Proceedings of the International rilem conference Materials, Systems and Structures in Civil Engineering 2016

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. 

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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. 

 

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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. 

 

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