Journal of Rock Mechanics and Geotechnical Engineering 17 (2025) 1889e1905

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Journal of Rock Mechanics and

Geotechnical Engineering
journal homepage: www.jrmge.cn

Review

A review of test methods for uniaxial compressive strength of rocks:

Theory, apparatus and data processing
Wei-Qiang Xie a, b, *, Xiao-Li Liu a, b, **, Xiao-Ping Zhang c, Quan-Sheng Liu c, En-Zhi Wang a
a
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, China
b
Yunlong Lake Laboratory of Deep Underground Science and Engineering, Xuzhou, 221000, China
c
The Key Laboratory of Safety for Geotechnical and Structural Engineering of Hubei Province, School of Civil Engineering, Wuhan University, Wuhan,
430072, China

a r t i c l e i n f o a b s t r a c t

Article history: The uniaxial compressive strength (UCS) of rocks is a vital geomechanical parameter widely used for rock
Received 12 December 2023 mass classification, stability analysis, and engineering design in rock engineering. Various UCS testing
Received in revised form methods and apparatuses have been proposed over the past few decades. The objective of the present
29 March 2024
study is to summarize the status and development in theories, test apparatuses, data processing of the
Accepted 14 May 2024
Available online 23 May 2024
existing testing methods for UCS measurement. It starts with elaborating the theories of these test
methods. Then the test apparatus and development trends for UCS measurement are summarized, fol-
lowed by a discussion on rock specimens for test apparatus, and data processing methods. Next, the
Keywords:
Uniaxial compressive strength (UCS)
method selection for UCS measurement is recommended. It reveals that the rock failure mechanism in
UCS testing methods the UCS testing methods can be divided into compression-shear, compression-tension, composite failure
Test apparatus mode, and no obvious failure mode. The trends of these apparatuses are towards automation, digitiza-
Data processing tion, precision, and multi-modal test. Two size correction methods are commonly used. One is to develop
empirical correlation between the measured indices and the specimen size. The other is to use a standard
specimen to calculate the size correction factor. Three to five input parameters are commonly utilized in
soft computation models to predict the UCS of rocks. The selection of the test methods for the UCS
measurement can be carried out according to the testing scenario and the specimen size. The engineers
can gain a comprehensive understanding of the UCS testing methods and its potential developments in
various rock engineering endeavors.
© 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This
is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/
4.0/).

1. Introduction 2020; Zhang et al., 2021a). The UCS is also a vital geomechanical
parameter in evaluation of rock mass classification during tunnel
The uniaxial compressive strength (UCS) of rock is one of the key excavation (Gong and Zhao, 2007; Yagiz, 2008; Xie et al., 2021,
parameters determining the mechanical behavior and failure 2023a, 2023b; Cai et al., 2022, 2023). Accurate and effective eval-
characteristics of rocks under loading/unloading conditions uation of the UCS is critically important for the design and con-
(Hajiabdolmajid and Kaiser, 2003; Yagiz, 2008; Yarali and struction of rock engineering. On the contrary, inaccurate
Kahraman, 2011; Tan et al., 2016; Xia et al., 2019; Meng et al., evaluation of the UCS would lead to excessive support (or insuffi-
cient support), resulting in economic waste, or even engineering
accidents.
The UCS is also a significant parameter for characterization of
* Corresponding author. State Key Laboratory of Hydroscience and Engineering, the mechanical properties of the rock/rock mass (Zhang et al.,
Tsinghua University, Beijing, 100084, China.
2011). In scientific research, the UCS is useful to analyze the me-
** Corresponding author. State Key Laboratory of Hydroscience and Engineering,
Tsinghua University, Beijing, 100084, China. chanical and fatigue behavior of rocks (Alizadeh et al., 2023; Haeri
E-mail addresses: xwqwhu@163.com (W.-Q. Xie), xiaoli.liu@tsinghua.edu.cn et al., 2023). A series of experiments and numerical simulations
(X.-L. Liu). based on uniaxial compression test have been carried out over the
Peer review under responsibility of Institute of Rock and Soil Mechanics, Chi- past decades to study the mechanical failures (Zhang and Wong,
nese Academy of Sciences.

https://doi.org/10.1016/j.jrmge.2024.05.003
1674-7755/© 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
W.-Q. Xie, X.-L. Liu, X.-P. Zhang et al. Journal of Rock Mechanics and Geotechnical Engineering 17 (2025) 1889e1905

2012; Liu et al., 2021; Fu et al., 2022). When stress is applied to a 2. Test methods for predicting UCS of rocks
rock, the micro-cracks initiate from the pores of the rock structure
and, after coalescing with one another, they tend to build a fracture The rock failure mode is an important characteristic of rock
plane which leads to rock failure. Therefore, one of the most under loading (Hoek and Martin, 2014; Haeri et al., 2020). It not
important characteristics of rocks is the fracture. These fractures only reflects the stress distribution, but also shows the influence of
have various applications in field, such as rock fragmentation and different test conditions on rock deformation and failure. Table 1
blasting, tunneling, hydraulic fracturing, reservoir characteriza- shows that a compressive stress is applied to rock specimen in
tions, and slope stability analysis (Abdollahipour and Marji, 2017; almost test methods (except the physical index tests). Thus,
Fu et al., 2022). The recognition of micro-cracks and crack orien- compression is an essential process in these methods. The failure
tation are of major concern to rock fracture engineers since it modes of these test methods are summarized in Fig. 1. There are
contributes to a better understanding and design of geo- four modes among the 19 test methods (Xie et al., 2023c), including
mechanical projects. In rock engineering, the UCS is a key param- compression-shear failure mode, compression-tension failure
eter to determine the compressive strength, which is widely used mode, composite failure mode, and no obvious failure mode. The
in numerical modeling, geophysical prospecting, geomechanics, tensile stress is presented in the test although it does not cause rock
and rock breaking engineering (Yagiz, 2008; Zhang et al., 2021b; specimen failure (Sonmez and Tunusluoglu, 2008). It is worth
Xie et al., 2023c). The UCS testing methods are beneficial for the noting that the rock specimen is broken due to the main function of
mechanism study because most of these methods can reflect the the mode. It does not mean that the failure mode is the only one in
anisotropy of rock mass (Khanlari et al., 2014; Zhang et al., 2016). the testing process. For example, the rock specimen in block punch
Thus, application of the UCS and UCS testing methods is signifi- index test fails mainly due to the compression-shear stress.
cantly important in rock mechanics and engineering practice.
Procedures for direct measurement of a precise UCS in labora- 2.1. Compression-shear failure mode
tory have been standardized by some societies, such as the Inter-
national Society for Rock Mechanics and Rock Engineering (ISRM) Compression-shear failure mode refers to as a type of failure
(ISRM, 1979). The standard direct method seems to be relatively mode in rock mechanics where rocks experience both compressive
simple. However, it is comparably expensive, time-consuming, and and shear stresses simultaneously (Cai and Liu, 2009; Yin et al.,
demands precise core specimen preparation (Szwedzicki, 1998a; 2021, 2023). This failure mode typically occurs when rocks are
Kahraman, 2001; Selçuk and Kayabali, 2015; Tang et al., 2021; Xie subjected to a complex stress state, involving both shear stresses
et al., 2021). In addition, there are difficulties to acquire the along the rock mass and compressive stresses perpendicular to
required quality specimens in some cases as preparation of the these shear stresses. Rock specimens experience axial compression,
standard cylindrical rock specimens in weak to very weak rock is leading to concentrated compressive stresses along the axial di-
quite difficult (Chang et al., 2006). rection of the rock specimen. Simultaneously, during loading, rocks
For this, evaluation of the intact rock/rock mass UCS trends to may undergo shear stresses due to external forces in the horizontal
use the indirect testing methods in engineering practice, such as direction or intrinsic structural properties (Arora and Mishra, 2015;
point load test (Broch, 1983; Singh et al., 2012; Kahraman, 2014; Liu Li et al., 2022).
et al., 2017), block punch index test (Ulusay and Gokceoglu, 1997; Under the compression-shear failure mode, shear fractures
Aksoy et al., 2011; Roghanchi and Kallu, 2014; Kahraman et al., develop within the rock specimen along the intersecting planes,
2016; Khajevand and Fereidooni, 2019), impact strength test creating a complex network of fractures (Miller and Sikarskie, 1968;
(Kahraman, 2001; Fener et al., 2005), indentation test (Szwedzicki, Pang et al., 1989). Shear fractures may intersect within the rock,
1998b; Haftani et al., 2013; Jeong et al., 2015; Cheshomi et al., 2017; forming a network of fractures that can contribute to the structural
Kitamura and Hirose, 2017; Xie et al., 2021), and single particle load breakdown of the rock mass. In some regions, the rock may expe-
test (Cheshomi and Sheshde, 2013; Cheshomi et al., 2015). All these rience fragmentation, especially under high pressures, resulting in
direct and indirect test methods are summarized in Table 1. For cracking and particle separation (Lundberg, 1974).
more details about these methods, the readers can refer to as the Fig. 2 shows the indentation test. In this figure, a compacted
Appendix. Most of the indirect methods, including point load test, fracture zone is generated under the normal loading. Simulta-
single particle load test, and indentation test, require precise pre- neously, lateral extrusion pressure near specimen surface is formed
pared specimens or rock samples with small sizes. The main ad- by the indenter with specific geometry (Benjumea and Sikarskie,
vantages of the indirect methods are of practicability, portability, 1969; Lundberg, 1974). Then shear failure will occur and new rock
and cost-effectiveness, and they employ quick and simple proced- fragmentation will be formed once the stress status at the slip
ures for widespread usability (Selçuk and Kayabali, 2015). They surface exceeds the shear strength of rock. In this process, the shear
usually do not require complicated specimen preparation, such as failure may occur multiple times, i.e. the force-penetration curve
the ultrasonic pulse velocity tests (Khandelwal, 2013; Mishra and will produce local force drop. Subsequently, the indenter continues
Basu, 2013) and the Schmidt hammer rebound (Fattahi, 2017). to invade the rock. Finally, a large force drop is formed. This theory
As shown in Table 1, the test purpose and test index are different can well explain the failure mechanism of uniaxial compression
from each other. Even though many indirect methods have been test, indentation test, block punch index test, and cylindrical punch
proposed to evaluate the UCS of different rock types, the engineers index test.
may be confused about which indirect test method should be used
to estimate the rock UCS when required cores are unavailable. 2.2. Compression-tension failure mode
Comprehensive review has been rarely reported to explain the
theory, test apparatus, data processing method, and application of Compression-tension failure mode refers to as a failure mode in
these indirect test methods. It is significantly important to help rock mechanics where rocks experience both compressive and
engineers and researchers to understand the differences of the tensile stresses simultaneously (Nemat-Nasser and Horii, 1984).
above-mentioned 19 test methods. The objective of the present This failure mode typically occurs when rocks are subjected to a
review is to summarize the status and development in theories, test complex stress state involving both compressive stresses along
apparatuses, data processing and method selection of the existing certain directions and tensile stresses along other directions. Rock
testing methods for evaluation of the UCS of rocks. specimens experience axial compression, leading to concentrated
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Table 1
The direct and indirect test methods for the UCS of rock.

