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ADE | Next, a Machine learning technique in facies identification is investigated in the paper titled "A
transfer learning approach for facies prediction using resistivity image well logs". Resistivity
image logs provide a high-resolution, 2-dimensional image of the borehole inner wall. These
logs contribute significantly to the characterization and understanding of structural
interpretation of the log interval. Interpretation of these logs is quite time-consuming complex
and subject to the interpreterβs experience specially in cases where the geological setting is
complex. There is a great need for an automated workflow to augment and optimise this
manual process. In this study a methodology to train a convolutional neural network on already
interpreted logs in one well is presented and the trained model is used to rapidly detect the
interpreted facies in a newly drilled well. A comparison of different network architectures is
carried out and their confusion matrix is interpreted. Prominent challenges when applying
convolutional neural networks to resistivity image logs were discussed and solutions to these
challenges are suggested. This investigation showed that convolutional neural networks are
able to detect details in the resistivity image logs that can be used to distinguish and classify
the facies. The accuracy at which this is achieved using image logs only was quantified.
Although the investigation concluded that other supplementary logs are needed for facies
classification, it also showed that resistivity image logs contribute significantly to the task. Two
novel pre and post processing methods were presented as well. The data preprocessing
methodology maximizes the training images extracted from logs. While the post processing
method enhances the accuracy and bed boundary detection resolution even further. This study
is delivered in chapter 4.
Lack of data is an intrinsic issue that hinders accurate characterization of reservoirs. Often
sparse data from biased locations in the field are extrapolated to extensive areas. To enhance
7 |
ADE | this process extra information can be derived from a conceptual image contributed by the
geologist known as the Training Image (TI). Furthermore, Correct characterization and use of
this data requires adopting methodologies that quantify and propagate uncertainty in the
process. In the paper titled "A variability aware GAN for improving spatial representativeness
of discrete Geobodies", a Novel Generative Adversarial Network (GAN) architecture is
proposed to generate model realisations that are geologically sound (realistic) and statistically
faithful. GANs are a family of deep generative models (DGM) that have shown great potential
in generating realizations of geological structures. This class of Neural Networks (NN), Can
approximate high dimensional probability distributions from sample data. In this study, we
evaluate the Ability of GANs in generating geological realisations that are (1) visually acceptable
(2) preserve the statistics of the training image and (3) maintain the variability of the structure.
Analysis of Distance (ANODI) is applied to quantify how well multiple point statistic of the
realizations are preserved and probability maps are utilized to quantify the variability of the
realizations. The effect of input data on variability is investigated by evaluating the proposed
network on two different data sets. The proposed architecture outperformed other popular
networks and significantly enhanced variability and reduced spatial bias wile better preserving
multiple point statistics of the realisations. A sensitivity analysis on the key parameters of the
proposed architecture was also conducted. As the application of generative models increases
in generating geological realizations this study presents a universal methodology to maintain
the variability of the output realizations. The investigation and findings of this study constitute
chapter 5.
Characterization of a reservoir model by tuning to one dimensional production data is referred
to as History matching. This type of characterization is generally a nonlinear problem that does
not have a closed-form solution. Characterization of numerical models β which integrates
8 |
ADE | numerous data sources with different dimensions and scales - by history matching is often an
optimization problem with many parameters. As such, it is computationally expensive and time
consuming. Advanced analytics and machine learning techniques can be adapted to enhance
computation efficiency of history matching problems. Since this study is not directly a
characterization technique, it has been attached as an appendix to this thesis. In the paper
titled "Accelerating CMA-ES In History Matching Problems Using an Ensemble of Surrogates
with Generation-Based Management" a surrogate-assisted Covariance matrix adaptation
evolutionary strategy (CMA-ES) is proposed that reliably accelerates history matching and
significantly reduces computation. The algorithm was tested on two simulation cases. The
effectiveness of an ensemble of surrogates to breakdown the complexity of the fitness function
was investigated. Furthermore, an online learning scheme to continuously improve the fidelity
of the proxies over the history matching process is presented. Other techniques such as
generation-based model management and evolution control were applied. The details and
results are presented in the Appendix.
2. Literature Review
Reservoir characterization is a combination of methodologies associated with geostatistics,
geophysics, petrophysics, geology and reservoir engineering (Jia et al., 2012). The main goals
of reservoir characterization research are to aid field development and reservoir management
teams in describing the reservoir in sufficient detail and developing 3D/4D data for reservoir
development planning. Equipped with this information, higher recoveries with fewer wells in
better positions at minimum cost can be obtained through optimization, increasing reserves,
improving stimulation and completion practices and reducing to a minimum uncertainty, in
production forecasts (Haldorsen and Damsleth, 1993, Johnston, 2004, Phillips, 1996). Large
9 |
ADE | quantities of data in different scales are collected during the life of a well, which are
subsequently utilised for reservoir characterization.
Advanced analytics and machine learning play a key role in deciphering these data. In this work
fractal analysis, generative adversarial networks and convolutional neural networks have been
utilized to enhance workflows in reservoir characterization.
2.1 Fractal Analysis
Since the introduction of Fractal analysis by Benoit Mandelbrot, many fields of science have
been revolutionized by this concept, and subsurface characterization is no exception. While
statistical methods continue to be useful, they ignore the fundamental concept that geological
structures are not developed through random processes, but rather deterministic causes
(Hardy et al., 1996).
2.1.1 Fractal character of wireline logs
Hewett in 1986 proved that porosity logs were fractal (Hewett, 1986). Using this the fractal
character Hewett generated porosity distributions that enhanced fluid flow simulation. A
similar approach was utilised by other authors (Aasum and Kelkar, 1991, Berta et al., 1994,
Crane and Tubman, 1990, Emanuel et al., 1988, Hardy, 1992, Hewett and Behrens, 1990,
Lozada-Zumaeta et al., 2012, Perez and Chopra, 1997). Avnir et al. (1985) showed that the pore
structure of rocks has fractal character. Others confirmed this finding in sandstones as well
(Katz and Thompson, 1985, Krohn and Thompson, 1986). Methods and techniques to calculate
the fractal dimension of these structures was also presented in these studies. Pang and North
(1996) in their work suggested that fractal character of well logs is related to the stratigraphic
heterogeneity. Their results showed that more heterogenous rocks produced logs with higher
fractal dimension. Shen et al. (1998) suggested that the fractal dimension of pore structure can
10 |
ADE | be used to classify rock type. They investigated 22 cores and concluded that the fractal
dimension can be related to oil recovery at water breakthrough and irreducible water. Wang
and Mou (2014) measured the fractal dimension of various wireline log data, including
compensated neutron, density, gamma ray and acoustic logs for 108 wells, and found
corresponding relationships between fractal dimension of logs and texture of volcanic rocks.
2.2 Convolutional neural networks
Convolutional Neural Networks (ConvNets or CNNs) are rather well known for their
applications in classification and computer vision tasks. The main components of these
networks are the convolutional layer, pooling layer, nonlinear activation layer and the fully
connected layer. Among these component the most significant is the convolutional layer
(Alzubaidi et al., 2021). These layers not only capture the spatial dependencies of the image,
but also use sparce connections and parameter sharing to avoid parameter size being too large
(Chen et al., 2021). The role of the pooling layer is to subsample the feature maps to smaller
ones (Gu et al., 2018) and make the feature maps more robust to single neuron errors (Liu et
al., 2017). The nonlinear activation layer introduces nonlinearity to the network which
significantly enhances the network performance (Gu et al., 2018). The fully connected layer is
usually located at the end of the network and is the classifier section and categorizes the
extracted local information (Sainath et al., 2013).
2.2.1 Development of Convolutional Neural Networks
The history of deep CNN's began with the appearance of LeNet Introduced by (LeCun et al.,
1995). AlexNet was developed and built based on LeNet-5 (Krizhevsky et al., 2017). With the
appearance of AlexNet for the first time learned features surpassed traditional manual feature
extraction. In 2014, an innovative CNN design with a modularized network was introduced This
11 |
ADE | design was called the Visual Geometry Group(VGG) (Simonyan and Zisserman, 2014). The main
drawback of this network was utilizing a large number of parameters which resulted in high
computational cost. Prior to the advent of the inception network, the simplest way to enhance
CNN performance was to increase their size. This caused two major issues, it made the models
prone to overfitting and dramatically increased the computational cost. The Inception network
(Szegedy et al., 2015) was designed to address the above issues. The inception module
computes 1X1, 3X3 and 5X5 convolutions within the same module, therefore it acts as a multi-
scale feature extractor. The output of these filters are then stacked along the channel
dimension and fed to the next layer in the network (Zaccone et al., 2017). ResNet was
introduced to address network degradation. With network depth increasing, accuracy is
saturated and then degrades rapidly (He et al., 2016) this is referred to as βNetwork
Degradationβ. The residual connection in ResNet is a method to break βdegradationβ and
enable deep neural networks to achieve high accuracy (Orhan and Pitkow, 2017, Chen et al.,
2021).
2.2.2 Transfer learning
Although machine learning has shown great success in different fields of science, it still has
limitations. The ideal scenario for machine learning is when labelled data is abundant. However,
this is rarely the case in real-word scenarios (Zhuang et al., 2020). In reality, and more so in
subsurface engineering labelled data is scarce. Furthermore, large networks required for
learning features of complex datasets are computationally expensive to train. Transfer learning
has proven to be a very effective technique to handle the above issues in the field of image
recognition and image classification (Tang, 2018). In deep convolutional neural networks, with
many layers, the lower layers detect the features while the final layers detect the class of the
12 |
ADE | image (Tang, 2018). In the case of image classification, transfer learning allows us to train the
classifier layers of the CNN with our specific set of images requiring far less training images and
computation power (Shao et al., 2014).
2.2.3 Application of CNN to image logs
High-resolution borehole image logs, provide detailed information on lithology, sedimentary
textures, paleo-flow directions, structural dip analysis, in situ stress analysis and fracture
evaluation (Lai et al., 2018, Nie et al., 2013, Kosari et al., 2015, Brekke et al., 2017, Ameen,
2014). These logs contribute significantly to the geological understanding of the logged interval
(Lai et al., 2018, Folkestad et al., 2012) and allow for structural features to be identified at
resolutions of only a few millimetres (Ja'fari et al., 2012). Machine learning and more
specifically computer vision techniques can be used to automate or augment facies
classification at well locations. Gupta et al. (2019) used a UNET architecture to pick induced
and natural fractures along with sedimentary surfaces from image logs. Lima et al. (2019)
proposed an unsupervised neural network model for pattern recognition and facies
categorization using borehole image logs. They used a non-linear autoencoder for
representational learning to reconstruct the original training images and applied cluster
analysis for categorization of the facies. Using the concept of transfer learning Lefranc et al.
(2021), trained a ResNet architecture on synthetic training data produced by models. However,
their method is still quite laborious since it requires sedimentary dips to be picked manually at
high density.
2.3 Generative adversarial networks
Creating a geological model requires detailed characterization of the reservoir. However
geological models are unable to fully describe the reservoir due to some parameters being
13 |
ADE | uncertain or unknown. This uncertainty in geological models must be adequately quantified
and considered in the applications of the model. understanding uncertainty in reservoir models
involves generating multiple realisations where governing equations are then solved for each
realisation to yield an understanding of the probability distribution of the model response
(Chan and Elsheikh, 2020). There has always been a desire to generate geological models that
not only honour the hard data but are visually acceptable and statistically faithful. To this aim,
different methodologies have evolved over time. Starting with stochastic methods followed by
Multiple point statistic methods that produced superior more realistic realizations. Recently
Deep Generative Models have been introduced and show great potential in this field.
2.3.1 Stochastic methods for generating realizations
Traditionally, stochastic simulation methods are the most popular methods for generating
realisations. Object-based methods and pixel-based methods are the two main subcategories
of stochastic simulation methods (Bai and Tahmasebi, 2020). The first category uses Boolean
object-based algorithms to characterise the simulated area by placing objects that resemble
geological features. Models generated using these algorithms are significantly more realistic
from a geological perspective. However, Conditioning to hard data is quite challenging in these
algorithms (Bai and Tahmasebi, 2020, Strebelle, 2002). Pixel-based Algorithms, Conduct the
simulation pixel by pixel. These algorithms do not pose this challenge and are relatively easier
to condition to hard data. examples of pixel-based algorithms are sequential gaussian
simulation and truncated gaussian simulation. The challenge with these algorithms is that they
are based on two point statistics which is inadequate to reproduce complex geological features
(Tahmasebi, 2018) such as curvilinear geometries (e.g. Sinuous channels) which are inherent
in many geological structures (Marini et al., 2018). As a result, when such geological systems
14 |
ADE | are being simulated using these algorithms, they appear geologically unrealistic. Other pixel-
based methods emerged in the literature such as Truncated pluri-gaussian (Le Locβh et al.) to
overcome some of these limitations and better preserved prior geological understanding
(Astrakova and Oliver, 2015). The main difficulty with applying this method is the inference of
the variogram models for the underlying multi gaussian functions (Mariethoz et al., 2009).
Multiple point Statistics (MPS) methods were introduced to address the problem of generating
realistic models of complex geological structures. These methods require large number of
samples which is generally not available in earth sciences (Marini et al., 2018). The extra
information can be provided by the geologist. The geologist's insight and understanding of the
targeted region is conceptualised in an image known as the Training Image (TI) (Meerschman
et al., 2013). The TI is designed under expert knowledge to replicate expected patterns and
statistical features of the subsurface. The MPS methods then generate realisations that
resemble this training image and honour any other available data. In this scenario the TI plays
and important role and guides the outcome. An example of such technique is the Single Normal
Equation Simulation (SNESIM). This algorithm scans the TI and stores the probability of all
pattern occurrences in a search tree. The probabilities are then retrieved based on existing
data to generate realisations. The challenge with these methods is that inversion using these
methods is computationally expensive. There are re-parameterisation techniques available
however the models provided using these techniques do not agree well with the TI.
2.3.2 Deep Generative methods
A more recent technique for generating realisations of geological models in the literature is
Deep Generative Models (DGM). DGMs are a class of Neural Networks (NN) that can
approximate high dimensional probability distributions when trained on sufficient samples
15 |
ADE | from the desired distribution. The trained model can then be used to generate realisations
from the underlying distribution (Ruthotto and Haber, 2021). A further advantage of DGM's is
that they re-parameterise the realisations by mapping the data to a latent space. Variational
Auto-Encoders (VAE) are an example of generative models that use variational Bayesian
inference to approximate the probability density function of a dataset of samples. They
generally consist of an encoder and a decoder. The encoder takes in sample training data and
reduces it to a latent space by passing it through layers with decreasing dimensionality. The
decoder then samples from the latent space and reproduces the initial sample (Sami and
Mobin, 2019). Laloy et al. (2017) Showed that inversion using VAEs produces superior results
compared to MPS-based inversion methods. Canchumuni et al. (2021) Combined a VAE with
an Ensemble Smoother with Multiple Data Assimilation to history match production data and
reported that trained VAE resulted in noisy facies reconstruction. In general VAEs have a lower
generative accuracy compared to Generative Adversarial Networks (Lopez-Alvis et al., 2021)
and are prone to fail at learning intractable or highly complex probability distributions (Sami
and Mobin, 2019). This is because, VAEs have a simpler architecture with only one loss function
(Kullback-Leibler divergence). As described above VAEs produce their output by compressing
the input to a latent space. Generative Adversarial Networks (GAN) on the other hand, search
for a balance point between the Discriminator and Generator in their two-player game, where
one tried to trick the other. As such, GANs have a more complex architecture and use two loss
functions.
2.3.3 Generative adversarial networks in subsurface applications
Generative adversarial networks (GAN) are a family of deep-learning-based generative models
where the paradigm of unsupervised learning is used in their training process. The GAN
16 |
ADE | architecture has two sub-models: Generator and Discriminator. Generator is used to generate
new plausible examples from the problem domain. The Discriminator is the sub-model that is
used for training the Generator. The architecture has the advantage that after being trained,
the sub-models can be used as standalone models for data generation or classification. The
training process of a GAN is based on a game theoretic scenario in which the generator
competes against an adversary. The generator network directly produces samples from a fixed-
length random vector, referred to as latent space, while the discriminator network, the
adversary, attempts to distinguish between samples drawn from the training data (real data),
and the generated samples.
Figure 1: Vanilla GAN workflow
Figure 1 illustrates the basic workflow of a vanilla GAN. Based on the figure, latent vector π§, is
fed to the Generator πΊ to generate sample πΊ(π§). FC stands for Fully Connected layers. It is
conventional to feed a batch of latent vectors to generate a batch of samples every time. The
Discriminator is trained to classify πΊ(π§) and real samples, X. This is accomplished by maximizing
the probability assigned to real and generated data at the output of the discriminator.
17 |
ADE | Among DGMs, Generative Adversarial Networks (GAN) introduced by Goodfellow et al. (2014)
have been applied to a variety of subsurface applications. GANs have been used to generate
realistic stochastic samples of porous media (Mosser et al., 2017, Mosser et al., 2018b).
Mosser et al. (2018b) Trained a modified version of the DCGAN (Radford et al., 2015) on
randomly extracted images from a micro-CT. They reported that computed two-point statistics
an effective property, showed excellent agreement between the GAN results and segments of
the micro-CT image. However, the generated samples showed less variation compared to the
input training dataset. Mode collapse was mentioned as one of possible reasons. Mode
collapse is defined as the case whereby the Generator can only generate one type of sample
or a small set of distinct samples. This is caused when the Generator learns to generate samples
from few modes of the data distribution but ignores other modes although they are present in
the input training data. This effect when generating geological realizations, will result in the
Generator producing multiple samples/realizations with one or more features replicated in
common locations. The realizations overall are therefore spatially biased towards those
features. There are a variety of reasons for this phenomenon e.g., vanishing gradients,
Discriminator overfitting, poor network architecture, etc. some solutions to reduce this effect
include using Wasserstein loss or progressively increasing resolution of generated images
during training. In chapter 5 of this thesis a solution suited to geological realizations is
presented.
Other subsurface applications of GANs includes application to seismic data. A Cycle-GAN was
used to perform stratigraphic seismic inversion based on a velocity model (Mosser et al.,
2018a). In Mosser et al. (2020), a DCGAN in combination with a numerical solution of the
acoustic inverse problem was trained to parametrize geological heterogeneities. Mode
collapse and its adverse effects on the study were discussed and use of alternative networks
18 |
ADE | that handle mode collapse more efficiently were suggested. GANs were also used to
reconstruct models retrieved by iterative geostatistical seismic inversion (Azevedo et al., 2020).
In this study, two GAN networks DCGAN and WGAN (Arjovsky et al., 2017) were trained on two
datasets, a set of binary facies and a continuous (P-wave propagation velocity) dataset where
an infill painting methodology (Yeh et al., 2017) was used for reconstruction of images. Laloy
et al. (2018) used a GAN architecture to perform MPS based geostatistical inversion for
parameter estimation. They proposed a 3D extension to the original 2D spatial GAN (SGAN)
(Jetchev et al., 2016) and incorporated it in a Markov chain Monte Carlo (McMc). Other
examples of applications of GAN in the literature are re-parametrization (Chan and Elsheikh,
2019a, Chan and Elsheikh, 2020). GANs have shown great potential in generating realistic
realizations of geological models. Multiple studies in the literature have used GANs to generate
realizations conditioned to hard data (Chan and Elsheikh, 2019b, Dupont et al., 2018, Mosser
et al., 2018a, Zhang et al., 2021). Different methodologies have been used to condition
geological models to hard data. Some used semantic inpainting methodology (Yeh et al., 2017)
to condition the model (Dupont et al., 2018). In this methodology, a GAN is trained to generate
geological realizations. The loss of the GAN during training is defined such that the Generator
outputs the closest realization in the latent space manifold whereby this realization honours
the hard data. Others like (Chan and Elsheikh, 2019b) proposed an inference network to be
added to the Generator to further refine the generator function space to produce only
conditioned realizations. Zhang et al. (2021) used a U-net architecture to generate conditioned
realizations. In this study the authors adopted a methodology where a loss term was
formulated to maximize the distance between generated images with respect to
corresponding latent vectors (Yang et al., 2019). Razak and Jafarpour (2020a, 2020b) and
19 |
ADE | Mosser et al. (2019) have gone a step further in their work by calibrating reservoir models using
non-linear production data.
Although GANs promise vast potential in generating realistic geological realizations, Mode
collapse is an important issue to thoroughly investigate when using GANs. Mode collapse can
induce significant error in uncertainty quantification of a model. Furthermore, conditioning to
hard data is not a trivial task when using GANs. The available methods have the potential to
reduce variability of the generated realizations. Currently research in this field is focused on
rectifying the above-mentioned limitations of GANs. It is expected that more applications and
usage of the reparameterization capability of GANS will be introduced.
Finally, to close this section, pros and cons of the mentioned geostatistical methods for
generating geological realizations are presented in Table 2.
Table 2: pros and Cons of different methods for generating geological realizations.
Methodology Variation pros cons
Stochastic methods Pixel-based ο· Easy to implement with little ο· Cannot produce visually acceptable
computation cost. and realistic realizations.
ο· Easy to condition to hard ο· Requires inference of the data
data variogram
Object-based ο· Realizations are more ο· difficult to condition to hard data
realistic compared to pixel-
based methods
Multiple point N/A ο· visually realistic realizations ο· algorithms are computationally and
statistics methods memory intensive.
ο· algorithm uses TI which can
incorporate geologistsβ ο· do not re-parametrize the
expertise realization
Deep Generative VAEs ο· easy to train. ο· fail at learning highly intractable
methods distributions.
ο· results are visually acceptable
GANs ο· results are visually ο· results affected by Mode collapse.
acceptable.
ο· more research required around hard
ο· Can learn complex data conditioning
distributions
20 |
ADE | Rocktypingandfaciesidentification TheAPPEAJournal 103
In conventional reservoirs, flow unit rock typing is usually logsanditsrelationshiptorocktexture.Consideringtheeffect
donebasedonporosityβpermeabilityrelations.Therearenumerous ofrocktextureontheresistivityoftherock,alongwiththefact
rock typing studies in the literature. The common evaluation thatporestructureofrocksisfractal,makesitlogicaltoexpect
techniquesare: that the fractal dimension of resistivity logs is related to rock
texture.
* Physical core description of large- and small-scale features, Theobjectiveofthisstudyistoshowthatfractaldimension
along with core measurements of porosity and permeability;
ofresistivitylogscanberelatedtorocktexture,andthuscanbe
dominantporethroatdiameterfrommercuryinjectioncapillary
usedasanewmethodtoidentifyrocktypes.First,abackground
pressure(MICP)data.
of fractal theory and resistivity of porous media is presented,
* Texture, composition and lithology of the rock, along with followed by details of our proposed method. Then, data and
consideringthedepositionenvironmentofthereservoir.
resultsareinterpretedanddiscussed.
* Identification of lithofacies from log analysis complemented
withcore-basedmeasurements.
Theory background
OthermethodsincludeuseofR35measurementsfrommercury
injection, proposed by Pittman (1992), in which average pore In this section, a background in fractal theory and some facts
throatradiusismeasuredfromthe35%injectionlevelofmercury. onresistivityinporousmediaarepresented.
Theconceptofrockqualityindexandflowzoneindicatorswas
introducedbyAmaefuleetal.(1993).Intightsands,however,
Fractaltheorybackground
useofalltheabovetechniquesneededtobecomplementedwith
rock texture and fabric descriptions to achieve more accurate A fractal is a geometric pattern that shows similarity to itself
results(Rushingetal.2008). at any level of magnification (scale). The pattern that causes
One way to infer rock types is by use of well logs. In this the self-similarity can be repeated at multiple scales to
method, statistical features are defined for the trend of the produce irregular shapes and surfaces that cannot be modelled
corresponding well log, and these features are used to identify by conventional geometry. This is the main feature that
thesamerocktypeinotherwells.However,sinceconventional differentiates fractal geometry from Euclidian geometry. The
interpretationsoflogsdonotprovideanydirectinformationon concept of fractals was introduced by Mandelbrot and has
complexporegeometries,itisdifficulttoconsiderporestructure been shown to be capable of mathematically modelling
inrocktypingmethodsusingwelllogs. irregularnaturalpatterns.
Fractalgeometryoffersanewapproachforinterpretingwell Beforetheintroductionoffractalgeometry,mathematicians
logs.Useoffractaltheoryinoilandgashasasignificanthistory. had come across many patterns and shapes that could not be
In1986,Hewettprovedthatporositylogswerefractal(Hewett modelled by Euclidian geometry. A turning point came when
1986). Using the fractal character, Hewett generated porosity BenoitMandelbrotintroducedamorecomprehensivedefinition
distributions and used them to enhance fluid flow simulation. ofdimension.Hestatedthatthedimensionofafractalmustbe
There were other similar studies (Crane and Tubman 1990; usedasanexponentwhenmeasuringitssize(Mandelbrot1983).
