- Email: [email protected]
Model for practical prediction of natural carbonation in reinforced concrete: Part 1-formulation
Accepted Manuscript Model for practical prediction of natural carbonation in reinforced concrete: Part 1formulation Stephen O. Ekolu PII:
S0958-9465(16)30757-0
DOI:
10.1016/j.cemconcomp.2017.10.006
Reference:
CECO 2922
To appear in:
Cement and Concrete Composites
Received Date: 30 November 2016 Revised Date:
10 April 2017
Accepted Date: 14 October 2017
Please cite this article as: S.O. Ekolu, Model for practical prediction of natural carbonation in reinforced concrete: Part 1-formulation, Cement and Concrete Composites (2017), doi: 10.1016/ j.cemconcomp.2017.10.006. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Model for practical prediction of natural carbonation in reinforced concrete: Part 1-Formulation Stephen O. Ekolu Department of Civil Engineering Science, University of Johannesburg, South Africa, [email protected], [email protected]
Abstract
2
A model is proposed for prediction of natural carbonation in reinforced concrete (RC)
3
structures, and is potentially applicable to existing and new RC structures. The major
4
components of the model comprise mathematical functions applied to predict the influence of
5
concrete composition, and environmental factors on natural carbonation.
SC
RI PT
1
This paper introduces the model concept and explains its structure including derivation,
7
optimization and calibration. Over 163 data sets taken from a 10-year carbonation study were
8
used in the model development and calibration. Only the experimental data that were based
9
on outdoor natural exposure environment were employed in this research. Also in this study,
10
the proposed model is compared with fib-Model Code 2010 using carbonation predictions
11
generated from 346 data sets involving real world, highway structures. It is shown that the
12
proposed model is comparably accurate and involves mainly basic tests with no major
13
anticipated costs.
14
TE D
M AN U
6
Keywords: Carbonation modelling; mathematical formulation; service life; reinforced
16
concrete; supplementary cementitious materials; durability design
17
EP
15
1. Introduction
19
Among the major concrete deterioration processes, corrosion of steel reinforcement is the
20
most widespread and common source of degradation in concrete (PCA, 2002), and is induced
21
either by carbonation from CO2 in the atmosphere or by chloride attack. Prediction models
22
can be used either at design stage for design of new structures or during repair and
23
maintenance of existing structures. For example, models for shrinkage and creep prediction
24
are now employed for design purposes and are recommended in internationally recognized
25
codes such as ACI 209, 1997; BS 8110, 1997; RILEM B3, 1995; Wendner et al., 2013; CEB-
26
FIP 1978, 1990a,b; AS3600, 2009; SANS 10100, 2000. With respect to reinforcement
27
corrosion, no similar achievements have been made in modeling, although some significant
28
progress has occurred over the past two decades, leading to proposal of some practical
AC C
18
1
ACCEPTED MANUSCRIPT models such as the LIFE 365 (Ehlen et al., 2009), Duracrete, 2000 / fib, 2006. In carbonation
30
modeling, the scientific and engineering fraternity has not yet achieved a level of employing
31
models in service life design codes, mainly for lack of plausible validated models. It is often
32
the case in engineering practice that methods that are suitable in particular contexts may not
33
suffice in others. So, development and use of different approaches and methods are needed to
34
provide alternatives.
35
RI PT
29
2. Carbonation prediction models and factors influencing carbonation prediction
37
2.1 Overview of carbonation prediction models
38
Carbonation modeling has been a subject of major interest over the past decades and an
39
extensive body of literature has been generated by researchers. Accordingly, a plethora of
40
experimental carbonation models have been proposed in various works including some
41
extensive literature reviews on the subject (Parrott, 1987; Sagues et al., 1997; Quillin, 2001;
42
Tang et al., 2010; Ikotun and Ekolu, 2012; Zhijian et al., 2013; Czarnecki and
43
Woyciechowski, 2015; Ekolu, 2016). The various types of models existing in the literature
44
may be divided into different categories, viz:
45
1. Empirical models are typically formulated based on relations or expressions developed
46
from experimental measurements. The core component(s) of empirical models are usually
47
mix design or composition parameters especially the water/cementitious ratio (w/cm),
48
cement content; or a material property of concrete. The core parameter for use in a
49
model is usually selected based on the presumption of its ability to depict or correlate
50
strongly with the ingress of CO2 into concrete. As such, empirical models in the literature,
51
may be grouped as follows:
52
(a) Permeability-based models, such as proposed by Parrott (1994), Zhang et al. (2013),
M AN U
TE D
EP
AC C
53
SC
36
Torrent (2014).
54
(b) Diffusion-based models. Examples of these models include those proposed by Xu et
55
al. (1996), Papadakis et al. (1991, 1995), Duracrete/fib (CEB,1997); Duracrete
56
(2000); fib 34 (2006); Tang et al. (2010), Wang and Lee (2009), Kari et al (2014).
57
(c) Strength-based models (Bob, 1999; Hakkinen, 1993; Kokubu and Nagatakis, 1989).
58
(d) Composition-based models (Nishi, 1962; Zhu, 1992; Zhang and Jiang, 1990; He and
59
Jia, 2011; also Parrott, 1987).
60
2. Statistical models are basically data-generated relations obtained through regression of
61
multiple variables and fitting of idealized or standard mathematical functions such as
62
linear, exponential, power, logistic equations, amongst others. Some statistical models of 2
ACCEPTED MANUSCRIPT 63
carbonation include those proposed by Atis (2004), Monteiro et al. (2012), Silva et al.
64
(2014), Hills et al. (2015). 3. Numerical models apply computational approaches that are reliant on computer software
66
for sophiscated analysis. Most numerical models utilize a hybrid of physico-chemical
67
equations representing the thermodynamic reactions and transport processes occurring in
68
concrete. Such models have been proposed by Saettaa and Vitaliani (2004, 2005);
69
Talukdar et al (2012); Zha (2015).
RI PT
65
4. Simulation models apply the artificial neural network technique. The neural network
71
comprises an algorithm consisting of input and output parameters, whose behavior is
72
trained to generate a known set of outputs. A trained algorithm can then be employed to
73
conduct predictions for new input data. Some attempts to apply these approaches have
74
been experimented by Seung-Jun and Song (2010); Luo et al. (2014); Buenfeld et al.
75
(1998).
M AN U
SC
70
76
It may be noted that most of the models in the literature are experimental. Each of the
78
different types of models has its limitations. The statistical, numerical and simulation models
79
typically require a wide range of input parameters including mix composition, environmental
80
exposure conditions, material properties. These include w/cm, cement type, cement content,
81
air content, curing, age; environmental factors of relative humidity and sheltering; diffusion
82
or permeability coefficient, compressive strength. The methods are also highly computational
83
and would often require the aid of computer software and programs. These issues have
84
implications on practical implementation of the models for design of concrete structures.
85
Whereas the concrete composition data for various parameters can be acquired and recorded
86
relatively easily at the construction stage of new structures, it would be extremely difficult to
87
find such data in the case of existing or old structures. It is often the case that for old
88
structures, records of construction data such as mix design, environmental conditions, curing,
89
28-day compressive strength etc., may not be available, perhaps having been lost or not
90
recorded appropriately. Testing of old concrete at late ages does not reliably replace the data
91
that is often acquired during the construction stage. This problem particularly applies to
92
models that are based on mix composition factors.
AC C
EP
TE D
77
93
As such, it is clear from a practical viewpoint that, empirical models based on
94
permeability, diffusion or strength properties of concrete may be advantageous. However,
95
permeability and diffusion properties characteristically give a high coefficient of variation
96
(CV) in the range of 30 to 50% (Hooton, 1988) compared to about 20 to 30% for compressive 3
ACCEPTED MANUSCRIPT strength (Shimizu et al., 2000; Ekolu, 2010; RILEM, 1996). The CV for permeability and
98
diffusion also has a wider spread than that of compressive strength. It has been found that
99
compressive strength property of concrete is effective in relating the influence of pore
100
structure of concrete on CO2 ingress (Silva et al., 2014). Strength also simultaneously
101
accounts for the amount of cement clinker. Besides, compressive strength data are easy to
102
acquire and are readily available from concrete construction, unlike permeability or diffusion
103
whose testing can be relatively complex and costly.
104
RI PT
97
2.2 Factors influencing carbonation
106
2.2.1 Choice of parameters for carbonation modelling
107
The wide range of factors influencing carbonation have been indicated in Section 2.1. These
108
factors may be grouped into four categories consisting of mix composition, material
109
properties, environmental factors, and serviceability conditions. As mentioned earlier,
110
attempting to utilize mix compositional parameters such w/cm, cement content, paste content,
111
hydration products mainly CH, CSH; unhydrated cement phases comprising C2S, C3S, C3A,
112
C4AF; degree of hydration, porosity, can have severe practical limitations. These mix
113
composition characteristics are usually the required inputs into physico-chemical models
114
(Papadakis et al., 1991; Ravahatra et al, 2014)
TE D
M AN U
SC
105
For practical purposes, it is well established that permeability or diffusion and
116
compressive strength are the main performance properties capable of effectively depicting
117
CO2 progression into concrete. Numerous literatures have shown consistent existence of
118
strong correlations between these properties and carbonation, and several experimental
119
models have been proposed on the basis of these relations (Parrott, 1987; Sagues et al., 1997;
120
Quillin, 2001). In the present study, carbonation-strength relationship is considered as the
121
core function which defines the general trend in carbonation prediction, while environmental
122
factors are incorporated as secondary or modifying parameters. As indicated in Section 2.1,
123
use of carbonation-permeability (or diffusion) relationship is undermined by high cost of
124
permeability/diffusion testing and the relatively high variability of permeability
125
measurements.
AC C
EP
115
126
The main environmental factors that significantly influence carbonation are known to be
127
relative humidity, sheltering and rain, CO2 concentration in the atmosphere. These factors are
128
discussed further in the subsequent sections.
129 130
2.2.2 Influence of relative humidity 4
ACCEPTED MANUSCRIPT In the literature (Parrott, 1987; Quillin, 2001), it is known that relative humidity (RH) of 50
132
to 70%RH is the ideal range at which carbonation progression occurs most rapidly in
133
concrete. At RH < 50%, there is inadequate presence of moisture for carbonation reaction to
134
occur. At RH > 70%, pore blockage by water presence tends to inhibit CO2 ingress as
135
concrete becomes more saturated. Carbonation progression is considered to occur maximally
136
at 60% to 65%RH, giving a pessimum or rather a mathematically parabolic relationship
137
between carbonation depth and RH in the vertical and horizontal axes respectively (Weirig,
138
1984; Parrott, 1987; Quillin, 2001).
139
RI PT
131
2.2.3 Influence of carbon-dioxide concentration
141
The gradient between [CO2] at the surface concrete and zero concentration at interior
142
concrete, is the primary driving force for CO2 ingress into concrete. Accordingly, higher CO2
143
concentration gives greater rate of carbonation (Chun et al. 2006; Lagerblad, 2005). It is
144
estimated that [CO2] in urban settings is about 10 times the [CO2] in rural areas or
145
countryside, while industrial areas usually exhibit generally elevated [CO2]. Typically,
146
normal atmospheric CO2 concentration is about 300 ppm, but some heavy traffic and
147
industrial areas would have [CO2] as high as 1000 ppm (Sagues et al., 1997). Fukushima’s
148
(1988) data indicates that an increase of [CO2] from 300 ppm to 600 ppm would raise
149
carbonation rate of concrete five (5) times (Lagerblad, 2005). Accordingly, a correction
150
factor would be required to convert model predictions from one level of [CO2] to another.
151
Ekolu (2016) gives detailed consideration on the influence of [CO2] and provides a correction
152
factor using the generalised relationship, given as
EP
TE D
M AN U
SC
140
α f r for 20 < fc < 60 MPa eco = c 1.0 for fc ≥ 60 MPa
154
Where eco is correction factor, fc is 28-day strength; α,r are given in Equation (10) for
155
various CO2 concentrations
156
AC C
153
157
2.2.4 Influence of temperature
158
With other factors remaining constant, small changes in ambient temperatures do not
159
significantly affect carbonation but high temperatures increase carbonation. Influence of
160
elevated temperature is relevant to arid climates. However, the simultaneous presence of low
161
atmospheric RH may mitigate the effect of elevated temperature. In temperate climates,
162
carbonation would be lower in winter season due to a combination of factors including low 5
ACCEPTED MANUSCRIPT 163
RH and low temperatures which generally retard chemical reaction activity in the outdoor
164
exposure. Generally, regions having similar RH but subject to elevated temperatures such as
165
30 to 40oC would be expected to show relatively increased carbonation activity compared to
166
regions of lower normal temperatures such as 18 to 25oC.
167 2.2.5 Influence of sheltering and rain
169
Precipitation or cyclic wetting /drying exposure are conditions responsible for the difference
170
in carbonation behaviours of sheltered and unsheltered concretes. Under unsheltered
171
exposure e.g. external walls of buildings, exposed retaining walls etc., CO2 ingress into
172
concrete may be intermittent as a result of periods of saturation under wet conditions, that
173
would temporarily block surface pores of concrete. Under sheltered exposure such as in
174
tunnels, bridge abutments, deck soffits etc., partial saturation conditions prevail consistently.
175
These effects are particularly important in environments classified under XC3 or XC4 (EN
176
206, 2000). Indoor exposure also gives higher carbonation depth than outdoor exposure
177
owing to similar reasons explained in the foregoing.
M AN U
SC
RI PT
168
Theoretically, the significance of sheltering effect on carbonation is well-established
179
(Parrott, 1987; Yoon et al., 2007; Gehlen and Sodeikat, 2002), with CEB-FIB (1990b) stating
180
the progress of carbonation, dc = k.tn, in elements sheltered from rain to be of a lower
181
exponent in the range of 0.2 < n < 0.5, implying greater carbonation rates, the maximum
182
carbonation rate corresponding to n = 0.5. In this carbonation equation, dc is carbonation
183
depth, k is the carbonation rate and t is age. Other researches have reported the effect of
184
sheltering to be small and not of statistical significance (Khunthongkeaw et al., 2006; Otsuki
185
et al., 2012).
EP
TE D
178
Attempting to account for effects of unsheltered exposures on carbonation can be quite
187
difficult due to a complex interplay of factors that may not be easy to isolate. Unsheltered
188
exposure is affected by not only the number of rain events but also the amount of
189
precipitation at the different events. This may vary from location to location and year to year,
190
making it quite difficult to generalize except through approximations. Besides, carbonation
191
behavior in unsheltered elements is also influenced by orientation of exposure surface to the
192
vertical or horizontal direction, since this orientation determines the residence time of
193
moisture precipitation after a rain event. For a vertical face, the direction it faces may also
194
influence carbonation, especially its orientation in relation to direction of the sun. The
195
presence of vegetation and other nearby structures that may curtail wind, raindrops, sun
196
radiation on a particular element may also influence carbonation behavior of the element. It
AC C
186
6
ACCEPTED MANUSCRIPT can be seen that accounting for carbonation in unsheltered elements needs detailed
198
examination of the microclimate and associated exposure conditions in the surrounding. It
199
should be considered that sheltered sections of elements give greater carbonation progression
200
than the unsheltered parts. These sheltered sections of the structure result in deterioration well
201
before the unsheltered areas and, so carbonation under sheltered exposure should form the
202
basis for predictions (Parrott, 1987). In cases where unsheltered elements are not crucial, it
203
may be prudent to avoid those areas of the structure when considering carbonation
204
predictions for the structure. But there are structures, although relatively few, that are fully
205
unsheltered such as retaining walls etc. As such, a practical means of accounting for
206
unsheltered exposure in structures is relevant and essential. In Ekolu (2016), natural outdoor
207
carbonation under sheltered and unsheltered exposures was analysed. The study found the
208
ratio (es) of natural carbonation for unsheltered to sheltered exposure in a given environment,
209
to be strength dependent. A general relationship es = fc0.2 was determined for estimating the
210
correction term for unsheltered exposure, where fc is 28-day cube strength.
211
M AN U
SC
RI PT
197
2.2.6 Influence of concrete quality
213
While the mix design, materials and processing factors all affect the quality of concrete, their
214
effects are compounded and realised in the pore structure. Low or poor quality concretes
215
typified by low strengths and high permeability, have a coarse, more open and continuous
216
pore network. Consequently, CO2 ingress is exacerbated in low quality concretes which in
217
turn leads to higher carbonation rates. The converse is true for high quality concretes.
218
Concretes of carbonation rates >10, 5 to 10, <5 mm/yr½ are considered to be of poor, average,
219
good quality respectively (Yoon et al, 2007; Sanjuan and del Olmo, 2001)
EP
AC C
220
TE D
212
221
2.2.7 Cement type and carbonation conductance
222
The use of pozzolans or supplementary cementitious materials (SCMs) in concrete has
223
become conventional. Cement types containing SCMs are now regarded as common cements.
224
All but one of the five cement types in EN 197-1 (2000), contain SCMs. The most common
225
types of SCMs in use are artificial pozzolans, fly ash (FA), ground granulated blast furnace
226
slag (GGBS) and silica fume (SF). But their use in cement has some implications on
227
structures. Apart from the environmental benefits, SCMs are known to improve durability of
228
concretes in properly designed mixtures. One of the disadvantages of SCMs is their
229
promotion of carbonation in concrete. When incorporated into concrete, SF, FA, GGBS, and
230
all the common pozzolans will increase carbonation of concrete relative to control. The rate 7
ACCEPTED MANUSCRIPT of carbonation is proportional to the amount of SCM in the mixture, with higher SCM
232
contents giving higher carbonation progression as shown by numerous studies in the literature
233
(Parrott, 1987, Lagerblad, 2005). Their effect is related to chemical dilution resulting from
234
reduced clinker content when some quantity of Portland cement is replaced by SCM. Not
235
only are less hydration products formed in SCM concretes, an important factor affecting the
236
infilling of initial pore spaces within the mixture, but pozzolanic activity also requires longer
237
curing under saturated conditions compared to hydration of ordinary Portland cement.
RI PT
231
Since SCM cement types promote carbonation relative to baseline ordinary Portland
239
cement or CEM I, an analogy of electrical conductance can be used whereby CO2 ingress is
240
considered to be the equivalent of an electrical flux. The rate at which a cement type
241
promotes carbonation can then be regarded in terms of carbonation conductance of the
242
cement. This concept is applied later in model derivation given in Section 3.3. The use of this
243
term here is strictly confined to the promotional effect of SCM cements on carbonation.
M AN U
SC
238
244
2.2.8 Influence of cracks and surface treatments
246
Cracks provide a direct pathway of CO2 into the concrete cover, leading to early
247
deterioration. Cracks larger than structural crack sizes of typically 0.2 mm should be regarded
248
as adverse and would cause greater CO2 ingress into concrete to the extent dissimilar to
249
uncracked concrete. Conversely, surface treatments such as paints and coatings are
250
preventative measures to external ingress of aggressive agents, and accordingly retard the
251
attack processes. Studies show that paint coatings on concrete surfaces can effectively retard
252
carbonation (Otsuki et al., 2012).
EP
253
TE D
245
2.2.9 Influence of special aggregates and recycled concretes
255
Special aggregate types comprise lightweight, heavyweight and recycled aggregates. The
256
effects of these special aggregate types on carbonation differ from influence of normal
257
aggregates. When used in concrete, recycled aggregates lead to higher carbonation relative to
258
normal aggregates (Silva et al. 2015; Lagerblad, 2005). The present study is limited to
259
concretes made using normal aggregates.
AC C
254
260 261
2.2.10 Influence of curing
262
Curing of concretes is responsible for the development of material properties at early ages.
263
Accordingly one can expect different curing types to influence concrete properties differently
264
and in turn correspondingly affect carbonation behaviour of the concrete. Different types and 8
ACCEPTED MANUSCRIPT lengths of curing are employed in concrete. The most common curing methods are moist-
266
curing, steam-curing, curing admixtures. When a given concrete mixture is subjected to the
267
different curing types, each method does produce different results. It would be concerning if a
268
model has to account for each type of curing and its duration. Infact, such information would
269
be quite difficult to obtain, especially for existing structures. Fortunately, it is interesting to
270
note from literature that the influence of different curing types dissipates in the long-term, for
271
structures exposed to natural outdoor environments (Greve-Dierfeld and Gehlen, 2014) as
272
shown by Buenfeld and Yang (2001). Cements containing SCMs particularly gain more
273
strength development and corresponding reduction in carbonation rate when heat-cured or
274
cured longer under moist conditions. However, it appears that these benefits are mainly
275
pronounced at early ages. At later ages after long-term exposure under field conditions of at
276
least 18 months, the differences from early-age beneficial effects of different curing types on
277
carbonation, become insignificant (Parrott, 1996, Balayssac et al. 1995). A detailed
278
evaluation on influence of various curing methods and durations on natural carbonation
279
[Ekolu, 2016] concluded that use of different common curing methods does not lead to major
280
change in natural carbonation behaviour. It was shown that a minimum of three-day moist
281
curing or its equivalent is sufficient for concrete to achieve stable behaviour against
282
carbonation. Accordingly, this paper does not give special consideration to account for
283
curing effects provided the minimum site curing requirements are achieved, as discussed in
284
Ekolu (2016).
285
TE D
M AN U
SC
RI PT
265
3. Formulation of model
287
3.1 Experimental data
288
The proposed model was developed using data from an extensive 10-year experimental
289
investigation reported in CSIR (1999). Table 1 gives the various mixtures used (Ekolu 2012).
290
In the experiment, concretes of strengths 25, 35 and 50 MPa were prepared in 100 mm cubes
291
cast using ordinary Portland cement (OPC) and rapid hardening Portland cement (RHC).
