Available online at www.sciencedirect.com
ScienceDirect
Procedia Engineering 191 (2017) 279 – 286
Symposium of the International Society for Rock Mechanics
Application of Artificial Neural Networks in Prediction of Uniaxial
Compressive Strength of Rocks Using Well Logs and Drilling Data
Adel Asadi*
Department of Petroleum Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Abstract
It is critical to obtain the rock strength along the wellbore to control drilling problems such as pipe sticking, tight hole, collapse
and sand production. The purpose of this research is to predict the uniaxial compressive strength based on data of sonic travel
time, formation porosity, density and penetration rate. For prediction of UCS, artificial neural networks were developed between
UCS and input data resulting a practical correlation. In this research, a long well segment possessing complete and continuous
data coverage has been analysed, and collected data of the wellbore are used to correlate data of the four mentioned input
parameters of artificial neural networks with uniaxial compressive strength data as network targets. Selection of input parameters
is based on a vast literature review in this area. Due to the fact that standard experimental test methods based on established
standards require costly equipment and that the methods for sample preparation is difficult and time-consuming, indirect methods
are more favourable. Using these methods, the UCS values are predicted in a simpler, faster and more economical way. In this
study, it is concluded that artificial neural networks are a good predictor of rock strength, and can reduce drilling costs
significantly. It is observed in this paper that UCS predicted values by neural networks are very close with lab and field data,
which is concluded by analysis of network performance results including mean squared error and correlation coefficient. It is also
concluded in this study that input parameters which are chosen in this study, have deep effects in UCS prediction studies, and
should be considered in other scientific studies. Conclusions show that using artificial neural networks to predict UCS of
formation rocks in petroleum fields around the world, would ease UCS estimation, optimize drilling plans and decrease costs.
© 2017
2017The
TheAuthors.
Authors.
Published
by Elsevier
Ltd. is an open access article under the CC BY-NC-ND license
©
Published
by Elsevier
Ltd. This
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of EUROCK 2017.
Peer-review under responsibility of the organizing committee of EUROCK 2017
Keywords: Uniaxial Compressive Strength; Artificial Neural Networks; Wellbore Drilling
* Corresponding author. Tel +98-910-283-6043.
E-mail address: adelasadi.pe@gmail.com
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of EUROCK 2017
doi:10.1016/j.proeng.2017.05.182
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Adel Asadi / Procedia Engineering 191 (2017) 279 – 286
1. Introduction
A geomechanical model requires a great deal of input information including measurements of magnitude of
vertical and minimum stresses, pore pressure, rock mechanics properties and drilling experiences, all oriented to
determine the magnitude of maximum horizontal stress. To conduct a geomechanical reservoir characterization, it is
essential to have the knowledge of the in-situ stress magnitudes and rock mechanical properties [17].
Uniaxial compression test (unconfined compression test) is one of the most important tests used to measure rock
strength. It is critical to obtain the rock strength parameters along the wellbore. Rock strength controls the drilling
rate of penetration (ROP) [1]. Knowledge of the in situ mechanical profiles of the reservoir interval is critical in
planning horizontal well trajectories and landing zones, placement of perforation clusters along the lateral, and
optimal hydraulic fracture simulation design. However, coring, logging and core analyses are expensive and time
consuming. In addition, as they are typically performed in a few wells that are assumed to be representative, there is
considerable uncertainty in extrapolating results across wide areas with known variability in stratigraphy, faults,
thicknesses, hydrocarbon saturations, etc. [2]. Thus, an integrated rock mechanical study can be considered
an investment in field development. In practice, however, many geomechanical problems in reservoirs must be
addressed when core samples are unavailable for laboratory testing. In fact core samples of overburden formations
are almost never available for testing [6]. Rock mechanical laboratory testing on core samples are the most accurate
methods for estimation of rock strength, but they never can lead to a continuous profile of rock strength along
wellbore. Coring is very expensive and results are very sensitive to stress unloading [3].
Indirect methods are relatively simple and generally do not require any sample preparation. Due to the fact that
standard experimental test methods based on established standards require costly equipment and that the methods
for sample preparation is difficult and time-consuming, indirect methods are more favourable [1]. The use of such
relations is often the only way to estimate the strength of rocks due to the absence of cores for laboratory tests.
The basis for these relations is that many of the same factors that affect the rock strength, also affect other properties
such as porosity. On the other hand, due to changes in the rock composition and properties, none of the correlations
could be applied as an exact universal one. In such conditions, the proposed artificial intelligence method could be
an appropriate candidate for estimation of the strength parameters.
