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NOMENCLATURE

E = Modulus of elasticity

fc = Concrete compression stress

f’c = Concrete uniaxial cylindrical compression strength

ft = Concrete tensile stress

ftr = Concrete uniaxial tensile strength

ß = En-echelon flow angle

1, 2 = Principal strains

x,y, xy = Stresses in the global coordinate system

1,2, xy = Principal stresses

1. Theoretical Background

Concrete is a heterogeneous material consisting of aggregates,

embedded in a cement-sand matrix. The mechanical properties are

influenced by the individual material properties and their interaction.

Aggregates exhibit a linear behavior up till failure, but the mortar

has a highly non-linear stress-strain relationship, even at low stress

levels. These phenomena have been confirmed by previous findings

concluding that the behavior of aggregate is brittle-linear with a

reversible deformation up to its limit, followed by a sudden failure.

These data confirmed the findings of former researchers

concluding that the behavior of both cement paste and aggregate are

brittle-linear with a reversible deformation up to limit, followed by

a sudden failure. Concrete on the other hand; demonstrates a quasi-

ductile behavior with a progressive decrease in load bearing

capacity after the ultimate load has been reached. Scrivener [1]

concluded that this behavior originated from the development of

micro cracking in the Interfacial Transition Zone (ITZ) between

aggregates and mortar. This interface physical structure is highly

dependent on the cement hydration products, resulting in the

crystals C3S2H8 (Calcium Silicate Hydrate), CH (Calcium

Hydroxide) and (ettringite). Hence, the resulting

concrete has a lower ultimate compressive strength compared to

that of the aggregates and the mortar.

1.1 Stress Concentrations around Inclusions Concrete consists of aggregates, embedded in a mortar matrix.

While the aggregate has a linear stress-stain behavior up to its

ultimate strength, the mortar exhibits a highly non-linear behavior.

The ultimate strength of the aggregates is also noticeably higher

than that of mortar (Table 1). Based on the test results it is shown

that the stiffness of both mortar and aggregates differs significantly.

The stress in a specimen with aggregates are best described by

observing the mortar stress-flow [2], where a stiff aggregate is

surrounded by a mortar with a much lower stiffness. Micro-cracks

http://dx.doi.org/10.6493/SmartSci.2014.221

The Effect of Aggregate Shape and Configuration to the Concrete Behavior

Han Ay Lie1,*, Ilham Nurhuda2 and Yanuar Setiawan2 1Structural and Material Laboratory, Diponegoro University, Semarang, Indonesia

2Department of Civil Engineering, Diponegoro University, Semarang, Indonesia * Corresponding Author / E-mail: ayliehan@indosat.net.id, TEL: +62-24-7472498, FAX: +62-24-7474561

KEYWORDS : shape, configuration, bi-axial stresses, stress and strain

It has long been acknowledged that the behaviour of concrete is influenced by the properties of its constitutive materials. The geometry of aggregates is believed to contribute to the strength and stress-strain relationship of concrete. However, advanced studies are still required to quantify the effect of such factor in determining the behaviour of concrete. This research was aimed at investigating the effect of aggregate shape and configuration on the stress-strain relationship of concrete. Four types of specimens were investigated. There was one single coarse aggregate with different shape placed in the centre part of the specimens. The specimens were subject to uni-axial compression and both the load and displacement were measured. The experiments were conducted at the Structural and Material Laboratory of Diponegoro University in Semarang. The results show that the specimen with a diamond shaped aggregate results in the lowest compressive strength. However, the initial tangent stiffness of all specimens is almost identical up to 25% of its ultimate strength. Finite element analyses were carried out to study stress distribution in the specimens. The results show that the stresses are concentrated at the corner of the aggregates. This stress concentration initiates cracks at the Interfacial Transition Zone (ITZ) around the corner of the aggregates. The cracks then propagate and spread to the mortar which then reduce the stiffness of the specimens.

Manuscript received: January 31, 2014 / Accepted: April 17, 2014

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are present but these cracks can only propagate when growing

external stresses are applied. The difference in stiffness and

Poisson’s ratio between adjacent materials, results in a

confinements at the top and bottom of the aggregate, creating a bi-

axial confinement (Fig. 1). The confined part has a conical form,

and shear stresses will occur at their boundaries, creating ”en-

echelon” shear stresses and cracks [3].

