Experimental and Numerical Assessment of Restrained Shrinkage Cracking of Concrete Using Elliptical Ring Specimens
Publication: Journal of Materials in Civil Engineering
Volume 26, Issue 11
Abstract
A new experimental method is proposed for assessing the cracking tendency of concrete using elliptical ring specimens subject to restrained shrinkage. To explore the mechanism of this method, a numerical model is developed to analyze stress development and crack initiation in concrete rings in which the effect of concrete shrinkage is simulated by a fictitious temperature drop applied on concrete causing the same strain as that induced by shrinkage. Stress developed in a concrete ring is then obtained through a combined thermal and structural analysis. Based on the maximum tensile stress cracking criterion, numerical results are in accordance with experimental results on cracking age for a range of circular and elliptical concrete rings with different geometries. Geometrical factor, i.e., the ratio between the major and minor semiaxes of an elliptical ring, is the main factor that affects tensile stress developed and consequently concrete cracking age in restrained ring specimens. Elliptical rings with appropriate geometry can enable crack initiation much earlier than circular rings, which consequently are able to accelerate the ring test for assessing the cracking potential of concrete. Discussions are made on effects of ring geometry on features of cracking, crack position, and stress development in concrete rings subject to restrained shrinkage to further explore the mechanism of the elliptical ring test for assessing the cracking potential of concrete.
Introduction
Due to low fracture resistance, early-age cracking can often be observed in concrete, particularly in flat concrete elements and structures such as industrial floors, concrete pavements, and overlays, with a large exposed drying surface area-to-volume (A/V) ratio. When volume change of concrete due to shrinkage is prevented, residual stress will develop and cracking may occur once the tensile stress developed exceeds the tensile strength of concrete. ASTM C341/C341M-13 (ASTM 2013) adopts 400-mm long and 100-mm square concrete prisms with all surfaces exposed for drying to assess free shrinkage of concrete through monitoring the longitudinal length change of the prisms. As is well-known, drying shrinkage of a concrete element is largely dependent on its A/V ratio. To directly use free shrinkage results conforming to ASTM C341/C341M-13 (ASTM 2013) through prismatic specimens in analyzing other concrete elements, in principle those concrete elements should have the same A/V ratio as the prism in ASTM C341/C341M-13 (ASTM 2013). It is not always possible to achieve this in reality. Furthermore, although free shrinkage data are useful in comparing different mix proportions, they do not provide sufficient information to determine how concrete will crack in service (Shah et al. 1998b). Rather, cracking tendency of concrete is normally evaluated under restrained conditions by qualitative means through a range of cracking tests, such as the ring, bar, and plate/slab tests, among which the circular ring test has been most widely used for decades due to its simplicity and versatility. Such research has been primarily focused on the effects of concrete mixture compositions (Li et al. 1999; Branch et al. 2002; See et al. 2003; Mokarem et al. 2005; Turcry et al. 2006; Tongaroonsri and Tangtermsirikul 2009; Passuello et al. 2009); specimen size/geometry (Weiss et al. 2000; Weiss and Shah 2002; Hossain and Weiss 2004; Moon and Weiss 2006); and moisture gradients and drying condition (Moon and Weiss 2006; Moon et al. 2006; Hossain and Weiss 2006) on cracking of concrete or other cement-based materials. A standard test method for assessing concrete shrinkage cracking tendency was developed in AASHTO PP34-99 (AASHTO 1999) through utilizing a 75 mm-thick concrete ring surrounding around a 12.5 mm-thick steel ring with the outer diameter of 305 mm and subject to outer circumferential surface drying. However, there is a low degree of restraint provided by the circular steel ring so that the time for the first crack occurring in concrete is fairly long (Attiogbe et al. 2003). To accelerate the test, a new ring geometry was proposed in ASTM C1581/C1581M-09a (ASTM 2009) by reducing the concrete ring wall thickness from 75 to 37.5 mm, which accelerates cracking in ring specimens to some extent.
