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December 2014 www.geomechanicscorner.com

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DECEMBER 2014

THE DELICATE MATTER OF ROCK

BRITTLENESS

Mehrdad Soltanzadeh, PetroGem Inc.

PART I – BRITTLENESS FROM A ROCK MECHANICAL

PERSPECTIVE

PART II – BRITTLENESS AND ELASTIC PROPERTIES

PART III – ELASTIC PROPERTIES, FRACTURE GEOMETRY AND

STRESSES

http://geomechanicscorner.com/2015/12/21/a-primer-on-the-geomechanics-behind-fracturing-pressure-curves/





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The Delicate Matter of Rock Brittleness by Mehrdad Soltanzadeh


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PART I – BRITTLENESS FROM A ROCK

MECHANICAL PERSPECTIVE

Her reputation is no less brittle than it is beautiful.

Jane Austen, Pride and Prejudice

FIGURE 1. EFFECT OF ROCK BRITTLENESS/DUCTILITY IN FORMING GEOLOGICAL STRUCTURES (A)

FOLDS FORMED IN DUCTILE ROCKS (B) FRACTURES DEVELOPED IN BRITTLE ROCKS. (SOURCES:

A: WWW.ESCI.UMN.EDU; B: WWW.GEOSCIENCE.WISC.EDU).


http://www.esci.umn.edu/

http://www.geoscience.wisc.edu/

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Introduction

We should not be surprised that oil producers appreciate quick measures such as ‘brittleness

index’ to tell them where to drill, complete, and fracture to achieve better hydrocarbon

production results in unconventional plays . Recently, we have seen different forms of this

index introduced to the industry though the definition of ‘brittleness’, as a mechanical

property of rock, has still remained a controversial matter among the experts from different

disciplines with different perspectives towards rock mechanics. In its typical application for

characterization of unconventional plays, brittleness index is expected to define the

mechanical behaviour of rock during fracture propagation.

Brittle rocks are usually expected to allow pressurized fractures to propagate the same way

‘a knife cuts through butter’1. The opposite to the case of ‘ductile’ rocks that tend to blunt

propagating fractures. Also, brittle rocks are considered good hosts for the proppants filling

the fractures as it does not swallow them as might be the case for ductile rocks. This will let

the fractures to remain functionally open and perform their primary role as fluid conduits

with proper permeability.

Some experts would rather using the term ‘fracability’ instead to define this behaviour of rock

probably because, since ole times, ‘brittleness’, as a technical term, has been reserved by

mechanical engineers to define a more general behaviour of materials as will be discussed

later in this article. Another main reason for using ‘fracability’ instead of ‘brittleness’ is to

emphasize that the process of fracture propagation is not just a function of mechanical rock

properties but it also depends on several other parameters such as in-situ stresses, fracturing

fluid 's type, rate, and pressure, existence of natural fractures, etc. This article intends to

review the concept of rock brittleness from different perspectives including rock mechanics,

fracture mechanics, geophysics, and petrophysics.

1 I burrowed this term from ‘Hydraulic Fracture Mechanics by Economides and Economides and Valkó (1996).

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Old Definitions, New Applications

Mechanical engineers, in general, have been traditionally using the two terms of ‘brittle’ and

‘ductile’ to define the behaviour of rock before its final failure. In response to

excessive loading, a brittle material (e.g., a steel knife blade) breaks abruptly without a

significant deformation while a ductile material (e.g., a copper wire) deforms significantly

before it breaks apart. Figure 1 shows examples of stress/strain behaviours of ductile and

brittle metallic materials during standard tensile strength tests. In reality, fracture

propagation in rocks during hydraulic fracturing is a tensile failure (i.e., Mode I failure) process

but, unfortunately, direct tensile tests similar to what is shown in Figure 1 are not usually

possible to be conducted for sedimentary rocks due to very small tensile strength2 . Therefore,

in rock mechanics, brittle/ductile behaviour of rocks is usually studied under compressive

loading instead of tensile loading. In this case, most likely, the sample will fail in a shear mode

(i.e., Mode 2 failure) and not a tensile mode.

During compressive loading (e.g., triaxial tests), rocks usually fail along shear failure planes.