292
Altogether 21 mixtures were prepared in 62 batches, all of slumps 50 to 70 mm. The mix
293
designs consisted of w/cm ratios varied from 0.46 to 0.78, and binder contents ranging from
294
240 to 490 kg/m3. The mixtures contained 15 to 50% fly ash (FA). Different curing regimes
295
were applied viz: 28-day fog room curing (regime-a), 28-day 50%RH/23oC curing (regime-
296
c); 24-hour curing at 80%RH /50oC plus 27 days at 50%RH/10oC (regime-b); 24-hour steam
297
curing at 60oC plus 27 days at 50%RH/23oC (regime-d); 24-hour oven-dry curing at 40oC
298
plus 27 days at 50%RH/23oC (regime-e). After 28 days of the various curing regimes and
AC C
EP
286
9
ACCEPTED MANUSCRIPT 299
treatments, samples were exposed to natural weather at a building roof. The typical
300
environmental conditions at this site location are: annual average of 60%RH, 17.3oC and 517
301
mm precipitation. Concrete strengths and carbonation measurements were done on site
302
exposed cubes, at ages of 3.5, 6 and 10 years. The use of compressive strength as the main performance property in the core function of
304
the model was preferred over permeability or diffusion owing to the overwhelming merits of
305
the former over the latter, as discussed under Section 2.1. The limitation of the data (CSIR,
306
1999) used to structure and calibrate the model during its development was absence of some
307
aspects of data that would be valuable. Such limitations are understandable since the
308
investigation (CSIR, 1999) was not purposely conducted to generate data for modelling.
309
Accordingly, some of the parameters were either not varied widely or not at all included as
310
part of the investigation. A case in point is the effect of RH which was not varied since all
311
samples were stored in the same site location. Also, a study on the effect of sheltering was
312
not part of the investigation. However, it is nearly impossible to find a relevant and extensive
313
investigation which incorporates each and every requirement for model verification,
314
especially when an investigation was not initially conducted for such a purpose.
315
Notwithstanding the foregoing, the CSIR (1999) study was quite comprehensive, covering
316
several variables and yielding high quality data. Use of these data has been crucial to
317
development of the proposed model.
TE D
M AN U
SC
RI PT
303
318 319
[Insert Table 1]
EP
320 3.2 Mathematical laws
322
This study essentially applies basic mathematical laws to carbonation prediction in concrete.
323
The seemingly, random material behavior and unrelated results of the various individual
324
concrete types, can be captured mathematically into a universal method which accounts for
325
the major factors of influence involving the phenomenon. However, a number of key steps
326
need to be undertaken in developing such a model (Bazant and Panula, 1978). Firstly,
327
appropriate mathematical laws must be identified and expressed in combined or suitably
328
structured forms of functions. Secondly, material coefficients used in the functions must be
329
determined, usually from experimental measurements conducted in the laboratory or from
330
real world conditions of the natural environment. An important challenge here is to establish
331
coefficients that account for concretes of various types, their heterogeneities and related
332
factors of influence. Appropriate coefficients are adopted once it can be shown that their use
AC C
321
10
ACCEPTED MANUSCRIPT consistently leads to reasonable prediction of the phenomenon. The third step is to establish
334
the conditions at which a particular model is applicable, accordingly defining its limitations.
335
Robustness of a model is demonstrated by its ability to apply universally to the various
336
concrete materials and/or types, and different environmental factors, while maintaining
337
reliable predictions. The study presented in this paper, covers all the above three steps,
338
leading to derivation of the proposed model functions and related coefficients. For calibration
339
purposes, comparison of measured and predicted observations was undertaken along with
340
statistical error analysis. Limitations of the model were also determined. The proposed model
341
was formulated using mathematical functions that are based on the following governing laws:
342
(1) Square-root function of time for carbonation, derived from Fick’s laws of diffusion
SC
343
RI PT
333
(Kropp, 1995; Liang et al, 2002).
(2) Growth rate function of time for compressive strength (ACI 209, 1997).
345
(3) Parabolic function for carbonation dependence on humidity (Quillin, 2001; Parrott,
346 347 348
1987; ACI 209, 1997).
M AN U
344
(4) Inverse power function for carbonation conductance by common cements of various types (Parrott, 1987).
In the process of developing the proposed mathematical model presented in this study, a great
350
deal of guidance was drawn from several literatures on this subject. These include the
351
published literature on theoretical mathematical relations for the carbonation phenomena
352
(Kropp, 1995; Liang et al, 2002) and on structuring of model components (Liang et al, 2002;
353
Hakkinen, 1993; RILEM, 1996)
EP
354
TE D
349
3.3 Derivations, data fitting and optimization
356
The model construction was intended to bear the merit of simplicity without compromising
357
the model’s performance and prediction accuracy. In assembling the model components,
358
consideration was given to using a minimum number of parameters, while preserving
359
robustness. Based on the mathematical laws discussed in the foregoing, the governing model
360
function was taken to be the square-root law given as dc = K.t½, where dc is the carbonation
361
depth, K is the carbonation coefficient of concrete and t is time or age of concrete. Prediction
362
of K is complex and remains to be the important overarching objective of prediction
363
modelling. From the literature discussed in the foregone, material factors consisting of
364
compressive strength and cementitious materials were identified to be the core or primary
365
parameters, while environmental factors comprising relative humidity, curing, sheltering, rain
366
were taken as secondary parameters which only modify the core carbonation behavior of the
AC C
355
11
ACCEPTED MANUSCRIPT 367
material system. The core parameters were expressed in mathematical functions and co-
368
joined into a coherent model structure. Since both, the carbonation process and compressive
369
strength growth are time-dependent; and strength is in turn influenced by cementitious
370
materials, the model concept can be expressed as
371
dc(t) = f(RH, shl, CO2).f(cem, fc(t)). t½
(1)
where dc(t) is the predicted time-dependent carbonation depth, f(RH, shl, CO2) is
373
environmental function(s) or terms accounting for the secondary effects of RH, [CO2], and
374
sheltering. The proposed model accounts for the influence of CO2 concentration as discussed
375
in Section 2.2.3. It applies [CO2] range of 300 to 400 ppm as its baseline. This range of CO2
376
concentration is typical of pollution levels at atmospheric conditions in urban settings.
377
Accordingly, correction factors are needed to account for different levels of [CO2] (Equation
378
10). The function f(cem, fc,t) represents time-dependent compressive strength and related
379
influence of cementitious materials used in the mixture. It gives the core carbonation
380
behavior of a given concrete material system.
M AN U
SC
RI PT
372
381
3.3.1 Functions for relative humidity and sheltering
383
(a) Correction terms for sheltered and unsheltered outdoor exposure
384
Ekolu (2016) used data taken from various studies to determine the correction term (es) for
385
unsheltered exposure environments relative to sheltered exposure, for concretes under the
386
same microclimate. The expression es = fc0.2 (Section 2.2.5) which was derived in Ekolu
387
(2016) is used in the proposed model. It should be recognized that some field conditions
388
cannot be fully accounted for by this equation such as the effects of vertical or horizontal face
389
allignment, orientation of elements to the sun, wind factor etc. as discussed Section 2.2.5.
EP
AC C
390
TE D
382
391
(b) Parabolic function for relative humidity
392
In Section 2.2.2, the influence of RH is discussed. Applying a RH correction factor,
393
incorporates versatility as this allows broader application of the model to various
394
geographical settings or climatic conditions. A RH - carbonation relationship must be known
395
under outdoor natural exposure conditions in order to develop a relevant mathematical
396
function. In this study, Weirig’s (1984) data were considered appropriate to use (Parrott,
397
1987). The data were curve-fitted to produce the expression for the RH correction factor, as
398
given in Equation (2). Figure 1 gives a plot of the correction term (eh) to account for changes
399
in ambient RH. It can be seen that the parabolic equation maintains eh =1.0 for 60 to 65% 12
ACCEPTED MANUSCRIPT RH, being the optimum RH for carbonation. The factor for lower and higher humidity levels
401
are gradually scaled down according to the parabolic relationship. In developing the present
402
RH equation, research conducted by Gardner (2004), ACI 209 (1997), Hassoun and Al-
403
Manaseer (2012), Muller and Hilsdorf (1990), Salvoldi et al. (2015), provided very useful
404
guidance. Based on understanding of RH influence on carbonation, as discussed earlier, the
405
author configured the parabolic RH function given in Equation (2), to be applied within the
406
range of 50 to 80% RH.
407
RH − 35 RH e h = 16 1 − 100 100
for 50% ≤ RH ≤ 80%
408 409
[Insert Figure 1]
410
(2)
SC
1.5
RI PT
400
3.3.2 Growth rate function for compressive strength
412
The mathematical concept needed to represent concrete strength as a function of time, was
413
identified to be the general growth rate Equation (3) recommended by ACI 209 (1997).
M AN U
411
414 Fc(t) =
t .f c28 a + bt
(3)
TE D
415
Where fc28 is the mean compressive strength at 28 days, Fc(t) is concrete strength at any time,
417
t while a, b are constants. In Equation (3), both the a-parameter and b-parameter are
418
influenced by cement type and curing type. Typically, for moist-cured concretes, a = 0.4, b =
419
0.85 for Type I ordinary Portland cement, and a = 2.3, b = 0.92 for Type III rapid hardening
420
Portland cement. It should, however, be noted that these coefficients apply to concretes
421
subjected to continuous moist curing and may not directly apply to concretes stored at
422
outdoor natural environment. Also, it should be considered that carbonation leads to
423
enhancement of concrete strength as a time-dependent variable. Accordingly, it becomes
424
necessary to modify the equation for purposes of strength prediction under the influence of
425
carbonation in the natural environment. As mentioned earlier, the experimental data reported
426
in CSIR (1999) were used throughout this process.
AC C
EP
416
427
During the process of data fitting, it was found impossible to de-couple the influence of
428
cementitious materials from the strength growth function. By introducing a coefficient which
429
is a scalar quantity, and an exponent to Fc(t), a correct prediction of carbonation behavior is
430
possible. Essentially, this leads to an inverse power function developed by modification of
431
Equation (3) to allow for composition effects, giving rise to Equation (4) 13
ACCEPTED MANUSCRIPT f(cem, f c(t) ) = cem.(Fc(t) )
g
432
(4)
Where cem is a scalar quantity for cement, and g is a shape factor but it really represents the
434
rate at which different cement types promote CO2 ingress, which is analogous to electrical
435
“conductance” of CO2 flux (Section 2.2.7). The term carbonation conductance factor is
436
therefore used in the present model to refer to, g. Both factors (cem, g) are dependent on the
437
type and proportion of cementitious materials used in the concrete.
RI PT
433
At this point, there are four unknowns (a, b, cem, g) whose values are to be determined
439
for each concrete material system under consideration. Determination of these constants was
440
done by data fitting and optimization operations conducted through an interative process
441
involving trial and error, regression, and curve-fitting methods, applied to data. Data fitting
442
was conducted on: (a) strength, fcbn at long-term ages of 3.5, 6 and 10 years; (b) strength, f28
443
at 28 days.
M AN U
SC
438
444
(a) Coefficients based on insitu concrete strength at long term ages
446
Initially, the graphs of long-term insitu concrete strength, fcbn versus measured carbonation
447
depths were plotted for ages of 3.5 and 6 years, and for cement types consisting of OPC and
448
RHC, with or without FA. Specifically, the graphs in Figure 2 were plotted for OPC,
449
OPC/30FA (i.e OPC containing 30% FA), RHC, RHC/25FA. Power curve regressions were
450
applied to each of the graphs. Expectedly, wide ranging coefficients and exponential factors
451
were obtained for each cement type, as shown in Table 2. At first sight, the regression
452
relationships appear spurious and unrelated. However, upon varying cem and g by means of
453
trial and error, a consistent relationship emerges, which was curve-fitted to approximately
454
cem = 950, g = -1.2. The scalar quantity was conveniently rounded-off to cem = 1000. Also,
455
trial constants (a,b) were estimated for strength prediction based on use of fcbn in lieu of f28.
456
Equation (5) was obtained as discussed later in this section.
AC C
EP
TE D
445
457
The Least Squares Method (LSM) was applied to examine the goodness-of-fit of the
458
models to the observed data. According to the method, the goodness-of-fit of a model y =
459
f(x) to observed data is evaluated by determining the sum of squared residuals or errors
460
(SSE). i
461
2
SSE = min ∑ [ f ( xi ) − yi ] , Where yi is the observed value. 1
14
ACCEPTED MANUSCRIPT 462
Accurate models give minimum SSE. The method can be used to optimize data fitting
463
through adjustment of the model coefficients. Also useful is the total sum of the error squares
464
(SST), calculated as (Sayed-Ahmed, 2012; Underhill and Bradfield, 2013) 2
_ _ SST = ∑ yi − y , where y is the average of observed values. 1 i
466 467
The coefficient of determination (R2) is obtained from the expression R 2 = 1−
RI PT
465
SSE SST
In this study, the various trial models (Figure 2) were analysed using the LSM method, giving
469
results shown in Table 2. It is however emphasized that the curve fitting method is used here
470
to establish the form of model based on carbonation-strength relationship, rather than fixed
471
values of the coefficients, at this early stage. Infact, other than a = 0.35, all the parameters in
472
the models determined for the carbonation-strength derivation, had to be adjusted iteratively
473
during optimization and calibration, as later discussed. These adjustments should be
474
understood in context of solving a 3D relationship between carbonation progression, strength
475
and time. From this point, two other relationships must be solved i.e. carbonation-time and
476
strength-time relations, which must then be compounded with the carbonation-strength
477
relationship.
TE D
M AN U
SC
468
Accordingly, the next stage was to data-fit the constants (cem, g) and (a, b) so as to
479
account for time-dependent behaviour. From mathematical knowledge of curves, the shape
480
factors for the functions are, g, for the inverse power curve and, b, for the growth rate curve.
481
To optimize the coefficients, the procedure adopted was:
483 484
(i) Varying g-value with age, while keeping (a = 0.35, b = 1.2) constant. This step leads to optimization of the g-value. (ii) Varying b-value with age, while keeping (a = 0.35, cem = 1000, g) constant
AC C
482
EP
478
485
The optimization was conducted using data of 3.5, 6 and 10 years. To simplify the process, g-
486
values used were limited to -1.4, -1.5, -1.6. Table 3 shows the coefficients of determination
487
obtained by varying the g-value. It is evident that the best data fit is given by g = -1.5 having
488
the best R2 value, overall. In interpreting the optimization given in Table 3, it is important to
489
note that while the best R2 is sought, it is not necessary to consider its numerical value in
490
terms of statistical significance.
491
The results given in Tables 2 and 3 can also be seen in the graphs shown in Figure 3 for g
492
= -1.4 and g = -1.5. As the g-value decreases, the carbonation rate predictions tend to shift
493
lower. A similar trend was observed for g = -1.6. A close inspection of the graphs shows that 15
ACCEPTED MANUSCRIPT the data fit is affected by age. Notably, the data fit for g = -1.5 at 3.5 years is poor compared
495
to the other ages. Similarly, the data fit for 10-year age is slightly offset, relative to that of 6
496
year data. This explains the R2 - value of -0.08 obtained at 3.5 years as compared to 0.44 and
497
0.36 for the ages of 6 years and 10 years respectively. These results imply that g-value alone
498
does not account for age-related effects and other parameter(s) need to be adjusted to allow
499
for time-effects. This naturally led to optimization of b-value as a necessary step, since it is
500
the only other key factor influencing the curve shape. To conduct this operation, cem = 1000,
501
g = -1.5, a = 0.35 were maintained constant while b-value was adjusted to obtain the optimum
502
value for each age 3.5, 6, 10 years.
503 [Insert Table 2]
505
[Insert Figure 3]
506
M AN U
504
SC
RI PT
494
507
As seen in the above analysis, the g = -1.5 data fitting was optimized at 6 year age with
508
(a=0.35, b = 1.2). Using this as a starting point and optimizing the data fitting for 3.5 year and
509
10 year data, b = 1.27 and b = 1.1 were obtained respectively. By conducting linear
510
regression, the equation b = 1.3-0.02t is obtained. b = 1.3 − 0.02t
(5)
TE D
511
However, recalling that b-value is the shape factor of the growth function given in Equation
513
(5), an inspection of the prediction curve based on Equation (5) quickly identifies 15 year age
514
as a crucial turning point that determines the type of curve, to be either an exponential curve
515
if the expression is used in the form given in Equation (5) or a growth curve when the
516
expression is restricted to b = 0.9 for ages greater than 15 years. The latter is undoubtedly the
517
appropriate function.
AC C
518
EP
512
519
(b) Coefficients based on concrete strength at 28 days
520
In order to use 28-day strength, fc28 of concrete for prediction of carbonation, the optimization
521
operation conducted above for long-term strength, fcbn was repeated using 28-day strength
522
data to determine the coefficients (cem, g, a, b). The same cement factors (cem = 1000, g = -
523
1.5) are applicable under both the long-term strength and 28-day strength. However, data
524
fitting and optimization gives a = 0.35 and Equation (6) for the b-value, based on fc28.
525
b = 0.6 − 0.02t
(6)
16
ACCEPTED MANUSCRIPT To maintain the growth curve shape, b = 0.4 must be constant for ages greater than 10 years.
527
But it was found that disjointing arises at the points where b in Equations (5) and (6)
528
transition to their respective constants. So, a purely mathematical operation was conducted to
529
develop the respective continuous functions equivalent to those given by Equations (5) and
530
(6) and adjusted for long-term behavior. This operation produced the Equations (11a,b) and
531
(12a,b). With Equations (5) and (6) derived, the optimization process was repeated based on
532
cement type. During the process, the conductance factors, g that were found to correctly
533
curve-fit the carbonation behaviors of the different cement types were: g = -1.5 for OPC,
534
RHC, 15%FA and g = -1.4 for 30%FA.
535
SC
RI PT
526
3.3.3 Accounting for influence of different cement types
537
The dual cement conductance factors (cem, s) account for the promoting influence of SCMs
538
on carbonation. The model allows for cement types containing up to 30% fly ash (FA) or
539
50% slag (SG) or 10% SF. These SCM proportions are equivalent to CEM I and CEM II
540
varieties of EN 197-1 (2000).
M AN U
536
The inclusion of the other SCMs (SF, SG) in the model specification has been partly
542
based on literature and inference from correlation behaviours. It is known that correlation
543
exists between the carbonation behavior of FA and other SCMs. CEM I and CEM II varieties
544
give similar long-term carbonation behaviours (Greve-Dierfeld and Gehlen, 2014).
545
Khunthongkeaw et al. (2006) reported that CEM I with or without 10% FA of Class C and
546
Class F (equivalient of CEM II/A) exhibited the same carbonation rates. Also, Ali and
547
Dunster (1998) showed that 30%FA had the same carbonation rate as 50% GGBS cements.
548
Studies on South African SCMs show that 10%SF, 30%FA and 50%GGBS give similar
549
carbonation behaviours (Alexander et al. 2001).
AC C
EP
TE D
541
550
Also in classifying cements, the EN 197-1 (2000) allocates the same cement class for FA
551
and GGBS, i.e. CEM II/A would contain, 6-10%SF, 6 to 20% FA or GGBS. CEM II/B would
552
contain 21 to 35% FA or GGBS which implies that within this range of the SCMs, FA and
553
GGBS would be expected to behave similarly. Infact EN 197-1 allows the use of any type of
554
SCM for CEM II provided its proportion is limited to 35%, as specified in Portland
555
composite cement CEM II/A-M and CEM II/B-M. This suggests that the SCMs may be used
556
interchangeably within these limits and they would be expected to show similar behaviours.
557
The experimental data (CSIR, 1999) used in this study had mixtures containing 0, 15, 30,
558
50% FA, which cover a wide range of cement varieties CEM I to CEM IV as given in
559
Equation (13). 17
ACCEPTED MANUSCRIPT 560 3.3.4 Model formulae
562
From derivations and the associated mathematical functions presented in the foregone
563
discussion, the complete model is expressed in Equations (7) to (13), and consists of: (1) the
564
material performance property, being concrete strength, (2) relative humidity, shelter, [CO2]
565
as the main environmental factors, and (3) the material composition represented by cement
566
type. In the proposed model, carbonation under both sheltered and unsheltered outdoor
567
exposure conditions are considered (Equation (9)). The correction factors for unsheltered
568
exposure were derived in Ekolu (2016), as explained in Section 2.2.5. The model also
569
accounts for carbonation under different levels of [CO2] taking concentrations of 300 to 400
570
ppm as baseline and giving correction factors for higher or lower CO2 concentrations using
571
Equation (10). Derivation of this equation is given in Ekolu (2016) as explained in Section
572
2.2.3.
M AN U
SC
RI PT
561
Curing methods and their effects are not considered to be of significant influence to long-
574
term carbonation (Section 2.2.10), provided a minimum of 3-day site curing or its equivalent
575
is achieved as typically required by recognized standard specifications (Ekolu, 2016). Based
576
on this condition, curing is not included as a separate parameter in the model. However,
577
curing effects are embedded in the cement type and concrete strength, both of which are
578
accounted for in the model. The mean 28-day cube strength, fc28 obtained from laboratory
579
moist-curing or insitu strength of concrete, fcbn extracted from existing structure at a given
580
age of its service may alternately be used by employing Equations (11a,b) and (12a,b),
581
respectively. No accelerated methods such as accelerated carbonation, permeability tests etc.
582
are used in any parameter of the model. Also, the model is not for use under indoor
583
conditions of exposure.
