Repairs by fly ash concrete to extend service life of chloride-exposed concrete structures considering environmental impacts

Construction and Building Materials 98 (2015) 799–809

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Repairs by fly ash concrete to extend service life of chloride-exposed concrete structures considering environmental impacts Aruz Petcherdchoo Department of Civil Engineering, Faculty of Engineering, King Mongkut’s University of Technology North Bangkok, 1518 Pibulsongkram Road, Bangsue, Bangkok 10800, Thailand

h i g h l i g h t s
Repairs by fly ash concrete on chloride-exposed concrete structures are assessed.
Time-dependent model of surface chloride and diffusion coefficient is used.
Model of CO2 emission from concrete production and repair processing is developed.
Present value of carbon price transformed from the amount of CO2 is predicted.
Threshold ratio of diffusion coefficient of original to repair concrete is also defined.

a r t i c l e

i n f o

Article history: Received 30 September 2014 Received in revised form 6 August 2015 Accepted 19 August 2015 Available online 4 September 2015 Keywords: Repairs by fly ash concrete Service life Chloride-exposed CO2 Carbon price

a b s t r a c t This study proposes a quantitative method to assess the corrosion-free service life and the environmental impact in terms of CO2 and carbon price due to repairs by replacing cover concrete with fly ash concrete on chloride-exposed concrete structures. The study takes advantage of the Crank–Nicolson based finite difference approach to simplify the assessment. Using the approach, the service life and the repair time for corrosion-free condition of concrete structures can be predicted. At the time of repairs, the CO2 occurs due to concrete production and replacement processing, and can be assessed using a CO2 emission model developed here. And, the amount of CO2 is transformed into the carbon price. From the study, it can be concluded that the increase of the amount of fly ash in repair concrete by 15% causes the reduction of the cumulative CO2 and carbon price by as high as 58% and 41%, respectively. The ratio of the diffusion coefficient of original concrete to that of repair concrete can be calculated, and its threshold ratio is defined. If the ratio is larger than the threshold ratio, deeper depth of repairs causes shorter extension of corrosionfree period. Furthermore, the threshold ratio apparently decreases with repair depth. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Very large amounts of wastes are being produced all around the world [1]. In many countries, fly ash which is a by-product from coal power plants is known as one of the wastes causing environmental impacts in the form of air and water pollution. In particular, it is currently found that the amount of fly ash production increases up to 600 million tons per year [2]. In the past, the most common method to manage fly ash was to dispose in landfills. However, this method was unsatisfactory in the situation where excessive amount of fly ash was produced. This led to a huge issue for fly ash management. Hence, another method was necessary. In the present, one of the methods to reasonably remedy the issue is to reuse fly ash. For years, the research topic on using fly

E-mail address: [email protected] http://dx.doi.org/10.1016/j.conbuildmat.2015.08.120 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.

ash to replace for cement in concrete has been intensively studied. And, the properties of fly ash concrete were subsequently reported, e.g., compressive strength, chloride resistance etc. [3,4]. This method is gaining attention, because it not only reduces the disposal area but also helps reduce the environmental impacts produced in cement production process. In particular, it is able to reduce the environmental impact in the form of the climate change resulting from the CO2 emission in two processes, i.e., calcinations, and generation of electrical power in cement plant [5]. Furthermore, it was reported that replacement for cement by 10% of fly ash can theoretically reduce the amount of CO2 in the cement production process as high as 25% [6]. It should also be noted that if the large amount of fly ash is available and there is a useful destination, such as partial cement replacement in concrete, the little amount of the environmental impact should be assigned to fly ash. However, in some countries, the amount of fly ash is not enough. And, there is a need of fly ash in order to achieve better

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concrete performance, e.g., in marine environment. If this is the case, the large impact of coal fired electricity production needs to be allocated to fly ash. More details on this can be found elsewhere [7,8] Although the reuse of fly ash in concrete is found to be useful, the performance in fly ash usage is also of interest. When fly ash is used in concrete structures exposed to marine environment, chloride attack is considered as one of the main factors in their deterioration process. Whenever the critical (or threshold) amount of chloride ions at the surface of reinforcement is reached combining with the condition of having enough oxygen and moisture, reinforcement corrosion may take place resulting in the deterioration of concrete structures. This could not only adversely affect their safety and serviceability, but also shorten their service life [9]. Hence, the long-term performance of concrete structures has to be assessed to avoid structure reconstruction which causes very large amount of environmental impacts [10]. If the long-term performance is unsatisfactory, a proper repair and maintenance action must be applied [11–13]. Although a repair or maintenance action is applied, it is unavoidable that the environmental impacts can occur. When concrete structures are repaired by replacing cover concrete with fly ash concrete, the environmental impacts in terms of the CO2 can occur during the production of fly ash concrete and the processing of cover concrete replacement. As a result, the assessment of the amount of CO2 in cover concrete replacement is necessary in order to satisfy low-carbon society. In this study, a method to assess the amount of CO2 and the time value of carbon price due to repairs for extending corrosionfree service life (or corrosion-free period) of chloride-exposed concrete structures is presented. For these, there are two issues to be addressed; prediction of corrosion-free service life, and assessment of the amount of CO2 and carbon price. In predicting the service life, the behaviors of chloride diffusion before and after repairs must be considered. And, the amount of CO2 and the carbon price must be related to repair application times. The two issues and the remedial solutions are presented as follows.