No. Test method Abbreviation Test philosophy Test index Index type

1 Laboratory uniaxial LUCT Cylindrical rock specimen is compressed under loading planes. The force-penetration Uniaxial Strength
compression test curve is recorded compressive
strength
2 In situ uniaxial compression IUCT Required rock specimen is compressed under loading planes. The force-penetration Uniaxial Strength
test curve is recorded compressive
strength
3 Point load test PLT Regular/irregular rock specimen is loaded by two conical indenters. The failure force Point load strength Strength
and fracture surface area are recorded
4 Block punch index test and BPIT/CPIT Cylindrical rock specimens are compressed by a punching block/cylinder. The failure Cylindrical punch Strength
cylindrical punch index test force and shear surface area are recorded index
5 Core strangle test CST Cylindrical rock specimen is circumferentially strangled in the middle. The failure force Core strangle Strength
and fracture surface area are recorded index
6 Indentation test IT Required rock specimens are loaded by a specific indenter. Force-penetration curve is Indentation Hardness,
recorded Indices Force/
penetration
7 Schmidt hammer rebound SHRT Rock specimen with a flat surface is hammered by Schmidt hammer. The rebound Schmidt hammer Hardness
test height of the Schmidt hammer is recorded rebound value
8 Scratch test ST Required rock specimen is scratched by a cutting element. The scratch depth, length Scratch depth, Hardness
and cutter wear are recorded length and cutter
wear
9 Shore hardness test SHT Rock specimen with a flat surface is hammered by a diamond-tipped hammer. The Shore hardness Hardness
relative rebound height of a diamond-tipped hammer that drops freely from a fixed
height onto the surface of a specimen
10 Leeb hardness test LHT An impact body from the diamond-tipped or tungsten carbide ball is applied to the Leeb hardness Hardness
surface of the specimen vertically
11 Abrasion hardness test AHT Rectangular rock specimen is loaded by different abrasion device. The abrasion value is Abrasion hardness Hardness
recorded
12 Cerchar abrasivity index CAIT Rock specimen is scratched 10 mm by a steel pin with a specific quality and geometry. Cerchar abrasivity Hardness
test A wear surface of 1/10 mm at the steel pin is recorded index
13 Impact strength test IST A 1.81 kg plunger that drops freely from a 305-mm height is used to impact the Impact strength Size
fragments of rocks 20 times. The number of fines below 3.18 mm is considered as the index distribution
impact strength index
14 Slake durability test SDT Rock specimen is processed by drying and wetting processes. The slake durability index slake durability Weight
is the percentage ratio of final to the initial dry weight of rock in the drum index
15 Needle penetration test NPT1 Rock is penetrated by a needle. The force-penetration curve is recorded Needle Force/
penetration index penetration
16 Nail penetration test NPT2 Rock specimen is shotted by a gasnailer. The depth of nail penetration is recorded Nail penetration Penetration
17 Single particle load test SPLT Spherical rock specimen is compressed by loading planes. The force-penetration curve Single particle Force
is recorded compression
strength
18 Ultrasonic pulse velocity UPVT It employs the principle of calculating the travel speed of the ultrasonic pulses through Ultrasonic pulse Physical
test a material medium by two sensors velocity index
19 Density and porosity tests DT/PT These parameters can be acquired by the corresponding physical tests Rock density, Physical
effective porosity index

compressive stresses along the axial direction of the rock specimen. 2.3. Composite failure mode
During the loading process, specimens may undergo tensile
stresses due to external forces or intrinsic structural properties. Rock frequently fails due to a complex status in the UCS testing
Tensile stresses act on specific planes within the rock specimen. methods. As mentioned above, rock specimen is broken due to the
Under the compression-tension failure mode, compression main function of the mode. It does not mean that only one mode
fractures may develop within the rock mass, particularly along present in the test. The rock failure mechanism in most tests can be
planes subjected to compressive stresses. Tension fractures may an integrated reflection of compression-shear and compression-
also occur in regions where tensile stresses are dominant, resulting tension failure modes, i.e. composite failure modes. The failure
in cracks or fractures that propagate perpendicular to the applied modes dominated by different rock areas and loading stages are
forces. The combination of compression and tension can lead to often different (Xie et al., 2023c). Moreover, the rock failure
complex fracture patterns, with both compression and tension mechanism is also related to the geometry of test apparatus,
fractures interacting within the rock mass. Taking the indentation loading type, confining pressure, and rock properties (Haftani et al.,
test as an example, Lawn and Swain (1975), Swain and Lawn (1976), 2015; Fang et al., 2019; Xie et al., 2021).
and Lawn and Evans (1977) proposed a rock breaking mechanism Portions of the rock specimens may experience shear failure,
model according to the rock crack propagation. As shown in Fig. 3, characterized by the development of shear cracks along pre-
the rock failure under indentation test can be divided into six existing planes or weaknesses within the rock mass. Simulta-
stages: (1) formation of an inelastic deformation zone under the neously, other parts of the rock may undergo tensile failure,
indenter, (2) initiation of intermediate crack, (3) intermediate crack forming tensile cracks or fractures. These fractures are often asso-
propagation, (4) intermediate crack closure under unloading, (5) ciated with the inherent structure and fracture systems within the
initiation of lateral crack, and (6) propagation and connection of rock specimen (Yu, 1982; Xie et al., 2021; Li et al., 2023). Shear and
lateral crack. tensile cracks can interact, leading to the formation of a more
intricate fracture network. The interaction between these types of
cracks influences the overall failure pattern. Different areas within

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Fig. 1. Failure modes of the test methods for UCS evaluation. (a) Uniaxial compression test, (b) Point load test, (c) Block punch index test and cylindrical punch index test, (d) Core
strangle test, (e) Indentation test, (f) Scratch test, Cerchar abrasivity index test and Abrasion hardness test, (g) Impact strength test, (h) Needle penetration test, (i) Nail penetration
test, (j) Single particle load test, and (k) No obvious failure mode, including Schmidt hammer rebound test, Shore hardness test, Leeb hardness test, slake durability test, ultrasonic
pulse velocity test, density and porosity tests. Red lines are the failure fractures after tests. The shapes of the tested specimens are cylindrical, spherical, square, and irregular.