Rock behaviour in response to this type of loading is very similar to what the earth crust

experiences under tectonic movements and, therefore, the results of compressive brittleness

tests have been traditionally used to characterize the rock behaviour in geological structures

(e.g., geological folds are usually formed in ductile rocks and faults are formed in brittle rocks,

see Figures 1 and 3), potential for seismicity (brittle rocks are likely to induce larger

2Rock tensile strength is usually measured indirectly using a loading pattern that is not tensile in

essence. The most common method is called Brazilian test that imposes a lateral edge loading on

a cylindrical sample of rock until it fails in a tensile mode. Point loading is another approach that

applies a concentrated load on a planar piece of rock. 3-point bending is another approach that is

less popular in rock mechanics.

http://en.wikipedia.org/wiki/Fracture_mechanics

http://en.wikipedia.org/wiki/Fracture_mechanics

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FIGURE 2. STRESS-STRAIN DIAGRAM OBTAINED FROM THE STANDARD TENSILE TESTS (A) DUCTILE

MATERIAL (B) BRITTLE MATERIAL (MODIFIED AFTER BUDYNAS AND NISBETT, 2008).

FIGURE 3. BRITTLE-DUCTILE BEHAVIOUR OF ROCKS UNDER COMPRESSIVE LOADING

(SOURCE: EVANS ET AL., 1990)

http://www.amazon.ca/Shigleys-Mechanical-Engineering-Richard-Budynas/dp/0073398209

http://link.springer.com/chapter/10.1007/3-540-26339-X_9

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earthquakes/seismic events than ductile rocks), and reservoir sealing integrity (comparing to

ductile sealing, the brittle ones are more likely to act as conduits).

While compressive failure tests are designed to study the rock's behaviour when it fails under

shear, some rock mechanics engineers believe that these results can also act as proxies for

the behaviour of rock in response to fracture propagation during hydraulic fracturing. It is

clear that failure criteria during compressive loading are distantly different from that of

tensile loading. Therefore, if we really want to measure the actual rock’s behaviour during

hydraulic fracturing, we need to develop more precise and comprehensive testing procedures

to quantify rock’s response during tensile loading3. However, compressive failure tests using

triaxial apparatus are commonly used to verify rock brittleness and ductility in laboratories.

Based on the results of these tests, the magnitude of brittleness index may be quantified in

different ways by using strains, rock strengths, or the work/energy during these tests. Figure

4 shows a list of some equations used in industry.

It must be remembered that compressive loading (e.g., triaxial) tests are strongly influenced

by testing condition such as in-situ stresses and ambient pressure and temperature. For

instance, experiments show that these tests are strongly dependent on the magnitude of

confining stress applied during testing. Rocks usually (though there are exceptions) show

more brittle responses at lower confining stresses and, with increasing in this parameter, their

responses become more ductile (Figure 5). The combined effects of confining pressure (i.e.,

in-situ stresses in here) and temperature on rock brittleness have been the main subject of

investigation for 'brittle-ductile transition zone' studies performed in plate tectonics,

seismology, and earthquake engineering.

3 Defining fracture toughness for quantifying the resistance against fracture propagation has been one of these efforts though the methodology implemented for its measurement can be argued for different reasons.

http://www.depts.ttu.edu/gesc/Fac_pages/Yoshinobu/4361_5361_Folder/2013-readings/Scholz,%201988%20B-Ptransition.pdf

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Drillers and geotechnical and mining engineers have also shown interest in the concept of

rock brittleness as they believe it is one of the parameters that governs the rate of penetration

rate drilling wells, mine shafts, and tunnels (the common name used for this character

is called drillability). Some of the relationships used in these practices calculate the rock

brittleness index as a function of rock compressive strength (Sc) and tensile strength (St).

These parameters have been used in different combinations to calculate rock brittleness (e.g.,

BI=Sc/St; BI=Sc x St/2; BI=(Sc - St)/(Sc + St). Even some standard tests have been designed

to measure rock brittleness in these disciplines.

Laboratory tests are costly and time-consuming and the scattered data found by running

these tests may not be enough for characterizing the rock behaviour in geological scales. This

might be the motivating reason for some experts in the petroleum industry to use the

abundantly available wireline log and seismic data for assessment of rock fracability and

brittleness in geological formations as will be discussed in the next section.

http://www.sciencedirect.com/science/article/pii/S0013795201001375

http://www.drillability.com/13A-98eng.pdf

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FIGURE 4. DEPENDENCY OF STRESS-STRAIN BEHAVIOUR TO CONFINING PRESSURE. THE NUMBERS

ON THE CURVES IN THE TOP FIGURE ARE CONFINING PRESSURES AND, IN THE LOWER FIGURE,

CONFINING PRESSURE IS INCREASED FROM A TO D. (SOURCE: PATERSON AND WONG, 2006).

