A framework for use of durability indexes in performance-based design and specifications for reinforced concrete structures

Abstract

Durability of reinforced concrete remains a pervasive concern. At present, as-built concrete quality and hence durability is inadequate in many cases. This relates partly to use of prescriptive specifications that do not appropriately address actual quality concerns. Performance-based specifications may offer greater advantages in improving concrete durability, but to be viable require suitable quality parameters to be defined and measured. In South Africa, a ‘Durability Index’ (DI) approach has been developed to address these concerns. ‘Durability indexes’ are quantifiable parameters which characterise concrete quality and are sensitive to material, processing, and environmental factors. The approach is based on measurement of transport-related properties of the cover layer of laboratory and in-situ concrete, thus reflecting the dual aspects of material potential and construction quality. Rational durability design and performance-based durability specifications are being developed and in some cases applied in actual construction. The paper presents a framework within which the DI approach is used to craft performance-based specifications, based on service life models that utilise the relevant DI values. Steps to establish appropriate DI test values for a given structure are described, and a procedure for implementing their use as a quality control measure is recommended. The approach is integrated, allowing for continual improvement and modification as additional data become available.

Resumé

La durabilité des structures en béton armé demeure une préoccupation importante. De nos jours, la qualité du béton, et donc sa durabilité, est encore dans bien des cas inadéquate. Cela est dû entre autre à des spécifications dans les devis qui ne tiennent pas compte correctement des besoins actuels de qualité. Les devis de performance peuvent mener à une amélioration substantielle de la durabilité, mais nécessite la définition et l’estimation de paramètres appropriés. En Afrique du Sud, une approche basée sur un ‘indice de durabilité’ a été développée pour répondre à ce besoin. Les ‘indices de durabilité’ sont des paramètres quantifiables qui caractérisent la qualité du béton en tenant compte du matériau, de sa mise en place et de facteurs environnementaux. L’approche est basée sur l’estimation des propriétés de transport de la couche de recouvrement de bétons de laboratoire et de chantier, afin de refléter la qualité de la mise en place et le potentiel du matériau. Les critères de durabilité sont développés et dans certains cas appliqués à des structures actuelles. L’article présente une approche dans laquelle les indices de durabilité sont utilisés pour établir des devis de performance, sur la base de modèles de durée de vie utilisant des indices de durabilité pertinents. Les étapes permettant d’établir les indices de durabilité pour une structure donnée sont exposées, et une procédure décrivant leur implantation comme mesure de contrôle de qualité est recommandée. L’approche peut être améliorée de façon continue au fur et à mesure que des données supplémentaires sont disponibles.

Appendix—Derivation of equations

This Appendix gives additional background and the statistical basis for the derivation of the various durability index values discussed in the main paper.

1.1 A1 Relationship between material potential and as-built characteristic values

1.1.1 A1.1 Definition of characteristic value

At this stage in the development of the method and since we are dealing with serviceability parameters, it is recommended that a 1 in 10 chance that the average of any three consecutive tests will fail the required limiting values be accepted as the appropriate confidence level.

1.1.2 A1.2 Differences between material potential and as-built values

The effect of site processing would be expected to be two-fold—a reduction in average quality and increased variability. Thus, the absolute differences in average values between the as-built and material potential specimens, as well as their variances, are required in order to establish the margin between material potential and as-built values. This has not been extensively studied, with one reference available examining this phenomenon in terms of South African durability indexes [21]. Gouws studied the quality of as-built structures and associated site-cast cubes from nominally identical concrete batches, using the South African DI tests. Regarding average values, the results were mixed. As-built values were generally worse, but occasionally better than the laboratory specimens. The occasional reversals were attributed to the methods of finishing; for example when considerable densification was given to the surface of well-cured ground slabs. In view of uncertainties, accounting for differences in average performance is therefore neglected at this stage. This issue is returned to later. Gouws et al. [21] reported variances for the laboratory (material potential) and as-built conditions. The coefficients of variation (COV) are shown in Table A1.

Table A1 Single-operator coefficients of variation [21]

1.1.3 A1.3 Derivation: chloride conductivity values

If average values are assumed to be the same for both as-built and material potential specimens (in the absence of better information), the situation is as shown in Fig. A1, where characteristic values represent poorer quality (i.e. higher numerical values), as is the case for the chloride conductivity test. The relationship between the characteristic value and average value is thus:

$$ \hbox{CC}_{\rm Char} = \left({1 + \frac{\hbox{Z}_{90\%}}{\sqrt{3}} \hbox{COV}} \right) \hbox{CC}_{\rm Average} $$

(A1)

where Z_90% refers to the one-sided 90% probability value from the standard normal distribution (=1.30), COV represents the coefficient of variation, CC_Char represents the characteristic chloride conductivity value, and CC_Average the average value. (The √3 is required in Eq. A1 because the relationship between characteristic and average value is for the average of 3 tests, but the COV is related to the variability of single test results.)

