Determination of c and phi from IDT and unconfined ... · and Unconfined Compression (UC) testing by Christensen and Bonaquist (2002). UC testing is one of the most common and simple

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Piratheepan, J., Gnanendran, C. T., & Arulrajah, A. (2012). Determination of c and

phi from IDT and unconfined compression testing and numerical analysis.

Originally published in Journal of Materials in Civil Engineering, 24(9), 1153–1164. Available from: http://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0000493

Copyright © 2012 ASCE. This is the author’s version of the work, posted here with the permission of the publisher for your personal use. No further distribution is permitted. You may also be able to access the published version from your library. The definitive version is available at http://ascelibrary.org/.

http://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0000493

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DETERMINATION OF c AND Φ FROM IDT AND

UNCONFINED COMPRESSION TESTING AND NUMERICAL

ANALYSIS

J. PIRATHEEPAN 1, C. T. GNANENDRAN 2 & A. ARULRAJAH 1

J. Piratheepan1

Lecturer,

Faculty of Engineering and Industrial Science (H38),

Swinburne University of Technology,

P.O Box 218, Hawthorn VIC 3122

Australia.

Email : [email protected]

Phone : +613-92145859

Fax : +613-92148264

C. T. Gnanendran2

Senior Lecturer,

School of Engineering and Information Technology

The University of New South Wales @ ADFA

Northcott Drive

PO Box 7916

CANBERRA BC ACT 2610

AUSTRALIA

Journal of Materials in Civil Engineering. Submitted May 13, 2011; accepted January 26, 2012; posted ahead of print January 28, 2012. doi:10.1061/(ASCE)MT.1943-5533.0000493

Copyright 2012 by the American Society of Civil Engineers

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Ph: +(61) 2 6268 8977

Fax: +(61) 2 6268 8337

Arul Arulrajah1

Associate Professor,




Australia.


Phone : +613-92145741

Fax : +613-92148264

Corresponding Author:

Dr. Piratheepan Jegatheesan




Australia.


Phone : +613-92145859

Fax : +613-92148264



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Abstract

This paper presents an alternative criterion (simplified method) to determine the cohesion (c)

and internal angle of friction ( ) properties for two granular materials lightly stabilised with

slag-lime and general blend (GB) cement-flyash using indirect diametral tensile (IDT)

strength and unconfined compressive strength (UCS). The c and values of the stabilised

materials obtained based on this criterion were related to the IDT strength and UCS. The

results suggest that the c and can be estimated using this criterion and the c can be

accurately related to either the IDT strength or UCS for lightly cementitiously stabilised

granular materials. However, the IDT strength is a better characteristic than the UCS to

estimate the c. In order to validate the criterion, the c and obtained from the proposed

criterion were input in the numerical analyses of IDT testing with Mohr – Coulomb failure

criterion using FLAC2D finite difference software. The predicted tensile stress – horizontal

diametrical deformation numerical results were compared with the corresponding

experimental results. Based on this numerical analysis, it was found that the c and

parameters estimated from this method predicted the experimental results well in the elastic

region but over predicted the ultimate stress.

Key words: IDT test, stabilised materials, GB cement-flyash, unconfined compression test,

Cohesion, internal angle of friction.



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Introduction

Shear strength of geological materials such as soils and rocks is often determined by Mohr-

Coulomb failure theory. In which, the shear strength is assumed to vary linearly with the

applied normal stress through two shear strength parameters commonly known as the

cohesion (c) and the angle of internal friction (Φ). Normally these properties are determined

through laboratory triaxial tests. Although the Mohr-Coulomb theory is widely used to

determine the shear strength properties of soils, it is applicable to lightly cementitiously

stabilised soils or aggregate bases and many researchers have carried out studies on cement

treated soils and aggregates using triaxial tests (e.g. Ismail et al. 2002; Lo et al. 2003).

However, the triaxial test needs very expensive equipment and consumes too much time for

sample preparation and testing, which is not suitable for routine laboratory or field

experiment practice. Therefore, an alternative approach was proposed to determine c - Φ

properties for asphalt concrete base material using Indirect Diametrical tensile (IDT) testing

and Unconfined Compression (UC) testing by Christensen and Bonaquist (2002).

UC testing is one of the most common and simple tests that can be carried out with minimum

laboratory facilities to determine the unconfined compression strength (UCS) of cohesive

soils and stabilised materials (Basha et al. 2005; Kolias et al. 2005a; Lim and Zollinger 2003;

Peethamparan and Olek 2008; Peethamparan et al. 2008; Piratheepan et al. 2010). Carneiro

and Barcellos (1952), two Brazilian engineers, originally developed the IDT test, known as

Brazilian test, to measure tensile strength of brittle materials by applying a compressive load

along two opposite generators of a cylinder. This test was later adopted by asphalt industry as

a common test method to determine the tensile strength and resilient modulus of hot mix

asphalt (Kennedy and Hudson 1968; Schmidt 1972). In an IDT testing, the stress state at the

vicinity of the centre of the sample is the same as that at the bottom of the cementitiously

stabilised (or asphalt) base layer in a pavement structure as schematically shown in Figure 1.



