Assessment of rock mechanical properties depends on sample size and testing methodologies. Even for samples cored from the same rock outcrop the difference in properties appears to be sensitive to the local thermal and stress histories of the rock structure. Variations in the fracture toughness, unconfined compressive strength and tensile strength of a suite of granite samples, when tested using different procedures, are discussed in terms of experimental errors of the loading system as well as the thermal history

Alehossein, Habib

Boland, J. N.

University of Queensland eSpace

SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
   
Strength, toughness, damage and fatigue of rock 
Habib Alehossein and J N Boland 
CSIRO Exploration and Mining, P O Box 883, Kenmore, Queensland, Australia 4069 
 
 
 
ABSTRACT: Assessment of rock mechanical properties depends on sample size and testing methodologies. 
Even for samples cored from the same rock outcrop the difference in properties appears to be sensitive to the 
local thermal and stress histories of the rock structure. Variations in the fracture toughness, unconfined 
compressive strength and tensile strength of a suite of granite samples, when tested using different 
procedures, are discussed in terms of experimental errors of the loading system as well as the thermal 
history.  
1 INTRODUCTION 
Intact rock samples generally exhibit a size effect in that the strength decreases with increasing 
sample size [Goodman, 1989]. The effects of sample size on the measurement of rock properties 
can generally be attributed to the microcrack density and distribution [Walsh, 1965; Wong, 1985] 
both of which will depend on the thermal and stress histories of the rock [Engelder 1987]. Further it 
has also been observed that rock strength is dependent on the type of test or test methodology. 
Examples showing this latter effect are: (1) tensile strengths as measured using the Brazilian (BTS) 
and direct tensile (DTS) strength tests and (2) the fracture toughness using the three point bend 
(TPBFT) and the short rod (SRFT) methodologies [Ouchterlony, 1988; Bazant et al, 1993]. This 
paper presents the results of a study of testing methods and thermal history on the mechanical 
properties of an Australian granite. 
2 ROCK AS A COMPLEX MATERIAL 
Rocks have deformation-stress memory. Unlike metals, the fatigue life cycle of a rock is 
comparatively very short, particularly at loads near peak strength [Costin, 1987, Alehossein & 
Boland, 1995]. This is because of the high stress concentration at the tips of micro fractures and 
flaws that are generated by processes such as thermal fluctuations or external loading conditions 
[Korinets & Alehossein, 2002] during the geological development of the rock. Such stress 
concentration effects contribute to crack growth from randomly oriented microcracks inducing 
further damage and reducing the rock strength.  
Substantial discrepancies are observed in the load-displacement curves of apparently identical 
rock samples taken from a specific geological location. Even though the source material may be 
characterised as intact rock having uniform geology, geochemistry and mineralogy, various parts of 
rock outcrop experience different thermal and stress histories and hence different crack size 
distributions.  
Brittleness factor, Kp, is defined as the ratio of the uniaxial compressive strength and the uniaxial 
tensile strength [Iyengar & Raviraj, 2001] for a strain-based definition of a brittleness factor. We 
observe that unlike metals where Kp ≈1 the brittleness factor for rocks is much greater than unity.  
In compressive loading, this difference is partially due to the large frictional shear stress needed to 
propagate the lateral wing cracks as well as the complex nature of crack interaction and coalescence 
[Horii & Nasser, 1985; Wong & Chau, 1998]. In tensile loading, only a limited number of critical 
cracks are required to induce failure – refer Figure 1. 
 
 
 
 
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Figure 1. Crack growth under (a) tensile and (b) compressive loading. 
Crack extension processes that are reflected in a non-unity brittleness factor account for the 
increasing strength of rock with confining pressure. For a rock sample with UCS/BTS = 20, the 
rock shear strength can increase by several times the original unconfined shear strength at a 
confining stress of half of the rock UCS depending on whether the material behaves according to 
the Mohr-Coulomb (MC) or Hoek and Brown (HB) failure models [Brady & Brown, 1993] . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2. Direct tensile (left) and indirect Brazilian tensile (right) strength tests. 
 
There are errors associated with the testing of rock samples. Tensile strength of a given rock 
sample (σt) should be independent of the method of testing. Theoretically it might be expected that 
the tensile strengths from a direct test (σDTS) and from a Brazilian test (σBTS) are both equal. In fact 
this is not generally the case because of the several uncontrolled experimental factors that are 
involved.  Consider one factor for example the eccentricity error (e = e1 + e2) that can arise in these 
two tests - Figure 2.  It is easy to show that the measured strength is different from the authenticated 
strength (σt). In other words:  
 