Fig. A1

Conceptual relationships between material potential and as-built test distributions for chloride conductivity test. differences between average quality neglected

Equation A1 holds for both material potential and as-built values. Thus the ratio between the characteristic values for material potential and as-built quality can be determined as:

$$ \frac{\hbox{CC}_{\rm Mat'l}}{\hbox{CC}_{\rm As-Built}} = \frac{\hbox{CC}_{\rm Average}\left( {1 + \frac{\hbox{Z}_{90\% }}{\sqrt{3}} \hbox{COV}_{\rm Mat'l}} \right)}{\hbox{CC}_{\rm Average}\left( {1 + \frac{\hbox{Z}_{90\% } }{\sqrt{3}} \hbox{COV}_{\rm As-Built}} \right)} $$

(A2)

where ‘Mat’l’ represents Material Potential throughout

Substituting the values from Table A1:

$$ \hbox{CC}_{\rm Mat'l} = 0.94\hbox{ CC}_{\rm As-Built} $$

(A3)

The desired material potential value is calculated as a function of the required as-built value, since the as-built value is the key value used in service life models and performance-based specifications.

In the absence of better information, Eqs. A2 and A3 were calculated assuming that the average as-built quality was the same as for the laboratory specimens representing material potential. This is unlikely to be the case. When coupled with the limited data used to derive the relationships, it is considered prudent to increase the margin between the as-built value and the material potential. Thus, as an interim measure the recommended relationship is:

$$ \hbox{CC}_{\rm Mat'l} = 0.90\hbox{ CC}_{\rm As-Built} $$

(A4)

1.1.4 A1.4 Derivation: oxygen permeability values

The procedure for developing the relationship between material potential and as-built quality for OPI is similar to that given above, but with this difference: the OPI value is the negative logarithm of the coefficient of permeability. Thus, OPI values cannot be assumed to be normally distributed, and therefore Eqs. A1 and A2 do not apply. However, these equations can be used for the coefficient of permeability, k, which decreases with increasing quality as for the chloride conductivity value. Equation A2 expressed for k becomes:

$$ \frac{\hbox{k}_{\rm Mat'l}}{\hbox{k}_{\rm As-Built}} = \frac{\hbox{k}_{\rm Average}\left({1 + \frac{\hbox{Z}_{90\%}}{\sqrt{3}} \hbox{COV}_{\rm Mat'l}} \right)}{\hbox{k}_{\rm Average}\left({1 + \frac{\hbox{Z}_{90\%} }{\sqrt{3}} \hbox{COV}_{\rm As-Built}} \right)} $$

(A5)

Taking the logarithms of both sides, and substituting OPI for –log (k) results in:

$$ \hbox{OPI}_{\rm Mat'l}= \hbox{OPI}_{\rm As-Built} -\log \left[ {\frac{1 + \frac{\hbox{Z}_{90\% }}{\sqrt{3}} \hbox{COV}_{\rm k,Mat'l}}{1+\frac{\hbox{Z}_{90\%} }{\sqrt{3}} \hbox{COV}_{\rm k,As-Built}}} \right] $$

(A6)

Coefficients of variation for k of 23% and 50% are equivalent to the coefficients of variation of 1% and 2% for material characteristic and as-built conditions respectively, for OPI [21]. Substituting these values and solving:

$$ \hbox{OPI}_{\rm Mat'l}= \hbox{OPI}_{\rm As-Built}+ 0.07 $$

(A7)

Transforming the k values to OPI values results in the margin becoming a fixed value, rather than proportional to the required value as was the case for chloride conductivity. Again it is deemed prudent to increase the margin, resulting in the proposed relationship:

$$ \hbox{OPI}_{\rm Mat'l}= \hbox{OPI}_{\rm As-Built} + 0.1 $$

(A8)

1.1.5 A1.5 Derivation: sorptivity values

The procedure for sorptivity is identical to that for chloride conductivity. The relationship between average and characteristic values is:

$$ \hbox{Sorp}_{\rm Char} = \left( {1 + \frac{\hbox{Z}_{90\%}}{\sqrt{3}} \hbox{COV}} \right) \hbox{Sorp}_{\rm Average} $$

(A9)

The relationship between material potential and as built quality is thus similarly:

$$ \frac{\hbox{Sorp}_{\rm Mat'l}}{\hbox{Sorp}_{\rm As-Built}}=\frac{\hbox{Sorp}_{\rm Average}\left( {1 + \frac{\hbox{Z}_{90\%} }{\sqrt{3}} \hbox{COV}_{\rm Mat'l}}\right)}{\hbox{Sorp}_{\rm Average} \left( {1 + \frac{\hbox{Z}_{90\%} }{\sqrt{3}} \hbox{COV}_{\rm As-Built}}\right)} $$

(A10)

In this case, the known value will be the material potential and not the as-built value. Substituting values from Table A1:

$$ \hbox{Sorp}_{\rm As-Built} = 1.04\hbox{ Sorp}_{\rm Mat'l} $$

(A11)

For similar reasons as for the chloride conductivity test, it is considered prudent to increase this margin, resulting in the recommendation of:

$$ \hbox{Sorp}_{\rm As-Built}= 1.10\hbox{ Sorp}_{\rm Mat'l} $$

(A12)

1.2 A2 Establishing target values

The materials supplier must establish target values so that the characteristic values are met consistently. Target values can be calculated by a method similar to that proposed for strength [33], except for the less stringent criterion of 1:10. Only chloride conductivity and oxygen permeability limits are used to control the mix design, and not the sorptivity. Relationships are thus derived only for these two tests. Between-batch coefficients of variation for the tests, that is the coefficient of variation of the average of multiple sets of samples taken from a single batch, are required. For the situation with a small number of batches, these were taken from [32], see Table A2.