As a test method for assessing cracking potential of concrete, the ability of generating a crack within a short period is desirable for large amount of materials assessment. In the ring test, the degree of restraint to concrete is largely dependent on the restraining steel ring. It is believed that a thicker restraining steel ring can provide a higher degree of restraint to the concrete surrounding it, thus generating higher tensile stress in the concrete. Concrete in a circular ring may not develop a visible crack if the restraining steel ring is not thick enough, i.e., the restraining stiffness is not big enough. Meanwhile, due to geometry effect there is an equal opportunity for the first crack occurring along the circumference of a circular concrete ring when subject to restrained shrinkage. Thus it is not possible to predict crack position, and considerable instruments and resources are required for detecting crack initiation and propagation in a circular concrete ring when subject to restrained shrinkage. In line with this, a novel elliptical ring geometry was adopted for assessing the effects of alkali on the cracking tendency of mortar by He et al. (2004). It was expected that the first crack occurs earlier in an elliptical ring than in a circular ring so that experiment duration is shortened. It was believed that there is higher stress intensity in an elliptical ring due to geometrical effects (He et al. 2004). It is also expected that the first crack in an elliptical ring appears at the same position given the ring geometry, concrete material properties, and drying condition. This largely reduces the instrumentation and effort needed for detecting crack initiation and propagation in the ring test. However, there was no scientific evidence to underpin such arguments provided by He et al. (2004). In analyzing cracking in elliptical rings, He et al. (2004) assumed that an elliptical ring specimen is subject to a uniform internal pressure enforced by the central restraining steel ring, which is the same assumption as that taken in investigating shrinkage cracking in circular ring specimens by many other researchers such as Kovler et al. (1993), Shah et al. (1998a); and Hossain and Weiss (2004). Due to the geometrical effect, radial deformation of the elliptical steel ring is not uniform along its circumference when concrete shrinks. Thus, it is believed that the uniform internal pressure assumption is not appropriate for analyzing elliptical ring specimens when subject to restrained shrinkage. The degree of restraint is largely dependent on the geometry of the restraining elliptical steel ring, especially its major and minor semiaxes. However, so far there is no research published on the effects of ring geometry on stress developed in elliptical concrete ring specimens under restrained shrinkage. In line with this, a series of circular and elliptical ring specimens with different geometries were tested subject to restrained shrinkage in the research reported in this paper. A numerical method was developed to analyze the behavior of concrete ring specimens under restrained shrinkage. Experimental results were compared with numerical results to verify the numerical model. The validated numerical model was then used to investigate further the effects of elliptical ring geometry on stress development and cracking in concrete rings under restrained shrinkage.
Numerical Model
Cracking age and position of concrete in a ring specimen are largely dependent on the degree of restraint provided by the central restraining steel ring. In the circular ring test, a higher degree of restraint can be achieved by increasing the steel ring wall thickness, which consequently results in higher stress development in concrete. In the elliptical ring test, although a thicker steel ring can provide a higher degree of restraint to the concrete surrounding it, the major restraining contribution comes from the elliptical shape of the steel ring with the major and minor semiaxes denoted as and , respectively (Fig. 1, in which denotes thickness or nominal thickness of the restraining steel ring). Although it seems well-known that an elliptical shape can generate higher stress concentration than a circular shape, the geometrical effects of a restraining steel ring on cracking of concrete has not been reported in the literature. Therefore, this paper quantifies the geometry effects of a steel ring on the degree of restraint to concrete for assessing its cracking tendency.
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Volumetric change of concrete is usually ascribed to two broad categories of effects, as follows: (1) thermal shrinkage, and (2) drying shrinkage (Hossain 2003; Weiss 1999). Thermal shrinkage in concrete is as a result of hydration and/or the changes of environment temperature, whereas drying shrinkage results from internal and external moisture movement in and from concrete. There is an obvious difference between thermal and drying shrinkage with the latter depending much more on the A/V ratio of a concrete element. When a concrete element is exposed for drying without any restraint, its length/area/volume will change, a phenomenon often referred as free shrinkage, which does not cause any stress in concrete. Shrinkage is an intrinsic property of concrete that is not usually possessed by many other engineering materials. In many finite element (FE) codes, there is no direct entry for shrinkage input as a material property for concrete. In developing the numerical model in the research reported in this paper, shrinkage of concrete is assumed to be caused by a fictitious temperature drop applied on it that causes the same value of the strain as that induced by shrinkage. Thus, by introducing the thermal expansion coefficient of concrete, the relationship between free shrinkage of the concrete and a fictitious temperature drop can be established for a concrete element. In numerical analysis, the derived fictitious temperature drop is then applied on the concrete element to simulate the shrinkage effect. The behavior of the concrete element under restrained shrinkage can thus be obtained by a combined thermal and structural FE analysis without direct input of shrinkage as a material property of concrete.
