Construction and Building Materials 122 (2016) 264–272
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Dimensional factors in oxidation induced fracture in reinforced concrete Michele Zulli a, Masoud Ghandehari b,⇑, Alexey Sidelev c, Surendra P. Shah d a
Province of Chieti, Dept. of Viability, School Construction and Spatial Planning, via Discesa delle Carceri n. 1, 66100 Chieti, Italy New York University, Dept. of Civil and Urban Engineering, 6 MTC Center, Brooklyn, NY 11201, USA c Parsons (PTG), Manhattan, NY, USA d Northwestern University, Dept. of Civil Engineering, Evanston, IL, USA b
h i g h l i g h t s A constant current accelerated corrosion testing program for reinforced concrete was carried out to facilitate modeling of to time to cracking by
corrosion. The specific aim was to investigate the effect of specimen dimensions, including bar size and concrete sample size. A model is proposed that incorporated the size factors and the corrosion current.
a r t i c l e
i n f o
Article history: Received 25 December 2015 Received in revised form 6 May 2016 Accepted 11 May 2016 Available online 9 July 2016 Keywords: Concrete Reinforcing bar Corrosion Cracking (fracture) Durability Bond Service life
a b s t r a c t Experiments on reinforced cylindrical concrete elements were carried out studying the influence of specimen size on corrosion of steel reinforcing bars and the extent of cracking of concrete. This work was achieved by accelerated corrosion of reinforced concrete cylinders subject to constant current conditions. Two concrete cylinder and reinforcing bar sizes were used. The effect of cracking on the specimen impedance and corrosion rate was evaluated and a correlation between time to concrete cover cracking and implications on service life was extrapolated. A cracking model as function of time and dimensions of the specimens was developed. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Fracture of concrete by steel corrosion is known to be the main mechanism of damage in the long term durability of reinforced concrete when exposed to chlorides and acidic environments. The corresponding reduction in the passivation of the steel surface and the reduction in the alkalinity of the concrete pore fluids lead to accelerated corrosion of the reinforcing steel [1,2]. Corrosion of steel by dissolution degrades the composite action in reinforced concrete structural elements, compromising its performance by reducing bond between steel and concrete [3–9,32]. Cracking of concrete in general and by corrosion allows accelerated ingression of water and chlorides and promotes the corrosion and cracking process [31]. It is believed that the appearance of the first crack ⇑ Corresponding author. E-mail addresses:
[email protected] (M. Zulli),
[email protected] (M. Ghandehari),
[email protected] (A. Sidelev),
[email protected] (S.P. Shah). http://dx.doi.org/10.1016/j.conbuildmat.2016.05.077 0950-0618/Ó 2016 Elsevier Ltd. All rights reserved.
in reinforced concrete elements is an indicator of the end of its service life [10,11]. Modelling the time to cracking by corrosion is challenging since the corresponding electro-chemo-mechanical processes involve complex interactions and are affected by parameters which vary with time and space across the structure [1,3,10–19]. The modeling of damage by cracking is also challenging. Products of the corrosion process of the reinforcing bar are multilayered and are composed of several chemical compounds with varying mechanical properties. The exterior layers of oxidized irons have greater access to chloride ions, with high iron to oxygen ratio, and as a result are less expansive [1]. This layer is believed to impede the further ingression of chlorides but not able to impede the ingression of oxygen, creating an inner, more expansive layer of rust, which is caused by a low iron/oxygen ratio. These products of steel corrosion are amorphous, and their bulk properties in the tri-axial state has been difficult to quantify; posing a challenge in the numerical simulation of cracking by corrosion.