EP
AC C
584
TE D
573
585
3.3.5 Calibration
586
Following the formulation discussed in the foregone sections, the model was calibrated
587
against experimental data. The calibration was an iterative process consisting of adjustments
588
to the model structure until its predictions were deemed acceptable. The model calibration
589
was done under the use of long-term concrete strengths, fcbn and under the use of 28-day
590
concrete strengths,fc28. The process employed use of data generated under different curing
591
regimes. Accordingly, the significance of curing on model predictions was examined. In the
592
evaluation, the model was used to predict carbonation depth or rate which in turn was
593
compared statistically against measured values. 18
ACCEPTED MANUSCRIPT 594 595 d (f, t) = e h . e s . e co .cem (Fc(t) ) . t g
596
(7)
597
Environmental factors for relative humidity and shelter:
598
RH − 35 RH e h = 16 1 − 100 100
599
1.0 for sheltered outdoor exposure es = -0.2 f c for unsheltered outdoor exposure; f c is 28 − day strength
600
Environmental factors for varied CO2 concentrations:
601
α f r for 20 < fc < 60 MPa eco = c 1.0 for fc ≥ 60 MPa Correction factor ec = αfc
fc ≥ 60
ec = 1.0
200 ppm 1.4 -1/4
606
(a) Using 28-day strength, (fc28)
608 609 610 611 612 613 614 615 616
EP
605
Time-dependent strength growth function (Fc(t)): t Fc(t) = .f c a + bt
607
RI PT
SC
(9)
(10)
CO2 concentration level 300 ppm 500 ppm 1000 ppm 1.0 2.5 4.5 0 -1/4 -2/5
2000 ppm 14 -2/3
TE D
20 < fc < 60
α r
r
(i) Short-term ages, t < 6 years a = 0.35, b = 0.6 − t
AC C
604
(8)
Where α,r are correction factors for natural carbonation under varied CO2 concentrations: 28-day strength (MPa)
603
for 50% ≤ RH ≤ 80%
M AN U
602
1.5
0.5
50
(11a)
(ii) Long-term ages, t ≥ 6 years a = 0.15t, b = 0.5 − t
0.5
50
(11b)
(b) Using long-term (field) strength, (fcbn) (i) Short-term ages, t < 15 years a = 0.35, b = 1.15 − t
0.6
50
(12a)
(ii) Long-term ages, t ≥ 15 years a = 0.15t, b = 0.95 − t
0..6
50
(12b) 19
ACCEPTED MANUSCRIPT 617 618 Cement factors for carbonation conductance: SCM
Cement types
20% any 30% fly ash 50% slag
CEM I, CEM II/A CEM II/B, CEM IV/A CEM III/A, CEM IV/B
(13) Scalar, cem 1000 1000 1000
Conductance factor, g -1.5 -1.4 -1.4
RI PT
619 620
621 622 623 624 625 626 627
Notes: Cube strength (fc) is related to core or cylinder strength (fcyl) through the conversion, fc = 1.25 fcyl. Strength values used in the equations must be ≥ 20 MPa. Moist-cured 28-day strength (fc28) is related to insitu strength (fcbn) using the expression, fcbn = fc28+13.
628
In order to examine the accuracy of the model, it is essential to conduct unbiased
629
statistical analysis of its predictions. For this purpose, the Root Mean Square (RMS) method
630
was employed (Bazant and Panula, 1979). RMS is the square root of the average of residuals
631
between measured values (MV) and predicted values (PV). By dividing the RMS by the
632
mean of measured values in the data set, a coefficient of variation (CV) of errors is obtained.
633
This parameter can suitably be used to compare model predictions with measured results. It
634
should be noted that this CV, is determined somehow differently from conventional CV
635
defined as the ratio of standard deviation to mean. The former is determined on the basis of
636
two variables (MV, PV) while the latter applies only to a single variable (MV or PV). Also
637
used as a statistical indicator is the ratio of average MV to average PV.
TE D
M AN U
SC
*SCM – supplementary cementing materials, NP – natural pozzolan
Figure 3 (g = -1.5) gives the model predictions made based on long-term concrete
639
strengths while comparison of measured values to predictions made based on 28-day concrete
640
strengths, is given in Figure 4. While the general fitting may look visually reasonable, as the
641
results lie along the line of equality, it is through statistical error analysis that the accuracy of
642
predictions can be effectively examined. Table 4 gives the statistical indicators showing the
643
predicted values relative to the measured values for predictions based on long-term concrete
644
strength and predictions based on 28-day concrete strength. For the model predictions based
645
on fcbn, the MV/PV ratio lies between 0.9 to 1.1; an average of 1.0. This result indicate that
646
the predicted values are nearly the same as the actual measured value of carbonation rate. The
647
MV/PV ratio for predictions based on 28-day concrete strength appear to be slightly higher,
648
giving between 1 to 1.2. However, these differences may vary depending on the data settings
649
and their embedded errors.
AC C
EP
638
The coefficient of variation of the model prediction is
20
ACCEPTED MANUSCRIPT 650
consistently between 23% to 33% and falls within the typical range of accuracy known for
651
code-type models (Bazant and Baweja, 1995). Finally, a boundary condition was determined prescribing model predictions to be invalid
653
for concrete strengths below 20 MPa. In the literature (Parrott, 1990; Guiglia and Taliano,
654
2013), the measured carbonation rate in real structures, indoors is reported to be about 10
655
mm/yr½ for low strengths of 21 MPa, compared to 5 mm/yr½ for medium strength and 2
656
mm/yr½ for concrete strengths > 45 MPa. Other researches (Ali and Dunster, 1998;
657
Lagerblad, 2005) have reported carbonation rates for outdoor sheltered environments to be
658
3.8, 6.2, 6.2 mm/yr½ for C30 concrete made with OPC, 30%FA and 50%GGBS respectively.
659
Concretes of strengths under 20 MPa are regarded as low strength, typically non-structural
660
concretes. In this study, it was found that when the strength of concrete falls below 20 MPa,
661
model predictions become drastically high. In order to examine this behavior, borderline data
662
sets were selected with values lying slightly above and below 20 MPa. Figure 5 gives the
663
difference in carbonation predictions when these strength data were plotted. It can be seen in
664
Figure 5 that when concrete strengths fall below 20 MPa, predictions rapidly rise higher
665
correspondingly with further decrease in strength. As such, the model in its current version is
666
not appropriate for concretes of strengths less than 20 MPa.
M AN U
SC
RI PT
652
667
[Insert Figure 4]
TE D
668 669
[Insert Table 4]
670
[Insert Figure 5]
671 3.3.6 Sensitivity analysis
673
Equations (9) to (13) of the model comprise primarily of material properties of concrete
674
(strength, cement type) and environmental exposure conditions (RH, sheltering, CO2 levels).
675
The method employed in sensitivity analysis was to identify the main parameter variables of
676
the model, then a range of boundary values for each input parameter was fixed at two
677
standard deviations and used to assess the parameter’s influence towards variation of model
678
output. Table 5 gives the model parameters and range of values used. Apart from strength
679
that was examined for medium strength and high strength concretes of 30 MPa and 60 MPa
680
respectively, the other parameters apply generally to the model. Figure 6 gives the results of
681
sensitivity analysis. It is evident that the parameters considered are important contributors to
682
variability of model outputs, as seen by significant changes when they were varied across
683
predetermined boundary values. The conductance factor is perhaps the most sensitive
AC C
EP
672
21
ACCEPTED MANUSCRIPT parameter in the model and should be strictly selected according to the respective cement
685
type. For example, a wrong choice of g = -1.4 in place of g = -1.5 would alter model outputs
686
of predicted carbonation by 40%. Such errors are possible if there are no clear details
687
available concerning the type of cement used in the concrete. Variability of the strength
688
parameter is dependent on strength grade (Figure 6b), with high strength concretes
689
contributing lower output changes of 12 to 16% for 60 MPa concrete compared to 20 to 30%
690
for 30 MPa concrete. The relative humidity parameter introduces errors of up to 15% for
691
50%RH or 75%RH. Evidently, sensitivity is remarkably low for 55 to 65%RH, an important
692
level of RH for carbonation.
RI PT
684
In addition, comparison of predictions obtained using fc28 and using fcbn is made to assess
694
closeness of results obtained from the two values. The assessment was conducted based on
695
the relationship fcbn = fc28+13, having been determined empirically using CSIR (1999) data.
696
The comparison covers all concrete strengths from 20 to 90 MPa for ages up to 100 years. In
697
Figure 7, it is seen that use of fcbn gives about 2 to 5 mm higher carbonation depths than the
698
values obtained using fc28. The difference in depths is about 4 to 5 mm for strengths of 20 to
699
50 MPa, diminishing to under 3 mm difference with increase in strengths up to 90 MPa. The
700
various concrete strengths give residuals falling within the 95% limits, and this behavior of
701
the model is consistent throughout the 100 year age. However, there are minor deviations at
702
ages below 5 years and above 60 years, where strengths greater and lower than 40 MPa
703
respectively, tend to breach the 95% limits. Overall, there is good agreement between results
704
obtained from the two values, fc28 and fcbn. Accordingly, fc28 and fcbn may be used
705
interchangeably in carbonation prediction, depending on the available data.
M AN U
TE D
EP
706
SC
693
3.3.7 Boundary conditions and constraints
708
Although several assumptions are embedded in the model, these are deemed necessary for
709
mathematical simplifications and adjustment of theoretical derivations to practical
710
engineering application. These assumptions mainly contribute to variability. The limitations
711
subsequently discussed, have been established during calibration of the model response to
712
data from outdoor natural environment.
AC C
707
713
In employing the model, concretes should be of cube strengths > 20 MPa made of the
714
specified cement types (CEM I, CEM II/A and II/B, CEM III/A, CEM IV/A and IV/B, CEM
715
V/A) accounted for in the model. It is crucial that selection of cement conductance factor, g is
716
made under strict consideration of cement type or SCM content in the binder, if this
22
ACCEPTED MANUSCRIPT 717
information is available. A correct selection of g is vital given the high sensitivity of model
718
outputs to the conductance factor. It has been shown in Section 3.3.5 Figure 4, that non-structural (low-strength) concretes
720
give poor predictions and high variability. The model applies to concretes subjected to all
721
conventional curing regimes but should be made of normal aggregates and may be air
722
entrained or non-air entrained provided the air content is within the conventional range of 5
723
to 8% (ACI 211, 2009). The influence of special aggregates types such as recycled and
724
lightweight aggregates is not accounted for in the proposed model.
RI PT
719
The model is applicable to real-world concrete structures in the natural outdoor exposure
726
environment with recommended average of 55% to 75% RH, and does not apply to indoor
727
environments. Effect of sheltering from rain is accounted for in the model, as explained under
728
Section 3.3.1, Equation (9). The atmospheric [CO2] in the natural exposure environment of
729
the structure should typically be in the range of 300 to 400 ppm, for most urban locations. If
730
the site of a structure is not within this CO2 range, a correction term to model predictions
731
must be applied as per Equation (10). The appropriate exposure classes for the model are the
732
carbonation-prone environments, XC3 and XC4. Data extracted from treated concrete
733
surfaces, corner areas of structural elements, cracked concretes and joints (Ann et al. 2010),
734
are not appropriate for use in the model for reasons explained in Section 2.0.
735
TE D
M AN U
SC
725
4. Potential applications
737
Consistent with the objective of maintaining practical relevance, only data obtained from
738
outdoor natural environment has been used in deriving and calibrating the model. The model
739
may potentially be used for service life design of new RC structures and for estimating the
740
residual life of existing structures. In both cases, the model’s structure remains unchanged but
741
the coefficients of some parameters assume different numerical values. The model is suitable
742
for use in conjunction with reliability concepts which employ stochastic applicative methods.
AC C
743
EP
736
744
4.1 Existing reinforced concrete structures
745
The model is applicable to existing structures using Equations (12a,b). In this case, cores are
746
extracted from the structure of known age, from which the mean strength fcbn, carbonation
747
depths, and cover depths are determined along with their CVs. Where necessary, 28-day
748
strength may be estimated from insitu results using the relationship fcbn = fc28+13, as
749
mentioned in Section 3.3.6. The model may then be applied using reliability principles to not
750
only back calculate the progression of carbonation hitherto but more importantly, to 23
ACCEPTED MANUSCRIPT stochastically estimate the residual service life of the structure (RILEM, 1996; ISO, 2012).
752
Arguments may be made that carbonation rate could be calculated directly from data and
753
used for predicting service life based on constant carbonation rate. However, such an
754
approach would be deterministic and has been employed in the literature (Alexander et al,
755
2007). Carbonation rate itself is not a constant value but varies with time. Therefore using a
756
constant rate leads to erroneous, unreliable estimation of service life, since it does not account
757
for variability of carbonation progression rate, cover depth, and material properties of
758
concrete. In prediction of service life using the proposed model, variability of the major
759
factors are incorporated through stochastic modeling. It is vital that correct age of a structure
760
and quality test data are used in the model, for it to give meaningful predictions. For example,
761
if data is extracted at the age of 20 years of an existing RC structure, the model can be used to
762
estimate residual lifespan, being the duration from the present time to the point when
763
carbonation would reach the level of steel i.e. when the full cover is carbonated. Since
764
carbonation does not occur uniformly throughout the structure, the criteria to be used in
765
deciding end of service life (ESL) should be based on probability. A 10% probability that full
766
cover depth is carbonated would be an appropriate criteria to use for ESL (Gjorv, 2009).
M AN U
SC
RI PT
751
It should be underscored that extreme care during data acquisition from existing structures
768
is absolutely necessary, as explained in Section 3.3.7. The issue is critical in ensuring that
769
appropriate and quality data is obtained for use in the model. The major locations of concern,
770
that should be avoided during testing for material properties include cracked sections, joints,
771
corners of elements, surface treated concrete layers, chloride-contaminated concretes, splash
772
and spray zones of structural elements. The appropriate locations for data extraction should
773
be non-surface treated, flat surfaces exposed to atmospheric zone without peculiar
774
obstructions.
EP
AC C
775
TE D
767
776
4.2 New reinforced concrete structures
777
The model also applies to service life design of new structures through use of Equations
778
(11a,b). Two possible concrete strength values may be used in the model at the design stage
779
i.e. strength grade of concrete (fck) or mean strength at 28 days (fc28). If the concrete mixtures
780
and strengths to be used in the structure are known, it is preferable to use the mean 28-day
781
cube strength, otherwise the design engineer may still employ the strength grade of concrete.
782
Incorrect predictions would arise if the concrete strength achieved after construction of the
783
structure is different from the assumed value applied to the model at design stage. In such a
784
case, design predictions may be revised based on actual insitu or 28-day strength results. 24
ACCEPTED MANUSCRIPT Again the conditions given in Section 3.3.7, requiring use of normal aggregate, a minimum
786
concrete strength of 20 MPa, and known cement type with known SCM content (if any), must
787
be adhered to. With implementation of the model at design stage, the designer employs a
788
scientific approach that can be used to maneuver the structure’s design parameters such as
789
cover depth, concrete strength etc., in order to estimate its service life with a measurable level
790
of certainty. As explained in Section 4.1, the main domain for use of the model is stochastic
791
applicative method which employs a probabilistic approach of reliability design (RILEM,
792
1996; ISO, 2012).
RI PT
785
In applying this model, it is notable that no major associated costs may be anticipated.
794
Only basic information, which is typically available at design and construction stage or
795
during repairs, is needed. No complicated tests, sophisticated equipment, computer software,
796
or specialized skills are involved.
M AN U
797
SC
793
5. Comparison of the proposed model versus fib-Model Code predictions
799
Most carbonation prediction models proposed in the literature are based on accelerated
800
carbonation tests and are mostly experimental models, as elaborated in Section 2.1. One of
801
the main problems encountered in carbonation modelling is lack of long-term data
802
measurements taken from real world structures. In this study, comparison of prediction
803
results is made between the proposed model and the fib-Model described in fib (2010);
804
Guiglia and Taliano (2013).
TE D
798
In an extensive investigation, that may be considered as the closest application of a model
806
to real world structures, Guiglia and Taliano (2013) developed a relation between carbonation
807
resistance parameter of the fib-model (R-1NAC, 0) and the 28-day compressive strength for the
808
structures that were investigated. In turn, they found that carbonation depth relation to
809
strength could be simplified to:
AC C
810
EP
805
x c(t) = 163. k e .f −2.1cm . . t for abutments and piers x c(t) = 206. k e .f − 2.1 cm . . t for tunnels
811
Using these equations, scatter plots were prepared comparing the measured and calculated
812
carbonation depths (Guiglia and Taliano, 2013). Their investigation covered about 135 km of
813
highway distance. Tests were done on uncracked concretes extracted from more than 120
814
structures consisting of bridges, viaducts, tunnels, flyovers, underpasses and retaining walls.
815
About 1350 compressive strength and carbonation tests were conducted using 100 mm cores
816
extracted from the reinforced concrete structures. The structures were no more than 5 years 25
ACCEPTED MANUSCRIPT old and were of medium strengths in the range of 20 to 50 MPa. There was no availability of
818
information on the concrete mix designs used for the various structures. However, reports
819
indicated CEM II/A-I, CEM II/B-L and CEM I as the cements that were most predominantly
820
used in the market. Locations of the structures were categorized into three classes of:-
821
64%RH (geographical area I), 67%RH (geographical area II), and 75%RH (geographical area
822
III). The structures were of exposure classes XC3 for external concrete sheltered from rain i.e
823
abutments, piers and tunnels; XC4 for concrete surfaces subject to water contact, such as
824
walls etc. (EN 206, 2000). Although data for walls was acquired, it was not used in the fib-
825
model owing to difficulties in assigning proper environmental coefficients, since walls are
826
unsheltered and also exposed to rain mainly through its vertical face.
SC
RI PT
817
The proposed model and fib-Model were applied to the same data (Guiglia and Taliano,
828
2013) to generate carbonation predictions made by both models. Scatter plots of results are
829
given in Figures 8a1, b1, c1 and Figures 8a2, b2, c2 for the proposed model and fib-Model,
830
respectively. Results are reported for abutments, piers and tunnels located in the three
831
geographical areas of different relative humidity levels. A visual overview of the scatter plots
832
show that both models correctly predict the progression of carbonation for the different
833
elements and at various ages, with data points lying along the line of equality. The wide
834
scatter in data does not necessarily appear to be a result of errors in the prediction models but
835
mostly associated with the random nature of measured data, which are exacerbated by the
836
often fluctuating or non-uniform field exposure conditions. The tendency of data points to
837
deviate from the equality line are attributed to incorrect predictions by the models. In both
838
models, data points show relatively wider scatter at higher carbonation rates or depths, while
839
at the same time veering away from the equality line. This behavior appears to be associated
840
with poor quality, typically low strength concretes. In strength characterization, poor or low
841
quality is also associated with high variability, which implies a high CV.
AC C
EP
TE D
M AN U
827
842
The error statistics generated are shown in Table 6 for each geographical area. These
843
statistics indicate that both models perform at a similar level, with fib-Model showing only a
844
slight edge. Both models have the same range of accuracy giving CV of errors = 40 to 50%,
845
which is quite typical of code-type models, as discussed in Section 3.3.5. These results are
846
also consistent with reports in literature which indicate the accuracy of fib 34 Model to be in
847
the range of CV = 30 to 45% (Lifecon, 2003; Marques et al, 2013).
848
Residuals for both models are shown in Figure 9. Clearly, both models give residuals
849
which fall within the 95% confidence interval. Accordingly, predictions by the models may
850
be considered a correct representation of true carbonation occurring in the real world 26
ACCEPTED MANUSCRIPT structures investigated. Both models have a tendency to under-predict carbonation in high
852
strength concretes and progressively over-predict as concrete strengths decrease. The fib-
853
Model appears to show this tendency slightly more prominently than the proposed model.
854
However, these under-predictions and over-predictions by the models should not be of much
855
concern since they are fairly small and fall within the 95% confidence limits. Also evident in
856
the residual plots is fanning out as the carbonation depths increased. This observation is
857
mostly attributed to the characteristic material behavior associated with increase in variability
858
as concrete strengths decrease. Since strength correlates strongly with carbonation
859
progression, the lower strength concretes are also highly carbonating concretes and
860
consequently show high variability of carbonation depths or rates.
SC
RI PT
851
It may be recalled that the fib-Model usually requires conduct of accelerated tests
862
especially to determine permeability or diffusion coefficient, a required input to the model. In
863
this regard, the proposed model is quite advantageous considering that only basic information
864
i.e mainly strength is required. Concrete strength results are readily available during design,
865
construction or repair of structures, as discussed in 4.2. No accelerated tests or use of
866
sophisticated costly equipment is involved.
M AN U
861
867
7. Conclusions
869
A new model is proposed for prediction of natural carbonation in reinforced concrete
870
structures. Model formulation was done by applying mathematical laws and empirical data
871
measurements. The model may potentially be used for service life evaluation of existing
872
structures and durability design of new reinforced concrete structures.
EP
TE D
868
Detailed description is given on development of the prediction model through derivations,
874
data fitting and optimization. The model was calibrated, statistically evaluated and compared
875
with fib-Model Code. The proposed model was found to give a similar level of prediction
876
accuracy as fib-Model Code. Further research is continuing on the proposed model.
877
AC C
873
878
Acknowledgments
879
The research presented in this paper was supported by the National Research Foundation
880
(NRF) of South Africa, Grant No. 96800. The author wishes to thank the NRF for financially
881
supporting this study.
882 883 884
References 27
ACCEPTED MANUSCRIPT ACI 209 (1997), American Concrete Institute (ACI) Committee 209, Subcommittee II. Prediction of creep, shrinkage and temperature effects in concrete structures, Report ACI 209 R92, (reapproved 1997) ACI 211 (2009), American Concrete Institute (ACI) Committee 211, Standard practice for selecting proportions for normal, heavyweight and mass concrete, ACI 211.1-91 (reapproved 2009), American Concrete Institute, Farmington Hills, Michigan, 1991
RI PT
Alexander M.G, Mackechnie J.R and Ballim Y. (2001), Guide to the use of durability indexes for achieving durability in concrete structures, Department of Civil Engineering, University of Cape Town, Research Monograph No. 2, 35p
Alexander M.G, Mackechnie J.R and Yam W. (2007), Carbonation of concrete bridge structures in
SC
three South African localities, Cement and Concrete Composites, 29, 750-759
Ali A. and Dunster (1998), A., Durability of reinforced concrete-effects of concrete composition and curing on carbonation under different exposure conditions. BRE-report, Garston UK.
