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									PROBABILITY-BASED SERVICE LIFE DESIGN OF STRUCTURAL
CONCRETE
Klaas van Breugel (1) , Rob Polder (1,2)

(1) Materials & Environment / Microlab, Faculty of Civil Engineering and Geosciences,
Delft University of Technology, Delft, the Netherlands
(2) TNO Built Environment and Geosciences, Delft, The Netherlands




Abstract
   Today there is an increasing demand for designing concrete structures with 80, 100 or 200
years service life and low maintenance costs. Predictions over such a long period are
impossible without reliable models. In order to allow for uncertainties in de model
parameters, probability-based models are needed. In this contribution a probability-based
guideline for service life design is presented. The guideline only deals with initiation of
corrosion due to chloride penetration for exposure classes defined as XD and XS. For
determining the resistance of the concrete against chloride penetration the Rapid Chloride
Migration test has been adopted. The basis for the guideline is the DuraCrete methodology,
developed in the nineties in a European research project [1]. For a required service life the
required maximum migration values depend on cover depth, type of binder and the exposure
class. For practical design purposes design tables have been compiled. The original DuraCrete
model and its parameters were used as the basis for these tables. Modifications were made
based on new results and additional knowledge. Three options are provided to the designer:
(1) maximum chloride migration coefficients for a range of concrete cover depths depending
on the binder type (2) semi-probabilistic calculation based on a safety margin on the cover
depth; (3) probabilistic calculations, for which a full set of parameters (including their mean
values, standard deviation and distribution type) are specified.


1.     INTRODUCTION
   Today contractors are increasingly faced with owners who require service lives of concrete
structures of 80, 100 or even 200 years. Currently used design codes generally do not give
sufficient guidance for designing concrete structures for that long service lives. In the Dutch
standards for designing concrete structures, for example, a service life of 50 years is only
implicitly assumed. In 2003 the initiative was taken to install a national committee in The
Netherlands with the task to develop a probability-based design guideline for designing
durable concrete structures with service lives up to 200 year. An important condition for the
new guideline was that the requirements of the prevailing Dutch concrete standards [2,3,4]
were met. Under these assumptions chloride-induced rebar corrosion is assumed to be the
dominant mechanism determining the service life, whereas carbonation-induced corrosion can
be ruled out safely.
   The proposed new guideline is based on the DuraCrete methodology for Service Life
Design (SLD) that was conceived in the 1980s by Siemes et al [5]. The concept was further
developed in much more detail in the nineties in the European research project DURACRETE
[1,6]. The structure of this guideline follows the structural design philosophy by stating that
the service life is the period in which the structure's resistance R(t) can withstand the
environmental load S(t). R(t) and S(t) are considered quantities with a statistical distribution.
For a structure designed in this way a particular performance is predicted with a
predetermined maximum probability of failure. The concept is shown schematically in Fig. 1.


                                              Distribution of R(t)
                             R(t)
         R,S
                                        Pf
                             S(t)
                                             Distribution of S(t)

                                                                    Mean service life         Time
                                     Failure probability
                                               Pf
               Target service life
                                                                               Sevice life distribution



            Fig. 1 Schematic representation of probabilistic durability design [1,6]

The limit state in our case is initiation of reinforcement corrosion due to penetration of
chloride ions into the concrete. As soon as the chloride content at the steel surface of the
reinforcing bars has exceeded the critical chloride threshold the structure is considered, by
definition, to fail. Now the load is represented by the chloride content of the concrete surface
that builds up due to exposure to chloride ions from de-icing salts or sea water. The resistance
is the chloride penetration resistance of the concrete cover, expressed by its chloride
penetration coefficient. This penetration coefficient changes with time due to continuing
hydration, binding of ions and carbonation, which complicates the modelling of the chloride
ingress. It is emphasized that the performance is considered in terms of absence of corrosion
initiation, which is not an ultimate limit state, because no direct danger for human lives is at
stake. It is a Serviceability Limit State (SLS), because corrosion means the upcoming need to
repair, which is an economic threat rather than a safety issue. Probabilities of failure for SLS
are usually in the range of a few percent (reliability index  1.5 – 2).
   The DuraCrete approach has been tested in an extensive research project in which six
marine structures were inspected and analysed as regards the actual chloride profiles [7,8].
From that project minor modifications of model parameters were deduced. This paper
describes how the DuraCrete approach is applied for service life design of concrete structures
in marine environment (exposure class XS) and exposed to de-icing salts (exposure class
XD). It is explained how data from chloride migration tests and field measurements (chloride
profiles) are used in a semi-probabilistic concept and are finally condensed into a set of tables
specifying maximum values for chloride penetration coefficients depending on cover depth,
cement type and required service life.
2.     A PROBABILITY-BASED PREDICTIVE MODEL
   A brief summary of the DuraCrete concept and its validation has been presented in [8]. The
basic components of the DuraCrete concept are the transport model, including a chloride
transport coefficient, several model parameters and the semi-probabilistic approach. For the
description of chloride ion transport into concrete a modification of Fick’s 2nd law is adopted.
Since Fick’s 2nd law describes diffusion processes, it is understandable that chloride ion
penetration has often been considered as primarily a diffusion process. In this paper the use of
Fick’s 2nd law and of the term diffusion coefficient does not imply, however, that the authors
are not aware of other mechanisms that contribute to the transport of chloride ions into the
concrete. This discussion, however, is no subject of this paper.