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Behaviour of cementitiously stabilised granular materials can be analysed using the Mohr-

Coulomb failure theory. According to this theory, the strength of a material such as the

stabilised material depends upon both cohesion (c) and internal angle of friction ( ). For a

simple shear loading with an applied normal stress σ, the shear stress at failure τmax

is given

by the following equation:

max tanc (1)

Where

c = cohesion

= angle of internal friction, degrees

σ = normal stress

The Mohr-Coulomb theory is often represented graphically by plotting a series of Mohr

circles representing stress states at incipient failure under increasing levels of confining stress

and then drawing a tangent to these circles, which represents the Mohr-Coulomb failure

envelope. Then c and are determined using the failure envelope. This method can be used

to determine c and of cementitiously stabilised granular materials by IDT and UC testings.

Figure 2 shows the Mohr circles for the stress state in the samples at failure under IDT and

UC testings. The magnitude of compressive stress at failure is three times the tensile stress in

IDT testing (i.e. y-IDT = 3 x-IDT). Thus, the mean principal (or normal) stress, p, value is ( 1

+ 3)/2 = ( y-IDT + x-IDT)/2 = (3 x-IDT - x-IDT)/2 = x-IDT = IDT (remembering that the IDT

strength x-IDT is negative (tensile)). In other word, the p value if simply equal to the absolute

value of the IDT strength. Similarly, the maximum shear stress, q, value is ( 1 - 3)/2 = ( y-

IDT - x-IDT)/2 = (3 x-IDT + x-IDT)/2 = 2 x-IDT = 2 IDT, or, simply put, q is equal to twice the

IDT strength. c is the UCS of the sample having the diameter to height ratio of around 1:1

and the same density as that of the IDT sample. Thus, p = q = c/2.



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From Figure 2;

cot sin2 2

c c c (2)

2 ( cot )sinIDT IDT c (3)

1

(2) cot 12 sin

cc

2

(3) cot 1sinIDTc

4

(2), (3) sin2

c IDT

c IDT

a

Thus,

1sin ( )a (4)

(2 )(3)

cosIDT a

c (5)

Or

(1 )2 cosc a

c (6)

The advantage of this approach is that it is much quicker and simpler compared with the

standard protocol and does not require a sophisticated triaxial testing facility or any other

special equipment. The IDT testing, being a measure of tensile strength is in fact a good

indicator of mixture cohesion.



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Experimental Investigation Undertaken

The experimental investigation carried out involved the study of the IDT strength and UCS

characteristics of two different granular materials stabilised lightly with slag lime and flyash.

Granular base materials obtained from two sources stabilized with 3–5 % slag-lime and 1.5 %

GB cement-flyash binders under the optimum moisture content (OMC) from standard Proctor

compaction conditions were chosen for this investigation. One of the parent materials,

hereafter referred to as granular base material 1 (BM1), selected was a freshly quarried

granular base material obtained locally in Canberra, Australia. This was classified as a WG—

well graded sandy gravel with some fines according to the Unified Soil Classification

System. The other material selected for this research was also a granular material, classified

as WG - well graded granular base material, obtained from Queensland, Australia. This is

hereafter referred as granular base material 2 (BM2). Further details of the parent materials

and binders can be found in Gnanendran and Piratheepan (2008; 2009; 2010) and Piratheepan

et al (2010).

Obtaining representative samples of such granular materials is very difficult and it often leads

to inconsistency of particle proportions in samples, resulting in considerable variability of

properties determined from different samples. To minimize such inconsistency, the

reconstituted materials with unchanged (or consistent) gradings shown in Figure 3 were

adopted for this research. These were achieved by sieving a large batch of granular material

from each material through standard sieves, separating the materials into different particle

size ranges in different containers and then remixing them at suitable weight proportions to

get the specified unchanged grading. It is noted that the reconstituted materials excluded

particle sizes greater than 19 mm.



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The moisture content (MC) - dry density relationships of the reconstituted materials as well

as the stabilized materials (i.e. the reconstituted materials stabilised with binders) were

determined initially in accordance to ASTM D698-91 (2007) for this investigation (see

Figure 4). The Atterberg limits determined on the material passing the No. 40 (opening size

of 0.425 mm) sieve in accordance to ASTM D4318 (2005) for BM1 were liquid limit = 18

and plastic limit = 15 and for BM2 were liquid limit = 25.2 and plastic limit = 20.6.

The IDT and UC tests were conducted on 7-days cured samples for GB cement–flyash

stabilised materials and 28-days cured samples for slag-lime stabilised materials. The IDT

test samples (150 mm diameter and approximately 85 – 90 mm thickness) were prepared by

gyratory compaction with 500-kPa vertical pressure and 250 gyrations and the UC test

samples were prepared and tested according to AS 1141.51. The loadings applied in both IDT

and UC tests were displacement control of 1 mm/min.

