Construction and Building
MATERIALS
Construction and Building Materials 19 (2005) 83–90
www.elsevier.com/locate/conbuildmat
Assessment of the expansion related to alkali-silica reaction by the Damage Rating Index method Patrice Rivard *, Ge´rard Ballivy Groupe de recherche sur lÕauscultation et lÕinstrumentation, Civil Engineering Department, Universite´ de Sherbrooke, Canada J1K 2R1 Received 3 December 2003; received in revised form 7 June 2004; accepted 15 June 2004 Available online 26 August 2004
Abstract Among all the quantitative methods that have been proposed for the quantification of the internal deterioration caused by alkalisilica reaction (ASR), the Damage Rating Index (DRI) appears to be one of the most valuable. This paper investigates the correlation between the measured expansion caused by ASR on laboratory-concrete prisms and the damage to concrete, as quantified by the DRI on polished sections prepared from these prisms. New experimental results on the relationships between various petrographic features and expansion levels are provided. Petrographic examinations were also conducted on cores extracted from 35 cm concrete cubes affected by ASR. In this study, the DRI method enables a relatively good estimate of the amount of expansion of concrete prisms made with different aggregates. Results suggest that weighting factors used with the DRI method are appropriate. However, expansion and damage stem from combinations of factors that do not affect aggregates in the same manner. For concrete mixtures incorporating Potsdam sandstone, the most relevant petrograhic feature is the reaction rim surrounding reactive particles. For concrete mixtures incorporating Spratt limestone, almost every petrographic feature (e.g. cracks in aggregate particles and in cement paste) increases consistently with expansion. This study also showed that, in cube specimens made with high W/C ratio and low modulus of elasticity concrete, damage is more severe in the surface zone compared with inner zone. No such difference was observed in concrete cubes of lower W/C ratio higher modulus of elasticity. 2004 Elsevier Ltd. All rights reserved. Keywords: Petrography; Alkali-aggregate reaction; Cracking; Concrete; Quantification
1. Introduction Certain siliceous aggregates may react with the highly alkaline pore solutions in concrete and lead to the swelling and cracking of concrete structures (Fig. 1). This reaction is known as alkali-silica reaction (ASR). It is a complex reaction between reactive silica phases in aggregates and hydroxyl ions in the concrete pore solution, which produces a gel that swells in the presence of moisture, commonly named silica gel. Increasing signs *
Corresponding author. Tel.: +1 819 821 8000x3378; fax: +1 819 821 7974. E-mail address:
[email protected] (P. Rivard). 0950-0618/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2004.06.001
of ASR in numerous concrete structures throughout the world have incited engineers and researchers to develop methods and techniques for the assessment of ASR related damage and expansion. Among all the quantitative methods that have been proposed [1–6], the Damage Rating Index (DRI) has turned out to be relevant and effective for the quantification of the internal deterioration caused by ASR. The DRI method has been developed by Dr. P.E. Grattan-Bellew [7] and it has been used recently to evaluate the condition of several concrete structures in Canada [8–13] and in Brazil [14]. It consists of a petrographic examination performed on a polished concrete section with a stereomicroscope in order to identify and count defects
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Fig. 1. Deterioration of concrete structure caused by alkali-silica reaction.
associated with ASR. Some of typical ASR symptoms are shown in Fig. 2. This paper investigates the correlation between the measured expansion caused by ASR in laboratoryconcrete prisms and the damage to concrete, as quantified by the DRI. It provides new experimental results on the relationships between various petrographic features and expansion.