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Notations Wexp Wth I t A Z F i
D d W xexp xth w
measured weight loss (g) theoretical weight loss (g) galvanic current (A) time (s or days) atomic weight of iron valency of the metal Faraday constant corrosion current
mr/s a
It has been shown that the splitting of concrete and the associated loss of bond strength is not only a function of the degree of corrosion, but is also a function of the size and geometry of the components of the element cross section [10,14,4,20]. Despite significant effort, modeling of expansion forces due to the corrosion process is not fully understood. This report aims to contribute to modeling of corrosion induced cracking in reinforced concrete by subjecting specimens of varying sizes to a constant current accelerated corrosion process. We have therefore initiated a study in order to investigate: (a) the extent of corrosion as a function of corrosion current, (b) the relation between steel mass loss and cracking of concrete, (c) the effect of size of both concrete cover and reinforcing bar on crack initiation, (d) the effect of cracking on rate of corrosion, (e) the correlation between cover cracking and service life. A number of concrete cylinder specimens were subjected to accelerated corrosion process by applying direct constant current. A model for cracking based upon the concrete cover to reinforcing bar diameter ratio is also presented. The validation of the model is demonstrated by comparing the predictions with experimental data obtained from this research and from other studies cited in this paper. 2. Experiment plan Four dimensional variations were used; the concrete cylinder specimens were 102 mm and 152 mm in diameter, with 203 mm and 304 mm length respectively, with two reinforcing bar diameters of 9.5 mm and 19 mm (Fig. 1 and Table 1). The specimens were labeled CsRs, CsRl, ClRs, and ClRl, where (C) and (R) stand for cylinder and reinforcing bar, and the subscripts (s) and (l) represent the specimen size (small or large).
The concrete mixture was designed for compressive strength average of 40 MPa in 28 days. Table 2 shows the mixture ingredients. At 28 days, the tested average cylindrical compressive strength of the concrete was 39.08 MPa, the average
l
Table 1 Specimen dimensions. Specimens
CsRl ClRl CsRs ClRs
Dimensions (mm) Cylinder diameter, D
Steel bar diameter, d
Length, L
C
C/d
102 152 102 152
19 19 9.5 9.5
203 304 203 304
41.5 66.5 46 71
2.18 3.50 4.87 7.50
C = size of concrete cover (D d)/2
Table 2 Mixture proportions. Cement Sand Gravel (maximum size 8 mm) Water W/C Unit weight
(kg/m3) (kg/m3) (kg/m3) (kg/m3) (kg/m3)
431 862 862 194 0.45 2349
splitting tensile strength was 4.28 MPa, and the average elastic modulus was 28.34 GPa. Grade 60 reinforcing steel bars were used with a tested average yield strength 413.7 MPa. The concrete was cast vertically in plastic molds with reinforcing steel positioned as shown in Fig. 1. A table vibrator was used for compaction. Twenty four hours after the casting, the plastic molds were removed and the concrete was cured in a steam room at 20 °C and 95% relative humidity for 28 days. In order to create an axisymmetric condition with respect to mass and ion transport, epoxy resin and silicon adhesive was applied to the end surfaces of the reinforcing bar and concrete cylinders respectively.
2.2. Corrosion test apparatus and galvanic current measurements
2.1. Mixing, casting and curing of specimens
l
concrete cylinder diameter reinforcing bar diameter original reinforcing bar weight measured corrosion penetration theoretical corrosion penetration measured crack width at the reinforcing bar ratio of specific volume of rust to steel scaling factor
s
Fig. 1. Specimen name designation.
Fig. 3 shows the series of electrochemical cells prepared for the accelerated corrosion testing. Four specimens in each size ratio were cast, resulting in total 16 specimens; four each corresponding to four target levels of corrosion of 2.5%, 5%,
s
Fig. 2. Accelerated corrosion setup.
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M. Zulli et al. / Construction and Building Materials 122 (2016) 264–272
Fig. 3. Test setup for application of constant current.