Emanuel et al. 1990; Hewett and Behrens 1990; Aasum and Asaresult,fractalscannotbedescribedwithintegerdimensions
Kelkar 1991; Hardy 1992; Hardy and Beier 1994; Perez and but require fractional dimension, hence the name fractal
Chopra1997;Lozada-Zumaetaetal.2012).Someauthorsfound geometry.
thattheporestructureofrockswasafractalproperty(Avniretal. Mandelbrot defined fractal as βa shape made of parts that
1985). Others investigated different sandstones and confirmed are similar to, or repeat the whole in some wayβ (Mandelbrot
their fractal character (Katz and Thompson 1985; Krohn and 1983). This is a definition of self-similar fractals. This type of
Thompson 1986). These workers also suggested methods to fractal is too regular to model natural phenomena. Self-affine
determine the fractal dimension of these structures. Pang and fractals, however, are defined as objects that are statistically
North(1996)suggestedthatthefractaldimensionofwelllogsis similar to themselves. For example, a fern leaf would look
related to stratigraphic heterogeneity; more heterogeneous similar to itself at different scales but would not be identical.
rock produced well logs with a larger fractal dimension. Shen Self-affine fractals are mainly used to model timeβdepth
etal.(1998)suggestedthatthefractaldimensionofporestructure sequences and spatial distributions. This property that objects
can be used to classify rock type. They investigated 22 cores can look statistically self-similar while also exhibiting some
and concluded that the fractal dimension can be related to oil variability in detail at different length scales is the central
recovery at water breakthrough and irreducible water. Wang feature of fractals in nature (Feder 1988). Fractals have been
and Mou (2014) measured the fractal dimension of various usedinmanyareasofnaturalsciences,e.g.rivernetworks,fault
wireline log data, including compensated neutron, density, lines,mountainranges,coastlines,thicknessoftreetrunks,heart
gamma ray and acoustic logs for 108 wells, and found ratesandearthquakes.
corresponding relationships between fractal dimension of logs Thescaleinvarianceoffractalsismathematicallydescribed
andtextureofvolcanicrocks. byapowerlaw.Apowerlawdistributionistheonlystatistical
In most studies, the fractal dimension of the pore structure distributionthatisscaleinvariant.
is derived from microscopic core images and images of thin One of the best methods for mathematical modelling of
sections using image processing techniques. Furthermore, no self-affine fractals is fractional Brownian motion (fBm). In
study has considered the fractal dimension of resistivity well termsofafunctionoftime,fBmisdefinedas: |
ADE | Rocktypingandfaciesidentification TheAPPEAJournal 105
The resistivity of the rock matrix is usually assumed to be or failed MICP tests were excluded. Eventually eight cores,
infinite,thusthe resistivity ispresumed to bea function ofthe with MICP data and a full suite of logs, were analysed. The
pore fluid alone. This is not entirely true as the matrix plays pore size distribution of the core samples were derived using
a passive role in resistivity of the rock. This passive role is MICP.Porosityandpermeabilityofthecoreswerederivedusing
dependent on the geometry of the pores, pore connections, routinecoreanalysis.
tortuosity and pore size distribution. Studies have shown that
resistivityoffluid-filledsedimentaryrocksismostlycontrolled Work flow
by pore structure (Archie 1942; Bigalke 2000). Wettability,
saturation history and temperature also play important roles Inthis study,weaimedtoinvestigate therelationshipbetween
(Swanson1985;Kumaretal.2010).Pore-structurecharacteristics the rock texture and the fractal dimension of resistivity logs.
can be estimated from electrical resistivity logs and used for For this purpose, core data and corresponding resistivity logs
abetterestimationofpermeability(Verweretal.2011). were analysed. The core data were used to classify the cores
Any clays present play an active role in conduction of the in rock types. Rock types were defined using porosity and
rock.Claysconductelectricityintwoways:throughporewater permeabilityofthecoresalongwithporesizedistribution.
andthroughclayitself(Rider1986).Theresistivityofreservoir The collected data were primarily quality controlled. Any
rocks depends on numerous factors which can collectively be cores or intervals with missing or noisy data or failed MICP
described as rock fabric. Rock fabric describes the spatial and tests were excluded. Based on these properties, the cores were
geometricconfigurationoftherock,andcanberepresentedby thendividedintothreedifferentrocktypes.
numerical engineering values complemented with geological The fractal dimension of the resistivity log corresponding
descriptionsoftherock. toeachcorewascalculated.Tocalculatefractaldimension,the
Katz and Thompson (1985) proposed that the pore spaces data need to be unimodal and stationary without imposing
of sandstones are fractal and presented several measurements anyspecifictrend.Thisisacriterionofhomogeneityrequired
tosupporttheirproposal.Theelectricalconductivityinporous for a meaningful fractal dimension. Homogeneous datasets
mediaobeysascalinglaw(Toledoetal.1994),whichsuggests exhibit a unimodal distribution, and a visual inspection of
thatresistivitywelllogshavefractalcharacter: the histogram is sufficient to ensure that just a single peak
exists in the data density distribution. It should be noted that
s w /S wmΓ°31 (cid:2)DΓ Γ°8Γ resistivity data are not Gaussian but log-normal. Thus, the
logarithmofresistivityvaluesshouldbetakenbeforeplotting
where,s istheelectrical conductivity oftheporous medium,
w thehistogram.Ifthehistogramisnotunimodal,theloginterval
S iswatersaturationandmisArchieβscementationfactor.
w needs to be broken down into more homogenous sections.
Weproposethatthefabricofarocktypeaffectsthevariability
Also,beforecalculationofthefractaldimension,thedataneed
ofresistivitylogs,andthiscanbeuniquelycharacterisedbythe
tobe normalisedwithzero meanand unit standard deviation.
fractaldimensionoftheresistivitylogs.
Given the type of data and common sampling rates of well
logs, Higuchiβs method was chosen for this study. Higuchiβs
algorithm was coded in Matlab software and used for
Data
calculating fractal dimensions.
The Cooper Basin is the most prospective onshore petroleum Finally, the fractal dimensions were compared with the
andnaturalgasprovinceinAustralia.Itisasedimentarybasin definedrocktypes.
that formed and developed from the late Carboniferous to
middle Triassic geologic periods. It unconformably overlies
Results and discussion
theWarburtonBasinandunconformablyunderliestheCretaceous
Eromanga Basin (Gravestock and Jensen-Schmidt 1998). The Cores from different locations in the Cooper Basin were
basinislocatedacrossthenorth-eastofSouthAustraliaandthe analysed. The cores were classified into three rock types. The
south-west of Queensland. The reservoir system comprises fractal dimension of the corresponding resistivity log to each
a multi-zone high-sinuosity fluvial sandstone ranging from corewasthencalculatedusingHiguchiβsmethodasmentioned
tight (unconventional) to good-quality conventional reservoir intheworkflow.
rocks. There is a large range of porosity and permeability in Based on the porosity and permeability measurements of
the basin due to combination of facies and burial depth. The the cores, along with the pore size distribution from MICP
main gas reservoir is within the Patchawarra Formation with tests, the cores were classified into three main rock types.
anaverageporosityof10.5%andpermeabilityupto2500mD, PropertiesoftherocktypesarepresentedinTable1.Thepore
and the Toolachee Formation with an average porosity of sizedistributionsofallcoresarepresentedinFigs1β3.Therock
12.4%andpermeabilityupto1995mD(Gravestocketal.1998). typesweredefinedasfollows:
Oil is produced from the low-sinuosity fluvial sand within Rock type I was characterised by porosities in the range of
the Tirrawarra Sandstone with average porosity of 11.1% and 13β20%andpermeabilityrangeof50β300mD.Theporethroat
permeabilityupto329mD(Gravestocketal.1998). size distribution ranged within 1β100mm throats. About 50%
In this paper, 59 core samples from different locations of the pore radiuses were in the range of 10β100mm. This
(laterally) in the Cooper Basin were chosen for analysis. The arrangementshowedthattherocktypeconsistedoflargegrain
datawasqualitycontrolledandcoreswithmissingorlow-quality sizesandthehighpermeabilitysuggestedgoodinterconnectivity
data such as noisy or low sample-rate logs, missing intervals inthestructure. |
ADE | 106 TheAPPEAJournal R.Koochaketal.
Table1. Propertiesofthedefinedrocktypes
Rocktype Porosity(%) Permeability(mD) Fractaldimension Description
I 13β20 50β300 1.145β1.158 Majorityofporethroatsintherange10β100mm
II 7β14 5β40 1.186β1.199 Majorityofporethroatsintherange1β10mm
III 5β14 0.096β3 1.221β1.286 Majorityofporethroatsintherange0.1β1mm
Rock type I - Pore size distributions
9
8
7
6
5
4 Core 1
Core 2
3
2
1
0
0.001 0.01 0.1 1 10 100 1000
Pore throat size (Β΅m)
Fig.1. PoresizedistributionofthecoresrelatedtorocktypeI.
Rock type II - Pore size distributions
12
10
8
Core 3
6
Core 4
Core 5
4
Core 6
2
0
0.001 0.01 0.1 1 10 100 1000
Pore throat size (Β΅m)
Fig.2. PoresizedistributionofthecoresrelatedtorocktypeII.
Rock type II featured porosities ranging within 7β14% and that of type II. Although the porosity was similar to type II,
permeability within 5β40 mD. The majority of the pore throat the permeability suggested that most of the porosity was
sizes were within 1β10mm, which was an order of magnitude ineffective. The grain sizes in this rock type were very fine
smallerthanthatoftypeI.Theporesizedistributionsuggested and pore throats were filled with clay.
that the grain sizes in this type were smaller and reduction in The fractal dimension of the resistivity well logs
permeabilitywasduetoincreaseincapillarypressures. corresponding to each core was calculated using Higuchiβs
Rock type III was a tight sandstone reservoir with method. Some of the well log intervals are presented in
porosities ranging within 5β14% and permeability within Figs 7 and 8 as examples. In order to calculate fractal
0.096β3 mD. The majority of the pore throats were dimension of logs, the data needed to be stationary and
0.1β1mm, which was an order of magnitude smaller than Gaussian. To achieve this, homogenous intervals were chosen
)%(
emulov
eroP
)%(
emulov
eroP |
ADE | 108 TheAPPEAJournal R.Koochaketal.
basedonthegammarayandsoniclogs.Thenumericalvaluesof Asthecomplexityofrockstructureincreased(duetosmaller
resistivity curves were then extracted and normalised by grain sizes and/orincreased clay content)and fluid flow inthe
subtracting the average and dividing by the standard deviation media became more difficult, the fractal dimension of the
ofthedata. corresponding resistivity log increased (Table 1). This indicates
AsperHiguchiβsmethod,serieslengthswerecalculatedfor that the complexity of the rock structure was reflected in the
different scales k. The log of the average length of each series variabilityoftheresistivitylogs.
(log(L(k)),wasplottedagainstthelogoftheinverseofthescale RocktypeIfeaturedlargeporesizesandhighporosityoverall.
(1/k).Theresultwasastraightline,withslopeequaltothefractal Large pore size indicated large, well-sorted matrix grains and
dimension of the resistivity log. The plots of k vs log(L(k) for thehighpermeabilityindicatedthatporeswerewellconnected.
every core are shown in Figs 4β6. The slope of the line was Thepore size distributions ofthe coresof type I areplotted in
determinedbyabestlinearfittothepoints.Therangeofthefractal Fig. 1. A considerable portion of the pore throat sizes ranged
dimensionsofeachrocktypeispresentedinTable1. within 10β100mm. The fractal dimension of the resistivity log
Plot of average series length vs Scale
Rock type III
8
y = 1.2211x + 7.4342
7
6
5
y = 1.2865x + 4.4326
4
Core 7
3
Core 8
2
1
0
β1.8 β1.6 β1.4 β1.2 β1 β0.8 β0.6 β0.4 β0.2 0
log (1/K)
Fig.6. Plotofscalevslengthofseries(welllog)relatedtorocktypeIII.
Fig.7. Welllogscorrespondingtocore1.
))k(L(
gol |
ADE | A Transfer Learning Approach for Facies Prediction
Thisresultsinhighaccuracyclassificationoffacieswithamuchlowerrequirementfortrainingdataanddemandfor
computingpower. Inthisstudy, thethreementionednetworkswereappliedusingtheinputimagelogdatasetanda
postprocessingmethodologywasdevelopedtoadapttheCNNarchitecturetobetterevaluatethecontinuousresistivity
imagelog. OurmaingoalwastoexplorewhetherCNNsareabletoextractfeaturesfromthismodalityofdataalone.
The remainder of this text is structured as follows: We continue with the geologic setting of the data. Next image
classification using deep CNNs is reviewed. Data preparation methodology and proposed deep learning model are
presented in the subsequent sections followed by results and discussions. Finally, conclusions and future work are
presented.
2. Geologicsetting
TheCO2CRCprojectfielddemonstrationsiteislocatedinsouth-easternAustralia,withintheonshoreOtwaybasin.
ThefacilityistothesouthwestofMelbourneinthestateofVictoria,betweenthecoastaltownsofPortCampbellto
theeastandWarrnambooltothewest. TheOtwayBasinisariftbasinstretchingnorthwestfromsoutheastofSouth
AustraliatothenorthwestofTasmania. ThebasinformedduringtheAntarctic-Australianseparationassociatedwith
the break-up of Gondowana (Willcox and Stagg, 1990). Local tectonic activity and eustatic sea level variation has
producedfivemajorgroup-levelsedimentarysuccessions:theOtway,Sherbrook,Wangerrip,NirrandaandHeytesbury
groups(WoollandsandWong,2001). DepositionofthelowermostOtwayGroupwascontrolledbytectonicactivity
priortolocalrelativesealevelchanges. Thedepositionalenvironmentwascontinental,producingfirstvolcaniclastic
sedimentsgraduatingtofluvialandshallowlacustrinesedimentsintheupperparts(Mishraetal.,2019;Woollandsand
Wong,2001). MarinebreakthroughisrecordedbytheSherbrookGroup,assealevelbecameregionalbaseleveltothe
depositionalenvironment. Thesuccessionvariesfrommarginalmarinesedimentsatitsbasetothoseofawidespread
deltaicplainenvironmentatthetop(BoydandGallagher,2001;Mishraetal.,2019;WoollandsandWong,2001). The
Wangerripgroupwasdepositedundervaryingconditionsfromlowenergymarginalmarinetoshallowmarine. The
depositional environment in this group is represented by a first-order transgressive-regressive cycle producing first
a fining up, then a coarsening upwards succession (Morton et al., 1994; Mishra et al., 2019). The Nirranda Group
developed under open marine conditions and the Heytesbury Group bears depositional environments varying from
innershelfatthebasetomid-shelfatthetop(Mishraetal.,2019;WoollandsandWong,2001). TheSherbrookGroup
is the primary interval of interest for πΆπ storage operations of the Otway Project. The Waarre Formation β the
2
primary petroleum reservoir within the onshore basin area β and the deep saline reservoir formations of the lower
Paaratte Formation were the first and second targets for πΆπ sequestration experiments respectively (Bunch et al.,
2
2012).
2.1. Faciescategories
Six high-level facies categories were chosen for training the CNN. These capture 15 sub-classes of mainly de-
positional sedimentary litho-facies interpreted manually following acquisition of core and image log data. The six
high-level categories are defined as Mudstone, Heterolithics, Muddy Sandstone, Clean sandstone, Cemented layers
andPebbles. TheMudstonecategorygenerallyshowsnovisibleinternallaminationswithcommontoabundantdis-
seminated pyrite. It can sometime have stress features like borehole breakouts or drilling induced tensile fractures
(whicharefarrarer). TheHeterolithicsfaciescategoryischaracterizedbyalternatinglayersofcentimetertodecimeter
thick,moderatelyresistivelayerswithsimilarlythickconductivemudstones. Thebedboundariesaregenerallysharp
but in some cases are diffuse as well. Tops and bases of layers are generally well defined but when they are rather
diffusethiscategoryisdifficulttodistinguishfromMuddySandstone. TheMuddySandstonecategorycomprisesof
alternatingresistive(possiblysand-rich)andlightlyconductive(possiblymuddy)layers. Thelayerboundariesaregen-
erallymorediffuse. Thethicknessofthelayersrangesbetweencentimeteranddecimeters. Dispersedpyritenodules
arecharacteristicofthiscategorypresentingassmalldarkconductivepatchesthroughoutthelayer. Whentheresis-
tivitycontrastrangeofthelayersishighthiscategorylookssimilartoHeterolithics. Thepresenceofpyritenodules
inthiscategorycansometimemeanthatitlookssimilartoMudstonewhenimagesaredynamicallynormalized. The
Cleansandstonefaciesgenerallyappearsinstructureless(βmassiveβ)thickerbedsoccasionallywithamottledresistiv-
ityfabric. Changesinresistivitycanbeduetochangeinporosity,grainpackingorcementation. Thisfaciescanlook
similartoMudsoneorsometimesHeterolithicswhenimagesaredynamicallynormalized. Cementedlayersrepresent
adistinctlypost-depositionaltypethatisindicatedbyhighlyresistiveintervalswithelevateddensityandreducedneu-
tronporosityvalues. TheresistivityofthesebedsmayexceedtheresistivityrangeoftheFMItoolandsaturatesthe
R Koochak et al.: PreprintsubmittedtoElsevier Page 3 of 15 |
ADE | A Transfer Learning Approach for Facies Prediction
lookedtotheconceptoftransferlearning. Intransferlearninganalreadytrainedmodelisrepurposedtoanewtask.
Thistechniquetakesadvantageofthetrainedfeatureextractingconvolutionallayers. Newfullyconnectedclassifier
layersthatareadaptedtothenewtaskclassificationcategories, willbeintroducedtothenetworkandtrainedbased
on the classification of the new task. Since the network has already learned to extract features, training on the new
taskwillbesignificantlylesscomputationallyintensiveandtimeconsuming. Afurtheradvantageofthistechniqueis
thatitcanachieveahigherperformancewithonlyasmallamountofdata. Toensurethattransferlearningissuitable
forourapplicationwetestedthreedifferentpre-trainednetworksi.e. VGG-16, Inception-V3andResnet-101onthe
sameinputtrainingdataset. Thesethreenetworksreachedatestingaccuracyof67.5%,78.1%and82.9%respectively.
DetailsoftrainingandtestingaccuracyofthethreementionednetworksarepresentedinTable2.
Table 2
Training and testing Accuracy of three CNNβs tested on the dataset.
CNN Name Training Accuracy Testing Accuracy
VGG-16 69.1% 67.5%
Inception-V3 99.7% 78.1%
ResNet-101 97.1% 82.9%
The comparison of the results showed that the accuracy trend complies with the trend on other data sets. This
compatibility of accuracy trend is confirmation that transfer learning is a suitable technique for our dataset. The
ResNet-101networkistheclassifierofchoiceforthisstudysinceitproducedthehighestaccuracy. Tofurtherevaluate
theperformanceoftheabovenetworks,aconfusionmatrixforeachnetworkwasdeveloped. Aconfusionmatrixisa
visualsummaryoftheperformanceofaclassifier. Theconfusionmatricesforthethreenetworkstrainedonoursix
faciescategoriesisshowninFigure8. Therowsandcolumnsofthematrixarethesixfaciescategoriesorganisedin
the same order. The diagonal elements denote the correctly classified outputs. The off-diagonal elements show the
incorrectlyclassifiedoutcomes. Thethreematrixesshowasimilarlearningpattern. Faciescategoryβ5ββCemented,
andβ6ββPebbles,arequiteaccuratelydetectedbyallthenetworks. TheCementedclassreturnsaresistivitythatmay
oftenbehigherthantheFMItoolcapacity,therebysaturatingthemeasurementtool. Theimageisthereforedistinctand
canbeeasilylearnedanddetectedbythenetwork. AnexampleimageoftheCementedcategoryisshowninFigure
9. Facies β3β and β4β are misclassified most often. Facies β3β is misclassified as Facies β4β 20% of the time, while
Faciesβ4βismisclassifiedasFaciesβ3β10%ofthetimeintheResNet-101confusionmatrix. Thesefiguresarehigher
intheVGG-16andInception-V3matricesrespectively,whichisinlinewiththetestingaccuracyofthesenetworksas
presentedinTable2.Thisisduetothesimilarityofthesedimentarytexturesrevealedinthesetwofaciescategories
by dynamically normalized images. Conceptually, both categories represent sandstone with a mixture of mud/clay.
Thelevelofmudintherockdeterminestheclass. Therefore,occasionallythesetwoclassescanbehardtodistinguish
formeachotherthoughalsousingthecorrespondingstaticallynormalizedimagemayhelp. Examplesoftwolabelled
intervals of Facies β3β and β4β are shown in Figure 10. It can be seen from the matrices that Facies β1β and β2β are
occasionally misclassified as either Facies β3β or β4β. Clearly, this occurs more often for VGG-16 and Inception-V3
thanforResNet-101. Thesemisclassificationsoccurbecausethesefaciesarevisuallysimilarinthelogeventhough
theyaregeologicallycategorizedindifferentcategories. Thislimitationisduetousingimagelogsalonewhichwas
aresearchquestioninourinvestigation. CNNsareabletoclassifyvisuallysimilarcategoriesfromimagelogsbetter
thanthehumaneye,buttoenhanceaccuracyofcategorizingthesefacies,otherdatatypessuchassupplementary1D
logsoftheconventionalwirelinesuiteshouldbeincorporatedaspartofthetrainingprocess. Thisisnotwithinthe
scopeofthecurrentstudyandthereforehasnotbeenaddressed. TheultimategoalofthetrainedCNNistoclassifythe
learnedfaciescategoriesinafull-lengthresistivityimagelog. Wehaveproposedapost-processingmethodologyto
adaptthearchitectureofaCNNtothistask. Thepost-processingtechniqueisappliedtotheoutputofResNet-101since
it produced the best transfer learning accuracy. The simplest strategy would have been to slide a 192Γ192 window
overtheresistivityimagewithauser-definedstrideandevaluateasingleimageaftereachshift. However,giventhe
accuracyofourbestnetworkResNetstandsat82%,thismethodologywouldreturnincorrectresults18%ofthetime
tothepost-processingstep. Resultswereinconsistenteveninthickintervalsofthesamefaciescategorywithincorrect
designations produced too often, requiring human intervention to correct and finalize. Another imperfection of this
methodistheverylowresolutionofbedboundarydetection. Aproposedsolutionwouldbeamovingwindowwith
a strideof one. After each shiftthe outcomeof the CNNclassifier whichis anarray with 6probability elementsis
R Koochak et al.: PreprintsubmittedtoElsevier Page 11 of 15 |
ADE | R.Koochaketal. ComputersandGeosciences166(2022)105188
methodsareunrealisticwhensimulatingsuchgeologicalsystems.Trun- generator captures few major modes of the input training data and
cated Pluri-Gaussian (Le Loch et al., 1994) is a pixel-based method ignores many small modes is referred to as mode collapse (Bang and
introducedtoovercomesomeoftheselimitationsandbetterpreserve Shim,2018).Thisresultsinreductioninvariabilityoftherealizations
priorgeologicalunderstanding(AstrakovaandOliver,2015).Thebasic thataregenerated.Inotherwords,therealizationslooksimilarinmost
ideainthismethodistosimulateseveralcontinuousgaussianfieldsand areas of the model with minor differences. This effect will severely
truncate them to produce a categorical variable. The main difficulty disturbuncertaintyquantificationorHistorymatchingasthegenerated
in applying this technique is the inference of the variogram models realizations will be biased towards certain areas in the model. Some
for the underlying multi-gaussian functions (Mariethoz et al., 2009). workhasaddressedthisissueusingaWassersteinGAN,whichtheoret-
Multiplepointsstatistic(MPS)methodswereintroducedtoaddressthe icallyreducesmodecollapse(Arjovskyetal.,2017).Ingeneral,there
problemofgeneratingrealisticmodelsofcomplexgeologicalstructures. aretwoformsofvariabilitythatneedtobemaintained:(1)thewithin-
Using multiple points requires a large number of samples which are realizationvariabilityand(2)thebetween-realizationvariability(Tan
usuallynotavailableinearthsciences(Marinietal.,2018).Thisextra etal.,2014).Thewithin-realizationvariabilityreferstoeachindividual
information can be derived from a conceptual image contributed by realization capturing the statistics (uni-variate, two-point, multiple-
the geologist known as the Training Image (TI). MPS methods can point, etc.) of the geological structure (training data set), while the
generate realizations that honor the training image. An example is between-realization variability refers to the dissimilarity of the gen-
SingleNormalEquationSimulation(SNESIM).Thisalgorithmscansthe erated realizations. Mode collapse refers to the output realizations
TIandstorestheprobabilityofallpatternoccurrencesinasearchtree, notbeingdiverse.Therefore,variabilityinthispaperalwaysrefersto
the probabilities are then retrieved based on existing data to gener- dissimilaritybetweengeneratedrealizations.
ate realizations (Strebelle and Journel, 2001). Inversion using these Inthisstudy,toimprovethevariabilityofgeneratedgeologicalre-
methods (JΓ€ggli et al., 2017; Laloy et al., 2016) is computationally alizationsweproposeanewGANarchitecture.Similartoconventional
expensive.Therearereparameterizationtechniquesavailable,however GANs, our architecture consists of a Generator and Discriminator. A
themodelsprovidedusingthesetechniquesdonotagreewellwiththe regularization term has been added to the Generator loss to improve
TI(Laloyetal.,2018). variabilityandreducespatialbias.Toevaluateourproposedarchitec-
Recently, a large body of research has applied Deep Generative ture,wetrainaDeepConvolutionalGAN(DCGAN)andaWasserstein
Models (DGM) to generate realizations of a geological model. DGMs GANwithgradientpenalty(WGAN-GP)togeneraterealizationsbased
are a class of Neural Networks (NN) that can approximate high- onthefamousStrebellebenchmarkreferencetrainingimage(Strebelle
dimensionalprobabilitydistributionswhentrainedsuccessfully,given andJournel,2001)ofastationarychannelizedfluvialsystem.Wethen
sufficient samples from the desired distributions. The trained model comparetheresultswiththosegeneratedbyourproposedarchitecture.
can then be used to generate realizations from the underlying distri- Weintroducethenewarchitectureusingthisbinarybenchmarkimage
butions (Ruthotto and Haber, 2021) and they have the added value since it is well known and frequently used in the literature, but the
ofre-parametrizingtherealizations,comparedtoMPSmethods.Vari- proposed methodology can potentially be extended to be applied to
ational Auto-encoders (VAE) are an example of generative models multiple-faciesrealizations.Therestofthispaperisstructuredasfol-
thatusevariationalBayesianinferencetoapproximatetheprobability lows:inSection2,wedescribesomerelatedwork.Ashortbackground
density.VAEsconsistofanencoderandadecoder.Theencodertakes of GANs and their training process along with brief description of
in sample training data, and passes it through layers with decreasing DCGAN,WGAN-GPandmodecollapseinpresentedinSection3.Our
dimensionality,mappingthedatatoalatentspace.Thedecoderthen proposedarchitectureisdiscussedinSection4followedbytheexper-
samples from the latent space and reproduces the initial data (Sami imentalsetupinSection5.Resultsanddiscussion,thenconclusionsof
andMobin,2019).InversionusingVAEshasbeenreportedtoproduce thestudyfollow,togetherwithideasforfuturework.
superiorresultscomparedtoMPS-basedinversion(Laloyetal.,2017).
