at the scale of the penetration; 2. • for analysis, the most desirable rock strength formulation is that which describes the complete variation of shear strength with mean stress; 3. • at velocities of up to a few hundred metres, rock penetration is most dependent on shear strength, which is pressure-dependent; it is less dependent on tensile strength and compressibility; 4. • it appears essential to incorporate in the models the comminution of rock, and post-fracture properties of the broken material; 5. • the internal friction angle of the target is more important than its cohesive strength in controlling penetration; 6. • however, a very uncertain aspect of the penetration process is the amount of frictional force applied to the penetrator; and this is compounded by uncertainties on the values of metal rock friction. (A power law variation of friction angle with sliding velocity has been proposed and a few data have been reported for tuff, sandstone and limestone by a single investigator. For tuff, the shear stress τ is given as equal to the static coefficient of friction m multiplied by an equivalent normal stress τ = μδeff. The δeff is equal to δ·e cδ ξ where δ is the actual normal stress, c is the sliding velocity, and ξ is found to be equal to 2 GPa m/sec for the three rocks tested; interestingly, ξ is reported to be the same for a wet and a dry sandstone. Regardless of the functional form of μ, it appears advisable to recognize the velocity-dependent nature of friction and to reliably estimate the contact area between the ground and the penetrator.); 7. • measurements of stresses and deformations in the medium are what is needed to evaluate the material models used; measuring only the penetrator deceleration and depth is not sufficient; 8. • the stresses induced around the penetrator diminish rapidly away from the body. (An order of magnitude decay takes place over a radial distance of about 2.5 times the projectile diameter; this gives the scale of the volume of target material involved in controlling penetration.); 9. • cavity expansion theories give higher contact stresses on the penetrator than finite element models, for example, because of artificial kinematic constraints, and lack of surface weakening of the target material; 10. • penetration depth for rock (and concrete) appears to scale linearly with the ratio of penetration weight over cross-sectional area.