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Geotechnical and Geological
Engineering
An International Journal
ISSN 0960-3182
Volume 35
Number 3
Geotech Geol Eng (2017) 35:1119-1140
DOI 10.1007/s10706-017-0168-1
An Investigation into the Rock Properties
Influencing the Strength in Some Granitoid
Rocks of KwaZulu-Natal, South Africa
M.Fakir, M.Ferentinou & S.Misra
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ORIGINAL PAPER
An Investigation into the Rock Properties Influencing
the Strength in Some Granitoid Rocks of KwaZulu-Natal,
South Africa
M. Fakir .M. Ferentinou .S. Misra
Received: 9 September 2016 / Accepted: 15 January 2017 / Published online: 7 February 2017
Springer International Publishing Switzerland 2017
Abstract The uniaxial compressive strength (UCS)
of rocks is a critical parameter required for most
geotechnical projects. However, it is not always
possible for direct determination of the parameter.
Since determination of such a parameter in the lab is
not always cost and time effective, the aim of this
study is to assess and estimate the general correlation
trend between the UCS and indirect tests or indexes
used to estimate the value of UCS for some granitoid
rocks in KwaZulu-Natal. These tests include the point
load index test, Schmidt hammer rebound, P-wave
velocity (V
p
) and Brazilian tensile strength (r
t
).
Furthermore, it aims to assess the reliability of
empirical equations developed towards estimating
the value of UCS and propose useful empirical
equations to estimate the value of UCS for granitoid
rocks. According to the current study, the variations in
mineralogy, as well as the textural characteristics of
granitoid rocks play an important role in influencing
the strength of the rock. Simple regression analyses
exhibit good results, with all regression coefficients R
2
being greater than 0.80, the highest R
2
of 0.92 being
obtained from UCS versus r
t
. Comparison of
equations produced in the current study as well as
empirical equations derived by several researchers
serves as a validation. Also illustrate that the reliability
of such empirical equations are dependent on the rock
type as well as the type of index tests employed, where
variation in rock type and index tests produces
different values of UCS. These equations provide a
practical tool for estimating the value of UCS, and also
gives further insight into the controlling factors of the
strength of the granitoid rocks, where the strength of a
rock is a multidimensional parameter.
Keywords Uniaxial compressive strength Point
load index Brazilian tensile strength Schmidt
hammer rebound Ultrasonic velocity
1 Introduction
Rock engineering properties such as the uniaxial
compressive strength (UCS) of intact rocks is a
significant mechanical property for engineering pro-
jects (Yesiloglu-Gultekin et al. 2013; Singh et al.
2013; Torabi et al. 2013; Momeni et al. 2015;
Armaghani et al. 2016). The UCS can be determined
experimentally through direct or indirect methods
(ISRM 2007), or it can be estimated from empirical
equations proposed in literature. At the preliminary
stage of a project, direct measurement of the UCS
requires high-quality samples and considerable time
(Shalabi et al. 2007; Cai 2010; Yagiz 2011; Basu et al.
M. Fakir M. Ferentinou (&)
Civil Engineering Science, University of Johannesburg,
Johannesburg, South Africa
e-mail: mferentinou@uj.ac.za
S. Misra
Geological Sciences, University of KwaZulu-Natal,
Durban, South Africa
123
Geotech Geol Eng (2017) 35:1119–1140
DOI 10.1007/s10706-017-0168-1
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2012; Ersoy and Kanik 2012; Azadan and Ahangari
2013; Ozcelik et al. 2013). Therefore, direct testing of
UCS may not always be possible to conduct at the
preliminary design stages of underground structures,
as a result of representative rock samples not being
obtained (Yesiloglu-Gultekin et al. 2013). Empirical
equations can assist scientists with the estimation of
such strength parameters for practical solutions.
Indirect tests such as the Point Load Index (PLI),
Schmidt hammer rebound (SHR), P-wave velocity
(V
p
), and Brazilian tensile strength (r
t
) are often
conducted to predict the values of UCS (Cargill and
Shakoor 1990; Aydin and Basu 2005; Kilic and
Teymen 2008; Heidari et al. 2011; Minaeian and
Ahangari 2011; Karaman and Kesimal 2012).
According to Bewick et al. (2015), the UCS simply
records the load at failure during uniaxial testing of a
cylindrical core. Therefore, the UCS value is not the
same as the Hoek–Brown parameter r
ci
, where the
mean UCS is often considered to represent a reliable
rock material property. The UCS value can therefore
only be regarded as a proxy for rock strength which is
dependent on many factors such as the loading rate
(Bieniawski 1967), specimen geometry (Hudson et al.,
1971), specimen size (Bieniawski 1968), and miner-
alogy. As a result, the UCS cannot be used to replace
the Hoek–Brown criterion parameter r
ci
, and differ-
entiation between the two parameters is required
(Bewick et al. 2015). Besides being an important
parameter for the assessment of failure criterions
(Hoek and Brown 1980) for intact rocks and rock
masses under triaxial conditions, the UCS has signif-
icant importance as it is employed in geotechnical
classification of rock masses such as the rock mass
rating (RMR) (Bieniawski 1989), Q-system (Barton
et al. 1974), as well as in tunnelling durability, and
bearing capacity assessment of foundations (Moomi-
vand 2011).
The expression of correlations among engineering
properties has long been the scope of experimental
research. This is aroused by the need to represent the
actual behaviour of rocks and to calculate the design
parameters accurately. In this paper we consider the
UCS from unconfined compressive strength tests and
differentiate between the properties influencing this
strength parameter, with specific focus on granitoid
rocks. Considering the spatial distribution of granitoid
rocks in KwaZulu-Natal, there is limited knowledge
concerning the behaviour of this type of material. We
investigate the strength properties affecting the UCS,
and utilize indirect methods of strength testing to
predict the UCS of granitoid rocks in Kwa Zulu-Natal.
An evaluation of previously published correlation
equations is conducted, followed by simple regression
to produce useful and practical equations for estimat-
ing the value of UCS from the PLI, SHR, V
p
, and r
t
.
