Masters Theses

Yuehui Fan

Date of Award

8-1991

Degree Type

Thesis

Degree Name

Master of Science

Major

Biosystems Engineering

Major Professor

Fred D. Tompkins

Committee Members

Eric C. Drumm, Philip W. Schaefer

Abstract

Monte Carlo simulation of soil particle packing, a fundamental problem encountered in modeling a soil system, and some immediate and potential applications of the model were examined. In the simulation, soil particles were dealt with as rigid spheres (or cylindric rods) with no overlap between them. The simulation is conceptually bifurcated: (i) simulation of particle size distribution, and (ii) simulation of particle location.

For the particle size simulation, a powerful Acceptance-Rejection (AR) method was adopted to deal with the continuous and irregular particle size distribution characteristic of soil. To enable the AR method to be used with a particle size distribution defined by weight the relationship between such a distribution and one defined by number was established. A cumulative size distribution was simulated by conversion, based on numerical differentiation, to the associated frequency density size distribution. Thus, a cumulative size distribution defined by 'percent finer by weight vs. particle size,' a distribution commonly used in agricultural and civil engineering practice, can be approached in such a particle packing simulation.

For the simulation of particle location, an 'inserting particle' technique was proposed. The particles were inserted, one at a time, to a random location, forcing particles which were already resident to sequentially move to eliminate overlap between adjacent particles and between the container boundary and individual particles. The process for generating and placing particles was continued until the overall porosity calculated for the simulated particle pack had reached the value specified by the user.

Since the simulation is founded entirely on realistic soil parameters (particle size distribution, overall porosity, etc.) and on the very nature of soil (discreteness, randomness, etc.), a wide range of applications is possible. A few of these applications are presented herein. Based upon this model, the displacement field of soil particles under load was predicted, and predicted results agreed reasonably well with physical observations made in controlled laboratory experiments. Densest packing of soil particles can be approached, and the smallest porosity associated with this densest packing can be computed. Even very difficult problems, such as dynamic response of soil to a penetrating object, can be addressed using this modeling technique. The simulation will likely prove useful for research and engineering practice as it is applied to soil systems and other granular systems.

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