This paper reports a method for estimation of mechanical rock properties in every well in a development.
The purpose of this research was to predict the uniaxial compressive strength as a function of sonic travel time,
penetration rate, density and formation porosity. In this work, a large well segment in Iran has been analysed which
there is no information break throughout the segment and it is investigated continuously. To accomplish
the objectives of this study, the drilling data from offset wells have been utilized to calculate the rock strength along
the wellbore. Field data sets are used in this research to predict UCS based on the data of four input parameters
chosen in the study.
Nomenclature
E
ROP
UCS
ȡ
ij
ǻt
MPa
m/s
psi
Vp
μs/ft
Young’s modulus
Rate of penetration
Uniaxial compressive strength
Bulk density
Formation porosity
Sonic travel time
Mega-pascal
Meter per second
Pound per squared-inch
P-wave velocity
Micro-second per foot
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1.1. Uniaxial compressive strength
The UCS has a significant importance as a rock strength parameter which have applications in various fields.
Rock engineers widely use the UCS of rocks in surface and underground structures. It can be used to design mine
plan. Safety measures in mines like the supports system could be put at proper places in the mines if UCS is known.
It can also be used to obtain a rough estimation about the rock strength or to get a rough idea about suitable drilling
fluid that will be used while drilling [7].
A drilling operation is an interaction between the rock and the bit and the rock will fail when the resultant stress
is greater than the rock strength. UCS value can be used for bit selection, real-time wellbore stability analysis,
estimation of optimized time for pulling up the bit, design of enhanced oil recovery (EOR) procedures, and reservoir
subsidence studies [12].
Determination of UCS at laboratory is a costly affair because drilled core samples are required to be collected
from well sites and then prepared for testing. Drilling for core samples and testing of rock mechanical properties of
those cores in the laboratory, hence obtaining UCS with depth is not possible by direct testing in the laboratory. So,
the aim of present study is to obtain the UCS values directly from the well logs instead of the laboratory testing.
Well logs are useful tools for predicting approximate values of rock strength. Several empirical relations have been
emerged to determine the rock strength. This would reduce the cost a lot and would easily give out an estimation of
rock strength parameter like UCS for any formations.
Uniaxial, triaxial, point load, Schmidt rebound hammer, scratch, indentation, and thick wall cylinder (TWC) tests
are the most common methods for estimation of rock strength. Among them, the triaxial test delivers the most
accurate results but not a continuous profile. Uniaxial compression tests are influenced by several factors, such as
the size and shape of the test sample, rate of loading, amount and type of fluid present in the rock sample,
mineralogy, grain size, grain shape, grain sorting, and rate of loading. In addition to weathering, rock structure
alteration due to diffusion of incompatible fluids and inaccurate handling of the cores in conjunction with stress
unloading causes differences between measured rock strength from reality [12].
No technique has been introduced until now for direct in situ measurement of rock strength. Although laboratory
tests are the best approach for estimation of rock strength, they result in only a few discrete data points. Continuous
estimates of rock strength along the well can be obtained by analysis of well logs. This helps to develop
a continuous rock strength profile along the wellbore either with or without a core [12].
A factor very influential for the magnitudes of compressive strength values is the confining stress. Several studies,
using triaxial testing, have shown an increase in UCS with increasing confining pressure, typically called Confined
Compressive Strength. CCS may be very important for oil well drilling [10].
The UCS of an intact rock sample is the amount of compressive force per unit area applied in a single direction
required to induce failure. UCS is calculated by dividing the compressive load at failure by the cross sectional area
of the sample. The uniaxial compressive test can also measure the Poisson’s ratio and Young’s modulus of an intact
rock sample [16].
1.2. Literature review
Table 1 shows a few of the published correlations in the literature between uniaxial compressive strength of
sandstone rocks and other physical properties and drilling parameters.
Table 1. Empirical relationships between UCS and other parameters.
No.
UCS (MPa)
Reference
1
0.0035 × Vp – 31.5
[19]
2
1200 × exp (-0.036 × ǻt)
[20]
3
3.87 × exp (1.14 × 10-10 × ȡ × Vp2)
[7]
4
357 × (1 – 2.8 × ij)2
[23]
5
323.01 × e -3.7 × ROP
[21]
6
2.28 + 4.1089 × E
[22]
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2. Data acquisition
Compressive strength data of rocks are collected from a wellbore drilled in a sandstone reservoir in Iran, and
analysis is performed between the data of input parameters chosen to predict rock strength for near field area by
constructing a new relationship for rock strength estimation. The testing of 77 core samples for UCS values were
carried out in the rock mechanics laboratory of the department of mining engineering at Tehran Science and
Research Branch of Islamic Azad University.
