Master Thesis 2012 Analysis of High Pressure Effects on Wellbore Integrity Using the Distinct...

Analysis of High Pressure Effects on Wellbore Integrity Using the Distinct Element

Method

by

Stacey J. Amamoo, BSc.

A Thesis

In

PETROLEUM ENGINEERING

Submitted to the Graduate Faculty

of Texas Tech University in

Partial Fulfillment of

the Requirements for

the Degree of

MASTER OF SCIENCES

In

PETROLEUM ENGINEERING

Approved

Dr. Malgorzata Ziaja

Chair of Committee

Dr. Shameem Siddiqui

Dr M. Rafiqul Awal

Peggy Gordon Miller

Dean of the Graduate School

May, 2012

COPYRIGHT 2012, S.J. AMAMOO

Texas Tech University, Stacey J. Amamoo, May 2012

ii

DEDICATION

To my parents Kobina (Dedi) and Alice (Meme) Amamoo and my sisters Mammie and

Effie


iii

ACKNOWLEDGEMENTS

I would like to thank the Almighty God for being my source of strength and granting me

the gift of perseverance especially during the times I genuinely believed completion of

this thesis was next to impossible.

I would also like to express my heartfelt gratitude to Dr Malgorzata Ziaja, for being my

mentor, professor and mother. I would also like to thank Dr Shameem Siddiqui and Dr.

Rafiqul Awal for accepting to be on the committee as well as providing the much needed

guidance to complete this work.

Sincere appreciation also goes the Texas Tech University Bob E. Herd Petroleum

Engineering Department for giving me the opportunity to obtain a masters degree and to

all the staff and professors for their help and knowledge.

In addition, I would like to express warm gratitude to my colleagues and friends

especially Joshua Momodu and Sarah Alajmi and to Wenjing Li for helping me figure out

the complex parts of the ITASCA Particle Flow Code.

Finally, I would like to thank my dearest aunt Nadia Aloghani for making my stay in the

United States pleasant and always looking out for my wellbeing.


iv

CONTENTS

DEDICATION .................................................................................................................... ii

ACKNOWLEDGEMENTS ............................................................................................... iii

CONTENTS ....................................................................................................................... iv

ABSTRACT ....................................................................................................................... vi

LIST OF TABLES ............................................................................................................ vii

LIST OF FIGURES ......................................................................................................... viii

NOMENCLATURE ........................................................................................................... x

1 INTRODUCTION ........................................................................................................... 1

1.1 Background ............................................................................................................ 1

1.2 Wellbore Failure .................................................................................................... 4

1.3 Mohr-Coulomb Failure Criterion .......................................................................... 5

2 LITERATURE REVIEW ................................................................................................ 7

2.1 Evaluation of Existing Numerical, Analytical and Experimental Cement-Casing

-Formation Systems ..................................................................................................... 7

2.2 Cement Bonding .................................................................................................... 8

2.3 Factors Affecting Casing-Cement Bond And Casing-Rock Bond ...................... 10

2.4 Experimental Tests Carried Out On Cement ....................................................... 11

2.5 Scope And Objectives ......................................................................................... 15

3 NUMERICAL MODELING OF CEMENT-CASING-FORMATION SYSTEM ........ 18

3.1 Finite Element Method ........................................................................................ 18

3.2 Finite difference Method ..................................................................................... 20

3.3 Boundary Element Method .................................................................................. 22

3.4 Distinct Element Method ..................................................................................... 23

3.5 Using PFC............................................................................................................ 27

4 METHODOLOGY ........................................................................................................ 36

4.1 Determination of Microproperties ....................................................................... 37

4.2 Algorithm for compression testing with PFC ...................................................... 38

4.3 Validation ............................................................................................................ 40


v

4.4 Analysis of high pressure on Well integrity – A Horizontal well Example ........ 46

5 RESULTS AND ANALYSIS ........................................................................................ 51

6 CONCLUSIONS............................................................................................................ 66

REFERENCES ................................................................................................................. 68

A DATA SET FOR FAILURE TEST 100MPA............................................................... 72

B DATA SET FOR FAILURE TEST 10 MPA ................................................................ 86

C DATA SET FOR FAILURE TEST 1MPA ................................................................. 100


vi

ABSTRACT

It is a proven fact that the analyses of the casing, cement and rock formation during the

life of a well is of utmost importance in the maintenance of wellbore integrity. This has

been done so far utilizing the continuity numerical methods such as the finite element

method together with experimental methods.

In using the finite element method to analyze wellbore integrity taking into consideration

the formation, cement and casing, the discontinuity of their interaction is lost and as such

fractures and other mechanisms such as debonding cannot be modeled.

The main objective of this research is to utilize the distinct element method in analyzing

wellbore instability so as to avoid or greatly minimize failure in wellbores. In this paper,

the cement-formation bond and cement-casing bond are thoroughly discussed as well as

their effect and contribution to well integrity. The ITASCA Particle flow code software is

used. It is validated and then used to analyze horizontal well using parameters from the

Barnett Shale.


vii

LIST OF TABLES

1 Conditions For Mohr’s Failure ........................................................................................ 6

2 Data used in Validation .................................................................................................. 41

3 Data used in Horizontal well example ........................................................................... 46


viii

LIST OF FIGURES

1 Graph Showing the Variation of Effective Stresses as a Function of Azimuth

(Zoback 2008) ..................................................................................................................... 4

2 An Illustration of Controllable and Uncontrollable Factors and Their Effects on the

Formation and Wellbore (PASIC 2007) ............................................................................. 5

3 Diagram Showing Mohr-Coulomb Failure Criterion (Soliman and Boonen 1999) ....... 6

4 Diagram Showing Casing Cement and the Formation ................................................... 9

5 Typical Triaxial Testing Cell ........................................................................................ 12

6 The Uniaxial or Brazilian Test ...................................................................................... 13

7 Setup for the Unconfined Compressive Test ................................................................ 14

8 Direct Shear Test.......................................................................................................... 14

9 Shear Displacement Curve ............................................................................................ 14

10 Cracks in Cement Sheath as Demonstrated by Ravi et al. (2002) .............................. 16

11 Plastic Deformation in Cement Sheath as Demonstrated By Ravi et al. (2002) ......... 16

12 Debonding in Cement- Formation Interface as Demonstrated by Ravi et al. (2002) . 17

13 Debonding In Cement-Casing Interface as Demonstrated by Ravi et al. (2002)........ 17

14 Numerical Methods Used in Geomechanics ............................................................... 18

15 Illustration of the Finite Element Method ................................................................... 19

16 Representation of Lagrangian FDM Where Domain is Divided into Nodes and

Zones ................................................................................................................................. 21

17 Particles during Motion (Courtesy Jing and Stephansson 2007) ................................ 25

19 Calculation Cycle of PFC ........................................................................................... 29

20 PFC Plot of Balls in Contact (Smooth Joint) .............................................................. 34

21 Determination of Microproperties of Materials .......................................................... 37

22 Part I of the Testing Procedure ................................................................................... 38

23 Part II of the Testing Procedure .................................................................................. 39

24 Part III of the Testing Procedure ................................................................................. 40

25 Sample Setup for Biaxial Test .................................................................................... 42

26 Sample after Failure Showing Deformation and Breaks in Parallel Bond ................. 43


ix

27 Deviatorial Stress Versus Axial Strain Graph Showing The Initial Yield of the

Sample (PFC) .................................................................................................................... 44

28 Deviatorial Stress versus Axial Strain Graph Showing the Initial Yield of the

Sample as Indicated By Stiles (2006) ............................................................................... 45

29 Elastic Load/Unload Test to Determine Properties of Formation Setup .................... 47

30 Elastic Load/Unload Test to Determine Properties of CEMENT Setup..................... 48

31 Elastic Load/Unload Test to Determine Properties of CASING Setup ...................... 49

32 Cement Casing Formation Setup ................................................................................ 50

33 Diagram Showing Slight Deformation of the Casing ................................................. 52

34 Diagram Showing Plastic Deformation Of Cement.................................................... 53

35 Diagram Showing Debonding Deformation Of Cement ............................................ 54

36 Diagram Showing Microcrack Formation At 10mpa ................................................. 55

37 Graph Showing Microcrack Development At 10mpa ................................................ 56

38 Diagram Showing Microcrack Formation At 100mpa ............................................... 57

39 Graph Showing Microcrack Development At 100mpa .............................................. 58

40 PFC Derived Shear Stress versus Effective Normal Strain (10mpa Overburden)...... 59

41 PFC Derived Deviatoric Stress versus Axial Strain @ 10mpa Overburden ............... 60

42 PFC Derived Normal, Tangential and Hoop Stresses at 10mpa Overburden ............. 61

43 Spreadsheet Analysis of Deviatoric Stress versus Axial Strain @ 10mpa

Overburden ....................................................................................................................... 62

