The Development of Theoretical Basis of Mathematical Model of Crushed Rock Particle-Particle Packing

The existing mathematical models that predict the poly-fractional granular media packing density do not take into account their packing degree, which gives a fairly large deviation of the simulation results from the actual experimental values (up to 20-25%). To increase the reliability of prediction of the elastic modulus of crushed rocks, it is necessary to develop the mathematical model that would give more adequate values, since it is known that a change in the granular medium packing density by only 5-10% can lead to a change in the elastic modulus up to 1.5-2 times. The conditions under which smaller particles can be placed in the free space formed after packing larger particles are determined in this work on the basis of the performed computer simulation. It is established that particles of the i-th component of crushed rock can be placed in the free space formed after packing all the previous (larger) components, if the free space volume exceeds the ratio of the actual volume of the particles of the considered component to the packing density of one-dimensional particles to a degree that is exponential function of the serial number of the component.