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The effect of coarse aggregate content and size on the age at cracking of bonded concrete overlays subjected to restrained deformation
Construction and Building Materials 69 (2014) 73–82
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
The effect of coarse aggregate content and size on the age at cracking of bonded concrete overlays subjected to restrained deformation Thomas Dittmer, Hans Beushausen ⇑ Concrete Materials and Structural Integrity Research Unit, Department of Civil Engineering, University of Cape Town, South Africa
h i g h l i g h t s Coarse aggregate content has a near-linear relationship with cracking age in overlays. Coarse aggregate size has a significant effect on overlay cracking. An analytical model for overlay cracking, depending on aggregate content is proposed.
a r t i c l e
i n f o
Article history: Received 8 January 2014 Received in revised form 6 May 2014 Accepted 29 June 2014
Keywords: Shrinkage Composite Physical properties Overlay Aggregate content Aggregate size
a b s t r a c t The influence of coarse aggregate content and size on cracking of bonded concrete overlays was investigated using the ring test. Specimen parameters included 4 different coarse aggregate contents, 2 aggregate sizes and 3 strength grades. Test results for relevant time-dependent material properties such as drying shrinkage, tensile strength, tensile relaxation and elastic modulus were used to predict the time to first cracking using previously established analytical models. Increases in both coarse aggregate volume content and size were shown to significantly prolong the time to first cracking in the ring test, while an inverse relationship was observed for crack intensity. The analytical model was found to be ineffective in detecting the influence of coarse aggregate content and size on the cracking behavior of bonded overlays. This was ascribed to the model’s inability to account for aggregate-related differences in strain softening and fracture mechanisms on a micro scale. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Internationally, a growing need exists for improved methods and understanding of concrete repair and retrofitting technology. This is the result of a number of different factors that result in existing concrete structures not reaching their intended service lives [1–3]. The economic implications of concrete repairs, which were often not accounted for in the original design, can have a profound effect on the continued feasibility and upkeep of major civil engineering, commercial and housing structures [1,3]. A major related problem links to the circumstance that currently only very limited design methods and material specifications are available for concrete repair, with many of the prevailing mechanisms of repair failure not being well understood. The bonded concrete overlay repair technique is the most commonly used method for concrete repair and is used extensively around the world [4]. The method, which involves casting a new ⇑ Corresponding author. E-mail address: [email protected] (H. Beushausen). http://dx.doi.org/10.1016/j.conbuildmat.2014.06.056 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.
layer of concrete over an existing substrate, can be used for structural repairs where the overlay is loaded and fulfils a structural role or simply for non-structural repairs to cover and protect exposed reinforcing steel or damaged concrete [2,4,5]. The concept of differential volume changes between the substrate and overlay is based on the notion that the overlay is subjected to shrinkage and thermal movement, while the substrate’s movements are usually completed or minimal. Bonded overlay deformation is therefore restrained at the interface to the substrate, resulting in tensile stresses, which in many cases is linked to overlay cracking [1– 3,5–7]. A number of time-dependent overlay material properties have been identified as contributing directly to overlay cracking characteristics, namely: shrinkage, tensile strength, tensile relaxation and elastic modulus. Researchers suggest that differential shrinkage, and in particular drying shrinkage, is considered the most critical influencing factor that contributes to differential volume changes and directly affect the cracking failure of bonded concrete overlay repairs [7–11,18,19,23]. In contrast, tensile relaxation has been identified as a key property that can help to alleviate some of the
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tensile stress induced by overlay shrinkage [7,18,19]. Tensile stresses due to restrained deformations are also significantly affected by the elastic properties of the overlay material, with an increase in repair material stiffness resulting in greater stresses [2,6,7]. The inclusion of coarse aggregates in concrete has been shown to have a significant influence on individual key material properties that impact overlay cracking as indicated above. Coarse aggregate volume, size, stiffness, shape and grading influence concrete shrinkage through the mechanisms of dilution and restraint, and therefore have a direct influence on stress-producing shrinkage deformations [12,13]. The elastic properties of coarse aggregates have further been shown to directly influence the elastic properties of concrete, which is particularly related to coarse aggregate size and content [13]. Considering material properties only, it can thus be assumed that an increase in coarse aggregate content in bonded overlays has the positive effect of reducing shrinkage and related tensile stresses. However, this is combined with the negative effect of increasing aggregate content which increases the overlay’s elastic modulus and the related stresses from deformation restraint. The effect of coarse aggregate on tensile relaxation has been shown to be more complex, with Alexander and Mindess [13] suggesting that in a larger ‘global’ context, the function of dilution and restraint due to coarse aggregate has a direct influence on tensile relaxation. However, in a more ‘local’ context, the effect of microcracking within the interfacial transition zone (ITZ) between the aggregate and the cement paste has been shown to result in increased stress relaxation [14]. In addition to the influence of aggregates on individual material properties, the inclusion of coarse aggregate particles on overlay cracking must also be considered on a ‘local’ scale around the actual location of cracking. This partly relates to the process of strain softening which involves the formation and nucleation of microcracks at stress concentration zones at the interface between the matrix and the aggregate inclusions [15,16]. The degree of strain softening will determine the specific fracture energy required for cracking to occur. Wittmann [16] and Hillerborg [17] have shown that fracture energy and strain softening are dependent on the length of crack propagation paths, and have been shown to increase with an increase in aggregate particle size and volume content. The above sometimes contradictory effects of coarse aggregates on material properties that affect stress development in bonded concrete overlays subjected to restrained deformation warrant closer experimental and analytical research. The ring test detailed in the AASHTO and ASTM standards [18] is the most widely used by researchers to evaluate the restrained shrinkage of repair materials. However, Bentur and Kovler [18] conclude that the ring test only provides a qualitative indication of the material cracking. Beushausen and Chilwesa [19] suggest that a more detailed and quantitative prediction of overlay cracking can be obtained by analyzing the key material properties affecting stress development as discussed above. An analytical model for the prediction of tensile stresses in bonded mortar overlays subjected to restrained deformation has been developed and successfully used by the second author [6,7,19,27]. While this model has shown to have an acceptable degree of accuracy for mortars, it had previously not been used to analyze overlays containing coarse aggregates. The objectives of this study were twofold. Firstly, to experimentally evaluate the influence of coarse aggregate volume content and size on the individual key material properties known to affect overlay cracking, as well as testing the direct influence of coarse aggregate content and size on overlay cracking with the ring test. Secondly, to evaluate the accuracy of the previously developed analytical model in accounting for the influence of coarse aggregate
content and size on the cracking of overlay materials. Comparing the predicted analytical outputs, which were based on the individually tested material properties, with the results obtained in the direct ring tests helped to achieve this objective. This assisted in determining if predictions based on individual material properties can account for ‘local’ fracture mechanisms and strain softening associated with the inclusion of coarse aggregate in bonded overlays.
2. Experimental details 2.1. Outline and approach The influence of coarse aggregate volume content and size on key material properties that influence overlay cracking was investigated. This involved the individual measurement and testing of free drying shrinkage, tensile strength, tensile relaxation and elastic modulus. Tests were conducted on two self-designed concrete mixes and one commercial repair mix. Each of the mixes was cast with 4 different volume contents of coarse 19 mm aggregate. A further set of mixes was made using different contents of a smaller 9.5 mm coarse aggregate, to examine the influence of coarse aggregate size. This is discussed in more detail in later sections. The mixes were further tested for cracking characteristics using the ring test, which included visual observation of the time to first cracking. Crack intensity was analyzed based on total crack area (in [mm2]) measured 14 days after initial cracking. The individual material properties that were measured in the experimental component of the study provided the inputs for the analytical model that was used to predict the time to failure of the different mixes. These predicted outputs were then evaluated and compared with the direct test results of the ring tests.
2.2. Mix designs Two self-designed overlay mixes were used with water/binder ratios of 0.45 and 0.60, referred to as LM45 and LM60 respectively. The mixes were made using a CEM II-42.5 (containing fly ash) and a 50/50 combination of siliceous pit sand and dune sand (both 0–2 mm). A liquid superplasticiser was used where required to achieve the required design workability, which was set at a slump of 50 ± 20 mm. In addition, a commercially available repair product was included in the study to enhance the relevance of the investigation to current practice in the concrete repair industry. This commercial mortar, in the following referred to as CM, is marketed as a high performance cementitious grout that can be used for concrete overlays and general repair purposes. The mortar was mixed in accordance with the specifications provided by the manufacturer. Due to its proprietary nature, no details were provided with regard to the composition of the CM. All of the 3 basic mixes (LM 45, LM 60, and CM) were manufactured with 4 different volume contents of coarse aggregates (0%, 25%, 35%, and 45%), using a 19 mm maximum size Greywacke stone. In addition, all LM 60 mixes were also manufactured with a 9.5 mm maximum size of the same Greywacke stone, resulting in a total of 15 different overlay mixes as detailed in Table 1. Aggregate grading has been shown in the literature to have a direct influence on shrinkage, creep, tensile strength, tensile relaxation and plastic properties of concrete [12,13]. A graded coarse aggregate, based on grading curves in the ASTM C33 code, was therefore used for both the 19 mm and 9.5 mm stone (Figs. 1 and 2).
2.3. Environmental conditions and curing Specimens were kept in the moulds for 24 h after casting and subsequently cured for an additional 6 days using wet hessian and plastic sheets. On completion of moist curing at 7 days of age, all specimens except the tensile relaxation specimens were exposed to and tested at controlled environmental conditions of 25 ± 2 °C and 55 ± 5% RH. The tensile relaxation specimens, which were tested outside the controlled environment for a test duration of 48 h, were coated in a wax layer to prevent moisture loss during that time.
2.4. Experimental test methods 2.4.1. Drying shrinkage Free drying shrinkage strain were tested using 100 100 200 mm prism specimens. Two pairs of Demec strain targets were attached to the specimens on opposite sides at 100 mm gauge lengths. A Demec strain extensometer with a 100 mm gauge length was used to measure shrinkage strains, which was recorded as the mean value obtained from 3 separate specimens per mix (i.e. from a total of 6 measurement locations). Shrinkage strains were measured several times a week over a total period of 56 days.