Collected data were used to correlate data of porosity, sonic travel time, density and penetration rate, as four
input parameters of artificial neural networks with uniaxial compressive strength data as network targets. Selection
of input parameters is based on a vast literature review in this area.
2.1. Methodology
Uniaxial compressive strength (UCS) test is widely used for estimating the mechanical properties of rock
material in rock engineering projects. In order to determine UCS, direct and indirect techniques are available. In
the direct approach, UCS is determined from the laboratory UCS tests. In indirect techniques determine UCS is
determined based on mathematical and empirical relationships. UCS is directly determined according to both
the American Society for Testing and Materials (ASTM) [4], the International Society for Rock Mechanics (ISRM)
[5] and other common standards.
It should be noticed that each one of these correlations has been developed from the specific ranges of the well
log data. Due to changes in the rock composition and properties, which result in changes in the data, none of
the correlations could be applied as an exact universal one because the accuracy of no correlation is guaranteed for
the data that is different from the one used for developing it. In such conditions, to overcome these problems,
intelligence techniques could be very useful and helpful. In the recent years, there has been an increasing interest in
developing intelligence models for prediction of the rock strength properties in the world [9].
An artificial neural network (ANN) is a synthetic computational system that tries to mimic neurons in the human
brain to discover sophisticated relationships between parameters. The capability of ANNs in prediction of
the complicated behaviour of complex functions led us to utilize this system for prediction of the UCS profile.
The ability of ANNs to monitor the behaviour of complex functions has been well proven in numerous studies [15].
A neural network model is a reliable approach for prediction of rock strength between wells that are in close
proximity to each other [12].
The estimation technique is advantageous due to the facts that it is relatively simple, cheap, and quick. The inputs
are available in most wells. Generally, well logs can provide a continuous record over the entire well, so the well-log
data, as the input, can be estimated over the whole well.
2.2. Input parameters
Porosity, density and penetration rate are three of the four parameters applied for the purpose of this research. To
choose the fourth one, we could use data of sonic travel time or P wave velocity .As sonic travel time is simply
the reciprocal of P-wave velocity, in this paper, only the sonic travel time is applied as one of the input parameters.
2.2.1. Density
In oil-well and rock drilling, sonic and density logging is always performed, particularly in difficult to drill wells.
Hence, data of sonic velocity and porosity or density is available. For this reason and for many years industry tried
to find good correlations of UCS versus sonic velocity or bulk density in order to assess in situ rock strength and
develop the drilling strategy accordingly. What is necessary of course is high quality of the field drilling data for
a first hand approximation of UCS [10].
Many researchers has proved that density logs should be considered in UCS estimation. As an example, as
a result of the study conducted by Chatterjee et al., the relationship derived between UCS from laboratory and
density from well log, showed linear regression relation with satisfactory goodness of fitting [7].
Adel Asadi / Procedia Engineering 191 (2017) 279 – 286
2.2.2. Penetration rate
“Rock – drill bit” interaction while drilling has been modeled for many years but a complete understanding of
the phenomena occurring has yet to materialize. Successful models will allow the prediction of rate of penetration in
a given environment and optimal selection of drill bit and drilling parameters thus minimizing exploration costs. In
most rock-drilling models the value of the unconfined compressive strength of the rock (UCS), one of the most
important engineering properties of rocks, is used in the predictive equations, within the concept of specific energy,
and the value of UCS is the percentage of the value of the stress applied on the drilling bit in order for the bit to
advance. While the exact percentage depends on the model used and it is not known with certainty, good knowledge
of UCS is nevertheless required before any decent prediction can be made on rate of penetration. Rock drillability,
defined as the time spent to drill one meter of rock, has been widely used as rock classification. From the literature
cited, UCS could be used as a rough estimate of rock drillability [10].
Kerkar et al. [2] reviewed and illustrated different published ROP models for UCS prediction. The models were
implemented using field data from different locations including the USA and Norway.
Nabaei et al. [12] also reviewed some penetration rate models which have established a relationship between
UCS and drilling operational parameters, including the studies done by Bingham [13] and Warren [14]. Thus, rock
strength can be interpreted as the inverse of drillability [12].
