117
International RILEM Conference on Materials, Systems and Structures in Civil Engineering
Conference segment on Service Life of Cement-Based Materials and Structures
22-24 August 2016, Technical University of Denmark, Lyngby, Denmark
mesoscale models
particles and cement paste have significantly different properties. This includes
the time-dependent hydration of the cement paste compared to the fixed properties
of the aggregates, only cement paste is prone viscous deformations and the
different properties, e.g. in the simplest case the Young’s modulus, lead to a
heterogeneous distribution of the quantity of interest, e.g. stresses.
2. Mesoscale
generation
In the following, a special focus is given to
mesoscale models.
For modelling purposes, the procedure of
simulating virtual concrete specimens with a
direct discretization of the mesoscale
structure can either be performed by
scanning real specimens [2] or by sampling
“virtual” concrete specimens. In the latter
case, the grading curve characterizes the size
distribution of the aggregates within the
material. In this case, the discretization can
be decomposed into a take and a place
phase. In the first phase, the particles
numbers shapes are generated, whereas in
the second step these particles are placed
into the specimen with the constraint that
overlapping is not allowed. In our current model, an algorithm based on [3] is used. The
particles are assumed to be spherical and inserted at random positions within the specimen
with a reduced diameter. This requires checks to avoid overlapping, but due to the reduced
diameter and the corresponding low particle volume this is computationally not expensive and
can be performed with standard checks enhanced with special subboxes to reduced the
number of overlapping checks. In the second step, an event-driven molecular dynamics
simulation is performed with initial random velocities of the particles and a slow growth of
the particle radii up to the envisages size. For detailed information, the reader is refered to [3].
An example of mesoscale geometries created with the enhanced algorithm is given in Figure
1.
3. Multiphysics modelling of shrinkage
Shrinkage in concrete is usually determined experimentally for stress free conditions. For
modelling purposes, this experimentally determined shrinkage strain is often subtracted from
the macroscopic strain assuming that shrinkage only produces stresses if the macroscopic
deformation of the specimen is constrained.
Looking at concrete on a mesoscale level, a heterogeneous material consisting of aggregates
and cement paste is present, where only the latter is prone to shrinkage deformations. As a
consequence, internal stresses at the particle boundaries occur. Especially at early ages, these
Figure 1 : Mesoscale geometry of a concrete
cube with spherical aggregates.
118
International RILEM Conference on Materials, Systems and Structures in Civil Engineering
Conference segment on Service Life of Cement-Based Materials and Structures
22-24 August 2016, Technical University of Denmark, Lyngby, Denmark
stresses are significant and lead to a microcrack evolution and a pre-damage (without any
mechanical loads).
In this paper, shrinkage is assumed to be a reversible process related to the moisture content
of the material. It is difficult to test this assumption experimentally, since fully rewetting the
specimen is not possible. Moreover, the aging effects are always present resulting in
additional permanent strains that are sometimes interpreted as permanent shrinkage strains.
A two-phase moisture transport model based on [4] has been implemented. In Figure 2, an
exemplary moisture distribution within a concrete specimen (40mm x 160mm) after 28 days
of drying is illustrated. A Fullers-curve for the aggregate size distribution with a maximum
aggregate size of 16mm was used. The drying process starts once the relative humidity of
95% is reduced to 40%. A large gradient of the moisture distribution is observed with the core
of the specimen remaining almost at the initial RH of 95%. Under the assumption of the
moisture content being the driving force of shrinkage strains, this leads to a very
heterogeneous distribution even for this small specimen as illustrated in Figure 3. Another
remark is related to the hydration of the concrete material that is characterizing the
development of the material strength. The hydration stops at relative humidities below 80%.
Figure 3 : Ratio between local and macrospic strain
in horizontal direction.
Figure 2 : Distribution of relative humidity after 28
days of drying.
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International RILEM Conference on Materials, Systems and Structures in Civil Engineering
Conference segment on Service Life of Cement-Based Materials and Structures
22-24 August 2016, Technical University of Denmark, Lyngby, Denmark
As a consequence, any experimental test that measures the concrete strength (or similar the
Young’s modulus) as a function of the time or degree of hydration should take this
heterogeneous distribution into account. Otherwise, size effects are present and the
generalization of the results is very difficult since other effects such as e.g. creep strongly
influence the results.
There are many different approaches on how to include the relation between shrinkage and
moisture content in the numerical model. The first approach follows a strain based model [5].
Based on the simulation of the moisture distribution and an experimental shrinkage tests, an
additional strain component is calculated. Note that when using this approach with a direct
discretization of the mesoscale structure, substantial tensile stresses are obtained.
Calibrating a shrinkage model based on weighting the specimen, that is calculating the loss of
water in a homogeneous way, might significantly deviate from the real situation, since – as
already discussed – the moisture distribution is strongly heterogeneous. Due to the drying
Figure 2 : Minimum principal stress after drying of
28 days (stress based approach).
Figure 3 : Maximum principal stress after drying of
28 days (stress based approach).