New Zealand Experiences with Concrete Service Life Prediction Models: A Brief History

N. Lee
Opus Research, Petone, New Zealand

SUMMARY: As an island nation, much of New Zealand’s infrastructure and many of our metropolitan areas are in close proximity to the sea and reinforcement corrosion due to chloride ingress has long been presumed to present the primary threat to the longevity of reinforced concrete structures. This paper presents an overview of progress in the adoption and evolution of service-life prediction models relevant to this deterioration mechanism over the past 25 years, for the purposes of durability design and asset condition assessment. It also highlights some of the key findings of research work conducted in this field with which the author was involved.

1. In the Beginning was the Building Code (The EARLY 90s)

In 1992, the New Zealand construction sector made a pioneering change by adopting a Building Code based on declared levels of performance rather than on prescriptive design. A unique feature introduced at this time was the ‘B2 Durability’ clause that effectively mandates that the structural components of buildings and other constructed assets will sustain an in-service life of at least 50 years (Building Industry Authority, 1992). In line with its new philosophy, the performance-based Building Code did not specify construction techniques to comply with this requirement. However it does reference a number of ‘Acceptable Solutions’ that provide guidance in this respect, and the NZS 3101 ‘Concrete Structures Standard’, which describes the minimum requirements for the design of reinforced and pre-stressed concrete structures, is one such document.

Consequently when NZS 3101 was revised in 1995, the authors identified the requirement to specifically address the durability of concrete as a primary concern. Many of New Zealand’s cities, and much of its infrastructure, are in close proximity to the sea and the Standard notes that “…corrosion of the reinforcement to be the most common and obvious form of durability failure”. A procedure was developed for durability design that involves assigning an exposure classification based on the geographic location of a proposed structure, followed by selection of the appropriate concrete quality, cement chemistry and depth of cover. The exposure classification zoning was based on environmental severity and determined by measured chloride ion deposition and exposed steel corrosion rate studies. Four principal classifications are recognised, ranging from benign inland country areas where carbonation of concrete is the only realistic durability threat, through to more aggressive environments where structures are splashed by, or partially or wholly immersed in seawater.

For each exposure classification, a table of permissible combinations of minimum cover and concrete quality, as indicated by specified strength, was established. The choice of prescriptive covers and concrete compressive strength to provide durability solutions was based on a combination of overseas research studies and the historical performance of reinforced concrete in the New Zealand environment.

2. A Need for Further Guidance

The 1995 NZS 3101 specifications were based upon Type GP concrete produced with binders consisting of ordinary Portland cement with a small amount (ca. 5%) of filler only. Even at the time, the advantage of cement blends containing supplementary cementitious materials (SCMs) such as blast-furnace slag and fly-ash, or the incorporation of silica fume and other high reactivity pozzolans was acknowledged. However, their introduction to the New Zealand ready-mix concrete industry was a comparatively recent development and, because of the lack of a suitably comprehensive performance record, the authors of the 1995 Standard revision considered they should not be included.

The approach to durability design established in NZS 3101:1995 was excellent for its time, and compares favourably with comparable international concrete design documents of the era. However limitations and shortfalls quickly became apparent, as concrete specifiers were increasingly compelled to deal with issues that are not directly addressed, for example, the increasingly common need to design major infrastructural assets for a 100 year intended service life. Furthermore, the spirit of the Standard explicitly recognised that a trade-off between concrete quality and cover was permissible. As was increasingly well-appreciated, laboratory test results for indicative durability parameters such as chloride ion diffusion coefficients could easily be an order of magnitude better for concrete containing SCMs than the equivalent Type GP grade. Given that the default covers were necessarily set very conservatively, designers began to ponder how far these could conceivably be reduced with a superior concrete mix before unacceptable results prevailed? 

Shortcomings in the Standard, a lack of clear guidance, and the commercial imperatives on concrete producers drove a need to demonstrate and quantify the benefits of the various supplementary cementitious materials. This was particularly acute in New Zealand where there are no local industries that have generated slag, fly-ash or silica fume by-products on a consistent and sustained basis that were suitable for incorporation into concrete. Consequently these waste materials are imported into the country and, rather than reducing the price of concrete, they are instead sold at a premium as durability enhancers. A natural pozzolan (amorphous geothermal sinter) is mined locally but is priced to be competitive with the other SCMs available.

2. Commercial Imperatives Drive the Adoption of Predictive Models (Late 90s)

In response to these deficiencies, by the late 1990s both of the major players in the ready-mixed concrete industry had introduced service-life prediction models for use by their customers on their own initiative. These allowed users to design alternative solutions to the prescriptive mix specifications of NZS 3101:1995, taking advantage of the superior durability performance characteristics of SCM concretes. In the absence of independent alternatives from reputable organisations such as the American Concrete Institute or the UK Concrete Society, both of whom were still developing solutions at the time, these proprietary models quickly gained some degree of acceptance by the specifying industry. In most cases however, designers and specifiers did not have the background knowledge to interrogate the suppliers regarding the validity of their models, and were usually satisfied by their existence, particularly if a warranty of durability performance was implied. Of course, a sceptic might question the usefulness or enforceability of such warranties in practice.

Each commercial model attempted to answer questions not addressed by NZS 3101:1995 by providing a quantitative measurement of the improvement in performance gained from using the specific SCM being promoted by the supplier. Both derive in principle, from the assumption that chloride ingress can be modelled by adopting tenets of classical theory describing one-dimensional chemical diffusion. However within this basic mathematical framework, each model embodied a somewhat different approach to durability prediction. Despite now being effectively obsolete, they are described in further detail below since many of the contradictions inherent in their conception and choice of terminology continue to confuse non-expert practitioners interacting with concrete durability models to this day.

3. Allied’s Model

This model derived from pioneering research work published by Bamforth (1993) regarding historical chloride penetration into in situ concrete, re-packaged as a user-friendly computer programme. The crux of the underlying algorithm is the concept of an ‘achieved’ chloride diffusion coefficient for a given concrete structure. This parameter, in combination with an environmental chloride load (effectively a force and a resistance), entirely describes the shape of the chloride concentration vs depth profile that you would expect to have developed in the concrete at any given age. Somewhat confusingly there is no standardisation in the literature for the way in which the terminology of diffusion theory has been co-opted for this quite specific and unique meaning, and other authors have adopted qualifiers such as ‘effective’ or ‘apparent’ to denote similar concepts of ‘diffusivity’.

The achieved diffusion coefficient was not derived from early-age laboratory characterisation testing but rather the observed performance of aged structures with equivalent concrete to the mix design under consideration. This empirical basis is the most compelling feature of the model – a rigorous and scientifically correct understanding of the transport mechanisms for chloride ions is not necessary because the combined effects of absorption, diffusion, convection and permeation are bundled together in a single parameter.