Table 1 Aggregate and mortar properties

Properties Aggregate Mortar

Modulus of Elasticity E (GPa) 12.73 7.69

Compression Strength f'c (MPa) 171.1 43.6

Poisson's Ratio υ 0.21 0.33

Fig. 1 Fracture mechanism of a single embedded aggregate

Aggregate sides perpendicular to the stress direction are

subjected to lateral splitting due to tensile stresses. The crack

propagation will stop at the confined cones, and can only proceed

through the en-echelon cracks. Since the ITZ is recognized as the

weak link in concrete [4], these stress concentrations will in turn,

lead to micro crack initiation in this area. The micro cracks

developed on ITZ will magnify the concentration of stresses

surrounding the aggregates. The values of the stresses are

dependent of the severity of the cracks and the shape of the

aggregates.

In a concervative approach, the effect of micro cracks

developed on ITZ can be studied by assuming no connection

between aggregate and mortar. This way, the aggregate can be

modelled as a hole in a mortar specimen. Previous studies [5], [6]

have shown that the magnitude of stress concentration is highly

dependent on the shape and orientation of the hole. With

rectangular holes as investigated in this research, a square shape

aggregate will produce the highest stress concentration. The

magnification of stress will even higher if the corner of the hole

faces the load or when the angle ß in Fig. 1 is closest to zero [6].

1.2 Stress combinations and the failure envelope The ITZ is subjected to a combination of stresses. When these are

shown in the rendulic (deviatoric) plane, a failure surface can be

drawn (Fig. 2).

Fig. 2 Mortar response to multiple stresses

The upper median represents the compressive median for σ3 <

σ1 where σ1 being the tensile stress (σtensile), the lower median is the

tensile median for stresses σ3 > σ1 with σ3 and σ1 being in tension.

The response of concrete to multi-stresses can be approached by

various criteria. Among the widely known are the Möhr-Coulomb,

Drucker-Prager and Kupfer-Hilsdorf-Rusch criteria. The Kupfer-

Hilsdorf-Rusch criterion is the most widely adopted (Fig. 3), and

predicts the failure surface most accurately.

Fig. 3 Bi-axial failure envelope [7]

Their findings indicate that the strength of concrete subjected to

bi-axial compression is up to 27% higher than that of concrete in

uni-axial compression. In the compression–tension zone, the

compressive strength will decrease as a function of tensile stress

increase. Hence, the areas in the ITZ with combination of tensile

and compression stresses are most susceptible to failure.

To further evaluate the combined stresses, one-quarter of a

model having a single square inclusion is presented. When a

uniform displacement with a small increment is applied, the

corresponding stresses will increase. The SAP 2000 program

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generates the node stresses in the global coordinate system (σx, σy

and τxy) and their corresponding principal stresses and direction (σ1,

σ2 and 2θ). The principal strains (ε1, ε2) are either in tension-tension,

compression-compression or tension-compression. The principal

tensile and compression stresses at each node can be plotted against

the Kupfer’s tension-compression zone failure area. The nodes

where the principal stress combination falls outside the boundary

are identified as having failed (Fig. 4). The ordinates of these nodes

in the global coordinate system can be drawn graphically.

Fig. 4 Bi-axial nodal stress failure criteria

Fig. 4 is a graphical presentation of the second and fourth

quadrant of the failure envelope, i.e. the tension-compression zone.

The horizontal axis is the compression stress, normalized to fc/f’c,

thus having a maximum of one. The vertical axis represents the

tensile stress, normalized to ft/f’c. Since ultimate tensile stresses are

assumed to be 10% of the compression strength, the boundaries for

ft/f’c is 0.1. The normalized principal stresses of nodes are plotted

graphically into this coordinate system; a visual analysis can show

whether the node under observation falls inside or outside of the

failure envelope.

2. Test Set Up

2.1 Mechanical properties of aggregate and mortar The most important properties of the concrete-making materials

are the modulus of elasticity (E), Poisson’s ratio (υ), tensile strength

(ftr) and compression strength (f’c). These properties are obtained

from laboratory tests results of specimens under uni-axial

compression. Mortar has an approximately similar stress-strain

relationship and mechanical behavior to concrete. The testing

method for concrete behavior is expected to be applicable to mortar.

Six cylindrical specimens of size 150 x 300 mm were cast, three

of which were used to obtain the Young’s Modulus of Elasticity and

Poisson’s Ratio of mortar in accordance to ASTM C469 / C469M -

10 Standard Test Method for Static Modulus of Elasticity and

Poisson's Ratio of Concrete in Compression; and the remaining to

obtain the stress-strain behavior up till failure. All specimens were

cast and vibrated to obtain good compression density. The

specimens were de-molded after 24 hours and submerged in water

to cure. The cylinders were tested at the age of 28 days. With the

aggregates, cylinders of size 20.80 x 40 mm were taken by core

drilling and tested.