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FIGURE 5. DIFFERENT TYPES OF BRITTLENESS INDICES DEFINED BASED ON COMPRESSIVE LOADING

TESTS (MODIFIED AFTER: YANG ET AL., 2013)

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PART II – BRITTLENESS AND ELASTIC

PROPERTIES

There’s something brittle in me that will break before it bends.

Mark Lawrence, Prince of Thorns

Considering the definition of rock brittleness discussed in the previous section, it is clear that

the dynamic elastic properties measured by sonic or seismic waves and even the static ones

measured in laboratories are not the most appropriate parameters for determining

brittleness as these parameters only describe the rock’s deformation long before it

reaches near failure or fracturing. This is more true for dynamic elastic properties as they are

measured when the rock is only agitated extremely small deformations. In other words, rock’s

behaviour during cracking or failure needs to be characterized by fracturing or failure criteria

and not elastic constitute models. However, there might be some justifiable reasons for using

dynamic elastic properties to identify brittle rocks from ductile rocks. In fact, there are some

technical evidence that justify using elastic properties, that are abundantly available from

wireline logs and seismic surveys, as proxies for brittleness.

In a general sense, more brittle rocks (e.g., granite or over-consolidated cemented

sandstones) are usually expected to show less deformation within their elastic limits and

before yielding (or failure) in comparison to more ductile rocks. Although this general pattern

may work for some rocks, in reality, brittleness/ductility is not equal to stiffness/softness. The


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existing inconsistencies will be discussed later in this article but let’s see how the idea of ‘less

deformability=more brittleness’ can be implemented to determine brittleness index using

elastic properties. In elasticity, less axial deformation means higher Young’s modulus (E) and

less relative lateral deformation means less Poisson’s ratio (v). Therefore, these two

parameters seem to be good candidates for estimation of stiffness and, consequently, rock

brittleness. In fact, this is the basis for the commonly used form of elastic brittleness index in

petroleum industry as proposed by Rickman et al. (2008) who gave the same weight to the

effects of Young’s modulus and Poisson’s ratio by simple arithmetic averaging of their effects:

𝐵𝑅 =1

2(

𝐸−𝐸𝑚𝑖𝑛

𝐸𝑚𝑎𝑥−𝐸𝑚𝑖𝑛+

𝜈𝑚𝑎𝑥−𝜈

𝜈𝑚𝑎𝑥−𝜈𝑚𝑖𝑛) (1)

max and min subscripts in this equation denote the maximum and minimum values of the

elastic parameters for the formation(s) of interest. Figure 6 shows an example of using this

equation where Young’s modulus and Poisson’s ratio are acquired from sonic and density

logs. Figure 7 shows the cross-section of a shale formation showing the brittleness index

variation. The dynamic elastic parameters in this case were derived from both sonic and

seismic data.

Reasons for Doubt

The idea of identifying brittle rocks using abundantly available log- or seismic-based dynamic

elastic properties sounds very appealing but there are reasons that make it hard to accept the

credibility of this method, inclusively. As discussed, one obvious reason is assumption of

equality of rock brittleness/ductility and stiffness/softness. In reality, brittleness and

fracability are functions of more than just elastic properties even in materials that follow the

rules of linear elastic fracture mechanics (LEFM). In fracture mechanics, other independent

parameters such as fracture toughness are the major factors that govern fracture

https://www.onepetro.org/conference-paper/SPE-115258-MS

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FIGURE 6. AN EXAMPLE OF BRITTLENESS CALCULATED FROM SONIC AND DENSITY LOG DATA. THE

DIRECTION OF ARROW SHOWS INCREASING IN BRITTLENESS INDEX AND THE DATA POINTS ARE

COLOR-CODED BY THIS PARAMETER. (MODIFIED AFTER VARGA ET AL., 2013).

propagation or blunting. This behaviour becomes even more complex in inelastic or plastic

materials such as rocks.