As other researchers had previously concluded (Takewaka & Mastumo, 1988; Mangat & Malloy, 1993), when the chloride penetration resistance of concrete structures is examined over time, the magnitude of the achieved diffusion coefficient appears to reduce. This can be expressed by equations of the form:

Dach,t=Drefttref-α   (1)

where D_ach is the average achieved chloride diffusion coefficient of the concrete over the time interval t since first exposure, D_ref is a reference measurement of diffusivity made at some earlier time t_ref, and the age exponent α is a constant ranging between 0 & 1 that depends on both the composition of the concrete and its environment (refer to Table 1 for the definition of other common abbreviations used in the text). Influential service life prediction models based on using Fick’s law and adopting this form of temporally-dependent reducing diffusion coefficient include ‘LightCon’ (Maage et al., 1995), ‘DuraCrete’ (1998), the UK Concrete Society’s ‘AgedDCA’ (Bamforth, 2004) and ‘Life-365’ (Ehlen et al., 2009), which is developed and maintained by a US concrete industry consortium including the National Ready Mixed Concrete Association.

A reduction in the diffusion coefficient corresponds to an apparent improvement in the durability performance of the concrete. The attractive feature of Bamforth’s (1993) work for the concrete ready-mix suppliers developing this particular service life prediction model was that his data suggested concrete incorporating a ground granulated blast-furnace slag binder displayed, on average, very large negative values for the age exponent α whereas Type GP concrete showed only nominal changes of diffusion coefficient with time. Given that blast-furnace slag was their favoured solution for aggressive marine environments, endorsement and promotion of the model had obvious marketing advantages.

Once the dependence of the diffusion coefficient on time (i.e. the magnitude of α) has been established, the standard ‘error function’ (erfc) solution to Fick’s 2^nd law of diffusion (Crank, 1975), stated by Eqn. (2), can be modified to incorporate this temporal dependence for lifetime prediction.

Cx,t=Ci+(Csa-Ci)∙erfcx2Dach, t∙(t-tex)   (2)

In this simple model, the design service-life solely equates to the initiation period i.e. the time for the chloride concentration at the cover depth, C_x, to exceed the critical chloride threshold for depassivation of the reinforcement, sufficient to allow corrosion to commence. The user needs to nominate the surface chloride concentration developed in the concrete over time, C_sa, which equates to the severity of the maritime exposure conditions. Some guidance is offered in this choice; for example 4% chloride by weight of cement is the default for the splash zone. The critical threshold for the onset of reinforcement corrosion is set as 0.4% chloride by mass of cement although again a knowledgeable user could override the default value.

Table 1.  Definitions for abbreviations & mathematical symbols used in the text

Algorithms within the model allow the user to estimate reference D_ref values for ordinary Portland cement concretes based on the compressive strength and interpolation from existing data sets, and furthermore add an allowance for a lowered initial diffusion coefficient due to the introduction of varying quantities of slag (or other SCMs). However, the model places greater emphasis on the benefit accrued from the (postulated) age-dependent improvement in slag concrete performance relative to OPC concrete, rather than the low early-age diffusion coefficients measured in the laboratory for slag concrete. This may reflect the fact that very low diffusion coefficients (D_lab < 2 x 10^-12 m²/s) generally require 60% or greater replacement of the cement by slag (Biljen, 1998), a replacement level which many construction companies deem impractical due to the corresponding drop in early-age strength.

Because of the significant age-dependent reduction in the achieved diffusion coefficient allowed for slag concrete, the model indicated that 80 to 100 year initiation times for corrosion were readily achieved with the cover requirements for marine situations that were then in force under NZS 3101:1995.

3. Firth’s Model

The competing proprietary service life prediction model commonly encountered in the late 1990s was intended to promote durable concrete mixes based on silica fume. In this model, calculation of the initiation time was again based on Crank’s solution to Fick’s 2^nd law (Eqn. 2), but utilised early age (< 90 day) diffusion coefficients measured on concrete specimens in the laboratory (D_lab), without allowance for any age-dependent improvement in field performance. The authors of the model (Scancem Materials) noted at the time that the evidence for allowing a changing diffusion coefficient is not conclusive and suggested any apparent observed reduction may simply reflect initial absorption effects (Frank Papworth, personal communication, 1998). Moreover, because laboratory specimens for diffusion tests are inevitably saturated, unlike field concrete, the model uses a worst-case scenario and so has built-in conservatism.

A consequence of choosing to adopt unmodified early-age diffusion coefficients as the primary input in this model was that even with data derived from laboratory testing of very durable concretes (e.g. D_lab = 1.0 x 10^-12 m²/s), maximum initiation times (based on a 0.4% corrosion threshold value) of the order of just 20 years were achievable with covers as given by NZ 3101:1995. To demonstrate that silica fume concrete could achieve performance life of 100 years or more, the model included an allowance for the propagation period, i.e. the latent time interval between corrosion initiation and the resultant damage becoming structurally unacceptable. This was achieved by a simple calculation of galvanic corrosion using standard electrical resistance formulae for rods in an electrolyte, postulating anode and cathode lengths equivalent to the longest continuous reinforcing element length. By assuming the potential difference for the corroding steel, the current flowing can be calculated and the corresponding rate of metal loss is obtained from Faraday’s Law. Finally, the time to spalling or structural failure is determined based on the loss of section necessary in each case. Propagation times had commonly been neglected on the assumption that they would prove to be negligible in comparison with the initiation period. The implications of this model’s calculations suggest this is not true for silica fume concretes which, even in the saturated state, have a resistivity greatly exceeding 20,000 ohm.cm. Consequently, corrosion rates are very low and the duration of the initiation and propagation phases become comparable, at least if the veracity of the model was accepted.

3. Degree of Acceptance

With the emphasis on guaranteeing durability in the New Zealand Building Code (Building Industry Authority, 1992), both concrete producers and specifying engineers came to increasingly rely on these models to demonstrate they were meeting tender requirements. Despite this, specifiers retained a degree of scepticism about both models, for which a number of obvious reasons could be identified:

1. The models functioned in the conflicting roles of both technical aids and as marketing tools, thus could not necessarily be relied upon as dispassionate distillations of current scientific understanding. 
2. The output of the models had not been empirically calibrated so that the predicted life is realistic for New Zealand conditions. Both models indicated that cover requirements for Type GP concrete within the splash zone were insufficient to meet the 50-year Building Code requirements, with calculated initiation times of < 10 years. This was being borne out by practical experience with such structures. However, based on typical input parameters, a similar inadequacy was implied for concrete exposed to prevailing onshore winds, a situation in which concrete structures had historically been observed to perform well.
3. Disparate philosophies: The models could be utilised to provide comparison between alternative mix designs proposed for a given project. However this process was complicated by the need for fairly converting the inputs of models with quite different viewpoints. Should diffusion coefficients be obtained by early-age laboratory testing or from the investigation of historical structures? Can one type of diffusion coefficient be translated to the other with any accuracy, or are achieved diffusion coefficients unique to a particular structure? Is it good engineering practice to assume a level of future durability performance (i.e. a temporal reduction in diffusivity) that is not initially in evidence? How should transport mechanisms such as sorptivity be accounted for? 