2 Literature Review
The PLI has long been regarded as the best interme-
diary for the UCS (Cargill and Shakoor 1990; Ghosh
and Srivastava 1991; Chau and Wong 1996; Tugrul
and Zariff 1999). It is relatively easy to conduct and
economical, and thus widely applied both in the field
and laboratory. Several authors have conducted PLI
and UCS tests for various lithologies to determine the
most effective conversion factor which converts the
PLI to the representative UCS value (Brook 1985;
Cargill and Shakoor 1990; Ghosh and Srivastava
1991; Chau and Wong 1996; Tugrul and Zariff 1999;
Basu and Aydin 2006) (Table 1). It is evident from
literature that the equations published exhibit a wide
range, varying from linear to quadratic, and power
laws. One of the problems commonly encountered is
with the vast range of correlation equations offered in
literature, there is often no agreement between authors
on a specific conversion factor. Given the great
variability of rock properties, even within the same
rock type, it is consequently difficult, and often not
very meaningful, to cite specific values for specific
rocks (Jaeger et al. 2007).
The Schmidt hammer is a handheld device which is
commonly used to assess the strength of rocks and
concrete (Kahraman 2001). It has also been used as a
tool to predict the amount of weathering a rock has
been subjected to since the rebound is related to the
strength of the rock (Deere and Miller 1964;
Yesiloglu-Gultekin et al. 2013; Tandon and Gupta
2013). There is a variety of equations (Table 2)
estimating the value of UCS from the measured SHR
(Ghose and Chakraborti 1986; Deere and Miller 1966;
Beverly et al. 1979; Aydin and Basu 2005; Selc¸uk and
Yabalak 2015).
The P-wave velocity has been successful as a non-
destructive test for the prediction of mechanical
properties of rocks (Vasconcelos et al. 2007; Tandon
and Gupta 2013; Azimian et al. 2013), where the
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Table 1 Empirical equations correlating Uniaxial Compressive Strength (UCS) and Point Load Index (PLI)
No. Author Lithology Empirical equation R
2
1 D’Andrea et al. (1964) Schistose UCS =15.3PLI ?16.3 –
2 Deere and Miller (1966) Granitic gneiss, slate, limestone, granitoid,
taconite, synenite, pegmatite, anorthosite,
basalt, serpentinite, rhyolite, dolomite,
slate, greenstone, gabbro, quartzite,
peridotite, marble schist, chalk
UCS =20.7(PLI) ?4.299 0.92
3 Broch and Franklin (1972) Igneous, sedimentary, metamorphic UCS =24PLI –
4 Bieniawski (1975) Sandstone, quartzite, norite UCS =23PLI –
5 Hassani et al. (1980) Sedimentary UCS =29PLI –
6 Singh (1981) Basalt, andesite, granodiorite, granitoid,
volcanic bomb, marble, serpentinite, gneiss,
schist, migmatite, limestone, dolomitic
limestone, sandstone, travertine
UCS =18.7PLI -13.2 –
7 Forster (1983) UCS =14.5PLI –
8 Gunsallus and Kulhawy
(1984)
UCS =16.5PLI ?51.0 –
9 ISRM (1985a,b) Various rock types UCS =(20–24)PLI –
10 Norbury (1986) UCS =8–54PLI –
11 Cargill and Shakoor
(1990)
UCS =23PLI ?13 –
12 Ghosh and Srivastava
(1991)
Granite UCS =16PLI –
13 Tsidzi (1991) UCS =(14–82)PLI –
14 Grasso et al. (1992) UCS =9.30PLI ?20.04 –
15 Singh and Singh (1993) UCS =23.37PLI –
16 Ulusay et al. (1994) Sandstone UCS =19PLI ?12.7 –
17 UCS =15.25(PLI) –
18 Chau and Wong (1996) UCS =12.5PLI 0.73
19 Tugrul and Zariff (1999) Granite UCS =3.86(PLI)
2?5.65(PLI)
–
20 Kahraman (2001) Basalt, andesite, granodiorite, metagabbro,
granitoid, volcanic bomb, marble, quartzite,
gneiss schist, migmatite, limestone,
serpenite anhydrite, travertine
UCS =8.41PLI ?9.51 0.85
21 Kahraman 2001 Igneous, sedimentary, metamorphic UCS =23.6(PLI) -2.7 0.85
22 Quane and Russel (2003) Pyroclastic UCS =24.4PLI –
23 Tsiambaos and
Sabatakakis (2004)
Sedimentary rocks UCS =23PLI –
24 Fener et al. (2005) Igneous, sedimentary, metamorphic UCS =9.08(PLI) ?39.2 –
25 Kahraman et al. (2005) Igneous, sedimentary, metamorphic UCS =10.91PLI ?27.41 0.84
26 Kahraman et al. (2006) UCS =24.83(PLI) -39.64 (for rocks
with n \1)
UCS =10.22(PL) ?24.31 (for rocks
with n [1)
–
27 Kahraman and Gunaydin
(2009)
Granitic rocks UCS =10.92(PLI) ?24.2 0.56
28 Diamantis et al. (2009) Igneous and metamorphic UCS =17.81(PLI)
1.06
–
29 Basu and Kamran (2010) UCS =11.03(PLI) ?37.657 –
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velocity of pulses traveling in the solid material
depends not only on mineral composition, pore
structure, fluid properties, but also vary with stress
and tempareture (Jaeger et al. 2007). The measure-
ment of the velocity of pulses can be used to indicate
the elastic strength of the rock specimens (Tandon and
Gupta 2015), and thus, the relationship between UCS
and V
p
has been investigated by a variety of
researchers (Kahraman 2001; Yasar and Erdogan
2004a; b; Entwisle et al. 2005; Sharma and Singh
2008; Cobanglu and C¸ elik 2008; Moradian and Behnia
2009; Khandelwal and Singh 2009; Diamantis et al.
2009; Dehghan et al. 2010; Kurtulus et al. 2011;
Khandelwal and Ranjith 2010; Yagiz 2011; Sharma
et al. 2011; Khandelwal 2013). Table 3lists selected
publications of equations correlating the UCS to V
p
.
