Experimental and numerical studies on the mechanical behaviour of Australian Strathbogie granite at high temperatures An application to geothermal energy.pdf

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Geothermics 54 (2015) 96108

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Experimental and numerical studies on the mechanical behaviour ofAustralian Strathbogie granite at high temperatures: An application togeothermal energy

Shishi Shao a, P.G. Ranjith a,, P.L.P. Wasantha a, B.K. Chen b

a Deep Earth EnergyResearch Lab, Department of Civil Engineering,MonashUniversity,Building60, Melbourne, Victoria 3800, Australiab Department of Mechanical & Aerospace Engineering, Monash University, Building 36,Melbourne, Victoria 3800,Australia

a r t i c l e i n f o

Article history:

Received 1 October 2012

Accepted 25 November 2014

Available online 13 January 2015

Keywords:

Geothermal

Granite

Brittleplastic

High temperature

a b s t r a c t

The effect oftemperature on the mechanical behaviour ofStrathbogie granite (fine-grained) was stud-

ied under unconfined stress conditions. Fracturing behaviour of test specimens was studied using an

acoustic emission (AE) detection system and some crack propagation was also performed using elec-

tron microscopy scanning (SEM). The stressstrain curves showed plastic and post-peak behaviour for

temperatures above 800 C and the brittleplastic transition was observed to occur between 600 and

800 C for the uniaxially tested Strathbogie granite at a strain rate of 0.1 mm/min and room humidity.

Specimens were heated at a rate of 5 C/min with a 1 h holding period before testing. The AE results

showed that the increasing temperature reduces the stress thresholds for crack initiation and crack dam-

ageand extends the duration ofstable crack propagation. Prevalence ofductile properties with increasing

temperature was also observed from AE results. The stressstrain and AE results reveal that the failure

modes ofStrathbogie granite specimens changed from brittle fracturing to quasi-brittle shear fracturing

and eventually to ductile failure with increasing temperature. Temperature was observed to influence the

colour ofgranite, and the initial white/grey colour changed to an oxidated reddish colour with increasing

temperature. The stressstrain data oftested specimens were incorporated into a finite element model

(ABAQUS 6.7.1), so that both plastic and ductile behaviour ofthe Strathbogie granite could be predictedover a wide range oftemperatures.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

Geothermal heat is now a recommended renewable energy

resource on the time-scales of both technological and soci-

etal systems, with cost, reliability and environmental advantages

over conventional energy resources (Rybach, 2003; Gallup, 2009;

Axelsson, 2010). Exploration of geothermal resources has posed

new challenges for engineers and geologists to counter rock engi-

neering problems at high temperatures. Laboratory testing is an

important aspect of rockmechanics, which provides essentialinput

data for the design of engineering structures in the Earths crust

and mantle subjected to tectonic forces. Since the 1970s, a large

number of laboratory studies have been carried out to investi-

gate the effect of temperature on the physical and mechanical

Corresponding author at: Deep Earth Energy Research Lab, Civil Engineering

Department, Clayton Campus, Monash University, VIC 3800, Australia.

Tel.: +61 3 99054982; fax: +61 3 99054944.

E-mail address: [email protected] (P.G. Ranjith).

properties of rocks in engineering applications, such as deep

mining, underground chambers for nuclear disposal storage (at

temperatures which generally vary from 100 to 300 C and will

increase over the storage period) and high-temperature thermal

cracking of rocks during mechanical drilling (at temperatures as

high as 1000 C),as well as the designof enhanced geothermal sys-

tems (EGSs) (at temperatures about 200 C) (Francois, 1980; Bauer

et al., 1981; Paquet et al., 1981; Heuze, 1983; Hirth and Tullis,

1989). The mechanical behaviour of rock can be significantly influ-

enced by elevated temperatures in such underground projects. In

addition, different types of underground engineering applications

encounter different temperatures, which varyfrom room tempera-

ture to extremely high temperatures. Therefore, understanding the

effect of temperature on the physical and mechanical properties of

rock is of great importance for the design of rock structures and

safety assessment in underground rock engineering.

During the 1970s1980s, investigations mainly focused on

understanding the natural processes in the Earths crust, such

as rock deformation (faulting, folding and shearing), geothermal

activity and magmatic intrusions. Most of these studies reported

http://dx.doi.org/10.1016/j.geothermics.2014.11.005

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S. Shao et al. / Geothermics 54 (2015) 96108 97

the influence of temperature on the mechanical behaviour of

granite (Heuze, 1983; Wang et al., 2002; Dwivedi et al., 2008;