Incombinationwiththeensemblesmootherwithmultipledataassim- 2. Relatedwork
ilation to history match production data, Canchumuni et al. (2021)
reported that the trained VAE resulted in ββnoisyββ facies reconstruc- In the field of geosciences several studies have been conducted to
tions. In general VAEs have a lower generative accuracy compared evaluate the effectiveness of GANs for generating realizations. Some
toGenerativeAdversarialNetworks(Lopez-Alvisetal.,2021)andare GAN variants have been proposed to improve the variability of gen-
pronetofailatlearningintractableprobabilitydistributions(Samiand erated realizations and conditioning to hard data. Note, to prevent
Mobin,2019).AmongDGMs,GenerativeAdversarialNetworks(GAN) confusionbetweenthegeologicalconceptualTrainingImage,andGAN
haveshowngreatpotentialforgeneratingrealizationsofageological inputtrainingdatawe,fromhereon,refertotheconceptualgeological
model.ThebasicGANcreatedbyGoodfellowetal.(2014)consistsof image as Reference Training Image (RTI). To emphasize, the RTI is a
twoneuralnetworks,GeneratorandDiscriminator,trainedend-to-end conceptual image of expected spatial structures and are usually built
toproducerealizationsofadesireddistribution.Sincetheintroduction basedonpriorinformation(Meerschmanetal.,2013).TheGANinput
of GAN in 2014, many GAN architectures have been developed and trainingdataareasetofrealizationsassembledbasedontheRTIand
tailoredtothespecificneedsoftheirapplication. usedtotraintheGAN.
Therearethreemaincomponentstogeneratingsatisfactorygeolog- GANs have been used to generate realistic stochastic samples of
icalrealizations:1.Therealizationsneedtobegeologicallysoundand porous media (Mosser et al., 2017, 2018b). In Mosser et al. (2018b)
visuallyacceptable,2.theymustpreservethestatisticsofthestructure a modified version of the DCGAN (Radford et al., 2015) was trained
or reference training image (that includes univariate, two-point and on randomly extracted images from a micro-CT. They reported that
multiple-point statistics) and 3. they must maintain the variability of computedtwo-pointstatisticsandeffectivepropertiesshowedexcellent
thestructure.Honoringharddataisanimportantfeatureofgeological agreement between the GAN results and segments of the micro-CT
realizations, however, the focus of this study is on unconditioned image. However, they observed far less variation in the generated
models. Most of the literature documenting studies that have utilized samples compared to the input training dataset. Mode collapse was
GANs in earth science applications have reported that GANs achieve mentioned as one of possible reasons. GANs have also been applied
the first two components quite well, while due to mode collapse the to seismic data. A Cycle-GAN was used to perform stratigraphic seis-
variabilitytendstodecrease(ChanandElsheikh,2020,2019b;Azevedo mic inversion based on a velocity model (Mosser et al., 2018c). In
et al., 2020). Training a GAN minimizes the divergence between the Mosseretal.(2020),aDCGANwastrainedtoparametrizegeological
probability Density Function (PDF) of the training data and the PDF heterogeneities and was combined with a numerical solution of the
that the generator samples. In this process the condition where the acousticinverseproblemusingtheadjointmethod.Modecollapsewas
2 |
ADE | R.Koochaketal. ComputersandGeosciences166(2022)105188
Fig. 4. Proposed framework for Variability Aware GAN(VA-GAN). In this framework, a probability map is produced for each batch of generated data in every iteration. Then
probabilitylossisusedtopunishspatiallybiasedbatches.
work through the training data in batches. To investigate the vari-
ability, we generated probability maps of the input training data and
GANgeneratedrealizations.Probabilitymapsareanexcellenttoolfor
evaluatingspatialbias,sincetheycanvisuallyshowthelocationofthe
spatialbiasandquantitativelymeasuretheseverityofit.Comparison
oftheprobabilitymapsgeneratedforinputtrainingdataandgenerated
realizations showed GAN results exhibit spatial bias. This comparison
sparked the idea to change the GAN architecture so that in every
iterationitpunishesspatiallybiasedbatches.
Fig.4showsourproposedframework.Asshowninthefigureour
proposedarchitectureconsistsofaDiscriminatorandaGeneratorthat
performthetraditionalfunctionality.However,aregularizationtermis
addedtothegeneratorlosstopenalizebatchesofdatathatshowspatial
bias. This is accomplished by introducing a loss component to the
Generator derived by the norm one distance between the probability
map of the batch data and the probability map of the input training
data. In the case of a stationary RTI, substituting with distance to a
uniformmapwouldsuffice.Inanon-stationarycase,though,wherefor
examplethegeologistpreferstoassignhigherprobabilitytoafeature
or channel in a specific location of the map, generating the input
Fig.5. Referencetrainingimageforabinaryfaciesmodelofafluvialdistribution. training data probability map would accommodate for that and is a
moregeneralapproach.
Assumeπ₯ βZπΓπ,whereπβ[1,2,β¦,π]isπthbinaryrealization
π 2 π
sample of size πΓπ from a dataset X β ZπΓπΓππ. π denotes the total
of showing sand while other areas are biased to shale. An example 2 π
number of realizations in a batch or input training dataset. Since π₯
of severe mode collapse is shown in Fig. 3. In this figure, 25 tiled
is a binary realization the pixel values are either 0 for background
visuallyacceptablerealizationsofachannelizedfluvialsystem(Fig.3b)
mud or 1 for channels. Summing all same index pixel values of all
havebeencomparedwith25tiledrealizationsofthesamegeological
realizationsinthedatasetXanddividingtheresultbyπ,willgenerate
systemgeneratedwithseveremodecollapse(Fig.3a).Clearly,despite π
theprobabilitymapπ (X)βRπΓπofsizeπΓπ,whereeachpixelinπ (X)
the introduced noise, under mode collapse the yellow channels are π π
hasavaluebetweenzeroandone,whichrepresentstheprobabilityof
reoccurringinmoreorlessthesamelocations.
sandoccurrenceatthatpixel.Ifeachrealizationisrepresentedbyan
πΓπ matrixthen:
4. ProposedGANarchitecture
π (X)= 1
βππ
π₯ (6)
π π π
Given a distribution of geological patterns, we aim to generate π π=1
realizations that are visually acceptable, honor the statistics of the Probabilitylossisdefinedas:
distribution and maintain variability. This study focuses on maintain-
ing the variability of the generated realizations at the same level as β π=βπ π(πΊ(π§))βπ π
β1 (7)
the input training data and reduce spatial bias as much as possible. where π (πΊ(π§)) is the probability map of a batch of realizations and
π
To achieve this, we have proposed a new GAN architecture with a π istheprobabilitymapoftheinputtrainingdata.Wewillfromhere
π
regularization term introduced to the Generator loss function. GANs onrefertothisarchitectureasVariabilityAwareGAN(VA-GAN).
5 |
ADE | R.Koochaketal. ComputersandGeosciences166(2022)105188
Fig. 12. Comparison of univariate statistics of Probability maps of input training data and generated realizations of GANs. The data sources for each probability map are as
follows:(a)ComparisonofprobabilitymapsproducedfromGANstrainedonDirectpatchdataset,(I)realizationsgeneratedfromDCGAN,(II)realizationsgeneratedfromWGAN-
GP,(III)realizationsgeneratedfromVA-GAN ,(IV)realizationsgeneratedfromVA-GAN ,(V)Directpatchinputdataset.(b)Comparisonofprobabilitymapsproducedfrom
βππππππ₯ βπ
GANstrainedonSNESIMdataset,(I)realizationsgeneratedfromDCGAN,(II)realizationsgeneratedfromWGAN-GP,(III)realizationsgeneratedfromVA-GAN ,(IV)realizations
βππππππ₯
generatedfromVA-GAN ,(V)SNESIMinputdataset.
βπ
realizations that preserve qualitatively the multiple point statistics of Table1
theRTI. EuclideannormoftheJensenβShannondistancesbetweengeneratedrealizationsand
thereferencetrainingimage.
Fig. 10 shows five randomly selected realizations out of a pool
GAN DirectPatch SNESIM
of 150 realizations generated by each GAN trained on the SNESIM
inputdata inputdata
dataset. Each row corresponds to a GAN as described above. While
DCGAN 0.41 0.64
all samples in Fig. 10 are visually acceptable and channel sinuosity
WGAN-GP 0.30 0.55
andwidthareconsistentwiththeRTI,thegeneratedsamplesareless VA-GAN 0.33 0.46
continuous. GANs trained on the SNESIM dataset produce samples
VA-GANβππππππ₯
0.27 0.45
βπ
thatoccasionallyshowartifactsandchannelsarelesscontinuous,with
shorter and more dispersed channels present in most of the sample
realizations. The cause of this issue is the SNESIM algorithm and the
andgeneratingresultsthatbetterpreservemulti-pointstatisticsofthe
discontinuity was introduced when SNESIM was applied to generate
referenceimageisafurtheradvantageofourproposedarchitecture.
theinputtrainingdataset.ThisisclearlyshowninFig.6andwasalso
Probabilitymapsweregeneratedforboththeinputtrainingdatasets
observedbyAzevedoetal.(2020).
andthegeneratedrealizations.Thesemapswereusedtoevaluatethe
As second measure of quality, ANODI was applied to generated
variability and spatial bias of generated realizations. The probability
resultsofallthe8settingsandtheinputtrainingdata.Theresultsof
maps of the input training data are shown in Fig. 7. Fig. 7a shows
JensenβShannondistancesareshowninMDSplotsofFig.11forbetter
the probability map of the Direct Patch input data and Fig. 7b is
visualization. In this figure, green shows the input realizations, blue
the probability map of the SNESIM dataset. Neither of these images
shows the generated realizations and the larger black dot represents
show any significant spatial bias. The range of the probability values
theRTI.Theleftandrightcolumns areresultsfromGANs trainedon
at all locations are similar and there are no significant outliers. The
the Direct patch and the SNESIM dataset respectively. The Euclidian
univariatestatisticsofthepixelvaluesofthemapsareshowninFig.12.
normoftheJensenβShannondistanceofall150generatedrealizations
totheRTIisusedtoevaluatewhichGANpreservesthemultiplepoint In this figure the blue box shows the 25th to 75th percentile and the
statistics of the RTI better than others. This distance for each GAN is red line in the middle is the median of the map pixel values. The
shown next to the Z-Axes of each plot in Fig. 11 and also presented whiskersshowtherangeofthedataandtheredcrossesaretheoutliers.
in Table 1 for convenience. In general, GANs trained on the Direct TheDirectpatchmaprangesbetween26β35%,whiletheSNESIMmap
patch dataset produced statistically closer results with lower Jensenβ hasrangebetween20β30%.Bothmapsshowanarrowrangewithfew
Shannon distances to the RTI, which is in line with observing more insignificant outliers. The probability maps of the input training data
continuouschannelsintherealizations.Regardlessoftheinputtraining wereusedasareferencefortheGANstrainedonthatinputdata.
data,WGAN-GP(Fig.11Row2)wasabletopreservebetterthemultiple ProbabilitymapsofsamplesgeneratedbyGANstrainedinthisstudy
point statistics of the RTI compared to DCGAN (Fig. 11 Row1). Our havebeenpresentedinFig.13.TheGANstrainedontheDirectpatch
proposedarchitecturehasreducedtheJensenβShannondistanceofthe dataset (column a), show significantly more spatial bias compared to
realizationstoRTIwhileenhancingvariabilityconsiderably.Asshown GANstrainedontheSNESIMdataset(columnb).TheDCGANstructure
inTable1,VA-GAN incomparisontoDCGANandVA-GAN clearlyshowsbiasinmultiplelocationswhentrainedonDirectPatch
βππππππ₯ βπ
compared to WGAN-GP have enhance the average JensenβShannon dataset (Fig. 13 a(I)). Severe outliers are observed, some areas show
distanceofrealizationsby19.5%and10%respectively. over80%chanceofsandoccurrenceandotherareaswithprobability
It should be noted that although DCGAN results show a higher lowerthan10%chanceofsandoccurrence.Thiscanalsobeobserved
JensenβShannon distance, the realization generated are still visually inthesamplerealizations(Fig.9).Arepeatedtrendisclearlyvisiblein
acceptable. However, the reduction of the JensenβShannon distance thesamplesgeneratedbytheDCGAN.TheresultsofDCGAN,however,
10 |
ADE | R.Koochaketal. ComputersandGeosciences166(2022)105188
Fig.13. Probabilitymapscreatedfrom150realizationsgeneratedbydifferentGANs.(a)(Leftcolumn)probabilitymapsofrealizationsgeneratedbyGANstrainedonDirectpatch
dataset.(b)(rightcolumn)probabilitymapsofrealizationsgeneratedbyGANstrainedonSNESIMdataset.(I)DCGAN,(II)WGAN-GP,(III)VA-GAN ,(IV)VA-GAN .Each
βππππππ₯ βπ
probabilitymapisofsize100Γ100.
are not as severe when trained on the SNESIM data set (Fig. 13 data. As mentioned in the related work section there have been a
b(I)).Nevertheless,outliersover50%andlowerthan10%arepresent number of attempts to generate conditioned realizations. However,
in the probability map when DCGAN is trained on SNESIM dataset. mode collapse and spatial bias caused by the GAN architecture and
VA-GAN significantlyenhancestheresults,narrowingtherange input training data often adversely affect the conditioning algorithm.
βππππππ₯
ofprobabilitiesandreducingtheoutliers(Fig.13RowIII). The extent of this adverse effect might be offset somewhat by the
WGAN-GP algorithm, as expected and reported in the literature, tendencyforasuitofconditionedrealizationstoexhibitlessvariability
reduces the effect of mode collapse. The results of this study have than unconditioned realizations. However, the specific focus in this
demonstrated this feature of the WGAN-GP (Fig. 13 Row II). Bias in study was on reducing the tendencies for mode collapse and spatial
the generated samples is not as severe. However, the range of proba- bias.
bility values is wide and outliers over 50% and lower than 10% are
occasionallyobserved.VA-GAN hasenhancedtheresultscompared 7. Discussions
βπ
toWGAN-GPaswell,bringingthespatialdistributionoftheprobability
mapsclosertothatoftheinputdata. Tobetterdemonstratetheimpactofπ½ inEqs.(8)and(9),wehave
TrainingGANsontheDirectpatchdatasetproducesmorerealistic conductedasensitivityanalysis.Thevaluesofπ½usedinthisanalysisare
and continuous channels. However, GANs trained on this dataset are given in Table 2. Both VA-GAN and VA-GAN were trained
βππππππ₯ βπ
pronetomodecollapse,andspatialbiasisobservedintheresults.Using usingtheDirectpatchdatasetandtheseπ½ values.
ourproposedarchitecture,itispossibletotrainaGANwiththeDirect Theproposedπ½ isthevaluewherebothlosscomponentsareatthe
Patchinputdataset,resultinginmorevisuallycontinuousrealizations sameorderofmagnitude(thisisthevalueusedtoderivetheresultsin
with better preserved multiple point statistics of the RTI and at the thepaper).Thisvaluewasderived,usingaHeuristicapproach,where
sametimemaintainvariabilityandreducespatialbias.Naturally,the the first 20 iterations of training were monitored. In each iteration,
nextstepwouldbetoconditionthegeneratedrealizationstoobserved bothlosscomponentswerecalculatedandcomparedtodeterminethe
11 |
ADE | R.Koochaketal. ComputersandGeosciences166(2022)105188
Fig.14. Samplerealizationsgeneratedfromtheπ½ sensitivityanalysis.π½ valueforeachsetofrealizationsisshownontheYaxis.(a)VA-GAN ,(b)VA-GAN .
βππππππ₯ βπ
Table2 Themethodofchoosingbetaisnotdetrimentaltothemethodologyall
Rangeofbetavaluesincludedinthesensitivitycheck. together.
GAN Oneorder Proposedπ½ Oneorder Twoorders There are numerous regularization methods in the literature with
smaller larger larger
the aim to stabilize GAN training and reduce Mode collapse (Kurach
VA-GAN βππππππ₯ 1πΈβ5 1πΈβ4 1πΈβ3 1πΈβ2 et al., 2019). Regularization methods generally strive to impose Lip-
VA-GAN 1πΈβ3 1πΈβ2 1πΈβ1 1.0
βπ schitz continuity on the discriminator to prevent the weights from
exploding during training (Lee and Seok, 2020). We have compared
theeffectivenessofourproposedarchitecturewithtworegularization
differenceintheorderofmagnitude.π½ valuesoneorderofmagnitude methods. WGAN-GP uses gradient penalty regularization. We have
lower and one and two orders of magnitude higher compared to the demonstrated, that Our proposed method can be applied to a GAN
proposed π½ were analyzed. π½ = 0 (regular GAN) has also been pre- in conjunction with other regularization methods to further enhance
sentedforbettercomparison.Fig.14showssamplerealizationsofthe results,aswehavedemonstratedwithWGAN-GP(Figs.12and13).We
trained GANs. Three samples were randomly chosen from a pool of have further compared VA-GAN with πΏ2 regularized DCGAN.
βππππππ₯
150realizationsgeneratedusingeachGAN.Astheimagesshow,when TheresultsshowedthatwhileπΏ2regularizationreducedoutliersinthe
increasingtheBetavalue,theβ componentoflossfunctionincreases, probability maps, it does not adequately reduce spatial bias. For the
π
andthefocusofthelossfunctionshiftstothiscomponent.Significantly sakeofconciseness,wehavenotpresentedtheπΏ2comparisongraphs
large values will prevent the GAN from learning the features of the here.
training data. On the other hand, as π½ becomes increasingly small,
there is less focus on the probability loss and with extremely small 8. Conclusion
values the component vanishes, therefore, results starts to resemble
theregularGAN.Theboxplotoftheprobabilitymapsgeneratedusing In this study, we developed a new GAN architecture to maximize
theserealizationsconfirmsthisfinding.AsshowninFig.15,π½ values variability of generated samples of subsurface spatial property. We
that do not maintain a balance between the loss components, tend applied our proposed architecture to generate unconditioned sample
to either introduce spatial bias or disturb the learning process of the realizationsbasedonthereferencetrainingimage.Thequalityandvari-
GAN. In Fig. 15(a), VA-GAN still provides acceptable results with abilityofresultsoftheconventionalGANsandourproposedGANswere
βπ
betavaluesoneorderofmagnitudelargerthantheproposedπ½.Thisis compared.Thenetworksweretrainedontwoinputdatasets,theDirect
becausetheGANcomponentofthelossinthisarchitectureincreasesas patchandSNESIMdatasets.Asqualitymeasures,visualinspectionand
thetrainingprogresses,therefore,largervaluesofπ½arestillacceptable. ANODIanalysiswereused.Probabilitymapswerealsoappliedtoeval-
Therearedifferentmethodsthatcanbeusedtoobtaintheoptimum uatespatialbiasandvariability.Ourproposedarchitecturesignificantly
betavalue.Userscanforexampleusesensitivityanalysisorsetuparule enhancedvariabilityandreducedspatialbiascomparedtoDCGANand
tobeappliedeveryiterationbasedonthevalueofthelosscomponents. outperformed WGAN-GP. The results showed that the input training
12 |
ADE | 6. Summary, Conclusions and Future Work
The primary objective of reservoir characterization is to produce geological models that
honour the available data. Adequate characterization of the reservoir results in better
understanding of the subsurface which in turn increase recovery factor, leads to better
reservoir management and is essential for post depletion activities such as carbon capture and
sequestration or storage. In recent years the subsurface energy sector has seen a surge in data
collection, however, traditional methods due to their inherent limitations are unable to fully
utilize these data. This thesis investigated and introduced novel techniques in subsurface
characterization using advanced analytics and machine learning that can handle large data
volumes and open new doors in the field of reservoir characterization. This thesis investigated
and introduced novel techniques in subsurface characterization using advanced analytics and
machine learning. The thesis explored Fractal analysis, Convolutional neural networks,
Generative adversarial networks and presented an enhanced optimization technique for
history matching in the appendix. For each of the problems, a novel technique is proposed with
the aim to enhance subsurface characterization using the available data.
The thesis began with Fractal analysis of the deep latero-log resistivity logs. A novel technique
was introduced for rock typing using the Fractal dimension of these logs. The fractal dimension
is a measure of the variability of the resistivity log. The research showed that as the complexity
of the rock texture and fabric increases the log shows higher variability and a higher fractal
dimension. The results of this investigation showed that fractal dimension of resistivity logs can
be used as new parameter in reservoir rock typing. Furthermore, it introduced a new technique
to extract more information from available resistivity logs that were never utilized before.
69 |
ADE | The thesis continued with introducing a methodology to automate/ augment interpretation of
resistivity image logs. The research emphasised on solely using the image logs and excluded
any other data types. Transfer learning was used to overcome some of the challenges faced in
this process and it was proven that transfer learning is applicable to subsurface datasets. Using
a trained network and novel post processing step the accuracy of the automated process
exceed 90%. The aim of this study was to determine the accuracy that can be achieved using
image logs alone. Generally, image logs are required to be accompanied by a suit of
supplementary logs that aid the interpreter in categorizing facies. Omitting the supplementary
logs would reduce the cost of the interpretation significantly. Although the result shows a high
accuracy from image logs alone, this workflow would benefit from some additional data.
Researching methodologies to incorporate multiple data sources in this workflow would be of
great interest. Another potential application of this workflow would be denoising the logs or
noise detection in the image logs.
In the next chapter, variability of geological model realizations generated using a Generative
adversarial network was investigated. The input training data was produced using a conceptual
image delivered by a geologist. The GAN was trained to learn the statistics of the training image
and produce realizations that are realistic and statistically faithful. The variability of the images
was investigated in detail and a novel method to update the loss function of the network with
the aim to maintain the variability of the output samples at the same level as that of the input
data. The proposed method outperformed the state-of-the-art methods in the literature used
for reducing the effects of mode collapse. GANs are a recently developed technique and their
application in geological model development is at the beginning of its journey. There are still
70 |
ADE | numerous challenges that need to be overcome. Mode collapse for one has a detrimental
effect on uncertainty evaluation and must be evaluated and addressed when using GANs.
Another important challenge is generating training data to train the network on. The method
introduced in this thesis although effective, it is applicable to stationary models only. Non-
stationary models or geological structures are quite challenging to train a GAN on.
Finally, in the appendix, an ensemble of surrogates (proxies) with generation-based model-
management embedded in CMA-ES is proposed to reduce the number of simulation calls. The
proposed method divides the likelihood term into multiple functions and represents each
function with a separate surrogate. The algorithm was used to history match two cases one
real with 59 uncertain variables and the other synthetic with 8 variables. The results showed
that up to 65% and 50% less simulation calls for case#1 and case#2 were required.
From this investigation into development of novel advanced analytics and machine learning
methods in subsurface characterization the following conclusions are drawn:
1. The fractal analysis of the deep resistivity logs revealed the correlation between the
variability of resistivity logs and complexity of rock fabric, making this analysis useful
for rock typing. Application of novel data analytics and machine learning techniques
can introduce new features in subsurface data that have traditionally been neglected.
2. Convolutional neural networks are effective and efficient tools to analyse subsurface
image data. It was shown on two occasions in this thesis that computer vision
algorithms can be extended to subsurface image logs given that the limitations of the
algorithm and how these limitations translate in subsurface analysis are well
understood and investigated.
