In this article we will discuss about:- 1. Definitions of Rheology 2. Representation of Rheological Behaviour in Concrete 3. Rheology of Hardened Concrete.
Definitions of Rheology:
Rheology is the science of the flow and deformation of the materials. It is concerned with the relationship between stress-strain, rate of strain and time. The term Rheology deals with the materials whose flow properties are more complicated than those of simple fluids as liquids and gases. The Rheological principles and techniques applied to concrete include the deformation of hardened concrete, handling and placing of freshly mixed concrete and the behavior of its constituents parts, namely cement paste and slurries.
The Rheology of fresh concrete like workability includes the parameters of stability, mobility and compatibility, which are necessary to determine the suitability of any concrete mix. For defining the Rheological properties of fresh concrete, the above parameters are defined in terms of forces involved in the transmission of mechanical stresses on the concrete. During handling and placing of fresh concrete, it is subjected to normal and shearing forces.
1. Stability:
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It can be defined as a condition in which the aggregate particles are held in a homogeneous dispersion by matrix and random sampling has shown the same particle size distribution during transportation, placing and compaction. The stability of concrete is measured by the characteristics of its segregation and bleeding.
2. Segregation:
It is defined as the mixture’s instability caused by the weak matrix that cannot hold the individual aggregate particles in homogeneous dispersion. The resistance to segregation depends upon the cohesion between the particles of the mix. Segregation in concrete may occur in wet as well as dry consistencies.
3. Segregation in Wet Mix:
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Segregation in wet mix may occur when water content in the mix is such that the paste is unable to hold the aggregate particles in the distributed position during the transportation, placement and compaction of the concrete.
4. Dry Segregation:
Dry segregation occurs when the concrete is of low water-cement ratio which results in crumbly mix during handling. If concrete is vibrated then crumbly mixes often have been found satisfactory as during vibration the matrix becomes fluid momentarily and develops shear resistance and cohesion.
5. Bleeding:
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It occurs when the mortar is unstable and releases free water. Bleeding should be controlled and reduced to a minimum.
6. Mobility:
Mobility of fresh concrete can be defined as its ability to flow under mechanical stresses. The flow is restricted by cohesive, viscous and frictional forces. The cohesive force is developed due to adhesion between the matrix and aggregate particles. It provides tensile strength to fresh concrete that resists segregation. The viscosity of the matrix contributes to the ease with which the aggregate particles can move and rearrange themselves with in the matrix.
At low stresses no flow takes place and the mix behaves as a solid of extremely high viscosity. As the stresses increase, the viscosity gradually decreases and the bond strength between particles becomes insufficient to prevent the flow and the concrete behaves like a liquid. The internal friction develops when a mixture is displaced and the aggregate particles translate and rotate.
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The resistance to deformation depends on the following factors:
i. Shape and texture of aggregate,
ii. Type of cement used,
iii. Richness of the mix, and
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iv. Water-cement ratio of the mix etc.
Thus the angle of internal friction plays an important role in the mobility of a concrete mixture. The mobility of a concrete mix may be determined by the laboratory tri-axial compression test. At the construction site the relative mobility characteristics may be determined by the Vee Bee flow test in conjunction with compacting factor test.
7. Compatibility:
It is a measure of the ease with-which the fresh concrete can be compacted. By compaction the entrapped air is expelled and the aggregate particles are repositioned in a dense mass without causing segregation. Compatibility is measured by the compacting factor test. This test has some limitations. The cohessive mix sticks in the hoppers of the test apparatus and mixes with low or very low workabilities produce results with wide variations.
The compacting factor test can be extended by taking the following two additional measurements:
1. Determination of the density of the concrete in its loose un-compacted state by filling the cylinder of the test apparatus with a hand scoop without compaction.
2. Determination of the density of mechanically vibrated concrete sample from the same batch. The concrete is loosely placed in three layers into the cylinder of the test apparatus and compacted with a 25 mm diameter needle vibrator.
These two measurements along with the values obtained from standard compacting factor test give an idea of the relative ease with which a mix changes from its loose state to the compacted one. The difference between the actually compacted state and theoretical maximum compaction gives a relative measure of void content of concrete. Thus an indication of the durability, permeability and relative strength of hardened concrete is obtained.