Fig. 2. Failure modes of indentation test under conical indenter loading. (a) The schematic diagram of the compression-shear model (after Miller and Sikarskie, 1968), and (b) the
mechanical model for compression-shear failure mode (after Pang et al., 1989). d1 is the depth of penetration pit. d2 is the maximum depth of fracture surface. q is the half angle of
the indenter. h1 is the depth indenter tip. j is the angle of fracture surface. b is the half length of the indenter contacted with rock surface. T is the shear force, and N is the normal
force in fracture surface. 4 is internal friction angle of rock.

more pronounced tensile failure. This is a result of the complex

stress distribution. The composite failure mode is characterized by
a non-uniform distribution of stresses across different directions
within the rock. Some regions may experience higher shear
stresses, while others might undergo significant tensile stresses
(Kou, 1995). The formation and propagation of cracks in this com-
posite failure mode are influenced by the intrinsic phys-
icomechanical properties of the rock, including strength, structure,
and geological characteristics.
Fig. 4 shows a typical composite failure mode under conical
indentation, which is proposed by Kou (1995). The specimen is
divided into five zones after indentation test, including rock broken
Fig. 3. Compression-tension failure mode of rock specimen under indentation test zone, intermediate crack zone, radial crack zone, lateral crack zone,
(after Lawn and Swain, 1975). The blue semicircle is the high-stress area. The pale blue and intact zone. This model can serve for general use in various
zone is the fracture. The purple zone is debris. kinds of rocks with different diameters of the spherical indenter.

the rock may experience different types of failure, with some re- 2.4. No obvious failure mode
gions undergoing predominant shear failure and others exhibiting
Some of the abovementioned methods are scatheless tests,
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apparatuses is expressed by the capacity of force, penetration, or

the kinetic energy before triggering, as shown in Table 3.
To carry out direct and indirect tests for UCS evaluation, the
corresponding test apparatuses are developed. For this, researchers
have developed different apparatuses for the same test. For
example, various test apparatuses have been proposed to carry out
point load test (see Fig. 5). Fig. 5a and b shows the PLT apparatuses
in 1970s. It displays that these apparatuses are portable. The testing
data are usually recorded manually. A computer is utilized in Fig. 5c,
which can record the rock failure data automatically. The similar
function can be realized by the test apparatus in Fig. 5d. Moreover,
it can continuously record the force and the corresponding pene-
tration along with time throughout the PLT process (Basu and
Fig. 4. Rock breaking mechanism under the spherical indenter (after Kou, 1995). Kamran, 2010). The entire force-penetration curve can be recor-
ded by the apparatus in Fig. 5e. In addition, it provides continuous
loading automatically in an electric control (Zhao et al., 2017). To
including the SHRT, SHT, LHT, SDT, UPVT, DT and PT. In these tests,
acquire more information about rock failure in PLT, researchers
no obvious failure can be found in the rock specimen. Normally, the
equip the test apparatus with acoustic emission device and high-
non-destructive test methods are good for the sample (Yurdakul
speed camera (Fig. 5f).
and Akdas, 2013). However, there are two reasons that limit the
The development trends of these test apparatuses include high
wide application of these methods. On one hand, the required
levels of automation, digitization, precision, and multi-modal test
indices were found poorly related to the UCS of rocks (Atkinson,

lu and Çelik, 2017). On the other hand, this no to improve test efficiency, accuracy, and reliability of data inter-
1993; Çobanog
pretation (Xie et al., 2023c). At the same time, concerns about
obvious failure mode is different from the destructive test, such as
environmental protection and sustainability may also drive the
uniaxial compression test. Schmidt hammer rebound test, Leeb
development of testing methods and equipment more environ-
hardness test, and Shore hardness test are proposed to evaluate the
mentally and friendly. These trends reflect the overall direction of
rock hardness, rather than strength (Bamford et al., 1978; Çelik and

lu, 2023; Kong and Shang, 2018). To analyze the differ- development in the field of technology and engineering. As science
Çobanog
and technology continue to advance, the test apparatuses for UCS
ences between the compression-shear failure mode, compression-
measurements will continue to evolve to meet the increasingly
tension failure mode, composite failure mode and no obvious fail-
complex and diverse engineering needs:
ure mode, the characteristics of these methods are summarized in
Table 2.
(1) Digitalization and automation. There is a trend toward digital
data collection and automated testing procedures to enhance
3. Test apparatuses for UCS evaluation efficiency, accuracy, and repeatability, as shown in Fig. 5.
(2) High precision. Advanced and more accurate sensor tech-
3.1. Development trends of test apparatuses nologies may be introduced to precisely measure stress,
strain, and other critical parameters. Better simulation of the
Researchers have developed various test apparatuses to perform working conditions of rocks in practical applications can be
the corresponding tests for rock properties. The main information realized, such as deep underground, high-temperature, and
about these test apparatuses is summarized in Table 3. For more high-pressure environments.
details, please refer to as Appendix. It shows that the direct test (3) Multi-modal testing. The development of multi-modal
apparatuses for UCS evaluation are larger in size and heavier in testing methods combines different types of tests to
weight than the indirect test apparatuses. This is consistent with comprehensively assess the mechanical properties of rocks.
the original intention of these indirect test methods (Karaman Testing equipment may become more versatile, suitable for
et al., 2015; Mishra and Basu, 2012; Selçuk and Kayabali, 2015). different types and scales of rock samples to meet a wide
Generally, the 17 indirect test apparatuses are portable. The NPT1 range of research and engineering needs.
apparatus has the minimum mass (approximately 1 kg). In addi- (4) Environmental and sustainability focus. Equipment designs
tion, the review shows that the loading type of the test apparatuses may pay attention to environmental friendliness and sus-
can be divided into electric control and manual control. There are tainability, aiming to minimize the impact on the
force control and penetration control types in electric control (Xie environments.
et al., 2023c). The manual control contains the instantaneous and (5) Strong applicability. The development of smaller, lightweight
non-instantaneous controls. For example, the PLT is frequently testing devices is to facilitate testing in the field in engi-
performed manually. It requires 10e60 s to fail. Thus, the loading neering practice. The application of advanced data process-
type of the PLT is non-instantaneous control. While that of the ing techniques and artificial intelligence algorithms aim to
SHRT is instantaneous control. The testing process is not controlled optimize the interpretation and application of test results.
once the test starts. Accordingly, the loading range of the test

Table 2
Summary of the failure mechanism of the 19 test methods.

Mode Method Characteristic

Compression-shear failure mode BPIT, CPIT, ST, AHT, CAIT Rock specimen under compression fails due to shear stress
Compression-tension failure mode PLT, CST, NPT1, SPLT Rock specimen under compression fails due to tensile stress
Composite failure mode LUCT, ICUT, IT, IST, NPT2 Rock specimen under compression fails due to coupling of shear and tensile stresses
No obvious failure mode SHRT, SHT, LHT, SDT, UPVT, DT/PT No obvious failure can be found in rock specimen

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Table 3
Characteristics of the test apparatuses for direct/indirect test methods.