Fig. 1. Chloride profile after cover concrete replacement.

2. Finite difference for chloride transport in repaired concrete

crete. Immediately after the repair, there are three principal stages as follows

2.1. Without cover concrete replacement The fundamental partial differential equation (PDE) for chloride ion diffusion based on Fick’s second law [14] can be written as

@C @ @C ¼ D @t @x @x

ð1Þ

where C is the chloride content as a function of position x and time t, and D is the chloride diffusion coefficient which can be either constant or in a function of x or t. 2.2. With cover concrete replacement According to REHABCON [15], cover concrete replacement was defined as an action causing removal of original cover concrete and replacement by a repair material, e.g., concrete, fly ash concrete, polymer-based material etc [16,17]. In addition to this definition, the cover concrete replacement in this study is carried out, whenever the corrosion of reinforcement initiates. This initiation occurs, if the chloride content at the outer surface of reinforcement reaches a threshold (or critical) value. With the replacement as shown in Fig. 1a, the concrete is taken off as deep as the distance of xp, called repair depth. Consequently, the chloride ions inside the taken-off concrete are also removed. After that, repair concrete, such as fly ash concrete, is replaced for the removed original con-

1. The remaining chloride ions in the non-removed or original concrete are about to distribute to both the original concrete and fly ash concrete, so mathematical complication will be involved in solving the partial differential equation (PDE) with nonlinear initial chloride profile at the time ti as shown in Fig. 1a. 2. When the remaining chloride ions penetrate through the original concrete and also back to the fly ash concrete [18], complicated PDE involving space-dependent diffusion coefficient will be encountered due to the difference between the diffusion coefficient of the original concrete and the fly ash concrete. These are represented in Fig. 1b. If the effect of timedependent diffusion coefficient due to aging of concrete structures [19] is included, the problem will be more complicated. For these, the partial differential equation (PDE) for the Fick’s second law [20] can be written as

@C @ @C ¼ Dðx; tÞ @t @x @x

ð2Þ

where D(x, t) is the chloride diffusion coefficient in a function of position x and time t. 3. When the penetrating surface chloride ions merge with the redistributing chloride ions at the point xm at the time ti+2 as shown in Fig. 1b, the complication in solving the PDE is faced again. If this kind of repairs is repeated, the problem will be even more complicated.

A. Petcherdchoo / Construction and Building Materials 98 (2015) 799–809

In order to overcome all the aforementioned difficulties, a Crank–Nicolson based numerical scheme in the finite difference approach is introduced. Let us consider the aforementioned three stages as a whole. It can be observed that all the problems only deal with the diffusion of chloride ions through the materials having different diffusion coefficients. According to the Crank–Nicholson based scheme [21], the solution for space- and time-dependent diffusion coefficients can be formulated as

crete pore structures [25]. In this study, the time-dependent diffusion coefficient (in mm2/year) at the exposure time (t, in years) is represented in terms of a decay function [4] as

DðtÞ ¼ Dref

 m t ref t

face, and ðDxp ;t Þo is set as ðDxp ;0 Þrep at repair depth xp. In general, ðDx;t Þo and ðDx;t Þrep are defined as the diffusion coefficient of original concrete and repair concrete, respectively, at the depth x and time t. By taking advantage of the finite difference approach, nonlinear chloride ion distribution can be considered by treating it pointwise. The time-dependent surface chloride and diffusion coefficient can also be included in computation by updating them with time. It is noted that if the diffusion coefficient is constant, Eqs. (2) and (3) will be respectively reduced to Eq. (1) and the following equation which is used to calculate chloride diffusion in concrete without cover concrete replacement [14] as

" # ci;jþ1  ci;j D ðciþ1;jþ1  2ci;jþ1 þ ci1;jþ1 Þ þ ðciþ1;j  2ci;j þ ci1;j Þ ¼ 2 Dt ðDxÞ2 ð4Þ 3. Parameters to be considered for service life prediction 3.1. Time-dependent surface chloride Several researchers have proposed close-formed equations for both time-independent and -dependent surface chloride models [22,23] which depend on many factors, for instance, concrete properties, location of concrete structures [24]. In this study, the surface chloride for normal and fly ash concrete is time-dependent [4], as shown Eq. (5):

pffiffi pffiffi C S ðtÞ ¼ C 0 þ k t ¼ 10½0:814ðW=BÞ0:213 þ 2:11 t

ð5Þ

where C 0 is the initial surface chloride (% wt. of binder), and k is a constant related to the rate of increase of surface chloride per square root of the exposure time (t, years). It is noted that the surface chloride in Eq. (5) was developed for concrete structures located in the tidal zone of the Gulf of Thailand [4]. 3.2. Time-dependent diffusion coefficient The corrosion of concrete structures is directly related to the resistance or diffusion coefficient of concrete. The diffusion coefficient was found to be time-dependent, because the process of cement hydration resulted in connection and condensation of con-