7.5%, and 10% (by weight of original reinforcing bar). The calculations for the target levels of corrosion are based on Faraday’s law, (Eq. (1a)) assuming 100% current efficiency [10]. The corresponding calculated current is shown in Table 3. The corrosion cell (Fig. 2) consists of a power supply, a copper plate as cathode, and the specimen with the reinforcing bar as anode submerged in the electrolyte solution composed of 5% sodium chloride (NaCl) by weight of water. The specimens were placed in this solution two days prior to the initial application of the corrosion current. The electrolyte solution was changed once per week to insure constant concentration of NaCl. One control specimen for each specimen size was immersed in tap water. In order to obtain the targeted corrosion level, specimens were subjected to direct constant current. All 16 specimens were controlled simultaneously as shown in Fig. 3. Each subcircuit of the parallel circuit system consists of the three resisting elements: the specimen (Rs, not to be confused with Rs denoting small reinforcing bar) in series with an adjustable resistor (Ra) and a fixed resistor (Rf = 10 X). The fluctuations in the galvanic current (I) caused by changes in the specimen impedance were recorded twice a day for each specimen. This was done by measuring the change in voltage (V) across the fixed resistor (Rf); and subsequently adjusting the resistors Ra to maintain the specified constant current.
Fig. 5. Dilation at reinforcing bar.
2.3. Sample preparation After attaining the prescribed exposure time and corresponding target mass loss of 2.5%, 5%, 7.5%, and 10% according to Faraday’s law, specimens were cut into 50 mm thick slices (Fig. 4) using a water lubricated round saw. This provided three
to five slices corresponding to the small and large cylinder sizes. The number of cracks, their length, reinforcing bar dilation and crack mouth opening displacement near the reinforcing bar surface were subsequently measured with a microscope (Fig. 5). 2.4. Weight loss measurements and corrosion penetration
Table 3 Corrosion current levels. Specimens
Currents I (mA)
CsRl ClRl CsRs ClRs
75 115 20 30
Theoretical design corrosion level, % i (A/m2) 6.16 6.16 3.29 3.29
7 days 2.5
14 days 5
21 days 7.5
Faraday’s law expresses the theoretical weight loss of a metal, oxidized by the passage of an electric current I in a given time interval, atomic weight A, valance of iron Z, the Faraday constant F [21]:
(
28 days 10
Wth ¼
) n X Ii þ Ii1 A ðti ti1 Þ 2 ZF i¼1
For the reinforcing bar, the mass conversion as a function of time in days versus corrosion current is:
Wth ¼ 25
( n X Ii þ Ii1 i¼1
Total 40 slices ClRl and ClRs
x x x x x
ð1Þ
Total 24 slices CsRl and CsRs
x x x
Fig. 4. Specimen examination for cracks.
ð2Þ
2.4.1. Gravimetric weight loss measurement At specified time intervals corresponding to the specified levels of corrosion, the cut pieces of reinforcing bar were carefully measured for mass loss. The [22] ASTM G1-90 procedure of chemical cleaning of corrosion products, C.3.1, was used in order to obtain the experimental weight loss Wexp for each slice of reinforcing bar. 2.4.2. Theoretical and experimental corrosion penetration Assuming uniform distribution of metal oxidation around the reinforcing bar [14] theoretical corrosion penetration can be correlated to the theoretical weight loss as function of steel density, and bar length and diameter:
xth ffi
t= 50mm, x,
2
) ðti ti1 Þ
W th
p L d cs
ð3Þ
From Eq. (2), the current density ii (Ii = ii p d L, Table 3) can be determined and by inserting this result into Eq. (3), the extent of theoretical corrosion penetration can be obtained (see Fig. 5):
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M. Zulli et al. / Construction and Building Materials 122 (2016) 264–272 n X ii þ ii1 ðti t i1 Þ 2 i¼1
ð4Þ
The concrete pore solution conductivity and the conductivities of other phases, such as corrosion product and interfacial transition zone (ITZ), can potentially be significant in the above calculations. However due to lack of data, their effects on the corrosion current density have been ignored. Given the experimental weight loss (Wexp), and assuming uniform distribution of corrosion, the measured corrosion penetration (xexp) can be deduced as function of bar diameter and the original bar weight:
xexp ffi
W exp d W 4
ð5Þ
It is acknowledged that uniform distribution of corrosion on the reinforcing bar is a crude assumption [33]. However results of such measurements shown for multiple sample replicas provide some backing for the calculations [14]. 2.4.3. Potential measurement A copper-copper sulfate (CSE: Cu-CuSO4) half-cell electrode was used for parallel measurement of corrosion potential [23]. A half-cell potential, which was more negative than 0.35 V CSE was considered indicative of reinforcing steel corrosion. Fig. 6 shows results of the potential measurements. These indicate that corrosion in all specimens was initiated within the first 2 days. Plotting the slope of specimens’ impedance versus time (Fig. 7) provides a correlative relation with corrosion potential for the first 2 days.