44 Spreadsheet Analysis of Deviatoric Stress versus Axial Strain @ 10mpa

Overburden ....................................................................................................................... 63

45 Spreadsheet Analysis Normal, Tangential and Hoop Stresses @ 10mpa

Overburden (Loading) ...................................................................................................... 64

46 Spreadsheet Analysis Normal, Tangential and Hoop Stresses @ 10mpa

Overburden (Unloading) ................................................................................................... 65


x

NOMENCLATURE

A= Cross sectional area

D= outer diameter of casing

E= Young’s modulus

E100%= amplitude for100%bond

Ec,= Young’s modulus of confining formation

Ecement = Young’s modulus of cement

Efree =Free pipe amplitude

Emeas =Measured amplitude

Er= Young’s modulus of reservoir

Esteel= Young’s modulus of steel

F = Force

G= weight of casing

H= height of cement column

I = normal or shear

K = Stiffness

L = length of casing

µ = coefficient of friction

Pp= pore pressure

Q= Heat flux

R = major radius

r = minor radius


xi

SHMAX = Maximum horizontal stress

Shmin = minimum horizontal stress

Sv = vertical principal stress or overburden stress

vc= Poisson’s ratio of confining formation

vcement= Poisson’s ratio of cement

vsteel = Poisson’s ratio of steel

Vmat = Volume of material within the region of interest

vr= Poisson’s ratio of reservoir

Vroi = Volume of region of interest

Vvoid = Volume of empty space

xp = position of a point p

x� ��= translational velocity

x� ��= velocity at a point p

x��= center of rotation

x��∅ = locationofabody�scentroid

x�� = locationofabody�scontact τ =Bond Strength

τn = shear stress which is acting on the bond interface

σn = adhesive strength

ϕ = internal friction angle

µ = coefficient of friction


xii

υ = Poisson’s ratio

δ = increment

σ�� = averagestressinparticlep

σ��" = averagestressinclumps ω =rotational velocity

%&& = radial stress

%''= hoop or tangential stress

%((= vertical stress


1

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

During the completion stage of the life of a wellbore, the wellbore is cased and cemented

in order to maintain its integrity. Wellbore integrity has been an issue in the drilling

industry since time immemorial and has cost the industry financially, socially and

environmentally. The objective of this work is to develop a better understanding of the

performance of the casing-cement-formation under high pressure using. Well integrity is

defined by the Norwegian Petroleum Industry (NORSOK) D-010 as “Application of

technical, operational and organizational solutions to reduce risk of uncontrolled release

of formation fluids throughout the life cycle of a well”. The study and analysis of

wellbore integrity is important because loss of well integrity results in loss of well control

and this may further lead to the damage of equipment, loss of reserves, reputational

damage, and cost of remediation and most importantly loss of human life. One of the

major contributory factors to the integrity of a well is the cement bond. The bond of

cement in a well consists of the bond between the cement and the formation and the bond

between the cement and the casing. Various tests, both experimental and numerical have

been performed to analyze the wellbore integrity. These tests have been successful to an

extent in that they have given some basis for cement as well as casing design. However,

cement formation bond mechanism understanding has been relegated to qualitative

observations involving formation permeability, the role of mud cake and mud

displacement practices (Wojtanowicz, 2008).

Wellbore integrity is first controlled by the wellbore stability during drilling. Here,

stability is often by the mud weight and consistent management of pressure. After

cementing, upward fluid migration through cement channels has also been cause for most

blowouts. When fluid seeps around the casing it may erode the borehole-casing annulus,

which may eventually lead to the formation of a crater. The cement sheath is constantly


2

checked after cementing and cement bond logs are used to evaluate the integrity of the

bonds. Despite all these checks, unforeseen events such as seepage of contaminated fluids

into the formation and blowouts may cause the wellbore to lose its integrity. The

accurate, proper design and planning of cement jobs are primary requirements for

preventing the upward migration of gas around the casing. As a result, a great deal of

effort has been exerted by the petroleum industry to reduce the channel formation

tendency in the cemented annulus during cementing.

The main causes of wellbore instability may be grouped under chemical and mechanical

factors. Mechanical causes of instability include failure around the borehole as a result of

high stresses, insufficient rock strength and inadequate drilling practices. Chemical

causes of instability are as a result of interaction between the formation and/or formation

fluid and fluid pumped into the wellbore. However, the well bore instability is usually

due to a combination of these factors. When there is a concentration of stresses around a

wellbore, it may result in compressive or tensile failures. Zoback (2007) referred to these

failures as stress induced breakouts (compressive) and drilling induced (tensile) wall

fractures. Effective stresses around a wellbore may be described as follows:

%&& = 12 �+,-./ + +1-23 − 2561 − 7898: + 12 �+,-./ − +1-23× 61 − 47898 + 37>9> : cos 2? +5@7898

(1)

%AA = 12 �+,-./ + +1-23 − 2561 + 7898: − 12 �+,-./ − +1-23× 61 + 37>9> : cos 2? +5@7898 − %∆C

(2)

D&A = 12 �+,-./ − +1-23 × 61 + 4298 − 37>9> : sin2? (3)


3

%EE = +F − 2G�+,-./ + +1-23 67898: cos 2? (4)

Where υ is Poisson’s ratio and θ is the angle measured from the azimuth of SHmax.

When the formation is in its original state it is often characterized by three states of

stress:

- Overburden or vertical stress in the z axis

- Horizontal stress in the x axis

- Horizontal stress in the y axis

The overburden stress is as a result of the overlying formation and the horizontal stresses

are mostly due to tectonic stresses. However, when a wellbore is drilled, the original state

of stress is greatly disturbed as a solid element (cylindrical in shape) is removed from the

mother formation. This eliminates the state of equilibrium which we normally attempt to

restore by replacing the void with a drilling fluid. When drilling on balance, the

hydrostatic pressure exerted by the drilling fluid is not enough to maintain the

equilibrium of the formation itself and the formation reacts by counteracting the stresses

exerted by the drilling fluid causing the formation to deform. It is only when this occurs

that equilibrium is restored (Gray et al., 2007). When the wellbore is cased and cemented,

the hydrostatic pressure exerted by the cement slurry usually not equal to that of the mud

and as a result the deformation cycle repeats itself to achieve stability. The same is true

about the hardening and shrinking process of the set cement (Gray et al, 2007).

The integrity of the wellbore may be compromised if the bond between the casing and the

cement as well as the casing and the formation are inadequately designed. Often the three

components of the system are designed separately using individual stress components. In

such a case the following may occur (Teodoriu et al, 2010):

- Cracks in the cement which will allow for gas and fluid migration

- Plastic deformation in cement or


4

- Debonding of the component’s interfaces

The first two will cause radial fluid migration and latter vertical fluid migration. The

above anomalies may be due to tensile failure caused by shrinkage as a result of the

dehydration of the cement. It may also be due to compressive shear failure as a result of

high abnormalities in principal stresses. The above may also jeopardize wellbore

stability. The formation surrounding the wellbore is subject to the effective hoop stress,

radial stress and the effective stress parallel to the axis of the wellbore. If the strength of

the formation is less than these stresses, the formation is set to fail. This is analogous to

the maximum stress criterion. However, as differential pressure, ∆P increases there is a

decrease in the effective hoop stress and this can result in what Zoback (2007) referred to

as drilling induced tensile failures.

Figure 1: Graph Showing the Variation of Effective Stresses as a Function of Azimuth (Zoback 2008)

1.2 WELLBORE FAILURE

Wellbore failure may be as a result of controllable or uncontrollable factors. However,

both of these factors contribute to numerous disturbances in a wellbore region and

affecting productivity and the formation as a whole. Figure 2 is an illustration of


5

controllable and uncontrollable factors and their effects on the formation and wellbore

behavior. There are several criteria for defining failure. In geomechanics the most widely

utilized and most applicable is the Mohr-Coulomb failure criterion.

Figure 2: An Illustration Of Controllable And Uncontrollable Factors And Their Effects On The

Formation And Wellbore (PASIC 2007)

1.3 MOHR-COULOMB FAILURE CRITERION

There are several different criteria of rock failure. However, the Mohr-Coulomb Failure

Criterion is the commonest and most applicable in the field of geomechanics. According

to the maximum normal stress criterion, when the maximum normal principal stress

reaches the uniaxial compressional strength or uniaxial tensile strength failure occurs.