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T. Dittmer, H. Beushausen / Construction and Building Materials 69 (2014) 73–82 Table 1 Mix design parameters and properties.
a b c
Mix
W:c ratio
Coarse agg. volume content (%)
CEM II 42.5 (kg/m3)
Water (kg/m3)
Sand (kg/m3)
Greywacke (kg/m3)
Superplasticiser (L/m3)
Slump (mm)
Comp. strengtha (28 days) (MPa)
LM45
0.45
0 25 35 45
556 508 458 400
250 229 206 180
1490 1034 851 647
0 582 865 1193
1.0 1.0 1.0 1.0
50 ± 10
41.5 47.3 47.6 47.8
LM60-19 and LM60-9.5
0.60
0 25 35 45
418 380 343 300
250 229 206 180
1605 1145 950 729
0 582 865 1193
1.0 0.5 0.5 0.5
50 ± 10
29.7b 31.7 34.7 39.1
CM
n.a.c
0 25 35 45
n.a. n.a. n.a. n.a.
261 203 175 143
n.a. n.a. n.a. n.a.
0 582 865 1193
n.a. n.a. n.a. n.a.
60 ± 10
78.4 78.7 78.7 83.0
Compressive strength values are measured on 100 mm cubes that have been cured for 7 days and stored in a constant environment. Compressive strength values are given for LM60-19 mixes made with 19 mm graded coarse aggregate. n.a. = data not available.
2.4.2. Tensile strength and tensile relaxation Direct uniaxial tensile strength was measured using notched ‘‘dog bone’’ specimens with a 170 40 40 prismic section (Fig. 3). The notch on either side of the centre of the specimen ensured that failure would occur at the same location for all specimens tested. The specimens were tested in accordance with the procedures specified in the SABS method 863:5-1994 using the Zwick Roell Z020 Testing Machine (UTM), shown in Fig. 4. ‘V’ shaped jaws that gripped the ends of the specimens were connected to the UTM crossheads with swivel bearings (Fig. 4) to ensure axial load application. Two specimens each were tested at ages of 7, 10 and 28 days with the average of the two specimens being used in the analysis. Relaxation tests were carried out using un-notched ‘‘dog-bone’’ specimens, with the same dimensions as discussed above (Fig. 3). Tests were conducted using a Zwick Roell Z020 Test Machine (UTM) (Fig. 4) or a Zwick Roel Z100 Test Machine (UTM) using the same test set-up described above for tensile strength. Specimens were loaded to a stress that was approximately equivalent to 80% of the tensile strength at that age. The resulting imposed strain was kept constant and the corresponding decay in stress was recorded for a period of 48 h. Two identical specimens were tested simultaneously, one in each of the two UTMs, and the mean value used in the analysis. Prior to exposure to the test frame, specimens were coated in paraffin wax to ensure full moisture retention during testing. The tests were conducted at 7 and 28 days, and a relaxation coefficient (w) was determined using the following equation:
w ð%Þ ¼ 100 1
rt r0
ð1Þ
where r0 is the original stress at time of loading and rt is remaining stress after 48 h.
2.4.3. Elastic modulus Elastic modulus was tested using 80 150 mm cylindrical specimens. As it was not practically possible to measure the elastic modulus in tension, the elastic modulus in compression was measured for this study. This was based on the opinion of many researchers, that the elastic modulus of normal strength concrete is very similar in tension and compression [12,20,21]. The modulus of elasticity was calculated by determining the gradient of the curve in the linear portion of the stress strain curve (from 5% to 20% of ultimate compressive strength at the test age). Three pairs of Demec strain targets were spaced evenly on the circumference of a cylinder at 100 mm gauge lengths, and strain measurements were taken with a Demec strain extensometer. Elastic modulus tests were conducted at the ages of 7 and 28 days and the mean value obtained from 3 separately tested specimens was used in the analysis.
2.4.4. Ring test Ring tests were conducted to observe restrained shrinkage cracking of the overlay mixes. As previously discussed, the ring test is the most common test method that is used for testing restrained shrinkage of mortars and concretes. The ring test method used for this investigation was based on the method described in ASTM C 1581-04 (2004), using a steel ring with a wall thickness of ±13 mm, an outer diameter of 326 mm and a height of 155 mm. The ring was mounted on a plywood base that had been treated with a non-absorptive substance to ensure that no moisture was lost through the base. The outer ring mould was made of PVC with a 380 mm inside diameter, resulting in mortar and concrete ring specimens with 22 mm thickness (Fig. 5).
Before casting, the outer surface of the steel ring and the inside surface of the PVC mould were coated with an oil based release agent. The ring was filled in two stages with vibration compaction being achieved using a vibrating table. Ring specimens were demoulded after 24 h, cured as outlined above, and subsequently exposed to controlled environmental conditions of 25 ± 2 °C and 55 ± 5% RH for the duration of testing. Once curing was complete, the exposed top surface of the mortar or concrete rings was sealed with paraffin wax to ensure that only circumferential drying would take place. The age at cracking was determined by measuring the time taken for the first crack to initiate on the ring specimens. This was done through careful visual inspection conducted twice daily during the entire exposure period. A magnifying glass and bright torch light were used to aid in identifying crack initiation. Crack intensity was determined by calculating the total cracked area of the specimen two weeks after the first initiation of cracking. This was calculated by multiplying the average width of the cracks by the total length of the cracks. Average width was determined by measuring crack widths at five positions evenly spaced along the length of the crack.
3. Experimental results and discussion 3.1. General Table 2 presents a summary of the 7-day and 28-day test results obtained for tensile strength, tensile relaxation and elastic modulus. A graphical comparison of test results for individual material properties, i.e. drying shrinkage, tensile relaxation, and elastic modulus, in relation to coarse aggregate volume contents are presented in Figs. 6, 9 and 11, respectively. The observed trends mostly indicate expected material behavior, with an increase in coarse aggregate content generally resulting in decreased drying shrinkage, decreased relaxation, and increased elastic modulus, as discussed in more detail in the sections to follow. For tensile strength, no clear relationship between aggregate content and test values could be obtained (Table 2). It was therefore concluded that the influence of coarse aggregate content on tensile strength was negligible and that the observed differences in results for specimens with different aggregate contents are linked to the scatter of test results expected with direct tensile strength testing. To evaluate the influence of coarse aggregate size on material properties, test results for specimens with maximum aggregate size of 9.5 mm (LM60-9.5) were compared to those of the same mix containing 19 mm aggregate (LM60-19). 3.2. Drying shrinkage For all mixes, the addition of coarse aggregates resulted in a reduction in free shrinkage strain, compared to plain mortar, as expected (Fig. 6). However, at early ages, different aggregate
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100
Grading envelope Grading used for mixes
% Passing through sieve
90
95
80 70
66.25
60 50 40
37.5
30 20 10 0
5 2.5
2.36
4.75
9.5
12.5
19
Nominal sieve size (mm) Fig. 1. 19.0–4.75 mm Grading Envelope (ASTM C33).
100
Grading envelope Grading used for mixes
% Passing through sieve
90
Fig. 4. UTM test set-up for tensile relaxation.
95
term strain but higher early-age strain, compared to LM45 and LM60, indicating a more rapid early strain development. The results suggest a direct influence of coarse aggregate size on drying shrinkage, the smaller 9.5 mm coarse aggregate mixes consistently having slightly higher strains compared to mixes with 19 mm aggregate (Fig. 7). As aggregate volume contents were the same for both LM60-9.5 and LM60-19, the diluting function of the coarse aggregate was the same for both mix types. Lower shrinkage at larger aggregate contents can therefore probably be attributed to the higher restraint offered by the larger stone size [12,13].
80 70 60 50 40
37.5
30 20
17.5
10 0
5 2.5
0.3
1.18
2.36
4.75
9.5
Nominal sieve size (mm) Fig. 2. 9.5–1.18 mm Grading Envelope (ASTM C33).
3.3. Tensile strength Tensile strength values for the LM mixes with varying coarse aggregate contents ranged between 2.2–3.3 MPa at 7 days and 2.7–3.4 MPa at 28 days, with coarse aggregate volume content having no consistent influence on tensile strength at both ages, as discussed above. Tensile strength values for the CM mixes were considerably higher than the LM mixes, ranging between 3.6– 4.6 MPa at 7 days and 5.1–6.9 MPa at 28 days, and again coarse aggregate volume content was shown to have no clear influence on tensile strength at both test ages. The influence of coarse aggregate size on 7-day tensile strength of the LM60 mixes was shown to be negligible (Table 2). However, the relationship observed for the 28-day tensile strengths of the LM60 mixes indicate that there was a noteworthy influence of aggregate size at later ages, smaller aggregate sizes consistently resulting in higher tensile strengths (Fig. 8). This is believed to be connected to the nature of direct tensile strength testing of specimens with relatively small dimensions of 40 40 mm. Larger aggregate sizes result in larger localized planes of weakness at the ITZ between coarse aggregate and paste, and hence larger areas prone to failure under direct tensile stress. In specimens with smaller aggregate size, tensile stresses are more evenly distributed between the stronger bulk paste and the ITZ.
Fig. 3. Notched and un-notched dog bone specimens used for tensile strength and relaxation testing (dimensions in mm).
3.4. Tensile relaxation
volume contents (i.e. 25%, 35% or 45%) had little influence on shrinkage values, as indicated in Fig. 6 by the similar 7-day strain values. For later age shrinkage, shown in Fig. 6 as the 56-day strain measurements, a near-linear trend between coarse aggregate volume and free shrinkage strain was observed. Since the paste is commonly the sole source of shrinkage in concrete, such linear relationship between aggregate (and hence, paste) content was expected. The commercial repair mortar showed the lowest long-
Relaxation coefficients for the various mortar mixes ranged between 77–83% at 7 days of loading and 84–88% at 28 days of loading, which corresponds to values obtained in previous studies [19,28]. Aggregate volume content was shown to be inversely proportional to tensile relaxation, the magnitude of relaxation reducing with increasing aggregate content (Fig. 9). This expected trend was evident for all mixes at both young and older ages of testing (7 and 28 days) and can be explained by the notion that relaxation, like creep, is a function of cement paste content [12].
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resulting in higher elastic moduli. A near-linear relationship was observed between aggregate volume content and elastic modulus at all test ages (Fig. 11), as expected from the notion that the source of elastic deformations in concrete is the cement paste. Comparing test results for LM60-9.5 and LM60-19 shows that smaller coarse aggregate sizes result in lower stiffness, which was observed for all aggregate volume contents and at both test ages (Table 2, Fig. 12). This was expected as the presence of a larger coarse aggregate provides better restraint to the concrete matrix [12].
3.6. Ring test
Fig. 5. Ring specimen before and after demoulding.