To use either of the models at the time, it was necessary to either ignore these difficulties or favour a particular philosophy without any firm evidence having been offered for its superiority. A further complicating issue was how to implement durability-related quality assurance testing for a given mix design, particularly if claimed performance was largely based on projected future diffusivity and cannot be easily related to early age testing.

Despite these limitations, it was clear that the models performed the highly useful function of guiding specifiers towards appropriately durable marine concrete mix designs at a time when this was not ensured by the default prescriptive solutions of the ‘Concrete Structures’ Standard.

3. Turn of the Century – Active Research

By the end of the 1990s, BRANZ, a building industry-funded independent research organisation, had recognised the need for reliable data concerning the performance of SCM concrete and instigated a marine concrete durability experimental programme to allow the outputs of service life prediction models to be verified. It was also hoped to resolve some of the more philosophical questions posed above.

In late 1998, thirty-six 1.0 m x 0.75 m x 0.35 m blocks of structural concrete were cast at a local ready-mix plant under the supervision of BRANZ personnel. Four series of mixes were initially produced, consisting of a set of controls formulated purely with a type GP cement and three further series in which a quantity of the binder was replaced with three common SCMs then available on the New Zealand market: ground granulated blast-furnace slag, silica fume and a natural silica pozzolan. Each series included mixes at three different levels of total cementitious material: 280 kg/m³, 325 kg/m³ and 400 kg/m³, as appropriate for the severity of the exposure environment for which they were intended. The mix designs were intended to be representative of commercial ready-mixed concrete and were wet-cured for 7 days after casting.

These concrete specimens were distributed amongst two natural experimental exposure sites established in the Wellington region, one at Weka Bay (at map coordinates 41°17’42.6″S, 174°48’17.1″E) in the inner harbour and the second at Oteranga Bay (41°17’40.2″S, 174°37’46.8″E) on the exposed southern end of Cape Terawhiti, 16 km west of the city. The concrete samples at Weka Bay are situated above the spring high tide line (Figure 1) but are regularly wetted by waves on breezy days and the site is considered to be a fairly aggressive example of an NZS 3101 ‘C zone’ exposure classification. At Oteranga Bay, the samples are situated within 100 metres of the shoreline and subject to high rates of salt deposition from wind-blown aerosols. As such, the site is considered to be a severe example of the ‘B2 zone’ (coastal frontage) exposure environment under NZS 3101.

Figure 1.  The Weka Bay exposure site in 1998

In 2004 the original mixes were supplemented with a new sets of blocks, as an additional series of concretes were produced incorporating a Class F and two Class F fly-ashes as partial cement replacements, reflecting the growing popularity of this variety of SCM. Due to a combination of technical considerations and budgetary constraints, the later fly-ash mixes were produced with a total binder content of 370 kg/m³ and located on the C zone exposure site only. Table 2 summarises the concrete types included in the study. More details of the study and its initial results are reported in Lee & Chisholm (2005).

Table 2.  Concrete mix varieties included in BRANZ concrete durability research programme

4. Measuring of Diffusion Coefficients

The concrete produced for the programme was characterised by measurement of a variety of physical and durability-related performance parameters, including compressive strength, hydraulic sorptivity, resistance to chloride penetration via NT Build 443 (1995) & 492 (1999), and drying shrinkage.

More importantly, at periodic intervals since the establishment of the sites, cores were removed from the surface of the blocks to determine the surface chloride concentrations (C_sa) and achieved diffusion coefficients (D_ach) appropriate to each mix type that are required as inputs to service life models based on Eqn. (2). Monitoring the change in the latter parameter over time also gives the appropriate value of the age reduction index, α, as per Eqn. (1). To obtain this information, it is necessary to have a ‘chloride profile’ i.e. experimental data for C vs x at any time t, for concrete exposed to a chloride-laden environment. In practice, such a profile is obtained by incrementally milling into the concrete, perpendicular to the exposed surface. The powdered concrete collected from each depth interval is collected and analysed for chloride content by x-ray fluorescence (XRF) spectrometry or an equivalent convenient technique. An example of a typical profile is shown in Figure 2 (left) and the milling equipment in Figure 2 (right).

Figure 2.  Chloride profile data measured on a concrete structure fitted to Crank’s equation (left) and the milling equipment used to generate specimens for analysis from extracted concrete cores (right).

The values of C_sa and D_ach are determined by fitting Eqn. (2) to the chloride profile through non-linear regression using least squares, i.e. minimising the sum S given by Eqn. (3) below:

S=n=1N∆C2n=n=1NCmn-Ccn2   (3)

where N is the number of concrete layers sampled; C_m(n) is the measured chloride concentration in the n^th layer (% by mass); and C_c(n) is the calculated chloride concentration in the middle of the n^th concrete layer (% by mass).

The data collected during this programme confirmed the validity of Eqn. (1) with all the concretes exposed on the C zone aggressive marine exposure site displaying statistically significant reductions in their achieved diffusion coefficient through time, with the magnitude of the reduction dependent on the cement binder type. 

Figure 3 displays some examples of temporal variation in diffusion coefficients observed. The plots are in a double logarithmic coordinate scale and include the best-fit line arising from a linear regression of log(D_ach) vs log(t) to verify whether the relationship given by Eqn. (1) holds. The gradient of this line provides the magnitude of the parameter α (the age reduction exponent) and the uncertainty in the position of this line at the 90% confidence level is indicated by the boundaries marked by dashed lines. 

The reduction in temporal diffusivity was found to be particularly marked for the blast-furnace slag and fly-ash concretes. Where the magnitude of the age exponent α is large, this rapidly becomes a more dominant control on the resistance of the concrete to chloride ingress than early-age diffusivity.

The study also attempted to develop a relationship between the achieved diffusion coefficient D_ach (i.e. the empirical parameter that reflects all the transport mechanisms that have given rise to the development of a particular chloride profile on a structure in the field) and the ‘instantaneous’ diffusion coefficient, D_lab that would be measured in the laboratory under controlled conditions on a completely-saturated concrete specimen by a method such as NT Build 443 (1995). It would be reasonable to propose that such a relationship might exist if the reason for the observed reduction in apparent diffusivity with time is related to continued hydration of the cement phases within the concrete. Hydration of the cement phases, supplemented by pozzolanic reaction for mixes containing SCMs, refines and tightens the pore structure of the hydrated cement gel, thereby increasing its resistance to chloride ingress over time. This is the usual explanation given for the temporal dependence of diffusion coefficients (Carlsen, 2000).

Figure 3.  Examples of measured variations in Dach for 400 kg/m3 binder concretes exposed on the severe marine exposure site.

