Correlation Between Unconfined
Compressive Strength and Indirect
Tensile Strength of Limestone Rock
Samples
Ramli Nazir
Associate Professor (Ir. Dr), Faculty of Civil Engineering, Department of
Geotechnics and Transportation, Universiti Teknologi Malaysia
Ehsan Momeni
PhD student in Geotechnical Engineering, Faculty of Civil Engineering,
Department of Geotechnics and Transportation, Universiti Teknologi
Malaysia; mehsan23@live.utm.my
Danial Jahed Armaghani
PhD student in Geotechnical Engineering, Faculty of Civil Engineering,
Department of Geotechnics and Transportation, Universiti Teknologi
Malaysia; danialarmaghani@yahoo.com
Mohd For Mohd Amin
Associate Professor, Faculty of Civil Engineering, Universiti Teknologi
Malaysia
ABSTRACT
In Geotechnical Engineering, determining the Unconfined Compressive Strength (UCS) of
rock is of prime importance as its role in design and analysis of geotechnical problems is
crucial. Although laboratory test is the most direct way for estimating the rock compressive
strength but UCS determination in the laboratory would be problematic if the rock masses are
weathered mainly because obtaining proper core segments for testing purpose is difficult in
this situation. Hence, the use of index testing as an alternative for predicting UCS is
investigated by researchers. It is well established that indirect tensile strength or Brazilian
Tensile Strength (BTS) is related to UCS. In this paper, in order to develop a new correlation
between UCS and BTS, some laboratory tests on dry limestone specimens including 20
Unconfined Compression Tests (UCT) and 20 Brazilian Tests (BT) have been conducted. The
paper also reviews some recent correlations between UCS and BTS as well as investigates the
reliability of these correlations. Findings show the results of the experimental tests are in good
agreement with previous studies. Based on the results, new strong correlation with coefficient
of determination of 0.9 is introduced for predicting the UCS of limestone core samples from
its BTS. A critical review on the degree of accuracy of recent correlations between UCS and
BTS shows that apart from Kahraman`s correlation, other correlations either overestimate or
under estimate UCS of rock samples to a significant amount.
KEYWORDS:
Brazilian Test, Indirect Tensile Strength, Limestone, Unconfined
Compressive Strength.
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Vol. 18 [2013], Bund. I
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INTRODUCTION
Unconfined Compressive Strength (UCS) of rock is considered as an essential parameter in
analysis of geotechnical problems such as rock blasting and tunneling. Although laboratory test is
the most reliable and direct method for estimating UCS, direct determination of UCS in
laboratory is time-consuming and expensive. In addition, in direct method of UCS determination,
having sufficient number of high quality rock samples is a prerequisite. However, it is not always
possible to extract proper cores for sampling purpose in highly weathered rocks (Romana, 1999;
Kahraman, 2001; Ceryan et al. 2012).Therefore, the use of various correlations for UCS
prediction has been highlighted in the literatures. These correlations often relate other rock index
parameters such as point load index, rebound number of Schmidt hammer, and indirect tensile
strength of the rock to UCS (Cargill and Shakoor, 1999; Sharma and Singh, 2008; Nazir et al.
2013). Implementing such correlations is of interest, mainly due to the fact that rock index tests
have the advantages of being relatively fast and economical.
Brazilian Test (BT) is used for indirect determination of tensile strength of rock samples. It is
established that Brazilian tensile strength is related to UCS. Oneof the most agreed correlation
between UCS and indirect tensile strength or Brazilian Tensile Strength (BTS) of the rock is
highlighted in the study by Sheorey (1997). According to his study, the compressive strength of
the rock is approximately 10 times its tensile strength. Nevertheless, Sheorey`s strength ratio
variation is high (Cai, 2006) and consequently cannot be generalized due to the fact that rock
behavior varies from place to place and is site specific. This paper proposes a new correlation
between UCS and BTS of specific type of rock i.e limestone as the relationship between
compressive and tensile strength of rock depends on rock type (Brook, 1993).