2. The Damage Rating Index method The DRI method can be applied to laboratory samples (prisms, cylinders) or to cores taken from large concrete structures. A diamond saw is first used to prepare 20–30 mm-thick sections; the sections are then
polished using abrasive powder or diamond-coated lap wheel down to 1 lm. Diamond-coated lap wheels are preferred to abrasive powder because they do not leave residues that would fill air voids or microcracks and cover silica gel. Thus, test specimens do not need to be washed extensively to remove the grit, which reduces leaching of alkali-silica gel from cracks and pores. A grid composed of 15 mm squares is then drawn on the polished section and the specimen is placed on a mobile stage of a stereomicroscope. The number of appearances of each one of the specific petrographic features (given in Table 1) is then counted for each one of the squares at 16· magnification. All types of defects are separately multiplied by a weighting factor. The factors were originally proposed to relate the defect to its probable contribution to the concrete deterioration and minimize the influence of other cracking mechanisms [7]. A critical review of these factors is found in another study [13]. The weighed values corresponding to each defect are then summed up and the total is normalized for a 100 cm2 surface. The number calculated is the DRI, a quantitative value representing the overall amount of deterioration of a given specimen. For instance, a core characterized by a DRI value of 300 is significantly more damaged than another one with a DRI value of 50. It is important to point out that DRI is a relative ranking of the amount of damage. DRI values are not absolute values and do not provide an absolute measurement. In this study, DRI was performed on 70–100 cm2 surfaces, obtained by cutting concrete prisms lengthwise. Moreover, an additional petrographic feature was recorded during examination, consisting of the number of cracks running through aggregate particles and extending into the cement paste, and noted as CA ) CP. Authors think that this feature is typical of ASR and is usually not associated with other deterioration mechanisms, such as mechanical fatigue, sulfate attack and freezing/thawing. No weighting factor has been applied yet to this defect and it has not been counted in the DRI value in this study.
Table 1 DRI weighting factors applied to each type of petrographic symptoms of AAR (from [7])
Fig. 2. Typical petrographic features associated with alkali-aggregate reaction: (a) reaction gel within reacted aggregate, (b) crack in coarse aggregate that extends into cement paste, (c) crack in cement paste filled with reaction gel and (d) dark reaction rim surrounding aggregate particle. This figure shows the Potsdam sandstone.
Defect type
Factor
Coarse aggregate with crack (CA) Coarse aggregate with crack and gel (CA + G) Coarse aggregate debonded (D) Reaction rim around aggregate (R)
0.25 2 3 0.5
Cement paste with crack (CP) Cement paste with crack and gel (CP + G) Air void lined with gel (AV)
2 4 0.5
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Table 2 Concrete mixture proportions
Aggregate type Cement content (kg/m3) Coarse aggregates (kg/m3) Fine aggregates (kg/m3) Water (kg/m3) W/C Total alkalis (kg/m3 Na2Oeq)
PO-Mass
PO-Structural
SP-Mass
SP-Structural
LM-Mass
Potsdam sandstone 320 1097 762 175 0.55 4.00
Potsdam sandstone 420 1063 739 167 0.40 5.25
Spratt limestone 320 1142 741 176 0.55 4.00
Spratt limestone 420 1113 742 168 0.40 5.25
Limeridge limestone 320 1142 741 176 0.55 4.00
3. Experimental
4. Results
3.1. Materials
4.1. Prism expansion
Three crushed aggregates were used for making the concrete; two reactive aggregates (Potsdam sandstonePO and Spratt limestone-SP) and one considered as non-reactive (Limeridge limestone-LM). Both limestones have a quite elongated/triangular shape whereas the Potsdam sandstone has a rounder shape. Two non-air entrained concrete mixtures were prepared, referred to as structural concrete and mass concrete. Mixture proportions are given in Table 2. The structural mixture was made following the Canadian CSA A23.2–14A specifications, with a W/C ratio of 0.40 and a cement content of 420 kg/m3. Two batches were made, one with the Potsdam sandstone (PO-Struc), and the other with the Spratt limestone (SP-Struc). The second mixture was designed to simulate a mass concrete, as it would be found in hydraulic dams, with a W/C ratio of 0.55 and a cement content of 320 kg/m3. A total of three batches were prepared with this mixture, one with the Potsdam sandstone (PO-Mass), one with the Spratt limestone (SP-Mass), and one with the Limeridge limestone (LM-Mass).
Expansion curves for all concrete mixtures are shown in Fig. 3. Expansion levels were different due to the reactivity of aggregates and the alkali content of the mixtures. Highest expansions were reached with Spratt limestone, which is well-known for its high reactivity in concrete. Limeridge limestone did not show significant expansion, which corroborates its non-reactivity. After more than 100 weeks, maximal expansion levels were 0.028% for LM-Mass, 0.093% for PO-Mass, 0.213% for PO-Struc, 0.267% for SP-Struc, and 0.323% for SP-Mass.