Test Apparatuses size Apparatuses Loading type and rate Loading range Source
method (mm
mm
mm) weight (kg)

LUCT 800
500
1500 1000 0.5e1.0 MPa/s 0e2000 kN ASTM (2014)
IUCT 1000
1000
2000 4500 0.15 mm/min 0e4800 kN Bieniawski and Bernede
(1979)
PLT 400
100
500 30 Manual, time to failure within 10 15e100 mm ISRM (1985)
e60 s
BPIT/CPIT 400
100
500 25 Manual, time to failure within 10 0e10 mm Ulusay et al. (2001)
e60 s
CST 1000
300
350 200 Motor-driven, time to failure Rock specimen with 200 MPa can be strangled Yilmaz (2009)
within 10e60 s
IT 200
150
450 20 Manual, 0.002e0.01 mm/s 0e250 kN Xie et al. (2023a)
SHRT 100
100
300 2 Manual, triggerable 0.735 N m and 2.207 N m Karaman and Kesimal
(2015a, b)
ST 1000
400
500 100 4 mm/s 0e4000 N Richard et al. (2012)
SHT 200
200
500 10 Manual, triggerable 0e140 mm Çobanog
lu and Çelik
(2017)
LHT 100
100
300 2 Manual, triggerable 0.011 N m Ghorbani et al. (2023)
AHT 1200
600
1000 300 75 r/min (294 ± 3) N Çobanog
lu and Çelik
(2017)
CAIT 250
250
400 15 1 mm/s 0e70 N Bamford et al. (1978)
IST 250
250
400 5 Manual, triggerable A 1.81 kg plunger that drops freely from a Evans and Pomeroy
305-mm height (1966)
SDT 1000
500
1000 60 e e Singh et al. (2005)
NPT1 50
50
200 1 e 0e100 N, 0e10 mm Ulusay et al. (2014)
NPT2 400
100
500 10 Manual, triggerable 130-J power Kayabali and Selcuk
(2009)
SPLT 400
100
500 80 0.77 N/s Rock specimen with 300 MPa can be tested Cheshomi and Sheshde
(2013)
UPVT 400
400
200 15 2000e6000 m/s e Mishra and Basu (2013)
DT/PT 200
200
100 5 e e Mishra and Basu (2013)

Fig. 5. Development of PLT apparatus. (a) Apparatus in Broch and Franklin (1972), (b) apparatus in Rusnak and Mark (1977), (c) apparatus in Basu and Aydin (2006), (d) apparatus in
Basu and Kamran (2010), (e) apparatus in Zhao et al. (2017), and (f) apparatus in Khadivi et al. (2023).

(6) Global standardization. The promotion of global standards is the past decades (Haftani et al., 2015; Kong et al., 2021; Xie et al.,
realized to ensure consistency and comparability of testing 2021). These specimens are summarized in Table 4. Generally,
equipment internationally. these specimens can be divided into regular and irregular speci-
mens according the specimen shape. The regular specimens
include cylindrical, prismatic, cubic, and spherical ones. The irreg-
3.2. Rock specimen for test apparatuses ular specimens are normally collected from the engineering prac-
tice. In addition, these specimens can roughly be divided into three
To carry out the direct/indirect tests, the corresponding rock classes: 100 mm class, 101 mm class, and 102 mm class according to
specimens should be firstly prepared, which is suitable for the test the specimen size (Xie et al., 2023c).
apparatuses. A great number of specimens have been tested over The regular specimens are frequently cut from the irregular

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Table 4
Information about the rock specimens used in the direct and indirect test methods.

Test Specimen shape Specimen size (mm) Specimen Rock strength Source
method number (MPa)

LUCT Cylindrical h 5 5 ASTM (2014)

d  54 mm, 2:5   3:0
d
IUCT Rectangular or cylindrical 300 mm  l w  1220 mm 3 3e50 Van Heerdan (1974)
0:5  w=h  3:39
PLT Regular or irregular wz50 mm 10 1e280 ISRM (1985)
0:3w < d < w
l > 0:5d
BPIT/CPIT Cylindrical d ¼ 42 mm; 5 mm  h  15 mm 5 5 Ulusay et al. (2001)
CST Cylindrical d  25 mm; 25 mm  h  140 mm 9 10 Yilmaz (2009, 2010)
IT Regular or irregular 2e197.83 mm 4 1 Xie (2022, 2023a)
SHRT Rectangular (60e150)-mm cube 20 10 Demirdag and Altindag (2009)
ST Rectangular or cylindrical Unknown 3e10 1 Richard et al. (2012), Naeimipour et al. (2018)
SHT Rectangular 80,000 mm3 20 1 Altindag and Güney (2006)
LHT Rectangular or cylindrical 10000 mm2 10e20 5e280 Ghorbani et al. (2023)
AHT Rectangular 71 mm
71 mm
71 mm 32 3e350 Çobanog
lu and Çelik (2017)
CAIT Rectangular or cylindrical d ¼ 42 mm 5 3e350 Teymen (2020), Moradizadeh and Cheshomi
30 mm  h  50 mm (2021)
IST Rectangular or cylindrical 50 mm  d  100 mm 20 4e200 Evans and Pomeroy (1966)
50 mm  h  100 mm
SDT Regular or irregular Thin sections 9 5e100 Danaei and Fereidooni (2023)
NPT1 cylindrical, cubic or 40 mm
40 mm
40 mm 3e5 0.2e40 Ulusay et al. (2014)
prismatic
NPT2 Regular or irregular Adjacent two points are larger than 10 2e100 Kayabali and Selcuk (2009), Palassi and Emami
75 mm (2014)
SPLT Spherical d ¼ 2; 3; 4 mm 20 15 Cheshomi and Sheshde (2013)
UPVT Regular d ¼ 50 mm 10 15 Mishra and Basu (2013)
DT/PT Regular or irregular Unknown 3e5 18 Mishra and Basu (2013)

samples with large size. Thus, it is relatively expensive and time- 4. Data processing methods for UCS measurement
consuming to prepare rock specimens with regular shape, like cy-
lindrical (Szwedzicki, 1998a; Kahraman, 2001; Selçuk and Kayabali, 4.1. Test indices for UCS evaluation
2015; Tang et al., 2021; Xie et al., 2021). Compared to cylindrical
specimens, the rectangle or cubic specimens needed to be cut 6 To establish the relationships between the direct test methods
times from natural stones. In addition, it is difficult sometimes to and the indirect test methods, the first work is to quantificationally
acquire the regular specimens. For example, it is quite hard to characterize the testing result. As summarized in Table 5, the test
prepare standard cylindrical rock specimens in weak to very weak indices can be acquired by carrying out the corresponding tests. The
rocks (Chang et al., 2006). The rectangle or cubic specimen is pre- indirect test for UCS evaluation is also called index test (Tang et al.,
pared in some UCS testing methods for its test simplicity. For 2021). Then, the empirical correlations between the UCS and the
example, the sensors are required to be attached to smooth spec- determined indices can be established (see Appendix). The calcu-
imen surfaces to acquire the ultrasonic pulse velocity (Mishra and lation method of these indices can be divided into two types, i.e. the
Basu, 2013; Yilmaz et al., 2014). Moreover, rectangle or cubic ratio and single value. Most of these indices are the ratios of the
specimen is used to study the crack propagation for its smooth testing parameters. The single value includes Critical transition
surface (Lawn and Swain, 1975; Xie et al., 2023c). It is also useful to force (CTF) and Schmidt hammer rebound value (SHR). Moreover,
carry out three-dimensional confining pressure using cubic speci- these indices are frequently acquired from the force-penetration
mens (Fang et al., 2019). As for the irregular rock specimens, (or stress-strain) curve. As mentioned in Table 1, these test
additional measures are needed to fix them for the UCS testing indices can characterize not only the rock strength, but also the
methods. For example, the irregular rock specimens are fixed in box hardness and physical properties (Yagiz, 2009; Jeong et al., 2015;
using casting materials (Jeong et al., 2015; Xie et al., 2021). Meng et al., 2020; Zhang et al., 2021b; Noori et al., 2022).
Compared to the direct test methods, the specimens for indirect
test are relatively easier to acquire in engineering practice, such as 4.2. Size effect and size correction
irregular specimens for the PLT (Liu et al., 2017) and spherical
particles for the SPLT (Cheshomi et al., 2015). Frequently, to ensure The ISRM Standard (ISRM, 1979) stated that the diameter of the
the accuracy of the test data, more than one specimen is needed, as specimen should be related to the size of the largest grain in the
summarized in Table 4. It seems that the minimum number for rock by the ratio of at least 10 : 1. However, the engineers and re-
these tests is three, including the IUCT, NPT1, DT and PT. The suitable searchers may be confused about the details of the core size for the
rock strength required for the test method is also summarized in strength test. For this, numerous tests have been carried out on core
the table. The maximum represents the maximum rock UCS that specimens with different diameters for uniaxial compression tests,
can be tested by the test method. The application of the UCS range as shown in Fig. 6. The UCS increases first and then decreases as the
will be further discussed in Section 5.1. There is a minimum UCS for specimen diameter increases. The peak UCS is observed at a spec-
the test method because the required rock specimens are not imen diameter of 40e60 mm. The UCS keeps at a relatively stable
available when the rock UCS is lower than this minimum value level when specimen diameter is larger than 75 mm. In other
(Chang et al., 2006). words, the specimen diameter of sedimentary rocks for the uniaxial
compression test should be greater than 75 mm to obtain a stable
UCS.
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Table 5
The test indices acquired from the corresponding test methods.

