Materials for engineering, 3rd Edition - (Malestrom)

Glasses and ceramics 151
is three or four times that of cement and one may calculate the value of the
modulus of a concrete mixture from the relation:
E
concrete
Va
=
⎡
+
⎣⎢ Ea
V
E
c
c
⎤
⎦⎥
–1
where V a and V c are the volume fractions of aggregate and cement, and E a
and E c are their moduli, with typical values of 130 and 32 GPa, respectively.
Values of V a can range from 0.45 to 0.75, giving moduli for such concretes
of the order 50 GPa.
Effect of porosity
We have seen that the strength of concrete develops over a period of time
and data are only significant when related to the time after casting. The 28-
day strength is often used as a standard parameter. Strength is commonly
described by subjecting a sample to a compressive axial load and recording
the crushing strength, although for other applications it may be tested in
flexure. The modulus of rupture so obtained is only about 10% of its
compressive strength, the reason for this being the effect of porosity, Fig.
4.12. The pore size distribution is very wide, with different sized pores
having a different effect on the strength of the cement. The smallest pores,
gel pores, are 10 nm and can be found between the fibres of C-S-H
outer product to form a three-dimensional pore network. Since these are
4.12 Optical micrograph of hydrated Portland cement showing
porosity, × 25. (Courtesy Dr G. W. Groves.)