If this hypothesis is correct, and ongoing cement hydration is solely responsible for the temporal changes in the achieved diffusion coefficients observed on the exposed concrete, then there should be a relationship linking D_ach to D_lab. Such a relationship is of great potential value. While only the achieved chloride diffusivity is ultimately important for service life, this information can only be determined ‘after the fact’ from field measurements or by analogy with existing concrete in a similar environment. This is information that may not be conveniently available at the design stage. In contrast, actual diffusivity is a material property that could be readily determined in the laboratory on trial mixes.

Existing information on the relationship between the two different diffusivity determinations is somewhat contradictory. Maage et al (1995) present data that suggests D_lab approximates D_ach shortly after exposure and that the ratio D_lab(t) / D_ach(t) decreases with age in a predictable way. However no simple association could be derived from the BRANZ data, and it was noted (Lee & Chisholm, 2005) that:

1. There was not necessarily a single time during the exposure period where D_lab ≈ D_ach and, even where such an intersection existed, it appears to be unique to each concrete type. 
2. D_ach values, at least in ‘splash zone’ type environments that typically present the greatest risk for reinforcement corrosion due to plentiful availability of both oxygen and water, are very much smaller than D_lab and also display greater reductions with time.
3. 2005 – Improvements to the Concrete Structures Standard

By 2003 it was obvious that the fact that NZS 3101:1995, the ‘Concrete Structures’ Standard, still permitted use of Type GP concrete in aggressive marine environments was an anachronism and would not permit the intended minimum service life of 50 years mandated by the New Zealand Building Code to be routinely achieved. Informed by the results of the BRANZ exposure site testing together with reference to a number of different predictive models, a new set of default durability solutions for minimum concrete quality and cover were provided in the current (2005) revision; these required use of an SCM in C zone exposure classifications. In the light of various uncertainties concerning the current state of knowledge regarding modelling of the propagation phase (i.e. the length of time elapsing from the onset of corrosion to the development of distress sufficient to compromise the serviceability of the structure), the drafting committee adopted an approach based on specifying mixes that could conservatively be considered to achieve a minimum time to corrosion initiation of 40 years and 80 years according to modelling, for Specified Intended Life of 50 and 100 years respectively. Thus the duration of the propagation phase is presently arbitrarily assumed to constitute 20% of the complete service life of the structure. 

It is acknowledged that the mainly prescriptive basis of the present Standard is still not a good fit with the performance-driven philosophy of the New Zealand Building Code. However, the supporting commentary recognises the power of service life prediction models as design tools and permits their use as an alternative to the default solutions. It also cautions against the risks of erroneous or non-conservative results where the designer does not have sufficient knowledge of the appropriate inputs needed by a specific model. To this end, guidance is provided on likely surface chloride concentrations (C_sa) developed in differing exposure environments and the range for the age reduction exponent (α) characteristic of different binder types.

5. 2012 – Reconsideration of the Exposure Site Data

Active work on the original BRANZ research programme concluded in 2003 following the completion of 5 years of data collection. In 2012 the opportunity was taken to resample the exposure site blocks in order to increase the confidence in the observed trends; this date represented 13 years’ exposure of the oldest concretes.

In the course of their summation of the original results, Lee & Chisholm (2005) made the claim after 5 years’ exposure that: “To a broad approximation, the surface chloride concentrations under the site’s spray/splash conditions appear to be (i) relatively constant and (ii) fixed early in the life of the concrete”. In examining the later data, it became evident that this contention was no longer sustainable because the most striking feature of the evolution of the profiles since the time of last inspection is the increase in their surface chloride concentration, as illustrated by the examples reproduced in Figure 4. 

Figure 4.  Development of chloride profiles through time for two 400 kg/m3 total binder content concrete mixes exposed on the Weka Bay C zone site

The literature regarding the temporal dependence of the surface chloride concentration with time appears somewhat contradictory. Mangat & Molloy (1994) and Maage et al. (1999) presented observations from experimental exposure programmes that indicate the chloride content of the exposed surface stabilises after approximately 2 years. However on the basis of inspections of unrelated historic structures of various ages, Uji et al. (1990) suggested that the concentration increases in accordance with the square root of the exposure duration, albeit with greatly varying proportionality constants for different environments (e.g. the tidal zone, splash zone and atmospheric zone). Later, Swamy et al. (1994) claimed that C_sa does not invariably increase following the square root of time but could be reasonably approximated by a more general power function where the exponent of time is less than one.

6. Mathematical Analysis

The existence of a time-dependent surface chloride value has potentially significant implications for the appropriate techniques for the modelling the performance and predicting future service life of concrete structures. The conventional approach using Crank’s error function solution, Eqn. (2), is a direct solution to the boundary value problem stated below:

∂C∂t=D(t)2C∂x2 x>0,  t>tex (Fick’s 2nd Law) C0,t=Csa t>tex (boundary condition) Cx,tex=Ci x>0 (initial condition) }   (4)

The boundary condition that must necessarily be imposed in Eqn. (4) in order to obtain a unique solution to the partial differential equation expressing Fick’s 2^nd law absolutely requires that the surface chloride value (C_sa) is invariant, or at least establishes a constant value very quickly. As noted, the latest BRANZ data does not support this postulate, particularly for the concrete on the C zone site exposed to direct wave splashing. Modelling these profiles with the assumption of a constant rather than increasing C_sa using variations on Eqn. (2) risks underestimating the average diffusivity of the concrete, which in-turn leads to an overly-optimistic assessment of service life. This effect is discussed further in section 5.4. 

Of course one possible solution to the problem of an unsuitable boundary condition is to resort to numerical methods (e.g. the finite difference technique) to solve the partial differential equation that expresses Fick’s 2^nd Law in Eqn. (4); this approach is used by some models such as Life-365 (Ehlen et al., 2009). However it was considered desirable to retain a simple analytical solution comparable to Cranks equation that could be implemented by potential users in a spreadsheet, to allow them to easily utilise the exposure site data and experiment with its implications if so desired.

A review of the literature reveals that the Danish mathematician Mejlbro (1996) had in fact derived a generalised analytical solution to Fick’s 2^nd law that allows for both a time-dependent diffusion coefficient and surface chloride concentration, at a small cost in computational complexity. Mejlbro considered the case in which C_sa is allowed to vary in accordance with a power function of time, as suggested by Swamy et al. (1994) on the basis their observations of existing concrete structures. The surface chloride concentration is explicitly linked to the concrete type and exposure environment by incorporating the value of the chloride ion diffusion coefficient:

Cx=0,t=Csa=S{t-texDt}p   (5)

Under this alternative boundary condition, the solution to Fick’s 2nd law (Poulsen & Mejlbro, 2006) is now expressed by: 

Cx,t=Ci+(Csa-Ci)∙pu   (6)

where

Csa=Srefttref1-p   (7)   and u=x2tDav,(tref)ttref-   (8)   for   t, treftex

Consequently the chloride accumulation in the concrete C_(x,t) at any depth x and time t can be completely specified providing four parameters are known: α, p, D_av,Ψ(tref) & S_ref. The values of α and p describe the rate of change with time of D_av and C_sa respectively and the other two parameters are point-wise measures of these properties after some reference period of exposure. For mathematical convenience, this is often chosen to be t_ref = 1 year.