T 
T 
e2 
e1 P 
P 
e2 
e1 
Direct 
Tensile 
Strength 
(DTS) 
Test 
Brazilian 
Tensile 
Strength 
(BTS) 
Test 
(a) Tensile (b) Compressive 
σt 
σt σc 
σc 
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DTS
DTS
t
DTS
D
eBA +
= σσ
     (1) 
2
1 ⎟⎟⎠
⎞
⎜⎜⎝
⎛−=
BTS
BTS
tBTS D
ebaσσ     (2) 
By elimination of σt from Equations (1) and (2) we have 
2
1 ⎟⎟⎠
⎞
⎜⎜⎝
⎛−⎟⎟⎠
⎞
⎜⎜⎝
⎛ +=
BTS
BTS
DTS
DTS
DTSBTS D
eb
D
eBAa σσ    (3) 
A, B, a and b are constants best obtained experimentally, although their theoretical values in ideal 
experiments are given by a = A = 1, b = 4 and B = 8; D is the sample diameter.   A Brazilian disc 
may not fail in pure tensile mode causing σBTS > σt, even in the absence of any eccentricity effects, 
i.e.  e = 0.  In this case a is greater than 1 because of the partial contribution of the shear strength of 
the rock, which is normally greater than rock tensile strength.   
3 EXPERIMENTS 
3.1 Compressive Strength (UCS) 
Five samples with a length to diameter ratio of 2.5:1 were prepared according to the suggested 
ISRM method [Brown, 1981]. The results of these mechanical UCS tests (Figure 3) are shown in 
Table 1. 
 
Table 1.  UCS tests results  
Parameter D (mm) H (mm) Moisture % ρ 
(gr/cc) 
ν 
Poisson's 
ratio 
E 
GPa 
σUCS 
MPa 
Minimum 57.86 144.21 0.003 2.64 0.19 77.5 212.5 
Maximum 57.96 145.40 0.003 2.65 0.26 80.8 254.4 
Average 57.94 144.76 0.003 2.65 0.22 79.6 238.6 
Standard 
Deviation 
0.04 0.47 0.0001 0.00 0.03 1.3 15.8 
 
Figure 3.  A UCS sample before (left) and after (right) the test 
3.2 Tensile Strength  
Direct Tensile Strength 
A tension test machine, in which loading is controlled by a stress-feedback method [Okubo & 
Fukui, 1996; Alehossein et al, 2003] was used to conduct the tests for direct tensile strength on 
cored and heat treated samples (DTS and DTST respectively). Figures 4a and 4b display the stress-
strain curves obtained from these two sets of tests.  
    
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Figure 4. Stress-strain behaviour of unheated and heated samples in tensile tests. 
 
The results of the ten samples tested for the direct tensile strength tests (Figure 5) are summarised in 
Tables 2 and 3.   
 
Table 2. Direct tensile strength tests results under non thermal condition (DTS) 
Parameter Minimum Maximum Average Standard 
Deviation 
σt = Tensile strength (MPa)  10.77 11.97 11.11 0.62 
E = Secant (0 ⇒ 0.5σt) Young’s 
modulus (GPa) 
64.8 70.1 67 2.34 
ν = Poisson’s ratio 0.187 0.208 0.199 0.01 
 
Table 3. Direct tensile strength tests results under thermal condition (DTST) 
Parameter Minimum Maximum Average Standard 
Deviation 
σt = Tensile strength (MPa)  5.28 6.79 6.10 0.54 
E = Secant (0 ⇒ 0.5σt) Young’s 
modulus (GPa) 
29.4 37 32 3.26 
ν = Poisson’s ratio 0.031 0.053 0.042 0.008 
 
A comparison of these two tables reveals the effects of the thermal cycle 25°C⇒300°C⇒25°C. The 
percentage strength loss is about 45%. Stiffness loss is 52% and the Poisson’s ratio reduction 79%. 
 
Figure 5. DTS samples            Figure 6. Two BTS  samples 
Brazilian Tensile Strength (BTS) 
Discs of 1:2 length to diameter ratios were cut from the cores for the Brazilian tensile tests 
(Figure 6). There was only slight deviation of the cracks from their symmetrical crack planes for 
(a) Un-heated (DTS ) 
(b) Heated (DTST) 
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any of the five samples tested. Results of these tests are summarized in Table 4 and compared with 
the DTS results in Table 2.   
 
Table 4.  BTS tests results 
Parameter D (mm) H (mm) σBTS 
MPa 
σDTS 
MPa 
Minimum 57.95 28.57 10.75 10.77 
Maximum 57.98 29.36 14.83 11.97 
Average 57.97 28.96 13.46 11.11 
Standard Deviation 0.01 0.30 1.57 0.62 
Figure 7.  Load-COD behaviour for TPBFTT (heated) samples 
3.3 Fracture Toughness 
Three Point Bending Fracture Toughness (TPBFT) 
Granite cores were prepared for three point bending tests according to the ISRM suggested 
methods. Two thermal conditions were used: (i) thermally unconditioned (25°C) and (ii) thermally 
conditioned (25°C⇒300°C⇒25°C) (TPBFT & TPBFTT respectively).  Only four out of the ten 
samples were appropriate for testing.  In these limited number of samples, the average specimen 
diameter, D = 58mm, length, H = 200mm and the average chevron tip distance from the specimen, 
a0 = 8.7mm. Loading was controlled by COD velocity constant and for each test load (P), COD and 
LVDT were monitored and measured during the test. Results of the fracture toughness calculations 
are summarised in Table 5 and shown in Figure 7. A major finding of these tests is that even a 
single heat cycle can reduce fracture toughness by about 15%.   
 