Aggregates (equal fractions of 5–10, 10–14 and 14–20 mm) were brought to SSD prior to batching. A normal ASTM Type I high-alkali cement was used in the preparation of all mixtures. Alkali content was raised to 1.25% Na2Oeq of the cement mass by adding NaOH pellets to the mixing water (completely dissolved prior to mixing). No other chemical or mineral admixtures were used. Several concrete prisms (75 · 75 · 300 mm in size) were cast from the five batches. The prisms were demolded after 24 h and stored over water in sealed 25-l plastic pails lined with damp terry cloth. The pails were stored in a heated room at 38 ± 1 C. The concrete expansiveness was regularly recorded using the provisions of CSA A23.2–14A ‘‘Procedure for length change due to alkali-aggregate reaction in concrete prisms’’.
At selected periods of time, one prism was removed from storage conditions, measured for expansion level and then cut lengthwise in three sections. The inner surface of the exterior sections was polished and petrographic examinations were performed on these two surfaces. Results from both polished sections were averaged. Detailed results of the petrograhic examinations are provided in Table 3. As previously found, DRI values
0,36 PO-Mass PO-Struc SP-Mass SP-Struc LM-Mass
0,32 0,28
Expansion (%)
3.2. Concrete batching and casting
4.2. Determination of the DRI on prisms
0,24 0,20 0,16 0,12 0,08 0,04 0,00 -0,04 0
8
16 24 32 40 48 56 64 72 80 88 96 104 112 Weeks
Fig. 3. Mean expansion curves for all concrete mixtures.
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Table 3 Results of the petrographic examinations Expansion (%)
Age (weeks)
Number of petrographic features (normalized for a 100 cm2 surface) CA
D
R
11.6 15.1 14.2 16.8 14.7 9.1
0 0.9 0 0 0 0
0 1.8 0 0 0 0.7
4.4 48.9 102.2 127 102 123.5
0.9 0.9 2.7 1.4 1.3 2.1
0.0 0 0 0.7 0.7 0.7
0 0 5.3 15.4 10.7 15.4
0 0 0 0.4 0.7 0.7
12 24 36 76 76 96 79
20.1 17.9 20.4 21.9 18.0 10.6 37.3
0 2.7 7.1 3.0 0 0.7 0.9
0 0 0.9 0 0 0 1.8
49.3 112.5 91.6 122.1 126.0 137.2 122.7
0 3.6 16.0 3.0 10.0 9.3 15.1
0 0.0 3.6 5.3 3.3 3.3 15.1
1.8 8.9 15.1 21.1 29.3 27.2 31.1
0 0 6.2 4.1 8.7 2.7 24.0
31 78 122 110 116 118 184
SP-MASS 0.016 0.100 0.139 0.251 0.270
12 24 36 52 76
56.9 72.0 75.9 73.5 84.4
3.6 5.3 5.4 10.8 48.0
0 0 0.9 0 0.9
0 0.9 0.9 0 0
10.7 30.2 28.6 32.3 46.2
0 8.0 10.7 19.7 37.3
3.6 15.1 17.9 14.4 24.9
5.3 24.0 22.3 34.1 72.0
44 129 142 191 374
SP-STRUC 0.169 0.214 0.227 0.270
36 71 76 76
96.0 88.2 106.7 136.0
15.1 31.2 74.7 54.2
0 0 0 0
0 0 0 0
22.2 8.7 21.3 18.7
12.4 29.1 33.8 54.2
42.7 41.4 35.6 28.4
24.0 33.3 51.6 65.8
170 239 372 411
LM-MASS 0.007 0.000 0.013 0.015
12 24 36 52
29.3 38.2 38.8 26.0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 2.0 0
0 0 0 0
0 0 0 0
0 0 0 0
4 12 52 82 76 82
PO-STRUC 0.010 0.042 0.065 0.103 0.149 0.167 0.244
increased with expansion [12]. Fig. 4 shows all DRI values plotted against expansion levels measured on prisms. DRI values measured on PO-Mass mixture ranged from 6.9 (4 weeks) to 81 (82 weeks). The most counted 450 PO-Mass PO-Struc SP-Mass SP-Struc LM-Mass
400 350
DRI
300 250 200 150 100 50 0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Expansion (%)
Fig. 4. Relationship between DRI values and expansion levels measured on prisms.