Mixes LM60-9.5 with a smaller coarse aggregate size consistently showed lower relaxation coefficients, compared to mixes LM60-19 (Fig. 10). Studies reported in [15–17] have indicated a direct relationship between cracking fracture energy and coarse aggregate size in concrete specimens subjected to tensile splitting stresses. This is related to the concept of strain softening discussed above. As the level and degree of microcracking is shown to increase with aggregate size, it is therefore possible that the higher tensile relaxation of the mixes containing the larger 19 mm coarse aggregate can be explained by the increase in strain softening associated with the increase in microcracking around the larger coarse aggregate particles. 3.5. Elastic modulus The influence of coarse aggregate volume on elastic deformations was consistent for all mixes, increasing aggregate contents
The ring test results for time to first crack and crack intensity are summarized in Figs. 13 and 15, respectively. The relationship between aggregate content and age at cracking was found to be near-linear for all mixes, larger aggregate volumes resulting in later ages at cracking as expected. The impact of coarse aggregate content was shown to be most significant for the LM60-19 mixes, with the 45% aggregate content mix failing 30 days after the plain mortar mix (0% aggregate content). Corresponding to the observations on age at cracking, crack intensity was found to decrease with increasing coarse aggregate contents. Neglecting the values for the mortar mixes (0% coarse aggregate), the relationship between aggregate content and crack intensity was also found to be nearlinear. The crack intensity of the mortar mixes was substantially higher than the crack intensity observed for mixes containing coarse aggregate. The trend of decreasing crack intensity with increasing aggregate content was most pronounced for the higher strength LM45 and CM mixes. Figs. 14 and 16 show the comparison of crack age and crack intensity between LM60-9.5 and LM60-19 mixes. It was interesting to note that mixes with smaller aggregate size consistently showed significantly younger ages at first cracking. This difference increased with increasing aggregate content, the 9.5 mm mix failing 8 days or 19 days before the 19 mm mix at 25% and 45% aggregate volume content, respectively. This suggests that the influence of coarse aggregate size becomes far more pronounced as the volume content of the aggregate increases. Corresponding to the influence of aggregate size on the age at cracking, crack intensity was also significantly different between LM60-19 and LM60-9.5 mixes, the former showing significantly lower crack intensity (Fig. 16). The reasons for the improved performance of the mixes containing larger aggregate size are analyzed further below.
Table 2 Summary of test results for tensile strength, relaxation coefficient and elastic modulus. Mix
Coarse agg. volume content (%)
w (%)
ft (MPa)
E (GPa)
7 day
28 day
7 day
28 day
7 day
28 day
LM45
0 25 35 45
2.7 3.0 2.5 3.1
3.2 3.4 3.4 3.3
20.9 15.5 19.4 14.3
15.5 19.4 14.3 16.4
29.0 32.4 35.0 38.0
42.0 44.4 47.1 48.4
LM60-19
0 25 35 45
2.2 2.7 2.6 3.3
2.8 3.0 2.7 3.3
22.3 17.8 20.6 16.7
17.8 20.6 16.7 17.5
21.5 25.4 29.0 32.5
29.3 34.0 37.4 39.1
LM60-9.5
0 25 35 45
2.2 2.5 2.8 3.3
2.8 3.6 3.8 4.4
20.6 16.7 17.5 15.7
16.7 17.5 15.7 16.3
21.5 21.3 24.2 27.7
29.4 27.2 29.3 32.4
CM
0 25 35 45
3.6 4.5 4.6 4.0
6.0 5.1 5.4 5.5
15.7 12.7 13.3 10.4
12.7 13.3 10.4 10.2
32.1 35.9 38.9 42.5
37.1 41.0 42.5 45.2
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LM45 (7 days)
LM45 (28days)
LM60 (56 days)
LM60 (7 days)
LM60 (28 days)
LM60 (7 days)
CM (56 days)
CM (7 days)
CM (28 days)
CM (7 days)
LM45 (56 days)
600
LM45 (7 days)
25
500
ψ (%)
Microstrain
20 400 300
15
200
10
100 0
0
10
20
30
40
50
5
Aggregate volume content (%)
0
10
20
30
40
50
Aggregate volume content (%) Fig. 6. Free drying shrinkage/aggregate volume content relationship at 7 and 56 days.
Fig. 9. Relaxation coefficient/aggregate volume content relationship at 7 and 28 days.
9.5 mm graded Greywacke 19 mm graded Greywacke
9.5 mm graded Greywacke
600
19 mm graded Greywacke 25
400
20
300
ψ (%)
Microstrain
500
200 100 0
0%
25%
35%
15 10 5
45%
0
Coarse aggregate volume
0%
25%
Fig. 7. Influence of coarse aggregate size on 56 day free drying shrinkage of LM60.
LM45 (28days)
4
LM45 (7 days)
LM60 (28 days)
LM60 (7 days)
CM (28 days)
CM (7 days)
50
3 2
45
1 0%
25%
35%
45%
Coarse aggregate volume Fig. 8. LM60 28 day tensile strength for mixes with varying coarse aggregate size and contents.
Elastic modulus (GPa)
Tensile strength (MPa)
Coarse aggregate volume
5
0
45%
Fig. 10. LM60 7 day tensile relaxation coefficient for mixes with varying coarse aggregate size and contents.
9.5 mm graded Greywacke 19 mm graded Greywacke
6
35%
40 35 30 25
4. Analytical prediction of overlay cracking 20
4.1. Analytical model and assumptions The analytical modelling method that was used in this investigation was based on the concept of using the time development of specific material properties to estimate the time of first cracking in the ring test. This was done by dividing the total test duration into a number of separate time intervals and using the change in shrinkage strain for each separate time interval in combination
0
10
20
30
40
50
Aggregate volume content (%) Fig. 11. Elastic modulus/aggregate volume content relationship at 7 and 28 days.
with the material properties at that time interval to determine the resulting additional stress increment. This approach relies on the principle of superposition, in that the strain increment applied
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at any time will not be affected by another strain applied before or after this time [22]. The following equation (Eq. (2)) for the remaining elastic stress (r) was therefore applied using the measured material properties as input parameters:
r¼ 1
w ða eFSS Þ EO 100
ð2Þ
where r is the tensile stress; w is relaxation coefficient; a is coefficient accounting for the magnitude of shrinkage restraint by the substrate; eFSS is free shrinkage strain and EO is elastic modulus. Due to the complex interaction of factors that influence overlay cracking and the mechanisms involved a number of assumptions had to be made with respect to shrinkage strain, time-development of tensile relaxation and the degree of restraint. Effective curing has been shown to mitigate and delay many of the different forms of shrinkage by preventing moisture loss from the concrete into the environment. However, autogenous shrinkage is independent on the environmental conditions and will therefore occur independent of curing procedures [1]. In this research the effects of autogenous shrinkage were not considered and stresses were calculated based only on drying shrinkage strains. It is the general consensus among researchers that the majority of stress relief from tensile relaxation occurs very soon after loading [14,23–25]. In order to facilitate analytical modelling of overlay stresses it was therefore deemed appropriate to account for relaxation as occurring instantaneously after loading. For the purpose of this investigation, the measured 48 h relaxation was taken as the ultimate value. In previous studies by Beushausen [26] and Beushausen and Alexander [27], it was shown that the restrained shrinkage due to the differential volume changes of the overlay and substrate was 60% of the overlay free shrinkage. Beushausen and Chilwesa [19] therefore used a coefficient of 0.6 to relate free shrinkage to restrained shrinkage in the model, and found that analytical prediction outputs correlated well with the overlay test results, but differed by a considerable deficit when compared to the ring test outputs. For the purpose of this study, it was therefore suggested, that the coefficient accounting for the magnitude of shrinkage restraint by the substrate be modified to generate predicted outputs that better relate to the ring test results. The results from the ring tests conducted by Beushausen and Chilwesa [19] were analyzed and compared with the model prediction outputs and it was determined that a coefficient of 0.85 produced predicted outputs that more accurately correlated with the outputs of the ring test results for all mixes tested.
The following modified equation (Eq. (3)) was therefore applied, with a (a) of 0.85, to determine the remaining elastic stress (ri ) at any time (t i ):
ri ¼ ri1 þ ð0:85 DeFSSi Þ Ei 1
ð3Þ
where ri is the remaining stress at time t i ; ri1 is remaining stress at time ti1 ; DeFSSi is change in free shrinkage in the interval ti1 t i ; Ei is mean elastic modulus in the interval t i1 t i and wi is relaxation coefficient for the magnitude of mean relaxation in the interval ti1 t i . 4.2. Time-dependent material parameters The experimental component of the investigation provided the inputs required for the analytical modelling. Free shrinkage strains were measured on a daily basis, but elastic modulus and tensile relaxation were tested only at ages of 7 and 28 days. Tensile strength was tested at 7, 10 and 28 days. The use of regression functions was therefore required to interpolate values for the periods when no test results were available. This was done based on the same logarithmic regression functions that were developed by Beushausen and Chilwesa and discussed in [19]:
Ei ðti Þ ¼ A lnðt i Þ þ B
ð4Þ
F Yi ðti Þ ¼ C lnðti Þ þ D
ð5Þ
wi ðt i Þ ¼ N lnðt i Þ þ M
ð6Þ
where Ei ðt i Þ is the mean elastic modulus in the interval ti1 t i ; F Yi ðti Þ is tensile strength at time ti ; wi ðti Þ is relaxation coefficient in the interval t i1 t i and A, B, C, D, N and M are constants depending on regression analysis. Table 3 summarizes Constants A–D, N and M, based on the experimental results obtained. In previous studies [18,19] the ring test was found to provide a good qualitative assessment of restrained shrinkage cracking, such that the cracking age of various materials can be evaluated on a comparative basis. 4.3. Model outcome and comparison with experimental results Predicted time-dependent stresses were plotted against tensile strength for all mixes. An example of this is shown in Fig. 17. The elastic stress calculated without considering relaxation, was included in the figure to illustrate the effect of relaxation on stress development and delay of cracking. The predicted stress development started directly on completion of the 7-day curing period,
9.5 mm graded Greywacke
LM45
45
19 mm graded Greywacke
LM60
CM
40
50
35
40
Age (Days)
Elastic modulus (GPa)
wi 100
30 20 10
30 25 20 15 10 5
0 0%
25%
35%
45%
Coarse aggregate volume
0
0
10
20
30
40
Aggregate volume content (%) Fig. 12. LM60 28 day elastic modulus for mixes with varying coarse aggregate size and contents.
Fig. 13. Time to first crack for LM and CM mixes.
50
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T. Dittmer, H. Beushausen / Construction and Building Materials 69 (2014) 73–82
9.5 mm graded Greywacke 40
19 mm graded Greywacke
35
Age (days)
30 25 20 15 10 5 0 0%
25%
35%
45%
Coarse aggregate volume Fig. 14. Time to first crack of LM60 mixes with varying coarse aggregate contents.