Table 5.  Three point bending fracture toughness tests 
Three-Point-Bending Fracture 
Toughness 
Minimum 
(MPam½) 
Maximum 
(MPam½) 
Average 
(MPam½) 
TPBFT 2.2 2.4 2.3 
TPBFTT 1.9 2.1 2.0 
Short Rod Fracture Toughness (SRFT) 
Nine SRFT test samples were prepared (D ≈ 58mm, length 1.45D). Each sample had a notch of 
width t ≈ 2.2mm cut parallel to the core axis with subtended chevron angle, θ = 560. Two semi-circle 
steel slices were bonded to the top of each sample using a two-part epoxy adhesive. A V-shaped notch 
with an angle of 420 was formed in the middle of the slices. The tensile load was applied by a steel 
0
500
1000
1500
2000
2500
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
COD[mm]
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wedge (angle 46o) inducing catastrophic crack growth in the ligament of the notched section during 
the test [Zhang et al., 1999] – see Figure 8. Four specimens were tested using a standard direct tensile 
or “pull apart” method. The tests were performed under displacement control with a loading rate of 
0.01 mm s-1. The results are summarised in Table 6.  
Table 6.  SRFT tests results 
Sample 
No 
Loading 
type 
D (mm) H 
(mm) 
RL 
(mm) 
RR 
(mm) 
a1 
(mm) 
KIC 
(MPam½) 
1  Wedge 57.95 85.51 27.16 28.3 54 2.75 
2 Wedge 57.91 85.07 28.28 27.24 54.72 2.25 
3 Pull-Out 57.96 84.31 27.3 28.42 54.66 2.31 
4 Pull-Out 57.95 84.45 28 27.98 54.94 2.67 
5 Wedge 57.96 85.24 28 27.98 55.54 2.71 
6 Wedge 57.93 85.22 28.34 27.26 55.24 2.14 
7 Wedge 57.92 84.87 28.1 27.68 54.78 2.10 
8 Pull-Out 57.96 84.56 27.42 28.54 54.42 2.49 
9 Pull-Out 57.94 84.73 28.08 27.66 54.64 2.60 
Minimum  57.91 84.31 27.16 27.24 54.00 2.10 
Maximum  57.96 85.51 28.34 28.54 55.54 2.75 
Average  57.94 84.88 27.85 27.90 54.77 2.45 
Standard Dev.  0.02 0.41 0.44 0.47 0.45 0.25 
 
 
 
Figure 8.  SRFT two test samples after the test;  left (wedge), right (pull-apart ) 
4 DISCUSSION 
Results of the direct tensile strength tests indicate that there was a 45% reduction in the strength of 
the rock resulting from one thermal cycle. The stiffness was reduced by 52% and Poisson’s ratio by 
79%. In contrast, the effect of the thermal cycling on the fracture toughness was significantly less – 
only 15%. The most likely explanation of such differences in the deformation of the granite samples 
is the marked differences in the microcrack lengths and densities (and their distributions) between 
the heated and unheated samples. Furthermore, tensile loading would activate the whole spectrum 
of microcracks throughout the sample while in 3-point bend testing for fracture toughness only 
those defects located in the vicinity of the notch would influence the response of the material. 
For unheated samples, Young’s modulus and Poisson’s ratio in tensile loading are both slightly 
less than those obtained during compressive loading. The average compressive strength of this rock 
was 238.6 MPa. Assuming a UCS/BTS of 20, the tensile strength is estimated at 12MPa. This value 
is between that measured by the Brazilian and the direct tensile methods – i.e. 13.46 and 11.11 MPa 
respectively.  
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Two different values of mode I fracture toughness have been obtained. The three point bending 
method gave a fracture toughness of 2.30 MPa m½, while the short rod method 2.45 MPa m½. The 
standard deviation from the two different testing methods was in the same range as the standard 
deviation from samples tested by one single method. Hence, on the basis of the limited sample 
numbers, it has not been possible to assess any intrinsic differences between these two testing 
methods.  
ACKNOWLEDGEMENTS 
In preparation of this paper we would like to thank and acknowledge contributions of our Japanese 
colleagues, Dr Tsutomu Yamaguchi, Dr Y. Oikawa, Dr M. Utagawa from AIST and our colleague 
at CSIRO, Mr Michael Cunnington. 
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Strength, Toughness, Damage And Fatigue Of Rock

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