Available via license: CC BY-SA 4.0
Content may be subject to copyright.
POLİTEKNİK DERGİSİ
JOURNAL of POLYTECHNIC
ISSN: 1302-0900 (PRINT), ISSN: 2147-9429 (ONLINE)
URL: http://dergipark.org.tr/politeknik
Estimating uniaxial compressive strength of
sedimentary rocks with leeb hardness using
support vector machine regression analysis
and artificial neural networks
Sedimanter kayaçların tek eksenli basınç
dayanımının leeb sertliği kullanılarak destek
vektör makineleri regresyon analizi ve yapay
sinir ağları ile tahmin edilmesi
Yazar(lar) (Author(s)): Gökhan EKİNCİOĞLU1, Deniz AKBAY2, Serkan KESER3
ORCID1: 0000-0001-9377-6817
ORCID2: 0000-0002-7794-5278
ORCID3: 0000-0001-8435-0507
To cite to this article: Ekincioğlu G., Akbay D. ve Keser S., “Estimating Uniaxial Compressive Strength of
Sedimentary Rocks with Leeb Hardness Using Support Vector Machine Regression Analysis and Artificial
Neural Networks”, Journal of Polytechnic, *(*): *, (*).
Bu makaleye şu şekilde atıfta bulunabilirsiniz: Ekincioğlu G., Akbay D. ve Keser S., “Sedimanter
Kayaçların Tek Eksenli Basınç Dayanımının Leeb Sertliği Kullanılarak Destek Vektör Makineleri Regresyon
Analizi ve Yapay Sinir Ağları ile Tahmin Edilmesi”, Politeknik Dergisi, *(*): *, (*).
Erişim linki (To link to this article): http://dergipark.org.tr/politeknik/archive
DOI: 10.2339/politeknik.1475944
Estimating Uniaxial Compressive Strength of Sedimentary Rocks
with Leeb Hardness Using Support Vector Machine Regression
Analysis and Artificial Neural Networks
Highlights
Predicting uniaxial compressive strength using index test method
Machine learning algorithm to demonstrate forecasting performance
Graphical Abstract
The uniaxial compressive strength (UCS) of sedimentary rocks was predicted as a function of Leeb hardness using
artificial neural networks (ANN) and Support Vector Machine (SVM) regression analysis. It was proved that the
models created with ANN and SVM regression can be used reliably in predicting UCS values.
Figure. Measured UCS vs predicted UCS
Aim
This study aims to estimate the uniaxial compressive strength of sedimentary rocks using ANN and SVM regression,
with a specific focus on using Leeb hardness as a measurement.
Design & Methodology
Leeb hardness and uniaxial compressive strength values obtained from the publications of researchers working on
this subject in the literature were used in both ANN training and SVM Regression analysis.
Originality
The uniaxial compressive strength of rocks as a function of Leeb hardness is predicted by ANN and SVM regression
methods.
Findings
For both ANN and SVM regression analyses, a high correlation of r=0.93 was obtained between measured UCS
values and predicted UCS values.
Conclusion
ANN and SVM regression models were found to give good results in predicting UCS values. If the models obtained
as a result of the study are used, time, labour and cost savings will be achieved in UCS estimation.
Declaration of Ethical Standards
The author(s) of this article declare that the materials and methods used in this study do not require ethical committee
permission and/or legal-special permission.
UCSp= 0.8528UCSm+ 11.218
r = 0.93
0
50
100
150
200
050 100 150 200
UCSp, MPa
UCS
m
, MPa
UCSp= 0.749UCSm+ 19.954
r = 0.93
0
50
100
150
200
050 100 150 200
UCSp, MPa
UCS
m
, MPa
Estimating Uniaxial Compressive Strength of
Sedimentary Rocks with Leeb Hardness Using Support
Vector Machine Regression Analysis and Artificial
Neural Networks
Research Article
Gökhan EKİNCİOĞLU1*, Deniz AKBAY2, Serkan KESER3
1Kaman Vocational School, Department of Mining and Mineral Extraction, Kırşehir Ahi Evran University, Türkiye
2Çan Vocational School, Department of Mining and Mineral Extraction, Çanakkale Onsekiz Mart University, Türkiye
3Faculty of Engineering and Architecture, Department of·Electrical and Electronics Engineering, Kırşehir Ahi Evran University,
Türkiye
(Received : 30.04.2024 ; Accepted : 10.07.2024 ; Early View : 09.08.2024 )
ABSTRACT
Uniaxial compressive strength (UCS) of rock materials is a rock property that should be determined for the design and stability of
structures before underground and aboveground engineering projects. However, it is impossible to determine the properties of
rocks such as UCS directly due to the lack of standardized sample preparation, necessary equipment, etc. In this case, the UCS of
rocks is predicted by index test methods such as hardness, ultrasound velocity, etc. Determining the hardness of rocks is relatively
more practical, fast, and inexpensive than other properties. In this study, the UCS of sedimentary rocks was predicted as a function
of Leeb hardness using artificial neural network (ANN) and Support Vector Machine (SVM) regression analysis. With the proposed
ANN and SVM regression models, it is aimed to obtain more accurate and faster prediction values. To better train the models
created in the study, the number of data was increased by compiling data from the studies in the literature. The UCS values predicted
by the models obtained with two different methods and the measured UCS values were statistically compared. It was proved that
the models created with ANN and SVM regression can be used reliably in predicting UCS values..