Test Index Symbol Definition Value Source

method type

LUCT UCS sc Ratio of the peak load to the cross-sectional area of rock specimen Ratio ASTM (2014)
Elastic modulus E Slope of the linear segment in stress-strain curve Ratio ASTM (2014)
IUCT UCS sc Ratio of the peak load to the cross-sectional area of rock specimen Ratio Van Heerdan (1974)
PLT Corrected point Isð50Þ Value of Is that would have been measured by a diametral test with d ¼ 50 mm Ratio ISRM (1985)
load strength
BPIT Corrected block BPIc Value of BPI that would have been calculated from a failure load converted to a corrected load Ratio Ulusay et al. (2001)
punch index for a nominal 50 mm diameter and 10 mm thickness by multiplying BPI with the correction
factors for thickness and diameter
CPIT Cylindrical punch CPI Ratio of the peak load to the shear area of rock specimen Ratio Jalali et al. (2019)
index
CST Core strangle index CSI Ratio of the peak load to the cross-sectional area of rock specimen Ratio
Yilmaz (2009, 2010)
IT Indentation indices CTF Critical transition force (peak load) in force-penetration curve Value
Copur et al. (2003)
IM Slope of the linear segment in force-penetration Ratio
Xie et al. (2021, 2023a)
IHI Ratio of the peak load to the corresponding penetration Ratio
Szwedzicki (1998a)
SHRT Schmidt hammer SHR Rebound height of the Schmidt hammer Value
Demirdag and Altindag
rebound value (2009)
ST Scratch depth ds Scratch depth of the indenter under the loading condition Value Richard et al. (2012),
Naeimipour et al. (2018)
SHT Shore hardness Sh Relative rebound height of a diamond-tipped hammer that drops freely from a fixed height Value Altindag and Güney (2006)
onto the surface of a specimen
LHT Leeb hardness HLD Dividing the rebound velocity (Vr ) by the impact velocity (Vi ) Ghorbani et al. (2023)
AHT Abrasion hardness HA Ratio of the material loss to contact area or the abrasion depth of contact surface Ratio Çobanog
lu and Çelik (2017)
CAIT Cerchar abrasivity CAI 10
Ratio of the diameter of wear flatness to the unit correction factor Ratio Teymen (2020), Moradizadeh
index and Cheshomi (2021)
IST Impact strength ISI Number of fines below 3.18 mm Value Evans and Pomeroy (1966)
index
SDT Slake durability SDI Percentage ratio of final to the initial dry weight of rock in the drum Ratio Danaei and Fereidooni (2023)
index
NPT1 Needle penetration NPI Ratio of penetration force to the corresponding penetration Ratio Ulusay et al. (2014)
index
NPT2 Nail penetration p Penetration depth of nail in the rock specimen Value Kayabali and Selcuk (2009),
Palassi and Emami (2014)
SPLT Single particle SCS Peak load of the force-penetration curve Value Cheshomi and Sheshde
compression (2013)
strength
UPVT Ultrasonic pulse Vp Ratio of the specimen distance to the propagation time between two sensors Ratio Yilmaz et al. (2014)
velocity
DT Rock density r Ratio of the rock mass to rock volume Ratio Mishra and Basu (2013)
PT Effective porosity ∅ Ratio of the effective pore volume to the surface volume of the rock Ratio Mishra and Basu (2013)

Fig. 6. Influence of the specimen diameter on the UCS of sedimentary rocks. Data are from Hoskins and Horino (1969), Hawkins (1998), Thuro et al. (2001), Pells (2004), and
Masoumi et al. (2015).

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In engineering practice, to quickly obtain the strength of the developed through simple regression analysis, such as linear, po-
surrounding rocks, large or small specimens have always been used wer, logarithmic and exponential functions (Teymen, 2020; Tang
in the direct/indirect testing methods for measurement of the rock et al., 2021; Xie et al., 2021). In rock engineering, multiple regres-
strength (Haftani et al., 2014; Cheshomi et al., 2017; Anemangely sion analysis and soft computation techniques have also been used
et al., 2018). Thus, size correction is one of the challenging issues evaluate the UCS of rocks (Mishra and Basu, 2013). However, only
when using these testing methods to evaluate the rock strength. few multiple regression equations (Table 7) have been proposed to
Some of these testing methods, such as the LUCT, PLT and BPIT, have estimate the UCS. The possible reason is that the data of a specific
been standardized. Meanwhile, the corresponding size correction rock test are not available in the engineering practice. In addition,
procedures have been developed (Eberhardt, 2009; Ulusay, 2015). these multiple regression equations are usually developed by
Thus, the specimen size is often fixed, or the specimen size varies in combining the parameters acquired from the 17 indirect test
a small range. While some of the remaining indirect tests, such as methods. Thus, it is simpler to correlate the UCS with these ac-
the LHT, CST, IT, NPT2 and SPLT, are still of non-standard methods. quired parameters using simple regression.
Rock specimens with various sizes and shapes are frequently tested Nowadays, more and more intelligent methods are being used in
in these methods. Unfortunately, some different parameters have rock engineering due to the rapid development of computer tech-
been defined in the same test method (e.g. the CTF and IM obtained nologies (Sheremetov et al., 2005; Krishna et al., 2020; Otchere
from indentation test). To eliminate the potential influences of et al., 2021). These methods provide great help for the design,
various factors on the test results, the test procedures should be construction and running of rock engineering. In the measurement
unified. of rock strength, apart from the conventional statistical methods,
In Table 6, rock specimens used in the direct and indirect test soft computation techniques such as the artificial neural network
methods can be divided into two categories: regular specimens and (ANN), fuzzy inference systems (FIS), and other hybrid algorithms
irregular specimens. Different sizes can be obtained in these regular have also been proposed. This is attributed to the fact that soft
and irregular specimens. The testing results vary when specimens computation techniques are feasible, quick, and promising tools to
with different sizes were used. Usually, two size correction ap- solve various engineering problems, especially when the relation-
proaches are used to reduce the size dependence of the measured ships between the independent variables and dependent variables
parameters. One is to develop the empirical correlation between are unknown (Torabi-Kaveh et al., 2015; Armaghani et al., 2016;
the measured parameters and specimen sizes, such as the size Tang et al., 2021). A schematic diagram of soft computation tech-
correction procedure of the BPIT method. The other is to use a niques for the prediction of the UCS is presented in Fig. 7. A com-
standard specimen to calculate the size correction factor, such as mon disadvantage of these techniques is that a large data set of rock
the size correction procedure of the PLT method. Then the size- properties needs to be trained to ensure an accurate test result.
corrected strength index is a multiplication of the measured in- Recent studies on the estimation of the UCS using soft computation
dex and size correction factor. It is found that most of the UCS techniques are tabulated in Table 8. It should be noted that pre-
testing methods reviewed in the present study do not have clear sentation of new data set and training the data sets for the same
size correlation procedures. Further work can be continued by type of prediction problems are important due to difference in rock
applying these two size correction approaches to the remaining nature as it varies from place to place (Momeni et al., 2015a).
non-standard test methods. Table 8 also suggests that three to five input parameters, such as the
SHR, Vp and ∅ are commonly utilized in developing predictive
models of the UCS.
4.3. Multiple regression analysis and soft computation technique

Conventionally, empirical correlations between the UCS and the

parameters acquired from the 17 indirect test methods are

Table 6
Representative studies on the size effect and size correction of the measured UCS and other mechanical properties.