LM45 LM60
577 mm2 at 0% 273 mm2 at 0% 291 mm2 90 at 0% 80
CM
Crack area (mm2)
100
70 60
4.4. Proposal for an improved analytical model
50 40 30 20 10 0
age at cracking corresponded to the outcome of the ring test. However, in the current study the influence of coarse aggregate content on the age at cracking was clearly evident in the ring test, but not in the analytical model. It is therefore obvious that the influence of coarse aggregate content on individual material properties such as shrinkage, relaxation, elastic modulus and strength is not the only aspect relating to the influence of aggregate content on overlay cracking. The observed discrepancy between analytical model and ring test can be explained with the concept of strain softening and fracture energy [15,16]. Studies have shown that there is a direct relationship between aggregate size and the specific energy required for cracking to occur in concrete, with increasing aggregate sizes corresponding to increasing fracture energy [16,17]. This is attributed to intensified microcracking (strain softening) and increasing crack propagation path lengths around large aggregate inclusions. Consequentially, increasing coarse aggregate volumes in concrete, as well as increasing aggregate size (at constant aggregate volume) result in increasing energy required for cracking to occur. This explains the observations made with the ring test, i.e. increasing age at cracking with increasing aggregate content or aggregate size.
15
20
25
30
35
40
45
50
Aggregate volume content (%) Fig. 15. Crack intensity for LM and CM mixes.
At constant aggregate size, the age at cracking of bonded overlays subjected to restrained deformation can be expected to decrease with increasing elastic modulus and shrinkage strain, and decreasing tensile relaxation and tensile strength, as discussed and experimentally verified in previous studies on bonded overlay cracking [6,7,19,23,27]. Correspondingly, the age of overlay cracking can generally be defined as the age at which tensile stresses exceed tensile strength. The following relationship (Eq. (7)) can therefore be used to illustrate this:
Crack area (mm2)
ft
r
120 9.5 mm graded Greywacke 19 mm graded Greywacke
100 80 60 40 20 0
25%
35%
45%
Coarse aggregate volume Fig. 16. Crack intensity of LM60 mixes with varying coarse aggregate size and contents.
as discussed earlier. Comparing the stress development curve with the tensile strength development results in the prediction of the age at cracking. The cracking prediction based on time-dependent material properties was compared with the results of the ring test to evaluate if the analytical model is able to correctly account for the effect of coarse aggregate content (Figs. 13 and 18). From the figures it is evident that the analytical model failed to account for the influence of coarse aggregate content on the age at cracking. For all mixes containing 19.5 mm coarse aggregate, the model did not yield a coherent relationship between aggregate content and age at cracking. In previous studies, the analytical model was found to provide a reliable method for prediction of cracking in cementitious mortars without coarse aggregates [19]. In those studies, the influence of changes in mortar material properties on the analytically modeled
6 1 ! cracking
ð7Þ
where ft is the material tensile strength and r is predicted tensile stress from material properties (Eq. (2)). In this study, the observed effect of coarse aggregate content on these individual overlay material properties was of mixed nature, increasing aggregate contents both resulting in positive (reduced shrinkage) and negative effects (increased elastic modulus, decreased relaxation). Using Eq. (7) for crack prediction indicated that the combined effect of changes in coarse aggregate contents on material properties was negligible, i.e. cracking performance could not be analytically linked to coarse aggregate content. The same negligible influence was noted for the effect of varying coarse aggregate size. Based on the observations made in the ring test and the above-discussed principles of strain softening and fracture energy, the following analytical relationship is therefore proposed:
ft
r
b 6 1 ! cracking
ð8Þ
where (b) is a coefficient accounting for the effect of coarse aggregate type, size and content on the combined aspects of fracture energy and strain softening. Further work and rigorous testing is required to determine a specific value (or range of values) for b that can be applied to effectively account for the significant influence of coarse aggregate in crack predictions. This should be addressed in future research. Another aspect that has to still be investigated is that of global material properties versus local fracture behavior. For example, an increase in coarse aggregate content in specimens with constant paste properties was observed to result in decreased shrinkage strain. This observation can largely be ascribed to the effect of
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T. Dittmer, H. Beushausen / Construction and Building Materials 69 (2014) 73–82 Table 3 Summary of constants used in material parameter regression functions.
a b
Mix
Coarse agg. volume content (%)
A
B
C
D
N
M
LM45
0 25 35 45
9.36 8.69 8.77 7.49
10.81 15.47 17.94 23.42
0.37 0.34 0.62 0.15
1.94 2.30 1.33 2.75
3.86 3.68 3.80 1.94
28.38 26.59 23.78 16.36
LM60 (19 mm)a
0 25 35 45
5.69 6.16 6.01 4.82
10.40 13.45 17.34 13.09
0.46 0.19 0.10 0.04
1.28 2.32 2.37 3.22
3.21 2.82 1.31 2.27
28.52 26.10 20.04 20.77
LM60 (9.5 mm)b
0 25 35 45
5.69 4.22 3.71 3.35
10.40 13.10 16.99 21.16
0.46 0.78 0.72 0.79
1.28 0.95 1.42 1.78
3.21 1.73 1.34 0.24
28.52 17.79 15.42 12.32
CM
0 25 35 45
3.55 3.65 2.62 1.91
25.23 28.82 33.81 38.77
1.722 0.46 0.59 1.09
0.23 3.59 3.39 1.92
2.18 2.10 0.62 1.12
19.93 17.43 11.36 9.77
LM60 mixes made using 19 mm graded coarse aggregate. LM60 mixes made using 9.5 mm graded coarse aggregate.
Tensile strength and tensile stress (MPa)
5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0
5
10
20
15
25
Days
Age (Days)
Fig. 17. Overlay tensile strength and stress development for LM60 (25% coarse aggregate content).
LM45
LM60-9.5
LM60-19
CM
mines the stress development (within the paste) and hence the cracking behavior of the concrete. Keeping this in mind it can be questioned if the modeling of bonded overlay performance should be based on the measurements of ‘‘global’’ material properties alone, or if a more refined material model needs to be developed for cracking prediction. As stated above, this should be addressed in future research. The influence of coarse aggregate type on overlay cracking should also be investigated in future research. In particular, it should be explored if the surface texture of the aggregate, i.e. smooth or coarse, which is known to affect bond strength between cement paste and aggregate, has an effect on cracking at the ITZ and hence an effect on crack development in bonded overlays. Another aspect to consider is that of thermal deformations of bonded overlays and thermal compatibility between aggregate and paste. The thermal coefficient of the coarse aggregate may have a significant influence on bonded overlay cracking, especially in environments with significant daily temperature changes.
20
5. Conclusions
15
In summary, the following general conclusions can be drawn from the research discussed in this paper:
10
5
0
0
10
20
30
40
50
Aggregate volume content (%) Fig. 18. Analytical model predictions for LM and CM mixes (LM60 mixes with both aggregates sizes shown).
dilution and restraint, with lower paste content obviously resulting in lower shrinkage strain when measured globally on the test specimen. However, it is to a large extent the shrinkage of the paste, not the shrinkage of the combined paste–aggregate system, that deter-
The cracking behavior of bonded concrete overlays subjected to restrained shrinkage is considerably improved by the inclusion of higher volumes of coarse aggregates. The experimental results indicate a near-linear relationship between coarse aggregate volume content and the age at cracking of specimens subjected to restrained shrinkage in the ring test. Correspondingly, the crack area generally decreased significantly when coarse aggregate content was increased. An increase in coarse aggregate volume content in concrete was found to generally result in decreased drying shrinkage and tensile relaxation, and increased elastic modulus, while tensile strength was not significantly affected. Analytically modeling the overall effect of these changes in material properties on the age at cracking in bonded overlays did not correspond to the observations in the ring test. This highlights the shortcomings of common analytical approaches to overlay cracking behavior, which do not account for the effects of strain softening and fracture energy.
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At equal coarse aggregate contents, an increase in aggregate size was found to improve cracking behavior of concrete subjected to restrained shrinkage. The effect of coarse aggregate size was especially pronounced at higher aggregate contents. Throughout the experimental investigation, lower strength concrete was found to result in better cracking performance compared to concrete with the same aggregate content but higher strength. This highlights that strength is not a good performance indicator for bonded overlay cracking performance. The test results highlighted that increased coarse aggregate contents result in improved cracking behaviour of bonded concrete overlays. Consequently it needs to be goal in overlay design to optimize aggregate grading in order to have higher aggregate content and correspondingly lower paste content.
References [1] Beushausen H, Alexander M. Concrete repair. In: Fulton’s concrete technology. South Africa: Cement & Concrete Institute; 2009 (Chapter 27). [2] Mangat P, O’Flaherty F. Influence of elastic modulus on stress redistribution and cracking in repair patches. Cem Concr Res 2000;30(1):125–36. [3] Banthia N, Gupta R. Repairing with fiber reinforced concrete repairs. ACI Concr Int 2006;28(11):36–40. [4] Bissonnette B, Courard L, Beushausen H, Fowler D, Trevino Vaysburd A. Recommendations for the repair, the lining or strengthening of concrete slabs or pavements with bonded cement-based material overlays. Mater Struct 2013;46:481–94. [5] Hassan KE, Robery PC, Al-Alawi L. Effect of hot-dry curing environment on the intrinsic properties of repair materials. Cem Concr Compos 2000;22:453–8. [6] Beushausen H, Alexander MG. Localised strain and stress in bonded concrete overlays subjected to differential shrinkage. Mater Struct 2006;40(2):189–99. [7] Beushausen H, Alexander MG. Failure mechanisms and tensile relaxation of bonded concrete overlays subjected to differential shrinkage. Cem Concr Res 2006;36:1908–14. [8] Granju JL, Sabathier V, Turatsinze A, Toumi A. Interface between an old concrete and a bonded overlay: debonding mechanism. Interface Sci 2004;12(4):381–8. [9] Rahman MK, Baluch MH, Al-Gadhib AH. Simulation of shrinkage distress and creep relief in concrete repair. Compos B 2000;31:541–53. [10] Weiss J, Yang W, Shah SP. Shrinkage cracking of restrained concrete slabs. J Eng Mech 1998;124(7):765–74.
