6.2 Modelling the concrete mechanical properties
6.2.4 Comparing the model results with measurements
The main experimental results from Chapter 4 were used to conceived the formulations that compose the material model and some other obtained results can as well be used to test its accuracy, i.e. to validate it. Some comparisons between test results and calcu- lations with the material model are presented below. The equations that constitute the developed model are summarized in Appendix E.
6.2.4.1 Strength and Stiffness
The tests of strength and stiffness were conducted on the concrete samples following defined conditioning schemata (see Chapter 3.2.1). In Fig. 6.6 the model is tested ac- cording to the conditioning scenario at which some samples of the concrete MRC were subject. Starting with a reference temperature of 20 °C and a mean relative humidity of 100 %, the samples were subject to drying during 100 days at 20 °C and 65 % RH. Then
6.2 Modelling the concrete mechanical properties
they were heated up to 80 °C and kept at a relative humidity of 65 % for 90 days longer.
The conditioning process is indicated on the top figure of the diagram.
0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 1 7 5 2 0 0
0 . 7 0 . 8 0 . 9 1 . 0 1 . 1 1 . 2 1 . 3 1 . 4 1 . 5
2 0 ° C / 1 0 0 % R H 2 0 ° C / 6 5 % R H 2 0 ° C / 6 5 % R H
Relative compressive strength, fc(T,h)/fc(20 °C, 100 % RH) [-] m e a s u r e d
c a l c u l a t e d 8 0 ° C / 6 5 % R H
0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 1 7 5 2 0 0
0 . 7 0 . 8 0 . 9 1 . 0 1 . 1 1 . 2 1 . 3 1 . 4 1 . 5
Relative tensile strength, fct(T,h)/fct(20 °C, 100 % RH) [-] m e a s u r e d
c a l c u l a t e d
0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 1 7 5 2 0 0
0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 1 . 1
Relative modulus of elasticity, Ec(T,h)/Ec(20 °C, 100 % RH) [-]
T i m e , t [ d ]
m e a s u r e d
c a l c u l a t e d
Figure 6.6: Comparison between calculations with the new material model and measurements of com- pressive strength (top), tensile strength (middle) and modulus of elasticity (bottom) for the concrete MRC after drying during 100 d at 20 °C / 65 % RH and then heated during 100 d at 80 °C / 65% RH
Measurements of the mechanical properties were carried out at reference conditions, after the end of the drying period at 20 °C, shortly after increasing the temperature and at the end of the period of sustained elevated temperature. In Fig. 6.6 the compressive strength, tensile strength and modulus of elasticity of the concrete relative to the proper- ties at reference conditions are plotted with time according to the conditioning process.
The measured values are depicted by the square icons including an indication of the scat- tering of the experimental results by displaying, between horizontal bars, the standard deviation. The results of the material model represented by the continuous lines fol- lows quite well the experimental results. It reproduces the increment on the compressive and tensile strength due to drying during the first 100 days, the sudden change in these strengths due to the increment of temperature from 20 to 80 °C and the increase of the strengths due to further drying afterwards. Unlike the strength development, in case of the modulus of elasticity, the model calculates an abrupt change in the concrete stiffness at the beginning of drying followed by an increment of it as the drying continues. In Ap- pendix E.2 the equations of the material model regarding the influence of temperature and moisture content on the strength and stiffness of concrete are summarized.
For the conditioning scenario considered in Fig. 6.6, the model is able to reproduce the behaviour of the concrete very accurately. However, other condition scenarios involving higher moisture content during the heating process cannot be reproduced by the model in the same way. An example of it is presented in Fig. 6.7. This figure presents the com- parison between model calculations and measurements of tensile strength and modulus of elasticity from samples that were stored at 20 °C and 95 % RH during 200 days and then heated up to 60 °C while the relative humidity was kept at 95 %.