6

The Mohr-coulomb criterion is based on the Mohr’s circle and coulomb’s maximum

normal stress criterion. According to the Mohr-Coulomb criterion, when the Mohr’s

circle at a point in a body is no longer enveloped by the Mohr’s circle for uniaxial tensile

strength and uniaxial compressional strength, failure will occur.

Figure 3: Diagram Showing Mohr-Coulomb Failure Criterion (SOLIMAN AND BOONEN 1999)

TABLE 1: CONDITIONS FOR MOHR’S FAILURE

Case Stress Maximum allowable value to avoid failure

1 Both in compression σ 1> 0 , σ 2> 0

2 Both in tension σ 1< 0 , σ 2< 0

3 σ 1 in compression, σ 2 in tension σ1σt +σ2σc < 1

4 σ 2 in compression, σ 1 in tension σ1−σc +σ2σt < 1


7

CHAPTER 2

LITERATURE REVIEW

2.1 EVALUATION OF EXISTING NUMERICAL, ANALYTICAL AND EXPERIMENTAL

CEMENT-CASING-FORMATION SYSTEMS

The integrity of the wellbore has been investigated over the years through various

experimental as well as numerical means. The experimental methods usually consist of

triaxial tests and other stress and strain tests. These experimental methods have been used

in the past by Carter and Evans (1964), Scott and Brace (1966), Evans and Harriman

(1972) Goodwin and Crook (1992), Stiles (2006) and many more. In these experiments

most of the attention was given to the cement sheath, its mechanical and elastic properties

and its role in maintaining wellbore integrity. Goodwin and Crook (1992) investigated

the effect of temperature and pressure on the mechanical and elastic properties of various

cements and concluded that cements with high elastic moduli were more likely to be

damaged. Early numerical analyses of wellbore integrity considering the cement-

formation and cement-casing bonds have been used by Goodwin and Zinkham (1962).

Other researchers like Gray et al (2007), Fleckenstein et al (2000), Ravi et al (2002),

Medhi et al (2006), Teodoriu et al (2010) and many others have also numerically

analyzed the integrity of the wellbore. However all of these analyses have been done

using the finite element method or other continuity methods. In 1962, Goodwin and

Zinkham used mathematical methods to analyze tensile and compressive stresses in an

unconfined cement sheath as well as compressive stresses in a confined cement sheath.

According to their computations, they were able to estimate the fracture initiation

pressure, effect of pipe size on cement stress and initial relationship between cement,

rock and casing. Medhi (2006) also used the finite element method in analyzing the

cement-formation and cement-casing bonds, how high temperature and high pressure

affect these as well as forecast the time of failure. He concluded that alternating high

temperature and high pressure effects can cause unexpected behavior in the cement

sheath, which will eventually lead to failure in the casing-cement bond.


8

According to Goodwin and Zinkham, laboratory tests to analyze wellbore integrity may

not be too applicable and as such a small field evaluation incorporated into mathematical

analysis may be the best option for the analysis of well integrity. The finite element

method, which is also vastly used in the modeling of well integrity, ignores the

discontinuity behavior of fractures and interfacial interaction between the cement and the

formation as well as the cement and the casing. The discrete element method is hardly

ever used due to its computational complexities (Jing and Stephansson 2002).

2.2 CEMENT BONDING

The major functions of cement are to prevent fluid migration or interaction with the

formations and to support the casing (Lake 2007). The integrity of a well is dependent

upon the casing-cement contact and its capability to seal the annulus throughout the life

of the well. It is therefore imperative to understand the performance of the casing cement

bond under well conditions that can lead to best practices and a model to predict well life.

Two types of bonds are necessary when considering the bond between cement and

casing. These are shear bond and hydraulic bond. Shear bond is necessary for the

mechanical support of casing in a hole, whereas, hydraulic bond is needed to prevent the

seepage of fluids in and out of the formation (Carter and Evans, 1964).

Shear bond: According to Coulomb’s theory, shear failure can occur if the following

condition is satisfied:

τK = c + μσK

(5)

or τK = c + tanφ ∗σK

(6)

Where

τK = the shear stress which is acting on the bond interface

c = the adhesive strength


9

φ = the internal friction angle between the cement sheath μ = the coefficient of friction

The stress relationship, showing the force required to produce shear failure along a bond

plane, is determined by measuring the force required to initiate pipe movement in the

cement sheath in the laboratory (Carter and Evans, 1964)

shearforcebond = forcecementcasingcontactsurfacearea (7)

During cement slurry design, therefore, the shear bond force should be an important

factor to be taking into consideration as this greatly affects the integrity of the well.

Figure 4: Diagram Showing Casing Cement and the Formation

Hydraulic Bond: This is defined by Carter and Evans (1964) as the bond that prevents the

migration of fluid into the cemented part and is determined by applying the pressure at

the pipe-cement interface until leakage occurs. In this experiment, special core holders

are built to determine the hydraulic bond of a specimen. The hydraulic pressure, when the

leakage appears at either end of the specimen, is defined as the bond failure pressure in

psi. The hydraulic bond prevents the longitudinal movement of fluid along the casing and

between cement and adjacent geological horizons. Hydraulic bond at the cement-

formation interface is influenced to a great extent by rock type and the presence or

absence of filter cake. Hydraulic bond is usually much better in Permeable formations

Cement

Casing Formation


10

because cement slurry develops a higher compressive strength as it loses water to the

formation (Scott and Brace, 1966).

2.3 FACTORS AFFECTING CASING-CEMENT BOND AND CASING-ROCK BOND

2.3.1 Wettability of contact specimen

Fluids only adhere to solids when the solid material is wet by that particular fluid

medium. It is very important to check whether and to what extent the cement slurry

wets the solids which are supposed to be cemented when investigating the causes of

bond between cement slurries, pipes and formation. This is because the more surface

wetted with the cement material, the higher the resultant shear bond strength value.

However, very few studies have been performed to investigate the wetting behavior of

fluids. The contact angle set up by the fluid drop characterizes the wetting ability of the

fluid. The wettability is good when the fluid shows a flattened drop (Scott and Brace,

1966).

2.3.2 Roughness of contact faces

During wetting, the bond of cement slurry to the contact surface is caused by the

intermolecular adhesive forces. The intimacy of the contact determines the strength of the

adhesive force. It is assumed that the cement slurry must penetrate the pores of the

contact surface therefore the roughness of the medium affects the bond between casing or

formation and the slurry. Experiments have shown that bond strength increases with

increasing roughness of the contact surface (Scott and Brace, 1966).

2.3.3 Degree of hydration of the cement

Degree of hydration may be defined as the ratio of cement that has completely reacted

with water as compared to the total amount of cement in the sample. This is usually

computed by measuring the slurry’s chemical shrinkage within twenty-four hours of

hydration. This is based on measuring the volume of water imbibed into a cement slurry

sample of known mass during hydration. Chemical shrinkage will be at a maximum when


11

the cement is hydrated completely and the products cease undergoing transformation.

Powers and Brownyard (1946).

2.3.4 Bond of cement under well conditions

Under well conditions the casing needs to be adequately supported. Bond strength needed

to support the casing is given by (Scott and Brace (1966)

τ = L ∗ GπDH (8)

Where

τ =Bond Strength

L = length of casing

G= weight of casing

H= height of cement column

D= outer diameter of casing, in the consistent system of units

The above mentioned factors are important when designing the a cased hole completion

and should be taken into consideration in order to prevent the wellbore from failing.

2.4 EXPERIMENTAL TESTS CARRIED OUT ON CEMENT

2.4.1 Triaxial Compression test

This is a test performed to determining Poisson’s ratio and young’s modulus. In 2006,

Stiles used it to determine effective compressive strength. In a triaxial compression test, a

constant confinement pressure is applied around the sample, usually, a cylindrical core

and the axial stress is steadily increased until failure is reached.


12

Figure 5: Typical Triaxial Testing Cell

2.4.2 Brazilian Compression Testing Method/ Splitting Tensile Stress Testing

Brazilian Compression Test is done to determine the indirect tensile strength. Specimen

is disk shaped with double compressive forces acting across the diameter. The load is

applied until failure occurs. The load induces tensile stress thereby making tensile failure

occur instead of compression. The indirect tensile strength can then be computed by the

equation:

%U = 2VWXY (9)

Where

%U= Brazilian tensile strength, psi

F= maximum applied load, lbf

L= Length of the specimen, in


13

D= diameter of the specimen, in

According to Heinold et al. (2003) the Brazilian compression tests gives a relatively

higher value as compared to the direct tensile testing method depending on the size and

aspect ratio however, Jaeger and Cook, 1976 believe they give very similar results. The

Brazilian compression tests are used more often because it is believed to be more

practicable and closely mimics the failure mode in most brittle materials.

