The objectives of this study were to: 

  • Quantify statistical penetration depths through explicit numerical simulations of projectile penetration for a variety of soil types, moisture contents, and impact conditions;
  • Evaluate the influence that pertinent microscopic parameters have on projectile-penetration resistance, including: projectile size and trajectory, mesoscopic changes in thermodynamic states of soil media, and soil macroscopic characteristics;
  • Quantify the effect of Coulombic damping at interparticle contacts in energy-dissipative capacities; and
  • Quantify the influence that size ratios of UXO to grain can have on penetration depths, and with respect to soil relative densities.

Technical Approach

This research combined analytical, numerical, and experimental methodologies for the quantification of the maximum penetration depth of unexploded ordnance (UXO) into dry granular media at thermodynamic equilibrium under gravitational lithostatic stress states. Penetration into in-situ granular media was explicitly simulated using a combined Discrete Element and Finite Element Methods. Solutions to the governing equations were sought specific to a set of unsteady-state boundary values that may refer to transient phenomena at a number of interrelated scales. These scales spanned across apparent contact areas of sub-microscopic and microscopic surface roughness, corresponding intragrain heterogeneous deformation and interparticle friction at grain scales, grain-scale damping and inertia in formation of force chains and corresponding particle rearrangement at continuum scales, and collective intergranular motion through semi-infinite domains. The research findings were presented for the proof-of-concept of proposed physics-based predictive methodology on high-velocity impact and penetration of granular media at prototype scales, in relation to variational thermodynamic states at underlying scales, where mass densities (i.e., packing densities) under lithostatic stress states may vary with respect to controlled, gravitational packing processes. The results obtained from physical laboratory testing at various scales, including nano-indentation, measurement of surface energy, scanning electron and probe microscopies, grain-to-grain force-deformation in loading and unloading cycles, tri-axial compression, and prototype projectiles’ penetration into a granular material in a geotechnical centrifuge, were presented alongside a series of corresponding analytical and numerical models that have been implemented in a new soft-particle contact algorithm for the combined Finite-Discrete Element Method. The test data measured at the interrelated scales were used to benchmark corresponding grain-, continuum-, and system-scale discrete and finite element analysis models. As for prototype system-scale validation, centrifuge tests of penetration depths and changes in body-force fields were conducted in mono-disperse systems for impact scenarios of a scaled-down semi-armor piercing (SAP) 2,000 lbs. projectile into assemblies of aluminosilicate spheres with two various mean diameters of 0.93±0.08 mm and 0.55 ± 0.05 mm.


The prediction of penetration depths per subsonic-velocity impact scenarios was found to be strongly dependent on initial lithostatic states as per packing density distributions at system scales (e.g., relative density distributions in an in-situ condition), where momentum transfer through intergranular kinematics controls energy dissipation mechanisms through collapse (buckling) of granular assembly (structure), volumetric changes in a control volume, particulate sliding and rolling friction, and corresponding intragrain deformation and intergranular motion during projectile penetration events in the time domain. In addition, a numerical parametric study was conducted to highlight the proof-of-concept with respect to a selected number of scale-interrelated model parameters. 


Both synthesis and critical analysis of the numerically generated and physically measured data from this project are to be carried out in establishing practical conclusions and recommendations for field applications. More specifically, those parameters which hold greatest significance can be identified by: 1) Tabulating numerical predictions of the UXO-soil system response alongside model input values and then, 2) Identifying trends in the tabulations of input values with respect to the penetration-depth quantities. Those parameters that retain significance (i.e., give indications of meaningful input-response trends) when processed in this way can be directly packaged (via graphs and tables) into graphical guidelines for use by the munitions response community. Further, this physics-based multi-scale quantification can further be elaborated as to complement previous research findings. For instance, given datasets for interrelated values of rate-dependent shearing resistance, damping forces, effective inertia, particle breakage and drag forces, corresponding terminal penetration depths can be evaluated as per granular properties, including, but not limited to, scale-dependent intergranular friction coefficient, grain size and shape, moisture contents and in-situ relative density states in comparison to cataloged and empirical parameter values of the existing design guidelines (e.g., “Demonstration of UXO-PenDepth for the Estimation of Projectile Penetration Depth,” ESTCP Project MR-200806). The successful outcome of the proposed research and development in phases includes:

  • Cultivating design-oriented input parameters to account for development of dynamic link libraries (DLLs), which can be functionally integrated (as modules) into the existing UXO PenDepth software program; and,
  • Cultivating design-oriented practical recommendations to incorporate the research findings into the Response Surface Map (RSM) module of the software PENCRV3D.
  • Penetration Modeling,

  • Land,

  • Penetration,

  • Soil Properties,

  • Analysis,