At high ambient humidities the concrete loses only a small amount of moisture to the environment and therefore the enhancement of the strength as well as the recovery of the modulus of elasticity after dropping down during drying are limited. In Fig. 6.7 it can be seen how the model reproduces the behaviour of the concrete during the drying process at 20 °C very well. Nevertheless, once the temperature is increased, the measured results differ from the prediction of the model considerably. This is due to the fact that the model neglects the influence of hydrothermal reactions. In case of compressive or tensile strength the hydrothermal reactions cause a healing of the microcracks produced by the thermal incompatibilities and therefore, unlike the model, the measured values do not show a decrease of the strength after heating. The healing of microcracks has however smaller effect on the concrete stiffness and in consequence, the model behaves better when predicting the behaviour of the modulus of elasticity.
6.2 Modelling the concrete mechanical properties
0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0
0 . 7 0 . 8 0 . 9 1 . 0 1 . 1 1 . 2 1 . 3 1 . 4 1 . 5
Relative tensile strength, fct(T,h)/fct(20 °C, 100 % RH) [-] m e a s u r e d
c a l c u l a t e d
2 0 ° C / 1 0 0 % R H
2 0 ° C / 9 5 % R H 6 0 ° C / 9 5 % R H
0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0
0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 1 . 1
Relative modulus of elasticity, Ec(T,h)/Ec(20 °C, 100 % RH) [-]
T i m e , t [ d ]
m e a s u r e d
c a l c u l a t e d
Figure 6.7: Comparison between calculations with the material model and measurements of tensile strength (top) and modulus of elasticity (bottom) for the concrete MRC after drying during 200 d at 20 °C / 95 % RH and then heated during 100 d at 60 °C / 95% RH
The comparisons presented in Figs. 6.6 and 6.7 correspond to two extremes in terms of the accuracy of the model. At lower moisture content the model delivers very accurate predictions because the influence of the hydrothermal reactions is negligible which is in accordance with the assumptions of the model. Meanwhile, by concretes containing a high amount of moisture, the hydrothermal reactions play an important role on the strength development that the model cannot reproduce. Further comparisons including other conditioning scenarios at which samples from the concrete MRC were subject are included in Appendix D.
6.2.4.2 Time dependent deformations
In the following diagrams results from the material model are compared with some se- lected measurements of shrinkage and creep. Additional comparisons including all the creep and shrinkage measurements conducted on samples of the three concrete mixtures are presented in Appendix D.3 and D.4. In order to predict the shrinkage and creep
deformations of the samples, the model has to recreate the whole history of storage con- ditions to which the samples were subject before being loaded. Previously to conducting the creep tests, the samples used for the measurements were conditioned for over 450 days at 20 °C and relative humidities of 95, 85 and 65 %. Moreover, the samples were loaded after the testing temperature in the chamber was reached (see Chapter 3.2.5).
Fig. 6.8 compares the shrinkage deformations measured on the concrete MHC during the creep tests conducted at 20 and 70 °C and 65 % RH with the calculations of the material model. The equations of the material model regarding shrinkage and creep are summarized in Appendix E.3 and E.4 respectively.
0 . 0 1 0 . 1 1 1 0
- 5 0
0
5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0
Shrinkage deformation, εcds [µm/m]
P r e c o n d i t i o n
R H / 2 0 ° C m e a s u r e d c a l c u l a t e d
6 5 %
8 5 %
T e s t i n g c o n d i t i o n s : 2 0 ° C / 6 5 % R H
6 0
0 . 0 1 0 . 1 1 1 0
- 1 0 0 - 5 0
0
5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0
Shrinkage deformation, εcds [µm/m]
D u r a t i o n o f d r y i n g d u r i n g l o a d i n g , t - ts [ d ] P r e c o n d i t i o n
R H / 2 0 ° C m e a s u r e d c a l c u l a t e d
6 5 %
8 5 %
T e s t i n g c o n d i t i o n s : 7 0 ° C / 6 5 % R H
6 0
Figure 6.8: Drying shrinkage calculated with the material model in comparison with the measured values for the concrete MHC during the creep tests conducted at 20 °C (top) and 70 °C (bottom) and 65 % RH
In Fig. 6.8 the shrinkage deformations are plotted against time. The time axis indi- cates the duration of loading which means that even when the material model is able to calculate the shrinkage deformations from the beginning of the drying process, only the
6.2 Modelling the concrete mechanical properties
shrinkage deformations occurring after applying the load were taken into account for the comparisons with the measurements.