Test Source Specimen size Representative size

method correction

LUCT Hoek and Brown (1980), Kong et al. (2021) Cylinder or cuboid sc ¼ sc;50 ðd=50Þk
h
1 < < 3; 10 mm < d < 400 mm
d
PLT Broch and Franklin (1972), Brook (1977, 1980), Forster (1983), Thuro and Plinninger (2001), Regular or irregular blocks, tz50 mm Fp
Isð50Þ ¼ f 2 , f ¼
Kahraman (2014), Liu et al. (2017), Xie et al. (2021) De


D 0:45
e
50
BPIT, Schrier (1988), Ulusay and Gokceoglu (1997), Mishra and Basu (2012), Roghanchi and Kallu Cylinder, 10 mm < d < 54 mm, BPIc ¼
CPIT (2014), Kahraman et al. (2016), Jalali et al. (2019) 5 mm < t < 15 mm 3499D1:3926 t 1:1265 Ft;D
CST Yilmaz (2009,2010), Yilmaz and Yucel (2014) Cylinder, d ¼ 54 mm, h  25 mm e
IT Mateus et al. (2007), García et al. (2008), Haftani et al. (2014), Ahmadi Sheshde and Cheshomi Small cube specimens and irregular CTF pffiffiffiffiffiffiffiffiffiffiffi
CTFn ¼ ; S ¼ Ss =Si
(2015), Haftani et al. (2015), Cheshomi et al. (2017), Xie et al. (2021) blocks, 0:6 mm  w < 200 mm S
D100 CTF
CTFn ¼ p ffiffiffiffiffiffiffiffiffiffiffi
Dc Df
SPLT Cheshomi and Sheshde (2013), Cheshomi et al. (2015), Ashtari et al. (2019) Sphere, 2 mm  d  10 mm Multiple linear
regression, UCS-(SCS, d)

Note: h e height;d(D) e diameter;t e thickness; w e width; sc;50 - uniaxial compressive strength with s specimen diameter of 50 mm; k - correction factor; f - correction factor;
Fp - peak load; De - equivalent diameter of fracture surface; Ft;D - peak load; CTFn - corrected CTF; S - correction factor; Ss - particle surface; Si - indenter surface; D100 e 100; Dc
- equivalent dimeter of cross-sectional surface; Df - equivalent diameter of fracture surface.

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Table 7
Multiple regression equations developed from the indirect test results to predict the UCS of rocks.

Source Multiple regression equation R2

Gokceoglu and Zorlu (2004) UCS ¼ 0:0065Vp þ 1:468BPI þ 4:094Isð50Þ þ 2:418st  225 0.64
Karakus and Tutmez (2006) UCS ¼ 13:1Isð50Þ þ 0:89SHR  1:68Vp  35:9 0.77
Yilmaz and Yuksek (2009) UCS ¼ 1:863Isð50Þ þ 0:480SHR þ 7:97Vp þ 0:248wc  23:86 0.89
Monjezi et al. (2012) UCS ¼ 0:801SHR þ 0:423r  0:172∅  225 0.77
Mishra and Basu (2013) UCS ¼ e0:011BPIþ0:065Isð50Þ þ0:029SHR 0.91
Armaghani et al. (2015) UCS ¼ 69:505r þ 0:025Vp  0:479Qtz  1:439Plg  158:796 0.55
Torabi-Kaveh et al. (2015) UCS ¼ 24:727  0:024Vp þ 46:875r þ 3:661∅ 0.88
UCS ¼ 90  0:021Vp þ 3r3 þ 0:019∅3 0.93
Gomez-Heras et al. (2020) UCS ¼ 102:604
HL1:444
D
VP0:172
e2:807∅ 0.96
Benavente et al. (2021) UCS ¼ 1:411  1:683∅  4:14
103 Vp þ 0:221HLD þ 0:226mdr 0.91
Armaghani et al. (2016) UCS ¼ 10:817eSHR þ 0:0005Vp1:242 þ 23:274Isð50Þ  36:567 0.79
Khajevand and Fereidooni (2019) UCS ¼  18:61  0:23∅ þ 1:68SHR  0:002Vp þ 1:55Isð50Þ 0.72
UCS ¼ 3:58  1:83∅ þ 0:65SHR  0:002Vp þ 4:41BPI 0.82
Teymen (2020) UCS ¼ 16:55CAI  0:99SHR þ 25:55CRS  39:1 0.95

Note: BPI - block punch index; st - Brazilian tensile strength; wc - water content; Qtz - quartz content; Plg - plagioclase content; CRS - coefficient of rock strength; mdr -
micro-drilling resistance.

Fig. 7. Schematic diagram of soft computation techniques for the prediction of UCS.

Table 8 5. Method selection for UCS evaluation

Some recent studies on the prediction of UCS using soft computation techniques.

Source Technique Input R2 5.1. Method selection according to the testing scenario
Garret (1994) ANN SHR, Vp , Isð50Þ , ∅ e
Meulenkamp and Grima (1999) ANN HL , Sg , r, ∅ 0.95 Rock mass properties are usually measured in laboratory using
Singh et al. (2001) ANN PSV e the direct/indirect test methods. However, the laboratory measured
Gokceoglu and Zorlu (2004) FIS BPI, Vp , Isð50Þ , BTS 0.67 parameters cannot truly represent the properties of rock mass.
Zorlu et al. (2008) ANN Qtz, Sg , r, cc 0.76
These parameters sometimes provide the misleading information
Yilmaz and Yuksek (2009) ANFIS SHR, Vp , Isð50Þ , wc 0.94
Dehghan et al. (2010) ANN SHR, Vp , Isð50Þ , ∅ 0.86 for engineering practice. The rock parameters obtained from in situ
Monjezi et al. (2012) ANN-GA SHR, r, ∅ e tests are found to be the most accurate evaluation of strength
Rabbani et al. (2012) ANN BD, Sw , ∅ 0.96 characteristics of rocks (Nizametdinov et al., 2016). Some of the 17
Yagiz et al. (2012) ANN SHR, Vp , r, ∅, SDI 0.5
indirect test methods mentioned in Section 1 can be used to the in
Beiki et al. (2013) GA Vp , r, ∅ 0.83
Ceryan et al. (2013) ANN PSV, Vp , ∅, SDI 0.88
situ measurement of rock mass properties in field condition due to
Mishra and Basu (2013) FIS SHR, Vp , Isð50Þ , BPI 0.98 the simple test scenario and portable apparatus (Ulusay et al., 2014;
Yesiloglu-Gultekin et al. (2013) ANFIS Vp , BTS 0.68 Xie et al., 2023a). Some of these indirect test methods can be per-
Yurdakul and Akdas (2013) ANN SHR, Vp , Sh e formed in field but cannot be used as an in situ testing. The
Rezaei et al. (2014) FIS SHR, r, ∅ 0.95
remaining methods can only be performed in a laboratory condi-
Mohamad et al. (2015) PSO-ANN BD, Vp , Isð50Þ , BTS 0.97
Momeni et al. (2015b) PSO-ANN SHR, r, Vp , Isð50Þ 0.97 tion. Thus, these indirect test methods can be categorized into the
Torabi-Kaveh et al. (2015) ANN Vp , r, ∅ 0.95 following three different classes:
Armaghani et al. (2016) ICA-ANN SHR, Vp , Isð50Þ e
Fattahi (2017) SVR-ABC SHR e (1) Class I. The first class contains the IT, SHRT, ST, SHT, LHT, NPT1,
Heidari et al. (2018) FIS SHR, Vp , Isð50Þ , BPI 0.91
Saedi et al. (2019) FIS BPI, Vp , ∅, BTS e
NPT2 and UPVT. These test methods have the potential to be
Wang et al. (2020) RFA SHR, Vp 0.90 used as in situ tests for evaluation of the rock mass proper-
Ceryan and Samui (2020) ELM, MPMR ∅, SDI 0.96 ties, as shown in Fig. 8. Little or no specimen preparation is
Barham et al. (2020) BP-ANN SHR, BTS, Isð50Þ 0.99 needed when performing these tests in field. The corre-
BP-ANN Vp , r, SDI 0.94
sponding test apparatus can be in contact with the rock mass
Mahmoodzadeh et al. (2021) LSTM SHR, Vp , Isð50Þ , ∅ 0.94
directly.
Note: BTS - Brazilian tensile strength; BD - bulk density; PSV - petrography study
(2) Class II. The second class contains the PLT, IST, DT and PT.
values; cc - concavo convex; HL - equotip value; Sg - grain size; Sw - water satura-
tion; GA - genetic algorithm; PSO - particle swarm optimization; FIS - fuzzy infer-
Although these test methods cannot be used as in situ tests,
ence system; ANN - artificial neural network; SVR - support vector regression; ABC - they can be carried out in field easily owing to the simple test
artificial bee colony algorithm; ICA - imperialist competitive algorithm. and portable apparatus. Thus, rock blocks can be prepared for