Xu et al., 2008a,b). For example, a review study (Heuze, 1983)

reported that some mechanical, physical and thermal properties of

granitic rocks, including deformation modulus, Poissons ratio, ten-

sile strength, compressive strength, cohesion and internal friction

angle and viscosity, all vary considerably with increasing tem-

peratures. Although some other scholars have also studied the

physical and mechanical properties of rocks under high temper-

atures, the vast majority of previous experimental studies have

been performed by heating the specimens to predetermined tem-

perature levels, but testing them at room temperature (Xu et al.,

2008a,b, 2009; Zhang et al.,2009). Since rocks in naturalgeothermal

reservoirs are subjected to continuous heating conditions, these

preheating test conditions may not exactly reproduce the in situ

temperature conditions. In addition, when pre-heated rock spec-

imens are cooling down to room temperature, micro-structural

changes and irreversible thermally induced micro-cracking can

takeplace.Therefore, theresultsof experimental studies performed

on pre-heated specimens at room temperature are insufficient to

represent the essential characteristics of rocks at high temperature

in geothermal applications. The aim of this paper is to investigate

the mechanical behaviour of granite, which is a common rock type

in the Earths crust, at high temperatures (with continuous heat-ing) under unconfined stress conditions using both experimental

and numerical studies.

A review of the mostpertinent studies in theliterature regarding

the basic mineralogy of granite, brittleplastic transition of granite

and fracturing behaviour of rock is presented in the following sub-

sections,followedby the results and discussion of the experimental

work and numerical simulation undertaken for the present paper.

1.1. Basic mineralogy of granitic rocks

Granites are generally medium- to coarse-grainedigneous crys-

talline rocks that form by crystallization of certain slow-cooling

magma. The main minerals that form granite are quartz, plagio-

clase feldspars and alkali feldspar, and some amount of biotite,muscovite and/or hornblende (Farndon, 2010). Granite is rich in

elements with heat-producing radioactive isotopes (K, Th, U), and

is thus commonly associated with temperature anomalies and ele-

vated geothermal gradients within the crust. This feature makes it

a suitable geothermal reservoir rock. It also has extremely lowper-

meability and high strength, which also make it a good potential

storage site for nuclear waste.

1.2. Brittleplastic transition of granitic rocks

Brittle to plastic transition in response to increasing tempera-

ture has been studied for differenttypesof rocks. Theexperimental

results ofTullis and Yund (1987) demonstrated a transition from

dominantly micro-cracking to dominantly dislocation at approxi-mately 300400 C for quartz and 550650 C for feldspar. Hueckel

et al.(1994) reported thatthe confining pressure at brittle to plastic

transition is generally reduced by elevated temperatures. Accord-

ing to their study, when westerly granite is subjected to triaxial

conditions, the confining pressure at brittle to semi-brittle transi-

tion drops from 2000 MPaat360 C toabout 500 MPa at 800 C,and

the compressive strength also drops as the temperature increases,

with a dramatic drop at 668 C.

Xu et al. (2009) had used different temperatures ranging from

room temperature to 1200 C for their testing. The results showed

that the phase-changing behaviour of brittleplastic transition

appears around 800C andthe mechanical properties of the granite

samples did not significantly vary before that (Fig. 1). This transi-

tion temperature is higherthan that of westerly granite, whichwas

Fig. 1. Stressstrain curves of granite after high temperature (Xu et al., 2008a,b).

found to be 668 C by Hueckel et al. (1994). Therefore, it is clear

that the brittleplastic transition temperature can be significantly

different, even for the same type of rock. This is understandable,

considering the variation of rock mineral composition and micro-structuralproperties for the same rocktype obtainedfrom different

sources.

1.3. Fracture development behaviour in rock

1.3.1. Stages of fracture development

Based on the characteristics of the axial stressaxial strain and

axial stresslateral strain curves of uniaxial compression tests,

Hoek and Bieniawski (1965) found that the crack propagation pro-

cess of brittle materials consists of three main stages: (1) crack

closure followed by an elastic region; (2) crack initiation followed

by a stable crack propagation region; (3) crack damage followed

by unstable crack propagation until ultimate failure. In previous

studies, various methods such as stressstrain analysis, scanningelectron microscopy, photoelasticity, and acoustic emission have

been used to identify these crack development stages (Bieniawski,

1967; Eberhardt et al., 1998; Ranjith et al., 2008). When the mate-

rial is subjected to compressive loading, closure of pre-existing

micro-cracksthat are inclinedto the applied loadingdirection takes

place(Bieniawski,1967). Linear elastic deformationoccurs afterthe

majority of pre-existing cracks have closed. This marks the begin-

ning of the stable crack propagation region and the stress at the

transition stage is known as the crack initiation stress threshold

(ci). In the stable crack propagation region the material deforms

elastically. As the loading is further increased, unstable crack prop-

agation begins and the stress at the transition from stable crack

propagation to unstablecrack propagationis referredto as thecrack

damage stress threshold (cd) (Eberhardt et al., 1998).

