ˇTable of Contents ˇCivil Engineering | A Device to Monitor Continuously the Setting of ConcreteL.ARNAUD and S. THINETLaboratoire Géomatériaux, DGCB URA 1652 C.N.R.S., Ecole Nationale des Travaux Publics de l'Etat, rue Maurice Audin, 69518 Vaulx-en-Velin Cedex, FRANCE. Tel : 04.72.04.72.88., Fax : 04.72.04.71.56. E-mail : laurent.arnaud@entpe.fr - sandrine.thinet@entpe.fr. Contact |
In this paper, we present the experimental device (the vibroscope) enabling to monitor the rheological evolution of heterogeneous materials. Hydraulic concrete is an heterogeneous mixture containing solid particles, fluid and gas (air bubbles trapped in the paste during mixing process, the volumic concentration is about 1-5%). Due to the hydration of hydraulic binders, it evolves from a liquid to a solid state during setting that lasts around 6 hours. This progressive evolution modifies significantly the character and the behaviour of the initial fluid mixture. Results are presented for various formulations.
Structure evolution and the presence of heterogeneities, the size of which ranges from a millimetre to a centimetre, are the subject of a complex rheological analysis. In addition, conventional tests are ineffective to monitor the setting continuously. First, the measurement ranges for rheometrical tests are too limited. Second, the presence of gas bubbles leading to low wave speed (C ť 50m/s), ultrasounds are scattered on the large heterogeneities and strongly attenuated (Sayers 1992). So, large frequency spectrum is required (Reinhardt 1996) or ultrasounds are only applied on fresh desaerated cement pastes or on concrete mortar.
For the propagation of compressional waves, the principle of the device is based on the large variations of the macroscopic compressibility of concretes while they evolved from a fluid state to a solid one (Boutin, Arnaud 1995). Due to the presence of gas bubbles, the inverse compressibility (Kg) of which is high as compared to those of the fluid and the solid phases, the wave speed is very low (Cp ť100m/s). Large wavelengths (l> 0,5m) as compared to the heterogeneity size are then achieved when using very low frequencies (f < 1kHz)
The principle of the device using shear waves is related to the variation of shear modulus while concretes are setting. In order to test the material inside the thickness of the viscous layer, very low frequency (20 - 200Hz) is used. This condition is fundamental to make sure the propagation of shear waves even when the material is in a fluid state. The shear waves are sensed by means of pressure transducers because they are oriented in principal stress directions ą p/4 compared to the direction of wave propagation (Arnaud, Thinet 1998).
For both cases, transient plane waves are generated by two vibrators attached to two plates in contact with the material. At regular time intervals, measurement values of velocity (Cp or Cs) and damping coefficients are obtained by means of four pressure transducers positioned inside the paste and removed at the end of each experiment. Note that we present the evolution of the ratio of the presure levels on the transducers (Dp and Ds). This ratio is inversely proportional to the damping coefficient. The material is in a heat insulated mold, so that the kinetics of the reactions in the fresh cement pastes are not disturbed.
In this test, very small solicitations are applied to the material to avoid damaging of the microstructure which is building up during setting (displacementť10mm, strain ť 10^{-5}, rate of strain ť 4.10^{-3}s^{-1} and pressure levels ranging from 10 to 200Pa.). Moreover, we verified experimentally at different moments during the setting, that the behaviour remains linear in a wide range around these values (see Fig. 1 where normalized signals are presented for different levels of solicitation). We can also conclude that this test is non destructive.
Fig 1: Example of signals recorded for various levels of solicitation( factor10). |
3.1. formulations
We present here different very classical formulations of hydraulic concrete (granulates 1767 kg/m^{3}, cement 420 kg/m^{3}, water 177 kg/m^{3}, air bubbles between 1 to 3% per volume).
Two different parameters were modified to obtain six formulations of concrete, involving different values of temperature of casing (10, 20 and 30°C) and ratio of water / cement (0,4 and 0,6).