Keywords: Leeb hardness, uniaxial compressive strength, sedimentary rocks, artificial neural network, support vector
machine regression.
Sedimanter Kayaçların Tek Eksenli Basınç
Dayanımının Leeb Sertliği Kullanılarak Destek Vektör
Makineleri Regresyon Analizi ve Yapay Sinir Ağları
ile Tahmin Edilmesi
ÖZ
Kayaların tek eksenli basınç dayanımı (UCS), yeraltı ve yerüstü mühendislik projelerinden önce yapıların tasarımı ve stabilitesi
için belirlenmesi gereken bir kaya özelliğidir. Bununla birlikte, standartlaştırılmış numune hazırlama, gerekli ekipman vb.
eksikliklerden dolayı kayaların UCS gibi özelliklerini doğrudan belirlemek mümkün olmamaktadır. Bu durumda, kayaçların
UCS'si sertlik, ultrases hızı gibi indeks test yöntemleri ile tahmin edilir. Kayaçların sertliğini belirlemek diğer özelliklere göre
nispeten daha pratik, hızlı ve ucuzdur. Bu çalışmada, sedimanter kayaçların UCS'si yapay sinir ağları (ANN) ve destek vektör
makineleri (SVM) regresyon analizi kullanılarak Leeb sertliğinin bir fonksiyonu olarak tahmin edilmiştir. Önerilen ANN ve SVM
regresyon modelleri ile daha doğru ve hızlı tahmin değerleri elde edilmesi amaçlanmıştır. Çalışmada oluşturulan modellerin daha
iyi eğitilmesi için literatürdeki çalışmalardan veriler derlenerek veri sayısı artırılmıştır. İki farklı yöntemle elde edilen modellerin
tahmin ettiği UCS değerleri ile ölçülen UCS değerleri istatistiksel olarak karşılaştırılmıştır. ANN ve SVM regresyonu ile
oluşturulan modellerin UCS değerlerini tahmin etmede güvenilir bir şekilde kullanılabileceği ortaya konmuştur.
Anahtar Kelimeler: Leeb sertliği, tek eksenli basınç dayanımı, sedimanter kayaçlar, yapay sinir ağı, destek vektör
makineleri regresyonu
1. INTRODUCTION
The physical and mechanical characteristics of rocks
must be ascertained before beginning anyengineering
project that involves rock, including surface and
subsurface mining, tunnels, underground apertures,
dams, and drilling foundations. Expensive and time-
consuming tests are performed to directly assess the
strength and deformation of rock. In particular, the
*Corresponding Author
e-posta : denizakbay@comu.edu.tr
process of preparing rock samples for testing is time-
consuming. For the aforementioned reasons, scientists
have created and applied indirect testing techniques to
ascertain and analyze the engineering characteristics of
rocks. According to Shalabi [1], indirect methods can be
quickly and cheaply applied, and they yield results
quickly. One of the most popular metrics for estimating
a rock's characteristics is its surface hardness [2].
One of the unique qualities of the minerals that comprise
a rock is its hardness, which is a measurement of the
mineral's resistance to surface abrasion or scratching.
Given that rocks are made up of mineral assemblages, the
hardness of the rock material is determined by the
proportion of low- or high-hardness minerals [3]. Çelik
et al. [4] state that hardness values can be used indirectly
to evaluate mechanical qualities or to compare with other
materials, but they cannot be used directly as physical
and mechanical properties in engineering projects.