Verification of c – Parameters from numerical analysis

In order to assess the validity and applicability of the criterion to lightly cementitiously

stabilised granular base materials and to validate the material properties (c and ) obtained by

the proposed method, a series of numerical analyses were carried out using the finite

difference stress analysis software FLAC2D. The calculated c and were input in Mohr –

coulomb built – in – model in FLAC2D finite difference software and the monotonic load

numerical results were compared with the actual experimental results.

Modelling with FLAC 2D

The IDT testing is performed on a cylindrical specimen of the material loaded diametrically

between platens of a testing machine. The IDT strength is then approximately determined

using an analytical expression from corresponding peak load at failure assuming that the



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material is homogeneous, linearly elastic and isotropic (Hondros 1959; Vuttukuri et al. 1974).

Details of the IDT test conditions performed in this investigation are shown in Figure 5. In

this verification investigation, the loading area is defined by 2α, which is the angular distance

over which the applied force, F, is assumed to be distributed radially.

The dimensions of the IDT specimens used in this investigation are 150 mm diameter (75

mm radius) and 85 - 90 mm thickness. The other material parameters for the analysis were

obtained for the experimental study carried out in this investigation.

The analytical solutions for the stress component normal to the loading diameter, σθ, and the

stress component along the loading diameter, σr, are given by the expressions (see Vuttukuri

et al. 1974):

2 2

0 012 4 2

0 0 0

1 sin 2 1

tan tan

1 2 cos 2 1

r rr rF

rt r r rr r r

(7)

2 2

0 012 4 2

0 0 0

1 sin 2 1

tan tan

1 2 cos 2 1r

r rr rF

rt r r rr r r

(8)

Where r0 is the radius of the specimen, t is the thickness and r is the distance from the centre

of the specimen. It is noted that the compressive stress was considered as negative in this

investigation.

The tensile strength of the material, σθc, at the centre of the specimen is



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0 0

sin 21c F F

r t r t (9)

This approximation is used to determine the IDT strength of the material. It is assumed that

the failure is independent of stresses that develop normal to the disk face, and is a plane-

strain solution.

Details of geometry and boundary conditions

A 40 × 40 size grid was generated to represent the 2D numerical model for the IDT specimen.

In this investigation, only the top half of the cylindrical specimen was modelled, because of

the symmetry of the IDT testing. The boundary conditions were applied to the model such

that the model was fixed in y direction at x = 0 m. The generated grid and the boundary

conditions for the numerical model are shown in Figure 6 and Figure 7 respectively.

Results and Discussion

Experimental and Analytical Results

Results of the proposed method to determine c and from UCS and IDT strength values for

four different stabilised mixtures (two granular materials stabilised with slag-lime and GB

cement-flyash) stabilised with various binder contents are given in Table 1. The cohesion

values obtained from the proposed method was plotted against the IDT strength values in

Figure 8. It can be noted that the cohesion values were related to the IDT strength with a

good coefficient of correlation (R2 = 0.998). Thus a good relationship was observed between

the IDT strength and cohesion:

1.846 IDTc Strength (10)



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Where c is cohesion of the stabilised material

From this observation, it can be concluded that the mixture cohesion can be accurately

estimated from the IDT strength. Similarly, a good relationship was developed between the

mixture cohesion and UCS with a high coefficient of correlation (R2 = 0.9574) as shown in

Figure 9. From the observations made in this investigation, both the IDT and the UC tests can

therefore be used to estimate the cohesion of cementitiously stabilised granular base materials

regardless of the material and binder types. Moreover, the determination of c and by this

method (using IDT strength and UCS) is more accurate than confined compression tests (i.e.

conventional triaxial tests). Because the separation between the confined stress test data in –

space (V in Figure 10) is generally much smaller than is usually the case using UCS and

IDT strengths (U in Figure 10). Also, the IDT strength data is very close to the vertical axis

and the cohesion is defined by the intercept of the failure envelope on the vertical axis.

Therefore, small variations in the UCS and IDT strength values make very little variations in

the c and estimates. Thus, the proposed method for the determination of the fundamental

properties of cementitiously stabilised granular materials provides both a better estimate of

the friction angle (the slope of the failure envelope) and the cohesion (intercept).

Figure 11 illustrates the variation of cohesion with BC for various stabilised mixtures. The

cohesion shows almost a linear variation with the BC for the two granular materials stabilised

with slag-lime and GB cement-flyash and the cohesion of stabilised BM1 was always higher

than that of the stabilised BM2. It was found from the figure that the cohesion increased by

an average of 36% for stabilised BM1 and 32% for stabilised BM2 with respect to the

cohesion value of the corresponding material stabilised with 4% slag-lime, when the BC was

increased by 1%. This trend indicates that the use of slag–lime and GB cement-flyash in

granular materials dramatically enhances the cohesion of the granular materials investigated



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in this study (i.e. 36 and 32% are substantial increment). It is also noted that the variations of

cohesion with BC were different for different granular materials and not different for

different binders.