In the research reported in this paper, numerical analysis was carried out using Ansys FE code (Ansys FE 13.0) to simulate stress development with respect to age in concrete ring specimens under restrained shrinkage until cracking initiates. Each numerical analysis is a two-stage exercise, i.e., (1) thermal, and (2) structural analyses. In thermal analysis, three-dimensional (3D) 20-node solid elements (i.e., SOLID90 elements in Ansys FE code) with a single degree of freedom (in this case temperature) at each node were used for simulating concrete, which have compatible temperature shapes and are well-suited to model curved boundaries, in this case circular and elliptical ring shapes. The temperature field in a concrete ring specimen was obtained through thermal analysis, which was then fed into structural analysis. In structural analysis, the equivalent structural elements, in this case SOLID186 elements in Ansys FE code, were used to model concrete, which are also 3D 20-node solid elements with three translational degrees of freedom per node. SOLID90 and SOLID186 elements are a matching pair with the former and latter for thermal and structural analysis, respectively, in Ansys FE code. The following material properties were employed in numerical simulation: (1) age-dependent elastic modulus [Eq. (1a)], and (2) tensile strength of concrete [Eq. (1b)]. Poisson’s ratio is taken as a constant of 0.2 for concrete; the elastic modulus and Poisson’s ratio for steel are 210 GPa and 0.3, respectively. The ring test, both the circular and proposed elliptical ring, is only for assessing the cracking potential of concrete and other cement-based materials. Therefore, numerical simulations in the research reported in this paper only cover from starting the ring test to the stage when cracking initiates. Thus, concrete is treated as a linear elastic material with age-dependent tensile strength determined from Eq. (1b). In preparing the ring test, the outer circumferential surface of the central restraining steel ring, which contacts the inner circumferential surface of the concrete ring, was coated with a thin layer of release agent as suggested by ASTM C1581/C1581M-09a (ASTM 2009) to eliminate friction between the concrete and steel rings. Accordingly, in numerical analyses, contact elements with zero friction between the contact pair of the concrete and steel rings were utilized to simulate this practice in the ring testwhere = age (days) of the concrete.
(1a)
(1b)
Shrinkage of a concrete element caused by drying is largely dependent on its A/V ratio (Almudaiheem and Hansen 1987; Neville 1996; Hossain 2003). Therefore, another assumption is made in developing the numerical model, which is the value of the free shrinkage being the same for concrete elements with the same A/V ratio but maybe with different geometries. By applying this assumption to a concrete ring specimen subject to restrained shrinkage, it means the ring will be subject to the same fictitious temperature drop as a concrete prism, with the same A/V ratio, used for measuring free shrinkage of concrete. The fictitious temperature drop applied on the ring specimen makes concrete shrink as that induced by shrinkage. Once it is restrained by the inner steel ring, tensile stress will be developed in concrete. In addition, early-age stress relaxation occurs as a result of creep of the concrete. Characterizing the creep of concrete is complicated as creep depends on the stress level, concrete age, loading age, degree of hydration, temperature, drying condition, and so on. In this paper, the age-dependent effective elastic modulus of concrete is reduced to be 60% of the actually measured elastic modulus to account for creep effects in numerical analysis. The same measurements in reducing elastic modulus to take into account the creep effect was taken by Moon et al. (2006) when analyzing cracking in circular concrete rings under restrained shrinkage. Taking all these into FE analyses, the circumferential tensile stress developed in a concrete ring specimen can be obtained by a combined thermal and structural FE analysis. When the tensile stress caused by the fictitious temperature drop exceeds the tensile strength of concrete, cracking will initiate. Otherwise, forward the numerical analysis to the next age until cracking initiates. In summary, the following five steps were taken in analyzing a concrete ring specimen subject to restrained shrinkage based on the proposed numerical model:
1.