The ability of an object to bounce back after collapsing
or hitting a rock is known as rebound hardness. The
degree of rebound is determined by the quantity of
impact energy lost due to rock fracture and plastic
deformation at the site of contact [5]. In the middle of the
1970s, Leeb hardness (HL) was presented as a dynamic
hardness testing technique for metallic material surface
hardness assessments [6]. But according to Wilhelm et al.
[7], its application in testing materials like rock and stone
has grown. Because of its wider hardness scale, this
approach was designed to give a new test that is quicker
and more useful that can be used in a range of test
orientations [8]. Although there are devices produced by
different manufacturers, the basic working principle of
these devices is the same. A tungsten carbide tip attached
to a wound and tensioned spring mechanism is released,
strikes the material surface and bounces back [9]. The
energy measuring principle serves as the foundation for
the device's tests. The HL value is obtained by
multiplying the ratio of the impact velocity (Vi) by 1000
and then by the rebound velocity (Vr) [10]. The harder
the material under test, the higher the rebound value.
When performing the Equotip tester test, the measured
HL values can be converted into equivalent values of
other conventional hardness measurement methods (e.g.
Vickers hardness, HS), which are usually programmed
on the display unit [11].
Some studies on HL, which has been widely used in
recent years, are summarized below. Hack et al. [12]
investigated the estimation of discontinuity wall strength
of rocks by ball rebound and Equotip hardness testing.
Verwaal and Mulder [13] performed both HL and UCS
tests on rock samples of different diameters. They
determined that rock strength can be predicted from
Equotip hardness values. Meulenkamp and Grima [14]
predicted the UCS values of rocks by using ANNwith HL
measured on 194 rocks consisting of sandstone,
limestone and granite samples. In their study, the authors
used the rocks' porosity, density, grain size and rock type
characteristics for artificial neural network (ANN)
training. Although the large number of input parameters
contributes to the training of the ANN, this makes the
prediction impractical. Kawasaki et al. [15] investigated
the relationship between UCS and HL on different rock
types and found that UCS can be predicted from HL
values. Aoki and Matsukura [16] used the Equotip
hardness tester as an indirect method to estimate the UCS
values of rocks. Their study emphasized that the Equotip
test has advantages over the widely used Schmidt
hammer test. Güneş Yılmaz [11] investigated the
suitability of different test procedures with the Equotip
hardness tester for UCS estimation of some carbonate
rocks. Lee et al [17] used HL hardness values to estimate
the UCS values of laminated shale formations. Mol [18]
stated that rock surface abrasion affects rock hardness
and used HL hardness to determine the degree of surface
degradation. Asiri et al. [19] stated that HL values can be
used to estimate UCS values on sandstone samples with
different sample sizes. Asiri [20] stated that HL values
can be used to predict UCS values as a result of HL and
UCS tests performed on various rock samples. Su and
Momayez [21] examined the relationships between HL
values of rocks and HS, mechanical properties of rocks
and drilling rate index. Corkum et al. [22] examined the
relationship between HL and UCS values on sandstone,
sedimentary, metamorphic and volcanic rocks. They
proposed formulas to calculate UCS values based on HL
values for every kind of rock. Güneş Yılmaz and Göktan
[23] used two different rock core holders and investigated
the effect of the holders on the HL values obtained on 16
different rocks. At the end of the study, they found highly
correlated relationships between the values obtained
from both holders and UCS values. Güneş Yılmaz and
Göktan [24] examined the relationship between HSR and
HL values and UCS values of different types of rock
samples. Çelik and Çobanoğlu [25] determined the HL,
HS and HSR hardness values of 40 different rock types.
They examined the correlations between the hardness
values they obtained and the physical and mechanical
properties of the rocks. Additionally, Çelik et al. [26]
looked into how the length/diameter ratio (L/D) affected
the HL measurements on five distinct rock samples. They
concluded that samples with a diameter of 50 mm and a
minimum L/D ratio of 1.5 would allow for more accurate
HL measurements.
When the studies in the literature were examined, it was
seen that the researchers examined the relationships
between HL values and UCS values determined on
different rock types by regression analysis. However,
with the exception of Meulenkamp and Grima [14], there
are not enough studies with artificial neural networks.