1.3.2. Acoustic emission (AE) detection method to study

fracturing development

Acousticemission(AE) detection is a non-destructive evaluation

method to study the crack propagation of a brittle material sub-

jected to a stress field (Ranjithet al.,2008). Brittle materialsuddenly

releases strain energy whena crack develops,whichcreatesan elas-

tic stress wave travelling from the location of energy release to the

samples surface. AE is used to detect and measure the transient

wave that is generated from the discrete acoustic waves produced

by each micro-crack, which can produce event data to interpret

the crack propagation of the material. AE detection is able to mon-

itor micro-crack slip and formation relative to the stressstrain

response.


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98 S. Shao et al. / Geothermics 54 (2015) 96108

Fig. 2. Summationof countsvs. axial stressof single fractured rock (Ranjith et al., 2004).

A number of previous studies used the acoustic emission tech-

nique to study crack growth in brittle material (Shield, 1997;Eberhardt et al., 1998; Rudajev et al., 2000; Cai et al., 2007). Eber-

hardt used a combination of AE technology and stressstrain curve

measurement data in their experimental study (Eberhardt et al.,

1999). Chang and Lee (2004) studied the cracking and damage

mechanisms of Korean Hwang-deung granite and Yeo-san mar-

ble under triaxial compression using acoustic emissions. These

researchers have divided theprocess of crack development intofive

different stages: crack closure, crack initiation, secondary cracking,

crack coalescence and crack damage, which mirror the divisions

established by Hoek and Bieniawski (1965) based on stressstrain

behaviour. A similar type of division of stress threshold has been

carried out by Ranjith et al. (2008) in their experimental studies

on fractured rock under uniaxial compression. They used the char-

acteristics of the curve of cumulative AE count versus axial stressto define the stress thresholds for different fracture development

stages. The crack initiation stress threshold (ci) has been defined

as the point where the curve of cumulative AE counts marks the

initial lift-off (Fig. 2). The region, which sustains a linear increase

of cumulative AE counts with increasing stress, is termed stable

crack propagation. When the curve starts exhibiting an exponen-

tial growth, the corresponding stress is called the crack damage

stress threshold (cd) and the region between crack damage and

failure is defined as unstable crack growth.

2. Experimental work

2.1. Specimen preparation

The tested rock specimens were produced from one macro-

scopically homogeneous Strathbogie granite block. The Strathbogie

granite is a high-level, discordant, composite granitoid intrusion in

south-eastern Australia. It is fine-grained and white grey and dark

brown in colour with a tested porosity of 0.463%. It contains mag-

matic garnet, and cordierite and biotite predominate in the bothlith

(Neil Phillips et al., 1981). Grain size (which is measured from the

thin section of rock samples) ranges from 0 mm to 200m, witha few grains larger than 300mm (Fig. 3). An optical microscopy

image of Strathbogie granite is presentedin Fig.4. At room temper-

ature, Strathbogie granite showed a bulk density of 1805.7kg/m3,

peak compressive strength of 215.97MPa and elastic modulus of

8.97GPa.

Fig. 3. Grain size distributionof thetesting material.

Cylindrical core specimens 22.5mm in diameter were prepared

following the International Society for Rock Mechanics (ISRM)

recommendations for uniaxial compressive strength testing. Core

samples with visible cracks were discarded. Core specimens were

then cut to limit their length to 45 m m. The two ends of the

specimens were ground in order to produce two parallel surfaces

perpendicular to the long dimension of the cylindrical specimen.

Fig. 4. Scanning electron microscopy image of Strathbogie granite.


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2.2. Testing methodology

Unconfined compressive strength testing was carried out to

study the mechanical behaviour of dry granite samples under

elevated temperatures. Specimens were tested at nine differ-

ent temperatures (i.e. 23C, 100 C, 200 C, 400 C, 600 C, 800 C,

900 C, 1000C and 1100C).

Specimens were heated in a high-temperature furnace, using

a heating rate of 5 C/min to reach the appointed testing temper-

atures, with the exception of 23C at which the specimens were

testedat room temperature.This heating rate was adopted in order

to avoid provoking thermal shock and the development of stress

fractures. The temperature was kept constant for two hours in the

furnace after it reached the assigned temperature, to ensure uni-

formity in temperature across the specimen.

The testing procedure was divided into two stages due to

the limitations of laboratory facilities. Tests for the temperatures

from 23C to 600 C were carried out using a servo-controlled

Instron testing machine with a loading capacity of 100kN, and

the experimental temperatures were achieved inside an environ-

mental furnace with a square transparent window (Fig. 5a). The

specimens were loaded in compression with a constant displace-

ment rate of 0.1mm/min (we conducted testing only with this

strain rate and different strain rates may produce significantly dif-ferent behaviours). Mechanical behaviours related to axial load

and axial strains were measured in the process of axial compres-

sion until specimens failed after exposure to high temperatures.

In addition, AE data were recorded in the AE detection system

during all testing to analyze the fracturing behaviour of test speci-

mens subjected to elevated temperatures. These AE measurements

were obtained using the attached piezoelectric transducers which

transducers identify AE events when they receive a signal with

amplification.