As another inconsistency, during shear failure experiments, there are occasions that rocks

with less elastic deformability (i.e., higher Young’s modulus and lower Poisson’s ratio) show

less brittle behaviour compared to the ones with more elastic deformability. Another

contradictory observation is the change in rock behaviour by increase in confining stress

during triaxial tests as discussed in the previous section. This behaviour might not be the case

for all the rocks but there are several types of rocks that follow this trend. The example given

in Figure 8 shows that with increase in confining pressure on samples in triaxial apparatus,

the elastic deformability of rock is not significantly affected but it becomes more ductile in a

shear failure mode. In other words, by increasing the confining stress, rocks become more

ductile and less brittle while their Young’s moduli remains almost the same.

http://csegrecorder.com/assets/pdfs/2013/2013-04-RECORDER-How_to_maximize_recoverable_reserves.pdf

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FIGURE 7. AN EXAMPLE OF BRITTLENESS INDEX PROFILE DERIVED FROM SEISMIC AND SONIC

DATA. YELLOWER COLOURS STAND FOR HIGHER BRITTLENESS AND BLUER COLOURS INDICATE LESS

BRITTLE ROCK (SOURCE: VARGA ET AL., 2013).

FIGURE 8. THIS FIGURE SHOWS HOW THE MECHANICAL BEHAVIOUR OF A LIMESTONE IN A SHEAR

MODE CHANGES WITH INCREASE IN CONFINING STRESS IN TRIAXIAL TEST. APPARENTLY, YOUNG’S

MODULUS DOES NOT CHANGE WITH CONFINING PRESSURE WHILE ROCK’S BEHAVIOUR BECOMES

MORE DUCTILE (SOURCE: WWW.HIGGS-PALMER.COM).

http://csegrecorder.com/assets/pdfs/2013/2013-04-RECORDER-How_to_maximize_recoverable_reserves.pdf

http://www.higgs-palmer.com/HIGGS-PALMER/Rock_Testing.html



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Different contradictory examples discussed here show that the idea of ‘lower v and

higher E = higher brittleness’ may not work as expected all the time. In addition, there are

others reasons that undermine credibility of this hypothesis. One is the effect of high pore

pressure in hydrocarbon plays on dynamic elastic properties. High pore pressure is known to

make the rock less consolidated and more deformable but the question is whether

dynamic Young’s modulus is always lower and dynamic Poisson’s ratio is always higher for

rocks with higher pore pressure or not. The answer seems to be YES for Young’s modulus and

NO for Poisson’s ratio as depicted in Figure 9. This figure shows Poisson’s ratio is only higher

for higher pressures if the occupying fluid is incompressible enough (e.g., brine) but for more

compressible fluids such as light oil or gas (as it is the case for many unconventional plays),

increase in pore pressure leads to decrease in Poisson’s ratio. In the case of more

compressible fluids, higher pore pressure still leads to less stiff and more deformable rocks

but this does not result in higher dynamic Poisson’s ratio as is the case for brine-filled rocks.

One other thing about the brittleness index defined in the given equation is the fact that it is

hard to agree with Young’s modulus and Poisson’s ratio having exactly the same share of

influence on rock brittleness as imposed by arithmetic averaging in the equation. Also, we

must remember that there are cases where a rock might have a very low elastic deformability

but, at the same time, it can also have a very high resistance against fracturing due to its

higher yield and failure strength. In these cases, for a certain amount of stress or fluid

pressure, this rock does not fracture while rocks with higher elastic deformability

(less brittleness index) and less resistance may fracture. Everything said here shows that the

presented equation for brittleness might not be always trusted as a measure of rock

brittleness but we cannot completely deny that there are cases where this index can work as

a proxy for this property of rock.

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FIGURE 9. THESE GRAPHS SHOW HOW PORE PRESSURE INCREASE AFFECTS ELASTIC PROPERTIES

SUCH AS (A) COMPRESSIONAL WAVE VELOCITY AND (B) COMPRESSIONAL WAVE IMPEDANCE AND

POISSON’S RATIO FOR DIFFERENT TYPES OF FILLING FLUIDS INCLUDING BRINE, OIL, AND GAS

(SOURCE: DVORKIN).

http://pangea.stanford.edu/~jack/Ppressure.pdf

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PART III – ELASTIC PROPERTIES, FRACTURE

GEOMETRY AND STRESSES

Broken things are powerful. Things about to break are stronger still. The last shot from the brittle bow is truest.

Eugene McCarthy

In this section, We will take a close look at some theories that relate elastic properties to

fracture characteristics. It is important to remember that what we will discuss in the

following is not directly related to brittleness or the criteria for fracturing or fracture

propagation and it merely explains the effect of elastic properties on the fractures

without considering their resistance against propagation. In other words, these fractures are

considered to propagate as ‘knife cuts through butter’.