Measure mechanical properties, in this case tensile strength and elastic modulus , of concrete using cylindrical specimens and free shrinkage through a series of concrete prisms with different A/V ratios at various ages;
2.
Calculate the fictitious temperature drop for the concrete prisms with different A/V ratios at various ages based on the free shrinkage measurement in Step 1, and convert the results into a relationship between the fictitious temperature drop and A/V ratio for a concrete element at various ages;
3.
Calculate the A/V ratio of a given concrete ring specimen, and derive the relationship between fictitious temperature drop and concrete age for the ring specimen by a series of linear interpolation from the relationships between the fictitious temperature drop and A/V ratio at various ages obtained in Step 2;
4.
Conduct a combined thermal and structural analysis to obtain the maximum circumferential tensile stress developed in a concrete ring at a certain age by applying the corresponding fictitious temperature drop obtained in Step 3; and
5.
Compare the maximum circumferential tensile stress in concrete ring from analyses with tensile strength of concrete; if former becomes greater than the latter, the ring will crack; otherwise, move forward to the next age, and repeat Steps 4 and 5 but with new concrete material properties until the ring cracks.
Experimental Investigation
Mechanical Properties of Concrete
Mechanical properties, in this case and , of concrete at various ages were measured from cylinders, three for each property at 1, 7, 14, and 28 days, respectively. The mix proportion of the concrete for the research reported in this paper was (cement:sand:aggregate:water) by weight, which represents a therapy of normal strength concrete, and the maximum aggregate size was 10 mm. After cured in sealed moulds for 24 h, the cylinders were demoulded and moved into an environment chamber with 23°C and 50% relative humidity (RH) for continuing curing until the desirable ages of testing. The 28-day average splitting tensile strength and elastic modulus of the concrete are 2.9 MPa and 17.8 GPa, respectively. Regression analyses were conducted on the experimental data to obtain continuous equations that could represent the age-dependent mechanical properties of the concrete. The elastic modulus (in gigaPascals) of the concrete can be predicted using Eq. (1a), and its splitting tensile strength (in megaPascals) can be obtained using Eq. (1b).
Free Shrinkage
To obtain the fictitious temperature drop for simulating the effects of concrete shrinkage, concrete prisms with dimensions of 280-mm length and 75-mm square in cross section, conforming to ISO 1920-8 (ISO 2009), were tested subject to drying in an environment chamber with 23°C and 50% RH, the same as that for curing concrete ring specimens and cylinders. The length change of each concrete prism was monitored by a dial gauge with a resolution of 0.001 mm mounted on the free shrinkage test rig (Fig. 2), which was then converted into shrinkage strain. Considering that concrete drying shrinkage largely depends on the A/V ratio of a concrete element, four different exposure conditions were investigated on the prisms (Fig. 2), as follows: (1) all surfaces sealed, (2) all surface exposed for drying, (3) two side surfaces sealed, and (4) three side surfaces sealed, with the corresponding A/V ratio being 0, 0.0605, 0.0267, and , respectively. In the experiments, double-layer aluminum tape was used to seal the desirable surfaces that were not intended for drying.