To measure the Poisson’s Ratio of mortar, cross plane lead wire

- integrated polyester resin-backing, type PLC-60-11 strain gauges

with a length and width of 60 by 1 mm were used. The gauge has a

backing length and width of 74 mm and a resistance of 120 Ω. For

the aggregate, two strain gauges type PFL-10-11 with a length and

width of 10 by 0.9 mm were used. These gauges have a backing

length of 17.5 mm and a breaking width of 5 mm with a resistance

of 120 Ω. The two gauges were placed perpendicular to each other

at the center of the specimen.

The modulus of elasticity was measured using a load cell type

CLC-500 kNA with a capacity of 500 kN and a sensitivity of

1.5mv/v and three LVDT’s type CDP-25M having a rated output of

10000x10-6 strain and a sensitivity of 2000x10-6 strain/mm. All

strain gauges, LVDT’s and the load cell were connected to the data

logger type TDS-303. Incremental load and displacements were

measured using the TDS-7130 software. All measuring devices are

products of Tokyo Sokki Kenkyujo, Japan.

The stress–strain behavior of specimens was recorded by the

Hung Ta, HT-8391PC Computer-Controlled Servo Hydraulic

compression apparatus with a capacity of 2000 kN. To diminish the

restraining effect between the compression apparatus loading plates

and the specimens, a double layer of 100 μm Teflon (PFTE or

polytetrafluorethylene) separated with a layer of bearing greased,

was placed on the top and bottom of the cylinders. The loading rate

was set to 0.25 MPa/s in accordance to ASTM 339/ C 39M-05. The

strain response of the Teflon sheets were measured separately, and

used to correct the strain response of mortar specimens.

2.2 Specimen testing and specification The experiment was designed to test the specimens in plane

stress condition. The specimens were constructed with an area of

100 x 100 mm and a thickness of 50 mm. All specimens were tested

at age of 28 days. Details of specimen type and aggregate diameter

are presented in Table 2. For all prototypes, eight specimens were

casted, from which six valid specimens were used for analyzes

purposes.

The mold was constructed from teak wood (jati) and made leak

proof using a sealant at the seams. Further, the cast was covered

with a thin layer of bearing grease to ensure waterproofing and to

prevent the mortar from attaching to the mold. Aggregates were

placed in the designated holes and the mortar was poured

surrounding the aggregates. Since the aggregates were positioned

vertically, the effect of bleeding can be eliminated. The specimens

were taken out of the mold after 24 hours, and cured by submerging

in water.

Before testing, the specimens were dried and leveled to obtain a

smooth, flat and leveled surface using a spirit/bubble level. Two

100 μm Teflon layers were placed on top and at the bottom of the

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specimen, and the loading increment was set at a rate of 1800 N/s in

accordance to ASTM 109/C 109M-02 Compressive Strength of

Hydraulic Cement Mortars. The load – displacement response was

recorded by the Hung Ta, HT-8391PC Computer-Controlled Servo

Hydraulic compression apparatus having a loading capacity of

2000kN.

Table 2 Specimen details

3. Test Results

3.1 Compressive strength The specimen's compressive strength was recorded and compared

to the mortar-only specimen, without an inclusion. The result is

shown in Fig. 5.

The data suggested that the specimen SP1 having a diamond-

configured inclusion, exhibits the weakest strength. The strength

degradation is measured to be 58% compared to the mortar only

specimen. A detailed compressive strength results and the relative

decrease to the mortar-only specimen are shown in Table 3.

Table 3 Compressive strength comparison of specimens

Specimen Compressive

strength f'c (MPa)

Compressive strength

decrease ratio to mortar (%)

Mortar-only 47.08 0

SP1 27.98 41

SP2 20.05 58

SP3 25.35 46

SP4 27.12 42

Fig. 5 Specimen compressive strength

These findings confirm previous numerical investigation

conducted by Pan [6]. The specimen with a diamond shaped

inclusion, with its corner facing the load, experiences the highest

stress concentration compared to other specimens. Test results from

other specimens also show a general trend that the concentration of

stress decreases as the angle ß increases (see Fig. 1). However, the

size of aggregate also influences the behaviour and the effect needs

to be analyzed. The low capacity of specimen SP2 is due to the high

stress concentrations at the upper most corner of the aggregate. This

theory was outlined by Griffith [8] who considered an elastic body

in tension and calculated the condition at which the total free

energy was minimized. This condition will lead to the initiation of

fracture and micro cracking in the mortar [9], [10]. The SAP 2000

analyzes outcome underlined the experimental results, since the

nodes for this specimen will have the highest bi-axial tension-

compression stresses, when compared to all other specimens. For a

given gradually increasing load increment, the nodes of specimen

SP2 will reach the boundaries of the Kupfer-failure envelope, firstly.