[11] Yuan Y, Li G, Cai Y. Modeling for prediction of restrained shrinkage effect in concrete repair. Cem Concr Res 2002;33:347–52. [12] Alexander M, Beushausen H. Deformation and volume change of hardened concrete. In: Fulton’s concrete technology. South Africa: Cement & Concrete Institute; 2009. p. 111–44 (Chapter 8). [13] Alexander MG, Mindess S. Aggregates in concrete. Abingdon, Oxon: Taylor & Frances; 2005. [14] Kordina K, Schubert L, Troitzsch U. Creep of concrete subjected to tensile stress. Deutscher Ausschuss fur Stahlbeton, Heft 498, Beuth Verlag, Berlin, Germany; 2000. [15] Chiaia B, van Mier JGM, Vervuurt. Crack growth mechanisms in four different concretes: microscopic observations and fractal analysis. Cem Concr Res 1998;28(1):103–14. [16] Wittmann FH. Crack formation and fracture energy of normal and high strength concrete. Sadhana 2002;27(4):413–23. [17] Hillerborg A. Results of three comparative test series for determining the fracture energy GF of concrete. Mater Struct 1985;18:407–13. [18] Bentur A, Kovler K. Evaluation of early age cracking characteristics in cementitious systems. Mater Struct 2003;36:183–90. [19] Beushausen H, Chilwesa M. Assessment and prediction of drying shrinkage cracking in bonded mortar overlays. Cem Concr Res 2013;53. http://dx.doi.org/ 10.1016/j.cemconres.2013.07.008. [20] Mehta KP, Monteiro PJM. Micro-structure of concrete. In: Concrete: microstructure, properties, and materials, vol. 21. McGraw-Hill Companies; 2006. [21] Neville AM. Properties of concrete. England: Pearson Education LimitedPrentice Hall; 1996. [22] Ghali A, Favre R, Eldbadry M. Concrete structures: stresses and deformations. 3rd ed. London: Taylor & Francis e-library; 2006. [23] Beushausen H, Alexander M. Crack development in bonded concrete overlays subjected to differential shrinkage: a parameter study. In: Proceedings of the international conference on concrete repair, rehabilitation and retrofitting, South Africa; 2005. p. 1053–58. [24] Morimoto H, Koyanagi W. Estimation of stress relaxation in concrete at early ages. In: Proceedings: RILEM symposium on thermal cracking in concrete at early ages. London: Chapman & Hall; 1995. p. 95–102. [25] Gutsch A, Rostásy S. Young concrete under high tensile stresses – creep relaxation and cracking. In: Proceedings: RILEM symposium on thermal cracking in concrete at early ages. London: Chapman & Hall; 1995. p. 111–6. [26] Beushausen H. Performance of bonded concrete overlays subjected to differential shrinkage. South Africa: University of Cape Town; 2005. [27] Beushausen H, Alexander MG. Localised strain and stress in bonded concrete overlays subjected to differential shrinkage. Mater Struct 2007;40(2):189–99. [28] Beushausen H, Masuku C, Moyo P. Relaxation characteristics of cement mortar subjected to tensile strain. Mater Struct 2012;45(8):1181–8.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
The effect of coarse aggregate content and size on the age at cracking of bonded concrete overlays subjected to restrained deformation Thomas Dittmer, Hans Beushausen ⇑ Concrete Materials and Structural Integrity Research Unit, Department of Civil Engineering, University of Cape Town, South Africa
h i g h l i g h t s Coarse aggregate content has a near-linear relationship with cracking age in overlays. Coarse aggregate size has a significant effect on overlay cracking. An analytical model for overlay cracking, depending on aggregate content is proposed.
a r t i c l e
i n f o
Article history: Received 8 January 2014 Received in revised form 6 May 2014 Accepted 29 June 2014
Keywords: Shrinkage Composite Physical properties Overlay Aggregate content Aggregate size
a b s t r a c t The influence of coarse aggregate content and size on cracking of bonded concrete overlays was investigated using the ring test. Specimen parameters included 4 different coarse aggregate contents, 2 aggregate sizes and 3 strength grades. Test results for relevant time-dependent material properties such as drying shrinkage, tensile strength, tensile relaxation and elastic modulus were used to predict the time to first cracking using previously established analytical models. Increases in both coarse aggregate volume content and size were shown to significantly prolong the time to first cracking in the ring test, while an inverse relationship was observed for crack intensity. The analytical model was found to be ineffective in detecting the influence of coarse aggregate content and size on the cracking behavior of bonded overlays. This was ascribed to the model’s inability to account for aggregate-related differences in strain softening and fracture mechanisms on a micro scale. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Internationally, a growing need exists for improved methods and understanding of concrete repair and retrofitting technology. This is the result of a number of different factors that result in existing concrete structures not reaching their intended service lives [1–3]. The economic implications of concrete repairs, which were often not accounted for in the original design, can have a profound effect on the continued feasibility and upkeep of major civil engineering, commercial and housing structures [1,3]. A major related problem links to the circumstance that currently only very limited design methods and material specifications are available for concrete repair, with many of the prevailing mechanisms of repair failure not being well understood. The bonded concrete overlay repair technique is the most commonly used method for concrete repair and is used extensively around the world [4]. The method, which involves casting a new ⇑ Corresponding author. E-mail address: [email protected] (H. Beushausen). http://dx.doi.org/10.1016/j.conbuildmat.2014.06.056 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.
layer of concrete over an existing substrate, can be used for structural repairs where the overlay is loaded and fulfils a structural role or simply for non-structural repairs to cover and protect exposed reinforcing steel or damaged concrete [2,4,5]. The concept of differential volume changes between the substrate and overlay is based on the notion that the overlay is subjected to shrinkage and thermal movement, while the substrate’s movements are usually completed or minimal. Bonded overlay deformation is therefore restrained at the interface to the substrate, resulting in tensile stresses, which in many cases is linked to overlay cracking [1– 3,5–7]. A number of time-dependent overlay material properties have been identified as contributing directly to overlay cracking characteristics, namely: shrinkage, tensile strength, tensile relaxation and elastic modulus. Researchers suggest that differential shrinkage, and in particular drying shrinkage, is considered the most critical influencing factor that contributes to differential volume changes and directly affect the cracking failure of bonded concrete overlay repairs [7–11,18,19,23]. In contrast, tensile relaxation has been identified as a key property that can help to alleviate some of the
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T. Dittmer, H. Beushausen / Construction and Building Materials 69 (2014) 73–82
tensile stress induced by overlay shrinkage [7,18,19]. Tensile stresses due to restrained deformations are also significantly affected by the elastic properties of the overlay material, with an increase in repair material stiffness resulting in greater stresses [2,6,7]. The inclusion of coarse aggregates in concrete has been shown to have a significant influence on individual key material properties that impact overlay cracking as indicated above. Coarse aggregate volume, size, stiffness, shape and grading influence concrete shrinkage through the mechanisms of dilution and restraint, and therefore have a direct influence on stress-producing shrinkage deformations [12,13]. The elastic properties of coarse aggregates have further been shown to directly influence the elastic properties of concrete, which is particularly related to coarse aggregate size and content [13]. Considering material properties only, it can thus be assumed that an increase in coarse aggregate content in bonded overlays has the positive effect of reducing shrinkage and related tensile stresses. However, this is combined with the negative effect of increasing aggregate content which increases the overlay’s elastic modulus and the related stresses from deformation restraint. The effect of coarse aggregate on tensile relaxation has been shown to be more complex, with Alexander and Mindess [13] suggesting that in a larger ‘global’ context, the function of dilution and restraint due to coarse aggregate has a direct influence on tensile relaxation. However, in a more ‘local’ context, the effect of microcracking within the interfacial transition zone (ITZ) between the aggregate and the cement paste has been shown to result in increased stress relaxation [14]. In addition to the influence of aggregates on individual material properties, the inclusion of coarse aggregate particles on overlay cracking must also be considered on a ‘local’ scale around the actual location of cracking. This partly relates to the process of strain softening which involves the formation and nucleation of microcracks at stress concentration zones at the interface between the matrix and the aggregate inclusions [15,16]. The degree of strain softening will determine the specific fracture energy required for cracking to occur. Wittmann [16] and Hillerborg [17] have shown that fracture energy and strain softening are dependent on the length of crack propagation paths, and have been shown to increase with an increase in aggregate particle size and volume content. The above sometimes contradictory effects of coarse aggregates on material properties that affect stress development in bonded concrete overlays subjected to restrained deformation warrant closer experimental and analytical research. The ring test detailed in the AASHTO and ASTM standards [18] is the most widely used by researchers to evaluate the restrained shrinkage of repair materials. However, Bentur and Kovler [18] conclude that the ring test only provides a qualitative indication of the material cracking. Beushausen and Chilwesa [19] suggest that a more detailed and quantitative prediction of overlay cracking can be obtained by analyzing the key material properties affecting stress development as discussed above. An analytical model for the prediction of tensile stresses in bonded mortar overlays subjected to restrained deformation has been developed and successfully used by the second author [6,7,19,27]. While this model has shown to have an acceptable degree of accuracy for mortars, it had previously not been used to analyze overlays containing coarse aggregates. The objectives of this study were twofold. Firstly, to experimentally evaluate the influence of coarse aggregate volume content and size on the individual key material properties known to affect overlay cracking, as well as testing the direct influence of coarse aggregate content and size on overlay cracking with the ring test. Secondly, to evaluate the accuracy of the previously developed analytical model in accounting for the influence of coarse aggregate
content and size on the cracking of overlay materials. Comparing the predicted analytical outputs, which were based on the individually tested material properties, with the results obtained in the direct ring tests helped to achieve this objective. This assisted in determining if predictions based on individual material properties can account for ‘local’ fracture mechanisms and strain softening associated with the inclusion of coarse aggregate in bonded overlays.
2. Experimental details 2.1. Outline and approach The influence of coarse aggregate volume content and size on key material properties that influence overlay cracking was investigated. This involved the individual measurement and testing of free drying shrinkage, tensile strength, tensile relaxation and elastic modulus. Tests were conducted on two self-designed concrete mixes and one commercial repair mix. Each of the mixes was cast with 4 different volume contents of coarse 19 mm aggregate. A further set of mixes was made using different contents of a smaller 9.5 mm coarse aggregate, to examine the influence of coarse aggregate size. This is discussed in more detail in later sections. The mixes were further tested for cracking characteristics using the ring test, which included visual observation of the time to first cracking. Crack intensity was analyzed based on total crack area (in [mm2]) measured 14 days after initial cracking. The individual material properties that were measured in the experimental component of the study provided the inputs for the analytical model that was used to predict the time to failure of the different mixes. These predicted outputs were then evaluated and compared with the direct test results of the ring tests.