Half Cell Potential (-1) mV (CSE)
0.7
3. Analysis of results 3.1. Extent of corrosion as a function of galvanic current and time A comparison of the measured weight loss Wexp and the theoretical weigh loss Wth for all specimens/slices is shown in Fig. 8. Wide variability between Wth (determined by Faraday’s law) and Wexp is seen at higher levels of corrosion. Normalized values of the theoretical weight loss Wth relative to experimental weight loss Wexp is shown in Fig. 9, exhibiting a normal distribution. Fig. 10 shows the variation of the ratio between the calculated and the measured weight loss Wth/Wexp for varying ratios of C/d, where C is the concrete cover and d is the diameter of the reinforcing bar. 15
Wexp= 2.57 + 0.57*Wth R2 = 0.47
10
5
N. of data= 41 0
0.6
0
5
10
15
Calculated Weight Loss, Wth 0.5 Fig. 8. Calculated vs. experimental weight loss.
0.4
- 350 mV
0.25
0.3
CsRs CsRl ClRs ClRl
0.2
0.1 0
24
48
72
96
120
144
168
192
Time, (Hours)
Normal model
μ = 1.17, σ = 0.37 Relative frequency
xth ffi 3185
)
Measured Weight Loss, Wexp
(
N. of data= 41
0.2 0.15 0.1 0.05
Fig. 6. Half-cell potential measurements vs. time.
0 0
0.4 0.8 1.2 1.6
2
2.4 2.8 3.2
Wth /Wexp 4
CsRl ClRl
Calculated / Measured Weight Loss of Rebar, Wth/Wexp
CsRs ClRs
3
dR/dt
Fig. 9. Relative frequencies with normal distribution.
2
1
0 0
24 48 Time, (Hours)
Fig. 7. Slope of specimens impedance vs. time.
72
3
CsRl ClRl CsRs
ClRs
2
1
0 0
2
4
6
8
10
C/d Fig. 10. Variation Wth/Wexp as function of C/d.
M. Zulli et al. / Construction and Building Materials 122 (2016) 264–272
Fig. 11 shows weight loss values versus time from both experimental data and from theoretical calculations. Calculations based on Faraday’s law seem to overestimate the weight loss for high value of concrete cover, and underestimate it for small concrete covers. Fig. 12 shows the predicted penetration xth based on Faraday’s law assuming corrosion was initiated immediately at the start of the test (Eq. (2)). The rate of corrosion indicated by the slope of the dashed lines depends on the corrosion current density I (Table 3). Fig. 13 shows a comparison of average values of measured and theoretical corrosion penetration. Correlation of current density by Faraday’s law and the experimental data on penetration depth is good, particularly with respect to bars’ size dependencies. The calculations based on Faraday’s law seem to be missing some of the final detail emerging from the bar and cover size.
Average of measured weigh loss, Wexp (%)
16
Faraday's law CsRs CsRl ClRs ClRl
12
8
4
0 0
200
400
600
800
Time, (hours) Fig. 11. Average of measured weight loss vs. time.