The Brazilian tensile strength has been widely used
as an indirect test to measure tensile strength (r
t
). It
has also been employed to produce estimates of UCS
strength as these two parameter are commonly
required and determined in most geotechnical projects
(Karaman and Kesimal 2012; Farah 2011; Altindag
2012). As r
t
can be easily determined from the
Brazilian tensile strength, due to sample preparation
requirements being less than UCS testing, it is useful
to find strong conversion factors between these two
parameters. Furthermore, Farah (2011) indicated that
indirect tensile strength may have a better correlation
with UCS than PLI, which is also confirmed in the
current study. Table 4shows selected regression
equations for estimation of UCS through r
t
measurement.
The correlation of UCS-E (tangent modulus of
elasticity) is usually referred to as the modulus ratio
(MR) which generally constitutes a common tool for
rock material (Deere and Miller 1966) and rock mass
(Hoek and Diederichs 2006) classification. Torabi-
Kaveh et al. (2014) aimed to predict UCS and E using
physical properties of Asmari limestones. They con-
ducted tests on 150 rock samples from two different
dam sites. Strong correlations were identified between
the UCS and physical properties. However, there were
no strong correlations between the predicted E and the
measured E. Vasconcelos et al. (2007) evaluated the
suitability of the ultrasonic pulse velocity method for
describing the mechanical and physical properties of
granites, and for the assessment of its weathering state.
Vasconcelos et al. (2007) confirmed that ultrasonic
pulse velocity can be effectively used as a simple and
economical, non-destructive method for a preliminary
prediction of mechanical and physical properties.
Young’s modulus (E) can also be estimated from
empirical equations listed in Table 5. Additionally,
Bell (1992) outlines a number of equations that relate
the Young’s modulus, Poisson’s ratio and ultrasonic
pulse velocity.
Table 1 continued
No. Author Lithology Empirical equation R
2
30 Karaman and Kesimal
(2012)
Igneous, sedimentary, metamorphic UCS =20.42PLI -5.146 –
31 Heidari et al. (2011) Gypsum UCS =5.557(PL) ?23.68 0.92
Table 2 Empirical
equations correlating
Uniaxial Compressive
Strength (UCS) and
Schmidt Hammer Rebound
(SHR)
Rrebound, qdensity
No. References UCS equation R
2
1 Deere and Miller (1966) UCS =6.9 910
(0.16 ?0.0087(Rq))
–
2 Beverly et al. (1979) UCS =12.74e
0.0185(Rq)
–
3 Singh et al. (1983) UCS =2R 0.72
4 Haramy and De Marco (1985) UCS =0.994(R) -0.383 0.70
5 Tugrul and Zariff (1999) UCS =8.36(R) -416 0.87
6 Katz et al. (2000) UCS =2.208e
0.067(R)
0.96
7 Yasar and Erdogan (2004) USC =4910
-6
(R)
4.2917
0.89
8 Aydin and Basu (2005) UCS =1.4459e
0.0706(R)
0.92
9 Kilic and Teymen (2008) UCS =0.0137R
2.2721
0.96
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The reliability of E for estimating the value of UCS
has been investigated by several researchers (Bradford
et al. 1998; Horsrud 2001; Golubev and Rabinovich
1976; Colwell and Frith 2006), with results indicating
that the UCS can be estimated from E. Bradford et al.
(1998) and Horsrud compiled test results on the North
Sea sandstone and shale respectively. The equations
typically take a power form, except for Bradford
(1998). Table 6lists selected empirical equations
correlating UCS—E. Equations with no specified
author are those which are unpublished.
It has been observed (Maji 2011), that failure
modes of a rock under compression will affect the
strength of the sample. Thus, as the compressive
strength of the rock material increases with an increase
in confining pressure, the UCS will provide a mini-
mum strength that the rock can withstand under
compression. As a result, the failure modes of the rock
under uniaxial compression can provide useful infor-
mation for safe and economic design of various
engineering structures (Basu et al. 2013).
However, failure modes are typically complex and
difficult to predict (Basu et al. 2013). At a laboratory
scale, mineralogy and geometric arrangement of
grains and voids, and fractures/microcracks, typically
control the rock mechanical behaviour (Sammis and
Table 3 Empirical
equations correlating
Uniaxial Compressive
Strength (UCS) and P-wave
velocity (V
p
)
No. References UCS equation R
2
1 Freyburg (1972) UCS =35.0V
p
-31.5 –
2 Militzer and Stoll (1973) UCS =2.45V
p
–
3 Golubev and Rabinovich (1976) log UCS =0.358V
p
-0.283 –
4 McNally (1987) UCS =1277e
-117/Vp
–
5 Goktan (1988) UCS =36.0V
p
-31.2 –
6 Tugrul and Zariff (1999) UCS =35.54V
p
-55 0.80
7 Kahraman (2001) UCS =9.95V
p
1.21
0.83
8 Yasar and Erdogan (2004) UCS =31.5V
p
-63.7 0.81
10 Sousa et al. (2005) UCS =22.032V
p
1.247
–
11 Sharma and Singh (2008) UCS =0.0642.V
p
– 117.99 0.90
12 Kilic and Teymen (2008) UCS =2.304V
p
2.4315
–
13 Cobanglu and C¸ elik (2008) UCS =56.71V
p
-192.93 0.81
14 Yagiz (2009) UCS =0.258V
p
3.43
0.92
15 Diamantis et al. (2009) UCS =110V
p
-515.56 –
16 Khandelwal and Singh (2009) UCS =133.3V
p
-227.19 –
17 Sharma and Singh (2010) UCS =36V
p
-45.37 –
18 Diamantis et al. (2011) UCS =0.14V
p
-899.33 –
19 Kurtulus et al. (2011) UCS =0.0675V
p
-245.13 0.92
UCS =0.0188V
p
-71.054 0.83
20 Yagiz (2011) UCS =49.4V
p
-167 0.92
21 Sarkar et al. (2012) UCS =0.038V
p
-50 –
22 Altindag (2012) UCS =0.258V
p
1.194
–
23 Khandelwal (2013) UCS =V
p
-34.83 –
Table 4 Recent
correlations between
Uniaxial Compressive
Strength (UCS) and
Brazilian Tensile Strength
(r
t
)
No. References Equation R
2
Lithology
1 Altindag (2012) UCS =12.38 9r
t
1.02725
0.89 Different rock types
2 Farah (2011) UCS =5.11 9r
t
-133.86 0.68 Weathered limestone
3 Kahraman (2012) UCS =10.61 9r
t
0.50 Different rock types
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Ashby 1986; Akesson et al. 2004; Basu and Aydin
2006; Szwedzicki 2007; Basu et al. 2009,2013).