Thus the knowledge of rheological properties of concrete is useful in selecting concrete mixes that can be efficiently compacted in the form. The normal prevalent methods of measurement of workability tests as slump, compacting factor, Vee Bee and other tests are of limited scope as they measure only one parameter. Hence these tests are known as single point tests.
Representation of Rheological Behaviour in Concrete:
The ideal liquids which obey the Newton’s law of viscous flow, (Shear stress being proportional to the rate of shear strain) are called Newtonian liquids. The constant of proportionality may be used as a physical constant characteristic of the materials. The flow behaviour of fresh concrete does not follow this law. The ratio of shear stress to shear rate is not constant, but depends upon the shear rate at which it is measured and it may also depend on the shear history of the concrete sample investigated.
At low shear rates which are important in practice, the rheological behaviour of concrete can be represented by a straight line which does not pass through the origin, i.e., which has an intercept on the stress axis. This intercept indicates the minimum value of stress below which no flow takes place. This straight line is of the form Y = mx + c.
The fact that concrete can stand in a pile (as in the case of slump test) suggests that for a flow to develop some minimum stress is necessary. This minimum stress is known as yield stress and denoted by the symbol τ0.
Thus the flow equation of concrete as suggested by Bingham can be written as:
τ = μ g + τ0 …(1)
where,
τ = shear stress
μ = a constant, having dimensions of viscosity and called plastic viscosity
τ0 = value of yield stress
γ = Rate of shear stress
The constants μ and τ are the parameters characterizing the flow properties of the material. Thus Bingham model distinguishes between the shear stress of the material expressed in terms of its cohesion, plastic viscosity and the rate at which the shear load is applied. At least two points are required to establish a straight line.
Thus the workability of concrete cannot be defined by the single point tests that determine only one parameter, i.e., provide only one single point. Thus to have a better understanding of concrete rheology some other tests have to be conducted in combination of the above test. For example to measure mobility and compatibility Vee Bee test can be used with compacting factor.
To overcome this shortcoming of Bingham model, Tattersal measured mobility characteristics by a single test method which provided two or more than two points (shear conditions). The procedure is based on determining the power required to mix concrete at different speeds and then calculating the torque by dividing the power by the speed. He suggested the following relation between the torque and mixing speed.
T = γ + hN
where,
T = Torque measured
N = No. of r.p.m.
g and h are constants proportional to the cohesion and plastic viscosity respectively of the mixture.
It has been observed that two mixtures which have identical values of g and h will also have identical values for consistency, Vee Bee time or degree and compacting factor. On the other hand if the values of g and h of the two mixtures differ, then the two mixtures may have similarity in one of the three standard tests namely consistency, Vee Bee time and compacting factor, but will behave differently in the other two.
It has been observed that concrete behaviour departs from the Bingham model significantly at least in one of the following respects:
1. The flow curve is not linear except over a very limited range of shear rates.
2. The yield stress is not well defined.
In case the flow curve is concave up wards i.e. its slope increases with shear rates. It shows that the sharing forces are destroying some structures that existed in the unstressed material. The progress of destruction of structure has been found greater for the higher rates of shear. If the rate of shear is increased gradually, a curve ABC is obtained as shown in Fig. 28.3.
If reaching at point C, the rate of shear is decreased steadily to zero the descending curve obtained does not coincide with the up curve. If the point C represents the break down in the structure under shear and the process of structural break down immediately and instantaneously is reversed, the decrease in shear rate from D will result in the progressive built up of the structure to the same level as it had on the up curve at the start, but time is required to rebuild the structure of the material.
Thus as the rate of shear is decreased, the shear stress at any particular rate of shear on the down curve will be less than the shear at the same rate on the up curve. Therefore the up and down curves will not be coincident and a hysteresis loop will be formed. The Bingham model can be applied to the fresh concrete under practical situations provided the limits are recognized.
Rheology of Hardened Concrete:
The rheology of hardened concrete like creep illustrates the mechanical behaviour of an ideal elastic, viscous and plastic component.
The gradual increase in strain with time, without the increase in stress is due to creep. Thus creep can be defined as the increase in strain under sustained stress. Under sustained stress with time, the gel, the adsorbed water layer, the water held in the gel pores and capillary pores yields, flows and readjust themselves. This behaviour is known as creep in concrete. Creep in concrete is considered to be an isolated Theological phenomenon and this is associated with the gel structure of cement paste. Thus cement paste plays a dominant role in the deformation of concrete.
