Gajda (2002) reports a simplistic method, which is briefly described in a Portland
Cement Association document. This method is useful if the concrete contains between
500 and 1000 lbs of cement per cubic yard of concrete and the minimum dimension is
greater than 6 ft. For this approximation, every 100 lbs of cement increases the
temperature of the concrete by 12.8 F. Using this method, the maximum concrete
temperature of a concrete element that contains 900 lb of cement per cubic yard and is
cast at 600F is approximately 1750F. This PCA method does not, however, consider
surface temperatures or supplementary cementitious materials (Gajda et al., 2002).
A more precise method is known as Schmidt's method. This method is most
frequently used in connection with temperature studies for mass concrete structures in
which the temperature distribution is to be estimated. Determining the approximate date
for grouting a relatively thin arch dam after a winter's exposure, the depth of freezing,
and temperature distributions after placement are typical applications of this step-by-step
method. Different exposure temperatures on the two faces of a theoretical slab and heat
of hydration of cement can be taken into consideration (Townsend, 1981).
In its simpler form, Schmidt's Method assumes no heat flow normal to the slab and
is adapted to a slab of any thickness with any initial temperature distribution. Schmidt's
Method states that the temperature, t2, of an elemental volume at any subsequent time is
dependent not only upon its own temperature but also upon the temperatures, ti and t3, of
the adjacent elemental volumes. At time At, this can be expressed as:
t2,At = [t + (M-2) t2 + t3] / M
Where M = [Cp(Ax)2]/[KAt] = (Ax)2/(h2At), since the diffusivity of concrete, h2
(ft2/hr), is given as K/Cp.