The hydration of cement particles and complex chemical reactions lead to built a solid skeleton and so, to the setting and hardening of concrete. This evolution lasts between five to eight hours depending on the formulations.
Another experiment is presented for the study of shear wave propagation.
3.2. celerity and damping coefficients
In case of compressional waves, for the different formulations investigated, the evolution of Cp and Dp are plotted versus time. From the very simple measurement of Cp, we observe clearly the evolution of the material in a wide range (50 < Cp < 2500 m/s), from its fluid state to its solid state. Time changes are detected by the device.
Fig 2:Evolution of compressional wave celerity versus time |
For all the formulations of hydraulic concrete, two phases appear. The transition can be related to the threshold percolation. Classical influence of the different parameters investigated are observed, for example an increase of the setting process when increasing the pouring temperature or decreasing the water/cement ratio.
According to shear wave propagation, similar coefficients (Cs and Ds) are presented in Fig.3 for one example of another experiment.
Fig 3: Evolution of Cs and Ds for shear wavepropagation versus time |
In both cases and for all the formulations investigated, we may observe with these measurements a significant evolution of the materials and we note that these evolutions are very consistent on both celerity and damping evolutions. The device allows to monitor the evolution and it is sensible to the mechanical changes related to the formulations tested.
A first analysis can be achieved in terms of viscoelasticity : Cp and Dp are related to the complex dometric modulus E. The evolutions of |E| versus time are presented for both materials (Fig. 3). Experiments clearly highlight, first the significant rheological variations for a given material during the setting, second the setting kinetics for each material.
A complementary analysis is obtained using the constitutive law obtained from the approach with the homogenization technique[Arnaud et al., 1999]. Considering the material as a suspension of gas bubbles in a viscoelastic matrix (complex shear modulus M^{*}), the isotropic macroscopic behaviour is that of a compressible viscoelastic medium:
where u is the displacement vector and K, the macroscopic compressibility of the material, is simply evaluated. The gas phase remains in quasi-adiabatic conditions because for the frequency used, the thickness of the thermal layer (ť 0,1mm) is small as compared to the bubble size (1mm or more). So, K = gP^{e}_{g} / c where g = 1,4 is the ratio of specific heat coefficients , the pressure of the gas phase is P^{e}_{g} = 105 Pa and c, the gas phase concentration, is measured precisely (about 1 to 3 % in case of hydraulic concrete).
It is important to note that under compressional wave propagation, the macroscopic shear modulus is proportional to the shear modulus of the interbubble mixture. The scalar numbers (a and b) depends on the local geometry of the elementary representative volume. The dometric modulus K+ (a+2b) M^{*}, (a+2b)M^{*} and the phasej of M^{*} can be deduced from the measurement of Cp and Dp.
Fig 4: Evolution versus time of the dometric modulus (modulus and phase y - left side) and of the shear modulus of the interbubble matrix (modulus and phase j). |
For the hydraulic concrete, rheological quantities are consistent with the following mechanical interpretation. At the beginning, the interbubble matrix is characterized by a viscous behavior (suspension in water of solid particles and crystals generated by binder hydration). At this stage, K and (a+2b)M^{*} are of the same order of magnitude. A transition is reached with the percolation threshold of the hydrates. When they become connected, a rigid elastic skeleton is being built. The development of the crystallization increases both the elastic and viscous properties of the material, as water is trapped inside the weak skeleton. The dominant term in E is thus related to (a+2b)M^{*} and not anymore to K. This transition is considered as the beginning of the mechanical setting. This effect goes on with a continuous increase of (a+2b)M^{*} corresponding to the hardening of the matrix.
Complementary adaptations of the device allow to obtain values of the Lamé coefficients in particular from the generation of shear waves. Works are developed to study at the same time the propagation of both compressional and shear waves.
This approach is adjustable for the study of many evolving materials. It can be adjusted to test other time-dependant heterogeneous materials during their mechanical evolutions in civil engineering and also in others fields, involving different evolutive process.
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