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Fig. 8. Applications of the indirect test methods in the field. (a) Indentation test (Xie et al., 2023a), (b) needle penetration test (Kahraman et al., 2018), (c) scratch test (Naeimipour
et al., 2018), (d) Schmidt hammer rebound test (Goktan and Gunes, 2005), and (e) nail penetration test (Selçuk and Kayabali, 2015).

these tests. The acquired parameters are the indicators of It is important to understand the applicability of the 17 indirect
rock properties instead of rock mass properties. test methods when they are used for the UCS measurement in the
(3) Class III. The third class contains the BPIT/CPIT, CST, AHT, field/laboratory conditions. The UCS of rock specimens used in
CAIT, SDT and SPLT. These test methods can only be per- these 17 indirect tests is reviewed in Table 4. The applicable scopes
formed in a laboratory condition due to the preparation of of them are summarized in Fig. 9. For example, needle penetration
precise core specimens and comparably heavy and expensive test is useful to estimate the strength of soft rocks or rocks with a
equipment. low UCS, while the indentation test and scratch test show a
comparably wide range of applicability. Generally, almost all these

Fig. 9. Ranges of applicability of the 17 indirect test methods for the evaluation of UCS (modified after Ulusay and Erguler (2012)).

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Fig. 10. Two types of drill bit and the corresponding rock collected from the drilling process. (a) PDC bit for common drilling and the collected rock fragments, and (b) drill bit for
cores sampling and the collected rock cores.

test methods (except NPT1) can be used to estimate the strength of process. Both the regular rock specimens and irregular rock
rocks with UCS ¼ 10e100 MPa. Thus, the appropriate testing fragments can be prepared for indentation test (Haftani et al.,
method can be selected according to the testing scenario and rock 2013, 2014), as shown in Fig. 11. In addition, the collected
UCS. fragments can be processed to spherical specimens for the
single particle load tests (Cheshomi and Sheshde, 2013;
Cheshomi et al., 2015), as shown in Fig. 12. Although the DT
5.2. Method selection according to specimen size and PT methods are simple to estimate the UCS of rocks,
there are relatively large deviations between the estimated
It is a common and important work for drilling a cylindrical hole UCS and the actual UCS (Chang et al., 2006).
with a diameter of about 100 mm and a depth from hundreds to (2) Class II. Majority of the methods are only applicable in con-
thousands of meters using drilling machine. During the drilling dition B, i.e. rock cores are available. These test methods
process, the hydraulic rotary drilling can be carried out horizontally include the LUCT, BPIT/CPIT, CAIT, CST, PLT, UPVT, NPT2, ST,
or vertically. Commonly, two types of drill bits are used for different SHRT, SDT. Usually, specimens with larger dimensions ( 10
purposes. A polycrystalline diamond compact (PDC) bit (Fig. 10a) is mm) are used in these methods. The selection of these
used to assist the hydraulic rotary drilling. A coring bit (Fig. 10b) is methods for the measurement of the UCS depends on the
often used to collect rock cores for the various laboratory tests. length of the drilled cores. For example, it is hard to acquire
To understand the applicability of the direct and indirect test enough length for the LUCT in a weak rock formation. In this
methods in rock engineering, the core length is used as the key case, the BPIT/CPIT and CAIT may be the good alternatives to
factor. These test methods are categorized into three classes, as estimate the UCS. There will be more options as the core
summarized in Table 9. Condition A is the common drilling using a length increases.
PDC bit, where the fragments have a small size. Condition B is the (3) Class III. The IUCT, NPT1, SHT, LHT, IST and AHT methods are
sampling drilling using a core bit, where large fragments can be not applicable to the evaluation of the UCS in engineering
collected. drilling. As illustrated in Appendix, the NPT1 method is
acceptable to rocks having a UCS < 9.8 MPa. The remaining
(1) Class I. The IT, SPLT, DT and PT methods are applicable in both four methods usually use cuboid specimens with large sizes
condition A and condition B. In other words, these methods ( 100 mm) to estimate the UCS of rocks. Although these
can be carried out using both the small rock fragments and methods cannot be used in engineering drilling, they are
large rock cores. In condition A, many rock fragments with good options for UCS evaluation in mining science and
large or small dimensions can be collected from the drilling

Fig. 11. Rock specimens collected from drilling for indentation test. (a) Regular rock specimens, and (b) irregular rock specimens. Modified form Haftani et al. (2013, 2014).

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W.-Q. Xie, X.-L. Liu, X.-P. Zhang et al. Journal of Rock Mechanics and Geotechnical Engineering 17 (2025) 1889e1905

Fig. 12. Rock specimens collected from drilling for single particle load test. (a) The specimen preparation, and (b) rock specimens with different diameters after test. Modified from
Cheshomi et al. (2015) and Cheshomi and Sheshde (2013).

tunnel construction (Ulusay and Erguler, 2012; Gomez-Heras choice. In addition, there is a relatively low coefficient of determi-
et al., 2020). nation (CD) between the UCS and the density/porosity. In other
words, the DT and PT may have a greater scatter in the UCS mea-
The review shows that the IT, SPLT, DT and PT can be used as the surement than the IT and SPLT methods. Therefore, the DT and PT
suitable methods for evaluation of the rock UCS in common drilling are recommended as alternatives when the IT and SPLT methods
when rock cores are not available. Usually, the specimen prepara- cannot be carried out.
tion in the IT process is easier than that of the SPLT because the When rock cores are available, there are many options (Class II)
preparation of square specimen is easier than that of spherical for the UCS measurement. In this case, selection of the test method
specimen (Cheshomi et al., 2015). It can be found that the speci- can be carried out according to the actual core length, as listed in
mens in Fig. 12 are not exactly spherical. In addition, it shows that Table 10. The advantages and limitations of these test methods in
indentation test is more widely used in engineering practice than Class II are compared, including CD, number of tests, UCS range, test
the single particle load test method (Xie et al., 2021, 2023a; Yagiz, apparatus, and others (Table 10). The CD and UCS range about these
2009). Thus, the SPLT method is recommended as a second methods are from the literature (see Appendix). Generally, the
engineers can select the proper test method(s) for the UCS mea-
surement according to Tables 9 and 10.
Table 9
The applicability of the direct test methods and 17 indirect test methods in engi-
neering practice. 6. Conclusions and prospects
Method Condition A Condition B Core length (specimen shape)
Various UCS testing methods have been proposed over the past
IT √ √  2 mm
decades. It is hard for engineers to quickly understand the suitable
SPLT √ √  2 mm
method for UCS evaluation in engineering practice. The present
DT and PT √ √  10 mm
study provides a review of the test methods for measurement of the
BPIT/CPIT √ 10 mm
UCS, including the laboratory/in situ uniaxial compression tests and
CAIT √  10 mm
17 indirect test methods. It starts with elaborating the theories of
CST √  25 mm
PLT  30 mm
the test methods. Then, the test apparatuses for UCS evaluation are
√
UPVT  50 mm summarized, along with their development trends, followed by a
√
NPT2  75 mm discussion on rock specimens for test apparatuses. The data pro-
√
LUCT √ 100 mm cessing methods are highlighted. Subsequently, the method selec-
ST √  100 mm tion for UCS measurement is recommended. The following
SHRT √  110 mm conclusions can be drawn:
SDT √  30 mm
NPT1  30 mm (1) The rock failure in the UCS testing methods can be divided
SHT  100 mm (cuboid) into compression-shear, compression-tension, composite
LHT  100 mm (cuboid)
failure mode, and no obvious failure mode. The compression-
IST  100 mm (cuboid)
AHT  200 mm (cuboid) shear failure mode contains the BPIT, CPIT, ST, AHT, and CAIT.
IUCT  300 mm (cuboid) The compression-tension failure mode contains the PLT, CST,
Note: Condition A is the common drilling using a PDC bit. Condition B is the sam-
NPT1, and SPLT. The composite failure mode contains the
pling drilling using a core bit. √ means that the test method can be carried out in the LUCT, ICUT, IT, IST, and NPT2. No obvious failure mode con-
corresponding condition. tains the SHRT, SHT, LHT, SDT, UPVT, and DT/PT.
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W.-Q. Xie, X.-L. Liu, X.-P. Zhang et al. Journal of Rock Mechanics and Geotechnical Engineering 17 (2025) 1889e1905

Table 10
The comparison of the indirect test methods for UCS measurement in rock engineering drilling.