Other tests (i.e. tests for the temperatures from 800 C to

1100 C) were carried out using a Universal testing machine with

a loading capacity of 500 kN and high temperatures were achieved

inside a cylindrical furnace (Fig. 5b). The specimens were loaded

in compression with a constant displacement rate of 0.1mm/min.During the entire deformation process the temperatures were

maintained constant at their designated levels for all specimens.

2.3. Results and discussion of mechanical testing

The results of the experimental work are discussed under four

sub-topics; (1) compressive strength, elastic modulus and strain

at failure, (2) failure mechanisms, (3) mineralogical analysis using

X-ray diffraction testingand (4)fracturingbehaviour using AE mon-

itoring.

2.3.1. Compressive strength, elastic modulus and strain at failure

The axial stress-axial strain plots of representative tests ateach temperature considered are given in Fig. 6. Table 1 summa-

rizes the important mechanical observations obtained from axial

stressaxial strain variations. According to Fig. 6, the stressstrain

curves of 23 C, 100 C, 200 C, 400 C, 600 C, 800 C, 900 C,

1000 C, 1100C show two different behaviours. The stressstrain

curves of 23C to 600 C display an initial elastic increase of stress

with increasing strain until peak strength is reached and then a

sudden drop of stress. On the other hand, the curves of tempera-

tures over 800 C display a more gradual decrease in stress after

peak strength with increasing strain at failure. The 1100C curve

presents a distinct difference from other curves, displaying a sig-

nificant strainincrease with a littleincrease in stress. This indicates

thatatorabove1100 C Strathbogie granite behaves as partial melt-

ing (granite melts at about 1200

C).

Table 1

Mechanical properties of Strathbogie granite at different test temperatures (aver-

aged results).

Temperature,C

Peak strength,

MPa

Elastic

modulus, GPa

Failure strain, %

23 215.98 8.98 2.70

100 190.64 8.28 2.60

200 234.02 8.48 3.15

400 203.67 7.95 2.95

600 119.56 5.78 2.55800 96.01 3.72 4.05

900 39.63 1.71 5.75

1000 37.07 1.34 5.75

1100 5.29 0.23 7.45

Variations of peak compressive strength, elastic modulus

and axial strain at failure (i.e. at peak compressive strength)

against the temperature are presented in Fig. 7(a)(c), respec-

tively. From Fig. 7(a) and (b) it can be seen that the peak

compressive strength and elastic modulus decrease with increas-

ing test temperature, with the exception of 200C. In addition,

salient drops of both peak strength and elastic modulus can

be observed when the temperature increases from 600 C to

800 C. Strains at failure do not show a noteworthy tem-perature dependence until the temperature reaches 600 C,

but increase dramatically with increasing test temperature from

800 C (Fig. 7(c)). Overall, from the plotted variations of three

mechanical properties (compressive strength, elastic modulus and

strain to failure) against test temperature, a clear transition stage

of the mechanical response can be identified when the temper-

ature increases from 600 C to 800 C for the tested granite. It is

believed that the brittleplastic transition for Strathbogie granite

(fine-grained) occurs within this temperature range (i.e. 600 and

800 C) under unconfined stress conditions.

The averagevalues of compressive strength, elastic modulus and

strain at failure were normalized to their respective values at room

temperature (i.e.23 C) for a bettercomparisonwithsimilar results

reported in the literature. The calculated average values and nor-malized values of compressive strength (c), elastic modulus (E)

and strain at failure () for different temperatures (T) are shown in

Table 2.

Normalized values of compressive strengthand elastic modulus,

observed in this study for Strathbogie granite, were plotted against

different temperatures, along with some results reported in the

literature for some other rock types (Figs. 8 and 9).

As a type of crystalline rock, granite displays significant variabil-

ity in characteristics, due to both its depositional history, such as

mineralogy, shape, size and size distribution,and post-depositional

experience, such as burial, thermal and fluid interaction history

and cementation. The results of compressive testing from Xu etal.

(2009) and Neil Phillips et al. (1981) present study show an ini-

tial strength weakening and softening pattern and subsequentstrengthening and stiffening (Fig. 8). This pattern continues up to

200 C inthis study,butin the study ofXu et al. (2009) it lasts up to

800 C. This may be due to the differences the mineral composition

and micro-structure of granite. In general, Strathbogie granite and

the UCS testing results ofBauer et al. (1981) and Xu et al. (2009)

show decreasing trends in both compressive strength and elastic

modulus with increasing temperature, which is more clearly visi-

blefor tests carried outat temperaturesabove 800 C (Figs.8and9).

The transition in mechanical character denoted by the more steep

negative deflection in the plots ofFig. 8 can be taken to mark a

transition in deformation mechanism withincreasingtemperature.