PREVIOUS STUDIES
Many studies have been conducted to show that UCS is related to other physical properties of
the rock samples (Sheorey et al. 1984; Shakoor and Bonelli, 1991; Ulusayet al. 1994; Romana,
1999; Tugrul and Zarif, 1999; Sachpazis, 1999; Katza et al. 2000; Kahraman, 2001;Yasar and
Erdogan, 2004; Chang et al. 2006; Guney et al. 2005; Tiryaki, 2006; Vasconcelos, 2008; Sharma
and Sing, 2008; Kilic and Teymen, 2008; Moradian and Behnia, 2009; Diamantiset al. 2009;
Ceryanet al. 2012; Kohno and Maeda, 2012; Nazir et al. 2013; Khandelwal, 2013).
Kahraman et al. (2012) conducted a research on compressive and tensile strength of different
type of rocks. Based on their results, they proposed a linear correlation between UCS and BT.
However, the coefficient of determination, R2, of their study was almost 0.5 which is not reliable
enough. Farah (2011) conducted a comprehensive study to obtain some correlations between
UCS and other physical properties of weathered Ocala limestone. According to his study, indirect
tensile strength i.e BTS has a better correlation with UCS than that of point load strength. In order
to discover correlations between UCS and other physical properties of the rock samples, Altindag
and Guney (2010) conducted a research for a wide range of strength values i.e UCS (5.7 - 464
MPa), BTS (0.5 - 30.5 MPa). They found a strong correlation between UCS and BTS of the
different rock types.Tungal and Zarif (2000) conducted another study on engineering properties
of limestone in Istanbul, Turkey.Their results show that there is a linear correlation between UCS
and BT. The positive linear relationship between UCS and indirect tensile strength is also
confirmed in the study by Gupta and Rao (1998). Din and Rafigh (1997) investigated the
relationship between UCS and BTS of two different types of limestone in Pakistan. According to
their findings, the UCS to BTS ratio is almost 7.5. However, Vutukuri et al. (1974) suggested that
strength ratio of most rocks varies from 10 to 50.
Vol. 18 [2013], Bund. I
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Table 1: Recent correlations between UCS and BTS
References
Correlation
R or R2
Rock Type
Kahraman et al.(2012)
UCS (
R2 = 0.5
Different rock types including limestone
Farah (2011)
UCS (
Altindag and Guney (2010)
UCS (MPa)= 12.38 * BTS1.0725
)
)
= 10.61 ∗ BTS
= 5.11 ∗ BTS − 133.86
R2 = 0.68
Weathered limestone
R = 0.89
Different rock types including limestone
LABORATORY ROCK STRENGTH TESTS
Rock strength test is to verify resistance of rock against loading. The strength test can be
direct or indirect where the term direct or indirect implies mode of loading under which rock
sample is subjected to. Since strength test involves destruction of sample, property being assessed
is direct indication on strength and it can be considered as afundamental data for detailed design.
Strength tests carried out in this study are: (1) Unconfined Compression Test (Direct strength
test), and (2) Indirect tensile strength test (Brazilian test).
Unconfined Uniaxial Compression Test
Uniaxial Compression Test, also termed as UCT, is used for estimating the compressive
strength of rock specimens under uniaxial loading. The compressive strength of rock sample is
obtained through loading rock specimens under either load-controlled condition or straincontrolled condition. The latter represents loading conditions more precisely in the field and
causes complete stress-strain curve (Figure 1) of sample to be obtained. Depending on monitored
parameters during test, several basic engineering properties of rock can be determined from this
test. Basically, UCT is used to determine ultimate uniaxial compressive strength (UCS). In fact,
UCS is the peak value in curve and the corresponding axial strain, a, where peak stress
occurs is termed as strain at failure (f %). Stillborg (1986) listed typical values for compressive
strength (UCS) for various rocks. According to his suggestion, UCS of limestone rocks ranges
from 50 MPa to 200 MPa. Nevertheless, if UCT is conducted with measurement on axial strain
(a) and horizontal strain (r) through installing a pair of strain gauges, besides UCS, several
important parameters pertaining to rock deformation such as strain at failure (f), Young’s
modulus (E) and Poisson’s ratio (), can be obtained (See Figure 1).
