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Equivalent functional unit in recycled aggregate concrete 311

though there is some inaccuracy in this (α 1 expresses the ratio between the mean
compressive strengths in RAC and NAC), this simplification is acceptable for
design purposes. The height of the slabs in RAC was obtained by multiplying the
corresponding NAC height by K, rounding to the nearest value in centimetres. The
minimum cover for the slabs in RAC (c min, RAC ) was the maximum of the product
of the minimum cover of the slab in NAC (c min, NAC )by α 3 or α 4 .

11.7.1 Missing data
The data collected in the literature review does not always provide all the informa-
tion required to do the full analysis. Those parameters need to be engineered, based
on general knowledge and adjusting the expressions for RAC reality. As an exam-
ple, Eurocode 2 provides Eq. (11.15) to define the secant modulus of elasticity
(E cm ) with the average compressive strength, at 28 days. To adjust this expression
to RAC, Silva et al. (2016) developed a comprehensive statistical analysis that led
to several trend lines. Eq. (11.16) gave the best correlation to express the average
relationship between α 2 and α 1 :

0:3
f cm
E cm 5 β 22 (11.15)
10
A previous comprehensive statistical analysis with information provided by
Silva et al. (2014) led to several trend lines. The value of β, for which the highest
2
coefficient of determination, R , is obtained, is used to express the average relation-
ship between α 2 and α 1 :

0:3
α 2 5 0:871 3 α 1 (11.16)
The carbonation coefficient and chlorides migration coefficients can be corre-
lated with the mean compressive strength of concrete (Hasaba et al., 1981). The
relationship is not affected by the replacement level, type or size of RA, as con-
firmed by Silva et al. (2015a e). The relationship between RAC and NAC can be
computed using the following Eqs. (11.17) and (11.18), for carbonation and chlo-
ride migration, respectively:

2;7 2;7

K c;RAC f cm;NAC 1
α 3 5 5 5 (11.17)
K c;NAC f cm;RAC α 1
r ffiffiffiffiffiffiffiffiffiffiffi
p p
D RAC ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
α 4 5 5 e 20:023ðf cm;RAC 2f cm;RC Þ 5 e 20:023 3 f cm;RC 3 ðα 1 21Þ (11.18)
D RC
where K c,RAC and K c,NAC are the coefficients of accelerated carbonation in RAC
and NAC, respectively, D RAC and D NAC , the respective 28-day chloride migration
coefficients, and f cm,RAC and f cm,NAC their 28-day mean compressive strength.