Quantification or prediction of failure modes is
therefore a complex and difficult task (Santarelli and
Brown 1989; Basu et al. 2013).
3 Methodology
As per the widely recognized high strength of
granitoid rocks, sampling proved rather difficult,
where serious complications about extracting suit-
able samples were encountered. Even were weathering
had advanced, a limited number of samples were
extracted due to the hard rigid structure of granitoid
rocks. As such, the limited number of rock samples
tested for UCS and of which are used to define the
relation among properties is employed as an indicator
to estimate the general correlation trends of the
granitoid rocks. The sample locations are within
KwaZulu-Natal, South Africa viz., Scottburgh,
Botha’s Hill, Jolivet, and White Mfolozi (Fig. 1).
The Scottsburgh granitoids are restricted to the
coastline, which lies within the Granitic Zone of the
eastern sector of the Natal-Namaqua Mobile belt
(Matthews 1985). These samples are weathered, with
the rock mass having an overall blocky structure
(Fig. 2a). The White Mfolozi River has incised a large
valley into the pre-Karoo rocks, exposing the Pongola
Supergroup and basement granitoids and gneisses.
(Matthews 1972), allowing the sampling of fresh
granitoid samples (Fig. 2b). The granitoids in this area
are intrusive igneous rocks and form part of the Natal
Metamorphic Province Granitoids, and part of the
Kaapvaal Craton Basement Granitoids. The rocks of
the Fafa pluton are restricted to the southern most part
of the Mzumbe terrane. They extend north and south
inland from the village of Jolivet, to west of
Mtwalume village. Two sample localities (F1 and
F2) were selected to provide a good representation of
this type of rock. The granitoids from these localities
typically form the basement granitoids. Within these
outcrops there is the constant presence of cracks, with
smaller fractures radiating from the crack (Fig. 2c).
There is a shear zone which is represented in Fig. 2d.
The foliation can be defined by the direction of the
mafic minerals. The granitoids at this second locality
are typically megacrystic.
Eleven large blocks (Fig. 3) were collected from
the four localities. This allowed for reasonable spatial
distribution as to provide representative samples. The
granitoid rocks were cored using a 54.7 mm diameter
Table 5 Empirical
equations to estimate the
value of Young’s Modulus
(E)
No. References Equation R
2
1 Vasconcelos et al. (2007)E=19.87V
p
-27,813 0.84
2 Khandelwal and Singh (2009)E=4.9718V
p
-7151 0.97
3 Diamantis et al. (2011)E=0.041V
p
-264.15 0.81
4 Kurtulus et al. (2011)E=0.0015V
p
-2.516 0.74
5 Yagiz (2011)E=20.1V
p
-53 0.95
6 Altindag (2012)E=0.919V
p
1.9122
0.79
Table 6 Empirical equations correlating Uniaxial Compressive Strength (UCS) and Young’s Modulus (E)
No. Equation References lithology
1 UCS =46.2exp(0.027E) – –
2 UCS =2.28 ?4.1089E Bradford et al. (1998) All rock types
3 UCS =25.1E
0.34
– Dolomite with 60–100 UCS (MPa)
4 UCS =13.8E
0.51
– Limestone with 10–300 UCS (MPa)
5 UCS =4.1141E
0.9176
Colwell and Frith (2006)–
6 UCS =7.97E
0.91
Horsrud (2001) Shales
7 UCS =7.22E
0.712
– Shales
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diamond coring bit. Samples were cut to the appro-
priate size for each test according to the ISRM (2007)
suggested methods. The core samples were ground
and lapped parallel to achieve an accuracy of
±0.2 mm. Each core sample prepared was carefully
investigated for macroscopic defects so that testing
Fig. 1 Sampling locations
in the study area
Fig. 2 a Scottsburgh outcrop with block structure, bWhite Mfolozi granitoid outcrop forming part of the basement rock, cFafa
granitoid exhibiting tension crack, dFafa granitoid exhibiting a shear zone
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would be free from fractures, cracks and fissures,
which may have occurred due to the coring and/or
cutting process. A total of 49 cores and 22 blocks
(Fig. 4) were prepared for index testing purposes. The
rocks employed in the current study are classified
within the granite group according to the Streckeisen
classification (1991) (Fig. 5).
The petrographic examination of the granitoid
rocks under investigation was conducted using an
optical Leica Olympus BX41 microscope. Twelve thin
SB1 SB2 SB3
SB4 SB5
BH F1 F2
WM1 WM2 WM3
Fig. 3 Field samples collected for index testing
Axial PLI Diametral PLI
Brazilian
Tensile Strength
UCS/ Vp
Fig. 4 Core test specimens used in the study
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sections for the granitoid rocks were prepared and
examined for the study. The volumetric percentages of
minerals present in the samples were determined by
X-ray diffraction (XRD). A detailed petrographic
description of the examined granitoid samples is
discussed in the impending section.
The physical properties of the granitoid rocks such
as porosity, density and water absorption were deter-
mined in accordance to the ISRM (2007) suggested
methods. The UCS of the granitoid rocks was deter-
mined using a servo-controlled compression testing
machine, which has a load capacity of 2000 kN. Each
sample was prepared with a length of ±110 mm and
diameter of 54 mm. The UCS machine applied a load
at a rate of 0.5–1.0 MPa/s to a core sample (Brown and
Hoek 1980).
Young’s modulus was estimated with empirical
equations developed by Vasconcelos et al. (2007)and
Torabi-Kaveh et al. (2014). The modulus ratio (MR) is
calculated as the Young’s modulus (E) divided by the
UCS (Deere and Miller 1966). The range of MR values
represent the boundary and expresses the ratio of E and
UCS of the intact rock. Poisson’s ratio was calculated
from the frequency of P-wavesaccording to Bell (1992).
The PLI was conducted on NX-size cores as well as
block/irregular lumps of the rock samples using a
point load testing machine in accordance to the ISRM
(2007) standard. Three different tests were conducted
to determine the PLI: axial, diametral and block/
irregular lump. The corrected index, Is
(50)
, is applied
to obtain the unique Point Load Strength Index (PLI).