The variation of with binder content shows (see Figure 12) not a clear pattern and it varies

between 40 – 50° for the materials stabilised with slag-lime and between 64°-66° for the

materials stabilised with GB cement – flyash. It can be noted that the values are always

higher for BM1 than that for BM2 and the similar trend was observed for the variation of c

with BC.

However, the values of c and can be dependent on other factors such as the densities of the

IDT and UC test specimens, height to diameter ratio of the UC test specimens and the testing

conditions including the rate of loading. To study the effect of the above mentioned factors,

the UCS and IDT strength results of several studies reported by other researchers were used

to develop the relationships. The relationship is very strong; assuming that the intercept is

zero, the mixture cohesion can be accurately estimated as 1.75-1.83 times the IDT strength

with a R2

value of 96 percent and above (see Figure 13).

White, G. (2006) conducted an experimental program to characterize granular base materials

stabilised cementitiously with slag-lime in terms of IDT strength and UCS (diameter to

height ration of 1:2). UCS and IDT tests were carried out on stabilised base material

specimens (28 days curing) prepared with gyratory compaction method with a vertical

deformation rate of 1 mm/min. The IDT strength and UCS results were utilised in this study

to evaluate the c and using the simplified method proposed. The c values were calculated

and plotted against the corresponding IDT strength and UCS values in Figure 13 and Figure

14 respectively. The developed relationship between c and IDT strength (cWhite = 1.80 IDT



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strength) is very strong with a R2

value of 0.9823, while the relationship between c and UCS

(cWhite = 0.31 UCS) is very poor with a R2

value of 0.1971.

Khattak and Alrashidi (2006) carried out a laboratory investigation on four different fiber

reinforced soils stabilised with 10% Type-1 Portland cement. The UCS tests were carried out

according to ASTM D 1633 (1994), in which a 101.6 mm diameter by 116 mm high

(diameter to height ration of 1:1.14) specimen was loaded at an axial strain rate of 1 mm/min

using the material testing system (MTS). The IDT tests were performed in accordance to the

modified AASHTO T 245 method, in which a stabilised specimen of 101.6 mm diameter by

63.5 mm height (diameter to height ratio of 1:0.625) was loaded to failure at 51 mm/min

deformation rate. The UCS and IDT samples were tested at 7 and 28 days curing period. The

calculated cohesion values using the simplified method were plotted against the

corresponding IDT strength and UCS values in Figure 13 and Figure 14 respectively. The

developed relationships between c and IDT strength for 7 and 28 days cured samples (cKhattak,7

= 1.79 IDT strength and cKhattak,28 = 1.77 IDT strength ) are very strong with R2

values of

0.9933 and 0.9942 respectively, while the relationships between c and UCS are: cKhattak, 7 =

0.33 UCS and cKhattak, 28 = 0.33 UCS with R2

values of 0.7579 and 0.9006 respectively.

UCS and IDT tests were carried out on three fine-grained clayey soils stabilised with high

calcium fly ash and cement by Kolias et al. (2005b). In this study, the IDT and UCS samples

were prepared with static compaction method (BS 1924, test 10) at the optimum moisture

content and cured for 7, 28 and 90 days. Samples of 50 mm diameter by 100 mm height

(diameter to height ratio of 1:2) were tested with a constant deformation rate of 1 mm/s in

both IDT and split tensile testings at different curing ages. The test results were utilised in

this study and the calculated c values were plotted against IDT strength and UCS in Figure 13

and Figure 14 respectively. The developed relationship between c and IDT strength (cKolias =



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1.76 IDT strength) is very strong with a R2

values of 0.999, while the relationship between

c and UCS (cKolias = 0.25 UCS) is also very strong with a R2

values of 0.9383.

Consoli et al. (2002) reported a laboratory investigation of evaluating UCS and split tensile

strength characteristics on polyethylene terephthalate fiber reinforced sand stabilised with

rapid hardening Portland cement varying from 0 to 7 % by weight. The UCS and split tensile

tests were conducted according to ASTM D 1633 (1990a) and ASTM C 496 (1990b). In both

tests, cemented specimens cured for 3 days of 50 mm diameter by 100 mm height (diameter

to height ratio of 1:2) were tested at a strain rate of 1.14%/min. the calculated c values from

the results of this study was plotted against IDT strength and UCS in Figure 13 and Figure 14

respectively. The developed relationship between c and IDT strength (cConsoli = 1.83 IDT

strength) is very strong with a R2

values of 0.9687, while the relationship between c and UCS

(cConsolis = 0.20 UCS) is with a R2

values of 0.6724.