71 |
ADE | 3. Convolutional neural networks can extract facies from resistivity images logs better
than human interpretation when the resistivity logs are the only information available.
However, complexity of the image distribution, lack of features in the images and
similarity of categorized facies means that to reach accuracy levels similar to human
full-suite interpretation, other logs and information need to be included in the network
training process.
4. Given the complexity of the distribution of subsurface images, large and deep networks
are required to learn the features of these images. Not only training these networks is
computationally expensive, but lack of adequate data and training images makes this
task even more challenging. Transfer learning has proven to be an efficient solution to
both above-mentioned issues. Furthermore, I was proven that transfer learning is
applicable to subsurface image datasets.
5. Generative adversarial networks (GAN) can adequately learn and generate geological
models that are realistic and statistically faithful. These networks however, depending
on their design can suffer from mode collapse which will hinder and reduce the
variability of the generated models.
6. Providing input training data that is sufficiently representative of the distribution the
network will learn, in variability, dataset size and image statistics is key to a successful
training. The input training data is detrimental in the training of the network.
This research provided novel techniques for subsurface characterization and answered
important questions in that field. Non-the-less this research can be extended in several ways.
Below are suggestions for future work:
72 |
ADE | P007
Accelerating CMA-ES In History Matching Problems Using
An Ensemble Of Surrogates With Generation-Based
Management
M. Sayyafzadeh* (University of Adelaide), R. Koochak (The University of Adelaide), M. Barley
(Santos Limited)
Summary
Because of the quasi-gradient update embedded in CMA-ES algorithm, it can outperform most of the
population-based algorithms, from a convergence speed standpoint. However, due to the computationally
expensive fitness function associated with history matching, the reduction of function (simulation) calls can be
favourable.
In this study, an ensemble of surrogates (proxies) with generation-based model-management is proposed to
reduce the number of simulation calls efficaciously. Since the fitness function is highly nonlinear, an ensemble
of surrogates (Gaussian process) is utilised. The likelihood term is divided into multiple functions, and each is
represented via a separate surrogate. This improved the response surface fitting.
In generation-based management, a stochastically selected measure (surrogate or reservoir-simulation) should
be used to evaluate all the individuals of each generation. CMA-ES requires ranking of the individuals to select
the parents. Therefore, the generation-based model-management fits well in CMA-ES, as surrogates are
normally better in ranking the individuals than approximating the fitness.
History matching for a real problem with 59 variables and PUNQ-S3 with eight variables was conducted via a
standard CMA-ES and the proposed surrogate-assisted CMA-ES. The results showed that up to 65% and 50%
less simulation calls for case#1 and case#2 were required.
ECMOR XVI 2018 β 16th European Conference on the Mathematics of Oil Recovery
3-6 September 2018, Barcelona, Spain |
ADE | STATEMENT OF ORIGINALITY
I certify that this work contains no material which has been accepted for the award of any other
degree or diploma in my name, in any university or other tertiary institution and, to the best of
my knowledge and belief, contains no material previously published or written by another
person, except where due reference has been made in the text. In addition, I certify that no part
of this work will, in the future, be used in a submission in my name, for any other degree or
diploma in any university or other tertiary institution without the prior approval of the
University of Adelaide and where applicable, any partner institution responsible for the joint-
award of this degree.
I give consent to this copy of my thesis when deposited in the University Library, being made
available for loan and photocopying, subject to the provisions of the Copyright Act 1968.
The author acknowledges that copyright of published works contained within this thesis resides
with the copyright holder(s) of those works.
I also give permission for the digital version of my thesis to be made available on the web, via
the Universityβs digital research repository, the Library Search and also through web search
engines, unless permission has been granted by the University to restrict access for a period of
time.
Selahattin Akdag Date: 2nd May 2019 |
ADE | Abstract
Experimental investigation of damage evolution during strain burst in brittle rocks for
deep mines
A Thesis submitted for the degree of Doctor of Philosophy
Selahattin Akdag
The School of Civil, Environmental and Mining Engineering
The University of Adelaide
Adelaide, 2019
The increasing demand for resources and depletion of near ground mineral resources caused
deeper mining operations under high-stress and high-temperature rock mass conditions. As a
results of this, strain burst, which is the sudden and violent release of stored strain energy during
dynamic brittle failure of rocks, has become more prevalent and created considerable safety
risks damaging underground infrastructures. This research focuses on the development of
experimental methodologies to better understand the fundamental knowledge concerning the
failure mechanism of strain burst and the influence of thermal damage, high confining pressure
and various loading rate on the overall mechanical behaviour of highly brittle granitic rocks
leading to strain burst.
Strain burst is related to the elastic stored strain energy and how this stored energy is released
during the unstable spontaneous failure. Therefore, it is significant to investigate the energy
state during strain burst from the viewpoint of energy theory. In this sense, circumferential
strain controlled quasi-static tests on Class II rocks over a wide range of confining pressures at
different heat-treatment temperatures were conducted to capture the snap-back behaviour and
calculate excess strain energy that is responsible for the spontaneous instability. A new energy
calculation method associated with acoustic emission (AE) was developed to express the
propensity of strain burst and investigate the post-peak energy distribution characteristics for
brittle rocks under the coupling influence of confinement and temperature. In order to quantify
the micro-crack density and reveal the micro-fracture characteristics of the brittle rocks
exposed to various temperatures, scanning electron microscopy (SEM) analysis was also
conducted. This is highly relevant to link the excess strain energy and the main failure
mechanism triggering strain burst under high-temperature condition.
v |
ADE | The failure process of strain burst is the outcome of the unstable growth and coalescence of
secondary micro-cracks. If the dissipative energy to grow pre-existing cracks and the secondary
cracks is smaller than the elastic stored strain energy in rock masses, the residual strain energy
will be released suddenly in the form of kinetic energy, resulting in ejecting high-velocity rock
fragments. Therefore, understanding the crack initiation and propagation in rocks is of great
concern for engineering stability and security. As an intrinsic property of rocks to resist crack
initiation and propagation, the rock fracture toughness is the most significant material property
in fracture mechanics. In this respect, the three-point bending method was applied using
cracked chevron notched semi-circular bend (CCNSCB) granite specimens subjected to
different temperatures under a wide range of loading rates in pure mode I. A suitable relation
for the dimensionless stress intensity factor (πβ) of SCB with chevron notch samples were
presented based on the normalised crack length (πΌ) and half-distance between support rollers
(π/2). The minimum dimensionless stress intensity factor (πβ ) of CCNSCB specimens were
πππ
determined using an analytical method, i.e., Bluhmβs slice synthesis method. In this study, the
influence of thermal damage and loading rate on the quasi-static mode I fracture toughness and
the energy-release rate using CCNSCB method was investigated. In the deep mining process,
the rock mass is subjected to a dynamic disturbance caused by blasting, and mechanical drilling
resulting in dynamic fractures in the forms of strain burst, slabbing, and spalling. The dynamic
rock fracture parameters, including dynamic initiation fracture toughness and fracture energy
which are an important manifestation of dynamic rock failure (strain burst) in deep
underground engineering and they are of great practical significance to assess the dynamic
fracture behaviour of deep rock masses. Since deep rock engineering operations in high
temperature and high pressure environment is prone to strain burst, the influence of thermally
induced damage on the dynamic failure parameters of granite specimens was investigated. The
damage evolution of granitic rocks were studied over a wide range of loading rates to reveal
the rate dependency of strain burst. Dynamic fracture toughness tests were carried out on
granite under different temperatures and impact loadings using a Split Hopkinson Pressure Bar
(SHPB) apparatus at Monash University. With dynamic force balance achieved in the dynamic
tests, the stable-unstable transition of the crack propagation crack was observed and the
dynamic initiation fracture toughness was calculated from the dynamic peak load.
The thermal damage influence on strain burst characteristics of brittle rocks under true-triaxial
loading-unloading conditions was investigated using the AE and kinetic energy analyses. A
unique strain burst testing system enabling to simulate the creation of excavation at the State
vi |
ADE | Key Laboratory for Geomechanics and Deep Underground Engineering in Beijing (China) was
used to replicate strain burst condition. Time-domain and frequency-domain responses AE
waves related to strain burst were studied, and the damage evolution was quantified by b-
values, cumulative AE energy and events rates that can be used as warning signals to rock
failure. The ejection velocities of the rock fragments from the free face of the granite specimens
were used to calculate kinetic energies which can be used as an indicator for quantitatively
evaluating the intensity of strain burst.
Based on the energy evolution characteristics of brittle rocks under uniaxial and triaxial
compression, true-triaxial loading-unloading and three-point bending, new strain burst
proneness indexes and strain burst criterion were proposed. The effects of temperature,
confinement and loading rate on strain burst proneness were discussed.
This study aims to advance the understanding on underlying processes that govern the macro-
behaviour of brittle rocks during strain burst and make use of this insight to further advance
our current predictive capabilities of strain burst with references to large-scale underground
mining. Using the developed experimental methodologies in this study, fractures around an
excavation to reduce the amount of excess strain energy leading to strain burst can be
determined and ultimately incipient strain burst in deep mines can be predicted avoiding
potential hazards. Using the methodology for forecasting of strain burst in this research can be
used for enhanced understanding of the design of rock support in strain burst-prone areas in
deep mining activities
The findings of this study will facilitate achieving a better and comprehensive understanding
of the damage process during strain burst in deep mines. This study underpins the development
of better and more efficient prediction methods for strain burst which will lead to better
planning guidelines and ultimately safer deep underground working conditions.
vii |
ADE | Publications
1. Akdag S, Karakus M, Nguyen GD, Taheri A, Bruning T (2019). Evaluation of the
propensity of strain burst in granite based on post-peak energy analysis. Underground Space.
(Accepted).
2. Akdag S, Karakus M, Nguyen GD, Taheri A (2019). Combined influence of increasing
temperature and confining pressure on the potential intensity for strain burst (to be submitted
to the International Journal of Rock Mechanics and Mining Sciences).
3. Akdag S, Karakus M, Nguyen GD, Taheri A (2019). Quasi-static and dynamic fracture and
energy characteristics of strain burst in granite under different temperatures and loading
rates (to be submitted Engineering Fracture Mechanics).
4. Akdag S, Karakus M, Nguyen GD, Taheri A (2019). New energy indexes for evaluating the
strain burst proneness of brittle rocks and their application to real engineering problems (to
be submitted to the International Journal of Rock Mechanics and Mining Sciences).
5. Akdag S, Karakus M, Taheri A, Nguyen GD, He M (2018). Effects of thermal damage on
strain burst mechanism for brittle rocks under true-triaxial loading conditions. Rock
Mechanics and Rock Engineering. 51 (6): 1657-1682.
6. Bruning T, Karakus M, Akdag S, Nguyen GD, Goodchild D (2018). Influence of deviatoric
stress on rockburst occurrence: An experimental study. International Journal of Mining
Science and Technology. 28 (5): 763-766.
7. Akdag S, Bruning T, Karakus M (2019). How can accumulated damage lead to a violent
rock failure? An innovative experimental study for rockburst. 53rd US Rock
Mechanics/Geomechanics Symposium, New York City, USA: American Rock Mechanics
Association.
8. Akdag S, Karakus M, Taheri A, Nguyen GD, He Manchao (2018). Effects of thermal
damage on strain burst mechanics of brittle rock using acoustic emission. In Litvinenko
(Ed.) Geomechanics and Geodynamics of Rock Masses, Proceedings of the 2018 European
Rock Mechanics Symposium (EUROCK) (pp. 581-585). Saint Petersburg, Russia.
ix |
ADE | πΎβ² Stress intensity factor for the new crack length
πΎ Quasi-static mode I fracture toughness
πΌπΆ
πΊ Mode I energy-release rate
πΌ
πΎπ Mode I dynamic initiation fracture toughness
πΌπ
πΎΜ Loading rate of dynamic fracture toughness test
πΌ
π P-wave velocity of the bar
π
πΈ Elastic modulus of the bar
π
π΄ Cross-sectional area of the bar
π
π Density of the bar
π
π ,π ,π Incident, transmitted, and reflected strains of the bar
π π‘ π
π ,π Dynamic forces in the incident and transmitted bar
1 2
πΜ(π‘) Strain rate of the specimen at time t during loading using the SHPB
π(π‘) Strain of the specimen at time t during loading using SHPB
π(π‘) Stress of the specimen at time t during loading using SHPB
πΆ One dimensional longitudinal elastic stress wave velocity of the bar
π΄ Initial cross-sectional area of the specimen
0
πΏ Initial length of the specimen
0
π£ Striking impact velocity
π π‘πππππ
Ο ,Ο UCS of cylindrical and rectangular prism specimen
c1 c2
π· Strain burst damage variable
ππ΅
πΊ Cumulative amount of AE energy or number of AE hits at a certain time
πΊ Cumulative amount of energy or number of hits during the whole test
π
π΄ Peak amplitude of AE events in decibels
ππ΅
N Incremental frequency
π£Μ
Initial ejection velocity of the ith rock fragment
π
π Mass of the ith rock fragment
π
xix |
ADE | Introduction
Chapter 1: Introduction
1.1 - General background
The increasing demand for mineral resources and depletion of near-surface reserves has driven
more mining applications into higher depth which has caused that stress-induced rock failure
processes are inevitable. Before excavation, rock mass at depth exists in a true-triaxial state of
stress equilibrium (π > π > π ) where π , π , and π are the maximum, intermediate, and
1 2 3 1 2 3
minimum principal stresses, respectively. Introducing an excavation which results in forming
an open free boundary condition changes the stress state of the rock mass near the excavated
boundary and elastic strain energy accumulates in the surrounding rock. When the excavation-
induced stress exceeds the carrying capacity of the rock mass, the stored elastic strain energy
within the rock mass is abruptly released, resulting in strain burst occurrence. Strain burst is a
nonlinear dynamic rock instability accompanied by violent rock ejection, which frequently
occurs during the excavation of hard brittle rock masses subjected to high stress ground
conditions, leading to severe rock mass damage. Strain burst can kill workers and usually
results in casualties and damages to equipment as well as delays the project schedule. Due to
its nature of unpredictability, destructiveness and suddenness, strain burst poses an increasing
threat to the safety and production of deep engineering operations. For instance, several intense
strain burst caused casualties, destruction of equipment and production delays with the
maximum excavation depth of approximately 3050 m at Jinping II hydropower station in China
(Li et al. 2012).
Deep mining activities for extracting deep mineral resources require an assessment of
mechanical rock behaviour and damage mechanism for long-term stability. Although,
considerable efforts have been devoted to the investigation of the strain burst, the fundamental
mechanism of strain bursting is still not adequately understood and should be further explored.
Mines under high-stress conditions are deemed to be operating at highly-stresses ground
conditions and the confinement controls the rock failures. With the advancement of extraction,
progressive build up stress in the rock mass takes place which may lead to the sudden violent
ejection of rocks. With the increasing of excavation depth, the influence of elevated ground
temperature becomes remarkably significant on triggering strain burst. The coupling of high-
stressed ground conditions and thermal damage will alter the overall mechanical behaviour of
1 |
ADE | Introduction
hard brittle rocks which may trigger strain bursting in deep engineering operations. Therefore,
an in-depth understanding the damage process of hard brittle rocks and how the overall
mechanical behaviour of rock is affected by high stress and high temperature is essential to
facilitate long-term stability maintenance of deep engineering constructions, reducing the
tendency of strain burst, which will impact on the safety of deep mining operations.
This research focuses on investigating the mechanism of strain burst and provides an insight
of this phenomenon and its relevance to deep mining operations. This research examines and
addresses the challenges in the experimental investigation of strain burst mechanism related to
the inherent difficulties in quasi-static and dynamic failure simulation. The strain burst
phenomenon is explored and an innovative experimental methodology is adopted to investigate
the underlying mechanism of strain burst and the influence of external factors such as high
confining pressure, elevated temperature, and loading rate on strain burst mechanism for brittle
rocks. This approach is intended to expedite in arriving at a systematic engineering
methodology that evaluates the propensity of strain burst whereby severe damage conditions
may exist and the excavations are vulnerable to strain burst damage.
1.2 - Research objectives
The main objective of this research is to investigate the damage mechanism of strain burst in
deep mines under high stress and elevated temperature conditions and provide guidelines for
the development of an effective and reliable method to forecast the propensity of strain burst.
In addition, this research aims to underpin the design of appropriate rock support systems in
strain burst-prone deep mines which will result in cost-effective deep mining operations under
safe working environments. These goals are achieved by accomplishing a series of tasks listed
below:
ο· Forecasting the propensity of strain burst of brittle rock based on post-peak energy
analysis.
ο· Investigating the combined influence of confining pressure and thermal damage on the
intrinsic potential for strain burst, energy evolution and mechanical behaviour of brittle
granitic rocks leading to strain burst.
ο· Characterisation of quasi-static and dynamic fracturing and energy evolution during
strain burst.
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ADE | Introduction
ο· Analysing the thermal damage and rate dependence of quasi-static and dynamic
fracture toughness and energy parameters for strain burst failure process.
ο· Investigating the effects of thermal damage on strain burst mechanism under true-
triaxial loading-unloading conditions.
ο· Evaluating the strain burst proneness based on the energy characteristics during strain
burst.
1.3 - Thesis organisation
The starting point of this research is a brief review of the damage processes and strain burst in
brittle rock, all of which are presented in Chapter 2. The emphasis in Chapter 2 is placed on
presenting the efforts devoted to investigating the real damage process of strain burst under the
condition of laboratory experiments within the context of damage and rock mechanics and
fracture mechanics. This chapter also includes the factors that contribute to strain bursting.
Chapter 3 of this thesis addresses the post-peak energy balance of Class II behaviour at
spontaneous failure and presents a newly developed energy calculation method based on the
post-peak energy distributions for brittle rocks using acoustic emission (AE). The methodology
used in a series of circumferentially-controlled quasi-static uniaxial and triaxial compression
tests for forecasting the propensity of strain burst is presented. The intrinsic potential intensity
for strain burst in granite is quantitatively assessed. Coupling influence of high confining stress
and thermal damage on the overall mechanical behaviour and post-peak energy characteristics
is analysed and the underlying mechanism is discussed. The crack evolution characteristics of
thermally-treated granite specimens were also examined.
Chapter 4 of this thesis focuses on exploring the fracture characteristics during strain burst.
Damage accumulation leading to strain burst is a static process followed by the dynamic release
of stored strain energy in which stored strain energy is converted to kinetic energy in the form
of rock fragment ejection. Hence, strain burst from initiation to end is a combined quasi-static
and dynamic failure process. In order to estimate the onset of strain burst failure process during
deep mining operations, it is significant to understand the behaviour of the rock subjected to
mode I fracturing as it is assumed that the mode I fractures dominate the failure process during
strain burst. Therefore, characterisation of fracture behaviour and energy evolution during
strain burst by conducting quasi-static and dynamic fracture toughness tests is presented. For
fracture toughness tests, cracked chevron notched semi-circular bend (CCNSCB) method is
3 |
ADE | Introduction
applied. Dimensionless stress intensity factor (πβ ) approach using a semi-analytical
πππ
synthesis method is adopted to determine the fracture toughness values. Coupling effects of
loading rate and temperature on quasi-static mode I fracture toughness and energy-release rate
are investigated. To provide a deeper insight into dynamic fracture propagation during strain
burst, Split Hopkinson Pressure Bar technique is adopted to perform dynamic fracture
toughness tests over a wide range of loading rates. The dynamic mechanical behaviours of
CCNSCB granite specimens at various impact velocities are studied. With the dynamic force
balance across CCNSCB samples, the evolution of dynamic stress intensity factor (SIF) is
analysed. Thermal damage influence and rate dependence of the dynamic mode I fracture
initiation toughness (πΎπ ) are investigated. Loading rate dependent progressive fracturing and
πΌπ
failure modes of CCNSCB granite exposed to different levels of temperature at various impact
velocities are assessed by analysing the High-Speed camera images.
In Chapter 5, simulating the damage process during strain burst by conducting true-triaxial
loadingβunloading strain burst tests is focused. The effects of thermal damage on strain burst
mechanism of brittle rocks under true-triaxial unloading conditions are investigated. The
variations in strain burst stress with temperature are used as indicators of strain burst
occurrence and compared with the strain bust criteria based on strength theory. The failure
processes of granite specimens induced by different temperatures are discussed based on the
recorded high-speed (HS) camera videos. The fracturing processes of strain burst under
different temperature conditions are investigated by assessing the evolution of instantaneous
and cumulative AE energy, hit, and counts characteristics. The damage caused by temperature
is quantified by the variation in AE signal characteristics and a strain burst damage variable is
proposed and temperature influence on damage accumulation rate is discussed. To assess the
degradation of rock and strain burst process during deformation stages, b-value analysis is
conducted and the influence of temperature on b-value, revealing the mechanism of micro- and
macro-cracking during strain burst. The frequency-amplitude characteristics of the AE waves
of thermally-treated granite are also presented. By analysing the recorded HS videos, ejection
velocities of rock fragments are calculated and the kinetic energies of the rock fragments which
can be used as a precursor for quantitatively evaluating the intensity of strain burst are analysed
and discussed in detail.
In Chapter 6, based on the energy evolution characteristics and mechanical behaviour of brittle
rocks under uniaxial and triaxial compression, true-triaxial loading-unloading and three-point
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Chapter 2: Damage processes and strain burst in brittle rock
2.1 - Introduction
Strain burst which is one of the major concerns in highly-stressed underground engineering,
poses a serious threat to workers and construction equipment and has become a topic of
increased research in the fields of rock mechanics and rock engineering. Despite there have
been substantial efforts of noteworthy contributions, the mechanism of strain burst associated
with the influencing factors is still unclear and a deeper insight is, therefore necessary to ensure
safe constructions and operation of deep underground excavations.
Deep mining and civil engineering related deep underground operations are challenging tasks
and costly projects, which need special attention and design considerations. When these deep
engineering activities go deeper, the rock is subjected to high stresses and elevated
temperatures leading to strain bursting. Therefore, an in-depth understanding the damage
process of hard rock and how the overall mechanical behaviour of rock leading to strain burst
is influenced by high confinement and temperature is of significance for facilitating cost-
effective design and long-term stability maintenance of these engineering structures. In
addition, rock mass is stressed dynamically during underground mining operations. Accurate
characterisation of dynamic fracturing over a wide range of loading rates are thus crucial.
However, to the best of our knowledge, all these features are either missing or not addressed at
length in the literature.
This chapter presents a brief overview of the progression of research on representing the real
damage process of strain burst under the condition of laboratory experiment in the context of
rock mechanics and fracture mechanics. First, assessment of strain burst mechanism based on
energy analysis under uniaxial and triaxial compression is presented and how high pressure
and temperature influence overall mechanical behaviour and energy characteristics of brittle
rock is analysed and discussed. The second part focuses on the quasi-static and dynamic mode
I fracture toughness tests, revealing the effects of temperature and loading rate on the fracturing
characteristics during strain burst. The final component of the literature review will cover the
investigation of strain burst evolution mechanism under true-triaxial loading-unloading
conditions. This section will identify the deficiencies of the existing methods for investigating
the mechanism of strain burst and provide motivation for this research. The understanding of
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ADE | Damage processes and strain burst in brittle rock
the underlying damage mechanism of strain burst and the mechanical characteristics under
different levels of confinement, temperature and impact loads will allow the development of
better support design and prediction methods for catastrophic rock failure reducing the impact
of strain burst so that future deep underground working environments will ultimately be much
safer.
2.2 - Assessment of strain burst mechanism based on energy analysis under
uniaxial and triaxial compression
As the depth of underground engineering construction increases, there are substantial problems
associated with high rock stress and high temperature leading to strain burst. The coupling of
high confinement and thermal damage will influence the overall mechanical behaviour of hard
brittle rock in which strain burst occurs frequently in an abrupt and violent manner
accompanied by violent rock ejection during deep mining activities. Strain burst can cause
severe damage to underground rock engineering applications and construction equipment as
well as serious injuries and fatalities. Therefore, elimination and mitigation of strain burst
hazard are one of the most challenging problems in rock engineering. Elastic strain energy
stored in hard rock which is one of the key factors induces and controls the brittle failure of the
rock mass, is the result of the redistribution of stresses near the underground excavation. If the
resulting imbalance of the energy of the system is severe enough, the stored energy is released
during a rapid post-peak strength degradation of the rock mass, displaying an unstable and
violent post-peak failure (strain burst). Strain burst is an energy-driven dynamic destabilisation
phenomenon, including energy accumulation, dissipation and release (Akdag et al. 2019).
Therefore, the damage of highly-stressed rock during strain burst can be assessed by evaluating
the dynamic energy characteristics from the energy evolution point of view. Hard brittle rocks
exhibiting Class II behaviour undergo self-sustaining fracturing due to excess stored strain
energy, which is accompanied by some energy release. Therefore, the principles of energy
redistribution during strain burst, in some regards, can be compared with the principles
involved in the spontaneous failure of brittle rocks in compression. Many researchers have
investigated the variation characteristics of energy in the failure process of strain burst (Li
2001; Hua and You 2001; Xie et al. 2009; He et al. 2012c; Tarasov and Potvin 2013; Li et al.