From the visual observation of the specimen during loading, it was

seen that the initial failure started at the top of the aggregate, and

cracks then propagated along the ITZ line in tension (Fig. 6).

The high stress concentration phenomenon also explains the

relatively lower compression strength of specimen SP3. Since the

aggregate in this specimen is narrow and the angle ß is small, the

area of the mortar on the top side of aggregates is subjected to

higher stress concentrations. Although the cracking pattern follows

a columnar formation (Fig. 6), the mortar in tension-compression

will undergo a higher stress level as compared to the wider

aggregates of SP1 and SP4. The specimens SP1 and SP 4 exhibit an

almost similar capacity. The fact that the specimen SP4 has a large

area facing the load does not result in a significant influence to the

load carrying capacity of the specimen.

3.2 Stress-strain relationship The stress-strain relationships of the specimens are shown in

Fig 7, and the maximum strains are tabulated in Table 4. Different

from the mortar only specimen, specimens with aggregates show a

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typical non-linear, concave response. The presence of coarse

agregates in the specimens affects the stiffness, compressive strength,

and the maximum strain of the specimens. The use of aggregates with

higher modulus of elasticity (E) increses the initial stiffness of the

specimens. As shown in Fig. 7, the behavior of specimens with

aggregates is relatively linear at low stress levels, and deviates to

non-linearity at stress levels of around 40% of the ultimate strength.

A small descending branch is observed for almost all specimens

except SP4. The initial tangent stiffness modulus is similar.

However, specimen SP1 shows a distinguishing higher stiffness

modulus at progressing strain stages. The nonlinearity of the stress

– strain curve of specimens with aggregates is due to the

development of micro cracks on the ITZ surrounding the aggregates.

These micro cracks gradually reduce the stiffness before the

specimens completely fail.

SP1 SP2

SP3 SP4

Mortar only specimen

Fig. 6 Crack modes of the specimens

With regard to the maximum stress and strain of the specimens,

the micro cracks developed surrounding the aggregates weaken the

specimens and decrease the ultimate stress at about 50% compared to

the mortar only specimen. Further, the ultimate strain of each

specimen decreases with respect to the ultimate strain of the mortar-

only specimen as shown in Table 4.

Fig. 7 Compression stress-strain behavior of specimens

Table 4 Strain comparison of specimens

Specimen Ultimate strain (%) Strain decrease ratio to

mortar (%)

Mortar-only 0.8 0

SP1 0.58 27

SP2 0.45 44

SP3 0.61 24

SP4 0.53 34

4. Conclusions

The single diamond shaped inclusions influences the

compressive strength of a specimen, negatively [11, 12] The source

of this decrease is originated from the ITZ that has been proven to

be the weakest link in concrete. The very high aggregate stiffness

and strength creates stress disparities in this ITZ. As the ITZ is

weak in tension, micro cracking will be initiate from the area with

the highest tension in the ITZ. The presence of flaws will in

intensify the tensile stresses in the ITZ, and the specimen with an

aggregate tip in the line of loading will result in an accumulation of

stresses in this area. Studies have shown that the energy distribution

between the aggregate and mortar is highly influenced by the

quality of the ITZ. The weak ITZ accounts for as much as 50% of

the drop in compressive strength.

In terms of ductility, it is also proven that the presence of single

aggregate in the specimens has a negative effect to the ultimate

strain of the specimen. However, the effect of aggregates on

ductility of concrete need to be further studied by investigating

variation of aggregate amount in concrete.

As in the case of ultimate strength, SP2 performed the poorest

in terms of ductility as well, suggesting that a larger area of

aggregate parallel to the direction of the load, will lead to higher

ultimate strain at failure. This conclusion is strengthened by the

almost identical ultimate strain observed from SP1 and SP3 that had

almost the same width.

This research work has proven that the shape and configuration

of aggregates with no doubt influences the strength and stiffness

behavior of the specimen. Since concrete is in reality a three-phase

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material consisting of the aggregate, the mortar and the ITZ, further

research is also required to study the behavior of inclusions with a

range of ITZ conditions, ranging from a perfect, fully bonded

interface to a condition with no bond.

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