Resistance of a granular medium to normal impact of a rigid projectile

Abstract

This dissertation is a study of vertical penetration of right-cylindrical projectiles into dry granular soil (Ottawa sand). Rigid projectiles were impacted into the soil at velocities less than 1000 ft/sec. Past theories for predicting penetration in soils have almost exclusively been based upon the impact velocity and the corresponding maximum penetration. In this research, the motion of the projectile during the penetration process was obtained by utilizing microwaves.

The motion characteristics were obtained by "bouncing" microwave signals from the bottom of the projectile as it moved downward, and recording the information on an Ampex CP 100 magnetic tape recorder. It was found that penetration of the projectiles into the granular media could successfully be predicted by expressing the resisting forces on the projectile by

-M dv/dt = Av² + Cz + D v > v_c and by -M dv/dt = Bv + Cz + D 0 < v < v_c where M = mass of projectile V = velocity of projectile at time t z = depth of penetration at time t A,B,C,D = constant coefficients.

v_c is a critical velocity at which the "flow'' of the soil changes from one regime to the other, and is believed to be related to the energy necessary for comminution of the sand particles.

The static coefficients, C and D can be found from the strength properties of the soil (c, φ and y) or from a static penetration test. A linear relationship was found between the static resistance, C , and the dynamic resistance coefficient, B. The value of A is believed to be related to the comminution energy, and is not greatly affected by density changes in the sand.

The stability of the projectile was found to be an important factor in the values of the penetration forces.