M AN U
Ann K.Y, Pack S.-W., Hwang J.-P., Song H.-W., Kim S.-H. (2010), Service life prediction of a concrete bridge structure subjected to carbonation, Construction and Building Materials, 24, 1494–1501
Atis C. D (2004), Carbonation-Porosity-Strength Model for Fly Ash Concrete, Journal of Materials in Civil Engineering, 16 (1), February 1, 91-94
Balayssac, J. P., Détriché, C. H., and Grandet, J. (1995), Effects of curing upon carbonation
TE D
of concrete. Construction and Building Materials, (9), 91-95.
Bazant Z.P and Baweja S (1995), Justification and refinements of Model B3 for concrete creep and shrinkage, 1. Statistics and sensitivity, Materials and Structures, 28, 415-430 Bazant Z.P, and Panula L. (1978), Practical prediction of time-dependent deformations of concrete.
EP
Materials and Structures (RILEM, Paris): Part I Shrinkage, Vol.11, 307–316. Bazant, Z.P., and Panula, L. (1979), Practical prediction of time-dependent deformations of concrete.
AC C
Part VI, Cyclic creep, nonlinearity and statistical scatter, Materials and Structures, 12, 175-183. Bob C. (1999), Durability of concrete structures and specification, Proceedings of the International Conference on Creating with Concrete Dundee (Ed. Dhir, R.K. and McCar-thy, M.J.), 311-318 BS 8110 (1997), Structural use of Concrete, Part 2, Code of Practice for Design and Construction, London, British Structural Institution, 389 Chiswick High Road, London, W4 4AL, United Kingdom Buenfeld N.R, Hassanein N.M, and Jones A.J (1998), An artificial neural network for predicting carbonation depth in concrete structures, In Artificial Neural Networks for Civil Engineers: Advanced Features and Applications (Chap 4), I. Flood and N. Kartam (eds.), American Society of Civil Engineers (ASCE), 277p
28
ACCEPTED MANUSCRIPT Buenfeld, N.R. and Yang, R. (2001), On-site curing of concrete - Microstructure and durability. Publication C530, CIRIA, London, UK. CEB (1997). New approach to durability design - an example for carbonation induced corrosion. In: Schiessl, P. (Ed.), Bulletin,vol. 238, Comite ´ Euro-International du Be ´ton, Lausanne CEB-FIP (1978), Comite’ Europeen du Be’ton-Federation Internationale De la Precontrainte, International System of Unified Standard Code of Practice for Structures, Vol II. CEB-FIP Model
RI PT
Code for Concrete Structures, (3rd Ed.), 56, 331-344
CEB-FIP (1990a), Bulletin d’Information n° 213/214 - CEB-FIP Model code 1990, Thomas Telford, London, UK
CEB-FIP (1990b), Structural concrete – textbook on behaviour, design and performance, updated
SC
knowledge of the CEB-FIP Model Code 1990. Bulletins 1-3
Chun Y.-m., Naik T.R. and Kraus R.N. (2006), Carbon dioxide sequestration in concrete in different curing environments. UWM Center for By-Products Utilization, University of
Milwaukee,
WI,
USA.
Accessed
M AN U
Wisconsin-Milwaukee,
29th
Dec
2015.
https://www4.uwm.edu/cbu/Papers/2006%20CBU%20Reports/REP-608_Chucds.pdf CSIR (1999), Final report on an investigation into the influence of fly ash on the durability of concrete, by W.R. Barker, Division of Building and Construction Technology, CSIR, PO Box 395, 0001 Pretoria, South Africa, 18p. Also, Ash Resources Also, Ash Resources (pty) Ltd, PO Box 3017, Randburg 2125
TE D
Czarnecki L. and Woyciechowski P. (2015), Modelling of concrete carbonation; is it a process unlimited in time and restricted in space? Bulletin of the Polish Academy of Sciences, Technical Sciences, 63 (1), DOI: 10.1515/bpasts-2015-0006 Duracrete (2000), General guidelines for durability design and redesign, Report R15, in ‘EU Brite-
EP
EuRam III project DuraCrete (BE95-1347): Probabilistic performance based durability design of concrete structures
AC C
Ehlen M.A, Thomas M.D.A, and Bentz E.C (2009), Life-365 Service Life Prediction Model™ Version 2.0 - Concrete International,. http://www.life-365.org/download.html Ekolu S.O (2010), Model validation and characteristics of the service life of Johannesburg concrete structures, Proc. of the National Symp. on Concrete for a Sustainable Environment, Concrete Society of Southern Africa, 3-4th August, Kempton Park, Johannesburg, Gauteng, p.30-39. Ekolu S.O (2012), Model verification, refinement and testing on independent 10-year carbonation field data, Proceedings of the 3rd Intl. Conf. on Concrete Repair, Rehabilitation and Retrofitting (ICCRRR), 3-5, Sept. 2012, Cape Town, South Africa, p.445-450. Ekolu S.O (2016), A review on effects of curing, sheltering, and CO2 concentration upon natural carbonation of concrete, Construction and Building Materials, 127 (2016) 306–320.
29
ACCEPTED MANUSCRIPT EN 197-1 (2000), Cement - Part 1: Composition, specifications and conformity criteria for common cements. European Committee for Standardization, CEN, 29p EN 206 (2000), Concrete – Part 1: Specification, performance, production and conformity, European Standard, Reu de Stassart, B-1050 Brussels EN 1992-1-1 (2004) Eurocode 2. Design of concrete structures. part 1-1. General and building rules and rules for buildings, December 2010, 227p
Lausanne, 1st edition, 126p, ISBN: 978-2-88394-074-1
RI PT
fib (2006), Model code for service-life design, fib bulletin 34, Federation International du Beton,
fib (2010), Model code 2010 final draft, vol 1 & 2, fib bulletin N. 65 & 66, Lausanne, 2012
Fukushima, T. (1988) Theoretical investigation on the influence of various factors on
SC
carbonation of concrete, Building Research Institute (Japan), BRI Research Paper No 127 (ISSN 0453-4972), Japan, 1988.
Gardner N.J (2004), Comparison of prediction provisions for drying shrinkage and creep of normal
M AN U
strength concretes, Canadian Journal for Civil Engineering, 31 (5) Sep-Oct, 767-775 Gehlen C., and Sodeikat C (2002), Maintenance planning of reinforced concrete structures: redesign in a probabilistic environment, inspection, update and derived decision making. In: Durability of Building Materials and Components, Proceedings of the 9th International Conference, 17-20th March, Brisbane, Australia
Francis, UK, 219 p
TE D
Gjorv, O.E. (2009), Durability Design of Concrete Structures in Severe Environments, Taylor and
Greve-Dierfeld v. S. and Gehlen, C (2014), Performance based deemed-to-satisfy rules, The Fourth International fib Congress, Feb. 10-14, Mumbai, Fédération International du Béton Guiglia M. and Taliano M. (2013), Comparison of carbonation depths measured on in-field exposed
EP
existing r.c. structures with predictions made using fib-Model Code 2010, Cement & Concrete Composites, 38, 92–108
AC C
Hakkinen, T. (1993), The influence of slag content on the microstructure, permeability and mechanical properties of concrete, Part 2, Technical and theoret-ical examinations Cement and Concrete Research, 23, 518-530 Hassoun M.N and Al-Manaseer A. (2012)., Structural concrete: theory and design, 5th Edition, John Wiley and Sons Inc, 1007p He R. X. and Jia H. J. (2011), Carbonation depth prediction of concrete made with fly ash, Electronic Journal of Geotechnical Engineering, 16(F), 605-614 Hills T.P, Gordon F., Florin N.H, Fennell P.S (2015), Statistical analysis of the carbonation rate of concrete, Cement and Concrete Research, 72, 98–107
30
ACCEPTED MANUSCRIPT Hooton R.D (1988), What is needed in a permeability test for evaluation of concrete quality, MRS Proceedings,
Volume
137,
Materials
Research
Society,
1989,
DOI:
http://dx.doi.org/10.1557/PROC-137-141 Ikotun J.O and Ekolu S.O (2012), Essential parameters for strength-based service life modeling of reinforced concrete structures - a review, Proc. 3rd Intl. Conf. on Concrete Repair, Rehabilitation and Retrofitting (ICCRRR), 3-5, Sept. 2012, Cape Town, South Africa, p. 433-438
Geneva 20, Switzerland
RI PT
ISO 16204 (2012), Durability - service life design of concrete structures, Case postale 56. CH-1211,
Kari O.P, Puttonen J., Skantz E. (2014), Reactive transport modelling of long-term carbonation, Cement & Concrete Composites, 52, 42–53
SC
Khunthongkeaw J., Tangtermsirikul S., and Leelawat T. (2006), A study on carbonation depth prediction for fly ash concrete, Construction and Building Materials, 20, 744–753 Kokubu, M and Nagatakis, S. (1989). Carbonation of concrete with fly ash and corrosion of
M AN U
reinforcement in 20-years tests. ACI, SP-114-14, 315-329
Kropp J, (1995), Relations between transport characteristics and durability. In Kropp J and Hilsdorf H.K (eds), Performance cirteria for conrete durability, E & FN Spon, London Lagerblad Björn (2005), Carbon dioxide uptake during concrete life cycle – State of the art. Swedish Cement and Concrete Research Institute, ISBN 91-976070-0-2. SE-100 44 Stockholm ISSN 0346-8240, CBI Report 2:2005
TE D
Liang M.T, Qu W., and Liang C-H (2002), Mathematical modeling and prediction method of concrete carbonation and its applications, Journal of Marine Science and Technology, 10 (2), 128-135 Lifecon (2003), Deliverable D 3.2 service life models: Life cycle management of concrete infrastructures for improved sustainability, Final Report by Dipl.-Ing. Sascha Lay, Technical
EP
Research Centre of Finland (VTT). 169p
Luo D., Niu D., and Dong Z. (2014), Application of neural network for concrete carbonation depth prediction, 4th International Conference on the Durability of Concrete Structures, 24–26 July,
AC C
Purdue University, West Lafayette, IN, USA Marques, P.F, Chastre C., and Nunes Â. (2013), Carbonation service life modelling of RC structures for concrete with Portland and blended cements, Cement & Concrete Composites, 37, 171–184 Monteiro I., Branco F.A., de Brito J., Neves R.(2012), Statistical analysis of the carbonation coefficient in open air concrete structures, Construction and Building Materials 29, 263–269 Muller H.S and Hilsdorf H.K (1990), CEB Bulletin d’Information, No. 199, Evaluation of the time dependent behaviour of concrete, Summary report on the work of General Task Group 9, September, 201p. Nishi T (1962), Testing of Concrete, RILEM International Symposium, Publishing House of the Czechoslavak Academy of Science, Prague, 485-489
31
ACCEPTED MANUSCRIPT Otsuki N., Gallardo R.S, Annaka T., Takaki S., and Nishida T. (2012), Field survey for carbonation depth of reinforced concrete buildings in the Philippines, 37th Conference on Our World in Concrete & Structures: 29 - 31 August 2012, Singapore. Article Online Id: 100037033
Papadakis V.G, Vayenas C.G, and Fardis M.N (1991), Fundamental modelling and experimental investigation of concrete carbonation. ACI Materials Journal, 4(88):363–
RI PT
373. Papadakis, Fardis and Vayenas (1995), Effect of composition, environmental factors and cement-lime mortar on concrete carbonation, Materials and Structures Journal, 1192 (25), 293-304
Parrott L.J. (1987), A review of carbonation in reinforced concrete. Cement and Concrete Association, BRE, 42p
SC
Parrott L.J. (1990), Carbonation, corrosion and standardization: In: Proceedings of the International Conference on Protection of Concrete, September 11-13, University of Dundee, E & F Spon, 1009-23
M AN U
Parrott L.J. (1996), Some effects of cement and curing upon carbonation and reinforcement corrosion in concrete, Materials and Structures, vol. 29, 164-173. Parrott P.J, (1994), Design for avoiding damage due to carbonation—induced corrosion. Proc. of the 3rd International Conference on Durability of concrete, Nice, France, ACI SP-145. Malhotra V.M. (Ed), 283–298
PCA (2002), Types and causes of concrete deterioration, Portland cement Association, 5420 Old
TE D
Orchard Road, Skokie, Illinois 60077-1083, 16p, www.cement.org Quillin K. (2001), Modelling degradation processes affecting concrete, BRE Centre of concrete construction, CRC Ltd 151 Rosebery Avenue, London, ECIR 4GB. ISBN 1860815316
Ravahatra N.R, De Larrard T, Duprat F., Bastidas-Arteaga E., Schoefs (2014). Sensitivity
EP
analysis of simplified models of carbonation - extension in spatial variability -updating through Bayesian network. Proceedings of the 2nd International Symposium on
AC C
Uncertainty Quantication and Stochastic Modeling, Jun 2014, Rouen, France. RILEM (1996), Durability Design of Concrete Structures, RILEM REPORT 14 (A. Sarja & E. Vesikari, Eds), E & FN Spon, UK, 1996, 165 p. RILEM B3 (1995), Creep and shrinkage model for analysis and design of concrete structures: Model B3, RILEM Recommendations. Materials and Structures. 357-365 (28), 415-430 (28), 488-495 (28) Saettaa, A.V and Vitaliani R.V (2004, 2005)., Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part I: Theoretical formulation, Cement and Concrete Research, 34, (2004), 571 – 579. Ibid. 2005, Part II. Practical applications, 958 – 967
32
ACCEPTED MANUSCRIPT Sagues A.A, Moreno E.I, Morris W. and Andrade C. (1997), Carbonation in concrete and effect on steel corrosion, Final Report, State Job No. 99700-3530-119, WPI 0510685, College of Engineering, University of South Floride, 4202 Fowler Avenue, tampa, Floride 33620-5350, 299p
Salvoldi B.G., Beushausen H., Alexander M.G. (2015), Oxygen permeability of concrete and its relation to carbonation, Construction and Building Materials, 85 (2015) 30–37 SANS 10100 (2000), Code of Practice for the Structural Use of Concrete, Part 1, & 2, Part 1: Design,
RI PT
Part 2: Materials. Pretoria, South African Bureau of Standards limited
Sayed-Ahmed M. (2012), Statistical modelling and prediction of compressive strength of concrete, Concrete Research Letters, 3 (2), 452-458
Seung-Jun and Song, Ha-Won (2010), Analysis of carbonation behaviour in concrete using neural
SC
network algorithm and carbonation modelling, Cement and Concrete Research, 40, 119–127
Shimizu Y., Hirosawa M.and Zhou J. (2000), Statistical analysis of concrete strength in existing
Kogakuin University, Tokyo, Japan, 8p
M AN U
reinforced concrete buildings in Japan, Department of Architecture, Faculty of Engineering,
Silva A., Neves R., de Brito J. (2014), Statistical modelling of carbonation in reinforced concrete, Cement and Concrete composites, 50, 73-81
Silva R.V, Neves R., de Britoc J., Dhir R.K (2015), Carbonation behaviour of recycled aggregate concrete, Cement and Concrete Composites, 62, September, 22–32. Talukdar S., Banthia N, Grace J.R (2012), Carbonation in concrete infrastructure in the context of
Composites, 34, 924–930
TE D
global climate, change – Part 1: Experimental results and model development, Cement & Concrete
Tang L., Utgenannt P., Lindvall A. and Boubitsas D. (2010), Validation of models and test methods for assessment of durability of concrete structures in the road environment, CBI Betonginstitutet
EP
AB, 100 44 Stockholm
Torrent R.J, Armaghani J and Taibi Y (2014), Evaluation of Port of Miami tunnel segments:
AC C
carbonation and service life assessemnt made using air permeability test data, Concrete Beton,
Journal of The Concrete Society of Southern Africa, No. 136, March, p.10-16 Underhill L and Bradfield D. (2013), Introstat, Chapter 12 Regression and correlation, Department of Statistical Sciences, University of Cape Town, 271-318 van Ede W.F and Ekolu S.O (2014), Condition assessment of a Johannesburg skyscraper, Proceedings of the International Conference on Construction Materials and Structures (ICCMATS), Johannesburg, South Africa, 24-26 November 2014, 1052-1059 Wang X.Y and Lee H-S (2009), A model for predicting the carbonation depth of concrete containing low-calcium, fly ash, Construction and Building Materials, 23, 725–733
33
ACCEPTED MANUSCRIPT Wendner R., Hubler M., and Bažant Z. (2013), The B4 Model for multi-decade creep and shrinkage prediction. In Mechanics and Physics of Creep, Shrinkage, and Durability of Concrete: pp. 429436. doi: 10.1061/9780784413111.051
Wierig H-J (1984), Longtime studies on the carbonation of concrete under normal outdoor exposure, Proceedings of the RILEM seminar on the durability of concrete structures,
RI PT
Hannover, Germany Xu A, Rodhe M. and Chandra S. (1996), Influence of alkali on carbonation of concrete, Durability of building materials and components, 7, vol. 1, C. Sjostrom (Ed.), Spon, p. 596-604
Yoon I-S, Copuroglu O. and Park K-B (2007), Effect of global climatic change on carbonation progress of concrete, Atmospheric Environment, 41, 7274–7285
SC
Yunusa A.A (2014), The effects of materials and micro-climate variations on predictions of carbonation rate in reinforced concrete in the inland environment, PhD Thesis, School of Civil Engineering & the Built Envir, Univ. of the Witwatersrand, Johannesburg, RSA
M AN U
Zha X., Yu M., Ye J. and Feng G. (2015), Numerical modeling of supercritical carbonation process in cement-based materials, Cement and Concrete Research, 72, 10–20
Zhang L. M. and Jiang W. H. (1990), A study on carbonation of concrete in natural condition and its correlation with artificial accelerated carbonation, Journal of Xi’an Institute of Metallurgy and Construction Engineering, 22 (3), 207-214
Zhang X., Zhou X., Zhou H., Gao K, and Wang Z (2013), Studies on forecasting of carbonation depth
TE D
of slag high performance concrete considering gas permeability, Applied Clay Science, 79, 36–40 Zhijian S.Z., Wang W., Cheng C., Tang X (2013), Predicting method for time-dependent concrete carbonation depth (I): Traditional model and its error distribution, Electronic Journal of Geotechnical Engineering (EJGE), 2013, 2298-2308
EP
Zhu A. M. (1992), Concrete carbonation and durability of reinforced concrete, Concrete, 6 18-21 Sanjuan M.A and del Olmo C. (2001), carbonation resistance of one industrial mortar used as a
AC C
concrete coating, Building and Enviornment, 36, 949-953.
34
ACCEPTED MANUSCRIPT
SC
RI PT
Table 1 Concrete mixtures (Ekolu, 2012)
M AN U
Table 2. Data fitting for model parameters Model type
Cement type
Coefficients
Correlation, R2
Regression
OPC
(cem = 63126, g = -2.304)
0.69
OPC/30FA
(cem = 17823, g = -1.901)
0.72
RHC
(cem = 1643, g = -1.385)
0.84
RHC/25FA
(cem = 1423, g = -1.285)
0.77
all the above
(cem = 950, g = -1.2)
0.08
all the above
(a = 0.25, b = 0.95)
0.99
all the above
(a = 0.35, b = 1.2)
0.30
TE D
Curve fitting
EP
Strength prediction (eqn. 5) Strength prediction (eqn. 5)
AC C
Table 3. Optimization of g-parameter for (a = 0.35, b = 1.2) constant (cem, g) Age (years) Determination coefficient, R2 (1000, -1.4)
(1000, -1.5)
(1000, -1.6)
3.5
0.24
6
0.20
10
0.23
3.5
-0.08
6
0.44
10
0.36
3.5
-0.21
6
0.13
10
0.04
35
ACCEPTED MANUSCRIPT
Table 4 Statistical indicators of the model predictions for carbonation rate Predictions based on long-term concrete strength, fcbn 3½ year data 6 year data 10 year data MV* PV MV PV MV PV 4.76 4.29 4.16 4.48 4.16 4.01 1.11 0.93 1.04 1.16 1.11 1.17 24.4 26.6 28.1
Mean Mean MV/PV RMS CV (%)
Parameter
Average
Carbonation conductance factor (c) Concrete strength (fc), MPa
CV (%)
Min
Constant
-1.5
-1.4
-1.3
10 10 3 3 3 3
25 54 47 52 56 70
30 60 50 55 60 75
35 66 53 58 64 79.5
TE D
Relative humidity (RH), %
30 60 50 55 60 75
Parameter values Mid Max
M AN U
Table 5. Parameters for estimating variability of model outputs
SC
*MV = measured value, PV = predicted value, CV = coefficient of variation
Predictions based on longterm concrete strength, fc28 3½ year data 6 year data MV PV MV PV 4.54 4.73 3.99 3.23 0.96 1.24 1.43 1.23 30.2 38.1
RI PT
Statistical indicators
Table 6. Prediction errors for the proposed model and for fib-Model Structural elements
EP
Sites
Abutments, piers Abutments, piers Abutments, piers, tunnels
AC C
Area I, 64%RH Area II, 67%RH Area III, 75%RH
Coefficient of variation of errors (%) Proposed Model fib-Model 42.3 36.9 46.8 41.6 47.2 45.7
36
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
Figure 1. Parabolic function giving the correction term for relative humidity
37
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
Figure 2. Data fitting and optimization of model parameters
38
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Figure 3. Optimization of g-parameter
39
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
Figure 4. Calibration for predictions based on 28-day concrete strength
Figure 5. Boundary condition for carbonation in low strength concretes below 20 MPa
40
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
Figure 6. Sensitivity analysis for up to 50 years
Figure 7. Comparison of predictions using 28-day strength and long-term insitu strength (UL = upper limit, LL = lower limit)
41
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Figure 8. Scatter plots comparing carbonation prediction by the proposed model and by fib-Model
42
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Figure 9. Residuals for the proposed model and for fib-Model
43
S0958-9465(16)30757-0
DOI:
10.1016/j.cemconcomp.2017.10.006
Reference:
CECO 2922
To appear in:
Cement and Concrete Composites
Received Date: 30 November 2016 Revised Date:
10 April 2017
Accepted Date: 14 October 2017
Please cite this article as: S.O. Ekolu, Model for practical prediction of natural carbonation in reinforced concrete: Part 1-formulation, Cement and Concrete Composites (2017), doi: 10.1016/ j.cemconcomp.2017.10.006. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Model for practical prediction of natural carbonation in reinforced concrete: Part 1-Formulation Stephen O. Ekolu Department of Civil Engineering Science, University of Johannesburg, South Africa, [email protected], [email protected]
Abstract
2
A model is proposed for prediction of natural carbonation in reinforced concrete (RC)
3
structures, and is potentially applicable to existing and new RC structures. The major
4
components of the model comprise mathematical functions applied to predict the influence of
5
concrete composition, and environmental factors on natural carbonation.