2.2.3. Formation porosity
Rock strength is resultant of contribution of rock properties such as grains texture, cement texture, porosity, fluid
content and also degree of compaction. In order to reach more accuracy by employing the undeniable porosity roles
in rock strength, it was decided to apply porosity data to estimate UCS [1]. Nearly all proposed formulae for
determination of the rock strength in literature utilize one of the parameters including porosity, P-wave velocity and
Young’s modulus [6].
One of the basic techniques to estimate UCS via non-destructive testing is by using sonic data, as velocity of
elastic waves in rock depends on rock density, stiffness and hence to rock strength. It is also known that velocity
depends strongly on rock mineralogy, grain size, porosity, weathering, stress level, water absorption, water content
and temperature, all of which complicate the issue and thus, no simple correlations exist or have been suggested. In
oil-well drilling, UCS is also estimated from porosity logs [10].
The results of the study done by E. M. M. Khair et al. [11] confirm and support the evidence of using porosity as
an index of mechanical properties specifically the unconfined compressive strength (UCS). Log porosities were
calculated from density, sonic and neutron logs, before starting the calculation borehole assessment and conditions
were studied to ensure logs quality.
2.2.4. Sonic travel time
Sonic travel time is one of the rock physical properties which mostly are used for reservoir evaluation and rock
mechanical studies. Sonic travel time logging of boreholes is routinely used in oil industry to realize reservoir
properties for more evaluation. It reflects the effect of lithology, porosity and fluid content. Research has been
focused on using that for rock property estimation from logs in situations where there is limited or non-availability
of core samples [1].
An extensive literature search has indicated that many correlations between UCS and sonic data were published.
Sonic (acoustic) velocity logging is a form of borehole geophysical logging that measures the transit time of
compression (P-wave) waves travelling through the rock mass surrounding the borehole [16].
Uniaxial Compressive Strength (UCS) and sonic velocity correlations are used widely in the Australian coal
mining industry to predict in situ rock strength. These models are cheap, fast and easy to produce, as well as easy to
understand and have a number of practical applications in mine planning and design [16]. Sonic logging has been
routinely used for many years in Australia to obtain estimates of the UCS of coal mine roof rock for use in roof
support design. The estimates are obtained through log measurements of the travel time of the compressional or P
wave, determined by running sonic geophysical logs in boreholes, which are then correlated with UCS
measurements made on core samples from the same holes [8]. Sonic travel time measured on cores can be correlated
with unconfined compressive strength derived from failure criteria.
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Sonic logging tools contain one or more transmitters which generate high frequency (generally 20 to 24 kHz)
sound waves, which then travel through fluid in the borehole and the formation, and are received by two or more
detectors. The difference in arrival times of the sonic wave train received by two detectors is then used to determine
the travel time of the first arrival of the compressional (or P) wave, the fastest component of the sound. It is also
possible to measure the shear wave (S wave) travel time, but most companies logging coal boreholes are not
prepared to do so. Generally sonic data are displayed in travel time per foot, with the travel times for almost all
sedimentary rocks falling in the range of 40 to 140 ȝs/ft [8]. Measuring the time difference between arrivals at two
receivers eliminates the common time spent by the signal in the borehole, leaving the time spent in the rock. This
produces an interval transit time, or delta-t log [16].
3. Data analysis
3.1. ANN overview
ANNs are a form of artificial intelligence, which by means of their architecture, try to simulate the behaviour of
the human brain and nervous system. A comprehensive description of ANNs is beyond the scope of this paper and
can be found in many publications [24]. As might be expected from the wide variety of network types, there are
many different areas in which ANNs have been successfully used in geomechanical systems.
ANNs learn from data examples presented to them and use these data to adjust their weights in an attempt to
capture the relationship between the model input variables and the corresponding outputs. Consequently, ANNs do
not need any prior knowledge about the nature of the relationship between the input-output variables, which is one
of the benefits that ANNs have compared with most empirical and statistical methods. If the relationship between
x and y is non-linear, regression analysis can only be successfully applied if prior knowledge of the nature of
the non-linearity exists. On the contrary, this prior knowledge of the nature of the non-linearity is not required for
ANN models [25].
ANNs are composed of three different layers of neurons. The input neurons consists of neurons which receive
information from external sources. The hidden layer processes the information received from the input neurons, and
passes it on to the output layer. The output layer receives signals from the hidden layer and transforms them into
a predicted value of the output. Additionally, a bias neuron lies in hidden layer. It is connected to all the neurons in
the next layer but none in the previous layer. Weights are also assigned to the connections between these neurons
[26].