This deflection in the curves ofFig. 8 (the elasticplastic transi-

tion) occurs at approximately the same temperature for the various

granites tested. However, the strength developing patterns defined


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Fig. 5. Two testing devices used for experiments (a) servo-controlled Instron machine with a loading capacity of 100kN and environmental furnace; (b) universal testing

machine with loading capacity of 500kN and cylindrical furnace.

Fig. 6. Axial stressaxial strain of Strathbogie granite over a range of temperatures.

by the curves ofFig. 9 are distinctly different, which illustrates a

variation in the mechanical response of the various granites tested

by heating.

2.3.2. Failure mechanisms

Failure mechanisms of tested samples evident from visual

inspection of post-failure samples can provide important infor-

mation about the behaviour of the tested granite samples atdifferent temperatures. Different failure mechanisms include

inherent mechanical characteristics such as the amount of

energy released at the failure and microstructural changes during

deformation. Therefore, the understanding of failure mechanisms

of rock at different temperatures is very important for geothermal

applications, to enable practitioners to be aware of the expected

failure mechanism at different temperatures. Typical post-failure

images taken at the conclusion of each test are shown in Table 3.

The post-failure images show some distinct characteristics for

different temperatures. The failure patterns for test temperaturesfrom 23Cto800 C are approximatelydiagonal and the specimens

were brokendownto a numberof littlepieces showingmore brittle

Table 2

Average and normalized values of compressive strength, elastic modulus and strain at failure.

T(C) Average c (MPa) Normalized c Average E(GPa) Normalized E Average Normalized

23 215.97 1 8.97 1 0.027 1

100 190.63 0.883 8.28 0.923 0.026 0.966

200 234.02 1.084 8.48 0.945 0.032 1.172

400 203.66 0.943 7.94 0.885 0.030 1.103

600 119.56 0.554 5.77 0.644 0.026 0.952

800 96.01 0.445 3.72 0.415 0.040 1.500

900 38.53 0.178 1.71 0.190 0.058 2.142

1000 37.07 0.172 1.34 0.150 0.057 2.134

1100 5.29 0.024 0.23 0.026 0.075 2.775


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Fig. 7. (a) Peak strength of Strathbogie granite at different test temperatures; (b) elastic modulus of Strathbogie granite at different test temperatures; (c) failure strain at

peak load of Strathbogie granite at differenttest temperatures. Thedashed line indicatesthe melting point (600 C) of quartz, K-feldspar, Na-plagioclase and micas.

characteristics. For the specimenstested at 900C and 1000C, fail-

ure occurred along only a few failure planes and closely resembled

shear failure. Specimens tested at 1100C showed a very differ-

ent failure mode, in which the failure took place in a more ductile

manner. The overall trend of the failure mechanisms clearly showsthat increasing temperature influences the failure mechanisms of

Strathbogie granite in such a way that the ductile properties are

dominant at higher temperatures.

The micro-structural changes which occur with increasing

temperature in granite influence the variation of failure mecha-

nisms for different temperatures. Scanning electron microscopic

(SEM) images of granite thin sections are provided in Fig. 10, and

indicate that cracks developed and opened up with increasing

temperature. The mineral composition of rock influences its

strength significantly, since cracks are propagated by the weak-

est plane within the rock. The crack propagation of igneous rock

is determined not only by the micro-cracks through grain bound-

aries, but also the inter-granular cracks in some of the weakermineral constituents, such as feldspar and biotite grains (Brace

et al., 1972). It is known that at low temperature and low confining

pressure, the brittle fracture of polycrystalline rocks may corre-

spondto general axialsplitting by macroscopic cracks (pre-existing

joints and faults) extending in the direction of axial compression

(Hoek and Bieniawski, 1965; Mogi, 1966; Nemat-Nasser, 1985).

When the temperature increases, the crystal particles of rock frac-

tures form new microscopic cracks (pre-existing grain boundaries)

Fig. 8. Normalized compressive strength vs. test temperature curves forthe present study and previous studies.


7/13


Fig. 9. Normalized elastic modulus vs. test temperature curves forthe present study andprevious studies.

Fig. 10. SEMimagesof finegrained Strathbogie granite: (a) thin section at room temperature; (b)thin section heatedto 400C; (c) thin section heated to 800 C.

between mineral grains, as a result of differential thermal expan-

sion between grains with different thermo-elastic moduli and

thermal conductivities (Dmitriyev et al., 1972; Heard and Page,

1982; Kranz, 1983).

Micro-cracking patterns and the distribution of inter- and intra-

granular micro-cracks in granites have been studied previously

(Kudo et al., 1992; Nasseri et al., 2005) and after being affected by

hightemperature(Nasserietal.,2007). Mineralogy is known to play

an important role in granite thermal degradation. As David et al.

