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

60

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 

 

by compressive stresses in the core. For structures like tanks or nuclear containment vessels, 

this cracking may significantly increase concrete permeability and reduce tightness. For other 

massive structures (bridges, tunnels…), the serviceability may be reduced due to the 

penetration of aggressive species (such as carbon dioxide, sulfate and chloride ions). 

 

Cracking highly depends on creep (essentially basic creep in massive structures). However, 

the question whether creep strains are the same in compression (such tests are “classical”) and 

in tension (difficult to perform) is not fully resolved. This literature review highlights the fact 

that there is no consensus in scientific community regarding basic creep in tension. Moreover, 

at early age, concrete structures can reach 60°C and thus, an important effect of this 

temperature evolution is expected on the concrete behaviour and especially on the basic creep 

strains rate. 

 

The behaviour of heterogeneous materials, as cement-based materials (concrete, mortar) 

depends on the behaviour of each phase of this material (cement paste and aggregates 

mainly), which can be very different depending on the loading. Tensile stresses are thus 

induced in the cement paste surrounding aggregates. They are also counterbalanced by 

compressive stresses in the aggregates (self-equilibrated state of stresses again), leading to 

debonding at the cement paste/aggregate interfaces and to the growth of intergranular cracks. 

To accurately predict the mechanical consequences of induced cracking, it is required to 

develop of a powerful numerical tool to account for the influence of drying loadings on the 

mechanical response. Indeed, several features should be considered, such as, drying, drying 

shrinkage, basic and drying creep (which relaxes inducing stresses), cracking in tension. 

 

The first part will be devoted to modelling at macroscopic scale. Influence of boundary 

conditions and basic creep strains at early age (age effect and temperature effect), including 

coupling between cracking and creep, and dissymmetric effect in compression/tension. This 

study is based on the RG8 experiment (CEOS national project, [4]) and on a concrete mix 

which is representative of a nuclear power plant which are used for numerical simulations. 

Effectf of drying on the behavior of reinforced concrete structures will be also studied. 

 

In the second part, restraint of shrinkage by aggregates will be investigated. Numerical 

simulations are compared to experimental results using digital images correlations on 

controlled heterogeneous specimens from a cylindrical aggregates obtained by coring and a 

cement paste cast around. Digital images correlation allows for extracting cracking patterns as 

crack openings  and displacement field (after post processing), which is more exhaustive than 

the use of global data from local sensors (drying shrinkage for instance). The numerical 

simulations show the great and positive impact of creep strains, which must be taken into 

account. If creep is not taken into account, cracking is overestimated largely (which may 

induce a large decrease of mechanical properties) after drying, which is not consistent with 

experimental data. 

 

 

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61

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 

 

2. Macroscopic 

scale 

 

The influence of the delayed strains is numerically quantified on the studied concrete 

structures. The total concrete strain is calculated according to: 

ttc

dc

bc

th

au

ds

elas

 

(1)

Where 

elas

; 

sh

; 

au

; 

th

; 

bc

; 

dc

; 

ttc

 are the respective elastic, drying shrinkage, autogeneous 

shrinkage, thermal strain, basic creep, drying creep strain and thermal transient creep. 

Classical models for drying, hydration and temperature predictions are used. 

The damage model proposed by Mazars [5] has been slightly modified [6]. In this model, a 

scalar mechanical damage variable is associated to the mechanical degradation process of 

concrete induced by the development of microcracks. The relationship, between apparent 

stress , effective stress  ~ , damage D (depending also on tensile strength f

t

), elastic stiffness 

tensor E and the previously defined elastic strain, reads: 

~

1 D

 and 

elas

E

~

 

(2)

According to the softening behavior, an energetic regularization [7] prevents of mesh 

dependency. All the main constitutive relationships can be found in [2] and [10]. 

 

2.1. Early-age behaviour 

 

2.1.1 Influence of thermal boundary conditions 

Investigating the maximal temperature reached at early age can be a good way to study the 

massive structure sensibility to cracking (due to restrained thermal and autogeneous 

shrinkage) and delayed ettringite formation (DEF). Besides, the early age cracking can be a 

consequence of a high temperature gradient between the core and the surface of an element. 

Both effects have been studied for a massive wall (thickness: 1.2m; height: 2m; length: 20m, 

see Figure 1) and with the assumption that the wind direction is parallel to the wall. 

 

 

Figure 1: Maximal temperature Tmax reached in a massive wall (thickness 1.2m) with respect 

to wind velocity and external temperature. 

 

In this study, only the external conditions (wind velocity and external temperature) are 

sources of variability but for an application to a real case, materials properties variability must 

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