Feed-forward networks generally have one or more hidden layer that followed by one output layer of neurons. As
the data presented to a feed-forward network, the information begin to propagate from the input layer. The network
modify its connection weights on the presentation of a training data set and employs a learning rule to come upon
a set of optimum weights that will produce the best input-output simulation that has the smallest possible error. In
process modelling, the back-propagation algorithm is the most common learning rule applied for training multilayer
ANNs [26].
Back-propagation learning algorithm includes two phases: forward and backward. In the forward phase,
a training data set is presented to the network and fed forward until a prediction is generated. The final output is then
compared with target value and an error signal is generated through subtraction. In the backward phase, the error
signal is back propagated in the network from output layer to input layer and the appropriate weight changes are
calculated using a mathematical criterion that minimizes the sum of squared errors [26].
The propagation of information in ANNs starts at the input layer where the network is presented with a historical
set of input data and the corresponding (desired) outputs. The actual output of the network is compared with
the desired output and an error is calculated. Using this error and utilising a learning rule, the network adjusts its
weights until it can find a set of weights that will produce the input/output mapping that has the smallest possible
error. This process is called “learning” or “training”. Once the training phase of the model has been successfully
accomplished, the performance of the trained model has to be validated using an independent validation set. [24].
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3.2. ANN analysis
In this study, a feed-forward back-propagation network with three layers is used. The optimal model geometry
was determined utilising a trial-and-error approach. Layer 1 contained 10 sigmoid hidden neurons, and the second
layer contained one linear output neuron. The input elements are sonic travel time, formation porosity, penetration
rate and density, and the target parameter is rock uniaxial compressive strength. The network was developed,
trained, validated and tested using 77 data sets of input parameters and UCS data. The chosen training algorithm was
Levenberg-Marquardt. In order to develop ANNs, collected data were divided into three parts of training (60 %),
validation (20 %) and testing (20 %) data.
The results of the ANN model showed very high accuracy in estimation of UCS values, due to the fact that R = 1
was obtained in testing data analysis, and mean squared error (MSE) of 0.0002663 at epoch 71 was reached. These
results confirm the accuracy and potential ability of ANNs in prediction of UCS values using drilling and well
logging data.
(a)
(b)
Fig. 1. (a, b) Artificial neural networks model results.
4. Results
The purpose of this research was to predict the uniaxial compressive strength based on well logs and drilling data.
To obtain continuous log strength along the wellbore ANN based relationships were developed between UCS and
affecting parameters including sonic travel time, formation porosity, penetration rate and density. They actually are
the outcome of artificial intelligence methods that resulting relationships are very practical to the area of the study. It
is observed in this paper that UCS predicted values by neural networks are very close with lab and field data, which
is concluded by analysis of network performance results including mean squared error and correlation coefficient. It
is also concluded in this study that input parameters which are chosen in this study, have deep effects in UCS
prediction studies, and should be considered in other scientific studies. Conclusions show that using artificial neural
networks to predict UCS of formation rocks in petroleum fields around the world, would ease UCS estimation,
optimize drilling plans and decrease costs. However, the proposed model cannot be considered as a perfect
substitute for direct estimation of rock mechanical properties. Results of this study can be useful for petroleum
industry when a range of geomechanical problems such as wellbore stability and in-situ stress measurements should
be addressed without direct strength information available.
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References
[1] A. Amani, Kh. Shahbazi, Prediction of Rock Strength using Drilling Data and Sonic Logs, International Journal of Computer Applications
(0975 – 8887), 81 (2) (2013) 7–10.
[2] P.B. Kerkar, G. Hareland, E.R.Fonseca, C.J. Hackbarth, Estimation of Rock compressive strength Using Downhole Weight-on-Bit and
Drilling Models, IPTC 17447, International Petroleum Technology Conference, Doha, Qatar, 2014.
[3] A. M. Raaen, K.A. Hovem, H. Joranson, E. Fjaer, FORMEL: A Step Forward in Strength Logging, in Proceedings of the SPE Annual
Technical Conference and Exhibition, Denver, Colorado, 1996.
[4] ASTM, Standard Test Method of Unconfined Compressive Strength of Intact Rock Core Specimens, ASTM Publication, 1986.
[5] ISRM, The Complete ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 1974–2006, International Society for
Rock Mechanics, Commission on Testing Methods, 2007
[6] C. Chang, M.D. Zoback, A. Khaksar, Empirical Relations Between Rock Strength and Physical Properties in Sedimentary Rocks, Journal of
Petroleum Science and Engineering 51 (2006) 223–237.