2014; Huang and Li 2014; Li et al. 2015; Carpinteri et al. 2018; Hauqin et al. 2018). Peng et
al. (2015) studied the variation in energy dissipation and release of coal under triaxial
compression and proposed two parameters based on the energy evolution to reflect the coal
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ADE | Damage processes and strain burst in brittle rock
deformation under different confinement (see Figure 2.1). Meng et al. (2016) analysed the
characteristics of energy accumulation, evolution and dissipation of sandstone specimens under
uniaxial cyclic loading and unloading compression, revealing the energy evolution of rock
deformation and failure (see Figure 2.2). The influence of different strain rates on fracture
toughness as well as the energy-release rate of gas shales under three-point bending was
investigated by Mahanta et al. (2017), and it was revealed that the fracture toughness and the
energy-release rate are functions of the strain rate increase with ascending strain rate, as
presented in Figure 2.3. Li et al. (2017) conducted triaxial compression tests on granite
specimens under different loading and unloading paths to identify the rules of energy
conversion and dissipation during the triaxial failure of hard rocks. They also identified the
micro-difference in the granite micro-cracks via a scanning electron microscope (SEM)
combined with an energy dispersive spectrometer (EDS), as shown in Figure 2.4. Strain energy
density factor approach was adopted to analyse the dynamic damage localisation behaviour of
rock mass by Zhou and Yang (2018) and the onset conditions of periodic distribution cracks in
a rock mass were determined. The above research results have enriched the knowledge of the
energy evolution mechanism of rocks under different loading conditions. However, to the best
of our knowledge, the studies mentioned above did not consider the combined influence of
temperature and confining pressure, critical external factors affecting the intrinsic mechanism
of strain burst, on the energy evolution and balance in the post-peak stage that occurs during
strain burst failure process. Hence, it is necessary to investigate and reveal the role of energy
redistribution in strain burst and how the mechanism and stored excess strain energy that is
responsible for the intrinsic potential energy of strain burst are influenced with thermal damage
and confining pressure from the perspective of energy. In this sense, obtaining the complete
stress-strain characteristics, i.e. the pre-peak and post-peak stress-strain regimes, are of great
significance for analysing the features of the post-peak energy balance in strain burst and
interpreting the process of rock deformation and failure.
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ADE | Damage processes and strain burst in brittle rock
Figure 2.4 Typical time history curve of strain energy and axial stress, SEM image of typical
granite and spectrum of line-scanning passing through cracks by SEM-EDS at 40 MPa
confinement (Li et al. 2017)
The thermodynamic state of rock is well represented by the stress-strain behaviour of the rock
which is the external manifestation of variation in energy during deformation and failure. It is,
therefore, necessary to obtain the complete stress-strain response of rock which plays a
paramount role in understanding the process of dynamic energy balance at the spontaneous
failure (strain burst). Under quasi-static compression, the complete stress-strain behaviour of
rocks can be categorised into two groups: Class I and Class II, as depicted in Figure 2.5: For
Class I behaviour which is characterised by a negative post-peak slope, additional energy is
required for further strength degradation. For rock exhibiting Class II behaviour or snap-back
behaviour, showing positive post-peak slope, the elastic energy accumulated within the rock is
sufficient to maintain the whole failure in which rock displays self-sustaining fracturing. Both
classes can be distinguished from the perspective of the post-peak energy balance. Table 2.1
presents the comparison of some methods for the energy balance at three stages of deformation,
energy accumulation, energy dissipation and energy release, in Class I and Class II behaviours.
10 |
ADE | Damage processes and strain burst in brittle rock
increases monotonically from the moment rock starts behaving as Class II (Munoz et al.
2016a). Therefore, to control the unstable failure and obtain the full stress-strain response of
Class II behaviour, the surplus energy is needed to be withdrawn by reducing the axial strain.
In this view, controlling the load by the circumferential-strain or lateral-strain as feedback
signal has become a more appropriate method to capture the post-peak stress-strain response
for brittle rocks (Wawersik and Fairhurst 1970; Fairhurst and Hudson 1999; Munoz et al.
2016b; Munoz and Taheri 2018; Bruning et al. 2018b).
In the deep mining operations, such elevated temperature and high confining pressure
conditions cause dramatic alteration in the physical and mechanical properties of the
surrounding rock mass which may activate strain burst. The behaviour of rock in the context
of deep and high stress mining, prone to strain burst, is still not adequately understood. It is
known that the mechanical behaviour of the rock depends on the confining pressure. It has been
experimentally demonstrated that the rock exhibits brittle-ductile transition with an increasing
confinement, which is as significant characteristic of rock deformation under high confining
pressure and temperature (Wawersik and Fairhurst 1970; Yang et al. 2012; Yao et al. 2016;
Walton et al. 2018). Yang et al. (2016) conducted a series of uniaxial and triaxial compression
tests on marble and quantitatively analysed the internal damage of the marble using a three-
dimensional X-ray micro-CT scanning system. The experimental results showed that the peak
and residual strengths of marble exhibited a clear linear relationship as increasing confinement,
which could be best described by the linear Mohr-Coulomb criterion (see Figure 2.6). In order
to simulate various geothermal reservoir conditions, Kumari et al. (2017a) carried out a series
of triaxial tests under different temperature and confining pressure conditions. They found that
rock strength and shear parameters increased up to a certain temperature and then decreased
with further rise of temperature due to induce-thermal cracking. With increasing confining
pressure additional plastic deformation occurred, exhibiting strain-hardening characteristics in
granite at high confinement. Xu and Karakus (2018) developed a thermo-mechanical damage
model based on the Weibull distribution and Lemaitreβs strain-equivalent principle for granite
to simulate the deformation and failure process of rocks under high temperature and pressure
conditions, as depicted in Figure 2.7.The progressive process of brittle failure was studied by
Renani and Martin (2018) on granite and limestone samples by damage-controlled uniaxial and
triaxial tests and the evolution of cohesion and friction at different confinement levels wa
analysed. However, the coupled influence of high confining stress and elevated temperature on
the post-peak energy balance during strain burst has been rarely investigated. This is a serious
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ADE | Damage processes and strain burst in brittle rock
gap in our knowledge as high stress and thermal damage will affect the overall mechanical
behaviour of brittle rocks which can trigger strain bursting in deep mining operations.
Therefore, this research aims to address this gap by conducting circumferential-strain
controlled uniaxial and triaxial compression tests and improve the understanding of energy
characteristics in the post-peak stage.
Figure 2.6 Deviatoric stress-axial strain curves and comparison of the peak and residual
strength of marble at different levels of confining stress (Yang et al. 2016)
Figure 2.7 Deviatoric stress-axial strain curves and comparison of the peak and residual
strength of marble at different levels of confining stress (Xu and Karakus 2018)
In the present research, to obtain the energy characteristics and analyse the post-peak energy
balance of snap-back behaviour of hard brittle Australian granite demonstrating Class II
behaviour in the post-peak region, a series of quasi-static circumferential strain controlled
uniaxial and triaxial compression tests was conducted. The stored elastic strain energy,
dissipated energy and the excess strain energy corresponding to the potential strain burst energy
were calculated. A new energy calculation method was developed based on post-peak energy
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ADE | Damage processes and strain burst in brittle rock
analysis. Acoustic emission (AE) which is an effective technique for analysing the damage
evolution in rocks was adopted to evaluate the energy and crack characteristics of granite
specimens. The coupled effects of elevated temperature (25 to 250 Β°C) and high confining
pressure (0 to 60 MPa) on the energy evolution characteristics and intensity of strain burst have
been systematically investigated and discussed, revealing the differences in the post-peak
energy balance.
2.3 - Mode-I fracture toughness investigation
Rock masses usually contain many structural defects, including cracks, flaws, cleavages,
bedding planes and natural fractures. These weaknesses can intensify the discontinuity of rock
when they are subjected to further mechanical and environmental actions and finally lead to
the failure of rock masses. It is thus essential to understand the load-carrying capacity of
fractured rock masses and the law of crack propagation in rock, to improve the stability of rock
structures under high stress concentrations that are prone to strain burst. To describe the
capacity of rock to resist unstable fracturing, rock fracture toughness is defined as the most
fundamental and important parameter in fracture mechanics. Rock fracture mechanics has been
widely employed in many diverse areas in the rock engineering applications related to
prevention of strain burst, such as rock fragmentation, cutting, drilling, rock slope stability,
rock quarrying, hydraulic fracturing, tunnel boring. Brittle failure is understood as a
consequence of crack propagation, and this failure pattern can be adequately described using
the theory of linear elastic fracture mechanics (LEFM), which is mainly extended from the
Griffith theory (Griffith 1921), and Irwinβs modification (Irwin 1957) that recognises the
significance of the stress intensity factor (SIF) at a crack tip. The critical value of SIF, also
known as fracture toughness is a key inherent material property used in analysing brittle failure.
SIF can be calculated for basic fracture modes based on the different loading: e.g. mode I (i.e.,
the tension/opening mode), mode II (i.e., the in-plane shear mode) and mode III (i.e., the tearing
mode or out-of-plane mode), as depicted in Figure 2.8. In rock fracture mechanics, rock
fractures easily occur under mode I in which the cracks tend to separate in direction normal to
the crack line and thus the opening mode failure is most frequently encountered failure mode
of rock against fracture. To predict the onset of catastrophic failures such as strain burst in such
rock structures due to crack growth, it is essential to understand the behaviour of rock material
subjected to mode I fracturing as it is assumed that the mode I fractures are dominant during
15 |
ADE | Damage processes and strain burst in brittle rock
strain burst. In this sense, both quasi-static and dynamic fracture toughness tests were carried
out to better understand the fracture characteristics during strain burst.
Figure 2.8 Three basic fracturing mode
2.3.1 - Quasi-static fracture tests
The strain burst is often considered as a process of crack formation and propagation in a rock
mass. Fracture toughness or the critical stress intensity factor (SIF) is a significant intrinsic
material property which represents the critical states of stresses or energy near the crack tip
required for the initiation of brittle fracture. Therefore, assessment of fracture toughness is
necessary for better understanding the mechanical behaviour of rock containing micro-cracks
or flaws during strain burst.
The International Society for Rock Mechanics (ISRM) has suggested four standard testing
methods, geometries and loading configurations, including chevron bend (CB) (Ouchterlony
1988), short rod (SR) (Ouchterlony 1988), cracked chevron notched Brazilian disc (CCNBD)
(Fowell 1995), and semi-circular bend (SCB) (Kuruppu et al. 2014) for measuring the quasi-
static mode I fracture toughness (πΎ ) of rocks, as shown in Figure 2.9. As given in the
πΌπΆ
literature, diverse testing method with various specimen geometry and loading configurations
have been proposed to measure πΎ of rocks, some of these methods are reviewed in Table 2.2.
πΌπΆ
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Damage processes and strain burst in brittle rock
notch allows a stable crack growth from the notch tip prior to the final fracture load and thus
chevron notched specimen can produce reasonable, versatile and reproducible data for fracture
toughness of rock. The details of the differences between chevron and straight notches will be
discussed more in detail in dynamic fracture tests section (Section 2.3.2).
The cracked chevron notched semi-circular bend (CCNSCB), originally developed by Kuruppu
(1997) and later developed by Dai et al. (2011) appears to have retained the merits of the ISRM-
suggested CCNBD and NSCB methods. Moreover, half-disc geometry inherently circumvents
the symmetrical crack propagation assumption of the CCNBD method. This chevron notched
SCB specimen geometry helps to avoid the difficulty of pre-cracking or fabricating a sharp
crack. Since pre-cracking is tedious, time-consuming and challenging to perform on hard rocks,
chevron notch in CCNSCB specimen can induce self-precracking during the test leading to
stable crack propagation along the chevron notch ligament when the specific crack length is
reached. Moreover, half-disc feature of this sample geometry facilitates the dynamic force
equilibrium within the specimen for the dynamic fracture toughness tests equipped with the
SHPB which is the prerequisite to employ the quasi-static data reduction method. This sample
geometry is also available for pure or mixed mode (mode I and mode II) fracture studies of
rocks. Therefore, given its merits on both quasi-static and dynamic mode I fracture toughness
measurements, the CCNSCB method was applied to more accurately determine the fracture
toughness values in this research.
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ADE | DDaammaaggee pprroocceesssseess aanndd ssttrraaiinn bbuurrsstt iinn bbrriittttllee rroocckk
Table 2.2 Some typical methods for measuring the quasi-static mode I fracture toughness (πΎ ) of rocks
πΌπΆ
Testing method Loading type Reference
Fowell and Xu 1994; Fowell 1995; Chang et al. 2002; Wang et al. 2003;
Iqbal and Mohanty 2006; Nasseri et al. 2006; Iqbal and Mohanty 2007;
Cracked chevron-notched
Brazilian-type compression Ayatollahi and Aliha 2008; Nasseri et al. 2010; Erarslan 2013; Aliha and
Brazilian disc (CCNBD) method
Ayatollahi 2014; Dai et al. 2015a; Xu et al. 2016a, b; Wei et al. 2016,
2017a,b; Ghouli et al. 2018; Yu and Shang 2019
Chevron bend (CB) method Three-point bending Ouchterlony 1988; Funatsu et al. 2015; Dai et al. 2015b
Aliha et al. 2010, 2012; Kuruppu et al. 2014; Ayatollahi and Sedighiani
Cracked straight through Brazilian
Brazilian-type compression 2012; Ayatollahi and Akbardoost 2014; Akbardoost et al. 2014; Wei et al.
disc (CSTBD) method
2017c
Flattened Brazilian disc method Brazilian-type compression Keles and Tutluoglu 2011
Straight notched disc bend Tutluoglu and Keles 2011; Aliha et al. 2015
Three-point bending
(SNDB) method Aliha and Bahmani 2017
Modified ring method Brazilian-type compression Tutluoglu and Keles 2012
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2.3.1.1 - Temperature influence on the quasi-static behaviour of rocks
Due to the thermal gradient in the deep rock mass, high-temperature conditions can cause
dramatic changes in the microstructures and mechanical behaviour of the rocks which are prone
to strain burst As a consequence, microstructure and mineral composition of rocks will be
altered due to the thermally-induced cracking. As being an inherent mechanical property of
rock, researchers have revealed that temperature is a significant factor influencing fracture
characteristics and rock fracture toughness. In recent years, a large number of researchers have
mainly investigated the effects of temperature on the quasi-static mode I fracture toughness of
rock. For instance, a study by Zhang et al. (2001) showed that the mode I fracture toughness
of gabbro decreased at 20-100 Β°C, likely due to the different structure and mineralogy. Funatsu
et al. (2004) investigated the changes in mode I fracture toughness of single-edge notched
round bar bend (SENRBB) and semi-circular bend (SCB) of Kimachi sandstone and Tage tuff.
The fracture toughness of Kimachi sandstone did not show significant change up to 125 Β°C and
increased from 125 to 200 Β°C in which this rising trend was attributed to the drying of the clay
material. For Tage tuff, the quasi-static mode I fracture toughness showed a decline with
ascending temperature up to 75 Β°C, after which it gradually rose from 75 to 200Β°C. Nasseri et
al. (2009) assessed the correlation between fracture toughness and fracture roughness for a
series of thermally-treated CCNBD Westerly granite. The researchers concluded that fracture
toughness and roughness exhibited a negative correlation as a function of temperature, on the
other hand, grain-grain boundary crack density and P-wave velocity showed an opposing
correlation. Research by Mahanta et al. (2016) demonstrated that mode I fracture toughness of
various types of Indian rocks increased from ambient temperature condition to 100 Β°C, and
after that diminished with increasing temperature up to 600 Β°C. Recently, Feng et al. (2017),
investigated the influence of temperature on the mode I fracture toughness of sandstone using
SCB specimens and found that the fracture toughness of sandstone decreased slowly before the
temperature threshold and followed a drastic drop after crossing the threshold due to the
thermal cracking. These studies have contributed to understanding the influence of temperature
on the fracturing of rock. However, there is a lack of research about the coupling influence of
temperature and loading rate on the quasi-static mode I fracture toughness and fracture
mechanism as the mechanical response of rock during strain burst under different loading rates
plays a vital role. In addition, CCNSCB method which has been considered as the most
promising testing configuration for both quasi-static and dynamic mode I fracture toughness
tests has yet to be investigated under the coupled influence of temperature and loading rate. In
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ADE | DDaammaaggee pprroocceesssseess aanndd ssttrraaiinn bbuurrsstt iinn bbrriittttllee rroocckk
this section, I aim to fill this research gap, and focuses on the impact of elevated temperature
and various loading rate on the quasi-static mode I fracture toughness behaviour, energy-
release rate and fracture mechanism.
2.3.1.2 - Loading rate dependence of the quasi-static behaviour of rocks
Rock fracture toughness can be used as a threshold value to predict the imminent fractures of
rocks during strain burst. The fracture mechanism and fracture parameters (fracture toughness,
fracture energy) of rock under static loading rate condition are significant for a better
understanding of the failure progress of rock during strain burst. A large number of studies has
been devoted for investigating the mechanical properties of rock material at various strain rate
or loading rate (Li et al. 2014; Liang et al. 2015). However, limited research has focused on
the effects of loading rate on the fracture toughness and fracture characteristics over a wide
range of loading rates. Mahanta et al. (2017), conducted experimental studies to better
understand the fracture behaviour of gas shale with various strain rates and it was concluded
that the fracture toughness gradually increases with increasing strain rate and the fracture
toughness for all the modes are comparable but vary significantly at higher strain rates.
Recently, Zhou et al. (2018) investigated the influence of loading rates on crack propagation
velocity and crack initiation toughness by using a new cracked tunnel specimen and stated that
crack propagation velocity and initiation toughness tend to increase with loading rate. In the
current study, the quasi-static mode I fracture toughness tests were carried out using CCNSCB
granite specimens exposed to different pre-heating treatments under varying loading rates. The
fracture mechanism and fracture toughness and energy-release rate of thermally-treated
Australian granite were investigated and the coupled influence of thermal damage and loading
rate on the fracture toughness and energy-release rate was evaluated and discussed more in
depth.
2.3.2 - Dynamic fracture tests
Dynamic fracture toughness test enables us to investigate the mechanical response of intact
rock under dynamic loading conditions in which increased loading rate has an influence on the
fracturing characteristics and mechanical behaviour. The effect of dynamic loading on rock is
critical to provide insight into dynamic fracture propagation which occurs during strain burst.
The typical rock dynamic problems encountered during underground engineering constructions
are illustrated in Figure 2.10.
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ADE | Damage processes and strain burst in brittle rock
Damage processes and strain burst in brittle rock
Table 2.3 Range of loading rates and time to fracture for different dynamic experimental
techniques for rock (modified after Zhang and Zhao 2014)
Loading Quasi- Dynamic
conditions static Intermediate loading rate High loading rate
Split
Servo- Pneumatic- Drop- Charpy Projectile
Loading Hopkinson
hydraulic hydraulic weight impact impact
techniques pressure
machine machine machine machine technique
bar
Loading
rate πΎΜ 1 101 β103 104 104 104 β106 104 β108
πΌ
(πππβπ/π
Time to
fracture π‘ > 106 105 β103 ~100 ~100 1β100 1β100
π
(ΞΌs)
Many researchers have investigated the dynamic fracture toughness and dynamic failure
mechanism of rocks over a wide range of loading rates (Zhang et al. 2000; Chen et al. 2009;
Dai et al. 2011; Zhang and Zhao 2013; Zhao et al. 2017; Shi et al. 2019). With the aid of SHPB
testing system, Zhang et al. (2000) quantitatively analysed the energy partitioning in the
dynamic fracture process of a short rod (SR) specimen over a wider range of loading rate. Dai
et al. (2010) employed the SHPB technique to measure the dynamic rock fracture toughness
by impacting cracked chevron notch Brazilian disc (CCNBD) specimen. A summary of typical
dynamic testing methods for the determination of dynamic fracture toughness using SHPB is
reviewed in Table 2.4.
Generally, an initial notch in the fracture toughness specimen is created either in a straight-
through notch or a chevron notch shape, as shown in Figure 2.11. For the sample with straight-
through notch, the pre-cracking through fatigue loading is required to avoid the potential errors
induced by a blunt, machined crack tip (Berto et al. 2017). In reality, pre-cracking or fabricating
a sharp crack is tedious, time-consuming and difficult to perform on hard rocks. Fortunately,
these difficulties in sharpening or pre-cracking the notch tip can be avoided by introducing a
chevron notch in the specimen. The crack initiates at the tip of the chevron notched ligament
under a very low load level and grows stably to a specific length in which the critical crack
associated with πΎ determination can be generated; thus, self-precracking can be achieved. In
πΌπΆ
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addition, this notch shape is particularly favoured in dynamic fracture tests due to its smaller
length compared to the specimens used in the other methods. The dynamic force at the two
loading ends of the sample is easily balanced for a shorter specimen, and thus, the quasi-static
data reduction method can be employed to determine the dynamic fracture toughness in the
SHPB tests (Zhou et al. 2012). Therefore, among the methods mentioned above, the CCNSCB
method is the most promising in the dynamic fracture tests to determine the mode I fracture
toughness of rocks due to its merits that will be presented in detail in Chapter 4. Only a limited
number of research has focused on investigating the dynamic fracture mechanism of CCNSCB
specimen. In this respect, the CCNSCB method was adopted for investigating the dynamic
progressive fracturing process during strain burst in SHPB testing in this research.
(a) (b) (c)
Figure 2.11 (a) Schematic of a semi-circular bend specimen geometry and loading scheme,
(b) straight-through notch, and (c) chevron notch
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Table 2.4 Summary of some typical dynamic testing methods for measuring the dynamic
fracture toughness using SHPB
Loading type Test method Reference
WLCT Klepaczko et al. 1984
Compact tension
(CT)
SR Ouchterlony 1988; Zhang et al. 2000, 2001
CSTBD Nakano et al. 1994; Wang et al. 2011; Yin et al. 2018
Brazilian disc
HNBD Lambert and Ross 2000; Wang et al. 2010
(BD)
CCNBD Dai et al. 2010
Mindess et al. 1987; Tang and Xu 1990; Zhao et al.
SENB
1999; Yang et al. 2009; Zhao et al. 2013
Chen et al. 2009; Yin et al. 2012; Zhou et al. 2012;
Bending
NSCB Dai and Xia 2013; Zhang and Zhao 2013a; Shi et al.
2019; Zhao et al. 2017; Zhou et al. 2019
CCNSCB Dai et al. 2011
WLCT wedge loaded CT, SR short rod, CSTBD cracked straight through BD, HNBD holed-
notched BD, CCNBD, cracked chevron notched BD, SENB single edge notch bending, NSCB
notched semi-circular bending, CCNSCB cracked chevron NSCB
2.3.2.1 - Thermal damage influence on the fracture toughness under dynamic load
The influence of temperature on rock mass becomes markedly important as the depth of
underground excavation increases which may result in undesirable structural failures (Yin et
al. 2012; Akdag et al. 2018). In the underground rock engineering, rock mass has to face not
only the effects of temperature environment, but also is exposed to dynamic power disturbances
leading to dynamic fracturing in the forms of strain burst, slabbing and spalling. We examined
the dynamic fracture characteristics of rock after thermal damage exposure. A limited research
in the literature has been focused on the coupled effects of temperature and loading rates on
the dynamic fracture characteristics of brittle rocks. Zhang et al. (2001) carried out dynamic
fracture tests on short rod (SR) Fangshan gabbro and Fangshan marble exposed to high
temperature (100-330 Β°C) by means of the SHPB system and they concluded that the dynamic
fracture toughness of the rocks mainly depends on the loading rate and it increases with loading
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rate as presented in Figure 2.12. Regarding the influence of temperature on dynamic fracture
of rock, Yin et al. (2012) utilised a notched semi-circular bend (NSCB) method with SHPB
apparatus to investigate the effect of temperature on the dynamic fracture toughness of
thermally treated Laurentian granite specimens (see Figure 2.13). They reported that the
dynamic fracture toughness increases with the loading rate and decreases with ascending
temperature level. It was also stated that the dependence of dynamic fracture toughness on the
temperature varies when temperature is below 250 Β°C and above 450 Β°C from other
temperatures. Recently, the coupling effect of temperature and static pressure (a given preload)
on the dynamic fracture toughness was studied (Yin et al. 2018). After performing dynamic
fracture tests on cracked straight-through Brazilian disc (CSTBD) specimens with a dynamic
and static coupling testing device based on the SHPB system, they reached a conclusion that
the dynamic fracture toughness of the specimens showed a decreasing trend with ascending
temperature.