ð6Þ

in which Dref (in mm2/year) is the diffusion coefficient at the reference time t ref of 28 days, which is equal to Eq. (7), cf. [4]

ci;jþ1  ci;j 1 ½Diþ1=2 ðciþ1  ci Þ  Di1=2 ðci  ci1 Þ;jþ1 ½Diþ1=2 ðciþ1  ci Þ  Di1=2 ðci;  ci1; Þ;j þ ¼ 2 Dt ðDxÞ2 ðDxÞ2

where ci;j is defined as the chloride content at the space i and time j, respectively. And, Diþ1=2 and Di1=2 are equal to ðDi þ Diþ1 Þ=2 and ðDi1 þ Di Þ=2 , respectively. In computation, Dx and Dt are the size of the mesh point (1 mm) and the incremental time step (1 week), respectively. When the cover concrete is replaced over the repair depth of xp at time t, the diffusion coefficient of cover concrete will be updated. For instance, ðD0;t Þo is set as ðD0;0 Þrep at a concrete sur-

801

!

Dref ¼ 10½1:776þ1:364ðW=BÞ þ ½5:806  18:69ðW=BÞ ½%FA

ð3Þ

ð7Þ

where W/B and %FA are the water to binder ratio and the amount of fly ash replacement (in percent), respectively. And, m ¼ 0:2 þ 0:4ð%FA=50Þ. It is noted that the diffusion coefficient in Eq. (6) is a decay function which approaches to zero at the infinity. This means that the concrete becomes completely impermeable. However, this situation is impossible. In practice, the diffusion coefficient will become a constant at the end. Therefore, in using Eq. (6), it should be ensured that the diffusion coefficient will not become zero. For this study, the considered time period is specified as 100 years, so it will not approach the infinity. 3.3. Critical chloride and repair application time Schiessl and Raupach [26] stated that the critical chloride content could be defined as the content that was necessary to sustain a local passive film on the surface of reinforcement before the process of corrosion initiation. Alonso et al. [27] stated that the critical chloride value depended on the roughness of reinforcement surface, the concrete properties, and the aggressiveness of the environment. Yokota and Iwanami [28] stated that the corrosion of reinforcement started and progressed rapidly, whenever the chloride content at the position of reinforcement reached its critical value. Several researchers also studied and defined the value for the critical chloride [24,29,30]. Angst et al. [31] reviewed the value for critical chloride content in reinforced concrete, and stated that the critical chloride value depended on numerous factors. And also, it was suggested that the condition of the steel-concrete interface, the pH of the concrete pore solution, and the steel potential all dominated the critical value. They also reviewed the case that the critical chloride decreased with increasing the amount of fly ash replacement, and claimed the following reviews. Fly ash improved the chloride binding capacity of the binder, so it could be attributed to both more efficient chemical binding due to higher proportions of active alumina often present in fly ash [32,33] and better physical adsorption of chloride as the result of more gel produced in the course of hydration [34]. On the other hand, the use of fly ash lowered the pH of the pore liquid [35,36]. Moreover, the reduction of pH appeared to be more pronounced than the improved chloride binding capacity and an increased Cl/OH ratio in the pore solution was found when fly ash was added to the binder [37]. In this study, repairs by cover concrete replacement are applied, whenever the chloride content at a specific threshold depth reaches a critical value. The threshold depth is defined as concrete cover or a distance between the outer surface of concrete and the surface of reinforcement. The critical value to initiate reinforcement corrosion is equal to 0.9%, 0.65%, 0.4%, 0.3%, or 0.2% wt. of

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A. Petcherdchoo / Construction and Building Materials 98 (2015) 799–809 Table 1 CO2 in producing concrete compositions. Material

CO2 emission (eq. g)

Cement 1 kg Fly ash 1 kg Fine aggregates 1 kg Coarse aggregates 1 kg Water 1 kg

820 27 13.9 40.8 0.112

trend lines, we get three linear equations which represent the amount of CO2 in concrete production for W/B of 0.45, 0.55, and 0.65. From these three equations, the amount of CO2 in concrete production can be formulated in terms of W/B and %FA as

COPD 2 ¼ 452  20ðW=BÞ  3:86 ½%FA

ð8Þ

For the last kind of data, Arskog et al. [41] presented the amount Fig. 2. Compressive strength vs %FA.