Measured corrosion penetration xexp, (μm)
800
Faraday's law, Rl Faraday's law, Rs CsRs r CsRl ba g n i ClRs c or inf ClRl re
600
400
g e rcin rg info La e r all Sm
200
bar
0
3.2. Impedance measurement and time to cracking 3.2.1. Evolution of specimen’s impedance Estimation of the specimen impedance was made by modeling the system as an electrical circuit with three resistors in series, using Ohms law where the values for the fixed, adjustable and specimen impedance were used:
V ¼ I ðRf þ Ra þ Rs Þ where V = voltage impressed by power supply. Having the galvanic current (I) and resistance across the adjustable resistor, the specimen resistance can be obtained by measuring the resistance across the fixed and adjustable resistors. The fluctuation of the specimen impedance (Rs) is consequently tracked as the corrosion progresses and as the concrete cracks (Figs. 14 and 15). The observed initial increase in the impedance is attributed to the initial oxidation and passivation of the reinforcing bar surface [1]. The specimen’s resistance ultimately reaches a maximum and remains until it begins cracking. All specimens reach the point of maximum impedance at approximately 5 days. The respective elapsed time up to first surface cracking is shown. The impedance drop shown in Figs. 14 and 15 corresponds to the time that a single visible crack appeared on the specimen surface. Following are some observations: – The small specimens with large reinforcing bar (CsRl) cracked first after 6 days, followed by 50% reduction in impedance in a period of about two days. – The small specimen with the small reinforcing bar (CsRs) cracked after 19 days, followed by a 50% reduction in impedance. The post-cracking impedance reached steady state in about a week.
Impedance of Specimens, Rs (Ω)
268
Crack on Specimens CsRs
300
200
100 Crack on Specimens CsRl
0 0
0
200
400
600
168
800
Time, (hours)
800
CsRs CsRl ClRs ClRl
600 400 200 0 0
200
400
600
800
Corrosion penetration, xth (μm) Fig. 13. Calculated vs. experimental corrosion penetration.
504
672
Fig. 14. Impedance of specimens vs. time for small cylinders Cs.
Impedance of Specimens, Rs ( Ω)
Corrosion penetration, xexp (μm)
Fig. 12. Average of corrosion penetration vs. time.
336
Time, (Hours)
300 No crack on Specimens ClRs
200
100
Crack on Specimens ClRl
0 0
168
336
504
672
Time, (Hours) Fig. 15. Impedance of specimens vs. time for large cylinders Cl.
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M. Zulli et al. / Construction and Building Materials 122 (2016) 264–272
– The large specimen with large reinforcing bar (ClRl) cracked after 13 days, followed by approximately 50% impedance reduction, then reaching a steady state in about a week. – The large specimen with small reinforcing bar (ClRs) did not crack and maintained constant impedance up to the end of week 4. The slower drop in impedance after cracking for the specimen with larger cover (ClRl vs. CsRl) is consistent with the accepted understanding that increasing the concrete cover is beneficial with respect to the rate of ionic penetration, even in cracked concrete. Examination of impedance measurements for specimens with the same concrete size but different bar sizes (CsRs vs. CsRl and ClRs vs. ClRl) shows increasing specimen impedance and time to cracking with decreasing bar size. While to some extent this can be attributed to increase in concrete cover, it is perhaps more so due to the influence of the size of a fracture and the smaller expansive forces generated by the corrosion of the smaller bars. For example in the case of samples with small concrete, those with large bars cracked after 6 days, while those with small bars cracked after 19 days.
Fig. 17. Specimen slices CsRl (a, b, c) and CsRs (d).
2.5
Cover Crack Width, (mm)
3.2.2. Corrosion induced cracking Fig. 16 shows cracked specimens for big and small concrete size at the designated corrosion showing example of internal cracks and those that emerged on the concrete specimen surface. Fig. 18 shows the evolution of crack width on the specimen surfaces. Note that here w (lower case) refers to crack width, whereas in previous sections W (upper case) referred to weight loss. The crack width for smaller specimens CsRl are in the range 0.25–2.2 mm, and the crack width on large specimens with larger bar ClRl are in the range 0.1–1.2 mm. Surface crack width on specimens CsRs are in the range 0.2–0.6 mm. The growth of surface crack width can be approximated as linearly proportional with time. Above results are consistent with results reported by others e.g. [10], where it was shown that after the first visible crack on the specimens surface, crack width growth is linearly proportional to time. Fig. 17(a)–(c) shows typical internal cracks for small specimens with large bar CsRl after 1, 2 and 3 weeks of corrosion. Fig. 17d shows typical internal cracking for the small specimen with small bar CsRs after 3 weeks of corrosion process when it first appeared. Results of the corresponding measurements of crack width near the reinforcing bar examined for all specimens is shown in Fig. 19.
