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Mechanical and Civil Engineering Seminar: PhD Thesis Defense

Tuesday, April 25, 2023
1:00pm to 2:00pm
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Interparticle forces and stress transfer in saturated and unsaturated granular systems
Zichen Gu, Graduate Student, Mechanical Engineering, Caltech,


Granular systems are ubiquitous in nature and engineering applications. The macroscopic behavior of such systems is governed by the behavior at the grain scale, including force transfer between adjacent grains. The correlation between continuum behavior and interparticle forces in granular systems is yet to be fully understood. For a saturated or unsaturated granular system under external load, it is important to decode stress partition and transfer in the solid, fluid, and gas phases. In the meantime, the presence of the fluid phase and gas phase greatly increases the difficulty of measuring interparticle forces in opaque granular systems. This thesis describes the theoretical and experimental works on interparticle forces and effective stresses in two types of granular systems: i) fully saturated granular media, and ii) unsaturated granular media.

The first part of the thesis focuses on the direct measurement of interparticle forces and the experimental validation of the concept of effective stress introduced by Karl Terzaghi. The grain-scale expression of Terzaghi's effective stress for saturated granular media under small deformation and quasi-static state is derived using stress decomposition and balance of forces and moments. For the experimental validation of the analytical solution, an experimental setup was designed to study 2D saturated rubber rod packing under classic 1D consolidation. A hybrid optical-mechanical method based on the Granular element method (GEM) and Digital image correlation (DIC) is applied. The interparticle forces are directly computed from 2D strain distribution of the grains, and the effective stress is calculated using the grain-scale forces. With pore water pressure measured by a pressure gauge, the summation of the effective stress and the pore water pressure is then compared with the external load applied in the 1D consolidation experiment, which is the core of Terzaghi's principle. The 1D consolidation experiment is also compared with the 1D consolidation model and matches the results from Discrete element simulations (DEM).

The second part of the thesis investigates the measurement of interparticle forces in more complex unsaturated granular systems consisting of solid, pore fluid, and pore air phases. In the case of quasi-static, point contact, and low saturation, an expression for the partition of stress is derived as a function of interparticle forces. To simplify the expression of the stress partition equation, capillary bridges, which are integral parts of unsaturated systems under low saturation condition, are simulated numerically using 2D finite element method (FEM) to further understand the influence of gravity on pore fluid clusters. As the original GEM for fully saturated systems focuses on interparticle interactions, the GEM is further developed for unsaturated systems based on the original GEM and considering capillary forces. Finally, a hybrid optical-mechanical approach combined with the granular element method (GEM) is developed to extract interparticle forces in a classic 1D consolidation experiment. The partition of stresses is determined by experimental results and compared with the analytical results.

The major contributions of this thesis are the theoretical derivation and experimental validation of the link between the grain-scale properties (interparticle forces, branch vectors, etc) and the stress transfer in fully saturated and unsaturated systems. The theoretical and experimental methodology employed in the thesis could pave the way for exploring the mechanics and physics behind the constitutive behaviors of a variety of poromechanical systems.

Firestone 384

For more information, please contact Jenni Campbell by email at [email protected].