SC
RI PT
1
This paper introduces the model concept and explains its structure including derivation,
7
optimization and calibration. Over 163 data sets taken from a 10-year carbonation study were
8
used in the model development and calibration. Only the experimental data that were based
9
on outdoor natural exposure environment were employed in this research. Also in this study,
10
the proposed model is compared with fib-Model Code 2010 using carbonation predictions
11
generated from 346 data sets involving real world, highway structures. It is shown that the
12
proposed model is comparably accurate and involves mainly basic tests with no major
13
anticipated costs.
14
TE D
M AN U
6
Keywords: Carbonation modelling; mathematical formulation; service life; reinforced
16
concrete; supplementary cementitious materials; durability design
17
EP
15
1. Introduction
19
Among the major concrete deterioration processes, corrosion of steel reinforcement is the
20
most widespread and common source of degradation in concrete (PCA, 2002), and is induced
21
either by carbonation from CO2 in the atmosphere or by chloride attack. Prediction models
22
can be used either at design stage for design of new structures or during repair and
23
maintenance of existing structures. For example, models for shrinkage and creep prediction
24
are now employed for design purposes and are recommended in internationally recognized
25
codes such as ACI 209, 1997; BS 8110, 1997; RILEM B3, 1995; Wendner et al., 2013; CEB-
26
FIP 1978, 1990a,b; AS3600, 2009; SANS 10100, 2000. With respect to reinforcement
27
corrosion, no similar achievements have been made in modeling, although some significant
28
progress has occurred over the past two decades, leading to proposal of some practical
AC C
18
1
ACCEPTED MANUSCRIPT models such as the LIFE 365 (Ehlen et al., 2009), Duracrete, 2000 / fib, 2006. In carbonation
30
modeling, the scientific and engineering fraternity has not yet achieved a level of employing
31
models in service life design codes, mainly for lack of plausible validated models. It is often
32
the case in engineering practice that methods that are suitable in particular contexts may not
33
suffice in others. So, development and use of different approaches and methods are needed to
34
provide alternatives.
35
RI PT
29
2. Carbonation prediction models and factors influencing carbonation prediction
37
2.1 Overview of carbonation prediction models
38
Carbonation modeling has been a subject of major interest over the past decades and an
39
extensive body of literature has been generated by researchers. Accordingly, a plethora of
40
experimental carbonation models have been proposed in various works including some
41
extensive literature reviews on the subject (Parrott, 1987; Sagues et al., 1997; Quillin, 2001;
42
Tang et al., 2010; Ikotun and Ekolu, 2012; Zhijian et al., 2013; Czarnecki and
43
Woyciechowski, 2015; Ekolu, 2016). The various types of models existing in the literature
44
may be divided into different categories, viz:
45
1. Empirical models are typically formulated based on relations or expressions developed
46
from experimental measurements. The core component(s) of empirical models are usually
47
mix design or composition parameters especially the water/cementitious ratio (w/cm),
48
cement content; or a material property of concrete. The core parameter for use in a
49
model is usually selected based on the presumption of its ability to depict or correlate
50
strongly with the ingress of CO2 into concrete. As such, empirical models in the literature,
51
may be grouped as follows:
52
(a) Permeability-based models, such as proposed by Parrott (1994), Zhang et al. (2013),
M AN U
TE D
EP
AC C
53
SC
36
Torrent (2014).
54
(b) Diffusion-based models. Examples of these models include those proposed by Xu et
55
al. (1996), Papadakis et al. (1991, 1995), Duracrete/fib (CEB,1997); Duracrete
56
(2000); fib 34 (2006); Tang et al. (2010), Wang and Lee (2009), Kari et al (2014).
57
(c) Strength-based models (Bob, 1999; Hakkinen, 1993; Kokubu and Nagatakis, 1989).
58
(d) Composition-based models (Nishi, 1962; Zhu, 1992; Zhang and Jiang, 1990; He and
59
Jia, 2011; also Parrott, 1987).
60
2. Statistical models are basically data-generated relations obtained through regression of
61
multiple variables and fitting of idealized or standard mathematical functions such as
62
linear, exponential, power, logistic equations, amongst others. Some statistical models of 2
ACCEPTED MANUSCRIPT 63
carbonation include those proposed by Atis (2004), Monteiro et al. (2012), Silva et al.
64
(2014), Hills et al. (2015). 3. Numerical models apply computational approaches that are reliant on computer software
66
for sophiscated analysis. Most numerical models utilize a hybrid of physico-chemical
67
equations representing the thermodynamic reactions and transport processes occurring in
68
concrete. Such models have been proposed by Saettaa and Vitaliani (2004, 2005);
69
Talukdar et al (2012); Zha (2015).
RI PT
65
4. Simulation models apply the artificial neural network technique. The neural network
71
comprises an algorithm consisting of input and output parameters, whose behavior is
72
trained to generate a known set of outputs. A trained algorithm can then be employed to
73
conduct predictions for new input data. Some attempts to apply these approaches have
74
been experimented by Seung-Jun and Song (2010); Luo et al. (2014); Buenfeld et al.
75
(1998).
M AN U
SC
70
76
It may be noted that most of the models in the literature are experimental. Each of the
78
different types of models has its limitations. The statistical, numerical and simulation models
79
typically require a wide range of input parameters including mix composition, environmental
80
exposure conditions, material properties. These include w/cm, cement type, cement content,
81
air content, curing, age; environmental factors of relative humidity and sheltering; diffusion
82
or permeability coefficient, compressive strength. The methods are also highly computational
83
and would often require the aid of computer software and programs. These issues have
84
implications on practical implementation of the models for design of concrete structures.
85
Whereas the concrete composition data for various parameters can be acquired and recorded
86
relatively easily at the construction stage of new structures, it would be extremely difficult to
87
find such data in the case of existing or old structures. It is often the case that for old
88
structures, records of construction data such as mix design, environmental conditions, curing,
89
28-day compressive strength etc., may not be available, perhaps having been lost or not
90
recorded appropriately. Testing of old concrete at late ages does not reliably replace the data
91
that is often acquired during the construction stage. This problem particularly applies to
92
models that are based on mix composition factors.
AC C
EP
TE D
77
93
As such, it is clear from a practical viewpoint that, empirical models based on
94
permeability, diffusion or strength properties of concrete may be advantageous. However,
95
permeability and diffusion properties characteristically give a high coefficient of variation
96
(CV) in the range of 30 to 50% (Hooton, 1988) compared to about 20 to 30% for compressive 3
ACCEPTED MANUSCRIPT strength (Shimizu et al., 2000; Ekolu, 2010; RILEM, 1996). The CV for permeability and
98
diffusion also has a wider spread than that of compressive strength. It has been found that
99
compressive strength property of concrete is effective in relating the influence of pore
100
structure of concrete on CO2 ingress (Silva et al., 2014). Strength also simultaneously
101
accounts for the amount of cement clinker. Besides, compressive strength data are easy to
102
acquire and are readily available from concrete construction, unlike permeability or diffusion
103
whose testing can be relatively complex and costly.
104
RI PT
97
2.2 Factors influencing carbonation
106
2.2.1 Choice of parameters for carbonation modelling
107
The wide range of factors influencing carbonation have been indicated in Section 2.1. These
108
factors may be grouped into four categories consisting of mix composition, material
109
properties, environmental factors, and serviceability conditions. As mentioned earlier,
110
attempting to utilize mix compositional parameters such w/cm, cement content, paste content,
111
hydration products mainly CH, CSH; unhydrated cement phases comprising C2S, C3S, C3A,
112
C4AF; degree of hydration, porosity, can have severe practical limitations. These mix
113
composition characteristics are usually the required inputs into physico-chemical models
114
(Papadakis et al., 1991; Ravahatra et al, 2014)
TE D
M AN U
SC
105
For practical purposes, it is well established that permeability or diffusion and
116
compressive strength are the main performance properties capable of effectively depicting
117
CO2 progression into concrete. Numerous literatures have shown consistent existence of
118
strong correlations between these properties and carbonation, and several experimental
119
models have been proposed on the basis of these relations (Parrott, 1987; Sagues et al., 1997;
120
Quillin, 2001). In the present study, carbonation-strength relationship is considered as the
121
core function which defines the general trend in carbonation prediction, while environmental
122
factors are incorporated as secondary or modifying parameters. As indicated in Section 2.1,
123
use of carbonation-permeability (or diffusion) relationship is undermined by high cost of
124
permeability/diffusion testing and the relatively high variability of permeability
125
measurements.
AC C
EP
115
126
The main environmental factors that significantly influence carbonation are known to be
127
relative humidity, sheltering and rain, CO2 concentration in the atmosphere. These factors are
128
discussed further in the subsequent sections.
129 130
2.2.2 Influence of relative humidity 4
ACCEPTED MANUSCRIPT In the literature (Parrott, 1987; Quillin, 2001), it is known that relative humidity (RH) of 50
132
to 70%RH is the ideal range at which carbonation progression occurs most rapidly in
133
concrete. At RH < 50%, there is inadequate presence of moisture for carbonation reaction to
134
occur. At RH > 70%, pore blockage by water presence tends to inhibit CO2 ingress as
135
concrete becomes more saturated. Carbonation progression is considered to occur maximally
136
at 60% to 65%RH, giving a pessimum or rather a mathematically parabolic relationship
137
between carbonation depth and RH in the vertical and horizontal axes respectively (Weirig,
138
1984; Parrott, 1987; Quillin, 2001).
139
RI PT
131
2.2.3 Influence of carbon-dioxide concentration
141
The gradient between [CO2] at the surface concrete and zero concentration at interior
142
concrete, is the primary driving force for CO2 ingress into concrete. Accordingly, higher CO2
143
concentration gives greater rate of carbonation (Chun et al. 2006; Lagerblad, 2005). It is
144
estimated that [CO2] in urban settings is about 10 times the [CO2] in rural areas or
145
countryside, while industrial areas usually exhibit generally elevated [CO2]. Typically,
146
normal atmospheric CO2 concentration is about 300 ppm, but some heavy traffic and
147
industrial areas would have [CO2] as high as 1000 ppm (Sagues et al., 1997). Fukushima’s
148
(1988) data indicates that an increase of [CO2] from 300 ppm to 600 ppm would raise
149
carbonation rate of concrete five (5) times (Lagerblad, 2005). Accordingly, a correction
150
factor would be required to convert model predictions from one level of [CO2] to another.
151
Ekolu (2016) gives detailed consideration on the influence of [CO2] and provides a correction
152
factor using the generalised relationship, given as
EP
TE D
M AN U
SC
140
α f r for 20 < fc < 60 MPa eco = c 1.0 for fc ≥ 60 MPa
154
Where eco is correction factor, fc is 28-day strength; α,r are given in Equation (10) for
155
various CO2 concentrations
156
AC C
153
157
2.2.4 Influence of temperature
158
With other factors remaining constant, small changes in ambient temperatures do not
159
significantly affect carbonation but high temperatures increase carbonation. Influence of
160
elevated temperature is relevant to arid climates. However, the simultaneous presence of low
161
atmospheric RH may mitigate the effect of elevated temperature. In temperate climates,
162
carbonation would be lower in winter season due to a combination of factors including low 5
ACCEPTED MANUSCRIPT 163
RH and low temperatures which generally retard chemical reaction activity in the outdoor
164
exposure. Generally, regions having similar RH but subject to elevated temperatures such as
165
30 to 40oC would be expected to show relatively increased carbonation activity compared to
166
regions of lower normal temperatures such as 18 to 25oC.
167 2.2.5 Influence of sheltering and rain
169
Precipitation or cyclic wetting /drying exposure are conditions responsible for the difference
170
in carbonation behaviours of sheltered and unsheltered concretes. Under unsheltered
171
exposure e.g. external walls of buildings, exposed retaining walls etc., CO2 ingress into
172
concrete may be intermittent as a result of periods of saturation under wet conditions, that
173
would temporarily block surface pores of concrete. Under sheltered exposure such as in
174
tunnels, bridge abutments, deck soffits etc., partial saturation conditions prevail consistently.
175
These effects are particularly important in environments classified under XC3 or XC4 (EN
176
206, 2000). Indoor exposure also gives higher carbonation depth than outdoor exposure
177
owing to similar reasons explained in the foregoing.
M AN U
SC
RI PT
168
Theoretically, the significance of sheltering effect on carbonation is well-established
179
(Parrott, 1987; Yoon et al., 2007; Gehlen and Sodeikat, 2002), with CEB-FIB (1990b) stating
180
the progress of carbonation, dc = k.tn, in elements sheltered from rain to be of a lower
181
exponent in the range of 0.2 < n < 0.5, implying greater carbonation rates, the maximum
182
carbonation rate corresponding to n = 0.5. In this carbonation equation, dc is carbonation
183
depth, k is the carbonation rate and t is age. Other researches have reported the effect of
184
sheltering to be small and not of statistical significance (Khunthongkeaw et al., 2006; Otsuki
185
et al., 2012).
EP
TE D
178
Attempting to account for effects of unsheltered exposures on carbonation can be quite
187
difficult due to a complex interplay of factors that may not be easy to isolate. Unsheltered
188
exposure is affected by not only the number of rain events but also the amount of
189
precipitation at the different events. This may vary from location to location and year to year,
190
making it quite difficult to generalize except through approximations. Besides, carbonation
191
behavior in unsheltered elements is also influenced by orientation of exposure surface to the
192
vertical or horizontal direction, since this orientation determines the residence time of
193
moisture precipitation after a rain event. For a vertical face, the direction it faces may also
194
influence carbonation, especially its orientation in relation to direction of the sun. The
195
presence of vegetation and other nearby structures that may curtail wind, raindrops, sun
196
radiation on a particular element may also influence carbonation behavior of the element. It
AC C
186
6
ACCEPTED MANUSCRIPT can be seen that accounting for carbonation in unsheltered elements needs detailed
198
examination of the microclimate and associated exposure conditions in the surrounding. It
199
should be considered that sheltered sections of elements give greater carbonation progression
200
than the unsheltered parts. These sheltered sections of the structure result in deterioration well
201
before the unsheltered areas and, so carbonation under sheltered exposure should form the
202
basis for predictions (Parrott, 1987). In cases where unsheltered elements are not crucial, it
203
may be prudent to avoid those areas of the structure when considering carbonation
204
predictions for the structure. But there are structures, although relatively few, that are fully
205
unsheltered such as retaining walls etc. As such, a practical means of accounting for
206
unsheltered exposure in structures is relevant and essential. In Ekolu (2016), natural outdoor
207
carbonation under sheltered and unsheltered exposures was analysed. The study found the
208
ratio (es) of natural carbonation for unsheltered to sheltered exposure in a given environment,
209
to be strength dependent. A general relationship es = fc0.2 was determined for estimating the
210
correction term for unsheltered exposure, where fc is 28-day cube strength.
211
M AN U
SC
RI PT
197
2.2.6 Influence of concrete quality
213
While the mix design, materials and processing factors all affect the quality of concrete, their
214
effects are compounded and realised in the pore structure. Low or poor quality concretes
215
typified by low strengths and high permeability, have a coarse, more open and continuous
216
pore network. Consequently, CO2 ingress is exacerbated in low quality concretes which in
217
turn leads to higher carbonation rates. The converse is true for high quality concretes.
218
Concretes of carbonation rates >10, 5 to 10, <5 mm/yr½ are considered to be of poor, average,
219
good quality respectively (Yoon et al, 2007; Sanjuan and del Olmo, 2001)
EP
AC C
220
TE D
212
221
2.2.7 Cement type and carbonation conductance
222
The use of pozzolans or supplementary cementitious materials (SCMs) in concrete has
223
become conventional. Cement types containing SCMs are now regarded as common cements.
224
All but one of the five cement types in EN 197-1 (2000), contain SCMs. The most common
225
types of SCMs in use are artificial pozzolans, fly ash (FA), ground granulated blast furnace
226
slag (GGBS) and silica fume (SF). But their use in cement has some implications on
227
structures. Apart from the environmental benefits, SCMs are known to improve durability of
228
concretes in properly designed mixtures. One of the disadvantages of SCMs is their
229
promotion of carbonation in concrete. When incorporated into concrete, SF, FA, GGBS, and
230
all the common pozzolans will increase carbonation of concrete relative to control. The rate 7
ACCEPTED MANUSCRIPT of carbonation is proportional to the amount of SCM in the mixture, with higher SCM
232
contents giving higher carbonation progression as shown by numerous studies in the literature
233
(Parrott, 1987, Lagerblad, 2005). Their effect is related to chemical dilution resulting from
234
reduced clinker content when some quantity of Portland cement is replaced by SCM. Not
235
only are less hydration products formed in SCM concretes, an important factor affecting the
236
infilling of initial pore spaces within the mixture, but pozzolanic activity also requires longer
237
curing under saturated conditions compared to hydration of ordinary Portland cement.
RI PT
231
Since SCM cement types promote carbonation relative to baseline ordinary Portland
239
cement or CEM I, an analogy of electrical conductance can be used whereby CO2 ingress is
240
considered to be the equivalent of an electrical flux. The rate at which a cement type
241
promotes carbonation can then be regarded in terms of carbonation conductance of the
242
cement. This concept is applied later in model derivation given in Section 3.3. The use of this
243
term here is strictly confined to the promotional effect of SCM cements on carbonation.
M AN U
SC
238
244
2.2.8 Influence of cracks and surface treatments
246
Cracks provide a direct pathway of CO2 into the concrete cover, leading to early
247
deterioration. Cracks larger than structural crack sizes of typically 0.2 mm should be regarded
248
as adverse and would cause greater CO2 ingress into concrete to the extent dissimilar to
249
uncracked concrete. Conversely, surface treatments such as paints and coatings are
250
preventative measures to external ingress of aggressive agents, and accordingly retard the
251
attack processes. Studies show that paint coatings on concrete surfaces can effectively retard
252
carbonation (Otsuki et al., 2012).
EP
253
TE D
245
2.2.9 Influence of special aggregates and recycled concretes
255
Special aggregate types comprise lightweight, heavyweight and recycled aggregates. The
256
effects of these special aggregate types on carbonation differ from influence of normal
257
aggregates. When used in concrete, recycled aggregates lead to higher carbonation relative to
258
normal aggregates (Silva et al. 2015; Lagerblad, 2005). The present study is limited to
259
concretes made using normal aggregates.
AC C
254
260 261
2.2.10 Influence of curing
262
Curing of concretes is responsible for the development of material properties at early ages.
263
Accordingly one can expect different curing types to influence concrete properties differently
264
and in turn correspondingly affect carbonation behaviour of the concrete. Different types and 8
ACCEPTED MANUSCRIPT lengths of curing are employed in concrete. The most common curing methods are moist-
266
curing, steam-curing, curing admixtures. When a given concrete mixture is subjected to the
267
different curing types, each method does produce different results. It would be concerning if a
268
model has to account for each type of curing and its duration. Infact, such information would
269
be quite difficult to obtain, especially for existing structures. Fortunately, it is interesting to
270
note from literature that the influence of different curing types dissipates in the long-term, for
271
structures exposed to natural outdoor environments (Greve-Dierfeld and Gehlen, 2014) as
272
shown by Buenfeld and Yang (2001). Cements containing SCMs particularly gain more
273
strength development and corresponding reduction in carbonation rate when heat-cured or
274
cured longer under moist conditions. However, it appears that these benefits are mainly
275
pronounced at early ages. At later ages after long-term exposure under field conditions of at
276
least 18 months, the differences from early-age beneficial effects of different curing types on
277
carbonation, become insignificant (Parrott, 1996, Balayssac et al. 1995). A detailed
278
evaluation on influence of various curing methods and durations on natural carbonation
279
[Ekolu, 2016] concluded that use of different common curing methods does not lead to major
280
change in natural carbonation behaviour. It was shown that a minimum of three-day moist
281
curing or its equivalent is sufficient for concrete to achieve stable behaviour against
282
carbonation. Accordingly, this paper does not give special consideration to account for
283
curing effects provided the minimum site curing requirements are achieved, as discussed in
284
Ekolu (2016).
285
TE D
M AN U
SC
RI PT
265
3. Formulation of model
287
3.1 Experimental data
288
The proposed model was developed using data from an extensive 10-year experimental
289
investigation reported in CSIR (1999). Table 1 gives the various mixtures used (Ekolu 2012).
290
In the experiment, concretes of strengths 25, 35 and 50 MPa were prepared in 100 mm cubes
291
cast using ordinary Portland cement (OPC) and rapid hardening Portland cement (RHC).