Method CD (R2) Number of tests UCS range (MPa) Test apparatus Note

BPIT/CPIT 0.784 5 5 BPT machine Portable

CAIT 0.800 5 3 70 N grinding wheel High precision requirements
CST 0.966 9  10 CST device Heavy, rock cores are needed
PLT 0.839  10 1 PLT machine Portable, low cost
UPVT 0.870 10  15 ultrasonic apparatus High-tech, regular rock specimens
NPT2 0.967  10 2 Gasnailer Professional in gasnailer
ST 0.569 3e10 1 Rock strength device Flat rock surface
SHRT 0.837  20  10 20 kg (L-type hammer) and 40 kg (N-type hammer) Heavy
SDT 0.397 9 5e100 Multiple test apparatus Complex test procedure, time-consuming, low CD

Note: CD is the coefficient of determination. It is the average value of the empirical correlations proposed in literature review. Details about CD and UCS range are presented in
Appendix.

(2) The development trends of the test apparatuses include (3) To improve the accuracy, reliability, and applicability of the
digitalization and automation, high precision, multi-modal proposed indirect test methods, the empirical correlations
testing, environmental and sustainability focus, strong should be validated through more tests using different rock
applicability, and global standardization. The specimen lithologies and specimen sizes. More studies are needed to
shape for test apparatuses is regular and irregular. The investigate the application of various test methods in rock
specimen size for these test apparatuses contains 100 mm engineering, especially the drilling operation.
class, 101 mm class and 102 mm class.
(3) Two size correction approaches are presented after the
literature investigation. One is to develop the empirical cor- CRediT authorship contribution statement
relation between the measured indices and the specimen
size. The other is to use a standard specimen to calculate the Wei-Qiang Xie: Conceptualization, Formal analysis, Investiga-
size correction factor. Three to five input parameters are tion, Writing e original draft. Xiao-Li Liu: Funding acquisition,
commonly utilized in developing predictive models of the Supervision, Writing e review & editing. Xiao-Ping Zhang: Vali-
UCS when soft computation techniques are used. Apart from dation, Writing e review & editing. Quan-Sheng Liu: Project
the simple regression, multiple regression analysis and soft administration, Resources. En-Zhi Wang: Supervision,
computation techniques have been also widely used to es- Visualization.
timate UCS of rocks owing to their merits.
(4) Two methods for test selection are commended. One is se- Declaration of competing interest
lection according to the testing scenario and rock UCS. The
reviewed 17 indirect test methods can be categorized into The authors declare that they have no known competing
three different classes. Class I methods can be used as in situ financial interests or personal relationships that could have
measurements of the UCS of rock masses. Class II methods appeared to influence the work reported in this paper.
can be carried out in the field easily but cannot be used as in
situ measurements. Class III methods can only be performed
Acknowledgments
in the laboratory conditions. The other is selection according
to specimen size.
The authors would like to thank the National Natural Science
Foundation of China (Grant Nos. 52308403 and 52079068), the
For the direct and indirect test methods for measurement of the
Yunlong Lake Laboratory of Deep Underground Science and Engi-
UCS, the following recommendations are proposed for further
neering (No. 104023005), and the China Postdoctoral Science
research:
Foundation (Grant No. 2023M731998) for funding provided to this
work.
(1) More work on the size effect and size correction method are
recommended to obtain more promising evaluation of the
Appendix A. Supplementary data
UCS using specimens with large ranges of size and shape
drilled from wellbore. The test apparatuses of the indirect
Supplementary data to this article can be found online at
test methods should be optimized to realize the goals of
https://doi.org/10.1016/j.jrmge.2024.05.003.
higher levels of automation, digitization, precision, and
multi-modal test to improve test efficiency, accuracy, and
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Engineering 169 (2018) 157e166]. J. Petrol. Sci. Eng., vol. 211, 109462. of uniaxial compressive strength of sandstones using petrography-based
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Xie, W.Q., Zhang, X.P., Tang, S.H., Liu, X.L., Li, X.F., Zhang, Q., Yan, F.Y., Xu, C., Liu, Q.S.,
2023a. Fast perception of rock mass strength and integrity in TBM tunnelling Dr. Weiqiang Xie obtained his PhD in Geotechnical Engi-
using an in-situ cone penetration testing system. Tunn. Undergr. Space Technol. neering and BSc in Civil Engineering from Wuhan Uni-
141, 105358. versity in 2022 and 2017, respectively. He worked as
Xie, W.Q., Zhang, X.P., Liu, X.L., Xu, C.Y., Li, X.F., Song, D.Q., Ma, Q., Hu, N., 2023b. assistant researcher at Tsinghua University from 2022 to
Rockemachine mutual feedback perception of TBM tunnelling using muck 2024. He is currently research fellow at Nanyang Techno-
image analysis. Tunn. Undergr. Space Technol. 136, 105096. logical University. His research interests include under-
Xie, W.Q., Liu, X.L., Zhang, X.P., Yang, X.M., Zhou, X.X., 2023c. A review of rock ground space, rock mechanics, intelligent TBM tunneling
macro-indentation: theories, experiments, simulations, and applications. and high-efficiency rock breaking. He has rich experiences
J. Rock Mech. Geotech. Eng. https://doi.org/10.1016/j.jrmge.2023.07.022. in field testing and has published more than 10 top-journal
Yagiz, S., 2008. Utilizing rock mass properties for predicting TBM performance in research papers. He serves on the youth editorial boards
hard rock condition. Tunn. Undergr. Space Technol. 23, 326e339. and reviewers in multiple academic journals.
Yagiz, S., 2009. Assessment of brittleness using rock strength and density with
punch penetration test. Tunn. Undergr. Space Technol. 24, 66e74.
Yagiz, S., Sezer, E.A., Gokceoglu, C., 2012. Artificial neural networks and nonlinear
regression techniques to assess the influence of slake durability cycles on the
prediction of uniaxial compressive strength and modulus of elasticity for car-
bonate rocks. Int. J. Numer. Anal. Methods GeoMech. 36, 1636e1650. Dr. Xiaoli Liu obtained his BSc and MSc from Liaoning
Yarali, O., Kahraman, S., 2011. The drillability assessment of rocks using the different Technical University, China in 2001 and 2004, respectively,
brittleness values. Tunn. Undergr. Space Technol. 26, 406e414. and his PhD from Tsinghua University, China in 2009. He
Yesiloglu-Gultekin, N., Gokceoglu, C., Sezer, E.A., 2013. Prediction of uniaxial serves as associate dean for the School of Civil Engineering
compressive strength of granitic rocks by various nonlinear tools and com- at Tsinghua University. He serves on the editorial boards of
parison of their performances. Int. J. Rock Mech. Min. Sci. 62, 113e122. several renowned international journals, including
Yilmaz, I., 2009. A new testing method for indirect determination of the unconfined Tunneling and Underground Space Technology, and Envi-
compressive strength of rocks. Int. J. Rock Mech. Min. Sci. 46, 1349e1357. ronmental Geotechnics. His research interests include
Yilmaz, I., 2010. Use of the core strangle test for tensile strength estimation and rock geotechnical and geo-environmental engineering, thermo-
mass classification. Int. J. Rock Mech. Min. Sci. 47, 845e850. hydro-mechano-chemical (THMC) coupling mechanism in
€ 2014. Use of the core strangle test for determining strength
Yilmaz, I., Yucel, O., geological system, tunnel boring machine (TBM) tunneling
anisotropy of rocks. Int. J. Rock Mech. Min. Sci. 66, 57e63. technique and underground storage of energies and
Yilmaz, I., Yuksek, G., 2009. Prediction of the strength and elasticity modulus of resources.

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