Where chloride ingress data is available for the same concrete from multiple inspections after varying periods of exposure, α & p have a simple graphical interpretation when the derived values for D_av and C_sa are plotted in a double logarithmic coordinate system, as illustrated by Figure 5.

Figure 5.  The geometric meaning of the regression parameters for C(x,t) data describing chloride profiles using Mejlbro’s model

The value of the Ψ function for any given p & z is evaluated by the expression:

pz=n=0+∞p(n)2z2n2n!- p+1p+0.5n=0+∞(p-0.5)n2z2n+12n+1!   (9)

where Γ(y) is the Gamma function:

y ∶= 0+∞uy-1e-udu   (10)

and p⁽ⁿ⁾ is the ‘falling factorial’ defined as:

p0=1; p1=p; p2=pp-1; …; pn=pp-1p-2∙∙∙p-n+1;  (11)

The difficulty of applying Mejlbro’s solution lies in the novelty of the Ψ (psi) function, which effectively provides a generalisation of the more familiar complementary error function (erfc) employed by Cranks solution in order to take account of the variable driving force for the diffusion imposed by a changing C_sa. For the special case of p=0, which denotes a surface chloride value that remains constant with time, Ψ₀(z) = erfc(z) and Crank’s solution Eqn. (2) is obtained as expected. Unlike erfc, Ψ is not an intrinsic function of numerical software, possibly a contributor to Frederiksen et al. (2009) describing Mejlbro’s result as “little known amongst concrete technologists”.

Irrespective of whether Crank’s erfc solution or Mejlbro’s Ψ_p alternative is used to model chloride profiles developed in exposed concrete, the value of the diffusion coefficient calculated is not an instantaneous variable that captures concrete performance at the point of inspection. Instead it represents the time-averaged value of the concrete’s resistance to chloride ingress since the time of first exposure, i.e.:

Davt=1t-textextDd   (12)

It is important to note that the values of D_av derived from fitting each solution to chloride profile data are not identical and that the assumption of a static surface chloride value in the conventional error function model will result in a persistent error in the estimation of the concrete’s diffusivity if this is not valid. Frederiksen et al. (2009) have demonstrated by both numerical methods and pure analysis that there is a relationship between the two estimates that depends only on p and is independent of time, according to the equation:

Dach,erfc(t)=1p2Dav,ψt   (13)

The value of the adjustment factor μ_p is given by the approximating polynominal:

p=1+0.5194p-0.0876p2+0.0185p3-0.0022p4   (14)

The relationship between the temporal dependence displayed by each estimation of diffusivity is remarkably simple however, with:

erfc=   (15)

6. Modelling Procedures

On the basis of the considerations described in the preceding discussion, the following procedure was adopted for analysis of the experimental data collected from the BRANZ exposure blocks. It is also useful for estimating the future durability of existing structures but if only a single chloride profile representing one specific time interval is available it is obviously necessary to make assumptions regarding the temporal dependence of both diffusivity and surface chloride accumulation, as appropriate to the exposure environment and cement binder composition.

1. The chloride profiles (e.g. Figure 4) are curve-fitted by non-linear regression analysis to the error function solution for C_(x,t) given by Eqn. (2), as previously described in section 3.1. This process produces the regression parameters C_sa and D_ach for a number of different inspection times, t.
2. The time dependence of D_ach is evaluated to obtain a best-fit estimation of α and a reference diffusivity D_ach,ref, assuming the conventional power law relationship given in Eqn. (1) applies (i.e. by plotting D_ach against t in a logarithmic coordinate system and fitting a straight line to this data).
3. The value of the age exponent (1-α)∙p describing the accumulation of the surface chloride concentration C_sa is evaluated similarly, along with a reference concentration S_ref, by assuming Eqn. (7) is valid.
4. A reference value for D_av,Ψ that takes into account the variable surface chloride boundary condition is determined by applying the correction factor μ_p² to D_ach as per Eqn. (13).
5. Using these derived parameters and the Ψ_p model expressed by Eqn. (6) through Eqn. (8), future values for C_(x,t) are estimated for each combination of concrete type and exposure condition, with particular reference to the critical corrosion threshold position (i.e. the depth at which the chloride concentration exceeds the minimum necessary to initiate corrosion). The time at which the threshold depth equals the cover to the outermost reinforcement represents one possible, albeit conservative, serviceability limit state for defining end of life.

The results of applying this procedure to parameterise the chloride ingress profiles collected for the concrete specimens exposed on the BRANZ experimental sites are summarised in Table 3. The principal features in the data include:

• The C zone concretes all show a statistically significant reduction in average diffusivity with time, as indicated by the value of the α parameter, and the reduction is greatest for the slag and fly-ash concretes. This trend is present but less certain for the B2 zone concrete where the reduction is smaller and there is greater scatter in the data as demonstrated by the very large uncertainties at the 90% confidence level.
• The C_sa values are very clearly a function of binder type, with concretes containing SCMs developing surface chloride concentrations in excess of double the comparable values for the GP control concretes. This difference is primarily reflected in the S₁ parameter (i.e. the surface chloride accumulation after year 1), rather than the power exponent for the rate of increase, (1-α)∙p, which is broadly similar for all the concrete exposed on the C zone site.
• Only the 325 kg/m³ concretes on the B2 site have surface chloride concentrations that can be approximated by a broadly constant value, as signified by their generally low values for p in Table 3.

Table 3.  Parameterisation of C & B2 Zone chloride profiles in accordance with the Mejlbro Ψ_p solution to Fick’s 2nd law with temporally-dependent apparent diffusivity and surface chloride concentration.

6. Service Life Prediction

With the appropriate values for α, p, D_av,Ψ(tref) and S_ref selected for a particular concrete type and exposure environment (e.g. by consulting an existing database such as Table 3), the prediction of service life becomes a case of solving the combined Eqns. (6) through (8) for t, given a nominal reinforcement cover x and assuming a minimum threshold concentration of chloride ions that must accumulate at this depth to initiate corrosion. It is widely recognised that the threshold level for corrosion to occur, C_cr, is not truly deterministic, i.e. it cannot be represented by a unique chloride concentration. However for simplicity, it has been assumed that C_cr = 0.4% chloride by mass of binder. This value is frequently quoted in the literature as a conservative choice for the critical threshold; below this concentration there is a negligible risk of mild steel reinforcement corrosion (BRE, 2000).

Solving Mejlbro’s equation for x or t rather than C_(x,t) is slightly complicated by the fact that no explicit inverse of the Ψ function has been mathematically defined. Accordingly, such values need to be obtained from pre-calculated look-up tables or by using an iterative regula falsi procedure; the latter can be conveniently implemented by employing the ‘Solver’ optimisation tool provided in Microsoft Excel.