binder for 0%, 15%, 25%, 35%, or 50% fly-ash replacement, respectively [38]. By cover concrete replacement, the chloride ions are eliminated, and the chloride content at the threshold depth can be controlled below the critical value for reinforcement corrosion. Hence, concrete structures can be designed to be free of corrosion for a period until the chloride content reaches the critical value again. Here, this corrosion-free period is also defined as corrosion-free service life. 3.4. Limitation on fly ash usage In using fly ash concrete, the initial compressive strength should carefully be taken into account. According to the test results of Chalee et al. [38], the compressive strength of normal and fly ash concrete at 28 days can be compared as shown in Fig. 2. With the same W/B, the initial compressive strength of fly ash concrete tends to be lower than that of normal concrete. And, the increase of W/B leads to lower initial compressive strength. To satisfy the compressive strength requirement, the initial compressive strength of repair concrete is recommended to be equivalent to that of the original concrete in this study. 4. Model of environmental impacts 4.1. Environmental impacts in term of CO2 Whenever a repair by cover concrete replacement is applied, the environmental impacts in terms of the CO2 can occur at the same time. To assess the amount of CO2 corresponding to concrete production and replacement processing, four kinds of data are needed. First, Table 1 shows the equivalent amount of CO2 in producing 1 kg of each concrete composition [39,40]. Second, from the study of Petcherdchoo [4], the data of the compositions in producing 1 m3 of concrete in terms of W/B and %FA are shown in Table 2. From Tables 1 and 2, the amount of CO2 produced from the concrete compositions of each mix can be calculated as also shown in Table 2. For example, the amount of CO2 produced from cement in the mix of M45 is equal to 392 eq. kg/m3 (82 0478 = 391,960 eq. g/m3). Third, the amount of CO2 produced in concrete batching is equal to 0.018 eq. kg/m3 [40] as shown in Table 2. In the final column in Table 2, the amount of CO2 in concrete production (composition and batching) is shown in a unit of eq. kg/m3. The amount of CO2 in concrete production can be plotted versus the amount of fly ash replacement (%FA) in Fig. 3. By adding

of CO2 in processing cover concrete replacement, COPC 2 , for the transportation distance of less than 30 km. Table 3 shows the amount of CO2 per application of replacement according to five processes; concrete transportation, hydro-jetting to remove concrete cover, cleaning of rebar, protective coating on rebar, and application of shotcrete. According to their unit, the five processes can be separated into two groups as shown in the second and third columns. It is observed that the unit of the amount of CO2 in the process of cleaning and coating rebars is inconsistent with that in Eq. (8) and in the second column Table 3. To eliminate this inconsistency, the unit is chosen as eq. kg/m2. Hence, the total amount of CO2 for cover concrete replacement can be expressed as PC CO2 ¼ COPD 2 þ CO2   ¼ ½452  20ðW=BÞ  3:86 ð%FAÞ  xp   þ 1968  xp þ 23:4

¼ ½452  20 ðW=BÞ  3:86 ð%FAÞ þ 1968  xp þ 23:4

ð9Þ

where xp is the repair depth. 4.2. Time value of carbon price The carbon price is defined as the amount of charges which are paid for the right to emit a ton of CO2 into atmosphere [42]. Carbon pricing usually takes the form of a carbon tax or a requirement to purchase permits to emit CO2. In the study of Kumer [43], the carbon price is equivalent to €10–15 per ton of CO2 emission. This study selects the carbon price as €15 per ton of CO2 emission. Hence, a factor to transform the amount of CO2 into the carbon price is equal to 0.015, which is called transformation factor (TF, €/eq. kg). Furthermore, due to the time value of money, this study considers the carbon price in terms of the present value of the carbon price at time t, PV(t), as follows

PVðtÞ ¼

0:015  CO2 ¼ TF  CO2  DF ð1 þ mÞt

ð10Þ

where DF is equal to 1/(1 + m)t, and also defined as the discounting factor. And also, m is the discount rate which refers to the interest rate used in discounted cash flow (DCF) analysis to determine the present value of future cash flows [44]. The discount rate in the DCF analysis takes into account not only the time value of money but also the risk or uncertainty of future cash flows; the greater the uncertainty of future cash flows, the higher the discount rate. Fundamentally, the discount rate is defined as the interest rate charged to commercial banks and other depository institutions on loans they receive from their regional Federal Reserve Bank’s discount window [45]. The Federal Reserve Banks offer three discount window programs to depository institutions: primary credit, sec-

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A. Petcherdchoo / Construction and Building Materials 98 (2015) 799–809 Table 2 Concrete compositions and CO2 for producing 1 m3 of concrete. Mix

Concrete composition (kg/m3) C

M45 M4515 M4525 M4535 M4550 M55 M5515 M5525 M5535 M5550 M65 M6515 M6525 M6535 M6550

FA

478 406 359 311 239 478 406 359 311 239 478 406 359 311 239

– 72 119 167 239 – 72 119 167 239 – 72 119 167 239

Aggregates Fine

Coa.