The P-wave velocity (V
p
) test was conducted on 8
core samples of NX size and in accordance to the
ISRM (2007) recommendations. The core ends were
polished and lubricated to create good coupling. The
PUNDIT Pulse Generator Unit with two transducers
(diameter of 50 mm and frequency of 0.5 MHz) was
utilized. The pulse transmission technique (ISRM
2007), where the transmitter is placed opposite to the
plane on which the receiver is placed, was employed.
To attain accurate results, the PUNDIT unit was reset
and calibrated with metal cores before each consec-
utive test. The average V
p
was determined for each
sample and used for analysis.
The Schmidt hammer rebound number (SHR),
ranges from 0 to 100. The N-type Schmidt hammer has
an impact energy of 2.207 Nm (Kahraman 2001) and
was used in the current study. Each test was conducted
in accordance to the ISRM (2007) suggested methods.
The rebound height is recorded on a linear scale which
provides an indication of the strength of the material.
In order to obtain reliable results, the hammer is placed
perpendicular to the surface, and was conducted by a
single individual to allow a consistent amount of force
to be applied.
Tensile strength (r
t
) was measured indirectly by
means of the Brazilian tensile strength. Each sample
was wrapped around its periphery with one layer of
Fig. 5 Classification of
rocks according to IUGS Le
Bas and Streckeisen (1991)
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masking tape and mounted in the apparatus in such a
way that the curved platens loaded the sample
diametrally. This allows analysis of the orientation
in which failure occurs.
The weathering classification of the studied gran-
itoid rocks is based on the ISRM (Brown 1981)
weathering grade classification. The granitoid rocks
are classified as ‘‘moderately weathered’’ to ‘‘fresh’’
rocks. The samples indicate less than half of the rock
material disintegrates, whereas in some cases slight
discoloration indicates weathering of the rock material
and discontinuity surfaces, with the majority of the
rock maintaining its original structure and being
intact.
4 Results
4.1 Petrographic Analysis
The granitoid samples employed are light coloured,
medium to coarse grained, and hypediomorphic to
allotriomorphic in nature (Fig. 6a). The petrographic
analysis revealed that in cases, the imprints of brittle
deformation are indicated by the undulating extinction
in quartz grains, with a moderately well-developed
foliation present. The major constituent minerals are
quartz, plagioclase, microcline, with minor propor-
tions of biotite in interstitial spaces of the major
constituents. The minerals are typically fractured and
Fig. 6 a Medium to coarse grained, hypediomorphic to
allotriomorphic texture of granitoid, bfracturing of granitoid
(see F
1
in figure) with granulations along the fracture plane,
ctwin lamellae in plagioclase showing displacement along the
fracture (F
2
); and dprismatic plagioclase grains partially altered
to sericite, estrained quartz exhibiting polygonal structure,
fpolygonal quartz showing dendritic sutured contact with
adjacent grains, gsting perthites within microcline, hinjection
of apilitic veins within coarse grained granites. Qquartz,
Pplagioclase, Mmicrocline, Bbiotite
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granulated (Fig. 6b). The plagioclase occurs as sub-
hedral laths with well-developed albite twins, where in
some cases, the twin lamellae exhibits displacement
due to fracturing (Fig. 6c). In cases, the granitoid
rocks contain megacrysts of K-feldspar, where these
prismatic plagioclase grains are up to 7 mm in length,
and partially replace by sericite at the margins
(Fig. 6d). However, the prismatic, tabular shape of
the plagioclase is still present. The quartz grains are
anhedral in shape, and are either shown as strained
quartz with polygonal shapes (Fig. 6e), or anhedral
grains with dendritic sutured contacts with adjacent
quartz grains (Fig. 6f). However, majority of the
quartz grains exhibit undulous extinctions. There are
large grains of potash feldspar set within the granular
matrix, with the smaller, more rounded grains sur-
rounding the larger ones, indicative of the brittle
behaviour of the granitoids under study. The micro-
cline grains are anhedral (size 0.5–3 mm), and show
perthitic structure where the perthitic intergrowths are
sting shaped (Fig. 6g). The microcline also displays
the signature of alteration. The flaky biotite is mostly
unaltered and occur in interstitial spaces between
quartz, plagioclase and microcline, where in cases,
bleached interstitial biotite is present. The hornblende
is the mafic mineral present in the rock and is typically
altered to biotite. The studies rocks have also been
subjected to aplitic vein injection (Fig. 6h). The
volumetric percentage of minerals present in selected
samples is shown in Table 7.
4.2 Statistical Analysis
The basic descriptive statistical variables from the
laboratory tests are shown in Table 8. According to the
histograms, the mean PLI is 4.37 MPa (Fig. 7a), r
t
is
9.73 MPa (Fig. 7b), SHR is 44.45 (Fig. 7c) V
p
7049.02 m/s (Fig. 7d), and UCS 113.23 MPa
(Fig. 7e). Young’s Modulus was estimated to be in
the range of 69–79 GPa. MR values range between
56.38 and 117.03, with a standard deviation of 23.46.
Poisson’s Ratio was calculated to have a mean of 0.22.
The standard deviation values are relatively high,
except for V
p
. The low value of standard deviation of
V
p
indicate the dependant and independent variables
employed in the present study are controlled by the
difference in mineralogical content. Therefore, V
p
is
affected much less when compared to the other
variables.
4.3 Regression Analysis and Prediction
Performance Assessment
The raw data (Table 9) obtained from laboratory
testing was subjected to curve fitting analysis, whereby
linear ðy¼ax þbÞ, logarithmic ðy¼aþlnxÞ, expo-
nential ðy¼aexÞ, and power approximations ðy¼
axbÞwere used to produce the best correlation. Linear
equations were produced for all correlations in the
current study (Table 10). A comparative assessment of
previous empirical equations was conducted to verify
the acceptability with regards to the current study
granitoid rocks. Furthermore, the regression coeffi-
cient value between the measured and predicted values
are calculated, as it is a good indicator of the
performance of the proposed relationship. The rela-
tionship between PLI and UCS is depicted in Fig. (8a).
