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

381

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 

 

between compressive strength and dynamic elastic modulus can be modelled by an 

exponential relationship such as f

c

=0.135 e

0.125 Ed

. 

 

 

Figure 1. Compressive strength evolution as a function of equivalent age (a) and dynamic 

elastic modulus (b) 

 

3.3. Tensile strength 

The effect of mineral additions and water content on the tensile strength of concrete is mainly 

similar to what is observed for compressive strength. However, Figure 2a indicates that for 

tensile strength, C-WAT and C-LMF present similar values. In addition, C-ECO has a higher 

tensile strength than C-BFS, which was the opposite for compressive strength. This 

demonstrates that both properties are not governed by the same mechanisms, and that there 

exists no direct relationship between both. As a consequence, the relationship between tensile 

strength and dynamic elastic modulus shows a dependency to the nature of the binder as 

demonstrated in Figure 2b. However, as for compressive strength, this relationship can be 

modelled by an exponential relationship such as f

t

=0.017 e

0.114 Ed

. The lower accuracy of this 

model's prediction in comparison with compressive strength is attributed to the higher 

scattering of the splitting tensile strength test. 

 

 

Figure 2. Tensile strength evolution as a function of equivalent age (a) and dynamic elastic 

modulus (b) 

 

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382

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 

 

3.4. Activation energy 

The apparent activation energy is determined through the well-established superposition 

method [13]. As presented before, this was previously made for semi-adiabatic measurements. 

In this study, ultrasonic tests are performed on all compositions except C-WAT. Indeed, it 

presents the same apparent activation energy than C-REF since both contain the same reactive 

compounds. Tests are performed at 10°C, 20°C, 30°C and 35°C. The results for one 

composition (C-ECO) are displayed in Figure 3a and 3b.  

The apparent activation energies that can be computed from the superposition method for the 

dynamic elastic modulus are shown in table 2, along with the corresponding results from the 

semi-adiabatic calorimetry. The well known effect of blast furnace slag is observed, since 

every composition containing BFS shows an important increase of apparent activation energy, 

whatever the method used. In parallel, LMF seems to induce a slight increase in the early age 

apparent action energy. Finally, the combination of BFS and LMF presents apparent 

activation energy similar to that of cement with BFS only. These results also confirm that 

semi-adiabatic calorimetry (chemical measurement) and ultrasonic pulse velocity (mechanical 

measurement) both provide similar values for the apparent activation energy by the 

superposition method. The interest of using the ultrasonic method is that these tests can be 

easily performed on a small volume of concrete and that as such, the temperature in the 

sample remains approximately constant, in contrast with semi-adiabatic calorimetry, which 

only works as long as temperature variations in the sample are significant. It should be 

noticed that considering the scattering of the results, it is considered that both methods used 

for the determination of  activation energies presented in table 2 yield equivalent results. This 

scattering is due to the variability of the calorimetry and ultrasonic methods, as well as to the 

chosen time scale during which the superposition method is applied. 

 

Table 2. Activation energy obtained from chemical and mechanical measurements 

[kJ/mol] 

C-REF C-BFS C-LMF C-ECO 

Semi-adiabatic calorimetry 

35.9 51.1 39.1 49.7 

Ultrasonic measurements 

38.3 48.9 41.6 48.3 

 

 

Figure 3. Dynamic elastic modulus evolution as a function of age (a) and equivalent age (b) 

for the C-ECO mix design at various curing temperature. 

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383

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 

 

 

 

4.  Conclusions and perspectives 

 

A continuous non destructive alternative to classical measurements of the setting time, 

compressive strength, tensile strength and apparent activation energy is presented in this 

study. These properties were determined through the monitoring of P-wave and S-wave 

transmission velocity from the casting up to a few days of hydration. These results indicate 

that: 

- The initial setting time can be determined from ultrasonic measurements as the time at 

which the S-wave velocity increases at its maximum rate. 

- The final setting corresponds to the time at which the rate of increase of the dynamic elastic 

modulus is maximal. 

- The compressive and tensile strengths can be correlated to the increase of dynamic elastic 

modulus through an exponential law.  The parameters of this model should be calibrated for a 

given concrete, except for slight variations in the nature of the binder, which does not affect 

significantly these relationships. 

- The apparent activation energy of concrete can be determined easily with the ultrasonic 

method. 

 

 

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