Stochastic particle packing with specified granulometry and porosity

TL;DR

This paper introduces a stochastic method for generating and placing particles with specific size distributions and porosity in arbitrary domains, useful for simulating granular media like sand and clay.

Contribution

It presents a novel technique combining granulometric analysis with stochastic placement to accurately model granular media with desired properties.

Findings

Effective particle size sampling from empirical distributions

Successful modeling of different granular materials

Generated samples suitable for Discrete Element Method simulations

Abstract

This work presents a technique for particle size generation and placement in arbitrary closed domains. Its main application is the simulation of granular media described by disks. Particle size generation is based on the statistical analysis of granulometric curves which are used as empirical cumulative distribution functions to sample from mixtures of uniform distributions. The desired porosity is attained by selecting a certain number of particles, and their placement is performed by a stochastic point process. We present an application analyzing different types of sand and clay, where we model the grain size with the gamma, lognormal, Weibull and hyperbolic distributions. The parameters from the resulting best fit are used to generate samples from the theoretical distribution, which are used for filling a finite-size area with non-overlapping disks deployed by a Simple Sequential Inhibition stochastic point process. Such filled areas are relevant as plausible inputs for assessing Discrete Element Method and similar techniques.