In practice, it is assumed that the volume of injected fracturing fluid is either lost to the

formation through leakoff or helped in creating the volume of fracture. This forms a volume

balance equation that is completed by knowing the fracture geometry. The necessary

equations for finding fracture geometry are usually derived using the principals of LEFM that

assumes elastic behaviour for the rock. Therefore, elastic parameters such as Young’s

modulus and Poisson’s ratio have a direct role in determining the characteristics of hydraulic

fractures. Depending on the complexity of modeling, different solutions have been suggested

and used in industry. In here, without getting into detail, we will look at one of the simplest

(although still practical) solutions called Perkins-Kern (PKN) that is based on assuming plane-


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strain geometry for the fracture4. This model assumes an ellipsoidal shape for the fracture

with a half-length of 𝑥𝑓 , maximum width of 𝑤𝑓 at the borehole wall, and constant depth

of ℎ𝑓 (Figure 10). If a Newtonian fracturing fluid with an injection rate of 𝑞 and viscosity

of 𝜇 for a time period of t is injected, it is possible to find fracture geometry by using the

following equations with assumption of no fluid loss to the formation:

𝑥𝑓 = 0.524(𝑞3𝐸𝑝𝑠

𝜇ℎ𝑓4 )

1/5

𝑡4/5 (2)

𝑤𝑓 = 3.04 (𝑞2𝜇

𝐸𝑝𝑠ℎ𝑓)1/5

𝑡1/5 (3)

The net pressure (i.e., the difference between fracturing fluid pressure and in-situ stress) at

the initiating point of the fracture at the wellbore wall can be found using the following

equation:

𝑝𝑛 = 1.52 (𝑞2𝐸𝑝𝑠

4𝜇

ℎ𝑓6 )

1/5

𝑡1/5 (4)

In these equations, Eps is an elastic parameter called plane-strain Young’s modulus that can

be written as a function of basic elastic properties:

𝐸𝑝𝑠 =𝐸

1−𝜈2=

2𝐺

1−𝜈 (5)

𝐺 in this equation is the rock’s shear modulus. Now, let’s examine and see how changes

in 𝐸 and 𝜈 will affect the geometry and net pressure of the fracture for a given injection rate

for a certain period of time. Figure 11a to 11c show the effects of these changes on 𝑥𝑓, 𝑤𝑓,

and 𝑝𝑛, respectively. According to these figures, increase in both Young’s

modulus and Poisson’s ratio leads to longer and narrower fractures that require higher net

pressure for propagation. Nevertheless, unlike the discussed brittleness index in the previous

section, significance of Poisson’s ratio in determining fracture characteristics is much less than

4 The equations for the PKN model have also been adopted from Valkó (1996).

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Young’s modulus. These results show that the dependency of fracture characteristics to

elastic properties is more complex than ‘high is good, low is bad’.

Depending on hydraulic fracturing design priorities, different values of elastic parameters

may be preferred but usually wider and longer fractures that can propagate with less

pressure of fracturing fluid are favoured.

FIGURE 10. GEOMETRY OF PERKIN-KERN (PKN) MODEL FOR HYDRAULIC FRACTURES (SOURCE:

MODIFIED AFTER ECONOMIDES AND VALKÓ, 1996)

http://ca.wiley.com/WileyCDA/WileyTitle/productCd-0471956643.html


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FIGURE 11. VARIATION OF DIFFERENT FRACTURE CHARACTERISTICS IN THE PKN MODEL WITH

YOUNG’S MODULUS AND POISSON’S RATIO: (A) FRACTURE’S HALF-LENGTH (𝒙𝒇), (B)

FRACTURE’S MAXIMUM WIDTH (𝒘𝒇), AND (C) FRACTURE’S NET PRESSURE (𝒑𝒏).


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Elastic Parameters and In-situ Stresses

Hydraulic fracturing engineers, geophysicists, and petrophysicists frequently use elastic

properties to calculate horizontal in-situ stresses in rocks (See Figure 12 for an example).