ANN algorithms have many advantages, but also
disadvantages such as complexity in their multilayer
structure, excessive learning, and the fact that the model
provides different outputs each time. also includes
negative features such as obtaining. Due to these
disadvantages of ANN, it is the subject of this study to
evaluate whether a machine learning model can be used
to predict UCS. In this study, the UCS values of
sedimentary rocks were tried to be predicted with the
help of models obtained from both ANN and SVM
regression (SVM-R) analysis..
2. MATERIAL and METHOD
Models obtained from ANN and SVM regression
analyses need to be trained with a large number of data
to make accurate predictions. Due to the limited number
of sedimentary rocks tested in the laboratory within the
scope of this study, HL and UCS values obtained from
the publications of researchers working on this subject in
the literature were used in both ANN training and SVM-
R analysis (Table 1).
Table 1. References from which the data compiled
References
Verwaal and Mulder [13]
Meulenkamp and Grima [14])
Aoki and Matsukura [16]
Su and Momayez [21]
Güneş Yılmaz and Göktan [23]
Çelik and Çobanoğlu [25]
Akbay et al. [27]
200 sedimentary rocks with 50 randomly chosen UCS
and HL values were used for testing in the study, while
the remaining 150 were used for training. This procedure
was carried out six times with different training and test
data in order to demonstrate the learning success of the
models. In ANN and SVM-R analyses, HL was used as
the input parameter and UCS as the output parameter in
the training and testing phase.
2.1. Artificial Neural Network
According to Kriegeskorte [28], ANNs are information-
processing systems that replicate the central nervous
system and brain's functional principles. Modelling
neurons, the biological components of the brain, and their
use in computer systems was the first step in this field of
study. Each connection that exists between neurons
indicates the strength, or more accurately, the
significance, of the input it receives. The foundation of
an ANN's long-term memory is its weights. By
continuously changing these weights, a neural network
learns [29]. Following the failure of single-layer neural
networks to address nonlinear issues, multilayer neural
networks (MLN) were created. These networks are made
up of an output layer, one or more hidden (intermediate)
layers, and an input layer where data is input. Transitions
between the forward and backward propagation layers
occur in an MLN. The network's output and error values
are computed during the forward propagation phase. The
link weight values between layers are adjusted
throughout the backpropagation phase in order to reduce
the predicted error value [30]. Figure 1 shows the
structure of the MLN.
Figure 1. Multilayer neural networks (MLN)
Since processing information and solving the problem in
ANN is realized by connecting the cells in parallel, the
data transferred is independent of each other. Since there
is no time dependency in the connections, the whole
network can work simultaneously. For this reason, it is
frequently preferred in prediction problems due to its
high information flow and processing speed [31]. In this
study, an ANN with one input, one hidden and one output
layer was used.
2.2. SVM Regression
A statistical analysis technique called regression analysis
is used to represent the cause-and-effect connection
between two or more variables. It is widely used in many
fields, including biology, medicine, economics, physics,
chemistry, and social sciences [32, 33, 34, 35]. The
SVM-R model was used as the regression model in this
study. The kernel of the model was chosen as quadratic
second-order polynomial kernel.
For regression and classification, support vector machine
(SVM) analysis is a widely used machine learning tool
[36]. SVM-R analysis is a nonparametric technique since
it is based on kernel functions. For ε-SVM-R analysis,
the training dataset, predictor variables, and measured
values are utilised. The objective is to develop a function
f(x) that is as flat as feasible for each training point x,
with a deviation from yn of no more than ε.
A linear model is insufficient to effectively characterise
certain regression problems. The method can be extended
to nonlinear functions in such a situation thanks to the
Lagrange dual formulation. A nonlinear kernel function
is used to replace the dot
product to create a nonlinear SVM-R model.
where x is mapped to a high-dimensional space by the
transformation φ(x). The built-in positive semi-definite
kernel functions for SVM are displayed in Table 2 below.
Table 2. Positive semi-defined kernel functions used for SVM
Kernel Name
Kernel Function
Linear (dot
product)
Gaussian
Polynomial
, where
is in the set .
The elements of the gramme matrix, , are
arranged in an n×n matrix. The inner product of the φ-
transformed predictors equals each element.
The corresponding element of the Gramme matrix
is substituted for the inner product of the predictors
in the dual formula for nonlinear SVM
regression. The coefficients that minimise are found
using the nonlinear SVM regression (Huang et al., 2005).