The regression coefficient for the point load test is
R
2
=0.82, given a linear form:
UCS ¼15:939 Is 50ðÞ
þ37:235;R2¼0:82 ð1Þ
From the 35 empirical equations used to estimate
the value of UCS from the PLI, only seven such
equations produced values close to that measured in
the lab. The relationship between the UCS and PLI is
compared well with other studies, and the results of
this relationships were close to the results obtained by
Deere and Miller (1966), ISRM (1985a,b), and
D’Andrea et al. (1964) (Fig. 8b).
Table 7 Volumetric
percentage of minerals in
selected samples
Sample Quartz (%) Albite (%) Microcline (%) Biotite (%)
SB 22 30 34 4
BH 30 25 41 4
WM 34 24 30 2
F1 30 38 26 2
F2 26 36 24 4
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The regression coefficient for the UCS versus V
p
is
R
2
=0.82 (Fig. 9). The correlation equation produced
is given a linear form:
UCS ¼0:0673 Vp
257:39;R2¼0:82 ð2Þ
None of the empirical equations outlined in Table 3
accurately estimate the UCS value tested in the lab.
The closest values to that tested is produced by
Kurtulus et al. (2011). Both equations are only
applicable to rock types with a V
p
[3700 m/s.
However, Kurtulus et al. (2011) overestimates the
moderately weathered granitoid samples UCS by
±40 MPa, but estimates the fresh granitoid samples
within ±5–10 MPa. Therefore, these equations should
only be used where fresh samples are available.
The regression coefficient for UCS versus r
t
is
R
2
=0.92, and takes a linear form (Fig. 10a). The
regression equation of the current study is within
bounds of previous empirical equations, with the
estimated values from Kahraman (2012) being the
closest to that tested in the lab (Fig. 10b). The
correlation equation produced is given by:
UCS ¼11:564rt13:1;R2¼0:92 ð3Þ
The regression equation for UCS versus SHR is
given by power law equation with a regression
coefficient of R
2
=0.86 (Fig. 11a).
UCS ¼0:0142ðSHRÞ2:3559;R2¼0:86 ð4Þ
A total of seven equations correlating the SHR to
the UCS was tested in the current study (Fig. 11b).
The Deere and Miller (1966) equation produced the
most reliable estimation for the value of UCS with a
variation between 1 and 5 MPa.
Since the Young’s modulus values are not obtained
through direct measurements, but obtained by empir-
ical equations, direct correlation with UCS is not
suggested. Therefore a range of MR values are
provided for the granitoid samples. MR values range
from 58.19 to 117.0 GPa, which is consistent with
those reported in literature (Hoek and Diederichs
2006).
In the current study, the failure modes are adopted
after Basu et al. (2013) (Fig. 13). The dominant failure
mode for UCS testing is shown in Fig. 12. For the
granitoids of the current study, failure modes up to a
UCS of 60 MPa corresponds to axial splitting (single
extensional plane or multiple plane). Shearing and
axial splitting occurred at UCS range of 65–100 MPa.
Shearing along a single plane manifested at higher
UCS values, typically between 135 and 150 MPa.
Therefore, as the UCS increases, the failure mode
changes from axial splitting to shearing along a single
plane.
5 Discussion
Granitoids are intrusive igneous rocks which are
commonly felsic and are subdivided on the basis of
relative proportion of quartz, alkali feldspar and
plagioclase feldspar (Nesse 2009). In order for a rock
to be classified as a granitoid, it must contain 20–60%
quartz and 5–65% feldspar. As such, the strength of
the granitoid rocks of the current study is highly
dependent on mineralogy of the rock.
The essential minerals found in the granitoids of the
current study are quartz, feldspar, biotite, microcline
and hornblende. The strength of the rock is influenced
by the grain size and modal mineralogy, in particular,
the size of phenocryst present in the granitoid rocks.
The UCS values of the investigated rocks depend more
on grain size, rather than modal mineralogy. This is
exhibited by the samples with similar mineralogical
composition but different phenocryst size having
different values of UCS. The granitoid with medium
to coarse grained phenocrysts is stronger than the
granitoid with very coarse grained phenocrysts. Thus,
Table 8 Statistic parameters
Density (g/cm
3
) n% UCS (MPa) PLI (MPa) V
p
(m/s) SHR (R) r
t
(MPa) MR (GPa)
N 29 18 8 70 29 58 22 8
SD 0.25 0.75 40.48 2.12 2057.44 5.91 3.48 23.46
Mean 2.65 1.47 113.23 4.23 6155.47 43.08 9.87 77.42
Min 2.23 0.57 58.41 1.06 4862.39 32.00 5.06 56.38
Max 3.48 2.91 167.67 8.55 9814.81 54.00 16.63 117.03
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Fig. 7 Histograms of aPoint Load Index, bTensile Strength (r
t
), cSchmidt Hammer Rebound (SHR), dP-wave velocity (V
p
),
eUniaxial Compressive Strength (UCS)
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the fresh granitoid samples show the highest strength,
in terms of petrography, mainly because:
•It contains roughly more quartz and less mica
minerals;
•Has a low fracture intensity;
•The grain size of the groundmass is in contrast to
the grain size of that of the minerals, especially the
phenocrysts present;
•The shape of the minerals, specifically the phe-
nocrysts, are highly irregular
There is a clear correlation between weathering and
density, weathering and SHR, and weathering and V
p
.
The values obtained from laboratory tests indicate a
decrease in SHR and V
p
with an increase in weath-
ering. The granitoids with a lower degree of weath-
ering have high V
p
values which is consistent with the
values obtained in previous studies (Tandon and Gupta
2015) on granitic rocks that are not weathered.