639

1024 1024 990 977 957 971 948 933 918 897 922 898 881 864 840

CO2 from composition (eq. kg/m3) W

215 215 215 215 215 262 262 262 262 262 311 311 311 311 311

C

392 333 294 255 196 392 333 294 255 196 392 333 294 255 196

FA

0 1.94 3.21 4.51 6.45 0 1.94 3.21 4.51 6.45 0 1.94 3.21 4.51 6.45

Aggregates Fine

Coa.

8.88

41.8 41.8 40.4 39.9 39.1 39.6 38.7 38.1 37.5 36.6 37.6 36.6 35.9 35.3 34.3

CO2 from batching (eq. kg/m3)

Total CO2 (eq. kg/m3)

0.018

443 386 347 308 250 441 382 345 306 248 439 380 342 304 246

W

0.024 0.024 0.024 0.024 0.024 0.0293 0.0293 0.0293 0.0293 0.0293 0.0348 0.0348 0.0348 0.0348 0.0348

Note: M4515, for example, means concrete mix containing W/B of 0.45 and FA of 15%. ‘C’, ‘FA’, ‘Coa.’, and ‘W’ mean cement, fly ash, coarse aggregates, and water, respectively.

the concrete cover depth or the threshold depth to monitor the chloride content is selected as 80 mm for concrete structures exposed to chloride environment [46]. And, repairs by cover concrete replacement are applied such that the lifetime of concrete structures are designed to be free of corrosion for 100 years [47]. Unless otherwise specified, the quality of repair concrete in terms of diffusion coefficient and initial compressive strength must be selected such that it is approximately equivalent to that of original concrete. 5.1. Effect of repair concrete

Fig. 3. CO2 from concrete production vs %FA.

Table 3 CO2 in replacing concrete. Process

CO2 emission (eq. kg/m3)

CO2 emission (eq. kg/m2)

Transportation Hydro jetting Cleaning and coating rebars Application of shotcrete Total

200 1680 – 88 1968

– – 23.4 – 23.4

ondary credit, and seasonal credit, each with its own interest rate. From the 20-year database [45], the discount rate ranges between 0.75–6.25%, 1–6.75%, and 0.15–5.65% for primary credit, secondary credit, and seasonal credit, respectively. In this study, the discount rate is chosen as 0% and 4% for comparison.

5. Numerical assessment Based on the aforementioned idea and data, a Crank–Nicolson based finite difference approach is developed for the assessment. There are three numerical examples to study the effect of repair concrete, repair depth, and original concrete. In these examples,

In the first example, an original concrete structure with W/B of 0.55 (D0.55,0%(t) or M55) is repaired by replacing cover concrete with fly ash concrete with W/B of 0.45 and 15%FA (D0.45,15%(t) or M4515) and normal concrete with W/B of 0.45 (D0.45,0%(t) or M45). The chloride content in the structure is computed and plotted versus concrete depth as shown in Fig. 4a–d. From Fig. 4a, chloride ions penetrate through the original concrete timedependently. At the surface, the chloride content increases with time due to the effect of time-dependent surface chloride. Moreover, the rate of chloride diffusion is slower with increasing time due to the effect of time-dependent diffusion coefficient. In the year 10, the chloride content at the threshold depth reaches the critical chloride value (0.9% wt. of binder) as shown by the chloride profile at the year 10B (‘B’ means Before repair). In fact, the chloride content reaches the critical value at the 48th week after the year 10. With the first repairs over 80-mm cover, the original concrete is replaced by the fly ash concrete of M4515 (shaded area) as shown in Fig. 4b. Immediately after that, the chloride profile becomes the profile at the year 10A (‘A’ means After repair). At the year 11, the chloride ions from the surface penetrate through the fly ash concrete (or new cover concrete). And also, the remaining chloride ions in the original concrete will both distribute back through the fly ash concrete and penetrate further through the original concrete. When the chloride content at the threshold depth again reaches the critical value in the year 47B as shown in Fig. 4c, the same repair as the first one is repeated leading to Fig. 4d. It is noted that the critical value for the second repair is equal to 0.65% which stands for the critical value of the fly ash concrete (M4515) replaced in the first repair. The chloride content at the threshold depth of 80 mm is plotted versus time as shown in Fig. 5a. Without repairs, the chloride con-

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a) Years 1 to 10B (Before repair)

b) Years 10A (After repair) to 30

c) Years 30 to 47B (Before repair)

d) Years 47A (After repair) to 80

Fig. 4. Chloride vs depth for original concrete of M55 with cover concrete replacement by fly ash concrete of M4515.