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Ring Test
Five different ring geometries, with the inner major radius equal to 150 mm but the inner minor radius varied from 150, 125, 100, 75, and 60 mm, and two rings for each geometry, in total 10 rings, were tested subject to restrained shrinkage under the drying environment of 23°C and 50% RH. The wall thickness was 12.5 and 37.5 mm for the steel and concrete rings, respectively. In experiments, four strain gauges were attached, each at one equidistant midheight, on the inner surface of the steel ring. They were then connected to a data acquisition system in a half-bridge configuration for continuously recording the circumferential strain of the inner surface of the restraining steel ring (Fig. 3). The ring tests were performed in a similar way to ASTM C1581/C1581M-09a (ASTM 2009), i.e., top and bottom surfaces were sealed using two layers of aluminum tape and drying was only allowed through the outer circumferential cylindrical surface. As concrete was getting mature, it shrank but was restrained by the inner steel ring. Therefore, tensile and compression stress developed in the concrete and steel rings, respectively. The increase of compression stress in the steel ring in accordance with age was reflected by the increase in strain recorded by the strain gauges attached on the steel ring. When the maximum circumferential tensile stress developed in a concrete ring exceeds the tensile strength of concrete, cracking will initiate. Tensile stress in concrete close to the crack is then released and the compression enforced on the steel ring by concrete then disappears, resulting in a sharp drop in compression stress in the steel ring, which is reflected by a sudden drop in the strain recorded by strain gauges. Therefore, age of cracking can be detected from the sudden drop in the measured strain, which is the same technique used for crack detection in the restrained ring test recommended by both AASHTO PP34-99 (AASHTO 1999) and ASTM C1581/C1581M-09a (ASTM 2009). Fig. 4 shows a graphical representation of strain recorded from a circular ring using the data acquisition system and a dramatic drop in strain can be seen from the measurement, indicating cracking initiated in the concrete ring.
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Results and Discussion
Free Shrinkage and Converted Fictitious Temperature Drop
Fig. 5 presents the measured free shrinkage strain of concrete prisms up to 28 days under the four exposure conditions, with four A/V ratios, which was then converted into a fictitious temperature drop by introducing a linear thermal expansion coefficient of concrete, in this case. Based on the converted fictitious temperature drop, a relationship between the fictitious temperature drop and A/V ratio was then established (Fig. 6) for a concrete prism, which applies to any concrete element irrespective of its shape. Although Fig. 6 only presents the curves at 3-day intervals, the fictitious temperature drop was calculated for each day, which was then used to update the input data for numerical analyses of concrete rings. The age-dependent fictitious temperature drop of a ring specimen was derived by inserting its A/V ratio into the relationship between the fictitious temperature drop and A/V ratio (Fig. 6). Fig. 7, as the outcomes of this exercise, presents the fictitious temperature drop for the elliptical ring with under three exposure conditions (cases), as follows: (1) top and bottom surfaces sealed but outer circumferential surface exposed for drying, (2) outer circumferential surface sealed but top and bottom surfaces exposed for drying, and (3) no surfaces sealed and all exposed for drying. Regression analyses were conducted to obtain continuous equations that can represent the age-dependent fictitious temperature drop applied to the ring specimen with the same effects as that induced by shrinkage (Fig. 7).
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Cracking Age and Sensitivity
Based on strain measurements, cracking ages of the 10 ring specimens tested under the exposure condition Case 1 were determined (Table 1). Cracking ages of the circular ring and elliptical rings with , i.e., in this case or 100 mm, are all close to 15 days. However, elliptical rings with , i.e., in this case or 60 mm, cracked much earlier at around 10 and 13 days, respectively, on average. In addition, a series of concrete ring specimens subject to restrained shrinkage were analyzed using the numerical model proposed in the research reported in this paper under the three exposure conditions mentioned previously. The inner circumferential surface of the concrete ring contacts the steel ring so it was not exposed for drying. Cracking ages of this series of circular and elliptical rings are obtained from numerical analyses (Table 2). For the circular ring specimens with , cracking initiates at 18 days under the exposure condition Case 1, and at 19 and 11 days under the exposure conditions Cases 2 and 3, respectively; for the elliptical ring specimens with , cracking initiates at 11 days under the exposure condition Case 1, and at 12 and 7 days under the exposure conditions Cases 2 and 3, respectively. Comparing the average cracking ages obtained from experiments and numerical analyses for the 10 rings (Fig. 8), they agreed reasonably well by considering the complexity of predicting early-age cracking of concrete, suggesting that the numerical model developed in the research reported in this paper is reliable.