2.1 Chloride penetration (diffusion) coefficient
   Since the introduction of the diffusion model for chloride penetration in concrete by
Collepardi et al. [9] several methods have been proposed for determining the resistance of
concrete against chloride penetration. In the 1990s, two test methods were standardised in the
Nordic countries, viz.:
1. A conventional immersion test, NT Build 443, formerly known as APM 302;
2. An accelerated (migration) test, NT Build 492, previously known as CTH method and
    nowadays as Rapid Chloride Migration test (RCM) (see Fig. 2).
The immersion test may be seen as a realistic representation of the natural diffusion process.
A drawback of this test is that it requires seven weeks exposure of the concrete specimens and
involves analysis of many samples for determination of the chloride content. The migration
test involves a different transport mechanism, but has a short execution time and is less
laborious. In the European research project CHLORTEST [10] both methods were studied
and compared in a Round Robin Test. A good linear correlation was found between chloride
diffusions coefficients, inferred from diffusion experiments, and chloride migration
coefficients, inferred from RCM tests. It was considered justified, therefore, to use the less
time and labour consuming RCM test instead of the diffusion test (see also [11]).
   In the past few years, the RCM-method has been applied to many concrete mixtures in
association with design for service life of large infrastructural projects in the Netherlands. As
a first step in setting up the guideline, the available data were analysed. In total 500 RCM-
values from 153 different concrete compositions (prefab and ready mix) were obtained. The
influence of the mix composition on the RCM-value was analysed. Cement types used in
those tests were mainly Portland cement (CEM I 32.5R, 52.5N, 52.5R) and blast furnace slag
cement (CEM III/A 52.5 R, CEM III/B 42.5 LH HS) and mixtures of these two cement types.
In addition, mixtures of powder coal fly ash with Portland or slag cement were present in the
data set. The binder contents ranged from 300 to 450 kg/m3 and the water/binder ratio from
0.33 to 0.65. The age at testing ranged from 28 days to 3 years with most data at an age
around 28 days.
   It was assumed that the RCM-value depends to a large extent on the type of binder (cement
type and reactive additions), the water-to-binder ratio (w/b) and age. The data were first
grouped with respect to the type of binder:
 Portland cement (CEM I);
 Slag cement (CEM III/A or III/B, slag content 50 - 76%);
 Portland and slag cement mixtures (slag content 25 - 38%);
 Portland cement with fly ash (21 - 30% fly ash).
Within these groups, experimental data of similar age were aggregated. Ages of 28 to 35 days
were considered as a single group (about 28 days). The influence of w/b on DRCM was then
analysed for the groups with a particular binder at an age around 28 days. In this analysis all
the fly ash present in the mixture was considered as cementitious material, so w/b = water /
(cement+fly ash). This analysis showed that the DRCM-value is linearly related to the
water/binder ratio:
          DRCM 28 d   A w / b   B                                                (1)
with A and B constants for particular cement types. Figure 2 shows this relation for 3 binder
types. Figure 2 clearly shows that DRCM-values strongly depend on the binder type. For
Portland cement the DRCM-value is also strongly influenced by the w/b. For slag cement this
influence turned out to be less pronounced. The regression coefficients (A, B) found in this
investigation for the different binders are in good agreement with those reported by Gehlen
[12]. The data suggest that in the range of practical w/b ratios between 0.35 and 0.55, some of
the lower RCM-values could not be obtained with particular binders.