As previously outlined, the current revision of the NZS 3101 Concrete Structures Standard (2006) attempts to ensure adequate durability performance to meet Building Code requirements by prescribing minimum concrete quality (strength and binder type) and reinforcement cover. As an indication of the adequacy or otherwise of these current durability provisions, a new set of service life estimations were completed based on the Ψp model and the Table 3 regression parameters; Figure 6 shows the results for the 370 to 400 kg/m³ total binder content specimens exposed in the C zone. As a more utilitarian alternative to an individual life calculation assuming a nominal reinforcement design cover, the plotted curves instead describe the modelled evolution of the critical corrosion threshold position as a function of exposure time. The plots are also annotated to include the minimum cover required by the Standard, as appropriate to the mix type and estimated strength class.

The position of the critical corrosion threshold for each of the concrete samples at inspection intervals, up to and including the most recent, is indicated on the Figure 6 plots by the red circles. These have been obtained from interpolation of the measured chloride profiles previously presented and provide some confidence that the parameterised model including increasing surface chloride accumulation and reducing diffusivity is fitting the measured chloride contamination correctly.

Figure 6.  Predicted evolution of the critical corrosion threshold depth (Ccr = 0.4% chloride by mass of total binder) with exposure time for the C Zone exposure site concretes. Dashed lines depict the NZS 3101 (2006) cover requirements for specified life of 50 & 100 years for the relevant binder and strength class

A number of features can be highlighted from these predictions:

• The slag concretes are performing extremely well. At the predicted rate of chloride ingress, a service life of 100 years looks easily achievable with the code minimum cover of 50 mm, even in the case of the 325 kg/m³ mix.
• The fly-ash concretes similarly show exceptional resistance to chloride ingress, albeit with the caveat that these samples have a significantly shorter exposure history and only two sets of chloride profile analyses have been conducted to date.
• The chloride resistance of the Type GP cement control concretes is insufficient to achieve even a 50 year design life, confirming the wisdom of their removal as a possible binder option for the C zone from the most recent revision of NZS 3101 (2006). The equivalent Australian Standard, AS 3600 (2009), still permits its use in this environment, but even with a 60 MPa specified strength and 60 mm cover the 400 kg/m³ GP concrete fails to achieve a 50 year life to corrosion initiation.
• The durability performance of the silica fume and natural silica pozzolan mixes appears to be adequate to achieve a 50 year design life, although they are clearly less chloride resistant than the slag and fly-ash concretes. Currently under the Standard there is no distinction made between the covers required for 50 or 100 years’ design life and the default value appears inadequate for the longer duration however.

It should be emphasised that durability predictions such as those above adopt a conservative definition for end-of-life, suited to design purposes, and neglect the duration of the propagation phase between the initiation of rebar corrosion and the subsequent development of spalling damage severe enough to compromise structural performance. Moreover, many of the variables treated here as deterministic values have a stochastic component when considered in relation to real structures. This is particularly true of the reinforcement cover distribution and the critical corrosion threshold.

A more comprehensive presentation of the most recent results from the BRANZ study, including the data pertaining to the B2 exposure site, on which chloride accumulation is purely due to aerosol deposition, can be found in Lee (2012).

6. Consequences of Inappropriate Application of Error Function Models

The simplifying assumption that C_sa is either constant, or quickly obtains this state after a short period of exposure will lead to significant errors in the parameterised values derived through fitting chloride ingress data to idealised profiles based on Eqn. (2). This is especially true for estimation of the achieved diffusion coefficient. By using short term exposure data and neglecting the time-dependence of C_sa, the calculated values of D_av obtained are low, i.e. they indicate the diffusivity of concrete, and hence its resistance to chloride ions, is much better than its true performance.

To quantify this error and the duration of ‘short term’, a series of calculations were made comparing the Eqn. (2) erfc and Eqn. (6) Ψ_p life estimates for each of the Weka Bay concretes for various inspection times since initial exposure. These calculations assumed that the chloride ingress is correctly described by the Ψ_p model with time-dependent surface chloride concentrations and diffusivities for each concrete specified respectively by the α & p parameters listed in Table 3. At various times t, up to 50 years after exposure, a hypothetical chloride profile is calculated and the resulting regression values for C_sa and D_av,erfc used for estimation of service life using both the erfc and Ψ_p models, assuming 50 mm cover and a critical corrosion threshold of 0.4% w/w chloride by mass of cement. Figure 7 illustrates some typical results.

Figure 7.  Comparison of the erfc and the Ψp model estimates for initiation time to corrosion for a cover depth of 50 mm using chloride profile data from different inspection times

The exact discrepancy between the erfc and Ψ_p life predictions as a function of time depends on the particular interplay between the increase in C_sa, which drives the chloride ingress, and the reduction in diffusivity D_av that resists it, for each concrete type. Figure 7 confirms that the differences between the two estimates converge as the inspection age increases, consistent with the reducing absolute change in each parameter as they (asymptotically) approach a constant value. However, it is clear that service life predictions with durations 1.5 to 2 times longer than they should be are a realistic possibility when using inspection data from structures less than 20 years old with an erfc-based model.

Consequently, time-to-corrosion estimates made with the error function type models that utilise short-term exposure data are likely to be overly optimistic. Given that this is the basis for a number of popular service life prediction models (e.g. DuraCrete, LightCon & AgedDCA), the validity of their inputs and outputs should be carefully scrutinised before being relied upon for design purposes. Due to the lessening rate of change in D_av & C_sa with time (the age exponents α & (1-α)∙p both being less than one), predictions made with long-term exposure data (e.g. > 30 years) is much less susceptible to this error. Unfortunately this information is frequently only available by inspecting existing structures, a situation where the limited ability to accurately characterise initial concrete quality often restricts the dataset’s usefulness for calibrating ingress models.

6. Practical Applications: The Assessment of the Fox & Ngakawau River Bridges

The widespread use of pre-stressed concrete beams in the New Zealand bridge stock has long been recognised as a potential vulnerability for structures in aggressive environments as they age. Few historic designs comply with current durability practice in regard to concrete cover or quality. Deterioration can be difficult to detect in visual inspections and has immediate structural implications. Moreover, there are technical challenges associated with both arresting further deterioration and restoring lost capacity, should corrosion develop on the pre-stressing tendons. For this reason, accurate prediction of future risk is critical for bridges to permit timely and effective intervention.

In response to this demand, Rogers et al (2013) conducted a threat classification for the entire stock of pre-tensioned bridges (810 in total) on the national State Highway network managed by the NZ Transport Agency. This was primarily a desktop exercise factoring era of construction, design characteristics, and geographic situation to map the prevalence and distribution of vulnerable structures. However a sub-sample of 30 bridges were also subjected to a physical inspection to assess current condition and to collect chloride ingress data to permit their residual life to be estimated using a simple erfc diffusion model, as per Eqn. (2). The latter work identified potential durability concerns with the Fox River and Ngakawau River Bridges on the West Coast of the South Island. For both bridges, located in aggressive marine (i.e. NZS 3101 ‘C Zone’) exposure environments, measurements of chloride ingress profiles in their beams led the authors of the report to conclude they would experience corrosion of pre-stressing strand within their 100 year design life and consequently recommend “urgent action” to achieve this intended longevity.

