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306 New Trends in Eco-efficient and Recycled Concrete

11.5.2.4 Cracking serviceability limit state

Cracking SLS are essentially dependent on fundamental parameter α 5 , which, in
turn, is affected by parameters α 2 and α 6 . The general compliance criteria are that
for RAC the characteristic crack width is smaller or equal to the one computed for
NAC (w k;RAC # w k;NAC ), and both of them have to comply with Eurocode’s limits.

11.6 Calculation of the equivalent functional unit

As stated, the RAC EFU will correspond to determining the required volume of
3
3
RAC (K m ) that has the same functionality as 1 m of NAC. This can be done by
conducting a parametric study, testing different NAC solutions and determining the
volume amplification modifier (K) for each case. All the parametric studies need to
have same design principles and conditions. This corresponds to having the same
target life, the same reinforcement and the same compliance criteria, regarding SLS
(both for deflection and cracking width). These criteria define the results of the var-
ious h RAC /h NAC . The parametric studies were conducted in slabs, assuming that K
should never be larger than 1.5, for feasibility and economic reasons.

11.6.1 K as function of durability
Eurocode 2 provides values for minimum cover (c min ) for NAC. For RAC, this
same cover in RAC (c min, RAC ) can be as a function of NAC if α 3 is included
[Eq. (11.8)]. The same principle goes for α 4 , giving a similar equation.

ð
h RAC h NAC 1 2 3 Δc h NAC 1 2 3 α 3 2 1Þ 3 c min;NAC
5 5 (11.8)
h NAC h NAC h NAC
A parametric study has been conducted, which included several NAC slab
heights, h NAC , as follows: 10, 12, 15 and 18 cm (Dobbelaere et al., 2016). The
results for α 3 and α 4 are presented in Figs. 11.3 and 11.4 and show K factors up to
1.75 for α 3 5 2.5, supporting the higher impact of carbonation on RAC structures.
For α 4 , the amplification factor reaches a maximum of 1.27 for the same limit. It
) values correspond to extreme design
should be mentioned that these K α 3 (and K α 4
conditions (h NAC 5 10 cm and XC4), that are unlikely to happen. To consider this,
the parametric study excluded situations that would lead ratios between the effec-
tive height (d NAC ) and the total height lower (h NAC ) than 0.75.

11.6.2 K as function of long-term deflection SLS
Long-term deflection is a function of ratios α 2 and α 6 . These will affect the struc-
tural element’s stiffness, by means of its moment of inertia and modulus of elastic-
ity. In this case, α 2 is affected by α 6 , as deflection should be computed using the
effect modulus of elasticity. This interconnected effect of both parameters leads to