Modeling soil penetration is a crucial task across multiple fields, including civil engineering and military applications. A thorough understanding of how objects interact with and penetrate granular materials is essential for optimizing design and ensuring safety. Over the years, numerous empirical and semi-analytical models have been proposed to predict soil penetration. However, the accuracy of these models has often been limited due to their inability to fully capture the fundamental phenomena involved in the process of projectile penetration. Such phenomena include the variation of soil strength with depth, changes in the projectile’s effective area during initial embedment, and the comminution of soil particles at high penetration velocities.
The GeoPoncelet equation, detailed below, addresses these challenges. This two-part drag model employs an incremental approach, making it easy to incorporate parameters that vary with depth, such as soil strength. Additional information regarding the model can be found detailed by Omidvar et al. (2024):
Soil strength variation with depth is quantified using tip stress data from cone penetration tests (CPT). This quasi-static stress is adjusted for strain rate effects to account for the higher penetration rates typical of ballistic scenarios. Additionally, nose shape effects are incorporated to reflect differences between the projectile’s geometry and the CPT cone.
Fig. 1: Variation of CPT tip stress with depth.
Fig. 2: Variation of projectile radius embedment of the projectile nose.
The influence of particle crushing is captured through a specialized high-stress “crushing” drag coefficient, which accounts for the energy dissipated due to particle comminution. The variation of fitting parameters for dry sands within the GeoPoncelet model is illustrated in Fig. 3. The efficacy of the model is shown in uniform sand (Fig. 3) and layered sands (Fig. 4).
Fig. 3: GeoPoncelet prediction of penetration in very dense sand.
Fig. 4: GeoPoncelet prediction of penetration in loose/dense layered sand.
References
- Omidvar, M., Dinotte, J., Giacomo, L., Bless, S., & Iskander, M. (2024). Dynamics of sand response to rapid penetration by rigid projectiles. Granular Matter, 26(3).
- Dinotte, J., Giacomo, L., Bless, S., Iskander, M., & Omidvar, M. (2023). Nose shape effects from projectile impact and deep penetration in Dry Sand. Conference Proceedings of the Society for Experimental Mechanics Series, 49–59.
- Omidvar, M., Dinotte, J., Giacomo, L., Bless, S., & Iskander, M. (2024). Prediction of High-Speed Penetration in Layered Sand Using Cone Penetration Tests. Journal of Geotechnical and Geoenvironmental Engineering, 151(1).