The objective of this project is to develop physically based models to predict the penetration depth of common military munitions in various soil conditions. Ultimately, the models will be used to determine probable depths of munitions in the soil of formerly used defense sites in support of planning for remediation. These results will be used to aid sensor detection and removal of these munitions.

Technical Approach

To model munitions penetration, a meshfree framework based on the Reproducing Kernel Particle Method will be developed for handling extremely large deformation. Multi-field meshfree formulations will be implemented in consideration of the porous nature of soils. Stabilized nodal domain integration schemes that ensure the accuracy and stability of the numerical solution will be developed for multi-field Galerkin formulations.

To accurately represent the behavior of the soil, a novel viscoplasticity model will be developed with regularized softening to account for large deformation of the soils. The model will account for the behaviors seen in penetrations problems, including nonlinear pressure sensitivity of shear strength, rate dependence, shear-enhanced dilation, and a compaction hardening due to pore collapse and grain crushing. The model will include a regularized softening with increasing porosity that can naturally transition to more fluid-like flow, including liquefaction that is sometimes observed during penetration. The viscoplasticity model will be extended to better capture transition from dilation to compaction, and embedded in a partially saturated multiphase framework, with the partially saturated framework. 

A fitting procedure for soil parameters will be created based on laboratory soils tests. The models will be verified against analytical and other numerical solutions and validated using published data both at the laboratory and field scale. Finally, the models will be run under different conditions to estimate the depth of buried munitions.


The project will benefit the Department of Defense (DoD) by providing a robust numerical framework for modeling penetration into soils. The results of the simulations will translate into a set of tables for probable depths of munitions based on soil conditions, projectile type, and firing conditions.

The modeling will also have broader impacts to the engineering and scientific communities. The framework will be able to model other penetration scenarios for soil, rock, and concrete, for applications as diverse as deep penetrators designed to target underground bunkers to meteor impacts on extraterrestrial bodies. The constitutive models will further the fundamental understanding of soil behavior as we move toward physically based models for capturing observed soil responses. In addition, the numerical algorithms will enhance the set of tools available to solve many physical problems, especially those involving large deformation, material separation, and coupled physics problems.

  • Modeling,

  • Impact Burial,