[7] R. Chatterjee, S. Paul, V.K. Mourya, Prediction of Uniaxial Compressive Strength from well log data in Jharia Coalfield, Department of
Applied Geophysics, Indian School of Mines, Dhanbad – 826 004, India, 2013.
[8] D.C. Oyler, C. Mark, G.M. Molinda, In situ estimation of roof rock strength using sonic logging, NIOSH-Pittsburgh Research Laboratory,
Pittsburgh, USA, 2010.
[9] M. Heidarian, H. Jalalifar, A. Rafati, Prediction of rock strength parameters for an Iranian oil field using neuro-fuzzy method, Journal of AI
and Data Mining 4 (2) 2016.
[10] V.C. Kelessidis, Need for better knowledge of in-situ unconfined compressive strength of rock (UCS) to improve rock drillability prediction,
3rd AMIREG International Conference: Assessing the Footprint of Resource Utilization and Hazardous Waste Management, Athens, Greece,
2009.
[11] E.M.M. Khair, S. Zhang, A.I. Mustafa, Correlation of rock mechanical properties with wireline log porosities through Fulla oilfield –
Mugllad basin – Sudan, SPE North Africa Conference and Exhibition, Cairo, Egypt, 2015.
[12] M. Nabaei, K. Shahbazi, A New Approach for Predrilling the Unconfined Rock Compressive Strength Prediction, Petroleum Science and
Technology, 2012.
[13] M.G. Bingham, A new approach to interpreting rock drillability, Oil Gas J. Reprint Series, 1965.
[14] T.M. Warren, Penetration-rate performance of tri-cone bits, J. SPEDE 32 (1987) 9–18.
[15] S.D. Mohaghegh, Virtual intelligence and its application in petroleum engineering, Part 1, artificial neural networks. Distinguished author
series, West Virginia University, 2000.
[16] N. Butel, A. Hossack, M.S. Kizil, Prediction of in situ rock strength using sonic velocity, Coal Operators’ Conference, The University of
Wollongong, Australia, 2014.
[17] E. Urban, R. Aguilera, Determination of principal in-situ stress magnitude from well logs in unconventional reservoirs: A practical
application in Willesden Green field Canada, SPE conference paper, 2015.
[18] G. Silva, C. Rabe, A.L. Nunes, J.R.E. Garcia, U. Prasad, Development of a New Correlation Based on Grain Size Distribution to Eatimate
Sandstone Reservoirs Uniaxial Compressive Strength, 13th International Congress of Rock Mechanics, Montreal, Canada, 2015.
[19] E. Freyburg, The lower and middle colourful sandstones of SW-Thuringen in their geological characteristics (In German), The East German
geological sciences society, Berlin, 176 (1972) 911 – 919.
[20] G.H. McNally, Estimation of coal measure rock strength using sonic and neutron logs, Geoexploration 24 (1987) 381–395.
[21] C. Zang, H. Huang, Prediction of rock mechanical parameters and rock mass classification by percussive drilling surveying in a rock tunnel,
in: Feng, Hudson & Tan (Eds.) Rock Characterisation, Modelling and Engineering Design Methods, Taylor & Francis Group, London, 2013.
[22] I.D.R. Bradford, J. Fuller, P.J. Thompson, T.R. Walsgrove, Benefits of assessing the solids production risk is a North Sea reservoir using
elastoplastic modeling, SPE/ISRM EUROCK 1998 Conference, Trondheim, Norway, 1998, pp. 261–269.
[23] R.A. Plumb, Influence of composition on the failure properties of clastic rocks, SPE/ISRM 28022, EUROCK 1994 Conference, Delft,
Netherlands, 1994, pp. 13–20.
[24] M.A. Shahin, M.B. Jaksa, H.R. Maier, Artificial Neural NetworkíBased Settlement Prediction Formula for Shallow Foundations on
Granular Soils, Australian Geomechanics, 2002.
[25] M.A. Shahin, M.B. Jaksa, H.R. Maier, Artificial Neural Network Applications in Geotechnical Engineering, Australian Geomechanics,
2001.
[26] V. Rashidian, M. Hassanlourad, Application of Artificial Neural Network for Modeling the Mechanical Behavior of Carbonate Soils,
International Journal of Geomechanics, 2013, (ASCE) GM.1943-5622.0000299.