2.2. Mix designs Two self-designed overlay mixes were used with water/binder ratios of 0.45 and 0.60, referred to as LM45 and LM60 respectively. The mixes were made using a CEM II-42.5 (containing fly ash) and a 50/50 combination of siliceous pit sand and dune sand (both 0–2 mm). A liquid superplasticiser was used where required to achieve the required design workability, which was set at a slump of 50 ± 20 mm. In addition, a commercially available repair product was included in the study to enhance the relevance of the investigation to current practice in the concrete repair industry. This commercial mortar, in the following referred to as CM, is marketed as a high performance cementitious grout that can be used for concrete overlays and general repair purposes. The mortar was mixed in accordance with the specifications provided by the manufacturer. Due to its proprietary nature, no details were provided with regard to the composition of the CM. All of the 3 basic mixes (LM 45, LM 60, and CM) were manufactured with 4 different volume contents of coarse aggregates (0%, 25%, 35%, and 45%), using a 19 mm maximum size Greywacke stone. In addition, all LM 60 mixes were also manufactured with a 9.5 mm maximum size of the same Greywacke stone, resulting in a total of 15 different overlay mixes as detailed in Table 1. Aggregate grading has been shown in the literature to have a direct influence on shrinkage, creep, tensile strength, tensile relaxation and plastic properties of concrete [12,13]. A graded coarse aggregate, based on grading curves in the ASTM C33 code, was therefore used for both the 19 mm and 9.5 mm stone (Figs. 1 and 2).
2.3. Environmental conditions and curing Specimens were kept in the moulds for 24 h after casting and subsequently cured for an additional 6 days using wet hessian and plastic sheets. On completion of moist curing at 7 days of age, all specimens except the tensile relaxation specimens were exposed to and tested at controlled environmental conditions of 25 ± 2 °C and 55 ± 5% RH. The tensile relaxation specimens, which were tested outside the controlled environment for a test duration of 48 h, were coated in a wax layer to prevent moisture loss during that time.
2.4. Experimental test methods 2.4.1. Drying shrinkage Free drying shrinkage strain were tested using 100 100 200 mm prism specimens. Two pairs of Demec strain targets were attached to the specimens on opposite sides at 100 mm gauge lengths. A Demec strain extensometer with a 100 mm gauge length was used to measure shrinkage strains, which was recorded as the mean value obtained from 3 separate specimens per mix (i.e. from a total of 6 measurement locations). Shrinkage strains were measured several times a week over a total period of 56 days.
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T. Dittmer, H. Beushausen / Construction and Building Materials 69 (2014) 73–82 Table 1 Mix design parameters and properties.
a b c
Mix
W:c ratio
Coarse agg. volume content (%)
CEM II 42.5 (kg/m3)
Water (kg/m3)
Sand (kg/m3)
Greywacke (kg/m3)
Superplasticiser (L/m3)
Slump (mm)
Comp. strengtha (28 days) (MPa)
LM45
0.45
0 25 35 45
556 508 458 400
250 229 206 180
1490 1034 851 647
0 582 865 1193
1.0 1.0 1.0 1.0
50 ± 10
41.5 47.3 47.6 47.8
LM60-19 and LM60-9.5
0.60
0 25 35 45
418 380 343 300
250 229 206 180
1605 1145 950 729
0 582 865 1193
1.0 0.5 0.5 0.5
50 ± 10
29.7b 31.7 34.7 39.1
CM
n.a.c
0 25 35 45
n.a. n.a. n.a. n.a.
261 203 175 143
n.a. n.a. n.a. n.a.
0 582 865 1193
n.a. n.a. n.a. n.a.
60 ± 10
78.4 78.7 78.7 83.0
Compressive strength values are measured on 100 mm cubes that have been cured for 7 days and stored in a constant environment. Compressive strength values are given for LM60-19 mixes made with 19 mm graded coarse aggregate. n.a. = data not available.
2.4.2. Tensile strength and tensile relaxation Direct uniaxial tensile strength was measured using notched ‘‘dog bone’’ specimens with a 170 40 40 prismic section (Fig. 3). The notch on either side of the centre of the specimen ensured that failure would occur at the same location for all specimens tested. The specimens were tested in accordance with the procedures specified in the SABS method 863:5-1994 using the Zwick Roell Z020 Testing Machine (UTM), shown in Fig. 4. ‘V’ shaped jaws that gripped the ends of the specimens were connected to the UTM crossheads with swivel bearings (Fig. 4) to ensure axial load application. Two specimens each were tested at ages of 7, 10 and 28 days with the average of the two specimens being used in the analysis. Relaxation tests were carried out using un-notched ‘‘dog-bone’’ specimens, with the same dimensions as discussed above (Fig. 3). Tests were conducted using a Zwick Roell Z020 Test Machine (UTM) (Fig. 4) or a Zwick Roel Z100 Test Machine (UTM) using the same test set-up described above for tensile strength. Specimens were loaded to a stress that was approximately equivalent to 80% of the tensile strength at that age. The resulting imposed strain was kept constant and the corresponding decay in stress was recorded for a period of 48 h. Two identical specimens were tested simultaneously, one in each of the two UTMs, and the mean value used in the analysis. Prior to exposure to the test frame, specimens were coated in paraffin wax to ensure full moisture retention during testing. The tests were conducted at 7 and 28 days, and a relaxation coefficient (w) was determined using the following equation:
w ð%Þ ¼ 100 1
rt r0
ð1Þ
where r0 is the original stress at time of loading and rt is remaining stress after 48 h.
2.4.3. Elastic modulus Elastic modulus was tested using 80 150 mm cylindrical specimens. As it was not practically possible to measure the elastic modulus in tension, the elastic modulus in compression was measured for this study. This was based on the opinion of many researchers, that the elastic modulus of normal strength concrete is very similar in tension and compression [12,20,21]. The modulus of elasticity was calculated by determining the gradient of the curve in the linear portion of the stress strain curve (from 5% to 20% of ultimate compressive strength at the test age). Three pairs of Demec strain targets were spaced evenly on the circumference of a cylinder at 100 mm gauge lengths, and strain measurements were taken with a Demec strain extensometer. Elastic modulus tests were conducted at the ages of 7 and 28 days and the mean value obtained from 3 separately tested specimens was used in the analysis.
2.4.4. Ring test Ring tests were conducted to observe restrained shrinkage cracking of the overlay mixes. As previously discussed, the ring test is the most common test method that is used for testing restrained shrinkage of mortars and concretes. The ring test method used for this investigation was based on the method described in ASTM C 1581-04 (2004), using a steel ring with a wall thickness of ±13 mm, an outer diameter of 326 mm and a height of 155 mm. The ring was mounted on a plywood base that had been treated with a non-absorptive substance to ensure that no moisture was lost through the base. The outer ring mould was made of PVC with a 380 mm inside diameter, resulting in mortar and concrete ring specimens with 22 mm thickness (Fig. 5).
Before casting, the outer surface of the steel ring and the inside surface of the PVC mould were coated with an oil based release agent. The ring was filled in two stages with vibration compaction being achieved using a vibrating table. Ring specimens were demoulded after 24 h, cured as outlined above, and subsequently exposed to controlled environmental conditions of 25 ± 2 °C and 55 ± 5% RH for the duration of testing. Once curing was complete, the exposed top surface of the mortar or concrete rings was sealed with paraffin wax to ensure that only circumferential drying would take place. The age at cracking was determined by measuring the time taken for the first crack to initiate on the ring specimens. This was done through careful visual inspection conducted twice daily during the entire exposure period. A magnifying glass and bright torch light were used to aid in identifying crack initiation. Crack intensity was determined by calculating the total cracked area of the specimen two weeks after the first initiation of cracking. This was calculated by multiplying the average width of the cracks by the total length of the cracks. Average width was determined by measuring crack widths at five positions evenly spaced along the length of the crack.
3. Experimental results and discussion 3.1. General Table 2 presents a summary of the 7-day and 28-day test results obtained for tensile strength, tensile relaxation and elastic modulus. A graphical comparison of test results for individual material properties, i.e. drying shrinkage, tensile relaxation, and elastic modulus, in relation to coarse aggregate volume contents are presented in Figs. 6, 9 and 11, respectively. The observed trends mostly indicate expected material behavior, with an increase in coarse aggregate content generally resulting in decreased drying shrinkage, decreased relaxation, and increased elastic modulus, as discussed in more detail in the sections to follow. For tensile strength, no clear relationship between aggregate content and test values could be obtained (Table 2). It was therefore concluded that the influence of coarse aggregate content on tensile strength was negligible and that the observed differences in results for specimens with different aggregate contents are linked to the scatter of test results expected with direct tensile strength testing. To evaluate the influence of coarse aggregate size on material properties, test results for specimens with maximum aggregate size of 9.5 mm (LM60-9.5) were compared to those of the same mix containing 19 mm aggregate (LM60-19). 3.2. Drying shrinkage For all mixes, the addition of coarse aggregates resulted in a reduction in free shrinkage strain, compared to plain mortar, as expected (Fig. 6). However, at early ages, different aggregate
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100
Grading envelope Grading used for mixes
% Passing through sieve
90
95
80 70
66.25
60 50 40
37.5
30 20 10 0
5 2.5
2.36
4.75
9.5
12.5
19
Nominal sieve size (mm) Fig. 1. 19.0–4.75 mm Grading Envelope (ASTM C33).
100
Grading envelope Grading used for mixes
% Passing through sieve
90
Fig. 4. UTM test set-up for tensile relaxation.
95
term strain but higher early-age strain, compared to LM45 and LM60, indicating a more rapid early strain development. The results suggest a direct influence of coarse aggregate size on drying shrinkage, the smaller 9.5 mm coarse aggregate mixes consistently having slightly higher strains compared to mixes with 19 mm aggregate (Fig. 7). As aggregate volume contents were the same for both LM60-9.5 and LM60-19, the diluting function of the coarse aggregate was the same for both mix types. Lower shrinkage at larger aggregate contents can therefore probably be attributed to the higher restraint offered by the larger stone size [12,13].
80 70 60 50 40
37.5
30 20
17.5
10 0
5 2.5
0.3
1.18
2.36
4.75
9.5
Nominal sieve size (mm) Fig. 2. 9.5–1.18 mm Grading Envelope (ASTM C33).
3.3. Tensile strength Tensile strength values for the LM mixes with varying coarse aggregate contents ranged between 2.2–3.3 MPa at 7 days and 2.7–3.4 MPa at 28 days, with coarse aggregate volume content having no consistent influence on tensile strength at both ages, as discussed above. Tensile strength values for the CM mixes were considerably higher than the LM mixes, ranging between 3.6– 4.6 MPa at 7 days and 5.1–6.9 MPa at 28 days, and again coarse aggregate volume content was shown to have no clear influence on tensile strength at both test ages. The influence of coarse aggregate size on 7-day tensile strength of the LM60 mixes was shown to be negligible (Table 2). However, the relationship observed for the 28-day tensile strengths of the LM60 mixes indicate that there was a noteworthy influence of aggregate size at later ages, smaller aggregate sizes consistently resulting in higher tensile strengths (Fig. 8). This is believed to be connected to the nature of direct tensile strength testing of specimens with relatively small dimensions of 40 40 mm. Larger aggregate sizes result in larger localized planes of weakness at the ITZ between coarse aggregate and paste, and hence larger areas prone to failure under direct tensile stress. In specimens with smaller aggregate size, tensile stresses are more evenly distributed between the stronger bulk paste and the ITZ.