292
Altogether 21 mixtures were prepared in 62 batches, all of slumps 50 to 70 mm. The mix
293
designs consisted of w/cm ratios varied from 0.46 to 0.78, and binder contents ranging from
294
240 to 490 kg/m3. The mixtures contained 15 to 50% fly ash (FA). Different curing regimes
295
were applied viz: 28-day fog room curing (regime-a), 28-day 50%RH/23oC curing (regime-
296
c); 24-hour curing at 80%RH /50oC plus 27 days at 50%RH/10oC (regime-b); 24-hour steam
297
curing at 60oC plus 27 days at 50%RH/23oC (regime-d); 24-hour oven-dry curing at 40oC
298
plus 27 days at 50%RH/23oC (regime-e). After 28 days of the various curing regimes and
AC C
EP
286
9
ACCEPTED MANUSCRIPT 299
treatments, samples were exposed to natural weather at a building roof. The typical
300
environmental conditions at this site location are: annual average of 60%RH, 17.3oC and 517
301
mm precipitation. Concrete strengths and carbonation measurements were done on site
302
exposed cubes, at ages of 3.5, 6 and 10 years. The use of compressive strength as the main performance property in the core function of
304
the model was preferred over permeability or diffusion owing to the overwhelming merits of
305
the former over the latter, as discussed under Section 2.1. The limitation of the data (CSIR,
306
1999) used to structure and calibrate the model during its development was absence of some
307
aspects of data that would be valuable. Such limitations are understandable since the
308
investigation (CSIR, 1999) was not purposely conducted to generate data for modelling.
309
Accordingly, some of the parameters were either not varied widely or not at all included as
310
part of the investigation. A case in point is the effect of RH which was not varied since all
311
samples were stored in the same site location. Also, a study on the effect of sheltering was
312
not part of the investigation. However, it is nearly impossible to find a relevant and extensive
313
investigation which incorporates each and every requirement for model verification,
314
especially when an investigation was not initially conducted for such a purpose.
315
Notwithstanding the foregoing, the CSIR (1999) study was quite comprehensive, covering
316
several variables and yielding high quality data. Use of these data has been crucial to
317
development of the proposed model.
TE D
M AN U
SC
RI PT
303
318 319
[Insert Table 1]
EP
320 3.2 Mathematical laws
322
This study essentially applies basic mathematical laws to carbonation prediction in concrete.
323
The seemingly, random material behavior and unrelated results of the various individual
324
concrete types, can be captured mathematically into a universal method which accounts for
325
the major factors of influence involving the phenomenon. However, a number of key steps
326
need to be undertaken in developing such a model (Bazant and Panula, 1978). Firstly,
327
appropriate mathematical laws must be identified and expressed in combined or suitably
328
structured forms of functions. Secondly, material coefficients used in the functions must be
329
determined, usually from experimental measurements conducted in the laboratory or from
330
real world conditions of the natural environment. An important challenge here is to establish
331
coefficients that account for concretes of various types, their heterogeneities and related
332
factors of influence. Appropriate coefficients are adopted once it can be shown that their use
AC C
321
10
ACCEPTED MANUSCRIPT consistently leads to reasonable prediction of the phenomenon. The third step is to establish
334
the conditions at which a particular model is applicable, accordingly defining its limitations.
335
Robustness of a model is demonstrated by its ability to apply universally to the various
336
concrete materials and/or types, and different environmental factors, while maintaining
337
reliable predictions. The study presented in this paper, covers all the above three steps,
338
leading to derivation of the proposed model functions and related coefficients. For calibration
339
purposes, comparison of measured and predicted observations was undertaken along with
340
statistical error analysis. Limitations of the model were also determined. The proposed model
341
was formulated using mathematical functions that are based on the following governing laws:
342
(1) Square-root function of time for carbonation, derived from Fick’s laws of diffusion
SC
343
RI PT
333
(Kropp, 1995; Liang et al, 2002).
(2) Growth rate function of time for compressive strength (ACI 209, 1997).
345
(3) Parabolic function for carbonation dependence on humidity (Quillin, 2001; Parrott,
346 347 348
1987; ACI 209, 1997).
M AN U
344
(4) Inverse power function for carbonation conductance by common cements of various types (Parrott, 1987).
In the process of developing the proposed mathematical model presented in this study, a great
350
deal of guidance was drawn from several literatures on this subject. These include the
351
published literature on theoretical mathematical relations for the carbonation phenomena
352
(Kropp, 1995; Liang et al, 2002) and on structuring of model components (Liang et al, 2002;
353
Hakkinen, 1993; RILEM, 1996)
EP
354
TE D
349
3.3 Derivations, data fitting and optimization
356
The model construction was intended to bear the merit of simplicity without compromising
357
the model’s performance and prediction accuracy. In assembling the model components,
358
consideration was given to using a minimum number of parameters, while preserving
359
robustness. Based on the mathematical laws discussed in the foregoing, the governing model
360
function was taken to be the square-root law given as dc = K.t½, where dc is the carbonation
361
depth, K is the carbonation coefficient of concrete and t is time or age of concrete. Prediction
362
of K is complex and remains to be the important overarching objective of prediction
363
modelling. From the literature discussed in the foregone, material factors consisting of
364
compressive strength and cementitious materials were identified to be the core or primary
365
parameters, while environmental factors comprising relative humidity, curing, sheltering, rain
366
were taken as secondary parameters which only modify the core carbonation behavior of the
AC C
355
11
ACCEPTED MANUSCRIPT 367
material system. The core parameters were expressed in mathematical functions and co-
368
joined into a coherent model structure. Since both, the carbonation process and compressive
369
strength growth are time-dependent; and strength is in turn influenced by cementitious
370
materials, the model concept can be expressed as
371
dc(t) = f(RH, shl, CO2).f(cem, fc(t)). t½
(1)
where dc(t) is the predicted time-dependent carbonation depth, f(RH, shl, CO2) is
373
environmental function(s) or terms accounting for the secondary effects of RH, [CO2], and
374
sheltering. The proposed model accounts for the influence of CO2 concentration as discussed
375
in Section 2.2.3. It applies [CO2] range of 300 to 400 ppm as its baseline. This range of CO2
376
concentration is typical of pollution levels at atmospheric conditions in urban settings.
377
Accordingly, correction factors are needed to account for different levels of [CO2] (Equation
378
10). The function f(cem, fc,t) represents time-dependent compressive strength and related
379
influence of cementitious materials used in the mixture. It gives the core carbonation
380
behavior of a given concrete material system.
M AN U
SC
RI PT
372
381
3.3.1 Functions for relative humidity and sheltering
383
(a) Correction terms for sheltered and unsheltered outdoor exposure
384
Ekolu (2016) used data taken from various studies to determine the correction term (es) for
385
unsheltered exposure environments relative to sheltered exposure, for concretes under the
386
same microclimate. The expression es = fc0.2 (Section 2.2.5) which was derived in Ekolu
387
(2016) is used in the proposed model. It should be recognized that some field conditions
388
cannot be fully accounted for by this equation such as the effects of vertical or horizontal face
389
allignment, orientation of elements to the sun, wind factor etc. as discussed Section 2.2.5.
EP
AC C
390
TE D
382
391
(b) Parabolic function for relative humidity
392
In Section 2.2.2, the influence of RH is discussed. Applying a RH correction factor,
393
incorporates versatility as this allows broader application of the model to various
394
geographical settings or climatic conditions. A RH - carbonation relationship must be known
395
under outdoor natural exposure conditions in order to develop a relevant mathematical
396
function. In this study, Weirig’s (1984) data were considered appropriate to use (Parrott,
397
1987). The data were curve-fitted to produce the expression for the RH correction factor, as
398
given in Equation (2). Figure 1 gives a plot of the correction term (eh) to account for changes
399
in ambient RH. It can be seen that the parabolic equation maintains eh =1.0 for 60 to 65% 12
ACCEPTED MANUSCRIPT RH, being the optimum RH for carbonation. The factor for lower and higher humidity levels
401
are gradually scaled down according to the parabolic relationship. In developing the present
402
RH equation, research conducted by Gardner (2004), ACI 209 (1997), Hassoun and Al-
403
Manaseer (2012), Muller and Hilsdorf (1990), Salvoldi et al. (2015), provided very useful
404
guidance. Based on understanding of RH influence on carbonation, as discussed earlier, the
405
author configured the parabolic RH function given in Equation (2), to be applied within the
406
range of 50 to 80% RH.
407
RH − 35 RH e h = 16 1 − 100 100
for 50% ≤ RH ≤ 80%
408 409
[Insert Figure 1]
410
(2)
SC
1.5
RI PT
400
3.3.2 Growth rate function for compressive strength
412
The mathematical concept needed to represent concrete strength as a function of time, was
413
identified to be the general growth rate Equation (3) recommended by ACI 209 (1997).
M AN U
411
414 Fc(t) =
t .f c28 a + bt
(3)
TE D
415
Where fc28 is the mean compressive strength at 28 days, Fc(t) is concrete strength at any time,
417
t while a, b are constants. In Equation (3), both the a-parameter and b-parameter are
418
influenced by cement type and curing type. Typically, for moist-cured concretes, a = 0.4, b =
419
0.85 for Type I ordinary Portland cement, and a = 2.3, b = 0.92 for Type III rapid hardening
420
Portland cement. It should, however, be noted that these coefficients apply to concretes
421
subjected to continuous moist curing and may not directly apply to concretes stored at
422
outdoor natural environment. Also, it should be considered that carbonation leads to
423
enhancement of concrete strength as a time-dependent variable. Accordingly, it becomes
424
necessary to modify the equation for purposes of strength prediction under the influence of
425
carbonation in the natural environment. As mentioned earlier, the experimental data reported
426
in CSIR (1999) were used throughout this process.
AC C
EP
416
427
During the process of data fitting, it was found impossible to de-couple the influence of
428
cementitious materials from the strength growth function. By introducing a coefficient which
429
is a scalar quantity, and an exponent to Fc(t), a correct prediction of carbonation behavior is
430
possible. Essentially, this leads to an inverse power function developed by modification of
431
Equation (3) to allow for composition effects, giving rise to Equation (4) 13
ACCEPTED MANUSCRIPT f(cem, f c(t) ) = cem.(Fc(t) )
g
432
(4)
Where cem is a scalar quantity for cement, and g is a shape factor but it really represents the
434
rate at which different cement types promote CO2 ingress, which is analogous to electrical
435
“conductance” of CO2 flux (Section 2.2.7). The term carbonation conductance factor is
436
therefore used in the present model to refer to, g. Both factors (cem, g) are dependent on the
437
type and proportion of cementitious materials used in the concrete.
RI PT
433
At this point, there are four unknowns (a, b, cem, g) whose values are to be determined
439
for each concrete material system under consideration. Determination of these constants was
440
done by data fitting and optimization operations conducted through an interative process
441
involving trial and error, regression, and curve-fitting methods, applied to data. Data fitting
442
was conducted on: (a) strength, fcbn at long-term ages of 3.5, 6 and 10 years; (b) strength, f28
443
at 28 days.
M AN U
SC
438
444
(a) Coefficients based on insitu concrete strength at long term ages
446
Initially, the graphs of long-term insitu concrete strength, fcbn versus measured carbonation
447
depths were plotted for ages of 3.5 and 6 years, and for cement types consisting of OPC and
448
RHC, with or without FA. Specifically, the graphs in Figure 2 were plotted for OPC,
449
OPC/30FA (i.e OPC containing 30% FA), RHC, RHC/25FA. Power curve regressions were
450
applied to each of the graphs. Expectedly, wide ranging coefficients and exponential factors
451
were obtained for each cement type, as shown in Table 2. At first sight, the regression
452
relationships appear spurious and unrelated. However, upon varying cem and g by means of
453
trial and error, a consistent relationship emerges, which was curve-fitted to approximately
454
cem = 950, g = -1.2. The scalar quantity was conveniently rounded-off to cem = 1000. Also,
455
trial constants (a,b) were estimated for strength prediction based on use of fcbn in lieu of f28.
456
Equation (5) was obtained as discussed later in this section.
AC C
EP
TE D
445
457
The Least Squares Method (LSM) was applied to examine the goodness-of-fit of the
458
models to the observed data. According to the method, the goodness-of-fit of a model y =
459
f(x) to observed data is evaluated by determining the sum of squared residuals or errors
460
(SSE). i
461
2
SSE = min ∑ [ f ( xi ) − yi ] , Where yi is the observed value. 1
14
ACCEPTED MANUSCRIPT 462
Accurate models give minimum SSE. The method can be used to optimize data fitting
463
through adjustment of the model coefficients. Also useful is the total sum of the error squares
464
(SST), calculated as (Sayed-Ahmed, 2012; Underhill and Bradfield, 2013) 2
_ _ SST = ∑ yi − y , where y is the average of observed values. 1 i
466 467
The coefficient of determination (R2) is obtained from the expression R 2 = 1−
RI PT
465
SSE SST
In this study, the various trial models (Figure 2) were analysed using the LSM method, giving
469
results shown in Table 2. It is however emphasized that the curve fitting method is used here
470
to establish the form of model based on carbonation-strength relationship, rather than fixed
471
values of the coefficients, at this early stage. Infact, other than a = 0.35, all the parameters in
472
the models determined for the carbonation-strength derivation, had to be adjusted iteratively
473
during optimization and calibration, as later discussed. These adjustments should be
474
understood in context of solving a 3D relationship between carbonation progression, strength
475
and time. From this point, two other relationships must be solved i.e. carbonation-time and
476
strength-time relations, which must then be compounded with the carbonation-strength
477
relationship.
TE D
M AN U
SC
468
Accordingly, the next stage was to data-fit the constants (cem, g) and (a, b) so as to
479
account for time-dependent behaviour. From mathematical knowledge of curves, the shape
480
factors for the functions are, g, for the inverse power curve and, b, for the growth rate curve.
481
To optimize the coefficients, the procedure adopted was:
483 484
(i) Varying g-value with age, while keeping (a = 0.35, b = 1.2) constant. This step leads to optimization of the g-value. (ii) Varying b-value with age, while keeping (a = 0.35, cem = 1000, g) constant
AC C
482
EP
478
485
The optimization was conducted using data of 3.5, 6 and 10 years. To simplify the process, g-
486
values used were limited to -1.4, -1.5, -1.6. Table 3 shows the coefficients of determination
487
obtained by varying the g-value. It is evident that the best data fit is given by g = -1.5 having
488
the best R2 value, overall. In interpreting the optimization given in Table 3, it is important to
489
note that while the best R2 is sought, it is not necessary to consider its numerical value in
490
terms of statistical significance.
491
The results given in Tables 2 and 3 can also be seen in the graphs shown in Figure 3 for g
492
= -1.4 and g = -1.5. As the g-value decreases, the carbonation rate predictions tend to shift
493
lower. A similar trend was observed for g = -1.6. A close inspection of the graphs shows that 15
ACCEPTED MANUSCRIPT the data fit is affected by age. Notably, the data fit for g = -1.5 at 3.5 years is poor compared
495
to the other ages. Similarly, the data fit for 10-year age is slightly offset, relative to that of 6
496
year data. This explains the R2 - value of -0.08 obtained at 3.5 years as compared to 0.44 and
497
0.36 for the ages of 6 years and 10 years respectively. These results imply that g-value alone
498
does not account for age-related effects and other parameter(s) need to be adjusted to allow
499
for time-effects. This naturally led to optimization of b-value as a necessary step, since it is
500
the only other key factor influencing the curve shape. To conduct this operation, cem = 1000,
501
g = -1.5, a = 0.35 were maintained constant while b-value was adjusted to obtain the optimum
502
value for each age 3.5, 6, 10 years.
503 [Insert Table 2]
505
[Insert Figure 3]
506
M AN U
504
SC
RI PT
494
507
As seen in the above analysis, the g = -1.5 data fitting was optimized at 6 year age with
508
(a=0.35, b = 1.2). Using this as a starting point and optimizing the data fitting for 3.5 year and
509
10 year data, b = 1.27 and b = 1.1 were obtained respectively. By conducting linear
510
regression, the equation b = 1.3-0.02t is obtained. b = 1.3 − 0.02t
(5)
TE D
511
However, recalling that b-value is the shape factor of the growth function given in Equation
513
(5), an inspection of the prediction curve based on Equation (5) quickly identifies 15 year age
514
as a crucial turning point that determines the type of curve, to be either an exponential curve
515
if the expression is used in the form given in Equation (5) or a growth curve when the
516
expression is restricted to b = 0.9 for ages greater than 15 years. The latter is undoubtedly the
517
appropriate function.
AC C
518
EP
512
519
(b) Coefficients based on concrete strength at 28 days
520
In order to use 28-day strength, fc28 of concrete for prediction of carbonation, the optimization
521
operation conducted above for long-term strength, fcbn was repeated using 28-day strength
522
data to determine the coefficients (cem, g, a, b). The same cement factors (cem = 1000, g = -
523
1.5) are applicable under both the long-term strength and 28-day strength. However, data
524
fitting and optimization gives a = 0.35 and Equation (6) for the b-value, based on fc28.
525
b = 0.6 − 0.02t
(6)
16
ACCEPTED MANUSCRIPT To maintain the growth curve shape, b = 0.4 must be constant for ages greater than 10 years.
527
But it was found that disjointing arises at the points where b in Equations (5) and (6)
528
transition to their respective constants. So, a purely mathematical operation was conducted to
529
develop the respective continuous functions equivalent to those given by Equations (5) and
530
(6) and adjusted for long-term behavior. This operation produced the Equations (11a,b) and
531
(12a,b). With Equations (5) and (6) derived, the optimization process was repeated based on
532
cement type. During the process, the conductance factors, g that were found to correctly
533
curve-fit the carbonation behaviors of the different cement types were: g = -1.5 for OPC,
534
RHC, 15%FA and g = -1.4 for 30%FA.
535
SC
RI PT
526
3.3.3 Accounting for influence of different cement types
537
The dual cement conductance factors (cem, s) account for the promoting influence of SCMs
538
on carbonation. The model allows for cement types containing up to 30% fly ash (FA) or
539
50% slag (SG) or 10% SF. These SCM proportions are equivalent to CEM I and CEM II
540
varieties of EN 197-1 (2000).
M AN U
536
The inclusion of the other SCMs (SF, SG) in the model specification has been partly
542
based on literature and inference from correlation behaviours. It is known that correlation
543
exists between the carbonation behavior of FA and other SCMs. CEM I and CEM II varieties
544
give similar long-term carbonation behaviours (Greve-Dierfeld and Gehlen, 2014).
545
Khunthongkeaw et al. (2006) reported that CEM I with or without 10% FA of Class C and
546
Class F (equivalient of CEM II/A) exhibited the same carbonation rates. Also, Ali and
547
Dunster (1998) showed that 30%FA had the same carbonation rate as 50% GGBS cements.
548
Studies on South African SCMs show that 10%SF, 30%FA and 50%GGBS give similar
549
carbonation behaviours (Alexander et al. 2001).
AC C
EP
TE D
541
550
Also in classifying cements, the EN 197-1 (2000) allocates the same cement class for FA
551
and GGBS, i.e. CEM II/A would contain, 6-10%SF, 6 to 20% FA or GGBS. CEM II/B would
552
contain 21 to 35% FA or GGBS which implies that within this range of the SCMs, FA and
553
GGBS would be expected to behave similarly. Infact EN 197-1 allows the use of any type of
554
SCM for CEM II provided its proportion is limited to 35%, as specified in Portland
555
composite cement CEM II/A-M and CEM II/B-M. This suggests that the SCMs may be used
556
interchangeably within these limits and they would be expected to show similar behaviours.
557
The experimental data (CSIR, 1999) used in this study had mixtures containing 0, 15, 30,
558
50% FA, which cover a wide range of cement varieties CEM I to CEM IV as given in
559
Equation (13). 17
ACCEPTED MANUSCRIPT 560 3.3.4 Model formulae
562
From derivations and the associated mathematical functions presented in the foregone
563
discussion, the complete model is expressed in Equations (7) to (13), and consists of: (1) the
564
material performance property, being concrete strength, (2) relative humidity, shelter, [CO2]
565
as the main environmental factors, and (3) the material composition represented by cement
566
type. In the proposed model, carbonation under both sheltered and unsheltered outdoor
567
exposure conditions are considered (Equation (9)). The correction factors for unsheltered
568
exposure were derived in Ekolu (2016), as explained in Section 2.2.5. The model also
569
accounts for carbonation under different levels of [CO2] taking concentrations of 300 to 400
570
ppm as baseline and giving correction factors for higher or lower CO2 concentrations using
571
Equation (10). Derivation of this equation is given in Ekolu (2016) as explained in Section
572
2.2.3.
M AN U
SC
RI PT
561
Curing methods and their effects are not considered to be of significant influence to long-
574
term carbonation (Section 2.2.10), provided a minimum of 3-day site curing or its equivalent
575
is achieved as typically required by recognized standard specifications (Ekolu, 2016). Based
576
on this condition, curing is not included as a separate parameter in the model. However,
577
curing effects are embedded in the cement type and concrete strength, both of which are
578
accounted for in the model. The mean 28-day cube strength, fc28 obtained from laboratory
579
moist-curing or insitu strength of concrete, fcbn extracted from existing structure at a given
580
age of its service may alternately be used by employing Equations (11a,b) and (12a,b),
581
respectively. No accelerated methods such as accelerated carbonation, permeability tests etc.
582
are used in any parameter of the model. Also, the model is not for use under indoor
583
conditions of exposure.