a
120
c = 104
MPa
80
Slope =
c/2
40
Slope = Et, Eav
-0.2
-0.1
r (%)
0
0.1
0.2
0.3
a (%)
Figure 1: Schematic figure of stress-strain curve
Vol. 18 [2013], Bund. I
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Indirect Tensile Strength
Tensile strength test is to verify tensile strength of rock samples or its resistance against
fracturing. Direct tensile test on rock sample is relatively difficult to undertake and Brazilian test
offers an indirect method to measure tensile strength. The term ‘indirect tensile’ implies that load
is applied under compression.
Figure 2 shows typical mode of failure associated with tensile stress. Typical values for
Brazilian tests or indirect tensile strength for various rocksare listed in the study by Stillborg
(1986). According to his work,BTS of limestone ranges from 5 MPa to 20MPa.
Figure 2: Mode of failure of rock samples in Brazilian test
TEST PROCEDURE
40 laboratory strength tests on dry limestone core samples including 20 unconfined
compression tests and 20 Brazilian Tensile Strength (BTS) tests were conducted in Geotechnical
Laboratory of University Teknologi Malaysia according to the procedure suggested by
International Society of Rock Mechanic (ISRM, 1981). More illustration regarding tests
procedures are given in the following paragraphs.
Uniaxial compression test
The uniaxial compression tests were conducted on Tinius Olsen (USA) Universal Testing
Machine (UTM). This machine with 3000 kN capacity can apply compressive load at constant
strain rate on the specimen. In this study, all compression tests were conducted at strain rate
equals to 0.5mm/mm/s. TML 500 kN load cell (see Figure 3) and a pair of strain gauges were
used to measure applied load and deformation during the test. In order to record data, both load
cell and strain gauges were wired to a data logging system. The stress-strain data was
continuously logged into a computer and the stress at failure was considered as the UCS of
limestone specimens.
Vol. 18 [2013], Bund. I
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Figure 3: 500 kN TML load cell and installed strain gauges
Brazilian Test
Th test was conducted using Brazilian test apparatus (MATEST of Italy) which is equipped
with digital display unit for displaying maximum load (see Figure. 4). Sample is placed on
specially fabricated steel cradle (Figure 5), and then mounted in between the loading platens. This
cradle ensures load acts tangentially on the disc-shaped sample and consequently induces tensile
fracture along its vertical diameter. Sample thickness (t) and diameter (D) were recorded, and
load was applied until sample fails under maximum compressive load (in kN). Having the sample
dimension and maximum tensile load at failure (F), the Brazilian Tensile Strength (BTS) is
obtained by using the following equation given by Gokhale (1960).
=
Figure 4: Brazilian test apparatus
2
Figure 5: Cradle for disc sample
Vol. 18 [2013], Bund. I
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Result and Discussion
The unconfined compression and Brazilian tests results are tabulated in Table 2. Previous
literatures show that results are in acceptable ranges. (Stillborg ,1986; Matsui and Shimada, 1993;
Reddish and Yassar, 1996; Din and Rafiq, 1997; Farah, 2011; Kahraman, 2012). As shown in the
Table 2, the UCS of limestone core samples ranges between 21.18 to 100 MPa while BTS ranges
between 3.02 to 14.2 MPa. In Table 2, apart from determined UCS and BTS in laboratory, UCS is
predicted by using recent correlations given in Table 1for further reliability analysis.