(1)
subject to ;
(2)
The prediction function for new values is equal to;
(3)
The Karush-Kuhn-Tucker (KKT) complementarity
conditions are;
(4)
(5)
(6)
(7)
The most often used method for resolving SVM issues is
sequential minimum optimisation (SMO) [37]. Two-
point optimisation is done via SMO. A working set of
two points is chosen at each iteration utilising quadratic
information and a selection procedure. We then apply the
method for finding the solution for this working set that
is presented in Lagrange multipliers [38, 39].
3. RESULTS of THE MODELS
In the study, 150 of the 200 UCS and HL data of the rocks
were randomly selected and used in the training of SVM-
R and ANN. The remaining 50 data were used for testing.
In this way, six training and six test data sets were
obtained and analysed for both SVM and ANN. In order
to determine the prediction performance of ANN and
SVM-R methods for different test sets in the database,
training and testing were performed six times. Some of
the data in a training set used for ANN were used for
validation. This ensured that the network learned well.
For SVM-R, only training and test sets were used. In the
training and testing phase of the models obtained in ANN
and SVM-R analyses, HL values of the rocks were used
as input and UCS values were used as output parameters.
The most appropriate models were created with SVM-R
analysis and ANN using the training sets. Afterwards,
UCS values were predicted with the test process.
3.1. UCS Prediction with ANN
In the network architectures created for ANN in the
study, HL stiffness values were considered as input
parameter and UCS strength as output parameter.
Levenberg-Marquardt as the training function, tangent
sigmoid in the input layer and purelin activation
functions in the output layer were used. In addition, a
hidden layer with 2 cells and a maximum number of 100
epochs (cycles) were used. Figure 2 shows the structure
of the ANN model developed within the scope of the
study.
Figure 2. Structure of the developed ANN model
The number of cells in the input layer, hidden layer, and
output layer were all fixed to one, two, and one
respectively throughout the investigation. The
relationships between the predicted and measured UCS
values for Training-1, Test-1, and All Data-1 obtained for
ANN are given in Figure 3.
Figure 3. Relationships between predicted UCS values and measured UCS values for training, testing, and the whole data set in
ANN model
The models and correlation values (r) expressing the
relationships between the predicted UCS and measured
UCS values for the training, test, and whole data set
generated by ANN are given in Table 3. In general
(training, test, validation and all data) correlation values
were found to be 0.90 and above. The high correlation
values indicate that uniaxial compressive strengths of
sedimentary rocks can be predicted from HL. Figures 4
and 5 show a comparison of the predicted and measured
values by ANN model for Training-1 and Test-1 data,
respectively.
Figure 4. The relationship between the predicted and measured UCS values by ANN model with training data
0
20
40
60
80
100
120
140
160
180
200
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
MPa
Data number
UCS Predicted UCS
Figure 5. Relationship between predicted and measured UCS values predicted by ANN with test data
The relationship between the UCS values predicted by
ANN analysis and the measured UCS values for the Test-
1 set is given in Figure 6. A high correlation (r=0.93) was
obtained between measured UCS values and predicted
UCS values.
Figure 6. The relationship between the predicted UCS values obtained from the ANN model and the measured UCS values
3.2. UCS Prediction with SVM Regression Method
A second order polynomial kernel was used in SVM
regression analysis. For each of the 6 training sets, a
regression model was obtained using SVM regression.
With the test sets corresponding to these training sets,
predicted UCS values were obtained. The r, RMSE, and
MAE values and models found by SVM Regression for
the six training and six test sets are given in Table 3.
Figures 7 and 8 show the comparative graphs of the
predicted UCS and measured UCS values obtained with
the SVM regression model for Training-3 and Test-3
data.
0
20
40
60
80
100
120
140
160
180
1357911 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
MPa
Data number
UCS Predicted UCS
UCSp= 0.8528UCSm+ 11.218
r = 0.93
0
20
40
60
80
100
120
140
160
180
020 40 60 80 100 120 140 160 180
UCSp, MPa
UCSm, MPa
Figure 7. Predicted and measured UCS values found with SVM regression model for Train-3 data
Figure 8. Predicted and measured UCS values found with SVM model for Test-3 data
The relationship between the UCS values predicted by an
SVM Regression analysis and the measured UCS values
for the Test-3 set is given in Figure 9. A high correlation
(r=0.93) was obtained between measured UCS values
and predicted UCS values.