(2012) reported, thecrack density of La Peyrattegraniteis increased

from 0.2 at room temperature to 4.4 at 600

C temperature. They

further stated that differences of thermal expansion between dif-

ferent minerals cause crack nucleation, and the dramatic increase

of crack density of La Peyratte granite between 500 C and 600 C

is a result of transition of quartz, which occurs at 576 C. Evenwith a temperature increase below the transition threshold, the

high and anisotropic thermal expansion leads to the fact that with

thevariation of quartzcontenta differentdeterioration is expected

upon the same temperature changes. Especially in crystalline rock,

the amount of quartz has a significant effect on thermally induced

micro-cracks because of the complexity of its thermal expansiv-

ity. It is reasonable to state that when the temperature increases


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Table 3

Post-failure images of tested specimens.

Gf5 at23 C Gf7 at 100 C Gf8 at 200 C

Gf12 at 400 C Gf13 at 600 C Gf19 at 800 C

Gf23 at 900 C Gf20 at 1000 C Gf24 at 1100 C

to 600 C or higher, the influence of temperature becomes greater

on the mechanical behaviour of granite, due to the significant ther-

mal response at higher temperatures.In addition, a clear change

of colour of the Strathbogie granite specimens can be observed

with increasing temperature (Table 3). The approximate coloursobserved for different temperatures are shown in Table 4. In gen-

eral, Strathbogie granite specimens appear white and green with

dark brownat 23 C, and the colourturnsto whiteand reddish from

400 C and subsequently the colour deepens to pink at 1100C.

2.3.3. Analysis of fracturing behaviour using AE monitoring

As discussed in Section 1.3.2, the stress thresholds of vari-

ous crack propagation stages can be determined by monitoring

AE counts. Typical variations of cumulative AE counts against

the axial stress for samples tested for temperatures from 23C

to 600 C are shown in Figs. 1115 (we had difficulties in

operating the AE device subjected to very high temperatures

such that no AE data are available for temperatures beyond

600 C).

2.3.3.1. Crack initiation stress threshold (ci). The cumulative AE

counts in Figs. 1115, for temperatures between 23 C and 400 C,

are characterized by a sudden increase of AE activities followed by

a few AE events occurring with little strength change. The stress

threshold for crack initiation (ci) for these cases was identified as

the point where the AE event counts first increase above the back-

ground level of events (Figs. 1115). AE activities at 600C showed

Fig. 11. Cumulative AE eventsvs. axial stressat room temperature 23 C (Gf6).

Fig. 12. Cumulative AE eventsvs. axial stressat temperature 100C (Gf7).


Fig. 14. Cumulative AE events vs. axial stressat temperature 400C (Gf12).

a smooth increase of cumulative AE counts with increasing stress

after thebeginningof crack initiation. This trend is analogous to the

trend observed by Ranjith et al. (2004), which is shown in Fig. 2. At

600 C, the crack initiation stress threshold is marked at the point

where the curve initially lifts off (Ranjith et al., 2012).

Table 4

Different colours observed at different temperatures for the tested specimens.

T(C) 23 100 200 400 600 800 900 1000 1100

Colour White and grey White and grey White and g rey White and reddish White and reddish White and reddish Reddish Reddish Pink


9/13



Table 5

Stress thresholds for different fracturing stages.

T(C) ci, MPa ci2, MPa cd , MPa peak, MPa

23 200 202 203 214.467

100 135.8 140.8 165.5 181.989

200 209 214.7 217.8 228.074

200 232.4 235 238.7 239.975

400 190 194 197 203.198

400 169.5 182.8 190 204.128

600 31.6 96.8 117.321600 35.900 115.8 121.804

Table 6

Normalized values of crack initiation and crack damage fordifferent temperatures.

Temperature (C) 23 100 200 200 400 400 600 600

ci/peak 0.93 0.75 0.92 0.97 0.94 0.83 0.27 0.29

cd/peak 0.95 0.91 0.95 0.99 0.97 0.93 0.82 0.95

2.3.3.2. Secondary cracking stress threshold (ci2). Tests performed

for temperatures between room temperature and 400 C showed

some stages with sudden AE count rises after the crack initiation.

Previous studies have defined the secondary cracking as the point

when the cumulative AE counts curve starts to diverge followedby crack initiation, and the corresponding stress as ci. Secondary

cracking was readily apparent for temperatures below 400 C, but

results were not available for 600 C. From Figs. 1014, it is clear

that at the test temperature of 600 C, the stable crack propagation

region is much longer than that at other lower temperatures. This

could be an indication of the changes in mechanical response to

heating changes for Strathbogie granite.

2.3.3.3. Crack damage stress threshold (cd). For test temperatures

below400 C, cd wasidentified as thepoint whereAE counts begin

to show an exponential growth. At 600C, cdwas identified as the

point where the cumulative AE curve switches from linear increase

to an exponential growth. The unstable crack propagation starts

from cd and continues until the failure of specimens.Stress thresholds for different crack development stages iden-

tified from plots of cumulative AE counts against axial stress are

summarized in Table 5. Average values of crack initiation and crack

damage stressthresholds for differenttest temperatures are graph-

ically presented in Fig. 16.