As it can be appraised on the top part of Fig. 6.8, the material model is able to predict the shrinkage behaviour of the concrete during the creep tests at 20 °C very well. For the samples that were previously conditioned at 65 % RH, the model predicts barely no change in the shrinkage deformations, because after 450 days of drying at 65 % RH, only small changes on the mean relative humidity may still occur if the ambient rel- ative humidity remains unchanged. This was found to be in perfect accordance with the measurements. The samples previously conditioned at 85 % RH can very well lose moisture to an environment with 65 % RH, and therefore the material model predicts the development of shrinkage deformations following the tendency shown by the measure- ments. The bottom part of Fig. 6.8 presents the comparisons between the calculations with the material model and the measurements of shrinkage during the creep tests con- ducted at 70 °C. The development of the shrinkage deformations as presented by the material model seems to be slower in comparison with the measurements. This may be due to the fact that the air blowers within the climate chambers accelerated the drying process during the creep tests (see Chapter 3.2.5). This acceleration is not taken into account by the model because the model of moisture transport was calibrated based on measurements conducted without any influence of air blowers.
The creep deformations measured in the concrete MRC during the tests conducted at 20 and 70 °C and 65 % RH are compared with the model calculations in Fig. 6.9. For the concrete MRC the samples were conditioned at three different ambient relative hu- midities before conducting the creep tests, namely 95, 85 and 65 %. The diagram on the top corresponds to the creep tests conducted at 20 °C and 65 % RH and the one on the bottom contains the results from the tests conducted at 70 °C and 65 % RH.
The model can reproduce the influence of moisture content on the development of creep.
For the creep tests conducted at 20 °C, the model follows the tendency of the measure- ments. The higher the moisture content at the beginning of loading, the higher the creep deformations that develops. In case of the tests conducted at 70 °C, the model also recognises the importance of the initial water content on the development of the creep deformations. A rather surprising good prediction is shown by the model for the samples previously conditioned at 95 % and 85 % RH. Both model and measurements show almost the same creep deformations for these samples. Following the definition of the hygrothermic coefficient of concrete (see Section 6.1.3), after increasing the tem- perature from 20 to 70 °C, the relative humidities reached by the samples previously conditioned at 95 % and 85 % are barely the same, and therefore the drying and basic creep that develops afterwards may also be similar.
0 . 0 105 0 . 1 1 1 0 1 0
1 5 2 0 2 5 3 0
Specific creep, εcc/σc [µm/(mMPa)]
P r e c o n d i t i o n
R H / 2 0 ° C m e a s u r e d m o d e l l e d
6 5 %
8 5 %
9 5 %
T e s t i n g c o n d i t i o n s : 2 0 ° C / 6 5 % R H
6 0
0 . 0 105 0 . 1 1 1 0
1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0
Specific creep, εcc/σc [µm/(mMpa)]
D u r a t i o n o f l o a d i n g , t - t0 [ d ] P r e c o n d i t i o n
R H / 2 0 ° C m e a s u r e d m o d e l l e d
6 5 %
8 5 %
9 5 %
T e s t i n g c o n d i t i o n s : 7 0 ° C / 6 5 % R H
6 0
Figure 6.9: Specific creep calculated with the material model in comparison with the measured values for the concrete MRC during the creep tests conducted at 20 °C (top) and 70 °C (bottom) and 65 % RH
In Section 6.2.3 the capabilities of the model regarding the effect that increasing the temperature has on creep were discussed. It was mentioned that, in case the samples are loaded after being heated, the model underestimates the creep deformations that occur during the first hours of loading because in the formulation of the hygrothermic coefficient of concrete no time-development function is considered. In Fig. 6.9 as well as all figures presented in Appendix D.4, where elevated temperatures are involved, the curves were intentionally dragged up to match the initial values att−t0=0.01 d. In this way, it is shown how the material model follows the tendency of the creep deformations.
It is known that, by neglecting the time dependency of the hygrothermic coefficient, the model is not able to reproduce the development of creep during the first hours after loading properly. Nevertheless, even though the results are affected by this weakness, the material model not only follows the tendency of the creep development but also achieves a quite good accuracy in comparison with the values of the tests results.