Figure 2.12 Loading rate vs the dynamic fracture toughness of gabbro and marble at various
pre-heating temperatures from the dynamic SR tests (Zhang et al. 2001)
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ADE | Damage processes and strain burst in brittle rock
Damage processes and strain burst in brittle rock
Figure 2.13 Typical recovered samples exposed to various pre-heating temperature from the
dynamic NSCB test (Yin et al. 2012)
In summary, the existing studies have shown that the elevated temperature and loading rate
have a remarkable influence on the dynamic fracture characteristics of the rock. However, the
coupled effects of the thermal damage and the loading rate on the dynamic fracture properties
of brittle rock have yet to be systematically investigated. In this sense, to investigate the effects
of thermal damage and dynamic disturbance on the dynamic fracture characteristics of
Australian granite during strain burst, a series of dynamic fracture toughness tests was
performed by means of a SHPB system in this research. The damage evolution of thermally-
treated granitic rocks over a wide range of loading rates was investigated. The mode I dynamic
initiation fracture toughness (DIFT) (πΎπ ) and the rate dependency of the phenomenon were
πΌπ
determined and compared for the pre-heated specimens at different temperatures. The
CCNSCB method which is the most favoured for dynamic fracture tests was adopted under the
condition of different loading rates after the action of elevated temperatures for the first time
in the literature.
2.3.2.2 - Rate dependence of dynamic fracture toughness
The rock is usually fractured under dynamic loading in rock engineering applications, such as
strain burst, blasting, rock cutting. It is an inherent dynamic parameter to characterise the rocksβ
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capability of resisting against tensile crack formation and propagation and also serves as an
index for rock fragmentation processes involving fracturing in strain burst, blasting, tunnel
boring, drilling and crushing. Accurate characterisation of the dynamic fracture toughness over
a wide range of loading rates is thus essential. So far, to understand the loading rate dependency
of the dynamic fracture toughness, a substantial amount of dynamic fracture toughness tests
have been performed on various types of rock materials such as granite (Dai et al. 2010, 2011;
Gao et al. 2015), marble (Wang et al. 2011; Zhang and Zhao 2014), gabbro (Zhang et al. 2000,
2001), sandstone (Wang et al. 2015; Zhou et al. 2019). A summary of some research conducted
to study the loading rate influence on the dynamic fracture toughness of various rocks using
different sample geometry configurations is reviewed in Table 2.5. It is concluded that the
fracture toughens significantly increases with the increasing loading rate. Compared with
substantial static researches regarding dynamic rock fracture characteristics of rocks under the
coupled influence of different temperature and loading rate in recent decades however,
researches associated with rock dynamic fracture were fewer in number, resulting in a limited
understanding of dynamic fracturing characteristics of rocks. A systematic experimental
investigation should be addressed to understand the combined influence of temperature and
loading rate on dynamic fracture characteristics of rock. Therefore, in the present study, the
mode I dynamic fracture toughness and dynamic characteristics of fracturing process of
CCNSCB Australian granite specimens with various temperature exposure over a wide range
of loading rates were analysed and discussed using the SHPB associated with high speed (HS)
cameras.
Table 2.5 Summary of research studied the rate dependency of dynamic fracture toughness of
various rocks
Rock type Test method Reference
SCB Chen et al. 2009
CCNBD Dai et al. 2010
Laurentian granite
CCNSCB Dai et al. 2011
NSCB Yin et al. 2012; Gao et al. 2015
Dai and Xia 2013a
Barre granite NSCB
Dai et al. 2013b
SR Zhang et al. 2000, 2001
Marble
CSTFBD Wang et al. 2011
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Damage processes and strain burst in brittle rock
NSCB Zhang and Zhao 2013b, 2014
Gabbro SR Zhang et al. 2000, 2001
CSTFBD Wang et al. 2015
Sandstone
NSCB Zhang and Zhao 2014; Zhou et al. 2019
SCB semi-circular bending, CCNBD cracked chevron notched Brazilian disc, NSCB notched
semi-circular bending, CCNSCB cracked chevron NSCB, SR short rod, CSTFBD, cracked
straight through flattened Brazilian disc
2.4 - Strain burst evolution mechanism of brittle rock under true-triaxial
loading/unloading conditions
Strain burst is the most common type of rock burst in the deep underground which is caused
by a sudden release of stored strain energy within the surrounding rock mass near the free
boundary after excavation. This dynamic rock failure in deep rock engineering occurs in an
abrupt manner accompanied by a violent rock fragment ejection at high speed. With its
unpredictable and violent nature, strain burst poses a major threat to the safety, construction
equipment and productivity in rock engineering operations. Prior to any excavation,
underground rock mass is in a true-triaxial state of stress equilibrium (Ο >Ο >Ο ) where Ο Ο
1 2 3 1, 2,
Ο are the major, intermediate and minor principal stresses, respectively. Introducing an
3
excavation in rock masses results in forming the free face boundary condition; at the same time,
redistribution of stresses around underground openings takes place, i.e., the radial stress (minor
principal stress, Ο ) releases suddenly, the tangential stress (the major principal stress, Ο )
3 1
increases sharply, while the intermediate principal stress (Ο ) varies slightly, as depicted in
2
Figure 2.14. Hence, it is imperative to better understand the failure mechanism of strain burst
more in-depth under true-triaxial loading-unloading condition.
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ADE | Damage processes and strain burst in brittle rock
Damage processes and strain burst in brittle rock
Figure 2.14 Stress state of the surrounding rock mass and the representative elementary
volume after excavation: π , π , π are the far-field major, intermediate and minor principal
1 2 3
stresses, respectively; π , π , π and π (π ) are the tangential stress, axial stress, radial
π π π ππ ππ
stress and shear stress of tunnel, respectively; π is the angular direction measured counter-
clockwise from the π direction; π is the radial distance from the axis of the hole; and π is the
3
tunnel radius (Su et al. 2017b)
It is known that laboratory tests have a significant role in understanding the mechanism of
strain burst, calibration of numerical models and assessment of mechanical parameters. Over
the last decade, substantial efforts in the laboratory have been devoted to exploring the real
damage process of strain burst (Wang and Park 2001; He et al. 2010, 2012a, b, c; Huang and
Li 2014; Gao et al. 2018; Li et al. 2018). In recent years, simulating strain burst process using
rectangular prism specimens through true-triaxial loading-unloading tests have become more
prevalent (He et al. 2010, 2012a, b, c; Zhao and Cai 2014; Su et al. 2017a, 2018a, b; Akdag et
al. 2018). The pioneering true-triaxial loading-unloading strain burst testing facility was firstly
developed at the State Key Laboratory for Geomechanics and Deep Underground Engineering
in Beijing, China by He et al. (2010) to realistically mimic the exact boundary conditions and
stress paths for rocks during an excavation in which strain burst occurs. The hydraulic true-
triaxial testing machine consists of a hydraulic controlling frame, a data acquisition system and
an AE monitoring system and high-speed cameras are employed to monitor the fracturing
behaviour and failure process during strain burst, as presented in Figure 2.16. Cai et al. (2008)
emphasised that the actual stress path in a rock mass during excavation is complex and
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ADE | Damage processes and strain burst in brittle rock
Damage processes and strain burst in brittle rock
accurately simulating the stress change is of great significance to capture correct rock mass
response. Hence, to simulate the stress change of rock mass during excavation using this testing
system can be described in detail as follows:
ο· Firstly, stresses along the six surfaces of rectangular prism sample are progressively
increased until reaching the in-situ stress state.
ο· Subsequently, to simulate the creation of an excavation, the rigid loading plate acting
along π direction is abruptly dropped, while π is kept constant.
3 2
ο· After unloading Ο3 from one of the rectangular prismβs surfaces that is exposed to air,
π is continuously increased until strain burst occurs (see Figure 2.15).
1
Hydraulic pumping systems are used to apply vertical and other two horizontal loads on a
rectangular prism rock specimen with a maximum capacity of 450 kN. The data acquisition
system is capable of recording 100,000 data points per second (see Figure 2.16). The largest
specimen tested by this system has dimensions of 160 x 65 x 35 mm, along with the π , π , π
1 2 3
directions, respectively. The loading range varies from 0.1 to 0.5 MPa/s, while the time interval
for each loading is about 5 min. The image resolution of the high-speed camera is of 1024 x
1024 pixels which enables to capture the abrupt fracturing and violent rock fragment ejection,
as shown in Figure 2.16. Two AE transducers with a diameter of 18 mm each are used to
investigate internal damage evolution during strain burst test. The AE sensors (type WD, from
the American Physical Acoustics Corp.) are mounted to the lateral side of the rock sample
tested via spring clips and adhesive tape is used for reducing friction between the specimen and
loading plate. The resonance frequency of the transducers is about 150 kHz with an operating
frequency range of 100 kHz β 1 MHz. The amplitude threshold for pre-amplification of two
AE sensors is set to 40dB to amplify the AE signals during loading. A PIC-2 AE system is used
to monitor the characteristic of cracking with a sampling rate of 10 msps (million samples per
second).
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Figure 2.15 (a) Designed loading-unloading stress path and (b) schematic illustration of the
stress state of the rock specimen in strain burst test (Zhao and Cai 2014)
Figure 2.16 Illustration of true-triaxial strain burst testing system (He et al. 2015)
Based on this testing system, many scholars have performed strain burst tests using different
types of rocks under different stress paths for gaining deeper understanding of strain burst
under true-triaxial loading/unloading conditions (Coli et al. 2010; He et al. 2010, 2012a, b, c;
Gong et al. 2015; Li et al. 2015; Sun et al. 2017). Based on a comprehensive database for strain
burst tests, Akdag et al. (2017) studied the influence of specimen dimensions on bursting
characteristics of rocks and revealed that the failure mode changes from strain burst to local
spalling when the height to width ratio of rock specimen is reduced from 2.5 to 1 (see Figure
2.17). Hence, all specimens with a height to width ratio of 2.5 were used in the present study.
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Zhao et al. (2014) investigated the effects of unloading rate on the strain burst behaviours of
brittle rock under true-triaxial unloading conditions and reported that the rock tends to strain
burst more often when the unloading rate is high and the failure mode changes from strain burst
to non-violent spalling as the unloading rate decreases. Sun et al. (2017) analysed the
mechanism of strain burst based on the infrared thermography and AE monitoring and
concluded that the infrared temperature declines prior to strain burst, including obvious
anomaly bands in AE and anomaly temperature differentiation in a different area. Su et al.
(2017) investigated the influence of tunnel axis stress on strain burst by using modified true-
triaxial rock burst testing apparatus. The experimental results indicated that intensive strain
burst is more likely to occur when the tunnel axis stress is high. Recently, to investigate the
failure process and mechanism of strain burst in a deep circular cavern under high stresses,
Gong et al. (2018) conducted true-triaxial tests on cubical specimens with a pre-fabricated
circular hole, as depicted in Figure 2.18. A wireless micro-camera was utilised to monitor the
bursting process on the sidewalls of the hole, and the entire bursting process was split into four
stages: calm period, pellet ejection period, rock fragment exfoliation period and rock bursting
period. The researchers also revealed that the intensity of rockburst varies with the stress
condition; when the vertical stress is constant, and the horizontal axial stress is low, the
rockburst severity decreases with the ascending horizontal radial stress. In summary, the true-
triaxial loading and unloading tests to assess the failure characteristics of different rocks are
reviewed in Table 2.6.
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Table 2.6 Summary of true-triaxial loading and unloading tests to characterise the failure type of rocks (modified after Akdag et al. 2018)
Specimen size
Type Loading step Rock type Failure mode References
(mm x mm xmm)
15 x 15 x 30 Dolomite Mogi (1971)
50 x 50 x 100 Marble Michelis (1985)
50 x 50 x 100 Sedimentary rocks Takahashi & Koide (1989)
57 x 57 x 125 Sandstone Fracturing & ductility Wawersik et al. (1997)
19 x 19 x 38 Granite Haimson & Chang (2000)
80 x 80 x 80 Sandstone Nasseri et al. (2014)
(1) apply Ο1, Ο2, Ο3
50 x 50 x 100 Granite Feng et al. (2016)
Loading (2) keep Ο2 and Ο3
Mixed tensile and shear
Xu et al. (2019)
(3) increase Ο1
60 x 60 x 110 fractures
50 x 50 x 100 Marble Brittle & ductile failure Zhao et al. (2018)
V-shaped secondary
Zheng et al. (2019)
50 x 50 x 100 fractures
Granite, marble, Spalling, brittle
Gao et al. (2018)
50 x 50 x 100 sandstone transgranular fractures
50 x 50 x 100 Sandstone Stable-unstable fracturing Kong et al. (2018)
Limestone, granite, He et al. (2010, 2012a,
30 x 60 x 150 Rockburst
sandstone, marble 2012b, 2012c)
20 x 40 x 100 Spalling Coli et al. (2010)
(1) apply Ο1, Ο2, Ο3 Marble
30 x 60 x 150 Rockburst and slabbing Gong et al. (2012)
(2) keep Ο2
Unloading
(3) Unload Ο3 3 0 x 60 x 150 Rockburst Zhao et al. (2014)
(4) Increase Ο1 30 x 60 x 150 Rockburst
30 x 60 x 120 Granite Slabbing Zhao and Cai (2014)
30 x 60 x 90 Shearing
30 x 60 x 150 Rockburst Gong et al. (2015)
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ADE | FDoarmecaagset ipnrgo tchees sperso apnedn ssittrya ionf bsturrasitn i nb ubrrsitt tle rock
At increasing depths, rock mass surrounding underground excavations becomes vulnerable to
the effects of temperature. Due to the thermal gradient in the deep rock mass, elevated
temperature conditions can cause dramatic changes in the microstructure and mechanical
behaviour of rocks which are prone to strain burst. As a consequence, microstructure and
mineral composition of rocks will alter due to the thermally-induced cracking under the action
of high temperatures which will directly influence the long term safety and stability of
underground rock structures. In recent years, a large number of researchers have investigated
the effects of temperature on the physical and mechanical properties of various rocks under
quasi-static loading (Keshavarz et al. 2010; Zhang et al. 2015; Peng et al. 2016; Xu and Karakus
2018; Xu et al. 2018). Liu and Xu (2015) studied the mechanical response of marble under the
combined effects of high temperature and mechanical load under uniaxial compression and the
mechanical damage and thermal damage caused by mechanical load and temperature
respectively were discussed. The researchers established a high-temperature damage
constitutive equation of rock based on the macroscopic damage mechanics and nonequilibrium
statistical methods. Kumari et al. (2017) carried out a series of unconfined compressive strength
tests on granite exposed to various temperatures up to 800 Β°C, followed by two cooling methods
(rapid and slow cooling). They found that the influence of rapid cooling is much higher than
that of slow cooling due to the abrupt thermal shock and the failure mode of the granite
specimens changed from brittle to quasi-brittle fracturing with increasing temperature. To
reveal the coupled effect of temperature and confining pressure on the failure mechanism of
deep rocks, a new statistical constitutive model of rock thermal damage under triaxial
compression was established by Xu et al. (2018). Besides, as being an intrinsic mechanical
property of rocks, researchers have revealed that temperature is a significant factor influencing
fracture characteristics and fracture toughness in the recent years (Yin et al. 2012; Mahanta et
al. 2016). Using semi-circular bend (SCB) method, Yin et al. (2012) studied the effect of
thermal treatment on dynamic fracture toughness of Laurentian granite and concluded that
fracture toughness increases with the loading rate, whereas decreases with the treatment
temperature. Mahanta et al. (2016) measured the static mode I fracture toughness of SCB
Indian sandstone specimens and revealed that fracture toughness increased between the room
temperature and 100 Β°C, thereafter decreased from 100 Β°C to 600 Β°C. However, to the best of
our knowledge, the influence of temperature on the energy release during strain burst and the
dynamic energy balance at spontaneous failure are still missing in the existing literature.
However, the aforementioned studies did not consider the influence of thermal damage on
38 |
ADE | Damage processes and strain burst in brittle rock
Forecasting the propensity of strain burst
strain burst mechanism under true-triaxial loading-unloading conditions. There is only a
limited number of research focusing on exploring the influence of temperature on strain burst
characteristics. Therefore, it is essential to investigate how strain burst mechanism is affected
with elevated temperature which provides the very motivation for the study presented for
accurate and better understanding of rock behaviour when strain burst occurs under high
ground temperature condition.
Additionally, sudden ejection of rock fragments is a unique failure behaviour of strain burst.
The kinetic energy of the rock fragments ejected from the free face of rock specimen in the
strain burst test can be used as a precursor to quantitatively express the potential intensity of a
burst event. A few studies in the available literature have addressed the kinetic energy
characteristics of strain burst failure. Therefore, detailed kinetic energy analysis may allow the
accurate interpretation of precursory information contained in strain burst damage and the
accurate prediction of strain burst under high-temperature condition.
In this research, the process of strain burst in deep hard rock excavations was effectively
reproduced by conducting true-triaxial strain burst tests and failure characteristics of strain
burst damage were analysed more in-depth and the influence of thermal damage on strain burst
mechanism and dynamic failure process was discussed. To quantify rock damage and monitor
the evolution of damage within a thermally-treated rock, AE technique was adopted and time-
domain, frequency-domain and b-value analyses were conducted to systematically study the
evolution of AE due to thermal damage influence on strain burst. A high-speed camera was
employed to observe and track the ejection of rock fragments during strain burst and kinetic
energy analysis was carried out based on the velocity of ejected rock particles.
2.5 - Summary and discussion
As the depth of mining and underground engineering construction increases, strain burst which
is a dynamic rock failure in highly-stressed ground, occurs more prevalently in an abrupt
manner accompanied by violent rock fragment expulsion at a high speed. Due to its
unpredictability, destructiveness and sudden nature, strain burst has become a serious disaster
for safety and production during deep mining operations. Therefore, it is an urgent problem to
better understand the underlying mechanism of the rock engineering disasters occurring in deep
underground working environments for deriving strategies to eliminate or mitigate and reduce
the potential intensity of strain burst.
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ADE | FDoarmecaagseti pnrgo tchees sperso panends sittyra oinf bsturrasitn ibnu brrsitt tle rock
Laboratory tests play a vital role for exploration the mechanism of strain burst, assessment the
mechanical parameters and behaviour and identification of the stress states in which a
spontaneous dynamic instability initiates. The primary goal for researches related to the
physical modelling of strain burst phenomenon including the triggering factors is to replicate
failure process of strain burst in the laboratory in a realistic manner and to mimic the stress
conditions under which strain burst occurs. Over the past few decades, significant progress has
been achieved in the characterisation of strain burst by conducting laboratory tests. However,
existing studies have not been thoroughly evaluated the damage evolution during strain burst
under the effects of different temperature, confinement and loading rate in various loading (and
unloading) conditions. This section briefly presents the efforts on representing the real damage
process of strain burst under the condition of laboratory tests within the framework of rock
mechanics and fracture mechanics. The following key conclusions can be drawn:
1. The manifestation of strain burst is related to the elastic strain energy accumulated within
the rock or rock mass and how this stored energy is released during energy-driven
spontaneous failure. From the perspective of energy, strain burst is a nonlinear dynamic
destabilisation failure process in which the energy is converted into kinetic energy by the
ejected rock fragments. Therefore, the principles of energy release during strain burst, in
some regards, can be compared with the principles involved in the spontaneous failure in
hard brittle rock exhibiting Class II behaviour under compression. Strain burst is frequently
encountered during the excavations in hard rock, which can store substantial amount of
strain energy prior to failure and can release the energy during a rapid post-peak strength
loss, displaying an unstable spontaneous and violent post-peak failure mode. In this
respect, it is necessary to obtain the complete stress-strain characteristics for assessing the
dynamic post-peak energy balance in strain burst. In addition, high rock stresses
(confinement) and elevated temperatures have a significant influence on leading to strain
burst as the underground excavations go deeper and extensive. Hence, it is also essential
to investigate the coupling effects of thermal damage and confining pressure on the energy
characteristics and potential intensity for strain burst.
2. The phenomenon of strain burst is mainly characterised by the nucleation, growth and
coalescence of micro-cracks in rock or rock mass. Rock fracture toughness which is the
critical SIF is an important intrinsic material property to resist fracturing can be used as a
threshold for estimating the imminent fractures of rock structures during strain burst.
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ADE | Damage processes and strain burst in brittle rock
Forecasting the propensity of strain burst
Therefore, to predict the onset of catastrophic failures such as strain burst in rock
engineering structures due to crack growth, it is necessary to better understand the fracture
characteristics and fracture parameters (fracture toughness, fracture energy) of rock during
strain burst. In this sense, quasi-static and dynamic fracture and energy evolution
characteristics in strain burst can be revealed by conducting fracture toughness tests. Rock
mass is exposed to not only different loading rate disturbances, but also is vulnerable to
the effects of elevated temperature as the depth of underground opening increases.
Coupling impact of various loading rate and thermal damage will affect the overall
mechanical behaviour of brittle rock which can trigger strain bursting in deep rock
engineering operations. Therefore, rate dependence and the influence of temperature on
quasi-static and dynamic fracture characteristics during strain burst are of great importance
for reinstating the thermally damaged deep underground engineering constructions under
the action of various loading rates.
3. Simulating the stress change and boundary of rock mass after excavation successfully is
crucial importance to investigate the occurrence and mechanism of strain burst near the
excavation boundary. In this respect, true-triaxial strain burst test has been conducted to
mimic the failure process of strain burst, demonstrating the progressive stress
concentration process during strain burst under true-triaxial loading-unloading condition.
Since the rock mass is vulnerable to the effects of temperature at increasing depths, it is
needed to explore the influence of thermal damage on strain burst characteristics under
true-triaxial loading-unloading condition.
Rock properties, particularly rock strength, fracture toughness, have a significant control
influence on the extent of strain burst mechanism and its propensity and severity. Rock strength
determines the amount of elastic stored strain energy within the rock before critical strain burst
stress level is reached, and rock fracture toughness determines the capacity of rock to insist
unstable fracturing. Therefore, in terms of the laboratory evaluation of rock strength and rock
fracture toughness, strain burst vulnerability can be initially identified.
It should also be noted that most of the experimental studies mentioned above are conducted
on limited rock specimen sizes as compared to most of the natural processes operated in the
field scale. Although some mechanisms of strain burst such as damage evolution and energy
redistribution during strain burst, which were well documented in the laboratory studies, have
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ADE | Forecasting the propensity of strain burst
Chapter 3: Forecasting the propensity of strain burst of
brittle rock based on the post-peak energy analysis
3.1 - Introduction
The magnitude of strain burst, amount of kinetic energy released, the volume of ejected rock,
ejection velocity and degree of rock fragmentation can show a considerable variation due to
the mineral composition of the brittle rocks. The manifestation of strain burst is related to the
elastic stored strain energy and how this stored energy is released during unstable spontaneous
failure (Tarasov and Potvin 2013; Akdag et al. 2018; Bruning et al. 2018). The first law of
thermodynamics states that the energy transformation process of strain burst in rock mass
involves energy storage, dissipation, and release. Hence, it is significant to investigate the
energy state during strain burst from the viewpoint of energy theory. Indeed, the failure of rock
is driven by energy activities, including absorption, evolution, dissipation, and the release of
strain energy (Huang and Li 2014; Peng et al. 2015; Li et al. 2017; Weng et al. 2017). Rocks
exhibiting Class II behaviour undergo self-sustaining fracturing due to excess stored strain
energy which is accompanied by some energy release. Hence, principles of the energy
redistribution during strain burst, in some regards, can be compared with principles involved
in the spontaneous failure of Class II, which implies that the role of energy in strain burst can
be better understood by analysing the energy characteristics of rock in compression. In this
respect, a series of quasi-static circumferential strain controlled uniaxial and triaxial
compression tests were conducted on Class II rocks exposed to various temperatures up to 250
Β°C over a wide range of confinement to capture the post-peak reaction of Class II rock or βsnap-
backβ behaviour and calculate stored strain energy, dissipated energy, and the excess strain
energy that is the intrinsic potential energy for strain burst in the rock. A novel energy
calculation method associated with acoustic emission (AE) was developed based on the post-
peak energy analysis. Combined effects of thermal damage and confining pressure on the
mechanical properties of granite including the post-peak behaviours, energy redistribution at
the post-peak regime, failure characteristics, strength and deformation parameters,
characteristics stresses in the progressive failure process have been systematically investigated.
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ADE | Forecasting the propensity of strain burst
In this chapter, an introduction to the relevant researches conducted to gain a better
understanding of the mechanism of strain burst, energy evolution characteristics of rocks under
different loading paths, and the thermal damage influence on mechanical behaviour of rocks
tests is presented. This is then followed by the experimental work included for estimating the
energy redistribution characteristics of brittle rock during strain burst. A novel energy
calculation method associated with AE to investigate the post-peak regime of rocks exhibiting
Class II behaviour was developed. Intrinsic potential intensity for strain burst in the rock was
quantitatively assessed. Coupling influence of thermal damage and confining pressure on the
post-peak energy redistribution and crack evolution characteristics of thermally treated
Australian granite specimens that ranged from ambient conditions (25 Β°C) to 250 Β°C was
analysed. In order to reveal the microstructural changes due to thermal effects, scanning
electron microscopy (SEM) analysis was also performed. This is highly relevant to link the
excess strain energy and the main failure mechanism triggering strain burst under high
temperature condition.
3.2 - Experimental methodology
Experimental work includes the investigation of the propensity of strain burst of rocks
exhibiting Class II behaviour under the coupling influence of high confining pressure and high
temperature. The main objective of this chapter is to quantitatively estimate the energy
redistribution characteristics of brittle rock based on a newly developed energy calculation
method, conducting circumferential strain controlled uniaxial and triaxial compression tests of
granite. Two groups of tests were carried out in this study: Group (1) was the circumferential
strain controlled uniaxial compression tests to quantitatively examine the potential intensity of
strain burst, and Group (2) was the circumferential strain controlled triaxial compression tests
to develop a new energy calculation methodology based on the post-peak energy balance of
snap-back behaviour and investigate the combined effects of increasing temperature and
confining pressure on the post-peak energy evolution characteristics. In order to support the
findings, SEM analysis was also performed to provide a better understanding of the associated
failure mechanism and the corresponding micro-structure alteration in granite.