Rheological Representation of Creep:
The mechanical behaviour of hardened cement paste which exhibits both elastic and inelastic components of deformation under load can be expressed in rheological terms. Thus the rheological approach illustrates the mechanical behaviour of ideal elastic, viscous and plastic components. The rheology of creep can be expressed in macroscopic and microscopic state.
Macroscopic Rheological Approach:
In case of macroscopic approach the structure of cement paste can be represented as a continuous solid phase having saturated voids of various sizes in a wide range. A macroscopic representation of deformational behaviour of hardened paste is shown in Fig. 28.4 (a). From this model time dependent volume changes can be demonstrated as long as the isotropic stresses are applied through the solid phase and the drainage of the liquid can take places as suggested by ORI.ISHAI.
The corresponding rheological model is shown in Fig. 28.4 (b). This model consists of a spring device representing the elastic mass around a central viscous desh-pot representing the confined liquid. With the help of this model the deformational behaviour of cement paste can be demonstrated.
Microscopic Rheological Approach:
In case of a microscopic approach the structure of cement gel can be represented as an anisotropic crystal clusters randomly oriented in a solid matrix as shown in Fig.28.5. The application of a macroscopic shear stress to the anisotropic system results in an irrecoverable volumetric contraction of the spaces in some of the clusters and a separation in other clusters as shown in Fig.28.5 (a) and a separation in other cluster as shown in Fig.28.5 (b). Only few i.e., a fraction of elements are subjected to pure shear as shown in Fig.28.5 (c). On removing the load, there is a visco-elastic recovery, but due to some deviatory stress component, certain local irrecoverable volume changes remain.
Further Fig.28.6 shows the sub microscopic models. They represent metastable crystaline gel consisting of two sheet like crystals separated by a layer of water.
Three basically different mechanism of deformation can be possible:
1. There may be compressive stresses normal to contact layer as shown in fig.28.6 (a).
2. Tensile stresses normal to the contact layer as shown in fig.28.6 (b).
3. Shear stresses parallel to the contact layer as shown in fig.28.6 (c).
In case (1) the liquid is compressed and squeezed out laterally. This results in the reduction of the inter-crystalline space. The rate of liquid movement is slow and decreases with the narrowing of space which tends towards a limit equal to a monomolecular compressed water layer. The main cause of time dependent irrecoverable changes in the cement gel is the squeezing out of liquid against the strong frictional forces.
In mechanism (2) visco-elastic elongation takes place at faster rate than in the compression. However this elongation is restrained by the solid matrix and delayed. Complete recovery may take a long time after the removal of the load.
Mechanism (3) according to Troxell, the shear stress results in water layers.
Below the elastic limit of the material, due to complex system of applied loading, various combinations of the above noted basic mechanism of deformation may take place. On the basis of the available experimental evidence, it can be assumed that the long term deformation mechanism in cement gel is that is involved in narrowing the inter-crystalline spaces. This is reflected in the slow and decreasing rate of time dependent deformation as well as in the irrecoverable components of the deformation which increase with loading time.
The time dependent deformation behaviour of loaded and unloaded hardened cement paste shows a distinct similarity between creep and its recovery, shrinkage and swelling. All these process are governed by the movement of various types of water held in the cement paste.
Further it can be explained as follows:
The most common type of loading is uniaxial compression. The application of uniaxial loading develops an instantaneous elastic response of both the solid and liquid systems. The external load applied is distributed between these two phases, under sustained loading the compressed liquid starts to diffuse and moves from high to lower stressed areas.
Under uniform pressure movement of water takes place out wards from the body. This mechanism is accompanied by the transfer of load from the liquid phase to the surrounding solid phase which increases the stress acting on the solid matrix gradually resulting in an increased elastic deformation.
It has been observed that the pressure on the capillary water gradually disappears after several days of under sustained load, being transferred to the surrounding gel. Similarly after some weeks of sustained load the pressure on the gel pore water disappears. However the pressure on inter and intra crystalline adsorbed water continues to act during the entire period of loading, though the magnitude of pressure decreases gradually.
Thus it can be said that the ultimate deformation of the hardened cement paste is the elastic response of its solid matrix, which behaves as if the spaces with in it were quite empty (the space with in the matrix filled with unstable gel).