Fig. 5. Chloride and CO2 for M55 with 80-mm replacement by M4515.

tent will continuously increase. This may cause corrosion initiation and concrete deterioration. If the corrosion-free period of the concrete structure is defined as the period of time in which the chloride content develops to reach the critical value (0.9% wt. of binder), its corrosion-free period is approximately of 10 years. But if the first repair by cover concrete replacement is applied at the year 10, the corrosion-free period will be extended. Immediately after the repair, the chloride content decreases to zero due

to removal of the chloride ions together with the taken-off original concrete. Later, the chloride content suddenly increases due to immediate redistribution of chloride ions from the original concrete (see the region near the repair depth in Fig. 4b). By the effect of the first repair, the corrosion-free period is extended by 37 years. At the year 47, the chloride content again reaches the critical value of 0.65%, so the second repair is applied. After that, the chloride content reaches the critical value again at the year 93, so the third repair is applied causing the extension of corrosion-free period over the design lifetime of 100 years. Using Eq. (9), the cumulative CO2 corresponding to the repairs can be calculated and shown in Fig. 5b. The CO2 occurs three times with the same amount of 211.7 eq. kg/m2 (30.8 for concrete production and 180.84 for replacement processing). At the end of the design lifetime of 100 years, the amount of CO2 is equal to 634.9 eq. kg/m2. If the normal concrete of M45 is used instead, the chloride content at the threshold depth and the cumulative CO2 are shown in Fig. 6a and b, respectively. There are five repair applications leading to five occurrences of CO2, so the cumulative CO2 for the design lifetime of 100 years is equal to 1081 eq. kg/m2. It is noted that the critical value is always equal to 0.9% wt. of binder, because the original concrete is the same as the repair concrete. In comparison, the amount of CO2 of each repair by the fly ash concrete of M4515 in Fig. 5b is a little lower than that by the normal concrete of M45 in Fig. 6b, because each repair by the fly ash concrete causes less CO2 than that by the normal concrete (see also Table 2). And also, the repairs by M4515 leads to longer extension of corrosion-free period, and this results in less number of repairs and less cumulative CO2 over the design lifetime of 100 years (634.9 eq. kg/m2).

A. Petcherdchoo / Construction and Building Materials 98 (2015) 799–809

Fig. 6. Chloride and CO2 for M55 with 80-mm replacement M45.

805

Fig. 8. Chloride and CO2 for M65 with 80- and 120-mm replacement by M55.

Hence, the repairs by concrete containing more amount of fly ash lead to not only lower CO2 in each repair but also lower cumulative CO2 at the design lifetime. Using Eq. (10), the cumulative CO2 in Figs. 5b and 6b can be transformed to the carbon price as shown in Fig. 7a and b, respectively. The undiscounted cumulative carbon price (0% discount rate) in both figures is calculated by multiplying the transformation factor (TF) of 0.015 to the amount of CO2 in Figs. 5b and 6b, while the discounted cumulative carbon price (4% discount rate) is calculated by multiplying both the transformation factor (TF) and the discounting factor (DF). Due to the time value of the carbon price, the undiscounted carbon price at the design lifetime of 100 years is about 3–4 times the discounted one.

5.2. Effect of repair depth The second example shows the assessment of an original concrete structure with W/B of 0.65 (D0.65,0%(t) or M65). Two kinds of applicable repair concrete are chosen as normal concrete with W/B of 0.55 (D0.55,0%(t) or M55) and fly ash concrete with W/B of 0.55 and 15%FA (D0.55,15%(t) or M5515). The repair depth is selected at least equal to the concrete cover depth (or the threshold depth)

Fig. 7. Present value of carbon price for M55 with 80-mm replacement by M4515 and M45.

Fig. 9. Chloride and CO2 for M65 with 80- and 120-mm replacement by M5515.

in order to control the corrosion at the surface of rebars. Here, it is equal to 80 and 120 mm for comparison. By varying the repair depth (xp), the chloride content and the cumulative CO2 for the concrete structure are shown in Figs. 8 and 9. For the original concrete of M65 with repairs by M55, the chloride content at the threshold depth of 80 mm is shown in Fig. 8a. After each repair, both the chloride content for 80-mm and 120mm replacement decreases to zero in the year 7. Prior to the second repair, it is observed that the chloride content for 80-mm replacement immediately increases at the beginning but gradually increases later. However, the chloride content for 120-mm replacement gradually increases at the beginning but quickly increases later. It should be also observed that the extension of the corrosion-free period for 80-mm replacement is shorter than that for 120-mm replacement. Moreover, there are seven and six applications for 80- and 120-mm replacement, respectively, over the design lifetime of 100 years. Hence, if the depth of concrete replacement is deeper, not only the extension of corrosion-free period after each repair is longer but also the total number of replacement is less. Fig. 8b compares the cumulative CO2 for 80-mm and 120-mm replacement. The amount of CO2 due to each of 80-mm replacement is lower than that due to each of 120-mm replacement,