As Fig. 16 depicts, crack initiation and damage occur at lower

levels of stress when temperature increases and the strength range

of stable crack propagation expands with increasing temperature.

Crack initiation stress and crack damage stress were then normal-

ized to the peak strength (Table 6), in order to understand the

proximity of crack development stages to the ultimate failure of

specimens for different temperatures. Fig. 17 revealsthat crack ini-

tiation normalized stress decreases with increasing temperature,

except for the case of 100

C. This reflects that the temperature

Fig. 16. Crack initiation and crack damage stressthresholds and peak compressive

strength for different temperatures.

Fig. 17. Normalized stress for crack initiation and crack damage at different tem-

peratures.

influencesthe crack initiation stress thresholds of Strathbogie gran-

ite and increasing temperature allows crack initiation to happen

earlier. The early occurrence of crack initiation as temperature is

increasedindicates the domination of ductile properties at elevated

temperature. This correlation is consistent with the prevalence of

ductile failure at higher temperatures (Table 3).

However, the normalized stress values for crack damage do not

showany important scatter withincreasingtemperaturefor Strath-

bogie granite, suggesting that crack damage occurs very close to

failure during uniaxial loading, but independent of the tempera-

ture.

3. Finite element modelling

Conducting a rigorous laboratory testing programme is usu-

ally time-consuming, labour-intensive and expensive. Validating a

numerical model using few experimental results and then extend-

ing the models for many other scenarios is a far more efficient

approach, and the availability of sophisticated and user-friendly

software packages has made this task much easier. This approach

is extremely useful, since results can be obtained even under

test conditions that the experimental approach fails to simulate.

In addition, some critical insights, such as stress/strain distribu-

tion within model specimens, such as the distribution of plastic

strain, can be comprehensively obtained from numerical simula-

tions. Therefore, the experimental results of this study were first

used to validate a finite element numerical model and then some


10/13


Fig. 18. Geometry of model specimen (a) specimen and the platens of the test-

ing apparatus (the shaded area is the portion of the specimen that was modelled

by ABAQUS) and (b) the two-dimensional axis-symmetric model of the uniaxial

compression test.

results were obtained from models under temperatures other than

the temperatures used in the experimental work.

3.1. Model geometry and material properties

A finite element model of the compression tests carried out on

Strathbogie granite specimens at elevated temperature was per-

formed using ABAQUS 6.7.1. A two-dimensional (axis-symmetric)

model of the compression test was set up in two parts. As Fig. 18(a)shows,onlya quarter of thespecimen andhalfof the topplaten was

modelled. The geometry of the model and boundary conditions are

shown in Fig. 20(b).

Temperature-dependent constitutive equations for Strathbogie

granite based on compressive tests performed over a range of tem-

peratures were used in this finite element model. The stressstrain

behaviour under unconfined uniaxial compression was found to be

strongly dependent on temperature and the brittleplastic transi-

tion was found to take place between 600 C and 800 C.

The temperature-dependent mechanical properties assigned to

Strathbogie granite are shown in Table 7 and they were incorpo-

rated into the finite element model via an in-built interpolation

routine. For the temperature range of 25C to 600 C, the material

properties were assumed to be elastic up to the failure strain. For

Table 7

Temperature-dependent mechanical properties of Strathbogie granite.

T(C) c (MPa) E(GPa)

23 215.97 0.027 8.97

100 190.63 0.026 8.28

200 234.02 0.032 8.48

400 203.66 0.030 7.94

600 119.56 0.026 5.77

800 96.01 0.040 3.72

900 38.53 0.058 1.711000 37.07 0.057 1.34

1100 5.29 0.075 0.23

Table 8

Temperature-dependent plastic propertiesof Strathbogie granite.

T(C) Yield s tress ( MPa) Ultimate y ield s tress ( MPa) Plastic s train

800 82.51 0

800 101.76 0.0125

900 26 0

900 38 0.0149

1000 25 0

1000 31 0.0140

1100 7.11 0

1100 7.65 0.0100

temperatures above 800C, an elasticplastic model was assumed.

The temperature-dependent plastic properties (first yield stress

andultimate yield stress of the material), assigned for thematerial,

are shown in Table 8.

To perform the finite element modelling, several assumptions

were made as follows:

(1) Uniform temperature across the entire granite was predefined

before the start of each analysis.

(2) The platen was assumed to be steel with elastic modulus of

210 GPa and Poissons ratio of 0.3 and the Poissons ratio of the

Strathbogie granite was assumed to be 0.25.

(3) The interaction between the platen (master) and granite

(slave) assumes a friction coefficient of 0.1. Vertically down-ward displacements were applied to the bottom surface of the

platen and enabled the granite to be loaded in compression.