Arabani and Veis Karami (2006) conducted UCS and IDT testings on 5 different clayey

sands stabilised with 3, 6 and 9% lime. The cylindrical stabilized specimens for both UCS

and IDT testings were of 50 mm diameter and 100 mm height (diameter to height ratio of

1:2). The UCS tests were conducted according to Iranian Code for Highway Design based on

AASHTO T 220 with a constant strain rate of 0.5 mm/min and the IDT tests were conducted

according to Iranian Code for Highway Design. The curing time of both tensile and

compressive samples was similar (i.e. 3 days). The developed relationship between c and IDT

strength (cArabani = 1.81 IDT strength) in this study is very strong with a R2

values of 0.994,

while the relationship between c and UCS (cArabani = 0.34 UCS) is with a R2

values of

0.7919.



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Sobhan and Mashnad (2002) carried out an experimental investigation including UC and split

tensile testings on a granular soil chemically stabilised with cement and fly ash, and

mechanically reinforced with recycled plastic strips (high-density polyethylene (HDPE)). The

specimens were prepared with maximum of 12% cement and 10% fly ash by dry weight of

the mix and contained an additional 0.25 - 0.80 % fibre of recycled plastic waste. The split

tensile (ASTM C 496) and UC testings were performed on 101.6 mm diameter by 190.5 mm

height (diameter to height ratio of 1:1.875) specimens cured at 28 days. The developed

relationship between c and IDT strength (cSobhan = 1.75 IDT strength) in this study is very

strong with a R2

values of 0.9992, while the relationship between c and UCS (cSobhan = 0.28

UCS) is also very strong with a R2

values of 0.9462.

The cohesion values plotted in Figure 13 against the corresponding IDT strength values for

the selected studies performed previously by several authors show that the relationships

derived between cohesion and IDT strength were very strong with high coefficient of

regressions and the cohesion varied from 1.75 to 1.83 times the IDT strength. Therefore,

these relationships are very close or almost the same. On the other hand, the relationships

derived between cohesion and UCS from all previous studies were scattered and the cohesion

varied from 0.2 to 0.34 times the UCS. The variations of the relationships between cohesion

and UCS could be due to the factors such as the density and the height to diameter ratio of the

UC test samples. However, the relationships derived between cohesion and IDT strength

were very close even though the densities and the height to diameter ratios of both IDT and

UC test specimens were different. Because, as discussed earlier, the IDT strength data is very

close to the vertical axis and the cohesion is defined by the intercept of the failure envelop on

the vertical axis. Therefore, the variations in the UCS and IDT strength values make very

little variation in the cohesion estimate. Therefore, it can be concluded that the IDT strength



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is a better characteristic than the UCS to determine the cohesion of a lightly cementitiously

stabilised granular material.

Numerical Analysis

The input parameters for the built – in Mohr – Coulomb model in FLAC are stiffness

modulus, Poisson’s ratio, cohesion, internal angle of friction and density. Figure 15 shows

typical stress strain curves from the experimental study for BM1 stabilised with 4% slag-lime

binder at OMC and the corresponding numerical analysis curve with the c and (c = 1.0105

MPa and = 50°) estimated from the simplified analysis. The stress – deformation plot from

numerical analysis with the input parameters c and calculated from Mohr – coulomb failure

criterion predicted the experimental results in the elastic region but over predicted the

ultimate stress. The ultimate IDT strength determined from the experiment study was 0.555

MPa, whereas the strength value obtained from the numerical analysis was 0.713 MPa, which

is 28.5 % higher than the experimental value. However, the maximum diametral horizontal

tensile deformations at the ultimate stress were the same for both the experimental and

numerical stress-deformation curves. The difference in ultimate strengths could be due to

either the estimated c and values were not accurate or the assumed loading area was

inappropriate.

The loading area was defined by 2α as discussed earlier (see Figure 5). To determine the

loading area over which the vertical load was applied, three cases of loading area were

considered: 2°; 5° and 7°. Figure 16 shows the variations of tensile stress at the centre of the

specimen with the horizontal diametral deformation for the three different loading areas

considered. It can be noted that the variation of stress with the deformation and the ultimate

strength for the 3 different loading angles were almost the same (see Figure 16 and Table 2).

However, the applied stresses or the loads were different for different loading angles. Table 2



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presents the details of the numerical analysis performed on different loading angles. The

failure load applied to the specimen during the actual experiment was 11.718 kN and the

failure load for the 5° loading angle from the numerical analysis was the closest to the

experimental value (the percentage difference was 16.5%). The percentage differences for the

other failure loads for 2° and 7° were 115% and 19.6% respectively. Therefore, it is

concluded that the best loading angle is 5° and this value was then used for the remaining

analysis.