3.2.1 - Specimen preparation and heating process
The granite specimens were collected from a borehole located in South Australia at depth
ranging from 1020 m to 1345 m. The grain size of the granite varies between 0.5 and 3 mm
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ADE | Forecasting the propensity of strain burst
within a coarse-grained matrix. The granite selected for testing mainly comprised of quartz,
feldspar, chlorite and potassium.
The granite specimens were sub-cored from 63-mm diameter drill cores and cut using diamond
coring and cutting apparatus to obtain cylindrical samples of 42 mm in diameter and 100 mm
in length in which the aspect ratio (i.e. length to diameter ratio) was maintained at 2.4 (Fairhurst
and Hudson 1999). The diameter of the specimens was more than 20 times bigger than the rock
grain size satisfying ISRM recommendations (Fairhurst and Hudson 1999). Both ends of the
specimens were then finely ground flat and parallel to each other within approximately 0.01
mm and polished to minimise the end effect during loading. The average uniaxial compressive
strength (UCS) of the granite samples is 158 MPa with a density of 2871 kg/m3, the average
elastic modulus is 38.6 GPa, and the average P-wave velocity of the specimens before thermal
damage is 5764 m/s.
The granite specimens were divided into four groups based on temperature exposure. In the
present study, the heating process of the rock samples was carried out in a high-temperature
tube furnace in the Mining Engineering Research Laboratory at The University of Adelaide.
Samples were first heated up to the target temperatures (25, 100, 175, and 250 Β°C) at a modest-
constant heating rate of 5 Β°C/min to avoid the development of cracks due to the thermal shock
during the heating process. Once the designated temperature was reached, the temperature
remained constant at the pre-determined level for about 12 h, to ensure uniform heating inside
the specimens. They were then allowed to cool down naturally to room temperature (25 Β°C)
prior to mechanical testing.
3.2.2 - Circumferential strain controlled uniaxial and triaxial compression tests
It is well-understood that the stress-strain behaviour of rock is the external manifestation of
energy evolution during deformation and failure. Therefore, the complete stress-strain response
of rock, importantly post-peak failure stage, is the fundamental information to describe the
processes of energy redistribution, evolution and rock deformation as strain burst takes place
at the post-peak failure stage. Numerous relevant attempts have been made by researchers to
obtain the full stress-strain response of rock in compression by controlling the application of
load through a feedback of axial load (Bieniawski and Bernede 1979), axial displacement
(Gowd and Rummel 1980), or axial strain rate (Okubo et al. 1990). However, these control
methods are only sufficient to measure pre-peak behaviour, not to capture post-peak stage of
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ADE | Forecasting the propensity of strain burst
Class II rocks which is characterised by a strong strain localisation as axial strain no longer
monotonically increases from the moment that rock exhibits Class II behaviour (Munoz &
Taheri, 2017). In this sense, the circumferential- or lateral-strain controlled method is more
appropriate to measure post-peak stress-strain response for brittle rocks (Wawersik and
Fairhurst 1970; Fairhurst and Hudson 1999; Munoz et al. 2016a, b). In this research, full stress-
strain behaviour and energy evolution characteristics of brittle rock were analysed by
performing circumferential strain controlled uniaxial and triaxial compression tests.
A series of uniaxial and triaxial compression tests were carried out on Australian granite.
Compression tests compiled with circumferential-strain controlled method in order to capture
the post-peak response of rock. To reveal the influence of temperature on rock energy evolution
characteristics, and post-peak energy distribution of Class II behaviour under self-sustaining
failure, a number of granite specimens exposed to different temperatures were tested. For UCS
tests, rock samples were subjected to a quasi-static monotonic axial loading by a closed-loop
servo-controlled Instron 1282 hydraulic compression machine, with a loading capacity of 1000
kN, which was stiff enough not to allow the elastic energy accumulated in the machine. (see
Figure 3.1). The applied axial load was initially controlled at an axial-strain feedback at a rate
of 0.001 mm/mm/s until reaching approximately 70% of the expected peak force (0.07 πΉ )
ππππ
and then the control mode was switched to circumferential control, in a way keeping lateral-
strain rate constant by the circumferential extensometer outlined in the ISRM method
(Fairhurst and Hudson 1999). In this sense, the electronics and computer program allowed the
hydraulic system to be adjusted continuously and automatically to ensure the load to respond
accordingly with the feedback signal and with the damage extent to the specimen.
In UCS test, each granite specimen was instrumented by a pair of strain gauges (30 mm in
length) oriented in the axial direction to measure the corresponding axial strain, π , as depicted
π
in Figure 3.1. Additionally, the vertical displacement of the granite specimens was measured
externally by a pair of LVDTs, which were mounted on both sides of the specimens. Besides,
direct-contact lateral ring-shaped extensometer was mounted along the perimeter and at the
mid-length of the specimens which eliminated the end-edge friction influence. This setup was
used to both control the axial load by lateral-strain feedback and record lateral strain, π . Figure
π
3.1 shows the arrangement of the instrumentation and experimental setup for uniaxial
compression tests under quasi-static monotonic loading conditions.
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ADE | Forecasting the propensity of strain burst
Testing machine
(INSTRON 1282
LVDTs
Lateral
extensometer
Figure 3.1 Experimental setup: servo-controlled closed-loop testing system and rock
instrumentation in uniaxial compression loading
To investigate the coupling influence of thermal damage and confining pressure on energy
evolution, circumferential strain controlled triaxial tests were conducted on the granite
specimens exposed to temperatures up to 250 Β°C over the confining pressures up to 60 MPa.
Triaxial compression tests were carried out using Instron 1282 with an axial loading capacity
of 1000 kN under three groups of confining pressures (20, 40, and 60 MPa). A Hoek cell with
a capacity up to 65 MPa was used to apply confining pressure in these tests. Circumferential
strain control was utilised by means of a Hoek cell membrane fitted with four strain gauges
internally within the cell, as depicted in Figure 3.2. The circumferential strain method
suggested by ISRM for obtaining the complete stress-strain curve was adopted in these tests.
The specimen was loaded axially with a constant growth of lateral strain of 1Γ10β6
mm/mm/s. The first step of the test was to apply hydrostatic pressure on the rock specimen
until the pressure reached the required magnitude of the confinement. After that, the axial
loading was applied using the circumferential strain control method while keeping the
confining stress constant.
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ADE | Forecasting the propensity of strain burst
compression loading and the pre-amplifiers of two AE sensors were set to 60 dB to amplify the
AE signals during loading. The resonance frequency of the AE transducers was 125 kHz,
associated with an operating frequency ranging from 100 kHz to 1 MHz. A PCI-2 AE system
was used to monitor the damage within the granite specimens during compression tests, and
the sampling rate was set to 2MSPS. The amplitude threshold for AE detection was set to 45
dB to ensure environmental noise was no longer registered during data acquisition.
3.3 - Evaluation of the experimental results
In this part, a new energy calculation method associated with AE for evaluating the post-peak
energy characteristics of brittle rock is introduced. According to the proposed formulas and
tests results, energy evolution during strain burst of Class II rock is analysed with the change
of temperature and confining pressure, and the underlying mechanism of strain burst is also
discussed. The combined influence of thermal damage and confinement on the mechanical
properties, failure modes and AE characteristics of Australian granite is investigated. Kinetic
energy analysis is conducted for quantitatively evaluating the intensity of strain burst, and the
effects of temperature on the severity of strain burst is studied. The fracturing mechanism of
granite under the combined effects of temperature and confining pressure is also discussed.
3.3.1 - New energy calculation method based on the post-peak energy balance of
snap-back behaviour
The stress-strain response is the phenomenological manifestation of the energy evolution
during rock failure. Under compression, the stress-strain curves of the post-peak behaviour of
rocks can be classified as Class I and II. Class I behaviour is characterised by a negative post-
peak slope which means that loading must be applied to generate additional energy for
maintaining the entire fracture process until the failure of the rock to occur. Class II rock
behaviour, on the other hand, shows positive post-peak slope and the elastic stored strain
energy in the rock specimen is sufficient to display self-sustaining failure which is
accompanied by some energy release. The post-peak behaviour is a reflection of some intrinsic
material properties which allows estimating the dynamic energy balance at spontaneous failure.
Therefore, full stress-strain behaviours of rock undergoing uniaxial and triaxial compression
play a significant role to describe the total energy evolution and rock deformation. In this
respect, the full stress-strain and the post-peak characteristics of hard brittle granite samples
exhibiting Class II behaviour under uniaxial and triaxial compression, which can be compared
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with the stress state of a strain burst, were obtained by utilising the circumferential-strain
controlled loading method.
Figure 3.3 shows the complete stress-strain curve of a granite tested at a confinement of 10
MPa. Area of the green triangle (ππ ) corresponds to the elastic stored strain energy within the
πΈ
specimen before it displays βsnap-backβ behaviour, which is the energy source for fracturing
and spontaneous failure (strain burst).
Figure 3.3 Class II behaviour and elastic stored strain energy of granite under 10 MPa
confinement
Tarasov and Potvin (2013) assessed rock brittleness under triaxial compression and established
a corresponding brittleness index based on the energy balance of the post-peak stage of the full
stress-strain curve. However, this energy calculation framework did not take into account the
energy dissipation due to cohesion loss and frictional failure and the excess strain energy
released during brittle failure (bursting). Herein, a new energy calculation method to
investigate the post-peak regime of rocks exhibiting Class II behaviour is proposed. Using the
AE characteristics during compression tests, fracture energy was split into two classes: 1)
energy consumed due to gradual loss of dominating cohesive behaviour and 2) energy
dissipated during the mobilisation of frictional failure (as shown in Figure 3.4). In Figure 3.4,
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ADE | Forecasting the propensity of strain burst
blue and yellow areas represent the energy consumed by cohesion weakening during stable
fracturing (πΞ¦ ) and the energy dissipated during the mobilising frictional sliding (πΞ¦ ),
πΆπ πΉπ
respectively. The green area is corresponding to the residual stored elastic strain energy (ππ ).
π
πΈ
For Class II rock behaviour, the elastic strain energy accumulated within the rock is sufficient
to maintain the entire failure of the rock which indicates that rocks exhibiting snap-back
behaviour are close to absolute brittleness. In this case, self-sustaining fracturing forces rock
failure which is accompanied by some energy release. The red area (subtended by snap-back
part) represents the excess strain energy released during brittle failure (energy in excess, πΞ¦ )
πΈπ
which is responsible for the intrinsic potential energy for strain burst in the rock. The above
assumptions on unloading without stiffness change and different stages of failure based on the
measured macro behaviour facilitate the calculation of energies in this study. I am aware that
they may not always truly reflect the underlying failure modes that are a combination of
microcracking and friction between microcrack surfaces. The links between macro behaviour
and underlying micro-structural processes require advanced experimental techniques that can
track the evolution of these processes in real time, given the very fast failure in rocks under
uniaxial/triaxial compression condition. This is beyond the scope of this study.
Figure 3.4 Schematic diagrams of energy calculation during Class II behaviour of granite
under 10 MPa confinement
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The Class II failure process between points A and C can be characterised by the following
types of specific (per unit volume) energy calculations (Equations 3.1-3.5):
(ππ΄)2
ππ = (3.1)
πΈ 2πΈ
2
π΅ (ππ)2 β(ππ+1) (πβπΈ)
dΞ¦ = β (3.2)
πΆπ 2πΈπ
π=π΄
πΆ (ππ)2 β(ππ+1)2(πβπΈ)
dΞ¦ = β (3.3)
πΉπ 2πΈπ
π=π΅
(ππΆ)2
ππ = (3.4)
π
πΈ 2πΈ
dΞ¦ = ππ βdΞ¦ βdΞ¦ βππ (3.5)
πΈπ πΈ πΆπ πΉπ π
πΈ
where π is the elastic stored strain energy after the point of Class II behaviour, Ξ¦ is the
πΈ πΆπ
energy consumption dominated by cohesion degradation during stable fracturing, Ξ¦ is the
πΉπ
energy dissipated during the mobilisation of frictional failure, π is the residual stored elastic
π
πΈ
strain energy, Ξ¦ is the excess strain energy released during brittle failure (bursting), ππ΄ is
πΈπ
the point of axial strain reversal, ππ΅ is the point of brittle failure intersection, πΈ is the elastic
stiffness of the specimen and π (π = πΏπ/πΏπ) is the post-peak modulus between two
incremental stress points.
The AE detection technology is a powerful non-destructive technique to investigate the failure
process and crack evolution mechanism in brittle rocks (Lockner, 1993). When a brittle rock
is under stress, strain energy is released during the development of new cracks or the widening
of existing cracks. This energy is released in the form of elastic waves from the crack tips, and
can be captured and amplified by an AE system. Therefore, AE detection technique has been
widely used in a number of previous researches to study the crack development mechanism in
brittle rocks (Carpinteri et al., 2013; Karakus et al., 2016; Kumari et al., 2017; Akdag et al.,
2018; Bruning et al., 2018; Weng et al., 2018). In this study, the AE technique was adopted to
assess the post-peak energy evolution characteristics of the granite specimens under various
confining pressures. Figure 3.5 shows axial stress-strain and AE hits characteristics for rocks
with Class II behaviour tested in triaxial compression (π = 10 πππ). From near peak (pre-
3
peak) to the point of axial strain reversal (ππ΄), some microcracking is mobilised that facilitates
fracture process, e.g. creating more surfaces to facilitate sliding. In Zone (1), the energy
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ADE | Forecasting the propensity of strain burst
dissipation of the rock specimen is provided by the initiation and further opening of
microcracks in the specimen. In this energy dissipation process, cohesion degradation and
frictional sliding facilitates simultaneously in which cohesion weakening is dominant, but the
energy needed to further fail the specimen is below the storage. During this process, further
degradation of cohesive strength leads to more fracture surface created and hence gradually
shows stronger interlocking. This is typified by the increasing AE activities as more
microcracks are opened. Once a certain level of microcrack generation is reached, the fractures
start to coalesce and propagate forming macrocracks (Zone 2). This allows frictional sliding to
dominate the fracture energy dissipation process. More energy is gradually required to further
fail the specimen, due to friction strengthening and also lower energy storage. At this stage the
sliding plane has formed in rock and a more constant rate of AE energy is recorded. Therefore,
with fracture propagation, dominating cohesion loss (Zone 1) is gradually substituted by the
mobilisation of frictional failure (Zone 2) which is accompanied by the decrease in bearing
capacity of the specimen from the cohesive strength to the frictional (residual) strength (Bazant,
1996; Landis et al., 2003; Tarasov & Potvin, 2013; Munoz & Taheri, 2018; Renani & Martin,
2018). This new method for determining the energy dissipation of compressive tests avoids
the grouping of all energy into the term βenergy lost due to stable fracturingβ. This is significant
when considering phenomena like strain burst as frictional processes are not likely to occur at
the excavation face due to the sudden ejection of rock fragments and spalling type of failure.
Therefore, these energy measures can be further studied to determine their role in strain burst
prediction and mechanism investigation.
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ADE | Forecasting the propensity of strain burst
Figure 3.6 Stress-strain curves of granite at different temperatures under various levels of
confinement
The variations of peak stress, peak strain and Youngβs modulus with confinement and
temperature are depicted in Figure 3.7. It can be expected that with the rise of confining
pressure, the peak strength increased (see Figure 3.7a). At low confinement, the peak strength
of thermally treated Australian granite was mainly controlled by the micro-cracks; however,
with increasing confining pressure, the effects of micro-cracks on the strength diminished as
the initial micro-cracks began to close due to the application of confinement. As shown in
Figure 3.7b, the peak strain increased by 26% as the temperature increased from 25 to 250 Β°C
due to the compaction of more micro-cracks inside high-temperature treated specimen
produced larger strain. The trend of the elastic modulus of granite specimen with increasing
temperature was similar to that of the peak strength. With the increase of temperature from 25
to 250 Β°C, the elastic modulus of Australian granite decreased by approximately 17% due to
the fact that different levels of fragmentation rendered the rock relatively weaker after heating
treatment (see Figure 3.7.c). This phenomenon can be attributed to the increased crack density
due to induced thermal crack development (Kumari et al. 2017a). This trend was consistent
with the temperature-dependent strength behaviour of the granite described above.
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Figure 3.7 Stress-strain curves of granite at different temperatures under various levels of
confinement
The failure modes of the granite specimens under the combined conditions of elevated
temperature and confinement are presented in Figure 3.8. The main feature is the multiple
longitudinal splitting failure pattern accompanied by local shear failure when π = 0 MPa. The
3
formation of extension cracks oriented in the direction of principal stress is the prevailing
pattern of macroscopic fracturing in uniaxial compression. In moderate confining pressures,
the granite specimens mainly failed by shear localisation along an inclined macroscopic shear
band. Under high confinement, a conjugate shearing or ductile failure was observed in which
the thermal heating could also enhance the ductility of the rock samples, as depicted in Figure
3.8. Confining pressure restricts the propagation and coalescence of longitudinal cracks which
helps to the expansion of the inclined cracks at an angle to the direction of the major principal
stress, and hence the failure mode changed. The longitudinal splitting cracks is a type of tensile
crack, which is easily opened and has a small displacement between crack surfaces. Therefore,
the dissipated energy needed to initiate and propagate the longitudinal splitting cracks is small.
However, granite specimens will slide along the surfaces after shear failure under a high
confinement. This process requires the testing apparatus to provide more energy to overcome
the friction and maintain the propagation of the macro-cracks.
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ADE | Forecasting the propensity of strain burst
Figure 3.8 Fracture patterns of granite specimens after heating to different temperatures under
different confining pressures
Progressive damage evolution and fracturing behaviour in Australian granite under uniaxial
and triaxial loading conditions were investigated by using AE monitoring technique in this
study. As indicated that cumulative AE energy characteristics reflect the damage evolution
better as the size of micro-cracks is related to the magnitude of the AE events, cumulative AE
responses were analysed in this study (Akdag et al. 2018). Figure 3.9 shows the cumulative AE
energy evolution for granite specimens at different levels of temperature for each confinement.
Based on the AE characteristics, the evolution of AE behaviour underwent two typical stages,
i.e. quiet stage and active stage. The quiet stage corresponds to the closure of pre-existing
cracks or other defects and linear elastic deformation in which AE energy responses were rare
when compared with the active stage. It can also be observed that the AE characteristics at the
quiet stage for brittle rocks are not dependent on temperature. With the increase of axial
deformation, stable and unstable crack propagation took place which contributed to the
progressive degradation of the inherent rock strength and thus resulted in a dramatic increase
of cumulative AE energy. In relation to the thermal damage influence, the accumulated AE
energy curves became smoother with the rising temperature which resulted in a delay in
damage evolution. Due to the thermally-induced micro-cracks, a delay in damage evolution
occurred which indicates that at higher temperatures, the granite specimens tended to burst in
a more intense manner.
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3.3.3 - The energy balance of Class II at spontaneous failure under the combined
conditions of elevated temperature and confining pressure
The release of excess strain energy and the increase of dissipated fracture energy caused a
reduction in the energy storage capacity of the rock so that rock deformation increased
gradually and tended to fail. The formation of macrocracks and failure surfaces in the rock
promoted the conversion of the accumulated elastic strain energy into the forms of energy to
be dissipated and released which resulted in spontaneous bursting. Due to the aggravation of
dramatic internal fracture expansion, further strength loss took place with a transition into the
residual stage in which some amount of strain energy was stored within the specimen (see
Figure 3.4).
In general, the higher the peak stress, the higher the elastic stored strain energy, with higher
excess strain energy which is the intrinsic potential energy for strain burst in the rock associated
with faster rock fragment ejection. The material strength drops along the increase of pre-
heating temperature. An increase in the temperature can exacerbate the fragmentation degree
of the sample that can weaken the interaction force between the particles and aggravate the
fragmentation degree. The results demonstrated that thermal damage affects strain burst
behaviour of brittle rock. Figure 3.10 shows the variations of elastic stored strain energy, total
fracture energy, excess strain energy by temperature. When the temperature increased from 25
to 250 Β°C, elastic stored strain energy, total fracture energy, excess strain energy decreased by
80, 82 and 43%, respectively (see Figure 3.10). Increasing temperature resulted in an alteration
of the grain-to-grain contacts in the rock matrix, which led to reduced cohesion at higher
temperatures.
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The influence of confinement on the elastic stored strain energy, the energy consumed by
dominating cohesion weakening, the energy dissipated during mobilisation of frictional failure
and the excess strain energy of the granite specimens are depicted in Figure 3.11. It can be seen
that the energy redistribution characteristics and material behaviour of Australian granite under
different levels of confinement are strongly dependent on confining pressure. When the
confining pressure increased to 60 MPa, elastic stored strain energy, energy consumed by
dominating cohesion weakening, energy dissipated during mobilisation of frictional sliding
were 8.74, 2.53 respectively, and 12.1 times the values at unconfined condition indicating that
the elastic energy accumulates more rapidly as the depth of an underground excavation rises
up, resulting in a more severe strain burst (see Figure 3.11a-c). At the pre-peak stage, the
growth of the accumulated elastic strain energy was faster than the dissipated energy, indicating
that the energy evolution behaviour of granite prior to the onset of βsnap-backβ behaviour was
mainly dominated by the elastic energy accumulation. This phenomenon implies that the ability
of granite specimens to store elastic strain energy was enhanced by the higher confining
pressure. In the post-peak regime, the accumulation of elastic energy began to slow down and
ultimately became stable and the dissipated fracture energy increased by the development and
further openings of micro-cracks leading to internal damage of rock progressively with a loss
of cohesive strength. The expansion, coalescence and propagation of micro-cracks to form
macro-cracks led frictional failure to dominate the fracture energy dissipation process in which
the sliding plane was formed. The excess strain energy diminished by 46% as the confining
pressure increased up to 60 MPa, as depicted in Figure 3.11d. As rising the level of
confinement, the frictional strength component was easily mobilised, which caused an increase
in frictional resistance to crack propagation. Thus, greater dissipated energy consumption is
required to promote crack propagation, revealing that the damage of deep granite is more severe
from the viewpoint of energy evolution.
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Figure 3.11 Variations of (a) elastic stored strain energy (b) energy consumed by dominating
cohesion weakening (c) energy dissipated during mobilisation of frictional sliding (d) excess
strain energy
3.3.4 - Kinetic energy analysis for strain burst due to thermal damage
Another parameter to quantitatively express the potential intensity of a burst event is the
ejection velocity of rock fragments (Akdag et al., 2018). The ejection velocity, denoted as π£,
refers to the velocity of rock fragments in a burst event, which is caused by the excess strain
energy Ξ¦ released during rock fragmentation. Assuming that the excess strain energy is
πΈπ
completely converted to kinetic energy to eject the rock fragments, one can obtain the following
expression for the ejection velocity:
2
π£ = β Ξ¦ (3.6)
π πΈπ
where π£ is in m/s, Ξ¦ in kJ/m3 and π is the density of the rock in kg/m3.
πΈπ
The influence of temperature on the potential ejection velocity of rock fragments of the granite
specimens treated with various temperatures is depicted in Figure 3.12. It can be seen that the
energy redistribution characteristics of Australian granite under uniaxial compression are
strongly dependent on the pre-heating temperature. When the temperature increased from room
temperature (25 Β°C) to 250 Β°C, potential rock ejection velocity decreased by 25% (see Figure
3.12).
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Figure 3.12 Potential rock fragment ejection velocity at different temperatures
The ejection velocity of the rock fragments showed a decline from 6.5 m/s to 4.8 m/s by gradual
treatment at elevated temperatures. Due to the anisotropy in the thermodynamic properties of
different rock minerals, the amount and width of the microcracks inside the specimen
increased, and this triggered the rapid thermal damage accumulation and bursting. In other
words, the fundamental reason for the decrease of peak stress and energy values is the thermally
induced damage by microcracking. Thermally induced damage caused less elastic strain energy
accumulation and hence the excess strain energy which is a measure for the intensity of the
intrinsic strain burst in the rock decreased with increasing temperature. The findings of this
weakening influence are in accordance with the previous studies (Zuo et al. 2014; Kumari et
al. 2017b).
3.3.5 - Corresponding alterations in granite micro-structure
After the pre-heating treatment, the damage created by external forces was assessed by
analysing the properties of the fracture. This analysis can help in to reveal the microscopic
characteristics and fracture modes of rock. The SEM images of the fractured surface of the
granite are shown in Figure 3.13. The SEM results indicated that microcracks are almost
invisible at room temperature which is due to the weaker effect at lower temperatures. When
the temperature was less than 100 Β°C, cracks mainly propagate along the boundary of mineral
particles, i.e. intergranular fracture mechanism, as depicted in Figure 3.13. SEM images for the
specimens exposed to temperatures of 100-250 Β°C showed coupled intergranular and
transgranular, the formation of cracks within the mineral grain, thermally induced
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ADE | Forecasting the propensity of strain burst
microfracturing was the primary mechanism triggering strain burst in the rock. Thermal
influence gradually became more significant, and the fracture surface also became increasingly
cluttered as the temperature increased, indicating that plastic deformation occurred.