          40
                        CEM I
                        CEM III > 50% slag
          30            CEM I, 18-30% fly ash
                        fly ash, extrapolated
 D(RCM)




          20



          10



          0
           0.30     0.35      0.40      0.45          0.50   0.55   0.60   0.65
                                                w/b

     Fig. 2 Correlation between w/b and DRCM value at about 28 days; all values * 10-12 m2/s

   Even though execution of the RCM-test is much faster than the diffusion test (NT Build
443), the test is still labour intensive. For a quick impression of the resistance against chloride
ingress also the Two Electrode Method (TEM) can be used. With that method the electrical
resistivity of the concrete is determined. In [11] a good correlation was reported between
these two methods. Particularly for production control the TEM test is suitable for a quick
indication of the potential of a certain mixture to meet prescribed durability requirements.

2.2 Modelling chloride ingress
   In the DuraCrete model the evolution of chloride profiles is approximated with:
                                                     x      
      C ( x, t )  C s  (C s  C i ) erf                                           (2)
                                          
                                              4 k D(t ) t 
                                                             
where C(x,t) is the chloride content at depth x at time t, Cs is the surface chloride content, Ci
the initial chloride content in the concrete, k a correction factor and D(t) the apparent
diffusion coefficient as a function of time. The surface chloride content was assumed to be
independent of mix composition for reasons of simplicity: 3.0% m/m of cement content for
marine structures [7] and 1.5% m/m for land based structures [13]. The initial chloride content
was taken equal to 0.1% m/m.
   The apparent diffusion coefficient D(t) is multiplied by a correction factor k to obtain the
chloride diffusivity of the concrete in a real structure. This correction factor depends on the
binder type, the environment and the curing. The k-values were taken from DuraCrete [1].
The critical chloride content was taken equal to 0.6% by mass of cement [13]

2.3 Time dependency of chloride penetration coefficient D(t)
   The rate at which chloride ions penetrate into concrete decreases with time. This is caused
by hydration, leading to narrowing of capillary pores (especially in mixtures with slag or fly
ash containing mixtures) and drying, leading to a decrease of the pore water volume near the
surface. In Fick’s 2nd law a decrease of the rate of chloride penetration can be described with a
time-dependent diffusion coefficient, viz. (see also Maage et al. [14]):
                       n
               t 
    D(t )  D0  0                                                                  (3)
               t 
where D0 is the DRCM-value at the reference time t0 (28 days) and n is the ageing coefficient.
The value of the ageing coefficient for a particular binder depends on the rate of hydration
and on the extent of drying (drying out of the pore system affects the diffusion process
substantially). The ageing coefficients for different binders were determined from DRCM-
values at different ages from the dataset. For a given mix this value is solely influenced by the
rate of hydration, because specimens were cured under water at 20C. Structures in the field
will dry out to some extent and hydration may occur slower than under water. In DuraCrete
values for the ageing coefficient for marine exposure (XS1 – XS3) were Table 1 Ageing
coefficients n (eq. 3) for different binders in two groups of environmental classes
                                                                    NEN-EN 206
  Environmental classes                                 Underground,         Above ground,
                                                        splash zone        marine atmospheric
  Type of binder                                          XD2, XS3          XD1, XD3, XS1
  CEM I                                                      0.40                   0.60
  CEM I, 25-50% slag, II/B-S; or III/A, <50% slag            0.45                   0.65
  CEM III 50-80% slag                                        0.50                   0.70
  CEM I with 21-30 % fly ash                                 0.70                   0.80
  CEM V/A (25% slag and 25% fly ash)                         0.60                   0.70