Table A2 Between-batch coefficients of variation [32]

For a large number of batches, the operator can choose to use the coefficient of variation from the actual test history to establish limits. The equations given in Sect. 6 were derived as given below for a small number of specimens.

The requirement that no single test result should fail the target value by more than some absolute limit was also adopted. The proposed limits are suggested as 0.2 mS/cm for the chloride conductivity test and 0.3 for the OPI, based upon the judgement of the authors (see Sect. 7).

1.2.1 A2.1 Chloride conductivity values

Here, the calculations are straightforward. Using the COV of 13.6% from [32] and that no single test is above the absolute maximum by more than 0.2 mS/cm, results in:

First Criterion: (average of three consecutive test results not less than target value):

$$ \begin{aligned} &\hbox{CC}_{\rm Target} = \hbox{CC}_{\rm Char} - \frac{1.30}{\sqrt{3}} \left( {\frac{13.6}{100}} \right) \hbox{CC}_{\rm Char}\\ &\qquad = 0.90 \hbox{ CC}_{\rm Char}\\ \end{aligned} $$

(A13)

and the second criterion (no single test result is 0.2 mS/cm more than target value):

$$ \begin{aligned} &\hbox{CC}_{\rm Target} = \hbox{CC}_{\rm Char}- 1.30 \left( {\frac{13.6}{100}} \right) \hbox{CC}_{\rm Char} + 0.2 \\ &\qquad = 0.82\hbox{ CC}_{\rm Char}+0.2 \\ \end{aligned} $$

(A14)

where ‘Char’ values refer to Material Potential values.

The more stringent of these two limits controls.

1.2.2 A2.2 Oxygen permeability values

For the OPI values, the concept is similar, although complicated by the logarithmic transformation. Again this is satisfied by developing the expressions for k values and then transforming. For the first criterion, and using a COV for k of 53% [32]:

$$ \begin{array}{l} \hbox{k}_{\rm Target}= \hbox{k}_{\rm Char} -\frac{1.30}{\sqrt{3}} \hbox{COV}_{\rm k} \hbox{k}_{\rm Char}=\hbox{k}_{\rm Char}\left( {1 -\frac{1.30}{\sqrt{3}} \hbox{COV}}\right)\\ -\log \hbox{k}_{\rm Target} = -\log \left[\hbox{k}_{\rm Char}\left( 1-\frac{1.30}{\sqrt{3}} (0.53)\right) \right]\\ \hbox{OPI}_{\rm Targ et} = \hbox{OPI}_{\rm Char} + 0.22 \end{array} $$

(A15)

For the second criterion, a margin of 0.3 for the OPI was deemed satisfactory. This results in:

$$ \begin{aligned} -\log (\hbox{k}_{\rm Targ et}) &= - \log \left( {\hbox{k}_{\rm Char}(1 - 1.30\hbox{ COV})} \right) - 0.30 \\ \hbox{OPI}_{\rm Targ et} &= \hbox{OPI}_{\rm Char}- \log \left( {1 - 1.30 (0.53)} \right) - 0.30\\ \hbox{OPI}_{\rm Targ et}& = \hbox{OPI}_{\rm Char} + 0.51 - 0.30\\ \hbox{OPI}_{\rm Targ et} &= \hbox{OPI}_{\rm Char} +0.21 \\ \end{aligned} $$

(A16)

where ‘Char’ values refer to Material Potential values.

Therefore the second criterion will always result in a lower value and can be discarded.

1.2.3 A2.3 Sorptivity values

For the water sorptivity test, using the COV of 13.6% [32] and taking that no single test is above the absolute maximum by more than 1 mm/hr^0.5, results in:

First Criterion: (average of three consecutive test results not less than target value):

$$ \begin{aligned} \hbox{S}_{\rm Target} &= \hbox{S}_{{\rm Char}} - \frac{1.30}{\sqrt{3}} \left( {\frac{13.6}{100}} \right) \hbox{S}_{{\rm Char}}\\ &\,\,=0.90\hbox{ S}_{{\rm Char}}\\ \end{aligned} $$

(A17)

and the second criterion (no single test result is 1 mm/hr^0.5 more than target value):

$$ \begin{aligned} \hbox{S}_{\rm Target} &=\hbox{S}_{{\rm Char}}-1.30 \left( {\frac{13.6}{100}} \right) \hbox{S}_{{\rm Char}}+ 1.0 \\ &\,\, =0.82\hbox{ S}_{{\rm Char}} +1.0\\ \end{aligned} $$

(A18)

where ‘Char’ values refer to Material Potential values.

The more stringent of these two limits controls.

The resulting equations are summarized in Table A3.

Table A3 Equations for calculated values