Density is one of the most fundamental properties
of a rock and is influenced by mineral composition and
the amount of void spaces (Bell 1987). The density of
Table 9 Experimental data base
No. Sample UCS
(MPa)
DiPLI
(MPa)
AxPLI
(Mpa)
Blck/irrg PLI
(MPa)
r
t
(MPa)
Di SHR
(MPa)
Ax SHR
(MPa)
V
p
(m/
s)
n% p (g/
cm
3
)
MR
(GPa)
1 SB1a 58.41 1.88 3.97 1.37 8.22 41 36 5071.77 2.5 2.48 117.03
2 F1a 64.39 1.91 4.22 1.32 10.8 35 35 5023.7 1.49 2.60 110.35
3 F1b 91.85 1.06 4.09 3.27 8.83 39 37 4976.53 1.47 2.61 76.12
4 F1c 99.71 2.61 4.16 1.74 5.31 38 32 5047.62 1.46 2.70 73.65
5 F1d 134.67 1.21 4.34 3.68 5.06 42 38 5023.7 0.61 2.77 56.38
6 WM1a 139.4 7.79 8.29 5.53 16.63 46 43 5000 0.6 2.80 64.76
7 WM1b 149.74 8.55 5.65 2.66 12.9 49 46 4953.27 0.59 2.80 62.90
8 WM1c 167.67 6.23 4.64 3.16 13.81 48 45 4862.39 0.57 2.93 58.19
9 SB2a 1.88 3.97 1.37 8.22 32 38 5071.77 2.18 2.68 23.46
10 SB2a 1.91 4.22 1.32 10.8 36 41 5023.7 2.91 2.52
11 SB2b 1.06 4.09 3.27 8.83 38 41 4976.53 2.1 2.23
12 SB3a 2.61 4.16 1.74 5.31 45 42 5047.62 2.62 2.30
13 BH 1.21 4.34 3.68 5.06 46 48 5023.7 1.46 2.55
14 F1d 6.23 5.11 5.53 8.11 48 49 5023.7 1.63 3.00
15 F1e 5.85 4.3 2.66 7.02 50 53 4976.53 2.74
16 F1f 3.71 3.16 51 54 5047.62 2.92
17 F2a 7.12 2.12 11.4 35 35 5023.7 1.00 2.88
18 F2b 6.67 6.26 9.69 39 37 9814.81 1.20 3.48
19 F2c 7.29 5.33 9.79 38 32 9724.77 1.14 2.62
20 F2d 7.68 1.57 8.2 42 38 9636.36 1.08 2.83
21 WM2a 7.79 8.29 2.05 16.63 46 43 9814.81 2.75
22 WM2b 8.55 5.65 5.11 12.9 49 46 9724.77 2.93
23 WM3 4.64 2.45 13.81 48 45 9814.81 2.61
24 WM4 4.95 7.24 41 48 9636.36 2.51
25 SB4a 3.24 53 50 5071.81 2.49
26 SB4a 4.37 54 51 5071.81 2.30
27 SB5a 7.53 42 46 5023.7 2.49
28 SB5b 3.72 44 42 4953.27 2.45
29 SB5c 5.86 48 45 5047.62 2.44
Nnumber of samples, SD standard deviation, n% porosity, PLI point load index, V
p
P-wave velocity, SHR Schmidt hammer rebound,
r
t
Brazilian disk, MR modulus ratio
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Table 10 Proposed simple
regression equations for
granitoid rocks
No. Correlation Equation R
2
Comment
1 SHR-UCS UCS =0.0142(SHR)
2.3559
0.86 SHR [20
2 PLI-UCS UCS =15.939(Is
(50)
)?37.235 0.82
3r
t
-UCS UCS =11.564r
t
-13.1 0.92
4V
p
-UCS UCS =0.0673(V
p
)-257.39 0.82 V
p
[3700 m/s
UCS = 15.939(Is(50)) + 37.235
R² = 0.82
0
20
40
60
80
100
120
140
160
180
200
0123456789
UCS (MPa)
Is(50) (MPa)
UCS vs PLI
0
50
100
150
200
250
300
350
400
450
500
0 2 4 6 8 10 12 14 16 18 20
UCS (MPa)
Is(50) (MPa)
Empirical Equations for UCS - PLI
Deere and
Miller (1966)
D'andrea et al
(1964)
Karaman and
Kesimal (2012)
ISRM (1985)
Bienawski
(1975)
Kahramann
(2001)
Diamantis et al
(2009)
Current Study
(b)
(a)
Fig. 8 a Uniaxial Compressive Strength (UCS) versus Point Load Index (PLI), bComparison between empirical equations and derived
equations for Uniaxial Compressive Strength (UCS) versus Point Load Index (PLI)
UCS = 0.0673Vp- 257.39
R² = 0.82
0
20
40
60
80
100
120
140
160
180
4000 4500 5000 5500 6000 6500
UCS (MPa)
Vp (m/s)
UCS vs Vp
(a)
0
50
100
150
200
250
300
350
400
0 2000 4000 6000
UCS (MPa)
Vp (m/s)
Empirical Equations of UCS-Vp
Freyburg (1972) Militzer and Stoll (1973)
Goktan (1988) Turgrul and Zarif (1999)
Yasar and Erdogan (2004a) Yasar and Erdogan (2004)
Sharma and Singh (2007) Kurtulus et al. (2011)
Yagiz (2011) Sakar et al. (2012)
Current Study
(b)
Fig. 9 a Uniaxial compression stress (UCS) versus P-wave velocity (V
p
), bComparison between empirical equations and derived
equation for UCS versus V
p
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a rock allows insight into the UCS. However, the study
shows that even though the granitoids of the current
study have similar values of density, the density alone
cannot be a reliable index for estimation of the UCS.
This can be attributed to the mineralogical composi-
tion not changing significantly (Sousa 2014). Only
when the weathering has advanced does it lead to a
significant reduction in the bulk density.
An additional factor influencing the strength of
these granitoids is the variation in crack intensity
across different rock samples, which may affect the
UCS, PLI, V
p
and SHR values (Tandon and Gupta
UCS = 11.564σt- 13.1
R² = 0.92
0
20
40
60
80
100
120
140
160
180
200
0 2 4 6 8 10 12 14 16 18
UCS (MPa)
σt (MPa)
UCS vs σt
(a)
0
50
100
150
200
250
300
0 2 4 6 8 101214161820
UCS (MPa)
σt (MPa)
Empirical Equations of UCS - σt
Altindag 2012 Farah 2011
Kahraman et al. 2012 Current Study
(b)
Fig. 10 a UCS versus r
t
,bComparison between empirical and derived equation for UCS versus r
t
UCS = 0.0142(SHR)2.3559
R² = 0.86
0
20
40
60
80
100
120
140
160
180
200
0 102030405060
UCS (MPa)
R
UCS vs SHR
(a)
0
40
80
120
160
200
240
280
320
0 10203040506070
UCS (MPa)
R
Empirical Equations of UCS - SHR
Deere and
Miller (1966)
Tugrul and
Zariff (1999)
Katz et al.