2.4.3 Unconfined Compressive Test

In this experiment, only the axial stress is taken into consideration. The lateral stress is

set to zero. Therefore the singular axial stress measured here is known as the unconfined

compressive stress. The unconfined compressive test is important because it is able to

provide the least strength estimate of the material under testing. This can also be used to

calibrate the Young’s and Poisson’s ratios using the basic Hooke’s law. The state of

stress at the center of the sample can be represented by:

%Z = %%8 = %[ = 0 (10)

Figure 6: The Uniaxial or Brazilian Test

F

D

L


14

Figure 7: Setup for the Unconfined Compressive Test

2.4.4 Direct shear Strength

This provides the shear strength properties along a plane of weakness

Figure 8: Direct Shear Test


15

Figure 9: Generalized Shear Stress and Shear Displacement Curve

Figure 8 Shows the Setup for the Direct Shear Test and Figure 9 Shows the Generalized Shear Stress

and Shear Displacement Curve Courtesy ASTME

2.5 SCOPE AND OBJECTIVES

The aim of this thesis is to model and analyze a cased horizontal well using the distinct

element method. Using this method, the discontinuity of the casing cement and formation

bonded together as well as a portion of their continuous behavior will be taken into

consideration. The overburden stress will also be considered. Micro-crack initiation,

plastic deformation, debonding and ultimately failure will be analyzed.

In order to achieve these, the ITASCA Particle Flow Code software which allows one to

model and analyze discontinuity in granular media will be used. Data will be obtained

from a Barnett Shale horizontal well field example by Vermylen (2011). Using PFC, the

steel casing, shale formation and cement will be modeled separately and then put together

to determine the stresses at the interfaces. Graphs and other trend line plots will then be

used analyze the stresses, strains, deformation and failure.


16

Figure 10: Cracks in Cement Sheath As Demonstrated By Ravi et al. (2002)

Figure 11: Plastic Deformation in Cement Sheath as Demonstrated By Ravi et al (2002)


17

Figure 12: Debonding In Cement- Formation Interface As Demonstrated By Ravi Et Al (2002)

Figure 13: Debonding In Cement- Casing Interface As Demonstrated By Ravi Et Al (2002)


18

CHAPTER 3

NUMERICAL MODELING OF CEMENT-CASING-FORMATION SYSTEM

Numerical methods used in geomechanics can be grouped under continuous methods and

discontinuous methods. The continuous or continuity methods are finite element method,

finite difference method and boundary element method. The discrete element method

falls under the discontinuous method.

Figure 14: Numerical Methods Used in Geomechanics

3.1 FINITE ELEMENT METHOD

This is one of the oldest numerical methods used in modeling continua. Many schools of

thought believe that it was in use long before the advent of computers. Using FEM,

partial differentials can be solved by separating the problem into numerous components

each with a shape peculiar to the component. Simple trial functions are then used to

approximate the solution. Due to these approximations it is always better to have a

greater number of components for better accuracy. FEM is widely used for engineering

stress analyses that do not require fragmentation of the material. According to Bobet


19

(2010) the finite element method relies on the displacement principle that implies that the

total external virtual work done by a deformable body, as a result of its virtual

displacement (however small) applied to the body, must be equal to the total internal

work associated with the virtual displacement field for a body to be in equilibrium. As a

result of its relative ease of computations, finite element method is used in geomechanics

than any other form of numerical analysis.

Figure 15: Illustration of the Finite Element Method

According to Jaeger and Cook (1979) the advantages of Finite Element Method include

- Computations are relatively easy

- The size and mode of selecting elements are random such that irregular

boundaries can be fitted easily, usually, a greater portion of nodal points can be

selected in regions of higher stress concentration.

- Different surfaces and forces can be easily utilized as the boundaries are not a

fixed shape.

- Homogeneity and isotropicity is not a requirement as each element has its own

stiffness matrix.

3 2

1 4

3

2

1

4


20

- Different rheological models may be utilized as it is not restricted to elastic

models only

- Friction and dilatants joints are allowed at joint surfaces

- The final output can be processed in the computer in any desired fashion.

Some disadvantages of the finite element method are

- for a specific problem, a specific solution is obtained thus making it impossible to

generalize the system’s behavior as a whole

- it is important to have a good and reliable FEM software in order to analyze a

system using FEM

- A large input and output data are required

- Approximation becomes a problem as computers can allow only a finite number

of significant figures

- Using grid systems does not model some geometrical figures accurately

- Effects like buckling cannot be accurately modeled

3.2 FINITE DIFFERENCE METHOD

This is also a very common method used in solving numerical problems especially partial

differential equations. Here, Taylor’s expansion is used to approximate the differential

equation. FDM usually requires the use of uniform grids which makes it very difficult to

solve complex problems requiring the use of non-uniform system of grids. (Ertekin et al)

The basic operators used in the approximation of the derivative of the finite difference

method are:

- Forward difference

- Central difference

- Backward difference


21

Forward Difference

∆]�^2 = ]�^2_Z − ]�^2 (11)

Central Difference

`]�^2 = ]a^2_Z 8⁄ c − ]�^2dZ 8⁄ (12)

or `]�^2 = ]�^2_Z − ]�^2dZ (13)

Backward difference

∇]�^2 = ]�^2 − ]�^2dZ (14)

The finite difference method is normally used in simulation of hydrocarbon reservoirs

usually for fluid flow but sometimes (rarely) used in geomechanics.

Figure 16: Representation of Lagrangian FDM Where Domain Is Divided Into Nodes and Zones


22

The main advantages of finite difference method are:

- Approximation methods make computations easier than the other numerical

methods

Disadvantages include:

- Uniform grid system makes it hard to solve problems involving non uniform grids

- Approximations make the source of error greater than the other numerical

methods

3.3 BOUNDARY ELEMENT METHOD

The boundary element method is used when the other continuity methods such as finite

element and finite difference have failed particularly in areas regarding better accuracy

such as stress concentration and infinite domains. The BEM requires that discretization is

done only at the boundaries instead of the whole domain.

Advantages of the boundary element method are:

- It requires less time to solve a problem

- It requires less data relative to the other numerical methods

- It requires less money since one only needs to discretize at the boundaries and

hence less data

- They are good for problems which involve rapidly changing stress

- Systems of equations are smaller and less cumbersome since discretization is at

the boundaries only

Disadvantages include

- The BEM is not applicable to non-linear flow equations

- Matrices used in BEM are unsymmetrical and fully populated making them

harder to solve than the other numerical methods.


23

3.4 DISTINCT ELEMENT METHOD

This is a method introduced by Cundall and Strack 1979 to model granular media. In

recent times it has been used to model rock mass that usually contains faults and cracks a

well as granular media cemented together.DEM uses a form of finite difference scheme

that helps to study groups of individual particles. By monitoring the interaction between

the elements, the behavior of the material as a whole can be determined. When using

DEM, stresses and displacement in a space or volume containing a huge number of

particles such as sand grains or grains in cement can be modeled. In distinct element

modeling, the material is represented as an assembly of independent particles which are

able to interact with each other. A boundary of each element can be represented through

the model explicitly reproducing the discrete nature of the discontinuities.

The DEM can also be used to model several materials that do not have a particulate

nature. This may be achieved by the assumption that the whole material may be

approximated into discrete particles which are cemented together or bonded together by

cohesive forces. DEM also allows the incorporation of heat/ temperature effects as well

as fluid pressure (Jing and Stephansson 2008).

The distinct element method was mainly created for mechanical deformation of

assembled elements and these are governed by the equations of motion of rigid or

deformable bodies. To simulate deformation, Cauchy’s equations are sometimes used,

Fourier’s law is also used for heat transfer and Navier-Stokes for fluid flow though micro

apertures.

Cauchy’s equation of motion for deformation: Although many may argue that

deformation of a body is generally a continuum process, it may be considered otherwise

on a microscopic scale. It is however true that translation leading to deformation is

indeed considered as continuum but this is only on a macroscopic scale. Discretization of

a continuum as described in Jing and Stephansson’s Fundamentals of Discrete Element

Methods for Rock Engineering(2007) may be described as an ‘’approximation of a


24

continuous system with infinite degrees of freedom by a discrete system of elements with

finite degrees of freedom’’.