Even though the loading angle of 5° predicts the failure load closest to the actual

experimental value, the IDT strength (ultimate stress) predicted from numerical analysis was

always higher than the experimental value (0.555 MPa). This could be because the c and

values determined from the simplified method are slightly varied from the actual values of

the stabilised material. Initially, a number of runs were performed for specimen of BM1

stabilised with 4% slag – lime to see the effects of on the model by changing the internal

angle of friction from 20 to 65 while keeping all other parameters constant. Figure 17 shows

the variation of horizontal tensile stress at the centre of the specimen versus horizontal

diametrical deformation from the numerical analysis for various values. It can be clearly

noted that the ultimate IDT strength is dependent on and does not affect the slope of the

linear part of the curve (i.e. stiffness modulus does not depend on ). As can be seen in

Figure 17, the IDT strength decreases with the increase of . From the numerical analysis

performed, the best value predicting the experimental result is 60°, which is 10° higher

from the value determined from the simplified method. Similarly, the c value was

determined such that the numerical analysis predicted the experimental curve and the c value

determined was 0.82 MPa (see Figure 18).



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However, the failure load applied for = 60° and c = 1.0568 MPa was 12.386 kN and for c =

0.82 MPa and = 50° was 9.069 kN. Therefore, it can be inferred from the results obtained in

the numerical analysis that a combination of adjusted c and can predict the experimental

stress-deformation behaviour and the failure load. Figure 19 shows such an attempt to find

the combination of adjusted c and predicting the stress-deformation curve and the failure

load. The failure load for this case is 11.224 kN, which is very close to the experimental

failure load (11.718 kN), and the corresponding c and are 0.89 MPa and 56°.

Table 3 presents the best combinations of c and and the corresponding failure loads for the

four different stabilised mixes used in this investigation. The results presented in Table 3

show that the c and values determined from simplified method predicted the IDT strength

in the numerical analysis always higher than the experimental values except for the materials

stabilised with GB cement-flyash. For the materials stabilised with GB cement-flyash, the c

and values determined from the simplified method predicted the IDT strength and the

failure load exactly the same as experimental values. However, the adjusted c values for the

slag-lime stabilised materials have a unique variation with the c values determined from the

simplified method (see Figure 20). On the other hand, the adjusted values for the slag-lime

stabilised materials are about 6° higher than the values calculated by simplified method.

Figure 21 presents some typical results of the IDT testing compared with the results of the

numerical simulation. The numerical model reproduces the experimental results with the

adjusted values of c and from simplified methods. It is noted that the input stiffness

modulus used for the numerical analysis was determined from the experimental IDT study

and the Poisson’s ratio assumed was 0.2. The stress-deformation curves from the numerical

analysis presented in Figure 21 do not exactly agree but agree reasonably well with the

corresponding experimental curves. In particular, the predicted and experimental curves agree



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very well in the elastic region and the numerical model predicts the failure load quite

accurately.

On the basis of the results presented in Table 3 and Figure 21, the c and values determined

from the simplified method are still very useful although they do not exactly predict the

experimental results. Therefore, the simplified method should be used only as an

approximation for the determination of c and at this stage. The shear strength parameters

determined from the simplified method might be same or different from the values

determined using triaxial test. Therefore, a separate study should be carried out in the next

phase of this research to achieve a correlation between triaxial c and and simplified c and .

Conclusions

This paper presents an alternative approach to determine the c and properties for lightly

cementitiously stabilised granular materials using IDT strength and UCS. The estimated c

and values obtained based on this approach were related to the IDT strength and UCS. A

comparison study on the relationships between c and IDT strength and c and UCS was also

performed with the help of previous investigations. Based on the results discussed in this

study, it was concluded that the c and can be estimated using IDT strength and UCS values

for lightly cementitiously stabilised granular materials. Moreover, the mixture cohesion (c)

can be accurately related to either the IDT strength or UCS. However, the IDT strength is a

better characteristic than the UCS to estimate the cohesion of a lightly cementitiously

stabilised granular material.

In order to validate the method to estimate the c - parameters of lightly cementitiously

stabilised granular base materials from IDT test data, the c and obtained from the proposed

approach were input in the numerical analyses of IDT testing with Mohr – Coulomb failure



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criterion using FLAC2D finite difference software. The predicted tensile stress – horizontal

diametrical deformation numerical results were compared with the corresponding

experimental results. Based on this numerical investigation, it was found that the c and

parameters estimated from the simplified method predicted well the experimental results in

the elastic region for all materials but over predicted the ultimate stress for most of the

materials. Moreover, it was concluded that the simplified method should be used only as an

approximation for the determination of c and of lightly cementitiously stabilised materials.

Acknowledgements

The writers would like to thank Mr. David Sharp and Mr. Jim Baxter of SEIT,

UNSW@ADFA for their technical assistance during the experimental work reported in this

paper. The contribution of Blue Circle Southern Cement Pty Ltd for providing the binders is

acknowledged and appreciated.



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References

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ASTM-D698. (2007). "Test Method for Laboratoiy Compaction Characteristics of Soil Using Standard Effort (12,400 ft-lbf/ft3 (600kN.m/m3))." Annual Book of ASTM Standards, Vol. 04.08, ASTM International, West Conshohocken, PA, USA.

ASTM-D4318. (2005). "Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils." Annual Book of ASTM Standards, Vol. 04.08, ASTM International, West Conshohcken, PA, USA.