0
20
40
60
80
100
120
140
160
180
200
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
MPa
Data number
UCS Predicted UCS
0
20
40
60
80
100
120
140
160
180
1357911 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
MPa
data number
UCS Predicted UCS
Figure 9. The relationship between the predicted UCS values obtained from the SVM Regression model and the measured UCS
values
3.3. Measured Results of ANN and SVM Regression
Models
The proposed models and calculated correlation numbers
as a result of SVM regression and ANN models are given
in Table 3. As can be seen from Table 3, SVM regression
gives better results than ANN for RMSE and MAE error
values both in training and testing when the correlation
(r) values are close to each other. In four of the six tests,
SVM regression r values are higher than ANN's r values.
Only the r-value of ANN in test-2 is higher than the r-
value of SVM regression and equal for test-3. These
results show that SVM regression gives better results
than ANN for RMSE and MAE, indicating the error rate
and r-value. In Table 3, Tr indicates training, and Ts
indicates test.
Table 3. Uniaxial compressive strength predictions and performance values of sedimentary rocks with ANN
The data
ANN
SVM
Model
RMSE
MAE
Model
RMSE
MAE
Tr-1
0,915
16.36
12.60
0,915
15.94
11.53
Tr -2
0,911
16.80
12.4
0,912
14.59
11.98
Tr -3
0,915
13.96
12.07
0.917
11.76
11.92
Tr -4
0,921
13.85
11.18
0,923
13.86
11.14
Tr -5
0,925
15.43
12.29
0,932
15.35
12.08
Tr -6
0,917
14.78
11.15
0,907
15.66
11.20
Ts-1
0,932
14.23
11.52
0,934
13.33
11.16
Ts-2
0,939
14.36
10.34
0,938
13.94
10.50
Ts-3
0,942
11.86
9.44
0,942
11.63
9.38
Ts-4
0,951
9.73
8.07
0,952
9.60
7.83
Ts-5
0,915
16.31
13.32
0,920
15.94
13.15
Ts-6
0,940
10.55
8.30
0,949
9.87
8.11
y = predicted UCS
x = measured UCS
UCSp= 0.749UCSm+ 19.954
r = 0.93
0
20
40
60
80
100
120
140
160
020 40 60 80 100 120 140 160 180
UCSp, MPa
UCSm, MPa
4. DISCUSSION
In this study, ANN and SVM regression analyses were
developed to predict sedimentary rocks' HL hardness
values and UCS values. As a result of the analyses, the
most appropriate model was determined. With ANN,
correlation (r), RMSE and MAE error values were found
for training, testing, validation and overall (all samples).
When the error values were analysed, it was seen that
SVM regression analyses gave generally lower error
values than ANN in training and test results. When the
correlation (r) values obtained with ANN and SVM
regression models were analysed, it was seen that both
models gave successful results. In all four tests, the
correlation values of the SVM regression model were
relatively higher than the r values obtained from ANN
models. The SVM regression model obtained the highest
prediction value with a correlation coefficient of 0.952
for Ts-4.
It is seen that UCS-HL values have a high positive
correlation. As a result, it was determined that SVM
regression and ANN models gave good results in
predicting UCS values.
When the literature was examined, it was seen that there
were a limited number of studies on the subject.
Meulenkamp and Grima [14] predicted the UCS values
of rocks by using ANN with HL measured on 194 rocks
consisting of sandstone, limestone and granite samples.
In their study, the authors used the rocks' porosity,
density, grain size and rock type characteristics for ANN
training. Although the large number of input parameters
contributes to the training of the ANN, this makes the
prediction impractical. Within the scope of this study, if
the models obtained from the study are used, time, labour
and cost savings will be achieved by estimating UCS.
In future studies, it is thought that the success of the
models will increase by using the number of rock groups
and Leeb hardness, as well as the hardness values
obtained from other hardness experimental methods
(Shore, Schmidt, etc.) in training the models because they
are economical and practical.
DECLARATION OF ETHICAL STANDARDS
The author of this article declare that the materials and
methods used in this study do not require ethical
committee permission and/or legal-special permission.
AUTHORS’ CONTRIBUTIONS
Gökhan EKİNCİOĞLU: Writing, software, validation,
visualization.
Deniz AKBAY: Data collection, data curation, review
and editing.
Serkan KESER: Writing, software, validation,
visualization.
CONFLICT OF INTEREST
There is no conflict of interest in this study.
REFERENCES
[1] Shalabi F. I., Cording E. J. and Al-Hattamleh O.H.,
“Estimation of rock engineering properties using
hardness tests”, Engineering Geology, 90(3–4): 138–
147, (2007).