Cauchy’s equation of motion can be derived from Newton’s second law – a body will

continue to move in a uniform state or, if at rest, remain at in that state unless acted upon

by an external unbalanced force. This unbalanced force will accelerate the body leading

to a change in direction, speed or both. Cauchy built equation based on this fact and came

up with the equation:

fYg2Yh = i%2ji j +k2

(15)

Where,

ρ = Density

t = Time

σ = Stress

b = Body force

(In the consistent system of units)


25

Figure 17: Particles during Motion (Courtesy Jing and Stephansson 2007)

Fourier’s law: To determine the temperature distribution in wellbore, we can safely use

Fourier’s law and the heat equation. The basic Fourier’s law states that “heat flux across a

unit cross sectional area A, is proportional to the temperature gradient”

l∞n ioi j

(16)

l = −p ioi j (17)

Cylindrical coordinates may be used to describe Fourier’s law in a wellbore

l =−p�ioi9 q + ioir s + ioit u (18)

As well as heat flow


26

p v19 ii9 w9 ioi9x + 198 iir w9 ioirx + iit wioitxy + z = f{@ ioih (19)

Where,

Q = Heat Flux

A = Cross Sectional area

T = Temperature

κ = Constant of Proportionality

cp = Specific Heat Capacity

ρ = Density

(In consistent system of units)


27

Figure 18: Cylindrical Coordinates for Fourier’s Heat Law

3.5 USING PFC

The particle flow code, like any distinct element method models discontinuum in any

area of research where several discrete particles which exhibit huge strain and/or

fracturing is needed. It helps to analyze as well as test the mechanical properties of these

particles. The particle flow code is good in such a way that it is not limited to specific

problems or applications. Variations in simulations include simulating flow of a

substance – rapid or otherwise, as well as the brittleness of a rigid structure which takes

into consideration micro and macro fractures alike.

Assumptions made by the PFC model include

- the elements/ particles are regarded as rigid

- the contacts occur over an unusually small area

- the soft contact method is utilized at the contacts thereby allowing the

rigid particles to overlap one another at these points

- the overlaps are relatively small as compared to the actual particle sizes


28

- The force displacement law relates the magnitude of overlap to the contact

force. The force displacement law is basically defined as

V2 = |2`2 (20)

Where,

F = Force

K = Stiffness

δ = increment

i = normal or shear

- Bonds may exist as contacts between particles

- All particles are spherical

As mentioned earlier, the PFC model, like any distinct element model allows continuum

to be adequately modeled by approximating the solid body into a compacted legion of

several particles. This allows the stress and strain to be measured accurately by defining

the average of the elemental volume.

3.5.1 The calculation cycle

The PFC utilizes a calculation cycle that involve the continuous cycle of the law of

motion and the force displacement law applied to each contact. The position of the walls

is also updated all the time. Contacts may be ball to ball, wall to wall or ball to wall

depending on the scenario.


29

Figure 19: Calculation Cycle of PFC

3.5.2 Boundary and initial condition

Boundary and initial conditions may be set for both balls and walls. For walls,

translational velocities, rotational velocities as well as centre of rotation may be specified

but the applied force cannot. However, in the balls the translational, rotational velocities

and the applied force can be specified. The equation for finding the velocity of a point p

is calculated by

�2} = �2~ +�2j��j~a^�}−^�~c (21)

Where

xp = position of a point p

�2~= translational velocity

ωw=rotational velocity


30

�2}= velocity at a point p

^�~= center of rotation

3.5.3 Contact Models

Selecting a contact bond is one of the most important steps in using ITASCA PFC 3d.

There are two main types of contact models of which other models have been derived.

The main contact bonds are:

- Linear

- Hertz

Each model is characterized by specific component behaviors namely stiffness, slip and

bonding behaviors.

Stiffness describes relative displacements and contact forces in the shear and normal

directions using the following equations for normal stiffness (secant) and shear stiffness

(tangent)

V23 =|3�3�2

(22)

∆V23 =−u��2� (23)

Slip, as its name suggests, describes the sliding nature of two contacting bodies. The

condition of slip is verified by calculating the maximum allowable shear contact force

defined by the equation:

V-./� = �|V23| (24)

If |V2�| > V-./� (25)

Then slip occurs and the magnitude of


31

|V2�| = V-./�

(26)

And V2� ← V2� 6V-./��V2�� : (27)

Where,

Kn = normal stiffness

Fs = shear force

ks = shear stiffness

Un = normal displacement

Us = shear displacement

Fsmax = Maximum allowable shear force

3.5.4 Bonding Behaviors

Contact bond: These are characterized by the following,

- Constant normal and shear stress acting at the contact point

- Allow tensile forces to develop at contact that is, when Un < 0 there is no overlap

- If |Fcn| ≥n bond, the bond breaks and both the normal and shear bonds are set to

zero

- If |Fcs| ≥ s_bond, the bond breaks but contact forces are not changed, provided the

FS is not greater than the friction limit and provided the shear force is compressive V3 > 0 → o��q�� 3 > 0 → �g�9��

- Precludes the possibility of a slip


32

Parallel bond: This is characterized by the following:

- Provides finite sized piece of a cementatious material deposited between two balls

that are treated as spheres

- Does not preclude the possibility of a slip

If

%-./ ≥%�

(28)

Or D-./ ≥D� (29)

Then the bond breaks

Where,

σmax = maximum normal stress

τmax = maximum shear stress

σc = normal stress at the contact

τc = shear stress at the contact

3.5.5 The Logic of Measurement in PFC

The following quantities are defined with respect to a specified measured volume in PFC:

porosity, coordination number, sliding fraction, stress rate and strain rate.

Porosity: The porosity φ is defined as the ratio of the empty volume in the specified

region of measurement to the whole volume of the measurement region. It may be

mathematically represented as:


33

∅ =�F�2��&�2 = �&�2 − �-.U�&�2 = 1 − �-.U�&�2 (30)

Where,

Vvoid = Volume of empty space

Vroi = Volume of region of interest

Vmat = Volume of material within the region of interest

Sliding Fraction: This is defined as the ratio of contacts within the region of measurement

that are slipping to the whole region of measurement. Also the magnitude of the shear

contact force should be in the neighborhood of 0.1% (one tenth of a percent) of the

maximum allowable shear force, Fsmax

Stress: Since stress is a continuum quantity, PFC uses averaging steps in order to

compute stress in a discrete medium on a microscale. The following mathematical steps

are used in the computation of stress

The average stress acting throughout the measuring volume%�2j can be given by:

%�2j = 1��%2j�� (31)

And since stresses are only present in spherical particles and clumps when considering a

granular material, the sum over Np particles and Nl clumps can replace the integral,

thereby giving:

%�2j = 1��%�2j�@�� +�%�2j��

��

(32)

Where,


34

%�2j�@ = averagestressinparticlep

%�2j�� = averagestressinclumps The average stresses in each body can be computed by:

%�2j�∅ = 1��∅ � ^2�� − ^2�∅¡Vj��,∅�£�∅

(33)

Where,

^2�∅ = Location of a body’s centroid ^2�� = Location of a body’s contact Vj��,∅= Force at a body’s centroid

Figure 20: PFC Plot Of Balls In Contact (Smooth Joint)


35

The volume associated with each body is represented by

� = ∑ ��@�� + ∑ ��1 − r (34)

Where φ is the porosity of the region of interest

The three equations can be combined to give the average stress:

%�2j = 6 1 − �∑ ��@�� ∑ �� :��%�2j�@�� +�%�2j��

��

(35)

%�2j = 6 1 − �∑ ��@�� ∑ �� :¥�� ^2�� − ^2�@¡Vj��,@�£�∅��+�� ^2�� − ^2��¡Vj��,��£�∅�� y

(36)

Where,

Nl = number of clumps

Np = number of particles

Vc = velocity at contact

nc = number of active contacts

Coordination number: This can be defined as the number of active contacts in a body and

it is calculated by the equation:

¦3 = ∑ ��@�� + ∑ ��§@ + §� (37)


36

CHAPTER 4

METHODOLOGY

In order to use the field properties of the materials, PFC needs to convert the

macroproperties into microproperties usable by PFC. Microproperties used in the

simulation are summarized in table 2 and table 3. Parallel bonds were assumed for steel

and cement whereas contact bonds were assumed for formation. Figure 21 to 24 shows

the step by step procedure for simulation in PFC 2D. The three materials: cement,

formation and casing were simulated separately to determine the correct microproperties

to be used. They were then combined and a biaxial compression test performed. Stress

and strain graphs as well as microcrack formation in the system were analyzed.