CsRs CsRl ClRl
2
1.5
ClRs no cracked
1
0.5
0 0
200
400
600
800
Time, (Hours) Fig. 18. Measured cover crack width on the specimen surface.
The following observations were made:
Fig. 16. Big and small cracked specimens.
– Small concrete, small bar specimen CsRs: Two internal cracks appeared at the end of week 1. These cracks exhibited stable growth for nearly two weeks and eventually appeared on the specimen surface by end of week 3. – Small concrete, large bar specimen CsRl: One crack appeared at the end of week 1. Four internal cracks were present by end of week 2. – Large concrete, small bar specimen ClRs: This series did not crack (internally or externally) at the end of weeks 1, 2, 3 or 4. – Large concrete, large bar specimen ClRl: Did not crack internally by end of week 1; but four internal cracks, some of which had propagated to the surface, were present at the end of week 2. Growth of small internal/radial cracks during the second week is represented by the gradual reduction in the specimen impedance in the second week.
M. Zulli et al. / Construction and Building Materials 122 (2016) 264–272
Total Crack Width at Reinforcing Bar, Σ w (mm)
270
4.1. Model assumption 4
CsRs - 2 cracks CsRl - 4 cracks ClRl - 4 cracks
The concrete was idealized as a thick wall cylinder subject to internal radial pressure with linear and elastic states of stress and strain [11,25,26]. It was further assumed that the concrete will crack when the tangential stress rt reaches the concrete tensile strength fct. We further assumed that the average tangent normal stress (hoop stress) is linearly proportional to the circumferential elongation resulting from corrosion. We then postulated a simplified model relating the corrosion current icorr and the specimens’ geometry to the time of cracking. Finally, we assumed that the corrosion penetration xcorr is uniformly distributed around the steel bar [26], and that the corrosion currents icorr is constant; the circumferential stress in concrete at the reinforcing bar is related to corrosion penetration xcorr and the concrete cover. The tangential stress rt prior to first cracking can be expressed as:
3
2
1
ClRs no cracked
rt ¼ f ðxcorr ; C=d; tÞ
0 0
200
400
600
800
where xcorr = corrosion penetration; C/d = ratio of cover thickness C to reinforcing bar diameter d; t = time. The simplest form of this expression will be linear and can be expressed as:
Time, (Hours) Fig. 19. Measured total crack width (Rwexp) at reinforcing bar.
rt ¼ k t þ b
3.3. Volumetric expansion An estimate of the volumetric expansion of the corroding reinforcing steel can be obtained using the measured radial penetration xexp and the measured crack opening at the reinforcing bar Rwexp (Fig. 9), as proposed by Molina, et al. 1993 [14]:
X
wexp ¼ 2pðmr=s 1Þxexp ) mr=s ¼
P
wexp þ1 2 p xexp
ð6Þ
where xexp = measured corrosion penetration (defined in Eq. (5)), wexp = measured crack opening at the reinforcing bar, d = reinforcing bar diameter, mr/s = ratio of specific volume of rust to steel. Cracks, when present, allow diffusion of products of corrosion away from the reinforcing bar, therefore the analysis above is more accurate for the estimation up to the onset of cracking, and to some extent prior to the crack reaching the sample surface. Based on the calculations, a volumetric expansion of 2 and 1.5 is derived for the corroded steel in the large and small reinforcing bar, respectively. This evaluation does not take into account the corrosion product that penetrated into interface micro cracks or the porous concrete interfacial transition zone. Therefore the actual value of the expansion maybe somewhat larger. Products of corrosion are expansive, and the expansion coefficients of such materials have been shown to depend on the type of iron oxides [12,24,14]. The materials are a mixture of oxides and hydroxides, and their contents depend on multiple variables such as oxygen availability, presence of ions in the electrolyte, temperature, rate of corrosion, prior state of corrosion, etc. [25]. In addition to the spatial differences of chemical contents, the products of corrosion may have different porosities. The volumetric expansion of such products is often assumed to be between 2 and 4 [10,14,1,25–27,11].
