65
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
Figure 6:
Finally, the presented results show the importance of considering the delayed strains in
structural analysis. It mainly controls the first crack initiation along the specimen. However,
the restraint phenomenon is reinforcement-ratio dependent. A specific analysis must be
therefore conducted for each specific structure.
3. Mesoscopic
scale
3.1. Description of the test
A cement paste with a water to cement ratio of 0.57 containing different contents of sandstone
cylindrical aggregates (with different diameters) is used as a ‘‘model’’ material mix [11]. The
specimen are demoulded and protected from drying by a plastic foil recovered by an adhesive
aluminium layer. The impermeability of the system has been checked by measuring its weight
evolution.
Thin layers of these mesostructures (10 mm width) are cut from each block of mesostructure
(100 × 100 × 50 mm
3
) after 28 days of hydration. The aggregates position is determined
precisely so as to be able to mesh easily these mesostructures for the numerical simulations.
Three thin layer mesostructures constituted of cement paste only are also cast so as to assess
cement paste behaviour during drying without interaction with aggregates effects (and check
that drying shrinkage gradient does not lead to cracking. The tests were carried out at 25°C
and 45 % of relative humidity.
A monitoring of the displacement field for the different mesostructures has been performed
using a digital camera (CANON EOS 350D), at the rate of one shot every 10 min during the
48 first drying hours, on one of the drying surfaces. The evolution of the displacement field
on the observed surface is determined by Digital Image Correlation (DIC) using the Correli-
Q4-LMT software developed in our laboratory (Besnard and Hild, [12]). The observed
surface is previously recovered by a spraying paint so as to obtain a random texture in order
to increase the correlation technique performance.
66
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
3.2. Numerical simulations
The simulation of the mesostructure “1D28” (one aggregate of 28 mm is located in the middle
of the specimen) is performed. Different scenarios have been considered:
FE (Finite Element) boundary conditions: only rigid body motion are prevented, by
eliminating 2 translations and 1 rotation (2D);
DIC (Digital Image Correlation) boundary conditions: experimental displacements
(
U
x
and U
y
) are imposed in the four edges. Note that one has to project the
displacements from the DIC to the generated mesh by the finite element code.
Another numerical simulation has been added,, where creep has not been taken into account.
The results are summarized in Figure 7. It should be noted that only the numerical simulations
with the DIC boundary conditions and with the take into account of creep has converged.
Figure 7: Evolution of vertical displacement for the mesostructure 1D28: comparison between
experiments and numerical simulations.
The difference between experimental and numerical displacements corresponds to the square
difference of both horizontal and vertical displacements in the whole surface:
V
FE
y
DIC
y
FE
x
DIC
x
dV
U
U
U
U
U
error
2
2
2
1
(3)
where
V
FE
y
FE
x
dV
U
U
U
2
2
2
(4)
U
x
FE
and U
y
FE
are horizontal and vertical displacements predicted by finite element
calculations, U
x
DIC
and U
y
DIC
are the experimental displacements determined by DIC.
67
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
The numerical simulations show that the take into account of creep and the use of DIC
boundary conditions give an error of about 5 %. One major horizontal crack at the right side
as the experimental result is obtained. But, another one is also visible at the left, which is not
so visible in experiments. In the case where creep is not taken into account, several significant
cracks are predicted very rapidly leading to no convergence. In the case where only rigid body
motions are prevented, the calculation also does not converge, but the cracking pattern is also
very different from experiments, as expected. Therefore, in this case, it is very important to
impose experimental boundary conditions in order to make a relevant comparison with
experiments. But it is not sufficient; a relevant model (including creep) should be also used.
4. Conclusion and perspectives
With the sake of durability, the modeling of reinforced concrete structures is more and more
focused on their cracking behavior. Specific attention is devoted to the influence of the
concrete delayed strains on the mechanical response of structures. The restraint of shrinkage
shows a significant effect on the cracking behavior. It has to be taken into account in order to
accurately design reinforced concrete structures.
In the first part, numerical simulations were performed on different concrete structures (RG8
beam, a massive wall, a RC tie) to analyze the effect of creep including the dissymmetry
compression/tension and the coupling with cracking, the effect of thermal boundary
conditions including the effect of wind and the reinforcement. They show:
The coupling between creep and cracking allows partially for retrieving experimental
results on the ring test and the RG8 beam experiment;
At early-age, there is a sign change of stresses (compression followed by tension) in
restrained massive structures. Taking into account dissymmetrical creep in tension and
compression leads to results which are noticeably different from results obtained with
considering equal creep in tension and compression;
Wind has a negligible effect on reached maximal temperature, but a significant effect
on temperature gradient;
Initial state of stress caused by shrinkage restraint should be taken into account in
order to assess the mechanical behavior of RC structures
In the second part, investigation of the prediction of drying in a “model” heterogeneous
material has been undertaken, constituted of cylindrical aggregates
surrounded by cement
paste. Drying shrinkage is restrained by the aggregates, which leads to cracking perpendicular
to the aggregate and debonding. Digital Image Correlation has been used in order to get
access to the displacements fields. Numerical simulations show that convergence is easily
obtained for the studied mesostructure, and that the cracking pattern is much more in
accordance between experiments and simulations. It has been also showed that a relevant
model should also be used: indeed, when creep is not taken into account, divergence occurs
rapidly, and too much damage is predicted.