PORTLAND CEMENT CONCRETE ROADS. 7 
The theory 3 has recently been advanced that the strength of the 
concrete depends entirely on the ratio of the amount of water to the 
amount of cement so long as the mix is workable. According to this 
theory variation in the grading of the aggregates affects the strength 
of the concrete made with a given amount of cement merely because 
it affects the amount of water that is required to produce a work- 
able consistency. If the proportion of cement be varied to main- 
tain a constant ratio of cement to water, any reasonable grading of 
aggregates can be made to yield a concrete of approximately any 
desired strength. An arbitrary quantity known as the " fineness 
modulus " is determined by sieve analysis of the aggregates and this 
quantity together with the maximum size of the aggregate determines 
the amount of cement to be used. The strength of the concrete made 
from the cement and aggregate in the determined proportions will 
depend upon the amount of water used. Tables and charts based 
upon experimental data supply the means for the practical applica- 
tion of the theory. 
Another theory 4 is based on the assumption that to produce con- 
crete of a given strength a certain amount of cement is required for 
each unit of surface area of the aggregate, taking into account the 
amount of water used in mixing. The particles are assumed to be 
spheres, and tables have been worked out from which the surface 
area of a given amount of the aggregate can be determined from the 
sieve analysis. 
It is worthy of note that each of these theories tends to the use 
of well-graded aggregates and rich mixes where strong concrete is de- 
sired. They have all been evolved in the attempt to design concrete 
of high strength, which is needed in pavement concrete to enable 
the pavement to resist temperature and impact stresses without 
excessive cracking. That concrete high in compressive strength is 
also highly resistant to abrasion is the conclusion drawn from tests 
conducted by Prof. Duff A. Abrams, Lewis Institute, Chicago. It 
was observed in these tests that the resistance to abrasion fell off 
sharply when the compressive strength dropped below 3,000 pounds 
per square inch. The tests conducted by the Bureau of Public Eoads 
do not support this conclusion, but indicate, rather, that the amount 
of wear of the concrete depends upon the character of the coarse 
aggregate. It should be noted that in the tests conducted by Pro- 
CD o 
fessor Abrams only two kinds of coarse aggregate were used. For 
any given coarse aggregate, however, it is likely that increase in 
compressive strength will result in corresponding decrease in wear. 
From experience it has been found that pavement concrete should 
be proportioned to have a compressive strength of not less than 3,000 
a Bulletin 1, Structural Materials Research Laboratory, Lewis Institute, Chicago. 
* Proceedings of the A. S. T. M. for 1918, pt. 2, p. 236. 