These calculations are usually performed by assuming poroelastic and uniaxial vertical

deformation during sedimentary deposition of rocks. Using this approach, horizontal stresses

are simply calculated by using vertical stress (𝑆𝑣), pore pressure (𝑃𝑝), and elastic

properties. Considering tectonic strains (𝜀𝐻𝑚𝑎𝑥 and 𝜀𝐻𝑚𝑖𝑛) or stresses in these calculations, it

is possible to account for the effect of tectonics and stress anisotropy in the rock. For instance,

minimum and maximum horizontal stresses (Shmin and SHmax, respectively) for a homogeneous

isotropic rock are calculated using the following equations:

𝑆ℎ𝑚𝑖𝑛 =𝜈

1−𝜈(𝑆𝑣 − 𝛼𝑃𝑝) +

1−2𝜈

1−𝜈𝛼𝑃𝑝 + 𝜈𝐸𝑝𝑠𝜀𝐻𝑚𝑎𝑥 + 𝐸𝑝𝑠𝜀𝐻𝑚𝑖𝑛 (6)

𝑆𝐻𝑚𝑎𝑥 =𝜈

1−𝜈(𝑆𝑣 − 𝛼𝑃𝑝) +

1−2𝜈

1−𝜈𝛼𝑃𝑝 + 𝐸𝑝𝑠𝜀𝐻𝑚𝑎𝑥 + 𝜈𝐸𝑝𝑠𝜀𝐻𝑚𝑖𝑛 (7)

𝛼 in this equation is Biot’s coefficient. In relaxed basins with low tectonic effects

(i.e., (𝜀𝐻𝑚𝑎𝑥~0 and 𝜀𝐻𝑚𝑖𝑛~0), Shmin and Shmax become equal. We must remember that these

equations are not the favorite equations of many geomechanics experts as they believe the

assumptions are over-simplistic and imprecise.

A hydraulic fracture propagates only if the pressure of the injected fracturing fluid

exceeds both Shmin and fracture resistance. Therefore, higher Shmin means less

potential for fracture propagation with a certain injection pressure. Now, let’s see according

to the uniaxial poroelastic theory, how this critical parameter is affected by variation in elastic

properties. Figure 13 shows how Shmin in the given equation changes with variation in Young’s

modulus (E) and Poisson’s ratio (v) for some example parameters. According to this figure,

increase in both E and v leads to

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FIGURE 12. THIS EXAMPLE SHOWS MINIMUM HORIZONTAL IN-SITU STRESS (SHMIN) CALCULATED

USING ELASTIC EQUATIONS FOR THE SOME SELECTED FORMATIONS (SOURCE: GRAY ET AL., 2012)

FIGURE 13. AN EXAMPLE GRAPH SHOWING HOW MINIMUM HORIZONTAL STRESS (SHMIN)

CHANGES WITH VARIATION IN YOUNG’S MODULUS AND POISSON’S RATIO ACCORDING TO THE

GIVEN EQUATION IN THE TEXT. IN THIS EXAMPLE, VERTICAL STRESS IS 20 MPA, PORE PRESSURE

IS 10 MPA, BIOT’S COEFFICIENT IS 1.0, MAXIMUM TECTONIC STRAIN IS 0.0001, AND MINIMUM

TECTONIC STRAIN IS ASSUMED TO BE ZERO.

http://www.cgg.com/technicalDocuments/cggv_0000013432.pdf



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higher Shmin or, in other words, fractures will have a harder time to propagate. This might

indirectly contradict yje assumption that higher elastic Young’s moduli lead to

more fracability.

Wrap Up

It seems that the simple assumption of using high or low elastic properties (or any similar

assumption) for brittleness evaluation does not have extensive theoretical and experimental

support. Use of just elastic properties is not satisfactory enough to characterize rock’s

brittleness and more parameters are required for this purpose. On the other hand,

considering abundant availability of elastic properties from seismic surveys and sonic logs, it

is not clever to completely rule these parameters out as with proper and precise treatment

they might be able to act as proxies for brittleness. To use these parameters properly,

probably the right option is implementing them besides other means such as laboratory

measurements of brittleness and correlating them with observed fractures in the field from

cores, image logs, and sonic scanners, or microseismic surveys. We can also compare them

with other types of brittleness such as mineralogical brittleness to ensure their

repressiveness. We also need to remember that instead of classifying the rocks based on high

or low values of elastic parameters, we need to find specific ranges of elastic parameters that

suit rock fracability. Soltanzadeh et al. (2015a and 2015b) provide good examples of such

applications.

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References

Budyans, R., Nisbett, K., 2014, Shigley’s Mechanical Engineering Design Published by McGraw-

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