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