determined from real structures and exposure tests. Based on the present dataset and
additional work, n-values were chosen for different binders in two groups of environmental
classes: very wet (XD2/XS3) and moderately wet (XD1/XD3/XS1) [7,15]. Values for n used
in further analysis are given in Table 1.
   The time needed to reach the critical chloride content at a certain depth can now be
calculated for any given mix (within the available data collection) in the exposure classes XS
and XD. Equation (1) can be used indicatively. For a specific calculation the DRCM of a
particular mix should be measured and used for the calculation.
2.4 Reliability considerations of the semi-probabilistic approach
   Equation (2) can be used for calculating the time needed for the critical chloride content to
reach the outer rebar layer; or to calculate the maximum value for D0 at 28 days in
dependence of the concrete cover and the required service life for different binders. Such a
calculation, however, is deterministic way and yields an average value. This means that the
probability of corrosion initiation of steel at that point in time and space is 50%. In practice
such a high probability is unacceptable. An acceptable probability of failure for this limit state
(SLS) may be 10%. This corresponds to a reliability index  = 1.3.
   To obtain such a low required probability, either the cover depth can be increased or the
maximum D0 can be decreased. If the former option is chosen, the required amount of
additional cover can be calculated for each individual case using probabilistic calculations. In
the guideline, however, it was chosen to add a fixed amount to the (deterministically deter-
mined) cover depth as a safety margin. This is a semi-probabilistic approach, comparable to
the introduction of a safety factor for a materials property or a load. An increase of the cover
depth by 15 to 20 mm will reduce the probability of corrosion from 50% (=0) to about 10%
(=1.3) [11]. This procedure has also been followed in the guideline. Calculations using
TNO's probabilistic software Prob2B have shown that a safety margin of 20 mm results in a
probability of failure of 10%; a safety margin of 30 mm produces a probability of 5%, which
are considered appropriate for reinforcing and prestressing steel, respectively.

3.     SERVICE LIFE DESIGN IN PRACTICE – EXAMPLES
   Following the method described above, including a safety margin to the cover depth of 20
mm for reinforcing steel and 30 mm for prestressing steel, combinations of required cover
depth and maximum DRCM-values were calculated for service lives of 80, 100 or 200 years.
The values are summarised in the Tables 2, 3 and 4. How these tables can be used in practice
for service life design will be illustrated in the following in two examples.

Example I
The first example concerns a reinforced concrete structure in XD1-3/XS1 environment. For
the type of cement a CEM III/B with 70% slag was chosen. The required service life is 100
years. From Table 3 it can be seen that with a cover depth of 45 mm (reinforcing steel), a
maximum DRCM,28 is required of 6.0 10-12 m2/s. With this cement and a w/b of 0.45, a DRCM-
value of 4.0 10-12 m2/s can be obtained rather easily (see Fig. 2). Going back to Table 3 it can
be seen that with a DRCM-value of 4.0 10-12 m2/s the cover depth could be reduced to 40 mm.

Example II
Assume the same structure as in Example I. The cover depth is 45 mm, but now a CEM I is
used. For CEM I and a cover depth of 45 mm Table 3 gives a maximum DRCM,28 of 8.5 10-12
m2/s. Even though this DRCM-value is higher than in case I, this value might be hard to achieve
with a CEM I (see Fig. 2). It would require quite a low w/b, probably below 0.4, which may
cause workability problems. Increasing the cover to 50 mm will allow an increase of DRCM,28
to 12 10-12 m2/s, which can be achieved with a w/b of about 0.45 indeed.

These two examples show the ease of using these tables. Navigating through all possible
options, the designer can find the economic optimum, while he can demonstrate to the client
that the required service life is always achieved.
Table 2 Maximum DRCM,28 for various cover depths as a function of binder type. Required
service life 80 years. Note: Boldface values are practically achievable by present-day concrete
technology with currently used w/b.
      Mean concrete
                                                              Maximum value DRCM,28 [10-12 m2/s]
       cover [mm]
                                           CEM l                 CEM l+lll             CEM lll            CEM ll/B-V
                    Prestressing
 Reinforcing




                                                                  25-50% S             50-80% S        CEM l+20-30% V
   steel



                      steel




                                   XD1,XD2         XS2    XD1,XD2      XS2     XD1,XD2       XS2       XD1,XD2    XS2
                                   XD3,XS1         XS3    XD3,XS1      XS3     XD3,XS1       XS3       XD3,XS1    XS3

        35               45          3.5           1.5      2.5         1.0      2.5         1.0          7.0          6.0
        40               50          6.0           2.5      4.5         2.0      4.0         2.0          12           10
        45               55          9.5           4.0      6.5         3.0      6.5         2.5          19           16
        50               60          13            6.0      10          4.0      9.0         4.0          27           24
        55               65          18            8.0      13          5.5      13          5.5          37           32
        60               70          24            10       17          7.5      16          7.0          49           42


Table 3 Maximum DRCM,28 for various cover depths as a function of binder type. Required
service life 100 years. See Note with Table 2.
  Mean concrete
                                                             Maximum value DRCM,28 [10-12 m2/s]
   cover [mm]
                                           CEM l                 CEM l+lll             CEM lll            CEM ll/B-V
               Prestressing
 Reinforcing




