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

128

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 

 

2.3 Compressive test results 

The experimental compressive creep results of [8] for four loading levels (25%, 35%, 50% 

and 65% of the compressive strength) were adopted. The creep law parameters were 

calibrated for the lowest loading level whereas the mechanical properties were calibrated with 

ordinary cement paste values [7] and to obtain no damaged element after the instantaneous 

loading at 25% of the compressive strength. 

 

A comparison between the experimental results and the mesoscopic approach with and 

without damage are presented in Table 1 and Figure 2. The figure and the table highlight that 

the simulation of creep evolution with damage are closer to the experimental ones than the 

simulation curves without damage. Assuming that creep of concrete occurs without damage 

means that there are no micro-cracks at the interface between cement paste and aggregate. 

Consequently, there is no additional creep strain that occurs normally due to these micro-

cracks. The mesoscopic approach reveals the nonlinearity between the creep strain and the 

applied load. It could be seen, for example, that for the highest loading level, the percentage 

of nonlinearity due to the incompatible strains and the associated damage is about 66%. 

Nevertheless, if an accurate prediction can be obtained with 2D model for tension test, for 

compressive test, 3D modelling is required. 

 

By comparing the field of damage for two loading levels 25% and 65%, one can remark that 

the damage amount is higher for 65% than that for 25% as expected.  That is related to the 

tensile stresses that develop at the cement paste - aggregates interface and lead to the cracking 

development. As the creep strain of cement paste is directly related to the loading level, the 

damage at the interface between cement paste and aggregates increases. 

 

 

Figure 2: Compressive creep strain evolution: comparison between experimental data and 

mesoscopic approach with and without damage 

 

 

0

50

100

150

200

250

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

Time (days)

St

ra

in

 (

μ

m/

m)

 

 

sim. 25%

sim. 35%

sim. 50%

sim. 65%

sim. without damage 65%

Exp. 25%

Exp. 35%

Exp. 50%

Exp. 65%

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129

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 

 

Table 1: Comparison of the experimental compressive creep results with those of mesoscopic 

approach with and without damage (Nonlinearity% = 100 (

wd 

- 

wod

) / (

exp

 - 

wod

) 

 

Loading level  

Exp. Results  

Sim. Results 

 

Explained 

Nonlinearity 

MPa 

/

25% 

(

exp

 )  10

-6

 at 

210days 

With damage 

(

wd

 ) 10

-6

 

 

Without damage 

(

wod

 )   10

-6

 

 % 

10.5 1.4  1153 

1026   

594 

 77.2 

15 2  2108 

1719   836   

69.4 

19.5 2.6  3183 

2476   

1087   66.3 

 

 

2.4 Numerical mechanical behaviour after creep loading in compression 

Fichant 

[

12] developed two damage models (isotropic model and orthotropic model) to solve 

problems with more complex loadings. In these models, the damage development is coupled 

with the cracking energy. When the radial loading is applied, the isotropic model is adequate 

while for the disproportionate loading, the orthotropic model is adopted. In both models, a 

coupling could be done with plasticity and unilateral effects.  

 

The damage affects the elastic part of the stress-strain relation behavior [12]: 

                                     

kl

ijkl

ij

C

                                                                                         (3) 

Where 

ijkl

C

 is the stiffness of the damaged material whereas 

ij

 and  kl

ijkl

C

 represent the 

components of the stresses tensors and elastic strain tensor. 

 

The equivalent strain is calculated from the elastic strain 

e

 and the damage evolution law is 

expressed as follows: 

))

(

(

exp

eq

0

d

t

eq

0

d

B

1

D

when 

0

D

                                                (4) 

where 

0

d

 is the threshold in tension. The parameter 

t

B

 is calculated as a function of cracking 

energy 

f

G

 and of the element size 

h

 with the following equation:   

                                    

f

t

t

G

f

h

B

/

                                                                                         (5) 

where

t

f

 is the tensile fracture stress of the material. This regularised technique based on the 

proposition of [13] allows to avoid strong mesh dependency.   

 

In this study, the isotropic model is used without plasticity and unilateral effect. Moreover, 

damage in compression is also unconsidered. Indeed, at the mesoscale, the rupture is assumed 

to be only due to extension. The geometric representation of the constituents and the contrast 

between material properties is assumed the source of complex behavior observed at the 

macroscopic scale. 

                                                               

Figure 3 represents the constitutive law of compressive behaviour after creep in compressive 

had taken place. It reveals that the maximum strength and in the Young modulus are lower for 

the concrete specimens that were under a higher creep loading and all are lower than the one 

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