37

4.1 DETERMINATION OF MICROPROPERTIES

Figure 21: Determination of Microproperties of Materials


38

4.2 ALGORITHM FOR COMPRESSION TESTING WITH PFC

Figure 22: Part I of the Testing Procedure

Creation and Packing of ‘Granular’

Particles

Define Platens

- Use

Extended

Walls

Define Groups

ie alter steel,

rock cement

properties

Define Assembly

- Porosity

- Volume

- # of Balls

Define

lateral wall

stiffness

Set

Parameters,

Assemble,

Create walls,

Plot


39

Figure 23: Part II of the Testing Procedure


40

Figure 24: Part III of the Testing Procedure

4.3 VALIDATION

In validation of the software, a paper by D. Stiles (2006) – ‘The Effects of Ultrahigh

Temperature on the Mechanical Properties of cement’ is used. The effect of extremely

high temperature on the mechanical properties of cement was investigated over a two

year period using experimental analysis. The sample selected for validation is low-

density thixotropic cement with a density of 14.5ppg and consisted of 92% class A, 8%

gypsum together with 40% silica flour by weight of blend.


41

From these experiments, he noted that the effective compressive strength (i.e. the

pressure at which confining the rock will cause it to fail) increased with time. He also

deduced that the Young’s modulus increased and stabilized. The conventional cement

system exhibited plastic behavior at room temperature but became brittle after continuous

exposure to high temperature. To convert the Stile’s laboratory macroproperties to PFC

readable properties, the microproperties of the cement are derived by the author and a

biaxial test is performed numerically on the sample. Figure 26 of the validation shows of

the sample and breaks in the parallel bond and deformation of the cylindrical sample.

Using PFC, initial yield occurred at 5.4 MPa (783 psi) was achieved which corresponds

to the initial yield estimated by Stiles as shown in Figure 28.

TABLE 2: DATA USED IN VALIDATION

Parameter Value

Young’s Modulus 7GPa

Poisson’s Ratio 0.06

Pb_kn 1.2e35

Pb_ks 1e2

Pb_nstrength 1.2e35

Pb_sstrength 1e2


42

Figure 25: Sample Setup for Biaxial Test

PFC2D 4.00

Casing-cement- formation

Job Title: ’Validation’

Step 1750 19:17:32 Sun Apr 08 2012

View Size: X: -1.466e+001 <=> 2.666e+001 Y: -1.380e+001 <=> 2.580e+001

Groupsample_rock

Wall


43

Figure 26: Sample after Failure Showing Deformation and Breaks in Parallel Bond

PFC2D 4.00



Step 34950 04:59:34 Tue Apr 10 2012

View Size: X: -2.463e+000 <=> 1.446e+001 Y: -2.110e+000 <=> 1.411e+001

Groupsample_rock

Wall

PBond Locations


44

Figure

27: Deviatorial Stress versus Axial Strain Graph Showing The Initial Yield Of The Sample (PFC)

PFC2D 4.00



Step 34950 04:55:56 Tue Apr 10 2012

History

0.2 0.4 0.6 0.8 1.0

Axial Strain x10^-1

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0Axial Stress Difference x10^7

2 devi (FISH Symbol) Linestyle 7.614e+003 <-> 2.004e+007

Vs. 3 deax (FISH Symbol) 7.177e-006 <-> 1.046e-001

Initial yield at

5.4MPa ~ 783psi


45

Figure 28: Deviatorial Stress versus Axial Strain Graph Showing the Initial Yield of the Sample As Indicated By Stiles (2006)


46

4.4 ANALYSIS OF HIGH PRESSURE ON WELL INTEGRITY – A HORIZONTAL WELL EXAMPLE

TABLE 3: DATA USED IN HORIZONTAL WELL EXAMPLE

Parameter Unit

Hole Size 7.875 inches

Casing OD 6.625 Inches

Casing ID 5.675 inches

Cement OD 7.875 Inches

Cement ID 6.625 inches

Reservoir pressure 9000 psi

Total Vertical Depth 5700 feet

Length of Lateral 3000 feet

Poisson’s ratio of shale formation 0.23

Young’s Modulus of shale formation 40 GPa


47

Figure 29: Elastic Load/Unload Test To Determine Properties Of Formation Setup


48

Figure 30: Elastic Load/Unload Test To Determine Properties Of CEMENT Setup

PFC2D 4.00


Job Title: ’Elastic

Step 1750 00:40:31 Thu Apr 05 2012

View Size: X: -7.330e+000 <=> 1.333e+001 Y: -6.900e+000 <=> 1.290e+001

Ball

Wall


49

Figure 31: Elastic Load/Unload Test To Determine Properties Of CASING Setup

PFC2D 4.00


Job Title: ’Elastic

Step 1750 00:39:20 Thu Apr 05 2012

View Size: X: -7.330e+000 <=> 1.333e+001 Y: -6.900e+000 <=> 1.290e+001

Ball

Wall


50

Figure 32: CEMENT CASING FORMATION SETUP

Set Up


51

CHAPTER 5

RESULTS AND ANALYSIS

Loss of integrity of the casing may be demonstrated by the slight deformation of the casing as

shown in figure 33. In analyzing the integrity of the cement, the plastic deformation and

debonding are represented in figures 34 and 35 respectively.

In using this method, the progression of microcrack formation in the cement and formation

bonded together can be determined up to the point of failure. Figure 36 and Figure 38 show

microcrack formation at 10MPa and 100MPa respectively. More cracks are observed in the

vertical direction as a result of increasing overburden stress and deformation. Formation of

microcracks occurred faster when 100MPa was applied than in 10MPa. The direction of

microcracks can also be ascertained using this method and this may be helpful in the creation of

microfractures for the use of stimulation.

The analysis of normal, tangential and radial stresses in the loading and unloading phases of the

biaxial test reveal high hoop stress which is an indication of rock yield (figure 45). According to

Ravi et al (2002) an increase in radial compressive stress (figure 46) may cause compressive

shear failure and this may also be a result of huge differences in principal stresses.


52

Figure 33: Diagram Showing Slight Deformation of the Casing

PFC2D 4.00


Job Title: Biaxial Test on Rock-Cement-Formation

Step 44950 20:33:18 Thu Apr 19 2012

View Size: X: -3.611e+000 <=> 9.611e+000 Y: -3.336e+000 <=> 9.336e+000

GroupNonecement_rockcasing_rock

Wall


53

Figure 34: Diagram Showing Plastic Deformation Of Cement

PFC2D 4.00



Step 46750 20:22:50 Thu Apr 19 2012

View Size: X: -3.611e+000 <=> 9.611e+000 Y: -3.336e+000 <=> 9.336e+000


Wall


54

Figure 35: Diagram Showing Debonding Deformation Of Cement


55

Figure 36: Diagram Showing Microcrack Formation at 10mpa

PFC2D 4.00



Step 39750 04:59:12 Fri Apr 20 2012

View Size: X: -2.289e+000 <=> 8.289e+000 Y: -2.069e+000 <=> 8.069e+000


FISH function crk_item


56

Figure 37: GRAPH Showing Microcrack DEVELOPMENT At 10mpa

PFC2D 4.00



Step 39750 06:38:35 Fri Apr 20 2012

History

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Deviatoric Stress x10^7

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

# CB failures in shear x10^2

51 crk_num_csf (FISH Symbol) Linestyle 0.000e+000 <-> 1.140e+002

Vs. 2 devi (FISH Symbol) 8.988e+003 <-> 9.342e+007


57

Figure 38: Diagram Showing Microcrack Formation At 100mpa

PFC2D 4.00



Step 39450 07:00:38 Fri Apr 20 2012

View Size: X: -1.231e+000 <=> 7.231e+000 Y: -1.055e+000 <=> 7.055e+000


FISH function crk_item


58

Figure 39: Graph Showing Microcrack DEVELOPMENT At 100mpa

PFC2D 4.00


Job Title: failure test 100MPa

Step 39450 07:08:01 Fri Apr 20 2012

History

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Deviatoric Stress x10^8

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

# CB shear failure x10^2

51 crk_num_csf (FISH Symbol) Linestyle 0.000e+000 <-> 2.950e+002

Vs. 2 devi (FISH Symbol) 1.601e+005 <-> 1.497e+008


59

Figure 40: PFC Derived Shear Stress versus Effective Normal Strain (10mpa Overburden)