| Circular ring | Elliptical ring, | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Number 1 | Number 2 | Number 1 | Number 2 | Number 1 | Number 2 | Number 1 | Number 2 | Number 1 | Number 2 |
| 14 | 15 | 14 | 15 | 14 | 15 | 10 | 10 | 11 | 15 |
| Case | Circular ring | Elliptical ring, | ||||
|---|---|---|---|---|---|---|
| 1 | 18 | 20 | 17 | 11 | 12 | 13 |
| 2 | 19 | 21 | 18 | 12 | 13 | 14 |
| 3 | 11 | 12 | 11 | 7 | 8 | 8 |
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Not all elliptical rings can accelerate cracking of concrete as might be expected. Experimental results (Table 1) indicate that elliptical rings with or 100 mm cracked at the same age as the circular rings, whereas numerical results reveal that the elliptical ring with cracked earliest as expected; next were the circular and elliptical rings with . The difference is marginal considering the complexity in predicting cracking of concrete. From a practical point of view, when the geometrical factor is too big, the ring becomes too sharp. It is not convenient to attach strain gauges on the inner surface of the steel ring for crack detection even though the elliptical ring geometry may provide a higher degree of restraint to enable concrete crack earlier. Therefore, an appropriate elliptical ring geometry, with the geometrical factor (approximate), is recommended for the restrained ring test to increase cracking sensibility and consequently accelerate the ring test so that concrete can crack in a shorter period compared with a conventional circular ring geometry.
Cracking Position
For a ring test, it is desirable if the position of cracking can be predicted in advance so that the resource required for detecting cracking occurrence and propagation can be minimized during the test. The discussion in this section is only based on Case 1 exposure conditions, i.e., top and bottom surfaces sealed with outer cylindrical surface exposed for drying same as that recommended by ASTM C1581/C1581M-09a (ASTM 2009). It is not possible to predict the position of initial cracking in circular ring specimens because of equal opportunity of cracking around their circumferences due to axisymmetric geometry. Fig. 9(a) shows the circumferential stress along the circular concrete ring when cracking initiates at 18 days, obtained through numerical simulation. However, due to geometrical effects, stress concentration may take place elsewhere, which is usually close to the two vertices on the major axis of the inner elliptical circumference. Figs. 9(b–d) present the circumferential stress contour of elliptical concrete rings, with the semiminor axis equal to 125, 100, and 75 mm, respectively, at the moment when cracking initiates. Stress concentration is more significant in the elliptical rather than circular ring. Therefore, cracking initiates close to the vertices on the major axis of an elliptical concrete ring. However, due to the inhomogeneity of concrete, the crack position on elliptical rings demonstrated three different scenarios as observed from experiments, as follows:
1.
There is only one visible crack, which occurred between the major and minor axes [Fig. 10(a)] in the elliptical ring with . In accordance with the stress contour [Fig. 9(b)] for this ring, the variation in tensile stress along the circumferential direction is not great and stress concentration is not significant either. Similarly to the circular ring specimen, the crack position may primarily depend on defects or inhomogeneity of the concrete, which results in the randomness of crack position along the ring circumference.
2.
Several cracks occurred along the major axis and other positions [Fig. 10(b)] for the elliptical concrete ring with . In Fig. 10(b), there are three cracks, marked as cracks 1–3. Crack 1 and 2 are close to the vertices on the major axis, but crack 3 is between the major and minor axes. There is an interesting phenomenon that is noteworthy. Cracks 1 and 2 did not propagate throughout the wall of the elliptical concrete ring from the inner circumference where they initiated to the outer circumference. Because of this, they could not be visually observed from the outer circumferential surface of the ring during experiments. As the top and bottom surfaces of the ring were also sealed, they could not be visually observed from these two surfaces either. They were found only after the test was stopped and the sealed aluminum tape and the inner steel ring were stripped off from the concrete ring specimen. This happened in the elliptical ring specimen with . The degree of stress concentration provided by this elliptical ring to concrete is less than that by other rings with or 75 mm, which is consistent with the findings from experiments.
