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

126

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 

 

Indeed, creep of concrete is related to the creep of cement paste rather than aggregates. 

Therefore, these lasts act as an obstacle and a resistance to the global creep. Consequently, 

tensile stresses arise close to the interface between cement paste and aggregates and lead to 

micro-cracks in this zone. A decrease of the modulus of elasticity and the strength of concrete 

and an increase in the amount of creep strain under the same loading level is therefore 

expected. This creep strain increase is seen as a nonlinearity of the strain with respect to the 

stress level. 

 

To reproduce this nonlinearity at a macroscopic scale, a coupling between damage and creep 

was proposed by [5]. Another solution was given by using a rheological law which depends 

on the stress level. Nevertheless, the tertiary creep could not be achieved when the concrete is 

considered as a homogenous material without coupling with damage. Recently, mesoscopic 

mesh has been used to study the failure of concrete beam under flexural load and highlight the 

presence of microcracking during the sustained load [6].  

 

The aim of this research is to study the influence of micro-cracks due to incompatible strains 

between cement paste and aggregates, on the creep strains amplitude. Hence, a visco-elastic-

damage model [2] is adopted for computing creep using a mesoscopic mesh for representing 

the greatest size of aggregate (more than 1mm) in the cement paste [7].  

 

After a short presentation of the model and the mesh used in this study, the first part of the 

paper is devoted to study the creep of concrete in compression. This part allows verifying the 

ability of this model in estimating the creep of concrete under variant loading levels and 

mainly for studying the nonlinearity of creep strain with respect to stress level. For studying 

the probability of cracking prediction in concrete under compressive creep, the experimental 

results of Roll [8] was adopted.  

 

Experimentally, the effects of creep strain on the residual mechanical properties of concrete 

like Young's modulus and compressive strength were not clearly mentioned in previous creep 

studies [6] and [9]. Therefore, the second part of this paper presents the evolution of the 

concrete compressive strength due to creep loading under two different loading levels (80% 

and 50%) and two age of loading. 

 

 

2.  Mesoscopic creep test simulation 

 

2.1 Mesoscopic mesh 

The algorithm of mesh generation used in this study was developed by [7]. Numerical 

simulations are performed in two dimensions (plane stresses) on a Representative Elementary 

Volume (REV) of concrete of 100×100 mm² (Figure 1). In this mesoscopic approach, two 

phases are considered; cement paste and aggregates. The mesh is not adapted to the exact 

shape of aggregates, but the properties of the material are projected on a finite element mesh 

square grid. The model used for aggregates is an elastic damageable model whereas the 

cement paste strains are described by a visco-elastic damageable model.  

 

---

127

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 1: Mesh of the REV 

2.2 Mechanical model 

The viscoelastic damage model used is described in [2] and [10]. The mechanical behaviour 

of concrete is modelled by an elastic damage model [11] uncoupled with creep. The 

advantage of using a mesoscopic approach arises in the possibility of using simplified 

behavior laws. The mesoscopic damage occurs due to the geometric representation of cement 

and aggregate which have different material properties. 

The relationship between apparent stresses  , effective stresses 

~

  , damage D, elastic 

stiffness tensor 

E

, total strain  , elastic strains 

e

, basic creep strains 

bc

, total strain  , is 

given by:  

                

bc

e

D

D

D

E

E

1

1

~

1

                   

              (1) 

The damage criterion defined by [Mazars, 86] reads: 

                

0

eq

k

f

                                                                                                            (2) 

Where 

eq

 is the equivalent elastic is strain and 

0

k

 is the tensile strain threshold and it is equal 

to 

E

f

t

. The post peak behaviour is calculated as a function of the cracking energy (G

f

) and of 

the element size (h). This regularised technique based on the proposition of Hillerborg (1978) 

allows to avoid strong mesh dependency.

 

The basic creep model use two Kelvin Voigt units (KV) (Figure 2)[2]. Creep is defined in the 

effective stress space, and then damage is added afterwards taking into account only the 

elastic part. 

 

Figure 2: Kelvin-Voigt elements for predicting creep strain [2] 

' 

' 

i

bc

 

k

1

bc

 

k

n

bc

 

n

bc

 

---