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because the amount of CO2 is in the function of the repair depth as shown in Eq. (9). It is also observed that the 7th application of 120mm replacement possibly occurs outside the design lifetime. On the other hand, if the design lifetime is specified longer, the number of applications for 120-mm replacement and its cumulative CO2 may increase. Therefore, the design lifetime also plays an importance role in repair planning. In some cases, although the repair depth is deeper, the extension of corrosion-free period after each repair is not longer. For example, let us consider Fig. 9. The original cover concrete of M65 is repaired by the fly ash concrete of M5515. From Fig. 9a, the general behavior of chloride diffusion in concrete with 80and 120-mm replacement is similar to that discussed in Fig. 8a. Except, the chloride content after 80-mm replacement reaches the critical value later than that after 120-mm replacement. On the other hand, deeper repair depth leads to shorter extension of corrosion-free period. This is different from the results in Fig. 8. This occurs, because, in Fig. 9, the diffusion coefficient of the fly ash repair concrete (M5515) is quite different from that of the original concrete (M65). Fig. 10 shows the comparison of their diffusion coefficient in range of the first and the second repair application time (the years 7 and 35, respectively). If the ratio of the diffusion coefficient for the original concrete to that for the fly ash concrete is defined as the diffusion coefficient ratio, so the ratio falls between 1.5 and 3.3 with the average of 2.4. It is noted that the original concrete is 7 years older than the fly ash concrete, because the fly ash concrete is applied when the age of the original concrete is 7 years old. Hence, the plot of the diffusion coefficient of the original concrete and the fly ash concrete is started at the year 7 and at the beginning of the age, respectively. To explain the diffusion behaviors for Fig. 9a in more details, let us consider the diffusion of chloride ions in concrete after 80- and 120-mm replacement in Fig. 11a and b, respectively. For both cases, the diffusion coefficient of the fly ash repair concrete is lower than that of the original concrete, so the chloride ions in the repair concrete basically tend to move toward the original concrete leading to the reduction of the chloride ions in the repair concrete. However, the resultant chloride content for both cases is not the same. For 80-mm replacement, the chlorides ions around the threshold depth can easily distribute from the repair concrete to the original concrete. However, for 120-mm replacement, the chlorides ions around the threshold depth cannot easily distribute to the original concrete, because the quality of the repair concrete is higher than that of the original concrete. This leads to slow diffusion of chloride ions in the repair concrete. And also, the chloride ions from the original concrete cannot easily redistribute to the repair concrete, because of two reasons. First, little amount of

a) Year 7A (After repair) to 34B (Before repair)

b) Year 7A (After repair) to 32B (Before repair) Fig. 11. Chloride vs depth for M65 with replacement by M5515.

chloride ions is left in the original concrete after repairs (see the profiles at the year 7A in Fig. 11b). Second, the repair concrete acts as a barrier due to its higher quality than the original concrete. These two reasons lead to the accumulation and quick increase of chloride ions around the threshold depth for 120-mm replacement. The cumulative CO2 for repairs by M5515 is shown in Fig. 9b. The amount of CO2 (eq. kg/m2) due to each 80-mm replacement is lower due to less repair depth, and also the cumulative CO2 (eq. kg/m2) at the design lifetime is lower due to less number of repairs. In comparison between Figs. 8b and 9b, it is found that the increase of the amount of fly ash in the repair concrete by 15% leads to the reduction of the cumulative CO2 at the design lifetime by as high as 58% and 32% for 80- and 120-mm replacement, respectively. The discounted cumulative carbon price for repairs by M55 and M5515 is compared in Fig. 12a and b, respectively. It is found that the increase of the amount of fly ash in the repair concrete by 15% leads to the reduction of the discounted cumulative carbon price at the design lifetime by as high as 41% and 35% for 80-mm and 120mm replacement, respectively. 5.3. Effect of original concrete

Fig. 10. Diffusion coefficient for M65 and M5515 and its ratio.

This example shows the durability design of an original concrete structure by varying its W/B between 0.45 and 0.65 while keeping %FA as 15%. For repairs, the fly ash concrete with W/B of

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Fig. 12. Present value of carbon price for M65 with 80- and 120-mm replacement by M55 and M5515.

0.45 and 25%FA (D0.45,25%(t) or M4525) is chosen. And, the repair depth is varied between 80 and 120 mm. For the original concrete of M6515 (D0.65,15%(t)), the first repair for 80- and 120-mm replacement occurs at the same time as shown in Fig. 13a. However, the second repair for 80-mm replacement occurs later than that for 120-mm. This shows similar tendency as observed in Fig. 9. Moreover, the diffusion coefficient ratio of the original concrete (M6515) to the repair concrete (M4525) falls in the range of 1.12–3.42 with the average of 2.27 as shown by the upper line in Fig. 16. Fig. 14a shows the case that the original concrete is selected as M4515 (D0.45,15%(t)). The first repair for both 80- and 120-mm replacement occurs at the same time. However, the second repair for 80-mm replacement occurs earlier than that for 120-mm. This agrees with the diffusion behavior in common sense in the way that deep depth of a repair leads to longer extension of service life. It is also observed that the diffusion coefficient ratio falls in the range of 0.64–1.88 with the average of 1.76 as shown by the lower line in Fig. 16. If the diffusion coefficient ratio is chosen between the ratio used in Figs. 13a and 14a, further observation can be found in Fig. 15a. The original concrete is chosen as M5515 (D0.55,15%(t)), and the ratio falls in the range of 0.83 to 2.52 with the average of 1.68 as shown by the middle line in Fig. 16. Apparently, the first and second repairs for both 80- and 120-mm replacement occur at the same time. If the diffusion

Fig. 13. Chloride and CO2 for M6515 with 80- and 120-mm replacement by M4525.