Figure 6 depicts the determined UCS versus obtained BTS in laboratory. As shown in this
figure, there is a strong correlation with high reliability between UCS and BTS. The new
proposed correlation for prediction of UCS is given in the following equation. The proposed
relationship between UCS and BTS is close to suggested ratio of compressive strength to tensile
strength given by Sheorey (1997) and Kahraman et al., (2012). In addition, the coefficient of
determination of developed correlation is 0.9 which is relatively higher than previous suggested
correlations. Apart from that,new correlation has the advantage of being developed for specific
type of rock which is limestone.
(
) = 9.25
.
Table 2: Laboratory tests results and Predicted UCS
\
Predicted
UCS (MPa)
Predicted
UCS (MPa)
Predicted
UCS (MPa)
Kahraman et al.(2012)
Altindag and Guney (2010)
Farah (2011)
82.55
111.11
38.83
52.67
69.39
92.23
32.50
3.02
21.18
32.04
40.27
14.51
Limestone
5.93
61.61
62.92
83.04
29.38
5
Limestone
5.78
51.73
61.33
80.79
28.61
6
Limestone
3.22
27.29
34.16
43.14
15.53
7
Limestone
4.98
52.20
52.84
68.86
24.52
8
Limestone
8.83
78.09
93.69
127.27
44.20
9
Limestone
6.90
53.14
73.21
97.69
34.34
10
Limestone
8.28
60.20
87.85
118.79
41.39
11
Limestone
10.36
83.26
109.92
151.06
52.02
12
Limestone
7.41
76.67
78.62
105.46
36.94
13
Limestone
7.29
58.5
77.35
103.62
36.33
No
Sample
Type
Determined
BTS (MPa)
Determined
UCS (MPa)
1
Limestone
7.78
70.56
2
Limestone
6.54
3
Limestone
4
14
Limestone
11.09
85.62
117.66
162.51
55.75
15
Limestone
6.2
54.6
65.78
87.10
30.76
16
Limestone
14.2
100.7
150.66
211.84
71.64
17
Limestone
5.4
42.3
57.29
75.11
26.67
18
Limestone
6.1
51.7
64.72
85.60
30.25
19
Limestone
7.5
60.4
79.58
106.83
37.40
20
Limestone
6.3
50.3
66.84
88.61
31.27
Vol. 18 [2013], Bund. I
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Figure 6: Proposed correlation between unconfined compressive strength
and Brazilian tensile strength
The reliability and degree of accuracy of recent correlations for UCS prediction using BTS is
shown schematically in Figure 7. A critical review on the correlations shows that Kahraman`s
correlation (2012) can predicts UCS much better than correlation proposed by Farah (2011) and
Altindag and Guney (2010).
In fact, in comparison to the observed UCS, Kahraman`s correlation overestimate UCS by a
factor almost equals to 1.27 while predicted UCS using Altindag and Guney`s is 1.7 times bigger
than the laboratory measurements. On the other hand, Farah`s correlation underestimates UCS by
60%.
Figure 7: Reliability of recent UCS-BTS correlations based on observed laboratory
results
Vol. 18 [2013], Bund. I
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CONCLUSIONS
Based on the findings, the following conclusions can be drawn:
1) A number of 40 laboratory tests including 20 unconfined compressive tests and 20
indirect tensile strength (Brazilian tensile strength) tests on dry limestone specimen were
conducted. The laboratory measurements showed that obtained UCS and BTS were in
good agreement with previous studies.
2) From the laboratory results, a new correlation with high reliability and degree of
accuracy i.e R=0.9 was proposed for predicting UCS of limestone specimens from its
BTS results.
3) Through a critical review on some recent correlations for UCS prediction, it was
observed that the correlation suggested by Kahraman (2012) can predict UCS much
better that other proposed correlation. However, Kahraman`s correlation which is very
close to well established correlation suggested by Sheorey (1997) overestimated the dry
UCS of limestone core samples by a factor of 1.27.
ACKNOWLEDGEMENTS
The second and third authors would like to thank University Teknologi Malaysia for its
financial support via allocating International Doctoral Fellowship.
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