Date of Award

Winter 1991

Document Type


Degree Name

Doctor of Philosophy (PhD)


Civil & Environmental Engineering


Civil Engineering

Committee Director

Isao Ishibashi

Committee Member

Robert Y. K. Cheng

Committee Member

Stephen G. Cupschalk

Committee Member

Y. Mikata


The macro characters of the granular materials depend upon micromechanical parameters such as the void ratio, particle shape, contact force distribution, and initial state of the fabric of the assembly. Since it is difficult to evaluate these internal parameters from laboratory experiments, a macro measure is desired which depends directly on these internal parameters. One such measure has been shown to be dynamic shear modulus but it was incomplete in predicting directional changes in the internal parameters. Therefore, it is hypothesized here that the complete elastic moduli matrix will have more direct information about the internal parameters, especially the dynamic elastic moduli in the principal material directions. This research, therefore, evaluates these moduli experimentally and numerically. The numerical tests provide the effect of internal parameters such as coordination number and fabric index ratio on the dynamic moduli. In the experimental tests measured wave velocities are used to recover the dynamic elastic constants.

The granular material selected for both tests is spherical particles. The tests were run in a cubical triaxial device (4" x 4" x 4") with three independent stress control and associated strain measurement systems. The three orthogonal sides are made of aluminum plates with rubber membranes for applying confining stresses. The other three orthogonal sides are flat plates of lucite. An innovative wave generation system is installed in the cubical device to obtain both compression and shear wave velocities in dry granular material. Both waves are generated by bender bimorph piezoelectric crystals with a unique transducer design for compression wave generation and receiver. Six compression wave paths and three shear wave paths are selected. These wave paths are sufficient to recover the elastic moduli for transversely isotropic material state and provide all diagonal elastic constants for the orthotropic isotropic material states.

The numerical tests are run by using a discrete element code "TRUBAL" which simulates random assemblies of spherical particles. The prediction by this model for stress-strain and volume change are compared with the experimental data to understand the micro and macro behavior of granular materials.

The experimental tests showed that the specimens contain initial anisotropy. The specimens had irrecoverable volumetric strains during the virgin loading and almost recoverable strains. The wave velocities and elastic moduli were not significantly affected by this plastic strain during initial virgin loading. The normalized moduli is developed to exclude the effect of the stress on the elastic moduli, which exhibited quite a similarity with the fabric index ratio. Since the fabric index ratio is a direct measure of the degree of contact normals in two orthogonal directions, this normalized moduli is established as a direct measure of the internal changes of the granular assemblies.