Rheology of Concrete - Bingham Model Representation

As we all know concrete is an artificial stone that indeed stays as fluid for a short period. This is why, concrete is given the name “liquid stone” from history. 

Rheology of Concrete - Bingham Model Representation
Rheology of Concrete - Bingham Model Representation

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The word liquid does not clearly describe the complexity of the concrete. It is indeed a combination of water, aggregates, cement that are materials with varied sizes. Each material having its own role in concrete formation. 

Concrete Composition


What is rheology of concrete?

Concrete rheology specifies the study of concrete in its fresh state. If i can provide you a proper definition, 

Rheology is the science of deformation and flow of materials. The study deals with the relationship between the stress, strain, their rate and time. Rheology study is applied on materials that show more complex behavior. 

The rheological or flow properties are a must study in construction industry because majority time the concrete is handled and placed in its plastic or fresh state. This is why large research is going on with concrete rheology. 

Being a complex material, there is no definite method to predict the flow nature of concrete. The complex nature is all about the size range of materials it possesses from 1mm cement grains to 100 grain and even more. 


Why should we research on concrete rheology? 


With time the concrete production and technology is increasing with processing methods that need better understanding of concrete in its fresh state. This is when the study of flow matter called the rheology takes its place.

How to apply rheological study in concrete?


Rheology study can be applied to fresh and hardened concrete state. In hardened state, the plastic behavior of the concrete is considered for rheological study. Rheological study on fresh concrete has more scope compared to hardened state.

Rheology of fresh concrete


Fresh concrete is a dispersion of aggregates on a liquid medium containing cement paste. As cement paste is itself a combination of solid materials, a fresh concrete forms a multi-phase material.

The determination of rheological characteristics or parameters of fresh concrete are based on the assumption that:

  1. The concrete as a multi phase material is a continuum. This means, a material with no discontinuity between any two points on it.
  2. The concrete as a multi phase material is a homogeneous mix. This means a material with uniform composition throughout.
  3. The concrete as a multi phase material is an isotropic material. This means, material of the same properties in all directions 
Yes, you have doubted the right!! How can all these assumptions together satisfy. It won’t. The degree of compliance with the assumptions i mentioned above is dependent on
  • the type of concrete mix
  • the micro-scale study performed
  • the state of concrete when the measurement is carried out
It also depends on how the mix is observed, i.e. The micro-scale study performed. Because in micro scale the concrete is unlikely to have a continuum.

Representation of Rheological behavior of Concrete

As we are relating concrete study with fluid study, i will start explaining with “newton’s law of viscous flow”.

The newton’s law of viscous flow states that “the shear stress is proportional to the shear strain when we study the forces between the layers of the fluid”.

Shear stress α shear strain 

Shear stress (τ) = constant x shear strain (γ)

Those fluid that obeys newton’s law of viscous flow is called as Newtonian liquids. The constant obtained by the above relation is a “physical constant” that represent the characteristic of the material studied.

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Bingham Model for Rheology of Concrete

Concrete is a non-Newtonian fluid whose rheological properties is represented by Bingham model. When we relate with the concrete material, the constant is related to the shear rate at which concrete is measured and the shear history of the same. 

Bingham Model Representation of Concrete Rheology
 Bingham Model Representation of Concrete Rheology


When the concrete is studied at a lower shear stress value, that is the practical case of fresh concrete, it is observed that, the linear curve obtained when drawing shear stress to strain curve do not pass through the origin. Instead, it starts at a particular value from the x-axis as shown. This intercept formed at the x-axis is the minimum stress value below which the concrete will not flow. 

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Consider an experimental condition, where the concrete can stay in a pile while conducting slump test. This means, a minimum stress value for this concrete will make the concrete to flow. This minimum stress value of concrete to start flowing is called as the yield stress and it is designated by the symbol, τ0.
Concrete Slump Test
Concrete Slump Test

Then the simplest flow equation can be given as:

τ= τo + μγ’ 

Here, , τo. Is the yield value that indicates the cohesion of the material. is the 
μ plastic viscosity that is a constant value giving dimensions of viscosity and this relation is called as Bingham model.

In a Bingham model, the parameters that represent the flow properties of the material are τ0 and μ. Bingham fluid, which is a non-Newtonian fluid which is most frequently used for the study of concrete.

Note: Non-Newtonian fluid is the fluid that does not obey newton’s law of viscosity.

In Bingham model a single -point test like workability only gives a single value. But to form a line we need minimum of two points. So we need to perform two or more tests like vee bee tests etc.

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Tattersal Model for Rheology of Concrete


The Tattersal model overcomes the shortcoming of the Bingham model. The Tattersal tests measures the mobility characteristics of the fluid that provides us two- point value of shear conditions. 

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Tattersal Model for rheology of concrete
Tattersal Model for rheology of concrete



In this method, the power required to run the concrete mixer at different speeds are calculated. After this, the torque ‘t’ is calculated by dividing the power by speed. Hence, Tattersal provided a relation as:

T = g + hN

Where, T= torque;

N is the number of r.p.m , g and h are constants proportional to the cohesion and plastic viscosity of the mixture.

It has been observed that two different mixtures with same g and h values shows identical values for consistency, vee-bee time and compacting factor test.

Comparison of Bingham model and Tattersal model of concrete


Compared to Bingham model, the yield stress is not well defined in the case of Tattersal model. Second important difference is that, the flow curve obtained in Tattersal model is not linear (except in some of the portions). 

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