CP + G
AV
CA ) CP
CA + G
PO-MASS 0.001 0.014 0.079 0.081 0.085 0.106
CP
DRI
6.9 37 63 81 65 81
7.3 9.5 13.8 6.5
petrographic feature were the reaction rims (R), which have already been visible after 4 weeks in accelerated storage conditions. The rim is a typical reactivity symptom of the Potsdam sandstone [15]. The number of reaction rims grew quickly to stabilize at around 52 weeks. Some cracks were found within aggregate particles (CA), but only a few were filled with gel (CA + G). Also, a limited number of cracks, with and without gel (CP and CP + G), were found in the cement paste, as well as a limited amount of gel in air voids (AV). Crack propagation from aggregate particle to cement paste (CA ) CP) was not a common feature in PO-Mass samples and it was only observed at expansion levels greater than 0.08%. DRI values measured on PO-Struc mixture prisms were higher than those measured on PO-Mass prisms. Expansion levels were greater for the PO-Struc prisms. DRI values ranged from 31 (12 weeks) to 184 (79 weeks). The most counted feature was the reaction rim, which contributed to amplify DRI values, espe-
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but most likely to other mechanisms, such as ancient tectonic forces, freeze–thaw action and, in case of quarried aggregates, quarrying operations (i.e. drilling, blasting and crushing) and also to sawing for petrographic examination. Such internal cracking in aggregate of sedimentary origin often appears parallel to the bedding.
cially at early age. Little amount of reaction gel filling cracks (in aggregate or cement paste) was observed. Compared with PO-Mass, a greater number of cracks initiated within aggregate particles and extended into the cement paste. SP-Mass mixture generally exhibited more damage features compared with the same mixture made with Potsdam sandstone (PO-Mass), even considering respective expansion levels. DRI values ranged from 44 (12 weeks) to 374 (75 weeks). These results mostly represent the degree of cracking observed on samples because, unlike the PO-Mass and PO-Struc mixtures, only a very limited number of aggregate particles exhibited reaction rims. More cracks were observed in aggregate particles and many of these cracks extended into the cement paste. As the expansion levels increased, a larger amount of reaction gel is also observed in aggregate particles and in cement paste. In the case of the SP-Struc mixture, a DRI value of 170 was obtained at 36 weeks. The highest DRI value was 411 (76 weeks). The degree of damage of SP-Struc was the highest among the five mixtures that have been analyzed. The high DRI values were mainly related to numerous cracks found in the aggregates and in the cement paste. The number of cracks originating within aggregate particles and extending into cement paste was high, and increased with time and expansion. Moreover, cracks were frequently filled (partially or fully) with a vitreous greyish to whitish gel, which contributed to an increase in the DRI values. The petrographic examinations confirmed the non-reactivity of Limeridge limestone. The degree of damage was quite low for LM-Mass mixture. The only petrographic defect that was observed are cracks in aggregate particles (CA). One should note that the number of cracked particles did not vary significantly with time and expansion. Let us recall that aggregate particles may exhibit cracking prior to their incorporation into concrete, especially with crushed limestone aggregates. For instance, previous results obtained from concrete specimens made with Spratt limestone have indicated that the proportion of pre-cracked aggregate particles ranged from 17% to 33% [13]. This proportion ranged from 12% to 18% in concrete specimens made with Potsdam sandstone. These microcracks cannot be attributed to ASR
4.3. DRI results on cores extracted from 35 cm cubes Petrographic examinations were also conducted on cores extracted from two concrete cubes (one made with a mass concrete mixture and one made with a structural concrete mixture). These cubes were made in the laboratory to monitor alkali-silica reaction effects in another study [16]. Cubes measuring 350 mm on a side were made with Spratt limestone. Mixture proportions are given in Table 4. Cubes have been kept humid at 38 C for over 1300 days. Expansion levels measured at the surface at the end of test program are given in Table 5. DRI measurements were performed on two cores (90 mm in diameter) extracted from each cube at the end of the ASR expansion testing. In an attempt to compare the amount of damage at the surface with the inner portion of the cube, two sections were examined on each core. Petrographic features were counted separately on the portion of the polished section 70 mm from the surface and then on the remainder of the section. Results are provided in Table 5. High DRI values were measured: mean values of 253 and 201 were obtained for the structural concrete cube (expansion = 0.21%) and the mass concrete cube (expansion = 0.17%), respectively. These values are in accordance with those measured on laboratory prisms made with Spratt limestone (see Fig. 4). Table 4 Concrete cubes: mixture proportions
Aggregate type Cement content (kg/m3) Coarse aggregates (kg/m3) Fine aggregates (kg/m3) Water (kg/m3) W/C Total alkalis (kg/m3 Na2Oeq)
Mass cube
Structural cube
Spratt limestone 250 1190 790 165 0.66 5.6
Spratt limestone 360 975 845 180 0.50 3.9
Table 5 DRI results on cores extracted from concrete cubes Cube
Expansion (%)
DRI inner
DRI surface
DRI mean
Structural core 1 Structural core 2 Mean
– – 0.21
257 244 251
255 258 257
256 249 253
Mass core 1 Mass core 2 Mean
– – 0.17
162 182 172
232 277 255
186 215 201
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Petrographic examinations suggest that the degree of damage did not vary on cores extracted from the structural concrete cube; DRI values were quite similar (251 for the inner section and 253 for the surface). However, in mass concrete cubes, the surface of the concrete was more damaged than the inner zone; a mean DRI value of 255 was determined for the surface zone whereas it decreased to 172 for the inner zone.
