A new simplified analytical model for soil penetration analysis of rigid projectiles using the Riemann problem solution

Abstract

A new simplified analytical model to analyze the penetration of rigid projectiles into soil media is presented. The soil medium is represented by a set of discs, responding in the radial direction under plain strain conditions. A convenient mathematical formulation is derived based on some simplifying assumptions. According to the present approach, the contact parameters in each disc are computed using the developed exact solution of the symmetrical Riemann problem for an irreversible compressible medium. One of the new features of the present model is the incorporation of the exact nonlinear equation of state including unloading-reloading thus considering another key variable that is the maximum medium density that is attained in the process of active loading before unloading is started. Thus the new model considers unloading in the soil medium during the progress of penetration. The present model focuses on the projectile motion and provides information on its velocity, deceleration and depth time histories. It also provides information on the interaction of the projectile with the surrounding soil such as the normal stress distribution along the projectile nose and is capable of determining the contact zone between the nose and the soil. Comparison of the present model results with two-dimensional numerical results as well as with different analytical models and with experimental data is performed. The present model predictions are found to be in good agreement with test data and superior to many existing simplified models. Contrary to many other simplified models, the present model is purely theoretical and does not require any empirical constants or special arbitrary assumptions for calculation of the contact pressures along the projectile nose at all times. The calculations require very small computer time and provide much information regarding the projectile motion in the soil medium.