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Fig. 14. Chloride and CO2 for M4515 with 80- and 120-mm replacement by M4525.

Fig. 15. Chloride and CO2 for M5515 with 80- and 120-mm replacement by M4525.

coefficient ratio which causes this phenomenon is called threshold ratio, it is seen that the threshold ratio for this case falls in the range of 0.83–2.52 with the average of 1.68. As a result, if the diffusion coefficient ratio is larger than the threshold ratio, deeper cover concrete replacement causes shorter extension of corrosion-free period as shown in Fig. 13a. But if the diffusion coefficient ratio is less than the threshold ratio, deeper cover concrete replacement causes longer extension of corrosion-free period as shown in Fig. 14a. Figs. 13b–15b show the cumulative CO2 in considering different original concretes. For the design lifetime of 100 years, the cumulative CO2 for 80-mm and 120-mm replacement on different original concrete is the same (208.57 and 301.16 eq. kg/m2, respectively), except that it occurs at a different time. If the repair depth is further chosen as 80 and 90 mm while keeping the same original concrete and the same repair concrete as those used in Fig. 15, some observations can be found. Fig. 17a represents the chloride profiles for M5515 repaired with M4525. It is found that deeper repair depth causes shorter service life extension. However, if the same original concrete and the same repair concrete as those used in Fig. 14 are chosen instead, Fig. 18a shows that the first and second repairs occur at the same time. Hence, if the repair depth is reduced from 120 to 90 mm, the threshold ratio will also be reduced. This shows that the repair depth also influences the threshold ratio.

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In comparison between Figs. 17b and 18b, it is found that in spite of the same number of repairs and the same repair depth, the present value of the carbon price is not the same due to the discounting factor. 6. Conclusion

Fig. 16. Ratio of diffusion coefficient for M6515:M4525, M5515:M4525, and M4515:M4525.

Fig. 17. Chloride and carbon price for M5515 with 80- and 90-mm replacement by M4525.

In this study, a Crank–Nicolson based finite difference approach is used to assess extension of corrosion-free service life (or corrosion-free period) of chloride exposed concrete structures after repairs by cover concrete replacement. Using the approach, the time for repairs can be predicted. At the predicted repair time, the environmental impacts, in terms of the CO2 and the carbon price dealing with production of repair concrete and with processing of cover concrete replacement, occur. These can be assessed using a CO2 emission model developed in this study. Subsequently, the present value of the carbon price is calculated by multiplying the CO2 with the transformation factor (TF) and the discounting factor (DF). From the study, it can be concluded that 1. Repairs by concrete with more amount of fly ash basically lead to not only lower CO2 in each repair but also lower cumulative CO2 because of longer extension of corrosion-free period after repairs. 2. The increase of the amount of fly ash in repair concrete by 15% leads to the reduction of the cumulative CO2 and the cumulative carbon price due to cover concrete replacement by as high as 58% and 41%, respectively, at the design lifetime. 3. If the ratio of the diffusion coefficient of original concrete to repair concrete is less than the threshold ratio, deeper depth of cover concrete replacement leads to longer extension of corrosion-free period as well as less number of repairs. However, this may cause larger amount of CO2 in each repair and also over the long-term design lifetime, because the amount of CO2 is a function of the repair depth. 4. If the ratio of the diffusion coefficient of original concrete to that of repair concrete is larger than the threshold ratio, deeper depth of cover concrete replacement causes shorter extension of corrosion-free period. This shows the necessity of the method proposed in this study in a long-term durability design. 5. In selecting a method of cover concrete replacement, it is important to consider the interaction between the repair material and the depth of repairs, because both of them are found to be related. This is observed, because the repair depth is found to be related to the threshold ratio which is the ratio of the diffusion coefficient of original concrete to that of repair concrete. 6. There are two recommendations for further study. First, different kinds of supplementary cementitious materials, such as silica fume, and etc., are used all around the world. Therefore, the long-term durability and sustainability design for these materials should be studied and compared to using fly ash. Second, the amount of CO2 due to fly ash usage in this study arises from transportation from coal power plants. However, in the countries which use fly ash in the concrete industry, the amount of CO2 in the process of fly ash production would dominate instead, because an allocated impact of coal fired electricity production needs to be assigned to it. Hence, this subject is recommended for further study.

Acknowledgement

Fig. 18. Chloride and carbon price for M4515 with 80- and 90-mm replacement by M4525.

The research was funded by King Mongkut’s University of Technology North Bangkok under the Contract No. KMUTNBNRU-58-22.

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