5. Discussion The above results suggest that the number of petrographic defects associated with ASR increases with expansion. Relationship between DRI values and expansion seems to follow a non-linear trend, with the curve showing an S-shape. Scattering in the data is greater at higher expansion levels.
The DRI method takes into account several petrographic features. Considered individually, these features do not seem to correlate well with the expansion levels (Figs. 5 and 6), which may be due to the limited number of specimens that were examined. Nevertheless, this suggests that weighting factors used with the DRI method are appropriate. However, expansion and damage stem from combination of factors that do not affect aggregates in the same manner. DRI values are not absolute, but are a relative indication for a particular aggregate or aggregate-cement combination of the extent of ASR damage. For concrete mixtures incorporating Potsdam sandstone, the most relevant petrograhic feature is the reaction rim (Fig. 7). The count of other features with expansion did not seem to follow a regular trend (Fig. 5). Gel in air voids (AV) shows the best correlation. For concrete mixtures incorporating Spratt limestone, almost every petrographic feature (except reaction rim) increases consistently with expansion (Fig. 6). The newly suggested petrographic feature of a crack extending into
CA CA+G CP CP+G AV CA-CP
16 14 12 10 8 6 4 2 0 0
0.05
(a)
0.1 0.15 0.2 Expansion (%)
0.25
90 Count of defect (for a 100 cm² equivalent surface)
Count of defect (for a 100 cm² equivalent surface)
18
40 30 20 10
0.05
0.1 0.15 0.2 Expansion (%)
0.25
0.3
160
20 15 10 5 0
CA CA+G CP CP+G AV CA-CP
140 120 100 80 60 40 20 0
0 (b)
CA CA+G CP CP+G AV CA-CP
50
0
Count of defect (for a 100 cm² equivalent surface)
Count of defect (for a 100 cm² equivalent surface)
25
60
(a)
CA CA+G CP CP+G AV CA-CP
30
70
0
0.3
40 35
80
0.05
0.1 0.15 0.2 Expansion (%)
0.25
0.3
Fig. 5. Relationships between individual petrographic features (except reaction rim) and expansion levels measured on prisms incorporating Potsdam sandstone as coarse aggregate: (a) PO-Mass mixture and (b) PO-Struc mixture.
0.1 (b)
0.15
0.2 0.25 Expansion (%)
0.3
Fig. 6. Relationships between individual petrographic features (except reaction rim) and expansion levels measured on prisms incorporating Spratt limestone as coarse aggregate: (a) SP-Mass mixture and (b) SPStruc mixture.
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Number of reaction rim (for a 100 cm² equivalent surface)
140 120 100 80 60 40 20 0 0
0.02
0.04
0
0.05
0.1
(a)
0.06 0.08 Expansion (%)
0.1
0.12
0.25
0.3
Number of reaction rim (for a 100 cm² equivalent surface)
160 140 120 100 80 60
The mass cube, being less rigid, could allow greater deformation without damage in the inner zone. The surface zone, where expansion is not restrained by surrounding concrete, suffers from tensile stresses that lead to cracking. In the more rigid structural concrete cube, cracking could occur more frequently in the inner part due to the low deformability of concrete. Furthermore, the lower permeability and porosity of the structural cube could have promoted higher inner cracking. In all cases, a limited number of specimens were studied, so findings presented in this paper must be judged with care. Other studies, for instance conducted on samples taken from field concrete structures, are required to confirm our results. Several parameters, which are thought to influence DRI results, would then be assessed. Among these parameters are stress relief subsequent to the core extraction, the presence of steel reinforcement in the concrete member, the size of aggregate particles, the use of air-entraining agent, and the occurrence of other deterioration processes (such as sulfate attack and freezing/thawing).
