“A FRACTURE MECHANICS-BASED METHOD

FOR PREDICTION OF CRACKING

OF CIRCULAR AND ELLIPTICAL CONCRETE

RINGS UNDER RESTRAINED

SHRINKAGE”

Published by

1. Mr.Wei Dong

2. Mr.Xiangming Zhou

3. Mr.Zhimin Wu

Presented by

Sajith Babu George

2MTMD -1567204

Christ University

Introduction

Experimental program

Material properties

Free shrinkage tests

Restrained ring tests

Numerical modelling

Modelling of restrained shrinkage

Crack driving energy rate curve (G-curve)

Resistance curve (R-Curve)

Cracking age

Conclusions

References

INTRODUCTION A new experimental method, utilizing elliptical ring specimens, is developed for assessing the

likelihood of cracking and cracking age of concrete subject to restrained shrinkage

To investigate the mechanism of this new ring test, a fracture mechanics-based numerical approach is proposed to predict crack initiation in restrained concrete rings by using the R-curve method.

When volume change of concrete from autogenous, drying or thermal shrinkage is restrained, residual stress will be developed and crack may occur once the residual tensile stress exceeds the tensile strength of concrete

Cracking in concrete can reduce load carrying capacity and accelerate deterioration, which shortens the service life of concrete structures and increases maintenance costs.

The circular ring test has been widely used for assessing cracking tendency of concrete and other cement-based materials due to its simplicity and versatility.It has subsequently become a standard test method for assessing cracking potential of concrete and other cement-based materials recommended by American Association of State Highway and Transport Officials (AASHTO)

Elliptical ring test as a better tool than the circular ring test for estimating the cracking tendency of concrete or other cement-based materials.

EXPERIMENTAL PROGRAM

The mix proportions for the concrete used for this study was 1:1.5:1.5:0.5 (cement:sand:coarse aggregate:water) by weight with the maximum aggregate size of 10 mm.

100 mm-diameter and 200 mm-length cylinders for measuring mechanical properties of concrete

75 mm in square and 280 mm in length prisms for free shrinkage test

notched beams with the dimensions of 100 100 500 mm3 for fracture test and a series of circular and elliptical ring specimens for restrained shrinkage test

Then the concrete specimens were covered by a layer of plastic sheet and cured in the normal laboratory environment for 24 h. Subsequently, all specimens were de-moulded and moved into an environment chamber with 23 C and 50% relative humidity (RH) for continuous curing/drying.

MATERIAL PROPERTIES

It has been found that the average 28-day compressive and splitting tensile strength of the concrete are 27.21 and2.96 MPa, respectively

In this study, fracture properties, including the critical stress intensity factor KIC and the critical crack tip opening displacement CTODC, of concrete were derived based on the two-parameter fracture model (TPFM)

FREE SHRINKAGE TESTS

Free shrinkage of concrete was measured on concrete prisms with the dimensions of 280 mm in length and 75 mm square in cross section conforming to ISO 1920-8, subject to drying in the same environment condition as for curing concrete cylinders and ring specimens

Considering that concrete shrinkage depends on the A/V ratio of a concrete element, four different exposure conditions, i.e. representing four different A/V ratios, were investigated on concrete prisms in free shrinkage test.

(1) all surfaces sealed, (2) all surface exposed, (3) two side surfaces sealed and (4) three side surfaces sealed, representing A/V ratio of 0, 0.0605, 0.0267, and 0.0133 mm1, respectively

In experiment, double-layer aluminium tape was used to seal the surfaces which were not intended for drying

RESTRAINED RING TESTS

The restrained circular ring test has been widely used to assess cracking tendency of concrete and other cement-based materials.

In restrained ring test, four strain gauges were attached, on the inner cylindrical surface of the central restraining steel ring and they were connected to a data acquisition system which is able to automatically record the circumferential strain of the inner surface of the restraining steel ring continuously.

The strain gauges were then connected to the data acquisition system, and the instrumented ring specimens were finally moved into an environmental chamber for continuous drying under the temperature 23 C and RH 50% till the first crack occurred.

It was found that the cracking ages of the circular rings are 14 and 15 days, respectively, while those of the elliptical ones are both 10 days

NUMERICAL MODELLING

In this study, finite element analyses were carried out using ANSYS code to simulate stress development and calculate stress intensity factor in concrete ring specimens under restrained shrinkage

Numerical process

Thermal Structural Fracture analysis

2-D 8- Node thermal elements(plane77)

2-D 8-Node elements(plane183)

MODELLING OF RESTRAINED SHRINKAGE

In order to take into account the non-uniform stress distribution in elliptical concrete rings, anumerical approach was proposed to simulate the effect of geometry factor on cracking inconcrete ring specimens subject to drying shrinkage.

In this approach, a derived fictitious temperature field is applied to concrete to simulate theshrinkage effect so that a combined thermal and structural analysis can be adopted to analyzecracking in a concrete ring specimen caused by restrained shrinkage

With the implementation of the Fictitious temperature field, shrinkage of concrete caused by thetemperature field is restrained by the inner steel core, resulting in compressive stress developedin the steel core and tensile stress in the concrete ring.

For a given concrete ring with certain exposure condition (i.e. certain A/V ratio), the relationshipbetween fictitious temperature drop and concrete age can be derived by linear interpolationfrom the relationship between A/V ratio and concrete age obtained in the given graph.

CRACK DRIVING ENERGY RATE CURVE (G-CURVE)

When shrinkage of concrete is restrained by the inner steel ring, internal stress is developed in concrete, which is uniformly distributed in a circular ring but non-uniformly distributed in an elliptical ring

The elliptical geometry dramatically influences the distribution of restraining pressure provided by the centralsteel ring when concrete is shrinking

The pressure enforced on the circular concrete ring distributes uniformly along its inner circumference and thevalue is 0.59 MPa; while the pressure on the elliptical one distributes non-uniformly, with the maximum andminimum values being 2.14 MPa and 0.28 MPa, and occurring on the vertices of the major and minor axes,respectively.