                                                                  25-50% S             50-80% S        CEM l+20-30% V
    steel


                  steel




                                   XD1,XD2     XS2        XD1,XD2      XS2     XD1,XD2      XS2        XD1,XD2   XS2
                                   XD3,XS1     XS3        XD3,XS1      XS3     XD3,XS1      XS3        XD3,XS1   XS3
  35              45                3.0             1.5     2.0          1.0     2.0             1.0      6.5          5.5
   40             50                5.5             2.0     4.0          1.5     4.0             1.5      12           10
   45             55                8.5             3.5     6.0          2.5     6.0             2.5      18           15
   50             60                12              5.0     9.0          3.5     8.5             3.5      26           22
   55             65                17              7.0     12           5.0     12              5.0      36           30
   60             70                22              9.0     16           6.5     15              6.5      47           39



4. CONCLUDING REMARKS
  In many cases obtaining a long service life for concrete structures is mainly a matter of
postponing the onset of rebar corrosion. The most important parameters in a model based
approach are:
- chloride load from sea water and de-icing salt environments
- chloride transport by diffusion
- time dependent diffusion coefficients
- coefficients taking into account environmental, curing and materials influences.
Table 4 Maximum DRCM,28 for various cover depths as a function of binder type. Required
service life 200 years. See Note with Table 2.
  Mean concrete
                                                      Maximum value DRCM,28 [10-12 m2/s]
   cover [mm]
                                     CEM l                CEM l+lll             CEM lll        CEM ll/B-V
               Prestressing
 Reinforcing




                                                          25-50% S             50-80% S     CEM l + 20-30% V
   steel



                 steel




                              XD1,XD2    XS2       XD1,XD2     XS2     XD1,XD2      XS2     XD1,XD2    XS2,
                              XD3,XS1    XS3       XD3,XS1     XS3     XD3,XS1      XS3     XD3,XS1
                                                                                                       XS3
    40            50           4.0           1.5     3.0         1.0      3.0         1.0      10           8.0
    45            55           6.5           2.5     5.0         1.5      5.0         1.5      16           12
    50            60           9.0           3.5     7.0         2.5      7.0         2.5      23           18
    55            65           13            4.5     9.5         3.5      9.5         3.5      31           24
    60            70           16            6.0     12          4.5      12          4.5      41           32
    65            75           21            7.5     16          5.5      16          5.5      51           40
    70            80           26            9.0     20          7.0      19          7.0      64           50


In this paper we have outlined a probability-based design procedure for determining
combinations of cover depth and 28-day chloride diffusion coefficients that are required to
guarantee a specified service life. Probabilities of failure are 10% and 5%, respectively, for
reinforcing steel and prestressing steel. Based on a semi-probabilistic simplification, the
required combinations of cement type, cover depth and diffusion coefficient are brought
together in simple design tables. The tables give limiting values for chloride diffusion
coefficients obtained with the RCM test for service lives of concrete structures of well over 50
years in marine (XS) or de-icing salt (XD) environments. From analysis of a large number of
test results, the dependency of the DRCM-value on w/b and cement type was determined and an
indication was obtained which values are possible using present-day concrete technology.
    Similar tables as proposed in this paper have recently been presented by Li et al. [16]. In
their tables, however, the compressive strength is still considered one of the durability
parameters. Instead of the parameter strength, here we have chosen for an explicit transport
parameter, i.e. the RCM-value, to indicate the concrete's susceptibility for chloride ingress.
    A similar probability-based approach to various degradation mechanisms has been
presented by fib [17]. Their model for chloride induced corrosion is slightly different from the
one described here.
    With the publication of the Guideline by CUR [18], the Dutch concrete industry enters a
new period with respect to practical service life design. All parties involved have agreed to
collect their experience using the Guideline, with the intention to evaluate it and if necessary,
to improve it in the near future.
    At the same time, however, it was realised that many items used in the calculations still
contain large uncertainties. It is hoped that research in the forthcoming years will contribute to
reducing them.
ACKNOWLEDGEMENT
This paper is based on ideas and results generated within the former international DuraCrete
consortium, by researchers of TNO and INTRON and, last but not least, within Dutch CUR-
committees B82 and VC81. The financial support and support in kind of the Dutch
Rijkswaterstaat and other committee members of VC81 are gratefully acknowledged.


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