EP
AC C
584
TE D
573
585
3.3.5 Calibration
586
Following the formulation discussed in the foregone sections, the model was calibrated
587
against experimental data. The calibration was an iterative process consisting of adjustments
588
to the model structure until its predictions were deemed acceptable. The model calibration
589
was done under the use of long-term concrete strengths, fcbn and under the use of 28-day
590
concrete strengths,fc28. The process employed use of data generated under different curing
591
regimes. Accordingly, the significance of curing on model predictions was examined. In the
592
evaluation, the model was used to predict carbonation depth or rate which in turn was
593
compared statistically against measured values. 18
ACCEPTED MANUSCRIPT 594 595 d (f, t) = e h . e s . e co .cem (Fc(t) ) . t g
596
(7)
597
Environmental factors for relative humidity and shelter:
598
RH − 35 RH e h = 16 1 − 100 100
599
1.0 for sheltered outdoor exposure es = -0.2 f c for unsheltered outdoor exposure; f c is 28 − day strength
600
Environmental factors for varied CO2 concentrations:
601
α f r for 20 < fc < 60 MPa eco = c 1.0 for fc ≥ 60 MPa Correction factor ec = αfc
fc ≥ 60
ec = 1.0
200 ppm 1.4 -1/4
606
(a) Using 28-day strength, (fc28)
608 609 610 611 612 613 614 615 616
EP
605
Time-dependent strength growth function (Fc(t)): t Fc(t) = .f c a + bt
607
RI PT
SC
(9)
(10)
CO2 concentration level 300 ppm 500 ppm 1000 ppm 1.0 2.5 4.5 0 -1/4 -2/5
2000 ppm 14 -2/3
TE D
20 < fc < 60
α r
r
(i) Short-term ages, t < 6 years a = 0.35, b = 0.6 − t
AC C
604
(8)
Where α,r are correction factors for natural carbonation under varied CO2 concentrations: 28-day strength (MPa)
603
for 50% ≤ RH ≤ 80%
M AN U
602
1.5
0.5
50
(11a)
(ii) Long-term ages, t ≥ 6 years a = 0.15t, b = 0.5 − t
0.5
50
(11b)
(b) Using long-term (field) strength, (fcbn) (i) Short-term ages, t < 15 years a = 0.35, b = 1.15 − t
0.6
50
(12a)
(ii) Long-term ages, t ≥ 15 years a = 0.15t, b = 0.95 − t
0..6
50
(12b) 19
ACCEPTED MANUSCRIPT 617 618 Cement factors for carbonation conductance: SCM
Cement types
20% any 30% fly ash 50% slag
CEM I, CEM II/A CEM II/B, CEM IV/A CEM III/A, CEM IV/B
(13) Scalar, cem 1000 1000 1000
Conductance factor, g -1.5 -1.4 -1.4
RI PT
619 620
621 622 623 624 625 626 627
Notes: Cube strength (fc) is related to core or cylinder strength (fcyl) through the conversion, fc = 1.25 fcyl. Strength values used in the equations must be ≥ 20 MPa. Moist-cured 28-day strength (fc28) is related to insitu strength (fcbn) using the expression, fcbn = fc28+13.
628
In order to examine the accuracy of the model, it is essential to conduct unbiased
629
statistical analysis of its predictions. For this purpose, the Root Mean Square (RMS) method
630
was employed (Bazant and Panula, 1979). RMS is the square root of the average of residuals
631
between measured values (MV) and predicted values (PV). By dividing the RMS by the
632
mean of measured values in the data set, a coefficient of variation (CV) of errors is obtained.
633
This parameter can suitably be used to compare model predictions with measured results. It
634
should be noted that this CV, is determined somehow differently from conventional CV
635
defined as the ratio of standard deviation to mean. The former is determined on the basis of
636
two variables (MV, PV) while the latter applies only to a single variable (MV or PV). Also
637
used as a statistical indicator is the ratio of average MV to average PV.
TE D
M AN U
SC
*SCM – supplementary cementing materials, NP – natural pozzolan
Figure 3 (g = -1.5) gives the model predictions made based on long-term concrete
639
strengths while comparison of measured values to predictions made based on 28-day concrete
640
strengths, is given in Figure 4. While the general fitting may look visually reasonable, as the
641
results lie along the line of equality, it is through statistical error analysis that the accuracy of
642
predictions can be effectively examined. Table 4 gives the statistical indicators showing the
643
predicted values relative to the measured values for predictions based on long-term concrete
644
strength and predictions based on 28-day concrete strength. For the model predictions based
645
on fcbn, the MV/PV ratio lies between 0.9 to 1.1; an average of 1.0. This result indicate that
646
the predicted values are nearly the same as the actual measured value of carbonation rate. The
647
MV/PV ratio for predictions based on 28-day concrete strength appear to be slightly higher,
648
giving between 1 to 1.2. However, these differences may vary depending on the data settings
649
and their embedded errors.
AC C
EP
638
The coefficient of variation of the model prediction is
20
ACCEPTED MANUSCRIPT 650
consistently between 23% to 33% and falls within the typical range of accuracy known for
651
code-type models (Bazant and Baweja, 1995). Finally, a boundary condition was determined prescribing model predictions to be invalid
653
for concrete strengths below 20 MPa. In the literature (Parrott, 1990; Guiglia and Taliano,
654
2013), the measured carbonation rate in real structures, indoors is reported to be about 10
655
mm/yr½ for low strengths of 21 MPa, compared to 5 mm/yr½ for medium strength and 2
656
mm/yr½ for concrete strengths > 45 MPa. Other researches (Ali and Dunster, 1998;
657
Lagerblad, 2005) have reported carbonation rates for outdoor sheltered environments to be
658
3.8, 6.2, 6.2 mm/yr½ for C30 concrete made with OPC, 30%FA and 50%GGBS respectively.
659
Concretes of strengths under 20 MPa are regarded as low strength, typically non-structural
660
concretes. In this study, it was found that when the strength of concrete falls below 20 MPa,
661
model predictions become drastically high. In order to examine this behavior, borderline data
662
sets were selected with values lying slightly above and below 20 MPa. Figure 5 gives the
663
difference in carbonation predictions when these strength data were plotted. It can be seen in
664
Figure 5 that when concrete strengths fall below 20 MPa, predictions rapidly rise higher
665
correspondingly with further decrease in strength. As such, the model in its current version is
666
not appropriate for concretes of strengths less than 20 MPa.
M AN U
SC
RI PT
652
667
[Insert Figure 4]
TE D
668 669
[Insert Table 4]
670
[Insert Figure 5]
671 3.3.6 Sensitivity analysis
673
Equations (9) to (13) of the model comprise primarily of material properties of concrete
674
(strength, cement type) and environmental exposure conditions (RH, sheltering, CO2 levels).
675
The method employed in sensitivity analysis was to identify the main parameter variables of
676
the model, then a range of boundary values for each input parameter was fixed at two
677
standard deviations and used to assess the parameter’s influence towards variation of model
678
output. Table 5 gives the model parameters and range of values used. Apart from strength
679
that was examined for medium strength and high strength concretes of 30 MPa and 60 MPa
680
respectively, the other parameters apply generally to the model. Figure 6 gives the results of
681
sensitivity analysis. It is evident that the parameters considered are important contributors to
682
variability of model outputs, as seen by significant changes when they were varied across
683
predetermined boundary values. The conductance factor is perhaps the most sensitive
AC C
EP
672
21
ACCEPTED MANUSCRIPT parameter in the model and should be strictly selected according to the respective cement
685
type. For example, a wrong choice of g = -1.4 in place of g = -1.5 would alter model outputs
686
of predicted carbonation by 40%. Such errors are possible if there are no clear details
687
available concerning the type of cement used in the concrete. Variability of the strength
688
parameter is dependent on strength grade (Figure 6b), with high strength concretes
689
contributing lower output changes of 12 to 16% for 60 MPa concrete compared to 20 to 30%
690
for 30 MPa concrete. The relative humidity parameter introduces errors of up to 15% for
691
50%RH or 75%RH. Evidently, sensitivity is remarkably low for 55 to 65%RH, an important
692
level of RH for carbonation.
RI PT
684
In addition, comparison of predictions obtained using fc28 and using fcbn is made to assess
694
closeness of results obtained from the two values. The assessment was conducted based on
695
the relationship fcbn = fc28+13, having been determined empirically using CSIR (1999) data.
696
The comparison covers all concrete strengths from 20 to 90 MPa for ages up to 100 years. In
697
Figure 7, it is seen that use of fcbn gives about 2 to 5 mm higher carbonation depths than the
698
values obtained using fc28. The difference in depths is about 4 to 5 mm for strengths of 20 to
699
50 MPa, diminishing to under 3 mm difference with increase in strengths up to 90 MPa. The
700
various concrete strengths give residuals falling within the 95% limits, and this behavior of
701
the model is consistent throughout the 100 year age. However, there are minor deviations at
702
ages below 5 years and above 60 years, where strengths greater and lower than 40 MPa
703
respectively, tend to breach the 95% limits. Overall, there is good agreement between results
704
obtained from the two values, fc28 and fcbn. Accordingly, fc28 and fcbn may be used
705
interchangeably in carbonation prediction, depending on the available data.
M AN U
TE D
EP
706
SC
693
3.3.7 Boundary conditions and constraints
708
Although several assumptions are embedded in the model, these are deemed necessary for
709
mathematical simplifications and adjustment of theoretical derivations to practical
710
engineering application. These assumptions mainly contribute to variability. The limitations
711
subsequently discussed, have been established during calibration of the model response to
712
data from outdoor natural environment.
AC C
707
713
In employing the model, concretes should be of cube strengths > 20 MPa made of the
714
specified cement types (CEM I, CEM II/A and II/B, CEM III/A, CEM IV/A and IV/B, CEM
715
V/A) accounted for in the model. It is crucial that selection of cement conductance factor, g is
716
made under strict consideration of cement type or SCM content in the binder, if this
22
ACCEPTED MANUSCRIPT 717
information is available. A correct selection of g is vital given the high sensitivity of model
718
outputs to the conductance factor. It has been shown in Section 3.3.5 Figure 4, that non-structural (low-strength) concretes
720
give poor predictions and high variability. The model applies to concretes subjected to all
721
conventional curing regimes but should be made of normal aggregates and may be air
722
entrained or non-air entrained provided the air content is within the conventional range of 5
723
to 8% (ACI 211, 2009). The influence of special aggregates types such as recycled and
724
lightweight aggregates is not accounted for in the proposed model.
RI PT
719
The model is applicable to real-world concrete structures in the natural outdoor exposure
726
environment with recommended average of 55% to 75% RH, and does not apply to indoor
727
environments. Effect of sheltering from rain is accounted for in the model, as explained under
728
Section 3.3.1, Equation (9). The atmospheric [CO2] in the natural exposure environment of
729
the structure should typically be in the range of 300 to 400 ppm, for most urban locations. If
730
the site of a structure is not within this CO2 range, a correction term to model predictions
731
must be applied as per Equation (10). The appropriate exposure classes for the model are the
732
carbonation-prone environments, XC3 and XC4. Data extracted from treated concrete
733
surfaces, corner areas of structural elements, cracked concretes and joints (Ann et al. 2010),
734
are not appropriate for use in the model for reasons explained in Section 2.0.
735
TE D
M AN U
SC
725
4. Potential applications
737
Consistent with the objective of maintaining practical relevance, only data obtained from
738
outdoor natural environment has been used in deriving and calibrating the model. The model
739
may potentially be used for service life design of new RC structures and for estimating the
740
residual life of existing structures. In both cases, the model’s structure remains unchanged but
741
the coefficients of some parameters assume different numerical values. The model is suitable
742
for use in conjunction with reliability concepts which employ stochastic applicative methods.
AC C
743
EP
736
744
4.1 Existing reinforced concrete structures
745
The model is applicable to existing structures using Equations (12a,b). In this case, cores are
746
extracted from the structure of known age, from which the mean strength fcbn, carbonation
747
depths, and cover depths are determined along with their CVs. Where necessary, 28-day
748
strength may be estimated from insitu results using the relationship fcbn = fc28+13, as
749
mentioned in Section 3.3.6. The model may then be applied using reliability principles to not
750
only back calculate the progression of carbonation hitherto but more importantly, to 23
ACCEPTED MANUSCRIPT stochastically estimate the residual service life of the structure (RILEM, 1996; ISO, 2012).
752
Arguments may be made that carbonation rate could be calculated directly from data and
753
used for predicting service life based on constant carbonation rate. However, such an
754
approach would be deterministic and has been employed in the literature (Alexander et al,
755
2007). Carbonation rate itself is not a constant value but varies with time. Therefore using a
756
constant rate leads to erroneous, unreliable estimation of service life, since it does not account
757
for variability of carbonation progression rate, cover depth, and material properties of
758
concrete. In prediction of service life using the proposed model, variability of the major
759
factors are incorporated through stochastic modeling. It is vital that correct age of a structure
760
and quality test data are used in the model, for it to give meaningful predictions. For example,
761
if data is extracted at the age of 20 years of an existing RC structure, the model can be used to
762
estimate residual lifespan, being the duration from the present time to the point when
763
carbonation would reach the level of steel i.e. when the full cover is carbonated. Since
764
carbonation does not occur uniformly throughout the structure, the criteria to be used in
765
deciding end of service life (ESL) should be based on probability. A 10% probability that full
766
cover depth is carbonated would be an appropriate criteria to use for ESL (Gjorv, 2009).
M AN U
SC
RI PT
751
It should be underscored that extreme care during data acquisition from existing structures
768
is absolutely necessary, as explained in Section 3.3.7. The issue is critical in ensuring that
769
appropriate and quality data is obtained for use in the model. The major locations of concern,
770
that should be avoided during testing for material properties include cracked sections, joints,
771
corners of elements, surface treated concrete layers, chloride-contaminated concretes, splash
772
and spray zones of structural elements. The appropriate locations for data extraction should
773
be non-surface treated, flat surfaces exposed to atmospheric zone without peculiar
774
obstructions.
EP
AC C
775
TE D
767
776
4.2 New reinforced concrete structures
777
The model also applies to service life design of new structures through use of Equations
778
(11a,b). Two possible concrete strength values may be used in the model at the design stage
779
i.e. strength grade of concrete (fck) or mean strength at 28 days (fc28). If the concrete mixtures
780
and strengths to be used in the structure are known, it is preferable to use the mean 28-day
781
cube strength, otherwise the design engineer may still employ the strength grade of concrete.
782
Incorrect predictions would arise if the concrete strength achieved after construction of the
783
structure is different from the assumed value applied to the model at design stage. In such a
784
case, design predictions may be revised based on actual insitu or 28-day strength results. 24
ACCEPTED MANUSCRIPT Again the conditions given in Section 3.3.7, requiring use of normal aggregate, a minimum
786
concrete strength of 20 MPa, and known cement type with known SCM content (if any), must
787
be adhered to. With implementation of the model at design stage, the designer employs a
788
scientific approach that can be used to maneuver the structure’s design parameters such as
789
cover depth, concrete strength etc., in order to estimate its service life with a measurable level
790
of certainty. As explained in Section 4.1, the main domain for use of the model is stochastic
791
applicative method which employs a probabilistic approach of reliability design (RILEM,
792
1996; ISO, 2012).
RI PT
785
In applying this model, it is notable that no major associated costs may be anticipated.
794
Only basic information, which is typically available at design and construction stage or
795
during repairs, is needed. No complicated tests, sophisticated equipment, computer software,
796
or specialized skills are involved.
M AN U
797
SC
793
5. Comparison of the proposed model versus fib-Model Code predictions
799
Most carbonation prediction models proposed in the literature are based on accelerated
800
carbonation tests and are mostly experimental models, as elaborated in Section 2.1. One of
801
the main problems encountered in carbonation modelling is lack of long-term data
802
measurements taken from real world structures. In this study, comparison of prediction
803
results is made between the proposed model and the fib-Model described in fib (2010);
804
Guiglia and Taliano (2013).
TE D
798
In an extensive investigation, that may be considered as the closest application of a model
806
to real world structures, Guiglia and Taliano (2013) developed a relation between carbonation
807
resistance parameter of the fib-model (R-1NAC, 0) and the 28-day compressive strength for the
808
structures that were investigated. In turn, they found that carbonation depth relation to
809
strength could be simplified to:
AC C
810
EP
805
x c(t) = 163. k e .f −2.1cm . . t for abutments and piers x c(t) = 206. k e .f − 2.1 cm . . t for tunnels
811
Using these equations, scatter plots were prepared comparing the measured and calculated
812
carbonation depths (Guiglia and Taliano, 2013). Their investigation covered about 135 km of
813
highway distance. Tests were done on uncracked concretes extracted from more than 120
814
structures consisting of bridges, viaducts, tunnels, flyovers, underpasses and retaining walls.
815
About 1350 compressive strength and carbonation tests were conducted using 100 mm cores
816
extracted from the reinforced concrete structures. The structures were no more than 5 years 25
ACCEPTED MANUSCRIPT old and were of medium strengths in the range of 20 to 50 MPa. There was no availability of
818
information on the concrete mix designs used for the various structures. However, reports
819
indicated CEM II/A-I, CEM II/B-L and CEM I as the cements that were most predominantly
820
used in the market. Locations of the structures were categorized into three classes of:-
821
64%RH (geographical area I), 67%RH (geographical area II), and 75%RH (geographical area
822
III). The structures were of exposure classes XC3 for external concrete sheltered from rain i.e
823
abutments, piers and tunnels; XC4 for concrete surfaces subject to water contact, such as
824
walls etc. (EN 206, 2000). Although data for walls was acquired, it was not used in the fib-
825
model owing to difficulties in assigning proper environmental coefficients, since walls are
826
unsheltered and also exposed to rain mainly through its vertical face.
SC
RI PT
817
The proposed model and fib-Model were applied to the same data (Guiglia and Taliano,
828
2013) to generate carbonation predictions made by both models. Scatter plots of results are
829
given in Figures 8a1, b1, c1 and Figures 8a2, b2, c2 for the proposed model and fib-Model,
830
respectively. Results are reported for abutments, piers and tunnels located in the three
831
geographical areas of different relative humidity levels. A visual overview of the scatter plots
832
show that both models correctly predict the progression of carbonation for the different
833
elements and at various ages, with data points lying along the line of equality. The wide
834
scatter in data does not necessarily appear to be a result of errors in the prediction models but
835
mostly associated with the random nature of measured data, which are exacerbated by the
836
often fluctuating or non-uniform field exposure conditions. The tendency of data points to
837
deviate from the equality line are attributed to incorrect predictions by the models. In both
838
models, data points show relatively wider scatter at higher carbonation rates or depths, while
839
at the same time veering away from the equality line. This behavior appears to be associated
840
with poor quality, typically low strength concretes. In strength characterization, poor or low
841
quality is also associated with high variability, which implies a high CV.
AC C
EP
TE D
M AN U
827
842
The error statistics generated are shown in Table 6 for each geographical area. These
843
statistics indicate that both models perform at a similar level, with fib-Model showing only a
844
slight edge. Both models have the same range of accuracy giving CV of errors = 40 to 50%,
845
which is quite typical of code-type models, as discussed in Section 3.3.5. These results are
846
also consistent with reports in literature which indicate the accuracy of fib 34 Model to be in
847
the range of CV = 30 to 45% (Lifecon, 2003; Marques et al, 2013).
848
Residuals for both models are shown in Figure 9. Clearly, both models give residuals
849
which fall within the 95% confidence interval. Accordingly, predictions by the models may
850
be considered a correct representation of true carbonation occurring in the real world 26
ACCEPTED MANUSCRIPT structures investigated. Both models have a tendency to under-predict carbonation in high
852
strength concretes and progressively over-predict as concrete strengths decrease. The fib-
853
Model appears to show this tendency slightly more prominently than the proposed model.
854
However, these under-predictions and over-predictions by the models should not be of much
855
concern since they are fairly small and fall within the 95% confidence limits. Also evident in
856
the residual plots is fanning out as the carbonation depths increased. This observation is
857
mostly attributed to the characteristic material behavior associated with increase in variability
858
as concrete strengths decrease. Since strength correlates strongly with carbonation
859
progression, the lower strength concretes are also highly carbonating concretes and
860
consequently show high variability of carbonation depths or rates.
SC
RI PT
851
It may be recalled that the fib-Model usually requires conduct of accelerated tests
862
especially to determine permeability or diffusion coefficient, a required input to the model. In
863
this regard, the proposed model is quite advantageous considering that only basic information
864
i.e mainly strength is required. Concrete strength results are readily available during design,
865
construction or repair of structures, as discussed in 4.2. No accelerated tests or use of
866
sophisticated costly equipment is involved.
M AN U
861
867
7. Conclusions
869
A new model is proposed for prediction of natural carbonation in reinforced concrete
870
structures. Model formulation was done by applying mathematical laws and empirical data
871
measurements. The model may potentially be used for service life evaluation of existing
872
structures and durability design of new reinforced concrete structures.
EP
TE D
868
Detailed description is given on development of the prediction model through derivations,
874
data fitting and optimization. The model was calibrated, statistically evaluated and compared
875
with fib-Model Code. The proposed model was found to give a similar level of prediction
876
accuracy as fib-Model Code. Further research is continuing on the proposed model.
877
AC C
873
878
Acknowledgments
879
The research presented in this paper was supported by the National Research Foundation
880
(NRF) of South Africa, Grant No. 96800. The author wishes to thank the NRF for financially
881
supporting this study.
882 883 884
References 27
ACCEPTED MANUSCRIPT ACI 209 (1997), American Concrete Institute (ACI) Committee 209, Subcommittee II. Prediction of creep, shrinkage and temperature effects in concrete structures, Report ACI 209 R92, (reapproved 1997) ACI 211 (2009), American Concrete Institute (ACI) Committee 211, Standard practice for selecting proportions for normal, heavyweight and mass concrete, ACI 211.1-91 (reapproved 2009), American Concrete Institute, Farmington Hills, Michigan, 1991
RI PT
Alexander M.G, Mackechnie J.R and Ballim Y. (2001), Guide to the use of durability indexes for achieving durability in concrete structures, Department of Civil Engineering, University of Cape Town, Research Monograph No. 2, 35p
Alexander M.G, Mackechnie J.R and Yam W. (2007), Carbonation of concrete bridge structures in
SC
three South African localities, Cement and Concrete Composites, 29, 750-759
Ali A. and Dunster (1998), A., Durability of reinforced concrete-effects of concrete composition and curing on carbonation under different exposure conditions. BRE-report, Garston UK.
