F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

62 Properties of structural concrete
known and it is prudent to use a higher margin than 1.64 times the
estimated standard deviation. For example, where the required characteristic
strength is 20 N/mm 2 or above, a margin of about 15 N/mm 2 should
be used in the initial mix design [37]. When a reasonably large number of
test results becomes available, the current margin is 1.64a. The use of small
samples in statistical analysis introduces undesirable unknowns. Forty tests
may be regarded as an approximate dividing line between large samples
and small samples. BS 8110 does not give much guidance on this point.
For characteristic strengths exceeding 20 N/mm 2 , the old code CP 110
recommends that where 40 test results are available, the current margin is
to be taken as l.64a or 7.5 N/mm 2 , whichever is greater; where 100 test
results are available, it may be taken as 1.64aor 3.75 N/mm 2 , whichever is
greater.
From the above discussions it is clear that the target mean strength to be
used in the mix design increases with the standard deviation. The poorer
the quality control, the higher the standard deviation, and the higher will
be the necessary target mean strength. A higher target mean strength will
increase the cost of manufacture. On the other hand, to reduce the
standard deviation will require better quality control and, therefore, higher
cost. In practice a compromise is necessary.
Table 2.8-1 gives some idea of the standard deviations that might be
expected under different conditions. The fact that Table 2.8-1 shows
standard deviations rather than coefficients of variation (see eqn 1.3-6)
might give the impression that the standard deviation is independent of the
mean strength level. Whether this is so, or whether it is the coefficient of
variation that is independent of the mean strength level, has led to some
controversy. Experience indicates that, above a strength level of about 20
N/mm 2 , the standard deviation seems to be fairly independent of the
strength level [37]. Below this level, it is more reasonable to assume that
the coefficient of variation is independent of the strength level.
The standard deviation [37] on about 60% of the sites in the UK is
between 4.5 and 7.0 N/mm2 . Values much lower than 4N/mm 2 can seldom
be achieved in practice, because the variability due to sampling and testing
alone corresponds to a standard deviation of the order of 2.3N/mm 2 ; also,
the variation due to the cement (of a nominally specified type) can
sometimes correspond to a standard deviation of 3-3.6 N/mm 2 .
Table 2.8-1 Standard deviations under different conditions
Conditions
Good control with weight hatching, use of
graded aggregates, etc. Constant supervision
Fair control with weight hatching. Use of two
sizes of aggregates. Occasional supervision
Poor control. Inaccurate volume hatching of
all-in aggregates. No supervision
Standard deviation (N/mm 2 )
4-5
5-7
7-8 and above