A fracture mechanics-based method for

prediction of cracking of circular and elliptical

concrete rings under restrained

Shrinkage

by

Wei Dong, Xiangming Zhou , Zhimin Wua

Tamonash Jana

001411202019

Introduction

Residual stress development during shrinkage of concrete.

Occurance and effect of crack formation.

Cracking potential test methods(Plate,Bar,Ring)

Why Ring test is preferred?

Circular ring for Ring Test

Long period of time is needed before the first cracking occurs in a restrained circular concrete than elliptical ring due to its geometry.

Initial cracking may appear anywherealong the circumference of a circularring specimen.

Restraining effect from the centralsteel ring to the surrounding concrete ring is uniform.

Geometry function depends on Ro/Ri only.

Higher degree of restraint can be provided by an elliptical geometry than a circular one.

Comparetively short period of time isneeded before the first cracking thanthe circuler one.

Crack initiates close to the vertices on the major axis of an elliptical concrete ring.

Geometry function depends on their inner major and minor radius-to-outer major and minor radius ratio, i.e. R1/(R1 + d) and R2/(R2 + d).

Elliptical ring for Ring Test

Specimen Setup

The mix proportions for the concrete is1:1.5:1.5:0.5 (cement:sand:coarse aggregate:water) by weight.

Following specimen are prepared. 1. 100 mm-diameter and 200 mm-length cylinders(for

measuring mechanical properties of concrete)2. 75 mm in square and 280 mm in length prisms(for free

shrinkage test)3. Notched beams with the dimensions of (100×100×500

mm3 (for fracture test).4. Series of circular and elliptical ring specimens.

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.

Mechanical properties of concrete, including elastic modulus E, splitting tensile strength ft and uniaxial compressive strength fc, were measured from the cylindrical specimens at 1, 3, 7, 14and 28 days.

Three specimens tested for each mechanical property at each age.

Material propertiesIt is found that the average 28-day compressive and splitting tensile strength of the concrete are 27.21 and 2.96 MPa, respectively.

Age-dependent Equations of mechanical properties, in this case are determined...

1) Elasticity Modulus in GPaE(t)=0.0002t3 + 0.0134t2 + 0:3693t + 12.715 [t≤28]

2) Splitting tensile strength, ft, in Mpafc(t)=1.82t0.13 [t≤28]

3) Critical Stress Intensity Factor in MPa mm1/2

KIC(t) = 3.92 ln(t) + 12:6

4) Critical Crack Tip Opening Displacement in mm

CTODC = 0.029t2 + 1.62t + 3.96

t is the age (unit: day) of concrete..

Free shrinkage testsFree shrinkage of concrete was measured on concrete prisms.

Prisms subjected to drying in 23°C and 50% relative humidity.

Longitudinal length change was monitored by a dial gauge, which was then converted into shrinkage strain.

Four different exposure conditions, i.e. representing four different A/V ratios, were investigated on concrete prisms:(1) all surfaces sealed, (2) all surface exposed, (3) two side surfaces sealed and (4) three side surfaces sealed.

Double-layer aluminum tape was used to seal the surfaces.

Shrinkage strain of concrete obtained from free shrinkage test

Restrained shrinkage ring testsThickness, Major and Minor radius of the elliptical ring is

taken 37.5, 150 and 75 mm.

Inner radius of the circuler one is taken 150.

Four strain gauges were attached, each at one equidistant mid-height, on the inner cylindrical surface of the central restraining steel ring.

The top and bottom surfaces of the concrete ringspecimens were sealed using two layers of aluminum tape.

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.

Cracking of concrete is indicated by the sudden drop in the measured strain, recommended by ASTM.

Two concrete ring specimens were tested per geometry.

Cracking ages of the circular rings are 14 and 15 days, respectively, for elliptical ones are both 10 days.

Numerical modelling restrained shrinkage

Finite element analyses were carried out using ANSYS codeto simulate stress development and calculate stressintensity factor.

Unlike circuler rings uniform internal pressure theory is not applicable to elliptical ones.

A derived fictitious temperature field is applied to concrete to simulate the shrinkage effect.

The elastic modulus and Poisson’s ratio of steel both remain constant as 210 GPa and 0.3.

Poisson’s ratio of concrete is set constant as 0.2.

Derived fictitious temperature drop with respect to A/V ratio for a concrete element

Crack driving energy rate curve (G-curve)

Shrinkage effect is simulated through applying the temperature drop on concrete in numerical analysis.

Internal stress is developed in concrete, which is uniformly distributed in a circular ring but non-uniformly distributed inan elliptical ring.

For circular ring pressure isDistributed uniformly along itsinner circumference, andthe value is 0.59 MPa

Pressure on the ellipticalone distributes non-uniformly, with the maxim-um and minimum values being 2.14 MPa and 0.28 Mpa.

The stress intensity factor (KI) for the circular and elliptical rings are determined based on the classic fracture mechanics theory

The fictitious temperature drops are applied on the ring in combined thermal and fracture analysis to simulate the mechanical effect of shrinkage of concrete.

Stress intensity factor KI in MPa mm1/2 of the circular ring can be formulated from numerical simulation as

While that of the elliptical ring is

T (in °C)=fictitious temperature drop, αc =linear thermal expansion coefficient of concrete

Energy supplied for crack propagation, i.e. G can be derived by

G-curves of circular and elliptical rings at various ages

Resistance curve (R-Curve)

Based on the work of Ouyang and Shah.. The R-curve is formulated as

α = ac /ao ac = critical crack length, ao =initial crack length,

α,β=R curve coefficients, ψ= Resistance parameter

The values of α and β can be determined by

and

In this study the R-curves for the circular and elliptical rings were approximately taken as that of an infinite large plate with a Side Edge Notch pre-crack.

CreepThe effect of creep on strain in a ring specimen is not taken into account when using the fictitious temperature drop to simulate the shrinkage effect.

But actually cracking of a concrete ring specimen is affected by not only shrinkage but also creep.

the total strain is the sum of elastic strain and creep strain and can be expressed as

σc (t0)=stress in concrete at the time of loading t0

= modulus of elasticity of concrete at loading time, J(t,t0)=creep function, φ(t,t0)=Creep Coefficient

Effect of creep on nominal stress

Effect of creep on nominal stress

Cracking age

The restraining effect provided by the steel ring can be regardedas the externally applied load on concrete.

The abrupt strain drop indicates that theapplied load has reached its peak. Corresponding crack length a is the critical crack length ac.

At the critical state corresponding to a = ac, the G and R curves intersect and have the same slope.

i.e. mathematicallyG = R = (KIC)2/E

Determination of cracking age for concrete rings

Determination of cracking age for concrete rings

ConclusionA fictitious temperature field to simulate the shrinkage of concrete to investigate the cracking behavior of concrete are appropriate and reliable.

The maximum circumferential tensile stress in an elliptical ring is about 3.6 times of that in a circular ring.

For a range of value of the critical crack length[ >or< 24 mm] cracking tendency of circuler and

elliptical ring is different.

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