Figure 3.13 SEM images of granite specimen exposed to elevated temperatures
3.4 - Summary and discussion
In this chapter, the coupling influence of thermal damage and confining pressure on the energy
characteristics and potential intensity for strain burst was investigated by conducting
circumferential strain controlled tests on Australian granite. The energy evolution during strain
burst of Class II rocks was analysed and the underlying mechanism was discussed. Based on
the acoustic emission, stress and kinetic energy analyses carried out on granite samples exposed
to various temperatures the following conclusions can be drawn:
1. An energy calculation method was developed based on the post-peak energy analysis. AE
responses during compression tests were used to assess the energy and crack evolution
characteristics of the granite under different confinement. Using AE characteristics,
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fracture energy was split into two class: 1) energy consumed dominantly by gradual
weakening of cohesive behaviour and 2) energy dissipated during the mobilisation of
frictional failure. A portion of elastic energy, released from the Class II rock, was defined
as excess strain energy which is a measure for the propensity of the intrinsic strain burst
in the rock. It directly determines the ejection velocity of the rock fragments when a
bursting event occurs. Therefore, this methodology can be used for quantitative predictions
of bursting strain energy in the field which could facilitate improving the early warning
efficiency and provides a comprehensive guideline for the mitigation methods to reduce
strain burst intensity.
2. Confinement has significantly affected the post-peak energy redistribution characteristics
and fracture mechanism of granite. The elastic stored strain energy, energy consumed by
dominant cohesion weakening, and energy dissipated during mobilisation of frictional
failure were 8.74, 2.53 respectively and 12.1 times the values at the unconfined condition,
resulting in more severe strain burst indicating that increase in the confining pressure
improved the efficiency of energy accumulation. This explains why the damage degree of
deep granite is more prominent in the process of deep mining operations.
3. Temperature has significantly affected the post-peak energy redistribution characteristics
and fracture mechanism of granite. The elastic stored strain energy, total fracture energy,
excess strain energy diminished by 80, 82 and 43%, respectively when the temperature
increased from room temperature to 250 Β°C. This declining trend was attributed to the
development of micro-cracks that were induced by elevated temperatures. Thermally
induced damage caused less strain energy accumulation and hence the excess strain energy
decreased with increasing temperature. Another parameter to express the intensity of a
burst event, ejection velocity, decreased as the gradual increase of temperature. The
proposed energy-based strain burst propensity forecasting approach can provide an early
warning of brittle rock instability, which is significant for strain burst assessment in deep
mining operations.
4. The fracturing mechanism of granite was influenced by both confining pressure
(excavation depth) and temperature. The dominant failure pattern of granite changed from
multiple splitting failure to splitting-shear composite failure as the level of confinement
71 |
ADE | Quasi-static and dynamic fracture toughness tests
Chapter 4: Quasi-static and dynamic fracture toughness
tests: The influence of loading rate and thermal damage on
strain burst
4.1 - Introduction
Rock masses are natural complex geological bodies which contain different scales of fractures,
defects from microns to kilometres. Since these natural fractural structures play a vital role in
the failure process and mechanical properties of rocks, rock fracture mechanics has been
employed as a useful and practical tool to solve different rock engineering problems. It has
been diversely applied to investigate brittle breakage and fracturing mechanism such as
rockburst, strain burst, hydraulic fracturing in the broad area of tunnelling, rock cutting,
underground excavation, rock slope stability, oil exploration and deep burial of nuclear waste.
Thus, understanding the crack initiation and propagation in rocks is of great concern for
engineering stability and safety.
As it was discussed in Chapter 3 and indicated that, strain burst is induced by the unstable
growth and coalescence of micro-cracks to form macro-cracks. Based on the post-peak energy
analysis conducted by Akdag et al. (2019), when the elastic stored strain energy in rock masses
is larger than the dissipated fracture energy to grow micro-cracks, the excess strain energy will
be transformed into the kinetic energy in the form of rock fragments at a certain speed, leading
to strain burst. As an intrinsic property of rocks to resist crack initiation and propagation, the
rock fracture toughness is the critical value of stress intensity factor (SIF) which is the most
significant material property in fracture mechanics. Since brittle rock is relatively weaker in
tension, the mode I (the tensile/opening mode) fracture is the most frequently encountered
failure mode of rocks against fracture (Tutluoglu and Keles 2011; Funatsu et al. 2015; Wei et
al. 2017a). As can be seen in Figure 4.1, the damage process is dominantly initiated by tensile
fracturing in hard brittle rock mass in deep underground openings leading to strain burst
(Diederichs et al. 2004). Therefore, extensive experimental and numerical studies were
conducted on granite to determine the mode I fracture toughness (K ), which is known as the
IC
critical mode I stress intensity factor at the onset of fracture, in this study.
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ADE | Quasi-static and dynamic fracture toughness tests
Figure 4.1 Schematic illustration of strain burst induced by tensile fracturing and an example
of strain burst at the headrace tunnel at Jinping II hydropower station (Chen et al. 2015)
During underground mining operations, rock mass is highly subjected to dynamic disturbance
caused by blasting, mechanical drilling and earthquakes resulting in dynamic fractures in the
forms of strain burst, slabbing and spalling. The dynamic fracture is a significant manifestation
of rock failure in deep underground engineering, and it is of great importance to assess the
dynamic fracture behaviour of the rock mass under high-stress and high-temperature
conditions. A good understanding of the dynamic behaviour of brittle rock under dynamic
loading is required for the prediction of the damage extent during strain burst, and proper design
as well as control of the underground rock structures. In this sense, dynamic fracture tests of
pure mode I were carried out to reveal the fracture mechanism of granite specimens subjected
to different loading rates using a Split Hopkinson Pressure Bar (SHPB) apparatus at Monash
University. The damage evolution of granitic rocks was studied over a wide range of loading
rates to reveal the rate dependency of strain burst.
Myriads of methods with different sample geometries have been proposed in the literature to
measure K of rocks under quasi-static loading conditions including short rod (SR) and
IC
chevron bend (CB) (Ouchterlony 1988), cracked straight-through Brazilian disc (CSTBD)
(Ayatollahi and Akbardoost 2014; Wei et al. 2017b), cracked chevron notched Brazilian disc
(CCNBD) (Fowell 1995; Wei et al. 2018), flattened Brazilian disc (Keles and Tutluoglu),
straight-crack semi-circular bend (SCB) (Ayatollahi and Aliha; Dai et al. 2015), cracked
chevron notched semi-circular bend (CCNSCB) (Kuruppu 1997; Ayatollahi et al. 2016; Wei
et al. 2017). Among them, CCNSCB specimen which inherently combines the merits of both
74 |
ADE | Quasi-static and dynamic fracture toughness tests
the SCB specimen and CCNBD specimen. This specimen configuration also overcomes major
shortcomings by avoiding the fabrication of a sufficiently sharp crack as self-precracking from
the chevron notch tip can inherently be induced during testing. Note that sufficient crack tip
sharpness is needed for the straight-through cracked specimens to be able to accurately
determine the fracture toughness and this process is tedious on hard rocks. Moreover, the
CCNSCB method is more promising in determining the dynamic mode I fracture toughness
(πΎ ), of rocks as the dynamic force at the two loading ends of the specimen is easily balanced
πΌπ
due its relatively shorter dimension in the loading direction compared with the full-disc (Dai et
al. 2011). The halved disc geometry also circumvents the symmetrical crack propagation
assumption of the CCNBD method. Therefore, due to the mentioned merits above, the
CCNSCB method was chosen for determining the mode I fracture toughness (K ), and energy
IC
release rates of granite specimens and critical/minimum dimensionless SIFs (πβ ) of the
πππ
CCNSCB granite specimens were determined using slice synthesis method (SSM).
In the underground rock engineering, rock masses not only suffer from dynamic loading but
also are vulnerable to the effects of high temperatures. Such high-temperature conditions cause
dramatic changes in the physical and mechanical properties of the surrounding rocks which are
prone to strain burst. As a consequence, microstructure and mineral composition of rocks will
be altered due to the thermally-induced cracking under the action of high temperatures which
will directly influence the long-term safety and stability of underground rock structures. In
recent years, a large number of researchers have investigated the effects of temperature on the
mode I fracture toughness of various rocks under quasi-static and dynamic loading conditions
(Mahanta et al. 2016; Feng et al. 2017; Liu and Xu 2013; Yin et al. 2018). Funatsu et al (2004)
evaluated the static fracture toughness of single edge-notched round bar in bending (SENRBB)
and SCB specimens of Kimachi sandstone and Tage tuff and showed that the fracture toughness
decreased from room temperature to 75 Β°C due to the thermally-induced microcracks, and then
increased from 75 Β°C to 200 Β°C which was attributed to the drying of the clay materials. Using
SCB method, Yin et al. (2012) studied the effect of thermal treatment on the dynamic fracture
toughness of Laurentian granite and concluded that fracture toughness increases with the
loading rate, whereas decreases with the treatment temperature. Mahanta et al. (2016) measured
the static mode I fracture toughness of SCB Indian sandstone specimens and revealed that
fracture toughness increased between the room temperature and 100 Β°C, thereafter decreased
from 100 Β°C to 600 Β°C. To our knowledge, there is not any attempt to investigate the influence
75 |
ADE | Quasi-static and dynamic fracture toughness tests
of thermal damage on the mode I fracture toughness using CCNSCB method and energy-
release rate in pure mode I.
The Chapter 4 is organised as follows. Section 2 presents the experimental methodology
conducted. Section 3 discusses the rate dependence and influence of temperature on quasi-
static fracture behaviour during strain burst in brittle rocks. Dynamic characteristics of strain
burst in brittle rocks exposed to thermal damage are analysed in Section 4. Section 5 includes
the summary and conclusion of the chapter.
4.2 - Experimental methodology
4.2.1 - The principles of cracked chevron notched semi-circular bend (CCNSCB)
method
The detailed CCNSCB specimen geometrical configuration and the valid range of the
geometric parameters including the specimen used in this study are schematically shown in
Figure 4.2. This specimen geometry can be fabricated by notching a semi-circular bend
specimen with a chevron notch or by cutting a CCNBD sample into two halves along the
diametrical plane which is perpendicular to the chevron notch plane.
76 |
ADE | Quasi-static and dynamic fracture toughness tests
a , a , and a denote the initial, critical, and final crack length, respectively which are also used
0 m 1
in their normalised (dimensionless) forms: thus, πΌ (=a /R), πΌ (=a /R), and πΌ (=a /R) are
0 0 π m 1 1
the normalised (dimensionless) initial, critical, and final crack length; πΌ (=B/R) is the
π΅
normalised (dimensionless) specimen thickness; S is the span between two supporting rollers
and π½ (=S/2R) is the ratio of the span to specimen diameter; and πΌ (=R /R) is the normalised
π S
(dimensionless) radius of rotary saw. Note that the following dimensional restrictions should
be satisfied to guarantee consistent testing results in the plain strain condition (Equation 4.1):
πΌ β₯ 0.4 πΌ β€ 0.8
1 1
πΌ β₯ πΌ /2 πΌ β₯ 1.1729 Γ πΌ 1.6666 (4.1)
1 π΅ π΅ 1
πΌ β€ 1.04 πΌ β₯ 0.44
π΅ π΅
The typically experimental CCNSCB specimen and its normalised (dimensionless) geometrical
parameters with the ISRM-suggested standards are given in Figure 4.3 and geometric
parameters of the CCNSCB specimen used in this investigation are tabulated in table 4.1,
respectively.
Figure 4.3 Demonstration of typical CCNSCB specimen used in this study
Table 4.1 Geometric parameters of the CCNSCB specimen used in this study
Description Value (mm) Dimensionless value
Radius, R 31.5 -
Thickness, B 25.9 πΌ = π΅/π
= 0.82
π΅
Initial crack length, π 10.57 πΌ = π /π
= 0.336
0 0 0
Final crack length, π 21.11 πΌ = π /π
= 0.67
1 1 1
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ADE | Quasi-static and dynamic fracture toughness tests
Saw radius, π
19 πΌ = π
/π
= 0.603
π π π
Supporting span, S 36.8-50 π½ = π/π· = 0.6-0.8
According to LEFM, the fracture toughness πΎ of CCNSCB specimen can be determined by
πΌπΆ
using equation 4.2:
π
πΎ = πππ₯ πβ (4.2)
πΌπΆ πππ
π΅βπ
in which πΎ denotes the mode I fracture toughness of rock material, π is the experimentally
πΌπΆ πππ₯
determined peak load, B and R the thickness and radius of CCNSCB specimen, respectively,
and πβ which is the most significant value of the rock material refers to the minimum value
πππ
of the dimensionless stress intensity factor (SIF) of the CCNSCB specimen, which can be
determined as in equation 4.3:
π
πβ = πΎ / (4.3)
(πΆπΆπππΆπ΅) πΌ
π΅βπ
where πΎ is the mode I SIF. Up to now, many analytical and finite element analyses have been
πΌ
used to determine πβwhich relies upon πΌ , πΌ , and πΌ . In this study, an analytical method, i.e.,
0 1 π΅
slice synthesis method (SSM) was adopted to assess πβ of the CCNSCB specimen.
πππ
Within the framework of LEFM, crack growth process can be considered in two stages: stable
crack growth and unstable crack growth. In the stable crack growth stage, it is usually assumed
that primary crack initiates from the tip of the chevron notched ligament (shaded area in Figure
4.1), and then propagates stably toward the apex of the semi-circular specimen with a perfect
straight-through crack front, as illustrated in Figure 4.4a-c. In addition, crack grows along the
centre of the notch width h, as shown in Figure 4.4. Subsequently, when the loading force
reaches is peak value (π ), unstable crack growth/propagation stage starts (point B in the
πππ₯
figure. 4.4d). At this moment, the normalised (dimensionless) SIF πβis assumed to meet its
minimum value of πβ (point B in the Figure 4.4e) in which crack length is the critical crack
πππ
length a . As can be seen in Figure 4.4e-d, the applied load and πβ exhibit opposite trends
m
during stable and unstable crack growth stages. The transition point between stable and
unstable crack growth stages is critical for determining the fracture toughness (Equation 4.2).
79 |
ADE | Quasi-static and dynamic fracture toughness tests
4.2.2 - Specimen preparation and heating process
The fabrication procedure of the CCNSCB specimen is illustrated in Figure 4.5. First, the rock
cores were sliced into circular discs with a thickness of 25.9 mm (Table 4.1), and both ends of
the specimens were then carefully ground using a grinding machine to ensure perfectly smooth
faces (Figure 4.5a). The polished discs were diametrically cut into two halves at the centre of
the discs to form SCB specimens using a circular saw in which the discs were clamped with a
holding apparatus to stay stable during sawing (Figure 4.5b-c). The surfaces of the SCB
specimens were carefully polished to produce flat regular surfaces via a face grinder prior to
notching (Figure 4.5d-e). A 3D-printed rig was designed and fabricated to hold the SCB
specimens stable while notching (Figure 4.5f-g). For CCNSCB specimens, chevron notches of
less than 1 mm were machined to the centre of each semi-circular half-disc in two cuts by
moving a rotary diamond-impregnated saw (with a radii π
= 19 mm and a thickness less than
π
1 mm) to meet the requirements of the permissible notch width in the ISRM suggested method
(Kuruppu et al. 2014). First, the semi-circular half-disc was hold in a 3D-printed fixture and
clamped, the rotary diamond-impregnated saw was located in the designed chevron notch plane
and moved to touch the edge of the specimen surface. Then the saw was moved to the designed
cutting depth β from one side along the axial direction of the CCNSCB specimen, as depicted
π
in Figure 4.5g. Subsequently, the first cut was made by moving the rotating diamond-
impregnated saw into the rock sample with a horizontal displacement. Finally, the second cut
was made by following the similar procedure after aligning the saw in the first chevron notch
plane, a desired CCNSCB specimen was thus prepared (Figure 4.5h). Special care was taken
during grinding and notch preparation to avoid any damage to the CCNSCB specimens.
The granite specimens were divided into four groups based on temperature exposure. In the
present study, the heating process of the rock samples was carried out in a high-temperature
tube furnace in the Mining Engineering Research Laboratory at The University of Adelaide.
Samples were first heated up to the target temperatures (25, 100, 175, and 250 Β°C) at a modest-
constant heating rate of 5 Β°C/min to avoid the development of cracks due to the thermal shock
during the heating process. Once the designated temperature was reached, the temperature
remained constant at the pre-determined level for about 12 h, to ensure uniform heating inside
the specimens. They were then allowed to cool down naturally to room temperature (25 Β°C)
prior to mechanical testing.
81 |
ADE | Quasi-static and dynamic fracture toughness tests
a b c
=
b
d e
f g h
Figure 4.5 CCNSCB specimen preparation
4.2.3 - Determination of πβ in CCNSCB using slice synthesis method (SSM)
To determine the minimum value of the dimensionless stress intensity factor (SIF) πβ of the
πππ
CCNSCB specimen, a semi-analytical slice synthesis method (SSM) was proposed first by
Bluhm (1975) to evaluate the fracture problems with curved crack fronts was used in this study.
When using this method, the thickness of the specimen is initially divided into a number of
slices each having a thickness βπ‘ as shown in Figure 4.6. Each slice is considered as a cracked
straight-through (CST) specimen to simplify the complex configuration of chevron notched
specimens for the analysis. Based on the equilibrium principle, an analytical equation for the
entire specimen can be obtained by combining the equations for each slice which enables
researchers to be able to extract appropriate analytical relations for the specimens with complex
configuration. In this method, the compliance function which is used for measuring SIF is the
most important output. Since it is tedious to obtain the compliance function in a geometrically
complicated specimens, i.e. CCNBD or CCNSCB, a new SSM was proposed by Wang et al.
(2004) as a constant term attributed to the corresponding part of the specimen without crack
82 |
ADE | Quasi-static and dynamic fracture toughness tests
was ignored for determining SIF of CCNBD specimen in Bluhmβs study (Bluhm 1975). In this
new procedure the output is directly related to the SIF, not the compliance, which has a better
accuracy for a wide-range of geometric parameters of CCNBD specimen with slight
corrections of an empirical factor.The same procedure was used for CCNSCB specimen.
At first, CCNSCB specimen, as depicted in Figure 4.6, was divided into many slices along its
thickness. Each slice could be considered as a SCB with straight-though crack with thickness,
βπ‘. In fact, there is no need to divide the central part of CCNSCB specimen with the straight
crack front thickness b into thin slices since it is itself can be considered as a SCB specimen
with a straight crack front of width b.
Figure 4.6 Slice synthesis method for CCNSCB specimen
Note that Equation 4.2 has been suggested for a crack, whereas, as can be seen in Figure 4.6,
only the central part of the specimen that is formed due to the crack growth is a real crack, thus,
the SIF of the central part is considered as πΎ . However, the SIFs of two lateral chevron parts
πΌ
which are not real cracks have lower value than πΎ . Therefore, a reduction factor for the slices
πΌ
other than the central part can be employed as:
πΎ central part
πΌ
πΎβ² = (4.4)
πΌ
πΎ /π½ other sides
πΌ
in which π½ is an empirical factor that has a value of always greater than one and depends on
the chevron geometry.
83 |
ADE | Quasi-static and dynamic fracture toughness tests
The thickness, βπ‘ and the normalised (dimensionless) crack length πΌ of each slice can also be
π
calculated as below:
π΅βπ
βπ‘ =
π
(4.9)
2
π π.βπ‘
πΌ = βπΌ2 β(βπΌ2 βπΌ2 β β )
π π π 0 2π
π
in which π is the slice number from the centre of the specimens apart of the central part having
the flat notch.
The normalised (dimensionless) SIF of CCNSCB specimen can be calculated by substituting
Equation 4.7 into Equation 4.3 as follows:
β1
π/2
2π/π΅ 4βπ‘/π΅
πβ = [ +β ] (4.10)
βππ΄π(πΌ) π½βππΌ π(πΌ )
πΌ π=1 π πΌ π
The empirical factor π½, reflecting the difference between the SIF of central part and the lateral
parts of the CCNSCB specimen, can be determined as in Equation 4.11:
πΌ βπΌ
1
π½ = 1+πΎ (4.11)
πΌ
π΅
Calculation of the empirical reduction factor π½ that is one of the most significant and difficult
part of the SSM method, was employed by three-dimensional finite element (FE) analysis and
the coefficient πΎ in Equation 4.11 was predicted as 0.9 for the CCNSCB specimen (Wang et
al. 2004).
Based on the FE analysis results, the obtained value of πβ is not sufficient, and thereby a new
πππ
form of Equation 11 was proposed to predict the coefficient π½ as follows (Ayatollahi et al.
2016):
πΌ βπΌ π
1
π½ = 1+πΎ( ) (4.12)
πΌ
π΅
Comparing the results from three-dimensional FE analysis and SSM for the CCNSCB
specimen in mode I loading, the coefficient πΎ and the power n were predicted as 0.9 and 0.5,
85 |
ADE | Quasi-static and dynamic fracture toughness tests
respectively (Ayatollahi et al. 2016). The minimum value of Equation 4.10 was obtained by
putting its derivative with respect to the normalised (dimensionless) crack length πΌ equal to
zero as the mode I fracture toughness can be calculated using the minimum value of the SIF.
Therefore, one can obtain the normalised (dimensionless) SIF and corresponding critical value
of the normalised (dimensionless) crack length πΌ by utilising SSM for CCNSCB specimen. In
this study, for the CCNSCB specimen; πΌ = 0.245,πΌ = 0.67,πΌ = 0.6,πΌ = 0.8, πππ π/
0 1 π π΅
π· = 0.8, the minimum SIF and critical value of normalised (dimensionless) crack length were
obtained as πβ = 5.00144 ππ‘ πΌ = 0.512 (Figure 4.7). It can be seen in Figure 4.7, the SIF
πππ π
for CCNSCB specimen initially decreases and subsequently increases as crack grows. It can
be stated that due to the high stress concentration at the tip of the chevron notch, crack growth
can be observed, and then, it propagates stably within the trajectory of chevron notch until the
crack length meets its critical value, i.e., πΌ β€ πΌ . Following the decreasing trend of the force,
π
unstable crack growth occurs rapidly and the final failure takes place in the specimen. In this
specimen geometry configuration, the chevron notch that is efficient for stabilising the crack
growth, allows to develop higher accuracy SIFs. In this sense, CCNSCB method is suitable for
determining the fracture toughness and investigating the mechanism of crack growth
postulation of rock masses and brittle materials.
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ADE | Quasi-static and dynamic fracture toughness tests
4.3 - Influence of the loading rate and the temperature on quasi-static fracture
behaviour during strain burst in brittle rocks
4.3.1 - Experimental setup
A hydraulic servo-controlled MTS CriterionTM Model 45 with a load-applying capacity of 300
kN was used to conduct the quasi-static loading experiments on the pre-heated and cooled
CCNSCB granite specimens. The specimens were placed on the loading platform such that the
span ratio S/R was 0.8 and make the pre-chevron cracking in the middle of the specimen
coincide with the centreline of the loading roller to provide mode I loading conditions and then
loaded under a three-point bending load configuration until failure. A constant displacement-
controlled testing manner was adopted for the compressive load on the specimens and the load-
displacement data was recorded by a data-acquisition system. During the tests, crack-opening
displacement (COD) was measured by a strain gauge with a length of 10 mm, which was
mounted in CCNSCB specimen and the crack mouth displacement was continually recorded.
Figure 4.8 shows the loading configuration and the experimental setup for the mode I CCNSCB
tests. The compression load on the specimen was applied in displacement control in which the
displacement rate was varied in the range of 0.02 mm/min to 0.1 mm/min.
88 |
ADE | Quasi-static and dynamic fracture toughness tests
where π,π are polar coordinates of the point.
Considering a crack of initial length π, with the application of load the cracks starts to propagate
and the initial crack length is extended by an incremental length of π₯π (see Figure 4.9). The
new crack length is πβ² = π+βπ and the stress intensity factor for the new crack length is
πΎβ²(πΎβ² = πΎ +βπΎ). At a distance π₯ from the previous crack tip, that is at a distance βπβπ₯
from the extended crack tip, the displacement of a crack face in the direction of the maximum
tension for π = 180Β° is given in Equation 4.14:
πΎβ² βπβπ₯ 2
π’ (π₯) = πΌ β( ) (4.14)
2 π 2π 1+π£
Each crack face in the portion of βπ has moved a distance of π’ (π₯) due to the influence of the
2
normal stress, π equal to:
22
πΎ
πΌ
π (π₯) = (4.15)
22
β2ππ₯
According to Irwin (1957), the total elastic work required by π to close the crack is equal to
22
the energy released.
Figure 4.9. Closure of the crack to find the relation between G and K (Mahanta et al. 2017)
I I
βππ΅π π’
22 22
πΊ π΅βπ = 2β« ππ₯ (4.16)
πΌ 2
0
where B is the thickness of the specimen. By taking the limit βπ β 0:
90 |
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