Environmental Engineering Reference
In-Depth Information
Modeling of the collapse of a macroporous material
Daniel Del olmo & alcibĂ­ades serrano
ETSICCP-UPM, Madrid, Spain
aBsTRacT: The macroporous materials are a mix of solid particles, joined together with bridges of
materials that may be the same or different of the solid particles. For example, volcanic rocks like volcanic
agglomerates. in this way, it is interesting to trying to explain how the collapse of these materials takes
place. With the great improvement of the numerical methods and the power of computers it has been pos-
sible to carry out a discrete analysis instead of a continuum one, like would had happened with the classi-
cal theories of continuum. This article shows the first steps taken in this path of modeling the collapse of
macroporous materials in a discrete way.
1
inTRoDUcTion
to generate it numerically. To achieve this, the
following hypotheses were assumed:
This article is trying to show the first steps in
modeling a macroporous material as a discrete media
and not as a continuum. That is to say, the macropo-
rous is modeled as a conjunction of particles joined
together by a breakable material and not as a homo-
geneous continuum material.
in this research, the macroporous material had
been modeled as a series of spheres particles that
are joined with a material of some stiffness with the
capacity of breaking. The model created in this way
is loaded similarly to a consolidated triaxial test. in
the model, it is observed how the contacts get broke
and how the collapse of the macroporous material
takes place.
The research and the article have been structured
in the following way:
- a numerical macroporous material was created.
- The equations of behavior of the material were
defined.
- a series of calculus were run, according to the
equations and to a criterion of failure of the
joining material.
- Finally some conclusions were obtained from
the calculus in order to improve the model and
take it to the next stage of development.
1. The granular material must be contained in a
container of prefixed shape and dimensions. The
chosen shape was a one meter mat cell. This cell
was chosen because from an operative point of
view, it is necessary that the boundary conditions
are separated enough to obtain results that are
not boundary affected. and in addition, a cubic
shaped container simplifies the numerical proc-
ess of filling it with particles.
2. For simplicity in the generation of the material
and attending to geometrical criterions only,
the particles are spherical shape. in this way,
when one sphere is placed over another, the
programmed process is simplified, compared
with other possible shapes of the particles as
ellipsoids, that would have made the process
much more complicated for not being a constant
radius shape.
3. When the spheres fall into the cell, they roll over
the others until a stable position is reached. a
position is considered to be stable whenever a
sphere is in contact with three other elements
or with the bottom of the cell. any wall or any
particle already inside the cell is considered to
be one of the three necessary elements to obtain
such stable position in addition to the bottom
of the cell.
4. The particles or spheres had a continuous
grain size distribution. This curve can be seen
in Figure 1. in the generation of the medium,
with this predetermined distribution, a certain
probability of size is established. in this way, the
2
cReaTinG The MacRoPoRUos
MeDiUM
To make the mechanical study of the three
dimensional macroporous medium, it is necessary
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