In this study, finite element method was used to calculate the stress intensity factor (KI) for the circular andelliptical rings. Based on the classic fracture mechanics theory, KI can be defined as following

The given equations are stress intensity factor for circular and elliptical rings, respectively.

In which T (in C) is the fictitious temperature drop acting on a concrete ring representing the effect of drying shrinkage, E is the elastic modulus of concrete (in GPa), and ac is the linear thermal expansion coefficient of concrete (in 1/C).

The given figure illustrates the finite element meshes of concrete rings with an initial crack length a = 12 mm, in which Fig. 7(a) and (b) present the overall mesh in a circular and an elliptical ring, respectively, and Fig. 7(c) shows the refined mesh at crack tip.

Based on classical fracture mechanics theory, the energy supplied for crack propagation, i.e. G-curve, can be derived based on KI and modulus of elasticity of material E as following:

The figure illustrates the derived

G-curves of both the circular and

the elliptical rings at the ages

of 5, 10, 15, 20 days, respectively.

RESISTANCE CURVE (R-CURVE)

• The R-curve is formulated as

• It should be noted that the R-curve derived from Eqs. (9)–(13) is based on the geometry of an infinitely large plate.

• R-curve is defined as an envelope of G-curves with different specimen sizes but the same initial crack length

CRACKING AGE

In the restrained shrinkage ring test, cracking age of a concrete ring is determined by the abrupt drop observed from the measured steel strain

By comparing the critical fictitious temperature drop obtained from fracture analysis with the age-dependent one derived from free shrinkage test, the cracking age can be determined.

Alternatively, cracking age of a restrained concrete ring can be determined by maximizing nominal stress r and comparing it with the maximum allowable tensile stress

According to the condition of G = R, the relationship between crack length a and allowable nominal stress r can be determined

Collecting rmax for each day, the relationship between allowable nominal tensile stress and concrete age can be established, which is presented below.

The cracking age of the circular ring is approximately 16 days and that of the elliptical one is approximately 12 days

These values are compared with their counterparts from experiment (see Table). It can be seen that they agree reasonably well with their experimental counterparts, indicating that the fracture analysis model proposed in this study for predicting crack initiation in concrete ring specimens subject to restrained shrinkage is reliable.

Based on the cracking age derived from Fig. 12, the G- and R-curves for circular and elliptical rings are illustrated in Fig. 13(a) and (b), respectively. At the cracking ages, G- and R-curves intersect and also have the same slope. The crack length corresponding to the point of intersection is the critical crack length afc for a ring specimen

CONCLUSIONS

Cracking ages from numerical analyses agreed well with experimental results for circular and elliptical ring specimens.

It indicates that using a fictitious temperature field to simulate the shrinkage of concrete and introducing resistance curve to investigate the cracking behaviour of concrete in restrained shrinkage test are appropriate and reliable.

Based on experimental and numerical results, it can be seen that the elliptical ring with R1/R2 = 2 cracks earlier than the circular ring, which can shorten the cracking period in restrained shrinkage ring test.

The numerical results indicate that restraining pressure caused by shrinkage enforced on a circular concrete ring distributes uniformly along its circumference, while that on an elliptical one distributes non-uniformly.

For the normal strength concrete investigated in this research, when afc< 24 mm, the driving energy in an elliptical ring is greater than that in a circular ring indicating that elliptical geometry can provide higher degree of restraint. In contrast, when afc > 24 mm, things are different. The driving energy in an elliptical ring becomes less than that in a circular ring, indicating that an elliptical ring needs a longer period to crack.

REFERENCES[1] Parilee AM, Buil M, Serrano JJ. Effect of fiber addition on the autogenous shrinkage of silica fume concrete. ACI Mater J 1989;86(2):139–44.

[2] Kovler K. Testing system for determining the mechanical behavior of early age concrete under restrained and free uniaxial shrinkage. RILEM Mater

Struct 1994;27(6):324–30.

[3] Kraai PP. A proposed test to determine the cracking potential due to drying shrinkage of concrete. Concr Construct 1985;30(9):775–8.

[4] Shales CA, Hover KC. Influence of mix-proportion and construction operations on plastic shrinkage cracking in thin slabs. ACI Mater J

1988;85(6):495–504.

[5] Carlson RC, Reading TJ. Model of studying shrinkage cracking in concrete building wall. ACI Struct J 1998;85(4):395–404.

[6] Grzybowski M, Shah SP. Shrinkage cracking of fiber reinforced concrete. ACI Mater J 1990;87(2):138–48.

[7] Weiss WJ. Prediction of early-age shrinkage cracking in concrete. Ph.D Dissertation, Northwestern University, Evanston, Illinois; 1999.

[8] Weiss WJ, Yang W, Shah SP. Influence of specimen size/geometry on shrinkage cracking of rings. ASCE J Engng Mech 2000;126(1):93–101.

[9] Weiss WJ, Shah SP. Restrained shrinkage cracking: the role of shrinkage reducing admixtures and specimen geometry. RILEM Mater Struct

2002;35(3):85–91.

[10] Bentur A, Kovler K. Evaluation of early age cracking characteristics in cementitious systems. RILEM Mater Struct 2003;36(3):183–90.

[11] Moon JH, Pease B, Weiss J. Quantifying the influence of specimen geometry on the results of the restrained ring test. J ASTM Int2006;3(8):1–14.

THANKYOU…….