Basha, E. A., Hashim, R., Mahmud, H. B., and Muntohar, A. S. (2005). "Stabilization of residual soil with rice husk ash and cement." Construction and Building Materials, 19(448 - 453).

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Christensen, W. D., and Bonaquist, R. (2002). "Use of Strength Tests for Evaluating the Rut Resistance of Asphalt Concrete." Asphalt Paving Technology, Association of Asphalt Paving Technologists-Proceedings of the Technical Sessions, 71, 692-711.

Consoli, N. C., Montardo, J. P., Prietto, P. D. M., and Pasa, G. S. (2002). "Engineering Behavior of a Sand Reinforced with Plastic Waste." ASCE Journal of Geotechnical and Geoenvironmental Engineering, 128(6), 462-472.

Gnanendran, C. T., and Piratheepan, J. (2008). "Characterization of a Lightly Stabilized Granular Material by Indirect Diametrical Tensile Testing." International Journal of Pavement Engineering 9(6), 445 - 456.

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Gnanendran, C. T., and Piratheepan, J. (2010). "Determination of Fatigue Life of a Granular Base Material Lightly Stabilized with Slag Lime from Indirect Diametral Tensile Testing." ASCE's Journal of Transportation Engineering, 136(8), 736 - 745.

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Ismail, M. A., Joer, H. A., Sim, W. H., and Randolph, M. F. (2002). "Effect of Cement Type on Shear Behavior of Cemented Calcareous Soil." ASCE's Journal of Geotechnical and Geoenvironmental Engineering, 128(6), 520 - 529.



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Kennedy, T. W., and Hudson, W. R. (1968). "Application of the Indirect Tensile Test To Stabilised Materials." Highway Research Record(235), 36-48.

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Kolias, S., Kasselouri-Rigopoulou, V., and Karahalios, A. (2005b). "Stabilisation of clayey soils with high calcium fly ash and cement." Cement and Concrete Composites, 27(2), 301-313.

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Peethamparan, S., and Olek, J. (2008). "Study of the Effectiveness of Cement Kiln Dusts in Stabilizing Na-Montmorillonite Clay." ASCE Journal of Materials in Civil Engineering, 20(2), 137–146.

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Piratheepan, J., Gnanendran, C. T., and LO, S.-C. R. (2010). "Characterization of Cementitiously Stabilised Granular Materials for Pavement Design Using Unconfined Compression and IDT Testings with Internal Displacement Measurements." ASCE's Journal of Materials in Civil Engineering 22(5), 495 - 505.

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List of Figures

Figure 1 Stresses in IDT sample and pavement

Figure 2 Mohr’s circle representing IDT and UC testing

Figure 3 Particle size distributions of granular base parent materials

Figure 4 Variation of dry density with moisture content

Figure 5 The IDT test configuration

Figure 6 FLAC mesh for the analysis IDT testing

Figure 7 Boundary conditions and the applied loading for the numerical analysis

Figure 8 Variation of Cohesion with IDT strength

Figure 9 Variation of cohesion with UCS

Figure 10 Mohr’s circle for triaxial and the proposed method

Figure 11 Variation of cohesion with binder content

Figure 12 Variation of internal angle of friction with binder content

Figure 13 Variation of Cohesion with IDT strength from various investigations

Figure 14 Variation of Cohesion with UCS from various investigations

Figure 15 Typical stress-deformation curves for experiment and numerical analysis

Figure 16 Stress-deformation curves for different loading areas

Figure 17 Stress-deformation curves for different internal angle of friction

Figure 18 Stress-deformation curves for BM1 stabilised with 4% slag-lime

Figure 19 Stress-deformation curves for experiment and numerical analysis with adjusted c and

for BM1 stabilised with 4% slag-lime

Figure 20 Variation of adjusted cohesion with the cohesion from simplified method



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Figure 21 Typical variations of stress versus tensile deformation: (a) BM1 stabilised with 5%

slag-lime; (b) BM2 stabilised with 3% slag-lime; (c) BM2 stabilised with 5% slag-lime; and (d)

BM2 stabilised with 1.5% GB cement-flyash



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List of Tables

Table 1 c and values calculated from the proposed simplified method

Table 2 Estimated stresses and loads for different loading areas

Table 3 Comparison of c, and failure load from the numerical analysis by FLAC2D



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Table 1 c and values calculated from the proposed simplified method

Material Binder type Binder content

/ (%) Sample number UCS / (MPa)

IDT strength / (MPa)

Cohesion / (MPa)

Internal angle of friction / (°)