PFC2D 4.00


Job Title: Failure Test

Step 72750 15:05:27 Sat Apr 07 2012

History

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Normal Stress x10^6

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Shear Stress x10^6

10 sstress (FISH Symbol) Linestyle 1.221e+003 <-> 2.171e+006

Vs. 5 nstress (FISH Symbol) 1.001e+006 <-> 5.627e+006


60

Figure 41: PFC Derived Deviatoric Stress versus Axial Strain @ 10mpa Overburden

PFC2D 4.00



Step 62350 22:36:58 Sat Apr 07 2012

History

0.5 1.0 1.5 2.0 2.5

Axial Strain x10^-1

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

deviatoric stress x10^6

2 devi (FISH Symbol) Linestyle 4.225e+003 <-> 4.589e+006

Vs. 3 deax (FISH Symbol) 9.311e-006 <-> 2.855e-001


61

Figure 42: PFC Derived Normal, Tangential and Hoop Stresses at 10mpa Overburden

PFC2D 4.00



Step 62350 22:55:41 Sat Apr 07 2012

History

2.10 2.12 2.14 2.16 2.18 2.20 2.22 2.24 2.26

Distance x10^1

-9.0

-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Stresses x10^6

5 nstress (FISH Symbol) Linestyle -5.884e+006 <-> -1.004e+006 6 hstress (FISH Symbol) Linestyle -9.178e+006 <-> -8.450e+003 7 rstress (FISH Symbol) Linestyle 4.225e+003 <-> 4.589e+006

Vs. 8 distx (FISH Symbol) 2.095e+001 <-> 2.266e+001


62

Figure 43: Spreadsheet Analysis of Deviatoric Stress versus Axial Strain @ 10mpa Overburden

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06

Sh

ea

r S

tre

ss

Effective Normal Stress

shear vs normal

stress


63

Figure 44: Spreadsheet Analysis of Deviatoric Stress versus Axial Strain @ 10mpa Overburden

0

500000

1000000

1500000

2000000

2500000

3000000

3500000

4000000

4500000

5000000

0 0.05 0.1 0.15 0.2 0.25 0.3

De

via

tori

c S

tre

ss

Axial Strain

devi vs deaxOnset of failure


64

Figure 45: Spreadsheet Analysis Normal, Tangential and Hoop Stresses @ 10mpa Overburden (Loading)

0

1

2

3

4

5

6

7

8

9

10

0.00E+00 1.00E+02 2.00E+02 3.00E+02 4.00E+02 5.00E+02 6.00E+02 7.00E+02 8.00E+02

stre

sse

s i

n M

pa

distance/ radius in metres

Stresses vs Distance (Loading)

hstress

rstress

nstress

Poly. (hstress)

Poly. (rstress)

Poly. (nstress)

High hoop stresses

may be an indication

of rock yield


65

Figure 46: Spreadsheet Analysis Normal, Tangential and Hoop Stresses @ 10mpa Overburden (Unloading)

-10000000

-8000000

-6000000

-4000000

-2000000

0

2000000

4000000

6000000

0.00E+00 1.00E+02 2.00E+02 3.00E+02 4.00E+02 5.00E+02 6.00E+02 7.00E+02 8.00E+02

Str

ess

es

in P

a

Distance

Sresses versus Distance(Unloading)


66

CHAPTER 6

CONCLUSIONS

- When the mud weight is higher than the tangential/ hoop stresses, fractures (axial)

may develop and using the DEM, we can adequately determine when this will

occur.

- Failure can also be determined from the plot of shear stress against effective

normal stress using the most suitable failure criteria – in this case the Mohr-

Coulomb failure criterion may be used to analyze it.

- The plot of deviatoric stress versus axial strain gives a fair estimate of when the

material reaches the plastic region (i.e. loses its elasticity) figure 44.

- Although there were some computational restraints such as unusually long time

for running simulation and complexities of the mathematics, it can be seen that

PFC was able to model stability/instability in a horizontal well.

- Debonding was clearly seen after the load/unload biaxial tests which would have

been very difficult with continuity modeling method. Although Gray et al

discussed debonding in his 2007 paper, a visual representation of the phenomenon

was not achieved possibly due to discretization constraints in the use of finite

element method

- Further processing and trend line analysis of the points generated from the PFC

histories resulted in a much better understanding of the downhole conditions

- The distinct element method is a computationally and mathematically intensive

analytical tool. However as technology improves by the day, the accuracy of

analyzing wellbore stability and integrity and other matters pertaining to the

geomechanics of petroleum engineering will be greatly improved.

- Modeling the steel region (casing) which is not a particulate or granular substance

was particularly challenging but due inverse modeling a good estimate was used.

- From this work, it can be inferred that the best way to model a scenario which

takes into consideration the casing- cement- formation bond would be to use a


67

numerical and analytical methods which combines both continuity and

discontinuity methods. If this proves feasible the following may be achieved:

• Adequate modeling of discontinuity such as cracks, fractures and

debonding of the interfaces.

• Adequate modeling of continuity such as deformation and representation

of continuous media like steel.

• Excellent representation and accurate modeling of temperature and fluid

flow effects.


68

REFERENCES

1. Al-Ajmi, Adel. 2006. Wellbore Stability Analysis Based on a New True-Triaxial

Failure Criterion. PhD Dissertation. KTH Royal Institute of Technology.

2. Al-Ajmi, Adel and Robert Zimmerman. 2006. A New 3D Stability Model for the

Design of Non-Vertical Wellbores. American Rock Mechanics Association

3. Austin, S., Robins, P., Pan, Y. 1999. Shear Bond Testing of Concrete Repairs.

Cement and Concrete Research, Volume 29, Issue 7, Pages 1067-1076.

4. Bobet, A. 2010. Numerical Methods in Geomechanics. School of Civil

Engineering, Purdue University, West Lafayette, the Arabian Journal for Science

and Engineering, Volume 35 Number 1B

5. Carter, L. G. and Evans, G. W. 1963. A Study of Cement- pipe Bonding,

presented at SPE Regional Meeting, Santa Barbara, California.

6. Cundall, P. A., and J. Marti. 1979. Some New Developments in Discrete

Numerical Methods for Dynamic Modelling of Jointed Rock Masses. In

Proceedings of the Rapid Excavation and Tunnelling Conference (Atlanta, June

1979), Vol. 2, pp. 1466-1477. Baltimore: Port City Press.

7. Cundall, P. A., and O.D.L. Strack. 1979. A Discrete Numerical Model for

Granular Assemblies. Géotechnique, 29, 47-65 (1979).23.

8. Cundall, P. A., and O.D.L. Strack. 1979. The Development of Constitutive Laws

for Soil Using the Distinct Element Method. In Numerical Methods in

Geomechanics, Vol. 1, pp. 289-317. Rotterdam: Balkema.

9. Ertekin, T., Abou-Kassem, J. H. and King, G. R. 2001. Basic Applied Reservoir

Simulation. Textbook Series. SPE, Richardson.

10. Goodwin K.J., Crook R.J. 1990. Cement Sheath Stress Failure. SPE 20453, Paper

Presented at the SPE Annual Technical Conference and Exhibition, New Orleans.

11. Gray, K.E., E. Podnos and E. Becker. 2007. Finite element studies of near-

wellbore region during cementing operations: Part I. In SPE (106998-MS), 31

March - 3 April, Oklahoma City, Oklahoma, U.S.A.


69

12. Heinold, T., R.L. Dillenbeck, M.J. Rogers and B.J.S. Company, 2003. Analysis of

tensile strength test methodologies for evaluating oil and gas well cement

systems. Proceedings of the Annual Technical Conference and Exhibition, Oct. 5-

8, Denver, Colorado, pp: 1-13.

13. Heinold, T.et al. 2003. Analysis of Tensile Strength Test Methodologies For

Evaluating Oil and Gas Well Cement Systems paper SPE 84565 presented at the

2003 SPE Annual Technical Conference and Exhibition

14. ITASCA PFC 2D/3D manual

15. Jaeger J.C. and Cook N.G.W., 1976. Fundamentals of Rock Mechanics.

Chapman and Hall, London, 2nd Ed., 585 Pp., Copyright © 1977 Published By

Elsevier B.V.