(2000)
Aydin and
Basu (2005)
Mishra and
Basu
Kilic and
Teymen
Yasar and
Sedir
Current Stud
y
(b)
Fig. 11 a UCS versus SHR, bComparison between empirical and derived equation for UCS versus SHR
Fig. 12 Schematic
representation of modes of
failure in UCS test (After
Basu et al. 2013)
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2015). It may be possible that the amount and the
intensity of the preferred alignment of mica minerals
mainly control the UCS, PLI, V
p
and SHR values,
which is examined by the alignment of minerals in
relation to fractures that lead to failure of the rock
specimen.
Three types of point load tests were conducted and
plotted against the corresponding UCS values. Broch
and Franklin (1972) proposed that for axial testing,
specimen length and diameter both influence the
results, where there is a ‘‘shape’’ effect in addition to
the ‘‘size’’ effect experienced in the diametral tests.
For the diametral test, the failure load is independent
of the length of the core, provided that the length of the
sample is sufficiently large. The strength index is
therefore not influenced by irregular geometry of the
end faces (Broch and Franklin 1972). The PLI
produced a regression coefficient of 0.82, indicating
the index tests to be a reliable tool for the estimation of
UCS, where care is taken when conducting the specific
tests.
The SHR is frequently used, because it is a fast and
reliable method for obtaining values of strength since
the rebound is related to other rock properties (Tugrul
and Zariff 1999). There is a slight tendency for the
SHR value and UCS to change simultaneously, as has
been observed by previous researchers (Yilmaz and
Sendir 2002; Yasar and Erdogan 2004). However,
many factors could influence the values of SHR. These
include the orientation of the hammer, or the surface
upon which the testing was conducted. Thus, the
Schmidt hammer may not always be a reliable tool for
the estimation of the UCS, if care is not taken when
conducting the test.
A strong regression coefficient for the UCS versus
V
p
was produced in the current study. However,
propagation of V
p
is a complex process which depends
on various factors which include, the amount of
minerals present, mineral shape, mineral size, orien-
tation, fluids present, cracks, porosity, pore shape and
size (Tandon and Gupta 2015). Tandon and Gupta
(2013) reported that there are one or two main factors
that control the velocity, and these will depend on the
rock type.
Tensile strength exhibits a strong regression coef-
ficient with UCS for the granitoid rocks of this study.
These two parameters are commonly required for
geotechnical projects and as such, it is a good idea to
find strong conversion factors for these two parame-
ters, to allow the prediction of UCS from the indirect
tensile tests. Comparatively, UCS versus r
t
produced
the highest regression coefficient. As such, estimation
of the UCS from the indirect tensile strength test
provides a better proxy than the PLI with regards to the
granitoid rocks of the current study.
Regression analysis exhibits strong correlation
coefficients, with all index tests producing R
2
values
greater than 80%. The results of the study clearly
Axial splitting
UCS = 58 MPa
Axial splitting
UCS = 149 Mpa
Multiple fracturing
UCS = 167 MPa
Shearing
UCS = 64 MPa
Axial splitting
UCS = 99 MPa
Fig. 13 Modes of failure under UCS test
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indicate that regression analysis can be successfully
employed as a predictive tool for the estimation of
UCS. The PLI has long been regarded as the best proxy
for the estimation of UCS, however, the highest
correlation is produced by UCS versus r
t
, which is
concurrent with the findings of Farah (2011). Further-
more, critical information about the rock of study can
be obtained by conducting V
p
test, allowing a better
understanding of the structure and behaviour of the
rock. As such, where critical information is required,
estimation of the UCS should not be relied on a single
index tests, but rather, several index tests should be
conducted to provide a better understanding of the
behaviour of the rock, and as such the UCS. The
equations produced in the current study can therefore
be used to predict the value of UCS for granitoid rocks
of KwaZulu-Natal.
Although there are numerous empirical equations
that have been proposed in previous studies which
have strong correlations, from the 65 equations used to
estimate the value of UCS, only 11 were able to
estimate UCS values that were close to that tested in
the lab. The reasons for this are that these equations
were developed in terms of the conditions of the
specific study and specific rock type. This indicates
that empirical equations should be used to allow
estimates of the UCS at the preliminary stages of a
project to allow estimates of the requirements for the
project. Thereafter the appropriate detailed testing
should be conducted.
6 Conclusion
There are many factors that influence the strength of a
rock. Subjecting it to the influence of a single property
or parameter may result in erroneous values, espe-
cially when reliable representative results are required.
The UCS can be sufficiently estimated with the aid of
simple index tests. However, the subject of estimation
is dependent on the in situ conditions and the rock
type, with various rock types producing a range of
UCS value. Thus, the geological origin and type of
rock (mineralogical composition) influences the
strength and should be taken into consideration when
estimating the strength of granitoid rocks, especially
with regards to the relationship between UCS and V
p
.
Furthermore, the study shows that the shape of
samples and direction of testing will affect calculated
estimates. Therefore, each test should be adopted with
care and an understanding of the potential accuracy
risks associated with each index test.
None of petrographic characteristics of the rock
individually control the strength of the granitoid rocks.
Each sample exhibited similar mineralogical compo-
sitions, but differed in mineralogical volumetric
percentage, grain size and texture, in some cases on
a microscopic scale. Therefore, it is a combination of
factors which appear to collectively contribute to
determine the rock strength.
Although the rocks have different volumetric
percentages of minerals, and thus may be subdivided
into different forms of granitoid rocks based on
various classification schemes, the UCS values fall
within the range of those that are characterized as
‘‘high strength’’ rocks when classified according to the
ISRM (2007) UCS strength classification. The charts
and equations produced in the study follow the trends
of published literature. It therefore provides additional
validation curves for the adopted testing methods and
adds to the existing correlations in literature.
It is suggested that the equations derived from this
study can be used during the preliminary stage of
design where detailed data is not easily accessible. The
proposed equation could serve as an indicator to
estimate the general correlation trend of UCS. Yet, the
results of the current investigation give further insight
into the controlling factors of the strength of the
granitoid rocks, where the strength of a rock is a
multidimensional parameter.
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