[2] Çelik S. B., Çobanoğlu İ. and Koralay T., “Investigation
of the use of LEEB HARDNESS in the estimation of
some physical and mechanical properties of rock
materials, Pamukkale University Journal of
Engineering, 26(8): 1385-1392, (2020).
[3] Siegesmund S. and Dürrast H., “Physical and mechanical
properties of rocks”, Stone in architecture, properties,
durability, Springer, Berlin, (2014).
[4] Çelik M. Y., Yeşilkaya L., Ersoy M. and Turgut T.,
“Karbonat kökenlı
doğaltaşlarda tane boyu ı
le knoop
sertlı
k değerı
arasindaki ı
lı
şkı
nı
n ı
ncelenmesı
”,
Madencilik, 50(2): 29–40, (2011).
[5] Atkinson R. H., “Hardness test for rock characterization”,
Comprehensive rock engineering: principles, practice and
projects. Rock testing and site characterization,
Pergamon, Oxford, (1993).
[6] Leeb D., “Dynamic hardness testing of metallic
materials”, NDT International, 12(6): 274–278, (1979).
[7] Wilhelm K., Viles H. and Burke O., “Low impact surface
hardness testing (Equotip) on porous surfaces – advances
in methodology with implications for rock weathering
and stone deterioration research”, Earth Surface
Processes and Landforms, 41:1027–1038, (2016).
[8] Kompatscher M., “Equotip—rebound hardness testing
after D.Leeb.” Conference on hardness measurements
theory and application in laboratories and industries,
Washington, DC, USA, 66–72, (2004).
[9] Çelik S. B., Çobanoğlu İ., and Koralay T., “Investigation
of the Use of LEEB HARDNESS in the Prediction of
Uniaxial Compressive Strength of Rock Materials”,
ENGGEO’2019: National Symposium on Engineering
Geology and Geotechnics, Denizli, Türkiye, 47-55,
(2019).
[10] Proceq SA, “Equotip 3, Portable Hardness Tester,
Operating instructions”, Proceq SA, Schwerzenbach,
Switzerland, (2007).
[11] Güneş Yılmaz N., “The influence of testing procedures
on uniaxial compressive strength prediction of carbonate
rocks from Equotip hardness tester (EHT) and proposal
of a new testing methodology: hybrid dynamic hardness
(HDH)”, Rock Mechanics and Rock Engineering, 46(1):
95-106, (2013).
[12] Hack H. R. G. K., Hingira J. and Verwaal, W.
“Determination of discontinuity wall strength by Equotip
and ball rebound tests”, International Journal of Rock
Mechanics and Mining Sciences and Geomechanics
Abstracts, 30: 151-151, (1993).
[13] Verwaal W. and Mulder A. “Estimating rock strength
with the Equotip hardness tester”, International Journal
of Rock Mechanics and Mining Sciences and
Geomechanics Abstracts, 30(6): 659-662, (1993).
[14] Meulenkamp F. and Grima M. A., “Application of neural
networks for the prediction of the unconfined
compressive strength (UCS) from Equotip hardness”,
International Journal of Rock Mechanics and Mining
Sciences, 36(1): 29-39, (1999).
[15] Kawasaki S., Tanimoto C., Koizumi K. and Ishikawa M.,
“An attempt to estimate mechanical properties of rocks
using the Equotip hardness tester”, Journal of the
Japanese Society of Engineering Geology, 43(4): 244-
248, (2002).
[16] Aoki and Matsukura, Estimating the unconfined
compressive strength of intact rocks from Equotip
hardness, Bulletin of Engineering Geology and the
Environment, 67: 23-29., (2008).
[17] Lee J. S., Smallwood L. and Morgan E., “New
Application of Rebound Hardness Numbers to generate
Logging of Unconfined Compressive Strength in
Laminated Shale Formations”, 48th U.S. Rock
Mechanics/Geomechanics Symposium, Minneapolis,
Minnesota, 972–978, (2014).
[18] Mol L., “Measuring rock hardness in the field”,
Geomorphological Techniques, British Society for
Geomorphology, London, (2015).
[19] Asiri Y., Corkum A. G. and El Naggar H., “Leeb
Hardness test for UCS estimation of sandstone”, The 69th
Canadian Geotechnical Conference, Vancouver, British
Columbia, Canada 1- 11, (2016).