BM1 Slag-lime 3 1 3.498 0.388 0.7131 45.64 BM1 Slag-lime 3 2 3.946 0.423 0.7843 46.64 BM1 Slag-lime 3 3 3.921 0.410 0.7652 47.36 BM1 Slag-lime 4 1 5.832 0.550 1.0572 50.14 BM1 Slag-lime 4 2 5.697 0.555 1.0568 49.29 BM1 Slag-lime 4 3 5.910 0.608 1.1393 47.83 BM1 Slag-lime 5 1 7.406 0.798 1.4776 46.49 BM1 Slag-lime 5 2 7.434 0.803 1.4859 46.42 BM1 Slag-lime 5 3 7.269 0.762 1.4213 47.28 BM2 Slag-lime 3 1 3.153 0.387 0.6949 42.43 BM2 Slag-lime 3 2 2.811 0.306 0.5651 46.19 BM2 Slag-lime 3 3 3.082 0.329 0.6107 46.76 BM2 Slag-lime 4 1 4.602 0.438 0.8398 49.90 BM2 Slag-lime 4 2 4.830 0.469 0.8939 49.38 BM2 Slag-lime 4 3 5.012 0.576 1.0495 44.55 BM2 Slag-lime 5 1 5.222 0.664 1.1838 41.22 BM2 Slag-lime 5 2 5.644 0.712 1.2714 41.50 BM2 Slag-lime 5 3 5.621 0.709 1.2660 41.50 BM1 GB - flyash 1.5 1 1.924 0.083 0.2141 64.90 BM1 GB – flyash 1.5 2 1.614 0.071 0.1817 64.63 BM1 GB – flyash 1.5 3 1.259 0.065 0.1556 62.23 BM2 GB – flyash 1.5 1 1.293 0.048 0.1321 66.90 BM2 GB – flyash 1.5 2 1.328 0.054 0.1429 65.71 BM2 GB - flyash 1.5 3 1.147 0.042 0.1163 67.07




Table 2 Estimated stresses and loads for different loading areas

Loading angle/area (2α)

Ultimate stress / (MPa)

Maximum applied pressure /(MPa)

Maximum applied load / (kN)

2° 0.725 42.83 25.141

5° 0.713 23.27 13.660

7° 0.733 16.05 9.421




Table 3 Comparison of c, and failure load from the numerical analysis by FLAC2D

Material Binder type

Binder content /

(%)

Sample number

Cohesion (C) / (MPa) Failure load / (kN) Friction angle ( ) By

simplified method

Adjusted value

Experimental With C from

simplified

With adjusted

C

By simplified

method

Adjusted value

BM1 Slag-lime 3 1 0.7131 0.5911 8.091 9.372 7.802 45.64 52 BM1 Slag-lime 3 2 0.7843 0.6451 8.820 10.229 8.428 46.64 52 BM1 Slag-lime 3 3 0.7652 0.6301 8.549 10.003 8.242 47.36 52 BM1 Slag-lime 4 1 1.0572 0.8975 11.588 13.636 11.213 50.14 56 BM1 Slag-lime 4 2 1.0568 0.8900 11.718 13.660 11.224 49.29 56 BM1 Slag-lime 4 3 1.1393 0.9570 12.937 14.406 12.025 47.83 54 BM1 Slag-lime 5 1 1.4776 1.2264 16.563 18.385 15.321 46.49 53 BM1 Slag-lime 5 2 1.4213 1.1790 15.772 18.404 14.529 46.42 53 BM1 Slag-lime 5 3 1.4859 1.2284 16.627 19.395 15.294 47.28 53 BM2 Slag-lime 3 1 0.6949 0.5837 7.477 8.522 7.159 42.43 51 BM2 Slag-lime 3 2 0.5651 0.4700 5.912 7.025 5.871 46.19 52 BM2 Slag-lime 3 3 0.6107 0.5069 6.356 7.546 6.226 46.76 53 BM2 Slag-lime 4 1 0.8398 0.7054 8.359 9.877 8.212 49.90 55 BM2 Slag-lime 4 2 0.8939 0.7464 8.951 10.603 8.657 49.38 55 BM2 Slag-lime 4 3 1.0495 0.8711 10.993 12.252 10.184 44.55 51 BM2 Slag-lime 5 1 1.1838 0.9875 12.516 13.493 11.467 41.22 50 BM2 Slag-lime 5 2 1.2714 1.0679 13.421 15.378 12.184 41.50 50 BM2 Slag-lime 5 3 1.266 1.0634 13.364 14.388 12.137 41.50 50 BM1 GB-flyash 1.5 1 0.2141 0.2141 1.662 1.658 1.658 64.90 64.90 BM1 GB-flyash 1.5 2 0.1817 0.1817 1.422 1.437 1.437 64.63 64.63 BM1 GB-flyash 1.5 3 0.1556 0.1556 1.302 1.355 1.355 62.23 62.23 BM2 GB-flyash 1.5 1 0.1321 0.1321 0.961 0.994 0.994 66.90 66.90 BM2 GB-flyash 1.5 2 0.1429 0.1429 1.081 1.079 1.079 65.71 65.71 BM2 GB-flyash 1.5 3 0.1163 0.1163 0.841 0.840 0.840 67.07 67.07




Documents

Determination of c and phi from IDT and unconfined ... · and Unconfined Compression (UC) testing by Christensen and Bonaquist (2002). UC testing is one of the most common and simple