Fig. 3. Notched and un-notched dog bone specimens used for tensile strength and relaxation testing (dimensions in mm).
3.4. Tensile relaxation
volume contents (i.e. 25%, 35% or 45%) had little influence on shrinkage values, as indicated in Fig. 6 by the similar 7-day strain values. For later age shrinkage, shown in Fig. 6 as the 56-day strain measurements, a near-linear trend between coarse aggregate volume and free shrinkage strain was observed. Since the paste is commonly the sole source of shrinkage in concrete, such linear relationship between aggregate (and hence, paste) content was expected. The commercial repair mortar showed the lowest long-
Relaxation coefficients for the various mortar mixes ranged between 77–83% at 7 days of loading and 84–88% at 28 days of loading, which corresponds to values obtained in previous studies [19,28]. Aggregate volume content was shown to be inversely proportional to tensile relaxation, the magnitude of relaxation reducing with increasing aggregate content (Fig. 9). This expected trend was evident for all mixes at both young and older ages of testing (7 and 28 days) and can be explained by the notion that relaxation, like creep, is a function of cement paste content [12].
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resulting in higher elastic moduli. A near-linear relationship was observed between aggregate volume content and elastic modulus at all test ages (Fig. 11), as expected from the notion that the source of elastic deformations in concrete is the cement paste. Comparing test results for LM60-9.5 and LM60-19 shows that smaller coarse aggregate sizes result in lower stiffness, which was observed for all aggregate volume contents and at both test ages (Table 2, Fig. 12). This was expected as the presence of a larger coarse aggregate provides better restraint to the concrete matrix [12].
3.6. Ring test
Fig. 5. Ring specimen before and after demoulding.
Mixes LM60-9.5 with a smaller coarse aggregate size consistently showed lower relaxation coefficients, compared to mixes LM60-19 (Fig. 10). Studies reported in [15–17] have indicated a direct relationship between cracking fracture energy and coarse aggregate size in concrete specimens subjected to tensile splitting stresses. This is related to the concept of strain softening discussed above. As the level and degree of microcracking is shown to increase with aggregate size, it is therefore possible that the higher tensile relaxation of the mixes containing the larger 19 mm coarse aggregate can be explained by the increase in strain softening associated with the increase in microcracking around the larger coarse aggregate particles. 3.5. Elastic modulus The influence of coarse aggregate volume on elastic deformations was consistent for all mixes, increasing aggregate contents
The ring test results for time to first crack and crack intensity are summarized in Figs. 13 and 15, respectively. The relationship between aggregate content and age at cracking was found to be near-linear for all mixes, larger aggregate volumes resulting in later ages at cracking as expected. The impact of coarse aggregate content was shown to be most significant for the LM60-19 mixes, with the 45% aggregate content mix failing 30 days after the plain mortar mix (0% aggregate content). Corresponding to the observations on age at cracking, crack intensity was found to decrease with increasing coarse aggregate contents. Neglecting the values for the mortar mixes (0% coarse aggregate), the relationship between aggregate content and crack intensity was also found to be nearlinear. The crack intensity of the mortar mixes was substantially higher than the crack intensity observed for mixes containing coarse aggregate. The trend of decreasing crack intensity with increasing aggregate content was most pronounced for the higher strength LM45 and CM mixes. Figs. 14 and 16 show the comparison of crack age and crack intensity between LM60-9.5 and LM60-19 mixes. It was interesting to note that mixes with smaller aggregate size consistently showed significantly younger ages at first cracking. This difference increased with increasing aggregate content, the 9.5 mm mix failing 8 days or 19 days before the 19 mm mix at 25% and 45% aggregate volume content, respectively. This suggests that the influence of coarse aggregate size becomes far more pronounced as the volume content of the aggregate increases. Corresponding to the influence of aggregate size on the age at cracking, crack intensity was also significantly different between LM60-19 and LM60-9.5 mixes, the former showing significantly lower crack intensity (Fig. 16). The reasons for the improved performance of the mixes containing larger aggregate size are analyzed further below.
Table 2 Summary of test results for tensile strength, relaxation coefficient and elastic modulus. Mix
Coarse agg. volume content (%)
w (%)
ft (MPa)
E (GPa)
7 day
28 day
7 day
28 day
7 day
28 day
LM45
0 25 35 45
2.7 3.0 2.5 3.1
3.2 3.4 3.4 3.3
20.9 15.5 19.4 14.3
15.5 19.4 14.3 16.4
29.0 32.4 35.0 38.0
42.0 44.4 47.1 48.4
LM60-19
0 25 35 45
2.2 2.7 2.6 3.3
2.8 3.0 2.7 3.3
22.3 17.8 20.6 16.7
17.8 20.6 16.7 17.5
21.5 25.4 29.0 32.5
29.3 34.0 37.4 39.1
LM60-9.5
0 25 35 45
2.2 2.5 2.8 3.3
2.8 3.6 3.8 4.4
20.6 16.7 17.5 15.7
16.7 17.5 15.7 16.3
21.5 21.3 24.2 27.7
29.4 27.2 29.3 32.4
CM
0 25 35 45
3.6 4.5 4.6 4.0
6.0 5.1 5.4 5.5
15.7 12.7 13.3 10.4
12.7 13.3 10.4 10.2
32.1 35.9 38.9 42.5
37.1 41.0 42.5 45.2
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LM45 (7 days)
LM45 (28days)
LM60 (56 days)
LM60 (7 days)
LM60 (28 days)
LM60 (7 days)
CM (56 days)
CM (7 days)
CM (28 days)
CM (7 days)
LM45 (56 days)
600
LM45 (7 days)
25
500
ψ (%)
Microstrain
20 400 300
15
200
10
100 0
0
10
20
30
40
50
5
Aggregate volume content (%)
0
10
20
30
40
50
Aggregate volume content (%) Fig. 6. Free drying shrinkage/aggregate volume content relationship at 7 and 56 days.
Fig. 9. Relaxation coefficient/aggregate volume content relationship at 7 and 28 days.
9.5 mm graded Greywacke 19 mm graded Greywacke
9.5 mm graded Greywacke
600
19 mm graded Greywacke 25
400
20
300
ψ (%)
Microstrain
500
200 100 0
0%
25%
35%
15 10 5
45%
0
Coarse aggregate volume
0%
25%
Fig. 7. Influence of coarse aggregate size on 56 day free drying shrinkage of LM60.
LM45 (28days)
4
LM45 (7 days)
LM60 (28 days)
LM60 (7 days)
CM (28 days)
CM (7 days)
50
3 2
45
1 0%
25%
35%
45%
Coarse aggregate volume Fig. 8. LM60 28 day tensile strength for mixes with varying coarse aggregate size and contents.
Elastic modulus (GPa)
Tensile strength (MPa)
Coarse aggregate volume
5
0
45%
Fig. 10. LM60 7 day tensile relaxation coefficient for mixes with varying coarse aggregate size and contents.
9.5 mm graded Greywacke 19 mm graded Greywacke
6
35%
40 35 30 25
4. Analytical prediction of overlay cracking 20
4.1. Analytical model and assumptions The analytical modelling method that was used in this investigation was based on the concept of using the time development of specific material properties to estimate the time of first cracking in the ring test. This was done by dividing the total test duration into a number of separate time intervals and using the change in shrinkage strain for each separate time interval in combination
0
10
20
30
40
50
Aggregate volume content (%) Fig. 11. Elastic modulus/aggregate volume content relationship at 7 and 28 days.
with the material properties at that time interval to determine the resulting additional stress increment. This approach relies on the principle of superposition, in that the strain increment applied
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at any time will not be affected by another strain applied before or after this time [22]. The following equation (Eq. (2)) for the remaining elastic stress (r) was therefore applied using the measured material properties as input parameters:
r¼ 1
w ða eFSS Þ EO 100
ð2Þ
where r is the tensile stress; w is relaxation coefficient; a is coefficient accounting for the magnitude of shrinkage restraint by the substrate; eFSS is free shrinkage strain and EO is elastic modulus. Due to the complex interaction of factors that influence overlay cracking and the mechanisms involved a number of assumptions had to be made with respect to shrinkage strain, time-development of tensile relaxation and the degree of restraint. Effective curing has been shown to mitigate and delay many of the different forms of shrinkage by preventing moisture loss from the concrete into the environment. However, autogenous shrinkage is independent on the environmental conditions and will therefore occur independent of curing procedures [1]. In this research the effects of autogenous shrinkage were not considered and stresses were calculated based only on drying shrinkage strains. It is the general consensus among researchers that the majority of stress relief from tensile relaxation occurs very soon after loading [14,23–25]. In order to facilitate analytical modelling of overlay stresses it was therefore deemed appropriate to account for relaxation as occurring instantaneously after loading. For the purpose of this investigation, the measured 48 h relaxation was taken as the ultimate value. In previous studies by Beushausen [26] and Beushausen and Alexander [27], it was shown that the restrained shrinkage due to the differential volume changes of the overlay and substrate was 60% of the overlay free shrinkage. Beushausen and Chilwesa [19] therefore used a coefficient of 0.6 to relate free shrinkage to restrained shrinkage in the model, and found that analytical prediction outputs correlated well with the overlay test results, but differed by a considerable deficit when compared to the ring test outputs. For the purpose of this study, it was therefore suggested, that the coefficient accounting for the magnitude of shrinkage restraint by the substrate be modified to generate predicted outputs that better relate to the ring test results. The results from the ring tests conducted by Beushausen and Chilwesa [19] were analyzed and compared with the model prediction outputs and it was determined that a coefficient of 0.85 produced predicted outputs that more accurately correlated with the outputs of the ring test results for all mixes tested.
