A Caltech Library Service

Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach


Jerves Cobo, Alex Xavier (2016) Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9GB2211.


Constitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions.

The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.

Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior.

In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media.

In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity.

Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:granular materials; constitutive modeling; discrete modeling; microscopic scale; grain scale; continuum scale; friction angle; critical state; real grains cloning; geometric stochastic cloning algorithm; GSC; grain morphology; sphericity; roundness; Mohr-Coulomb; dilation angle; vorticity; granulance; inter-particle friction; level sets; discrete element method; LS-DEM; Monte Carlo; Embryo; clone; peak friction angle
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Andrade, Jose E.
Thesis Committee:
  • Ortiz, Michael (chair)
  • Bruno, Oscar P.
  • Asimaki, Domniki
  • Andrade, Jose E.
Defense Date:13 April 2016
Non-Caltech Author Email:alexjerves982 (AT)
Funding AgencyGrant Number
National Science FoundationUNSPECIFIED
California Institute of TechnologyUNSPECIFIED
Keck Institute for Space StudiesUNSPECIFIED
Record Number:CaltechTHESIS:05042016-174005898
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch. 2 adapted for ch. 3 DocumentKeck Institute for Space Studies report DocumentPaper: Related work's Project: Keck Institute for Space Studies VideoAuthor's YouTube Channel
Jerves Cobo, Alex Xavier0000-0002-6556-8727
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9701
Deposited By: Alex Xavier Jerves Cobo
Deposited On:10 May 2016 19:42
Last Modified:28 Oct 2021 23:08

Thesis Files

PDF (Thesis (Ph.D)) - Final Version
See Usage Policy.


Repository Staff Only: item control page