Since concrete is a multiphase solid, no direct relationship can exist between its density and modulus as in single-phase solids such as metals. The modulus is influenced by density, porosity, mix proportion, moduli of elasticity of the ingredients, and the characteristics of the transition zone. These parameters determine the elastic behaviour of concrete.
Effect of Aggregates
Dense aggregate leads to a high value of E for concrete. A larger proportion of coarse aggregate leads to a high value of E as well. Table summarizes the values of E for various ingredients. Note that a very large value of E of the aggregate will lead to an elastic mismatch among the aggregate, mortar and cracks in the transition zone.
Modulus of elasticity of aggregate, cement paste, and concrete
|Description||E (105 MPa)|
|Sandstone||0.2 – 0.5|
|Expanded Shale||0.07 – 0.21|
|Hydrated cement paste||0.07|
|Concrete||0.1 – 0.2|
Effect of Hydrated Cement Paste
The elastic modulus of cement paste is determined by its porosity. The water to cement ratio (w/c), air content, admixture dosage and degree of cement hydration control the porosity of cement paste. The modulus of elasticity of concrete can be represented based on the following simple equation:
Ec = Eag + Ep(1-g)
Where E is the modulus of elasticity of concrete.
Ea is the modulus of elasticity of aggregate.
Ep is the modulus of elasticity of cement paste.
g is the volume fraction of the aggregate and
1 – g is the volume fraction of the cement paste.
Ep is low due to the poor density of the transition zone.
Effect of the Transition Zone
Void space and micro-cracks influence the stress-strain behaviour. The existing cracks in the transition zone and the orientation of C-H crystals as well as existing void spaces make the transition zone weak. This causes the elastic modulus to drop gradually with increasing loads.