The following modified equation (Eq. (3)) was therefore applied, with a (a) of 0.85, to determine the remaining elastic stress (ri ) at any time (t i ):
ri ¼ ri1 þ ð0:85 DeFSSi Þ Ei 1
ð3Þ
where ri is the remaining stress at time t i ; ri1 is remaining stress at time ti1 ; DeFSSi is change in free shrinkage in the interval ti1 t i ; Ei is mean elastic modulus in the interval t i1 t i and wi is relaxation coefficient for the magnitude of mean relaxation in the interval ti1 t i . 4.2. Time-dependent material parameters The experimental component of the investigation provided the inputs required for the analytical modelling. Free shrinkage strains were measured on a daily basis, but elastic modulus and tensile relaxation were tested only at ages of 7 and 28 days. Tensile strength was tested at 7, 10 and 28 days. The use of regression functions was therefore required to interpolate values for the periods when no test results were available. This was done based on the same logarithmic regression functions that were developed by Beushausen and Chilwesa and discussed in [19]:
Ei ðti Þ ¼ A lnðt i Þ þ B
ð4Þ
F Yi ðti Þ ¼ C lnðti Þ þ D
ð5Þ
wi ðt i Þ ¼ N lnðt i Þ þ M
ð6Þ
where Ei ðt i Þ is the mean elastic modulus in the interval ti1 t i ; F Yi ðti Þ is tensile strength at time ti ; wi ðti Þ is relaxation coefficient in the interval t i1 t i and A, B, C, D, N and M are constants depending on regression analysis. Table 3 summarizes Constants A–D, N and M, based on the experimental results obtained. In previous studies [18,19] the ring test was found to provide a good qualitative assessment of restrained shrinkage cracking, such that the cracking age of various materials can be evaluated on a comparative basis. 4.3. Model outcome and comparison with experimental results Predicted time-dependent stresses were plotted against tensile strength for all mixes. An example of this is shown in Fig. 17. The elastic stress calculated without considering relaxation, was included in the figure to illustrate the effect of relaxation on stress development and delay of cracking. The predicted stress development started directly on completion of the 7-day curing period,
9.5 mm graded Greywacke
LM45
45
19 mm graded Greywacke
LM60
CM
40
50
35
40
Age (Days)
Elastic modulus (GPa)
wi 100
30 20 10
30 25 20 15 10 5
0 0%
25%
35%
45%
Coarse aggregate volume
0
0
10
20
30
40
Aggregate volume content (%) Fig. 12. LM60 28 day elastic modulus for mixes with varying coarse aggregate size and contents.
Fig. 13. Time to first crack for LM and CM mixes.
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9.5 mm graded Greywacke 40
19 mm graded Greywacke
35
Age (days)
30 25 20 15 10 5 0 0%
25%
35%
45%
Coarse aggregate volume Fig. 14. Time to first crack of LM60 mixes with varying coarse aggregate contents.
LM45 LM60
577 mm2 at 0% 273 mm2 at 0% 291 mm2 90 at 0% 80
CM
Crack area (mm2)
100
70 60
4.4. Proposal for an improved analytical model
50 40 30 20 10 0
age at cracking corresponded to the outcome of the ring test. However, in the current study the influence of coarse aggregate content on the age at cracking was clearly evident in the ring test, but not in the analytical model. It is therefore obvious that the influence of coarse aggregate content on individual material properties such as shrinkage, relaxation, elastic modulus and strength is not the only aspect relating to the influence of aggregate content on overlay cracking. The observed discrepancy between analytical model and ring test can be explained with the concept of strain softening and fracture energy [15,16]. Studies have shown that there is a direct relationship between aggregate size and the specific energy required for cracking to occur in concrete, with increasing aggregate sizes corresponding to increasing fracture energy [16,17]. This is attributed to intensified microcracking (strain softening) and increasing crack propagation path lengths around large aggregate inclusions. Consequentially, increasing coarse aggregate volumes in concrete, as well as increasing aggregate size (at constant aggregate volume) result in increasing energy required for cracking to occur. This explains the observations made with the ring test, i.e. increasing age at cracking with increasing aggregate content or aggregate size.
15
20
25
30
35
40
45
50
Aggregate volume content (%) Fig. 15. Crack intensity for LM and CM mixes.
At constant aggregate size, the age at cracking of bonded overlays subjected to restrained deformation can be expected to decrease with increasing elastic modulus and shrinkage strain, and decreasing tensile relaxation and tensile strength, as discussed and experimentally verified in previous studies on bonded overlay cracking [6,7,19,23,27]. Correspondingly, the age of overlay cracking can generally be defined as the age at which tensile stresses exceed tensile strength. The following relationship (Eq. (7)) can therefore be used to illustrate this:
Crack area (mm2)
ft
r
120 9.5 mm graded Greywacke 19 mm graded Greywacke
100 80 60 40 20 0
25%
35%
45%
Coarse aggregate volume Fig. 16. Crack intensity of LM60 mixes with varying coarse aggregate size and contents.
as discussed earlier. Comparing the stress development curve with the tensile strength development results in the prediction of the age at cracking. The cracking prediction based on time-dependent material properties was compared with the results of the ring test to evaluate if the analytical model is able to correctly account for the effect of coarse aggregate content (Figs. 13 and 18). From the figures it is evident that the analytical model failed to account for the influence of coarse aggregate content on the age at cracking. For all mixes containing 19.5 mm coarse aggregate, the model did not yield a coherent relationship between aggregate content and age at cracking. In previous studies, the analytical model was found to provide a reliable method for prediction of cracking in cementitious mortars without coarse aggregates [19]. In those studies, the influence of changes in mortar material properties on the analytically modeled
6 1 ! cracking
ð7Þ
where ft is the material tensile strength and r is predicted tensile stress from material properties (Eq. (2)). In this study, the observed effect of coarse aggregate content on these individual overlay material properties was of mixed nature, increasing aggregate contents both resulting in positive (reduced shrinkage) and negative effects (increased elastic modulus, decreased relaxation). Using Eq. (7) for crack prediction indicated that the combined effect of changes in coarse aggregate contents on material properties was negligible, i.e. cracking performance could not be analytically linked to coarse aggregate content. The same negligible influence was noted for the effect of varying coarse aggregate size. Based on the observations made in the ring test and the above-discussed principles of strain softening and fracture energy, the following analytical relationship is therefore proposed:
ft
r
b 6 1 ! cracking
ð8Þ
where (b) is a coefficient accounting for the effect of coarse aggregate type, size and content on the combined aspects of fracture energy and strain softening. Further work and rigorous testing is required to determine a specific value (or range of values) for b that can be applied to effectively account for the significant influence of coarse aggregate in crack predictions. This should be addressed in future research. Another aspect that has to still be investigated is that of global material properties versus local fracture behavior. For example, an increase in coarse aggregate content in specimens with constant paste properties was observed to result in decreased shrinkage strain. This observation can largely be ascribed to the effect of
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T. Dittmer, H. Beushausen / Construction and Building Materials 69 (2014) 73–82 Table 3 Summary of constants used in material parameter regression functions.
a b
Mix
Coarse agg. volume content (%)
A
B
C
D
N
M
LM45
0 25 35 45
9.36 8.69 8.77 7.49
10.81 15.47 17.94 23.42
0.37 0.34 0.62 0.15
1.94 2.30 1.33 2.75
3.86 3.68 3.80 1.94
28.38 26.59 23.78 16.36
LM60 (19 mm)a
0 25 35 45
5.69 6.16 6.01 4.82
10.40 13.45 17.34 13.09
0.46 0.19 0.10 0.04
1.28 2.32 2.37 3.22
3.21 2.82 1.31 2.27
28.52 26.10 20.04 20.77
LM60 (9.5 mm)b
0 25 35 45
5.69 4.22 3.71 3.35
10.40 13.10 16.99 21.16
0.46 0.78 0.72 0.79
1.28 0.95 1.42 1.78
3.21 1.73 1.34 0.24
28.52 17.79 15.42 12.32
CM
0 25 35 45
3.55 3.65 2.62 1.91
25.23 28.82 33.81 38.77
1.722 0.46 0.59 1.09
0.23 3.59 3.39 1.92
2.18 2.10 0.62 1.12
19.93 17.43 11.36 9.77
LM60 mixes made using 19 mm graded coarse aggregate. LM60 mixes made using 9.5 mm graded coarse aggregate.
Tensile strength and tensile stress (MPa)
5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0
5
10
20
15
25
Days
Age (Days)
Fig. 17. Overlay tensile strength and stress development for LM60 (25% coarse aggregate content).
LM45
LM60-9.5
LM60-19
CM
mines the stress development (within the paste) and hence the cracking behavior of the concrete. Keeping this in mind it can be questioned if the modeling of bonded overlay performance should be based on the measurements of ‘‘global’’ material properties alone, or if a more refined material model needs to be developed for cracking prediction. As stated above, this should be addressed in future research. The influence of coarse aggregate type on overlay cracking should also be investigated in future research. In particular, it should be explored if the surface texture of the aggregate, i.e. smooth or coarse, which is known to affect bond strength between cement paste and aggregate, has an effect on cracking at the ITZ and hence an effect on crack development in bonded overlays. Another aspect to consider is that of thermal deformations of bonded overlays and thermal compatibility between aggregate and paste. The thermal coefficient of the coarse aggregate may have a significant influence on bonded overlay cracking, especially in environments with significant daily temperature changes.
20
5. Conclusions
15
In summary, the following general conclusions can be drawn from the research discussed in this paper:
10
5
0
0
10
20
30
40
50
Aggregate volume content (%) Fig. 18. Analytical model predictions for LM and CM mixes (LM60 mixes with both aggregates sizes shown).
dilution and restraint, with lower paste content obviously resulting in lower shrinkage strain when measured globally on the test specimen. However, it is to a large extent the shrinkage of the paste, not the shrinkage of the combined paste–aggregate system, that deter-
The cracking behavior of bonded concrete overlays subjected to restrained shrinkage is considerably improved by the inclusion of higher volumes of coarse aggregates. The experimental results indicate a near-linear relationship between coarse aggregate volume content and the age at cracking of specimens subjected to restrained shrinkage in the ring test. Correspondingly, the crack area generally decreased significantly when coarse aggregate content was increased. An increase in coarse aggregate volume content in concrete was found to generally result in decreased drying shrinkage and tensile relaxation, and increased elastic modulus, while tensile strength was not significantly affected. Analytically modeling the overall effect of these changes in material properties on the age at cracking in bonded overlays did not correspond to the observations in the ring test. This highlights the shortcomings of common analytical approaches to overlay cracking behavior, which do not account for the effects of strain softening and fracture energy.
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At equal coarse aggregate contents, an increase in aggregate size was found to improve cracking behavior of concrete subjected to restrained shrinkage. The effect of coarse aggregate size was especially pronounced at higher aggregate contents. Throughout the experimental investigation, lower strength concrete was found to result in better cracking performance compared to concrete with the same aggregate content but higher strength. This highlights that strength is not a good performance indicator for bonded overlay cracking performance. The test results highlighted that increased coarse aggregate contents result in improved cracking behaviour of bonded concrete overlays. Consequently it needs to be goal in overlay design to optimize aggregate grading in order to have higher aggregate content and correspondingly lower paste content.
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