40 20
6. Conclusions
0
(b)
89
0.15 0.2 Expansion (%)
Fig. 7. Relationships between reaction rim and expansion levels measured on prisms incorporating Potsdam sandstone as coarse aggregate: (a) PO-Mass mixture and (b) PO-Struc mixture.
the cement paste (CA ) CP) shows a good correlation with expansion in both mass and structural mixtures. It might be introduced as a new criterion for assessing expansion and damage on ASR-affected concrete. Regarding examinations conducted on cores, the DRI indicated that the degree of damage in structural concrete cubes was about the same in the first 70 mm from the surface zone and the rest of the core. On the other hand, a significant difference was found in the mass concrete cube, suggesting that surface expansion could be lower than inner, so tension stresses occurred close and at the surface, generating cracks. This difference might be also associated with the difference in the modulus of elasticity of the two concrete mixtures. Testing performed at expansion level = 0% on the cubes indicated a modulus of elasticity of 27.5 GPa for structural cube and a value of 23.6 GPa for mass cube, the difference being mainly related to the W/C ratio much higher in mass concrete. A second evaluation at the end of expansion showed that the modulus of elasticity decreases to 22.2 GPa in the case of the structural cube but remains similar in the case of the mass cube (23.5 GPa), suggesting severe cracking throughout the structural cube. The surface cracking did not seem to have a significant influence on the modulus of elasticity.
Petrographic examinations conducted according to the DRI enable the quantification of concrete deterioration related to ASR. Despite DRI can be time consuming and painstaking, it remains a relatively inexpensive method and requires minimal equipment. A lot of information can be drawn: extent of the damage in the structure, distribution of cracking, relative amount of gel, etc. In this study, the DRI method provided an estimate, with a relatively good accuracy, of the amount of expansion reached by laboratory concrete prisms exhibiting ASR. It also shows that, in mass concrete, damage is more severe in the surface zone compared with the inner zone. No difference was observed in the structural concrete. This is thought to be related to a differential expansion in the mass cube and to the higher modulus of elasticity and lower porosity of the structural concrete, which makes it more susceptible to inner cracking. The petrographic nature of the reactive coarse aggregate has an effect on the types of defect that are generated in the concrete. For instance, a typical petrographic feature associated with the Potsdam sandstone is a dark reaction rim, whereas the rim is seldom observed surrounding Spratt limestone particles. However, an additional important petrographic feature is a crack initiated in an aggregate particle and extending into the cement paste. Good correlation was observed between this feature and the amount of expansion, especially for concrete made with Spratt limestone. Statistical analyses are being carried out on the influence and the relevance of each spectrographic feature counted in the DRI, for one thing to quantify the benefit of the
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new feature (CA ) CP) in improving correlation between DRI and expansion. These analyses may help to determine how significant a change in DRI values is necessary to detect an appreciable difference in concrete condition. Besides, petrographic examinations (in complement to mechanical testing and ultrasonic pulse velocity measurements) are currently being preformed on cores taken from a large lock affected by ASR in order to compare field results with laboratory results. A systematic program based on the petrographic monitoring of the deterioration of ASR-affected structures would enable an assessment of the extent and progression of the deleterious reaction. A petrograhic index could thus be incorporated into a maintenance program of any concrete structure. In numerous cases, DRI has been suitable for determining the degree of damage in a structure affected by ASR. When combined with other evaluation techniques, such as mechanical properties assessment or non-destructive techniques (i.e. ultrasonic pulse velocity, radar, etc.), the DRI would provide information to validate the results of other techniques and numerical modeling.
Acknowledgements Financial support has been provided by the Natural Science and Engineering Research Council of Canada (NSERC) and by the Fonds que´be´cois de recherche sur la nature et les technologies (FQRNT). Technical help from G. Lalonde is also acknowledged.
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