Given the relative youth of these structures (Fox was then approximately 25 years old and Ngakawau 22), their importance to the network, and the limited viable repair options for pre-stressed elements once strand corrosion is established, it was considered important to conduct further inspection and sampling to better define the durability threat to each bridge. In particular, the sampling conducted by Rogers et al. (2013) was restricted to terrestrial spans: It was conceivable that spans over the estuarine river channels crossed by these bridges represent a more severe exposure environment where chloride deposition is even higher. This work was carried out by Opus Research on behalf of the NZ Transport Agency.

7. The Bridges

The Fox River Bridge carries State Highway 6 across the river mouth at Woodpecker Bay (42°01’54.3″S, 171°22’57.2″E) in the Buller District. The bridge was completed in 1988 and consists of six spans, with four pre-stressed 40 MPa f´c Type GP concrete I-beams per span supported on cast in-situ hammerhead pier caps founded on a conventionally-reinforced octagonal column. Five of the spans use 20 m beams with both pre- and post-tensioning, while beams in the shorter (16 m) sixth span are pre-tensioned only. Figure 8 shows a general view of the bridge. It is situated in an exposed location on an open surf beach, with waves breaking directly beneath the bridge. Spans 3 through 5 are located wholly above salt water at high tide; Span 1 is largely situated at beach level above the high tide mark and Span 6 is somewhat sheltered from the prevailing wave direction by a small promontory to the west of the bridge.

Figure 8.  The Fox River Bridge and its environs

The Ngakawau River Bridge is located on State Highway 67 between Westport and Karamea at 41°36’25.5″S, 171°52’36.1″E. It is a five span bridge, constructed in 1983 from precast pre-tensioned 20 metre span U-beams cast from 40 MPa f´c GP concrete. There are 7 beams per span, supported on hammerhead piers with a central conventionally-reinforced concrete stem column.

The bridge is located over saline water, at the river mouth (Figure 9), which opens into a surf beach. However the bridge is set back approximately 150 m from the coastline and the beachfront provides some buffer against waves breaking directly under the bridge. Consequently the exposure environment, whilst legitimately an example of a C Zone classification under NZS 3101 is arguably somewhat less severe than that experienced by the Fox River Bridge. The height of the piers over the channel at high tide is also approximately 2 m greater.

Figure 9.  The Ngakawau River Bridge

7. Significance of Choice of Corrosion Threshold

A preliminary review of the chloride analyses on which the original unfavourable durability predictions were based suggested that the duration of residual service life was heavily dependent on the subjective choice of corrosion threshold, i.e. the minimum chloride ion concentration necessary to initiate corrosion. Moreover the thresholds chosen by Rogers et al. (2013) of 0.03% & 0.05% by mass of concrete, whilst in line with some published literature values, are relatively conservative and possibly more appropriate for design purposes than assessing the risk of premature failure of a well-constructed modern structure in service.

Chloride ions are unique and specific agents for the corrosion of mild steel reinforcement; in sufficient concentration they destroy the protective surface oxide layer that ordinarily develops on steel surrounded by alkaline concrete. However, the potential for corrosion to occur is influenced by a great many variables, including but not limited to: cement chemistry; concrete quality (cement content, w/c ratio, curing); ambient environment; and the homogeneity of the cement paste phase at the interface with the reinforcement. It is also generally accepted that the corrosion risk is controlled by both the chloride and hydroxide ion concentrations within the pore fluid of concrete, with mild steel reinforcement vulnerable under conditions where [Cl ]/[OH ] > 0.6 (Hausmann, 1967). However due to the absence of a simple and reliable technique for measuring alkalis in pore fluid and the fact that hydroxide ion concentration is, to a first approximation, constant in uncarbonated concrete, the convenient fiction is adopted that corrosion risk threshold can be formulated in terms of chlorides alone for practical purposes.

Thus any assumption of a deterministic chloride threshold concentration that will invariably initiate corrosion is an over-simplification, and this variable is better considered in probabilistic terms. Figure 10, reproduced from a Federal Highway Authority (2012) review article, graphically summaries the maximum and minimum corrosion initiation thresholds reported in the recent literature for corrosion of black steel in concrete. The range of values emphasises that there is considerable subjectivity inherent in selecting a corrosion threshold for service life modelling with chloride profiles collected from existing structures. There is clearly no single ‘right’ answer that applies in any given situation. The UK Concrete Society (1984) has suggested that chloride concentrations of 0.05% by mass of concrete (ca. 0.4% by mass of cement) represent ‘some risk’ of corrosion, whilst 0.15% would represent a ‘high risk’

Corrosion of pre-stressing steel is a greater concern than that of conventional reinforcement due to the possibility that localised reduction in the cross-sectional area of the strand will result in an abrupt failure. The high pre-tensioning stresses also render the strand more vulnerable to stress corrosion cracking and, where the loading is cyclic, to corrosion fatigue. For these reasons, the maximum permissible chloride content in fresh concrete is lower for casting of pre-stressed elements than that permitted for conventionally-reinforced concrete. Under NZS 3101 (2006) these figures are 0.50 kg/m³ and 0.80 kg/m³ respectively, or approximately 0.022% & 0.035% by mass of concrete respectively depending on the mix density. 

Despite this presumed greater vulnerability, one of the few reported studies specifically examining the performance of pre-stressing tendons on exposure to chloride ions found that unstressed strand had a corrosion threshold up to six times greater than conventional black steel reinforcement (Pfeifer et al., 1987). When stressed, the strand was more susceptible to corrosion but still showed markedly better resistance to chloride contamination than conventional mild steel reinforcement. The cause of this unexpectedly good corrosion resistance is believed to be a residual chemical film of rod treatment and wiredrawing lubricants, particularly zinc phosphate and calcium stearate, which remain on the surface of the strand even after high temperature tempering for stress relief (Osborn et al., 2008). However since such residual films are detrimental to bond development they are ideally minimised during manufacturing and their presence and efficacy as corrosion inhibitors cannot be relied upon. On balance, while the potential consequences of pre-stressing strand corrosion are more severe than those associated with conventional reinforcement, there is no reason to suggest that the strand itself is more susceptible to chloride-induced corrosion under normal service conditions.

Figure 10.  Examples of published threshold concentrations for chloride-induced corrosion of carbon steel reinforcement (Federal Highway Authority, 2012)

7. Sampling Undertaken

On each bridge, instrumented testing of the pre-tensioned beams in three spans was undertaken to verify reinforcement cover and determine chloride ingress profiles and the extent of carbonation. The spans were chosen to represent a range of possible variation in micro-exposure environment across each bridge and complement the existing test data obtained by Rogers et al. (2013); three beams were selected in each span across the length of each bridge.