4. Cracking model Experimental results were used to introduce a cracking model incorporating the corrosion current icorr and ratio of concrete cover to reinforcing bar diameter, C/d. The model is demonstrated by comparison with experimental data reported by other researchers.
Assuming that rt = 0 at t = 0, this can will be simplified as:
rt ¼ kt The coefficient k can be expressed with a multiplier a and the ratio C/d as:
k ¼ aðC=dÞ ) rt ¼ aðC=dÞt
ð7Þ
C/d is a unique non dimensional parameter which influences the time to cracking for a given corrosion current. Using the experimentally measured data of corrosion penetration vs. time, shown in Fig. 12, the multiplier a can be evaluated for each case (see Table 4). Fig. 20 shows a linear fit function for the corrosion penetration versus time normalized with C/d ratio. An expression for the tensile stress in concrete as function of corrosion rate, specimen geometry and time is therefore as follows.
rt ¼ aðC=dÞt
ð8Þ
Fig. 21 shows the corresponding estimated stress in concrete. The concrete splitting tensile strength 4.3 MPa indicated in the figure was measured using the splitting cylinder test. Note that the large specimen with small reinforcing bar did not develop a full crack. We nevertheless extrapolated the corresponding time value to obtain a closed form solution. Referring back to observed time to cracking for the various samples, the order of cracking of specimens can also be seen in Fig. 21, where CsRl cracked in one week, ClRl in two weeks, and CsRs in three weeks. ClRs did not crack within the 4 weeks test duration. The prediction shown in Fig. 21 follows the current experimental results reasonably well, giving some confidence to the validity of the formulation. The discrepancy between the experimental results and the formulation for specimen CsRs is most likely due to experimental error. Table 4 Parameters for conversion of corrosion penetration to tensile stress in concrete. Specimen
C/d
Multiplier, a
CsRl ClRl CsRs ClRs
2.18 3.50 7.50 4.87
0.067 0.054 0.094 0.109
271
Ratio of corrosion penetration to C/d, (μm)
M. Zulli et al. / Construction and Building Materials 122 (2016) 264–272
400
and its effect on cover cracking; Vu et al. 2005 [28] studied the effect of concrete quality and cover on cracking; Andrade et al. 1993 [10] studied small reinforced beams corroded by applying impressed current; Alonso et al. 1998 [29] studied the relationship between the corrosion level and cover cracking by accelerated corrosion; Maaddawy et al. 2005 [30] investigated the combined effect of corrosion and sustained loads on the structural performance for concrete beams.
Linear fit functions: Y= 11,606 *X R2= 0,978 Y= 0,419 *X R2= 0,916 Y= 2,155 *X R2= 0,845 Y= 0,632 *X R2= 0,9112
350 300 250 200
CsRl
ClRl
150
4.3. Scaling factor (a) and time to cracking
100
CsRs 50
ClRs
0 0
7
14
21
28
Time, (Days) Fig. 20. Corrosion penetration normalized with ratio C/d vs. time.
Concrete tensile hoop stress, (MPa)
10
CsRl ClRl CsRs ClRs
9 8 7
a ¼ f ct =ðtcr C=dÞ
Tensile strength: 4,3 MPa
4
ð9Þ
An estimation of the time to cracking is calculated accordingly. A comparison between calculated and measured cracking time is shown in Fig. 23.
