Computational Geomechanics @Caltech
Multiscale Modeling of Granular Matter for Earth and Space
of the geomechanics group at Caltech is to understand, model, and predict the
mechanical behavior of granular materials, and hence contribute to the
understanding of a wide range of natural and man-made processes such as
liquefaction, landslides, and planetary exploration. Geomechanics aims to
describe the mechanical behavior of geologic materials such as soils, rocks,
and concrete. While significant progress has been made in understanding
material behavior, much of it has been predicated on phenomenology. Access at
lower scales was not available and engineering problems had to be solved.
However, the phenomenological approach has neared its predictive limits,
especially in predicting instabilities, which truly originate at the grain
scale. It is only in recent years that access to the grain scale has become
available experimentally (e.g., X-ray CT) and computationally (e.g., DEM). Yet
most of these grain scale techniques remain qualitative and continue to lack
connection with the macroscopic framework (e.g., plasticity theory, critical
state soil mechanics).
In light of the aforementioned
advances and challenges, there remain a number of fundamental questions that we
are interested in and require answers: what is the micro-origin of
macro-strength, strength-dilatancy? How is critical state achieved
micromechanically? What is the micromechanical state at the onset of
instabilities? Why are instabilities localized or diffused? How do fluid-solid
material transitions occur even in granular materials?
These questions take our group
into the realm of engineering science and provide the intellectual motivation
for our interdisciplinary work at Caltech. To attempt answering these
fundamental questions,we combine concepts in mechanics,
physics, applied math, computational science, and geoscience, to develop a
number of computational and analytical
tools: novel micromechanical models to compute and measure grain-scale states,
accurate macroscopic frameworks, and multiscale techniques to connect macro and
We are currently transforming
micromechanical models such as DEM by accounting for particle shapes and by
connecting the method directly to advanced experimental techniques based on
imaging (e.g., X-ray CT). We have invented a method called granular element
method (GEM) that moves beyond photoelasticity and enables the inference of
inter-particle forces in real (opaque), three dimensional, granular materials.
These two techniques promise to transform experimental mechanics by enabling
the extraction of kinematics and contact forces at the granular level with an
unprecedented level of accuracy. These kinematics and forces at the grain level
can then be used within the multiscale techniques that we have pioneered in
granular mechanics, where basic plastic internal variables in continuum models
are updated directly from the micromechanics. These advances are leading us to
develop physics-based constitutive models that can be used to predict
instabilities that are localized or diffused, drained or undrained.
The impact of the current advances in geomechanics is very broad, even
in scales. From the micro scale, we can begin to understand the basic
mechanisms at the heart of continuum phenomena such as compaction bands and
critical state. At the meso scale, we can begin to understand the processes
controlling granular flow, which impacts earthquake nucleation and landslides.
At the engineering scale, we can begin to understand the complex interaction
between rovers and sampling tools under low atmospheric pressure and gravity in
celestial bodies or planets. We can begin to abandon phenomenology.
Andrade et al. Multiscale ‘tomography-to-simulation’ framework for granular
matter: the road ahead. Geotechnique Letters, 2:135-139, 2012.
- K. W. Lim and J.E. Andrade. Granular Element Method (GEM) for
three dimensional discrete element simulations. International Journal for
Numerical and Analytical Methods in Geomechanics, in press, 2013.
- J.E. Andrade et al. On the rheology of dilative granular media:
bridging solid- and fluid-like behavior. Journal of the Mechanics and Physics
of Solids, 60:1350-1362, 2012.
- J.E. Andrade and C.F. Avila. Granular element method (GEM):
linking inter-particle forces with macroscopic loading. Granular Matter,
- A.M Ramos et al. Modeling diffuse instabilities in sands under
drained conditions. Geotechnique, 62:471-478, 2012.
- W.-C. Sun et al. Connecting microstructural attributes and
permeability from 3D tomographic images of in situ shear-induced compaction
bands using multiscale computations. Geophysical Research Letters, 38:L10302,
- J.E. Andrade et al. Multiscale modeling and characterization of
granular matter: from grain kinematics to continuum mechanics. Journal of the
Mechanics and Physics of Solids, 59:237-250, 2011.
- J.E. Andrade. A predictive framework for static liquefaction.
Geotechnique, 59:673-682, 2009.