[20] Asiri Y., “Standardized process for field estimation of
unconfined compressive strength using Leeb Hardness”,
MSc Thesis, Dalhousie University, Applied Science,
(2017).
[21] Su O. and Momayez M., “Correlation between Equotip
hardness index, mechanical properties and drillability of
rocks”, Dokuz Eylul University Journal of Science and
Engineering, 19(56): 519-531, (2017).
[22] Corkum A. G., Asiri Y., El Naggar H. and Kinakin D.,
“The LEEB HARDNESS test for rock: An updated
methodology and UCS correlation”, Rock Mechanics
and Rock Engineering, 51: 665-675, (2018).
[23] Güneş Yilmaz N. and Göktan, R. M., “Analysis of the
LEEB HARDNESS test data obtained by using two
different rock core holders”, Süleyman Demirel
University Journal of Natural and Applied Sciences,
22(1): 24-31, (2018).
[24] Güneş Yilmaz N. and Göktan, R. M., “Comparison and
combination of two NDT methods with implications for
compressive strength evaluation of selected masonry and
building stones”, Bulletin of Engineering Geology and
the Environment, 78(6): 4493-4503, (2019).
[25] Çelik S. F. and Çobanoğlu İ., “Comparative investigation
of HS, HSR, and LEEB HARDNESS tests in the
characterization of rock materials”, Environmental
Earth Sciences, 78(554): 1-16, (2019).
[26] Çelik S. B., Çobanoğlu İ. and Koralay T. “Investigation
of the use of LEEB HARDNESS in the estimation of
some physical and mechanical properties of rock
materials”, Pamukkale University Journal of
Engineering Sciences, 26(8): 1385-1392, (2020).
[27] Akbay D., Ekincioğlu G., Altındağ R. and Şengün N.,
“Farklı cihaz ve yöntemler ile belirlenen HS sertlik
değerlerinin sedimanter kayaçların gevreklik değerlerinin
tahmininde kullanılabilirliğinin incelenmesi”,
Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi,
27(3): 441-448, (2021).
[28] Kriegeskorte N., “Deep neural networks: a new
framework for modelling biological vision and brain
information processing”, Annual Review of Vision
Science, 1: 417-446, (2015).
[29] Nguyen H. H. and Chan, C. W., “Multiple neural
networks for a long term time series forecast”, Neural
Computing & Applications, 13: 90-98, (2004).
[30] Kanti K. M. and Rao P. S. “Prediction of bead geometry
in pulsed GMA welding using back propagation neural
network”, Journal of Materials Processing Technology,
200(1-3): 300-305, (2008).
[31] Basheer I. A. and Hajmeer M., “Artificial neural
networks: fundamentals, computing, design, and
application”, Journal of Microbiological Methods,
43(1): 3-31, (2000).
[32] Shehab M., Abualigah L., Shambour Q., Abu-Hashem M.
A., Shambour M. K. Y., Alsalibi A. I. and Gandomi A.
H., “Machine learning in medical applications: A review
of state-of-the-art methods”, Computers in Biology and
Medicine, 145: 105458, (2022).
[33] Balabin R. M. and Lomakina E. I. “Support vector
machine regression (SVR/LS-SVM)—an alternative to
neural networks (ANN) for analytical chemistry?
Comparison of nonlinear methods on near infrared (NIR)
spectroscopy data”, Analyst, 136(8): 1703-1712, (2011).
[34] Zhang X., Hu L. and Zhang, L., “An efficient multiple
kernel computation method for regression analysis of
economic data”, Neurocomputing, 118: 58-64, (2013).
[35] Hindman M., “Building better models: Prediction,
replication, and machine learning in the social sciences”,
The Annals of the American Academy of Political and
Social Science, 659(1): 48-62, (2015).
[36] Vapnik V., “The Nature of Statistical Learning Theory”,
Springer, New York, (1995).
[37] Platt J., “Sequential Minimal Optimization: A Fast
Algorithm for Training Support Vector Machines”,
Technical Report MSR-TR-98–14, (1999).
[38] Fan R. E., Chen P. H. and Lin C. J., "A Study on SMO-
Type Decomposition Methods for Support Vector
Machines", IEEE Transactions on Neural Networks, 17:
893–908, (2006).
[39] Kecman V., “Support vector machines–an introduction”,
Support vector machines: theory and applications,
Springer, Heidelberg, (2005).