3.2. Results and discussion of simulation

The results of the numerical simulation for different temper-

atures along, with the corresponding experimental results are

shown in Fig. 19. Numerical simulation was not performed for

1100 C temperature as thematerial behaved similar tomolten lava

in the experimental study for that temperature. The experimen-

tal stressstrain results obtained from compression tests appear

to show two sections of linear elastic behaviour through all tested

temperatures: (1)from 23 to 600C, witha low modulus at the ini-

tial stage of loading up to a strain of about 0.0025, followed by arelatively higher linear modulus up to the failure strain; (2) from

800 to 1000C, with a low modulus at the initial stage of loading

up to a strain of 0.010.015 followed by a relatively higher linear

modulus up to the failure strain. The constitutive equation is based

on the temperature-dependent modulus after a small correction

is applied to the initial strain, which allows the model to predict

the axial stress up to the failure strain of the specimen with an

acceptable measure of success.

The FEM model is able to reproduce the results of the experi-

ments for test temperatures below 600 C (elastic behaviour), and

for the test temperatures of 800, 900 and 1000 C (plastic and

ductile behaviour), as shown in Fig. 19. After validation and cal-

ibration of the finite element model, it can be used to predict

the stressstrain response of Strathbogie granite under unconfined


11/13


Fig. 19. Experimental results vs. values predictedby FEM (red squares) fordifferent test temperatures.

stress conditions at anygiven temperature between 23 and1000 C.

For example, although compression tests were not performed at

temperatures of 500 and 700 C, the stressstrain response can be

predicted using the model. The FEM results for these two tempera-

tures are shown in Fig. 20(a) and (b), respectively. For comparison

with the predictions of finite element modelling, experimentally

observed curves for 400 and 600 C and 600 and 800 C test

temperatures are shown in Fig. 20(a) and (b), respectively. The

results show that the finite element model has excellent capability

for predicting the behaviour of temperature-dependent materials.

The evolution of plastic strains with increasing compression

can be visualized in finite element models. These plastic strain

distributions dictate the failure mechanisms for different test tem-

peratures.The distributionof plastic strain in thespecimenthat was


12/13


Fig. 20. Predictedcompressive strength of Strathbogie granite using FEM(red squares) for(a) 500C and (b) 700 C.

Fig. 21. The distributionof plastic strain in thespecimendeformedat 800C (a) strain= 0.0251, (b) strain= 0.0343 and (c)strain =0.0457.

deformed at 800 C at the onset of plastic strain, partway through

the plastic deformation and just before final failure, is shown in

Fig. 21. Plastic strain initially develops at the corner and gradually

extends through the specimen at an inclined angle of about 45C

before failing roughly at that angle. Experiments also confirm that

failure of compressed cylindrical Strathbogie granite specimens

occurs in this fashion.

4. Conclusions

A series of unconfined compressive strength tests was car-

ried out on Strathbogie granite (fine grain) specimens at various

temperatures between 23 C and 1100C. Specimens were heated

at a rate of 5

C/min and deformed at a displacement rate of0.1mm/min. A finite element model for predicting the thermo-

mechanical behaviour of Strathbogie granite was analyzed using

ABAQUS 6.7.1 to cover the range of test temperatures. Both

experimental and numerical investigations revealed significant

behaviours of granite at higher temperatures as follows.

(1) When the testing temperature was increased from room tem-

perature to 200 C, both compressive strength and elastic

modulus were found to increase. Further increase of temper-

ature caused a decrease in compressive strength and elastic

modulus. Above 800 C, the stressstrain curves showed a sig-

nificant increase in strain with very little change in stress,

and the compressive strength decreases dramatically at tem-

peratures greater than 800

C. The brittleplastic transition

temperature of thistype of granite under unconfined conditions

was found to be between 600 and 800 C.

(2) Analysis of the changes of stress thresholds for vari-

ous crack propagation stages at different temperatures

using acoustic emission monitoring showed a consider-

able dependence on the testing temperature. Increasing

temperature reduced the stress thresholds for crack ini-

tiation and crack damage and extended the stable crack

propagation stage. In addition, the increasing temperature

was observed to produce crack initiation earlier, indicat-

ing that ductile/quasi-brittle properties dominate at higher

temperatures.

(3) Finite element modelling showed stressstrain behaviours

that reproduced the experimentally observed stressstrain

variations. Numerical modelling work was extended tostudy the mechanical behaviour of Strathbogie granite under

temperatures other than those considered in the experimen-

tal work. Moreover, the plastic strain distributions within

numerical specimens were compared with the observed fail-

ure patterns of the experiments and close similarity was

observed.

This paper reports an initial study of the behaviour of Strath-

bogie granite under unconfined stress conditions and elevated

temperatures. The results of more detailed investigations under

very high confining pressures and very high temperatures (using

the experiments that the authors are currently conducting) will be

published later.


13/13


Acknowledgement

The authors acknowledge the use of facilitieswithin the Monash

Centre for Electron Microscopy.

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