6 5
The multiplier a was calculated for the experiments carried out by the researchers mentioned above. This was done using the reported information about the corrosion current and the dimensional features of the specimens and plotted as function of corrosion current divided by the ratio C/d (Fig. 22). Corrosion current here was used as a surrogate to the corrosion penetration used to derive the multiplier a. Assuming a direct relation between corrosion current and corrosion, we scaled the results of our experiment by a factor of icorr/100 to arrive at a common reference value of corrosion current when compared to that used in the other investigators’ experiments. a was calculated using values for cracking strength, cover to bar diameter and time to cracking:
3 1
α = 9,8 10-3 * (Icorr / C/d) - 0,1582
2
R2= 0,9455 1
Zulli et al. (current study) Maaddawy et al. [30] Andrade et al. [10] Alonso et al. [29] Lu C. et al. [11] Vu et al. [28]
0.8 0 0
7
14
21
28
Multiplier α
Time, (Days) Fig. 21. Stress in concrete vs. time.
0.6
0.4
4.2. Consideration of studies by others 0.2
Selected studies reported by other researchers (see Table 5) were tabulated and analyzed with respect to the application of Eq. (8), considering that the multiplier a is a function of corrosion current. We chose those experiments with comparable corrosion currents, in this case approximately 100 lA/cm2. Lu et al. 2011 [11] analyzed corrosion induced radial pressures by studying the effect of mechanical properties of corrosion layer
0 0
20
40
60
80
100
icorr / (C/d) Fig. 22. Correlation between the multiplier a and the ratio icorr/(C/d).
Table 5 Selected data from experiments carried in various other studies. Researchers
Bar diameter, d (mm)
Concrete cover, C (mm)
Time to cracking, tcr (h)
Corrosion current, icorr (lA/cm2)
Tensile concrete strength, fct (MPa)
Lu et al. [11] Vu and Stewart [28] Andrade et al. [10] .Alonso et al. [29] Maaddawy et al. [30]
16 16 16 16 16
19.5–29.5 25–50 20–30 20–70 33
87–112 134–195 86–120 113–264 95
100–150 100 100 100 150
3.7 3.06–4.2 3.6 3.9 4.9
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M. Zulli et al. / Construction and Building Materials 122 (2016) 264–272
Experimental cracking time, days
24
Zulli et al. (current study) Maaddawy et al. [30] Andrade et al. [10] Alonso et al. [29] Lu C. et al. [11] Vu et al. [28]
20
16
12
8
4
No. of data: 19 0 0
4
8
12
16
20
24
Theoretical cracking time, days Fig. 23. Theoretical vs. experimental values of concrete cracking time.
5. Conclusions Experiments were carried out to study the effect of dimensional factors governing the oxidation of steel reinforcing bars and the corresponding cracking of concrete. Constant current, accelerated corrosion tests on different specimens were carried out showing distinct features of cracking associated with size of concrete cylinder and reinforcing bar size. Comparison of the measured weight loss and the theoretical weight loss based on Faraday’s Law indicates an overestimation by the theoretical method. We observed that the ratio of concrete cover to reinforcing bar diameter can be used as a dimensional factor for prediction of concrete cracking subject to reinforcing bar corrosion. A multiplier incorporating the corrosion current and the dimensional ratio above is shown to predict the time to cracking. This formula was subsequently applied to experiments carried out by number of researchers showing strong correlation. Research significance This study is designed to evaluate the influence of concrete as a barrier to corrosion of reinforcing steel, and to evaluate the influence of reinforcing bar diameter on corrosion based cracking of concrete. These effects are explored from the point of view of chloride penetration and fracture. This information is significant not only for design of new structures but also for the health and life prediction of existing structures. Acknowledgements Generous support from the National Science Foundation Center for Advanced Cement Based Materials is gratefully acknowledged. The support of the scholarship from Ferdinando Filauro Foundation and University of L’Aquila – Italy to Dr. Michele Zulli, visiting scholar at Northwestern University, is also greatly appreciated. References [1] K. Wang, P.J. Monteriro, Corrosion products of reinforcing steel and their effects on the concrete deterioration, in: Odd E. Gjorv (Ed.), Symposium on Concrete for Marine Structures, Third CANMET/ACI International Conference on Performance of Concrete in Marine Environment, St. Andrews by the Sea, New Brunswick, Canada, 1996, pp. 83–97.
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