Crack propagation in concrete usually undergoes stable and unstable stages after initiation. In the stable propagation stage, crack can propagate only under the increasing driving force or energy. The driving force/energy for crack propagation in a concrete ring is actually provided by shrinkage of concrete. As concrete gets mature, its shrinkage increases. Therefore it can be reasonably concluded that the driving force increases for crack propagation as concrete gets mature. The stress contour [Fig. 9(c)] obtained from numerical simulation indicates that the stress gradient in the area close to the major axis is greater than anywhere else. The circumferential stress evolves from tension at the inner circumference to compression near the outer circumference. Therefore, for this case, cracks 1 and 2 maybe initiated earlier close to the vertices on the major axis, which were detected by strain gauges. Afterwards, circumferential tensile stress elsewhere increased and the new crack (in this case crack 3) generated and propagated throughout the wall of the concrete ring reaching the outer circumferential surface, thereby becoming visible. Due to stress, thus strain energy, in the zone close to cracks 1 and 2 was partially released after their initiation, the position of crack 3 should be far away from them, i.e., from the major axes. The circumferential stress gradient near crack 3 is smaller than those near cracks 1 and 2, resulting in that crack 3 eventually penetrated through the wall of the concrete ring earlier than cracks 1 and 2. Therefore, in this case, crack 3 was visually observed on the outer circumferential surface of the concrete ring.
3.
There is only one crack occurring close to one vertex on the major axis [Fig. 10(c)], which is in the zone where the maximum circumferential tensile stress occurs. This happened in the elliptical ring specimens with and 75 mm, which provide the highest degree of stress concentration to the concrete surrounding it. Fig. 9(d) shows the circumferential stress contour of the elliptical ring with from numerical analyses. Stress concentration in this elliptical ring is most significant compared with the other three elliptical rings.
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Although there are three different scenarios of crack positions in restrained concrete rings as discovered in the research reported in this paper, it can be concluded based on experimental and numerical results that crack position depends on the degree of stress concentration in a concrete ring subject to restrained shrinkage, which is ascribed to the geometrical factor of an elliptical ring. When is between 2 and 3, the crack position observed from experiments agreed very well with that predicted by the numerical model proposed in this paper. This further validates the reliability of the numerical model in analyzing cracking behavior of concrete rings subject to restrained shrinkage. The verified numerical model is able to underpin the mechanism of the proposed elliptical ring test for assessing the cracking potential of concrete and other cement-based materials.
Conclusions
An elliptical ring test method was proposed for assessing the cracking potential of concrete. A numerical model was developed for predicting stress evolution and cracking age in concrete ring specimens subject to restrained shrinkage to underpin the mechanism of the proposed elliptical ring test. Assuming shrinkage in concrete results from a fictitious temperature drop applied on it, crack initiates when the maximum circumferential tensile stress developed in a concrete ring exceeds concrete tensile strength. To use the proposed method, a free shrinkage test was carried out to obtain the age-dependent relationship between the fictitious temperature drop and A/V ratio of a concrete element. The proposed method was then applied to simulate stress development and crack initiation based on the maximum tensile stress cracking criterion in a range of circular and elliptical concrete ring specimens subject to restrained shrinkage. Based on experimental and numerical studies, the following conclusions can be drawn:
•
Cracking ages from numerical analyses agreed well with experimental results for a series of circular and elliptical ring specimens, indicating that the proposed numerical model is reliable.
•
Both experimental and numerical results suggested that the geometrical factor of an elliptical ring is the main factor affecting stress developed in a concrete ring when subject to restrained shrinkage. Compared with traditional circular rings, elliptical rings with between 2 and 3 can provide a higher degree of restraint, which leads to shorter cracking period in a restrained shrinkage ring test.
•
There are three cracking scenarios in elliptical concrete ring specimens under restrained shrinkage, depending on the geometrical factor , a finding that was discovered for the first time. By comparing experimental and numerical results, it can also be concluded that crack position in elliptical concrete rings subject to restrained shrinkage can be predicted reasonably well by the proposed numerical model.
Acknowledgments
Financial support from the U.K. Engineering and Physical Sciences Research Council (EPSRC) under grant EP/I031952/1 and EPSRC Doctoral Training Accounts allocation to Brunel University is gratefully acknowledged.
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Journal of Materials in Civil Engineering
Volume 26 • Issue 11 • November 2014
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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, http://creativecommons.org/licenses/by/4.0/.
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Received: Jun 24, 2013
Accepted: Dec 4, 2013
Published online: Dec 6, 2013
Published in print: Nov 1, 2014
Discussion open until: Nov 17, 2014
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