M AN U
Ann K.Y, Pack S.-W., Hwang J.-P., Song H.-W., Kim S.-H. (2010), Service life prediction of a concrete bridge structure subjected to carbonation, Construction and Building Materials, 24, 1494–1501
Atis C. D (2004), Carbonation-Porosity-Strength Model for Fly Ash Concrete, Journal of Materials in Civil Engineering, 16 (1), February 1, 91-94
Balayssac, J. P., Détriché, C. H., and Grandet, J. (1995), Effects of curing upon carbonation
TE D
of concrete. Construction and Building Materials, (9), 91-95.
Bazant Z.P and Baweja S (1995), Justification and refinements of Model B3 for concrete creep and shrinkage, 1. Statistics and sensitivity, Materials and Structures, 28, 415-430 Bazant Z.P, and Panula L. (1978), Practical prediction of time-dependent deformations of concrete.
EP
Materials and Structures (RILEM, Paris): Part I Shrinkage, Vol.11, 307–316. Bazant, Z.P., and Panula, L. (1979), Practical prediction of time-dependent deformations of concrete.
AC C
Part VI, Cyclic creep, nonlinearity and statistical scatter, Materials and Structures, 12, 175-183. Bob C. (1999), Durability of concrete structures and specification, Proceedings of the International Conference on Creating with Concrete Dundee (Ed. Dhir, R.K. and McCar-thy, M.J.), 311-318 BS 8110 (1997), Structural use of Concrete, Part 2, Code of Practice for Design and Construction, London, British Structural Institution, 389 Chiswick High Road, London, W4 4AL, United Kingdom Buenfeld N.R, Hassanein N.M, and Jones A.J (1998), An artificial neural network for predicting carbonation depth in concrete structures, In Artificial Neural Networks for Civil Engineers: Advanced Features and Applications (Chap 4), I. Flood and N. Kartam (eds.), American Society of Civil Engineers (ASCE), 277p
28
ACCEPTED MANUSCRIPT Buenfeld, N.R. and Yang, R. (2001), On-site curing of concrete - Microstructure and durability. Publication C530, CIRIA, London, UK. CEB (1997). New approach to durability design - an example for carbonation induced corrosion. In: Schiessl, P. (Ed.), Bulletin,vol. 238, Comite ´ Euro-International du Be ´ton, Lausanne CEB-FIP (1978), Comite’ Europeen du Be’ton-Federation Internationale De la Precontrainte, International System of Unified Standard Code of Practice for Structures, Vol II. CEB-FIP Model
RI PT
Code for Concrete Structures, (3rd Ed.), 56, 331-344
CEB-FIP (1990a), Bulletin d’Information n° 213/214 - CEB-FIP Model code 1990, Thomas Telford, London, UK
CEB-FIP (1990b), Structural concrete – textbook on behaviour, design and performance, updated
SC
knowledge of the CEB-FIP Model Code 1990. Bulletins 1-3
Chun Y.-m., Naik T.R. and Kraus R.N. (2006), Carbon dioxide sequestration in concrete in different curing environments. UWM Center for By-Products Utilization, University of
Milwaukee,
WI,
USA.
Accessed
M AN U
Wisconsin-Milwaukee,
29th
Dec
2015.
https://www4.uwm.edu/cbu/Papers/2006%20CBU%20Reports/REP-608_Chucds.pdf CSIR (1999), Final report on an investigation into the influence of fly ash on the durability of concrete, by W.R. Barker, Division of Building and Construction Technology, CSIR, PO Box 395, 0001 Pretoria, South Africa, 18p. Also, Ash Resources Also, Ash Resources (pty) Ltd, PO Box 3017, Randburg 2125
TE D
Czarnecki L. and Woyciechowski P. (2015), Modelling of concrete carbonation; is it a process unlimited in time and restricted in space? Bulletin of the Polish Academy of Sciences, Technical Sciences, 63 (1), DOI: 10.1515/bpasts-2015-0006 Duracrete (2000), General guidelines for durability design and redesign, Report R15, in ‘EU Brite-
EP
EuRam III project DuraCrete (BE95-1347): Probabilistic performance based durability design of concrete structures
AC C
Ehlen M.A, Thomas M.D.A, and Bentz E.C (2009), Life-365 Service Life Prediction Model™ Version 2.0 - Concrete International,. http://www.life-365.org/download.html Ekolu S.O (2010), Model validation and characteristics of the service life of Johannesburg concrete structures, Proc. of the National Symp. on Concrete for a Sustainable Environment, Concrete Society of Southern Africa, 3-4th August, Kempton Park, Johannesburg, Gauteng, p.30-39. Ekolu S.O (2012), Model verification, refinement and testing on independent 10-year carbonation field data, Proceedings of the 3rd Intl. Conf. on Concrete Repair, Rehabilitation and Retrofitting (ICCRRR), 3-5, Sept. 2012, Cape Town, South Africa, p.445-450. Ekolu S.O (2016), A review on effects of curing, sheltering, and CO2 concentration upon natural carbonation of concrete, Construction and Building Materials, 127 (2016) 306–320.
29
ACCEPTED MANUSCRIPT EN 197-1 (2000), Cement - Part 1: Composition, specifications and conformity criteria for common cements. European Committee for Standardization, CEN, 29p EN 206 (2000), Concrete – Part 1: Specification, performance, production and conformity, European Standard, Reu de Stassart, B-1050 Brussels EN 1992-1-1 (2004) Eurocode 2. Design of concrete structures. part 1-1. General and building rules and rules for buildings, December 2010, 227p
Lausanne, 1st edition, 126p, ISBN: 978-2-88394-074-1
RI PT
fib (2006), Model code for service-life design, fib bulletin 34, Federation International du Beton,
fib (2010), Model code 2010 final draft, vol 1 & 2, fib bulletin N. 65 & 66, Lausanne, 2012
Fukushima, T. (1988) Theoretical investigation on the influence of various factors on
SC
carbonation of concrete, Building Research Institute (Japan), BRI Research Paper No 127 (ISSN 0453-4972), Japan, 1988.
Gardner N.J (2004), Comparison of prediction provisions for drying shrinkage and creep of normal
M AN U
strength concretes, Canadian Journal for Civil Engineering, 31 (5) Sep-Oct, 767-775 Gehlen C., and Sodeikat C (2002), Maintenance planning of reinforced concrete structures: redesign in a probabilistic environment, inspection, update and derived decision making. In: Durability of Building Materials and Components, Proceedings of the 9th International Conference, 17-20th March, Brisbane, Australia
Francis, UK, 219 p
TE D
Gjorv, O.E. (2009), Durability Design of Concrete Structures in Severe Environments, Taylor and
Greve-Dierfeld v. S. and Gehlen, C (2014), Performance based deemed-to-satisfy rules, The Fourth International fib Congress, Feb. 10-14, Mumbai, Fédération International du Béton Guiglia M. and Taliano M. (2013), Comparison of carbonation depths measured on in-field exposed
EP
existing r.c. structures with predictions made using fib-Model Code 2010, Cement & Concrete Composites, 38, 92–108
AC C
Hakkinen, T. (1993), The influence of slag content on the microstructure, permeability and mechanical properties of concrete, Part 2, Technical and theoret-ical examinations Cement and Concrete Research, 23, 518-530 Hassoun M.N and Al-Manaseer A. (2012)., Structural concrete: theory and design, 5th Edition, John Wiley and Sons Inc, 1007p He R. X. and Jia H. J. (2011), Carbonation depth prediction of concrete made with fly ash, Electronic Journal of Geotechnical Engineering, 16(F), 605-614 Hills T.P, Gordon F., Florin N.H, Fennell P.S (2015), Statistical analysis of the carbonation rate of concrete, Cement and Concrete Research, 72, 98–107
30
ACCEPTED MANUSCRIPT Hooton R.D (1988), What is needed in a permeability test for evaluation of concrete quality, MRS Proceedings,
Volume
137,
Materials
Research
Society,
1989,
DOI:
http://dx.doi.org/10.1557/PROC-137-141 Ikotun J.O and Ekolu S.O (2012), Essential parameters for strength-based service life modeling of reinforced concrete structures - a review, Proc. 3rd Intl. Conf. on Concrete Repair, Rehabilitation and Retrofitting (ICCRRR), 3-5, Sept. 2012, Cape Town, South Africa, p. 433-438
Geneva 20, Switzerland
RI PT
ISO 16204 (2012), Durability - service life design of concrete structures, Case postale 56. CH-1211,
Kari O.P, Puttonen J., Skantz E. (2014), Reactive transport modelling of long-term carbonation, Cement & Concrete Composites, 52, 42–53
SC
Khunthongkeaw J., Tangtermsirikul S., and Leelawat T. (2006), A study on carbonation depth prediction for fly ash concrete, Construction and Building Materials, 20, 744–753 Kokubu, M and Nagatakis, S. (1989). Carbonation of concrete with fly ash and corrosion of
M AN U
reinforcement in 20-years tests. ACI, SP-114-14, 315-329
Kropp J, (1995), Relations between transport characteristics and durability. In Kropp J and Hilsdorf H.K (eds), Performance cirteria for conrete durability, E & FN Spon, London Lagerblad Björn (2005), Carbon dioxide uptake during concrete life cycle – State of the art. Swedish Cement and Concrete Research Institute, ISBN 91-976070-0-2. SE-100 44 Stockholm ISSN 0346-8240, CBI Report 2:2005
TE D
Liang M.T, Qu W., and Liang C-H (2002), Mathematical modeling and prediction method of concrete carbonation and its applications, Journal of Marine Science and Technology, 10 (2), 128-135 Lifecon (2003), Deliverable D 3.2 service life models: Life cycle management of concrete infrastructures for improved sustainability, Final Report by Dipl.-Ing. Sascha Lay, Technical
EP
Research Centre of Finland (VTT). 169p
Luo D., Niu D., and Dong Z. (2014), Application of neural network for concrete carbonation depth prediction, 4th International Conference on the Durability of Concrete Structures, 24–26 July,
AC C
Purdue University, West Lafayette, IN, USA Marques, P.F, Chastre C., and Nunes Â. (2013), Carbonation service life modelling of RC structures for concrete with Portland and blended cements, Cement & Concrete Composites, 37, 171–184 Monteiro I., Branco F.A., de Brito J., Neves R.(2012), Statistical analysis of the carbonation coefficient in open air concrete structures, Construction and Building Materials 29, 263–269 Muller H.S and Hilsdorf H.K (1990), CEB Bulletin d’Information, No. 199, Evaluation of the time dependent behaviour of concrete, Summary report on the work of General Task Group 9, September, 201p. Nishi T (1962), Testing of Concrete, RILEM International Symposium, Publishing House of the Czechoslavak Academy of Science, Prague, 485-489
31
ACCEPTED MANUSCRIPT Otsuki N., Gallardo R.S, Annaka T., Takaki S., and Nishida T. (2012), Field survey for carbonation depth of reinforced concrete buildings in the Philippines, 37th Conference on Our World in Concrete & Structures: 29 - 31 August 2012, Singapore. Article Online Id: 100037033
Papadakis V.G, Vayenas C.G, and Fardis M.N (1991), Fundamental modelling and experimental investigation of concrete carbonation. ACI Materials Journal, 4(88):363–
RI PT
373. Papadakis, Fardis and Vayenas (1995), Effect of composition, environmental factors and cement-lime mortar on concrete carbonation, Materials and Structures Journal, 1192 (25), 293-304
Parrott L.J. (1987), A review of carbonation in reinforced concrete. Cement and Concrete Association, BRE, 42p
SC
Parrott L.J. (1990), Carbonation, corrosion and standardization: In: Proceedings of the International Conference on Protection of Concrete, September 11-13, University of Dundee, E & F Spon, 1009-23
M AN U
Parrott L.J. (1996), Some effects of cement and curing upon carbonation and reinforcement corrosion in concrete, Materials and Structures, vol. 29, 164-173. Parrott P.J, (1994), Design for avoiding damage due to carbonation—induced corrosion. Proc. of the 3rd International Conference on Durability of concrete, Nice, France, ACI SP-145. Malhotra V.M. (Ed), 283–298
PCA (2002), Types and causes of concrete deterioration, Portland cement Association, 5420 Old
TE D
Orchard Road, Skokie, Illinois 60077-1083, 16p, www.cement.org Quillin K. (2001), Modelling degradation processes affecting concrete, BRE Centre of concrete construction, CRC Ltd 151 Rosebery Avenue, London, ECIR 4GB. ISBN 1860815316
Ravahatra N.R, De Larrard T, Duprat F., Bastidas-Arteaga E., Schoefs (2014). Sensitivity
EP
analysis of simplified models of carbonation - extension in spatial variability -updating through Bayesian network. Proceedings of the 2nd International Symposium on
AC C
Uncertainty Quantication and Stochastic Modeling, Jun 2014, Rouen, France. RILEM (1996), Durability Design of Concrete Structures, RILEM REPORT 14 (A. Sarja & E. Vesikari, Eds), E & FN Spon, UK, 1996, 165 p. RILEM B3 (1995), Creep and shrinkage model for analysis and design of concrete structures: Model B3, RILEM Recommendations. Materials and Structures. 357-365 (28), 415-430 (28), 488-495 (28) Saettaa, A.V and Vitaliani R.V (2004, 2005)., Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part I: Theoretical formulation, Cement and Concrete Research, 34, (2004), 571 – 579. Ibid. 2005, Part II. Practical applications, 958 – 967
32
ACCEPTED MANUSCRIPT Sagues A.A, Moreno E.I, Morris W. and Andrade C. (1997), Carbonation in concrete and effect on steel corrosion, Final Report, State Job No. 99700-3530-119, WPI 0510685, College of Engineering, University of South Floride, 4202 Fowler Avenue, tampa, Floride 33620-5350, 299p
Salvoldi B.G., Beushausen H., Alexander M.G. (2015), Oxygen permeability of concrete and its relation to carbonation, Construction and Building Materials, 85 (2015) 30–37 SANS 10100 (2000), Code of Practice for the Structural Use of Concrete, Part 1, & 2, Part 1: Design,
RI PT
Part 2: Materials. Pretoria, South African Bureau of Standards limited
Sayed-Ahmed M. (2012), Statistical modelling and prediction of compressive strength of concrete, Concrete Research Letters, 3 (2), 452-458
Seung-Jun and Song, Ha-Won (2010), Analysis of carbonation behaviour in concrete using neural
SC
network algorithm and carbonation modelling, Cement and Concrete Research, 40, 119–127
Shimizu Y., Hirosawa M.and Zhou J. (2000), Statistical analysis of concrete strength in existing
Kogakuin University, Tokyo, Japan, 8p
M AN U
reinforced concrete buildings in Japan, Department of Architecture, Faculty of Engineering,
Silva A., Neves R., de Brito J. (2014), Statistical modelling of carbonation in reinforced concrete, Cement and Concrete composites, 50, 73-81
Silva R.V, Neves R., de Britoc J., Dhir R.K (2015), Carbonation behaviour of recycled aggregate concrete, Cement and Concrete Composites, 62, September, 22–32. Talukdar S., Banthia N, Grace J.R (2012), Carbonation in concrete infrastructure in the context of
Composites, 34, 924–930
TE D
global climate, change – Part 1: Experimental results and model development, Cement & Concrete
Tang L., Utgenannt P., Lindvall A. and Boubitsas D. (2010), Validation of models and test methods for assessment of durability of concrete structures in the road environment, CBI Betonginstitutet
EP
AB, 100 44 Stockholm
Torrent R.J, Armaghani J and Taibi Y (2014), Evaluation of Port of Miami tunnel segments:
AC C
carbonation and service life assessemnt made using air permeability test data, Concrete Beton,
Journal of The Concrete Society of Southern Africa, No. 136, March, p.10-16 Underhill L and Bradfield D. (2013), Introstat, Chapter 12 Regression and correlation, Department of Statistical Sciences, University of Cape Town, 271-318 van Ede W.F and Ekolu S.O (2014), Condition assessment of a Johannesburg skyscraper, Proceedings of the International Conference on Construction Materials and Structures (ICCMATS), Johannesburg, South Africa, 24-26 November 2014, 1052-1059 Wang X.Y and Lee H-S (2009), A model for predicting the carbonation depth of concrete containing low-calcium, fly ash, Construction and Building Materials, 23, 725–733
33
ACCEPTED MANUSCRIPT Wendner R., Hubler M., and Bažant Z. (2013), The B4 Model for multi-decade creep and shrinkage prediction. In Mechanics and Physics of Creep, Shrinkage, and Durability of Concrete: pp. 429436. doi: 10.1061/9780784413111.051
Wierig H-J (1984), Longtime studies on the carbonation of concrete under normal outdoor exposure, Proceedings of the RILEM seminar on the durability of concrete structures,
RI PT
Hannover, Germany Xu A, Rodhe M. and Chandra S. (1996), Influence of alkali on carbonation of concrete, Durability of building materials and components, 7, vol. 1, C. Sjostrom (Ed.), Spon, p. 596-604
Yoon I-S, Copuroglu O. and Park K-B (2007), Effect of global climatic change on carbonation progress of concrete, Atmospheric Environment, 41, 7274–7285
SC
Yunusa A.A (2014), The effects of materials and micro-climate variations on predictions of carbonation rate in reinforced concrete in the inland environment, PhD Thesis, School of Civil Engineering & the Built Envir, Univ. of the Witwatersrand, Johannesburg, RSA
M AN U
Zha X., Yu M., Ye J. and Feng G. (2015), Numerical modeling of supercritical carbonation process in cement-based materials, Cement and Concrete Research, 72, 10–20
Zhang L. M. and Jiang W. H. (1990), A study on carbonation of concrete in natural condition and its correlation with artificial accelerated carbonation, Journal of Xi’an Institute of Metallurgy and Construction Engineering, 22 (3), 207-214
Zhang X., Zhou X., Zhou H., Gao K, and Wang Z (2013), Studies on forecasting of carbonation depth
TE D
of slag high performance concrete considering gas permeability, Applied Clay Science, 79, 36–40 Zhijian S.Z., Wang W., Cheng C., Tang X (2013), Predicting method for time-dependent concrete carbonation depth (I): Traditional model and its error distribution, Electronic Journal of Geotechnical Engineering (EJGE), 2013, 2298-2308
EP
Zhu A. M. (1992), Concrete carbonation and durability of reinforced concrete, Concrete, 6 18-21 Sanjuan M.A and del Olmo C. (2001), carbonation resistance of one industrial mortar used as a
AC C
concrete coating, Building and Enviornment, 36, 949-953.
34
ACCEPTED MANUSCRIPT
SC
RI PT
Table 1 Concrete mixtures (Ekolu, 2012)
M AN U
Table 2. Data fitting for model parameters Model type
Cement type
Coefficients
Correlation, R2
Regression
OPC
(cem = 63126, g = -2.304)
0.69
OPC/30FA
(cem = 17823, g = -1.901)
0.72
RHC
(cem = 1643, g = -1.385)
0.84
RHC/25FA
(cem = 1423, g = -1.285)
0.77
all the above
(cem = 950, g = -1.2)
0.08
all the above
(a = 0.25, b = 0.95)
0.99
all the above
(a = 0.35, b = 1.2)
0.30
TE D
Curve fitting
EP
Strength prediction (eqn. 5) Strength prediction (eqn. 5)
AC C
Table 3. Optimization of g-parameter for (a = 0.35, b = 1.2) constant (cem, g) Age (years) Determination coefficient, R2 (1000, -1.4)
(1000, -1.5)
(1000, -1.6)
3.5
0.24
6
0.20
10
0.23
3.5
-0.08
6
0.44
10
0.36
3.5
-0.21
6
0.13
10
0.04
35
ACCEPTED MANUSCRIPT
Table 4 Statistical indicators of the model predictions for carbonation rate Predictions based on long-term concrete strength, fcbn 3½ year data 6 year data 10 year data MV* PV MV PV MV PV 4.76 4.29 4.16 4.48 4.16 4.01 1.11 0.93 1.04 1.16 1.11 1.17 24.4 26.6 28.1
Mean Mean MV/PV RMS CV (%)
Parameter
Average
Carbonation conductance factor (c) Concrete strength (fc), MPa
CV (%)
Min
Constant
-1.5
-1.4
-1.3
10 10 3 3 3 3
25 54 47 52 56 70
30 60 50 55 60 75
35 66 53 58 64 79.5
TE D
Relative humidity (RH), %
30 60 50 55 60 75
Parameter values Mid Max
M AN U
Table 5. Parameters for estimating variability of model outputs
SC
*MV = measured value, PV = predicted value, CV = coefficient of variation
Predictions based on longterm concrete strength, fc28 3½ year data 6 year data MV PV MV PV 4.54 4.73 3.99 3.23 0.96 1.24 1.43 1.23 30.2 38.1
RI PT
Statistical indicators
Table 6. Prediction errors for the proposed model and for fib-Model Structural elements
EP
Sites
Abutments, piers Abutments, piers Abutments, piers, tunnels
AC C
Area I, 64%RH Area II, 67%RH Area III, 75%RH
Coefficient of variation of errors (%) Proposed Model fib-Model 42.3 36.9 46.8 41.6 47.2 45.7
36
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
Figure 1. Parabolic function giving the correction term for relative humidity
37
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
Figure 2. Data fitting and optimization of model parameters
38
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Figure 3. Optimization of g-parameter
39
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
Figure 4. Calibration for predictions based on 28-day concrete strength
Figure 5. Boundary condition for carbonation in low strength concretes below 20 MPa
40
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
Figure 6. Sensitivity analysis for up to 50 years
Figure 7. Comparison of predictions using 28-day strength and long-term insitu strength (UL = upper limit, LL = lower limit)
41
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Figure 8. Scatter plots comparing carbonation prediction by the proposed model and by fib-Model
42
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Figure 9. Residuals for the proposed model and for fib-Model
43