The most critical sampling locations in terms of micro-exposure environment could not be determined absolutely by inspection because the beams are not currently showing any evidence of distress. Therefore the only reasonable approach to a robust risk assessment is sufficient testing to permit a statistical evaluation of achieved diffusion coefficients and surface chloride concentrations. Characteristic, in addition to mean values, of these parameters were adopted for subsequent modelling with appropriate tolerance limits to avoid over-estimation of durability performance. In recognition that pre-stressed concrete elements are very difficult to maintain once corrosion begins to propagate, the appropriate characteristic value was selected as the 90% upper one-sided tolerance limit for both D_ach & C_sa at the 90% confidence level. Assuming a normal statistical distribution for these parameters, 90% of the beams could reasonably be expected to display better durability performance than the case represented by this characteristic value. To calculate these values, the new Opus dataset was combined with the earlier chloride profiles collected by Rogers et al. (2013).

7. Analysis & Results

A series of modelling scenarios was completed with these derived values using the predictive models based on Fickian diffusion discussed in this paper. Examples of the results for the Fox River Bridge beams are presented in Figure 11, which shows the projected development of the chloride contamination vs. depth profiles through the beams at a series of different exposure periods (age).

The first plot (i) in Figure 11 employs the characteristic upper bound values calculated for D_ach & C_sa in conjunction with the simple Crank’s erfc solution, i.e. Eqn. (2), in which both the diffusion coefficient and surface chloride concentration are assumed to be invariant with time. 

The second plot (ii) repeats this calculation using the more generalised Mejlbro Ψ_p model, Eqn. (6), which permits a time-dependent reduction in diffusivity and the gradual accumulation of surface-deposited chlorides. Because the rate of change indices α & p cannot be determined from chloride profiles collected at just a single age, accurate values appropriate for the Fox River Bridge concrete and its exposure environment are unknown. The choice of values for these parameters, which was guided by the BRANZ exposure site data for type GP concrete (Table 3), is therefore somewhat subjective and while the Mejlbro model is more realistic than Crank’s solution it is not necessarily more accurate given this limitation. Under the Mejlbro scenario modelled, the hypothetical time to corrosion initiation is typically reduced at any given cover depth because the improvement in concrete diffusivity through time does not quite compensate for the increased driving force created for diffusion as the surface chlorides accumulate. 

(i)

(ii)

Figure 11.  Hypothetical future development of chloride contamination in the Fox River Bridge pre-stressed beams considering various scenarios: (i) a conventional Fick’s law model using upper bound characteristic values for an invariant Dach & Csa; (ii) upper bound values for Dach & Csa which are allowed to vary with time

Figure 12 & Figure 13 summarise the results for both bridges for what proved to be the most pessimistic scenarios, i.e. use of the Mejlbro solution with upper bound values for D_ach & C_sa. The plots show the chloride accumulation through time at specific depths pertinent to the reinforcement cover distribution (nominally 40 mm design cover to the pre-stressing strand for both bridges).

It is apparent that the estimated residual life to corrosion initiation is very dependent on the supposed value of the corrosion threshold. The inference of a premature threat of pre-stressing corrosion is entirely valid for the critical corrosion threshold of 0.05% by mass of concrete assumed by Rogers et al. (2013) in their analysis. However, as a practical limit state denoting the end of the serviceable life of a pre-stressed concrete member, this threshold is possibly too conservative, even allowing for the limited remediation options available once corrosion commences. 

In Opus’ extensive experience carrying out condition inspections of deteriorating bridge structures, it is rare to observe significant propagation of corrosion at such low chloride concentrations in practice. In precast elements, the reinforcement should also be well-encapsulated in cement-rich concrete with abundant alkalis, which also helps preserve the critical chloride:hydroxide ion ratios. 

Figure 12.  Modelled evolution of chloride ingress with time in the Fox bridge beams, based on statistical upper bound values for diffusivity & surface chloride accumulation

Figure 13.  Modelled evolution of chloride ingress with time in the Ngakawau bridge beams, based on statistical upper bound values for diffusivity & surface chloride accumulation

For this reason, it is believed that modelling of deterioration with a 0.10% chloride by mass of concrete threshold is a pragmatic choice that better reflects the likely in-service performance of the bridge beams. Assuming this threshold, the results obtained suggest that the most probable residual life before corrosion-induced spalling could be expected to develop in the poorest performing beams is a minimum of 47 years for Fox and 22 years for Ngakawau. If mean rather than characteristic durability performance values are modelled, the predicted residual life for both bridges extends beyond 100 years before corrosion of the critical pre-stressing strands becomes pervasive. By this point, the structural capacity of the beams would potentially be gravely compromised however. 

On the basis of this result, the NZ Transport Agency have implemented a strategy of ‘watchful waiting’ (i.e. taking no immediate remedial action), with a re-sampling programme scheduled for 2023 to confirm ongoing satisfactory performance (or sooner if routine service inspections detect any evidence of corrosion in the intervening period). This approach was considered an appropriate fit with an operational imperative to avoid any unnecessary upfront maintenance cost whilst still allowing sufficient time for intervention if unanticipated problems develop.

This experience has highlighted that a better understanding and evaluation of threshold chloride concentrations for corrosion initiation is essential if prediction models are to be of practical assistance to asset owners for planning management and maintenance. 

7. Conclusions

Knowledge of the factors influencing the accuracy of durability predictions for concrete in the marine environment has advanced significantly in the quarter of a century of history canvassed. It is hoped that this paper has served to present some additional information that may prove useful to researchers working in this field.

However it continues to prove difficult to codify this information in a form which answers the fundamental question of the industry: what lifetime can be expected for a particular environment, concrete and cover? A number of competing approaches purport to answer this question, but absence of agreement on fundamental concepts such as the practical definition of ‘diffusion coefficient’, the importance of temporal variations in surface chloride accumulation, and appropriate values of corrosion initiation thresholds makes it difficult to compare their results or use them to full advantage.

To make progress in this area it is now necessary to standardise on a single philosophy for service-life prediction, incorporating uniform definitions of terms, measurement techniques and assessment criteria. At this point, the author has come to believe that a unified approach allowing unbiased comparison between alternative solutions is of greater importance than modelling chloride ingress with the utmost scientific rigour. The latter can be incorporated later as understanding develops. Any model needs to be accompanied by comprehensive guidelines which will allow non-specialist practitioners to use it with a degree of confidence. Until we begin to do this, the application of marine concrete durability research will be limited, as will our ability to fully benefit from the enhanced durability of high performance concrete. To this end, the work of the Concrete Institute of Australia’s Durability Technical Committee to prepare a Recommended Practice for Durability Modelling is commendable; it is hoped the forthcoming release of that document will usher in a new era for robust service life prediction of concrete structures in Australasia. 

8. Acknowledgments 

The exposure site programme described in this paper was funded by BRANZ from the Building Research Levy.

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10. Author details