16. Jing, L. and Stephansson, O. 2007. Fundamentals of Discrete Element Methods

for Rock Engineering: Theory and Applications. Volume 85, Pages 1-545

17. Jones, P.R., and Berdine, D. 1940. Factors Influencing Bond Between Cement

and Formation. API Drilling and Production Practice, Union Oil Companies of

California, Wilmington, California (March),

18. K. Ravi, Halliburton, M. Bosma, Shell International E & P, and O. Gastebled,

TNO Building and Construction Research. 2002. Improve the Economics of Oil

and Gas Wells by Reducing the Risk of Cement Failure. Paper presented at the

2002 IADC/SPE Drilling Conference, Dallas, Texas, 26-28 February.

19. Khandkam, R. K. 2007. Leakage Behind Casing Drilling Specialization Thesis

Work, NTNU, 2007

20. Jing L., Hudson, J.A. 2002. Numerical methods in rock mechanics. International

Journal of Rock Mechanics and Mining Sciences, Volume 39, Issue 4, June 2002,

Pages 409-427

21. Ladva, H.K.J. ;. Braster, B; Jones, T.G.J. ; Goldsmith, G. ; Scott, D. ; The

Cement-to Formation Interface in Zonal Isolation (2004) IADC/SPE 88016,

Kuala Lamour, Malaysia, Sep. 13-15

22. Lake, Larry. 2007. Drilling Engineering. Petroleum Engineering Handbook Vol.2

Society of Petroleum Engineers Society of Petroleum Engineers, 770 pages


70

23. Ma, Yong et al. 2007. How to Evaluate the Effect of Mud Cake on Cement Bond

Quality of Second Interface SPE/IADC 108240

24. Mohiuddin, M.A., Khan, K., Abdulraheem, A., Al-Majed, A., Awal, M.R. 2007.

Analysis of wellbore instability in vertical, directional, and horizontal wells using

field data, Journal of Petroleum Science and Engineering, Volume 55, Issues 1–2,

January 2007, Pages 83-92, ISSN 0920-4105, 10.1016/j.petrol.2006.04.021.

25. NORSOK Standard D-010 Well integrity in drilling and well operations Rev. 3,

August 2004

26. Orszulik, Stefan T. 2008. Environmental Technology in the Oil Industry (Ed.) 2nd

ed., 2008, XII, 408

27. Pašić, B., Gaurina-Međimurec, N., Matanović, D. 2007. Wellbore Instability:

Causes And Consequences University of Zagreb, Faculty of Mining, Geology and

Petroleum Engineering, Pierottijeva 6, 10000 Zagreb, Croatia, Rud.-geol.-naft.

zb., Vol. 19.

28. Powers, T. C. and Brownyard T. L. 1946. Studies of the Physical Properties of

Hardened Portland Cement Paste. Journal of the A.C.I., 18 (1946), page 101/131.

29. Saint-Marc, Jérémie and Garnier, André Total, and Bois, Axel-Pierre CurisTec:

Initial State of Stress: The Key to Achieving Long-Term Cement-Sheath

Integrity. 2008 SPE 116651 ATCE, Denver, USA

30. Scott, J. B. and Brace, R. L.: Coated Casings - A Technique for Improved Cement

Bonding, Drilling and Prod. Prac., API (1966) 43-47.

31. Shahri, A.M., 2005. Detecting and modeling cement failure in high pressure/high

temperature wells, using finite element method. M.Sc. Thesis, A and M

University, Texas, USA.

32. Soliman, M. and Boonen, P. 2000. Rock mechanics and stimulation aspects of

horizontal wells, Journal of Petroleum Science and Engineering. Volume 25,

Issues 3–4, March 2000, Pages 187-204,

33. Stiles, D. 2006. Effects of Long-Term Exposure to Ultrahigh Temperature on the

Mechanical Parameters of Cement. 98896-MS IADC/SPE Drilling Conference,

21-23 February 2006, Miami, Florida, USA


71

34. Teodoriu, C., Ugwu, I., Schubert, J. 2010. Estimation of Casing-Cement-

Formation Interaction using a New Analytical Model. (SPE-131335) SPE

EUROPEC 2010, 14-17 June 2010, Barcelona, Spain

35. Vermylen, John P. 2011. Geomechanical Studies Of The Barnett Shale, Texas,

Usa Phd Dissertation Stanford University May 2011

36. Zoback, Mark .D. Reservoir Geomechanics Cambridge University Press, New

York, NY, USA (2007) 449 p


72

APPENDIX A

DATA SET FOR FAILURE TEST 100MPA

Step Confining

Stress Deviatoric

Stress Axial Strain Volumetric

Strain Distance

x Distance y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

2.65E+03 -1.00E+08 1.99E+06 1.73E-04 3.25E-03 8.53E+00 8.61E+00 -1.00E+08 -3.98E+06 1.99E+06 -9.95E+05

2.85E+03 -1.00E+08 2.14E+06 7.84E-04 3.43E-03 8.53E+00 8.61E+00 -1.00E+08 -4.27E+06 2.14E+06 -1.07E+06

3.05E+03 -1.00E+08 2.32E+06 1.79E-03 2.60E-03 8.53E+00 8.61E+00 -1.00E+08 -4.64E+06 2.32E+06 -1.16E+06

3.25E+03 -1.00E+08 2.64E+06 3.18E-03 1.36E-03 8.52E+00 8.61E+00 -1.00E+08 -5.28E+06 2.64E+06 -1.32E+06

3.45E+03 -1.00E+08 3.01E+06 4.97E-03 -2.85E-04 8.52E+00 8.61E+00 -1.00E+08 -6.03E+06 3.01E+06 -1.51E+06

3.65E+03 -1.00E+08 3.49E+06 7.15E-03 -2.27E-03 8.51E+00 8.61E+00 -1.00E+08 -6.99E+06 3.49E+06 -1.75E+06

3.85E+03 -1.00E+08 4.06E+06 9.72E-03 -4.63E-03 8.50E+00 8.61E+00 -1.00E+08 -8.11E+06 4.06E+06 -2.03E+06

4.05E+03 -1.00E+08 4.72E+06 1.27E-02 -7.34E-03 8.49E+00 8.61E+00 -1.00E+08 -9.43E+06 4.72E+06 -2.36E+06

4.25E+03 -1.00E+08 5.45E+06 1.60E-02 -1.04E-02 8.48E+00 8.62E+00 -1.00E+08 -1.09E+07 5.45E+06 -2.73E+06

4.45E+03 -1.00E+08 6.29E+06 1.98E-02 -1.39E-02 8.47E+00 8.62E+00 -1.00E+08 -1.26E+07 6.29E+06 -3.14E+06

4.65E+03 -1.00E+08 7.15E+06 2.37E-02 -1.74E-02 8.46E+00 8.62E+00 -1.00E+08 -1.43E+07 7.15E+06 -3.58E+06

4.85E+03 -1.00E+08 8.03E+06 2.76E-02 -2.10E-02 8.45E+00 8.62E+00 -1.00E+08 -1.61E+07 8.03E+06 -4.02E+06

5.05E+03 -1.00E+08 8.92E+06 3.16E-02 -2.46E-02 8.44E+00 8.62E+00 -1.00E+08 -1.78E+07 8.92E+06 -4.46E+06

5.25E+03 -1.00E+08 9.81E+06 3.55E-02 -2.82E-02 8.43E+00 8.62E+00 -1.00E+08 -1.96E+07 9.81E+06 -4.90E+06

5.45E+03 -1.00E+08 1.07E+07 3.94E-02 -3.17E-02 8.41E+00 8.62E+00 -1.00E+08 -2.14E+07 1.07E+07 -5.35E+06

5.65E+03 -1.00E+08 1.16E+07 4.33E-02 -3.53E-02 8.40E+00 8.63E+00 -1.00E+08 -2.32E+07 1.16E+07 -5.80E+06


73

Step Confining

Stress Deviatoric


Strain Distance

x Distance y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

5.85E+03 -1.00E+08 1.25E+07 4.73E-02 -3.89E-02 8.39E+00 8.63E+00 -1.00E+08 -2.50E+07 1.25E+07 -6.25E+06

6.05E+03 -1.00E+08 1.34E+07 5.12E-02 -4.25E-02 8.38E+00 8.63E+00 -1.00E+08 -2.68E+07 1.34E+07 -6.70E+06

7.05E+03 -1.00E+08 1.80E+07 7.08E-02 -6.04E-02 8.32E+00 8.64E+00 -1.00E+08 -3.60E+07 1.80E+07 -9.00E+06

7.25E+03 -1.00E+08 1.89E+07 7.48E-02 -6.40E-02 8.31E+00 8.64E+00 -1.00E+08 -3.79E+07 1.89E+07 -9.47E+06

7.45E+03 -1.00E+08 1.99E+07 7.87E-02 -6.75E-02 8.30E+00 8.64E+00 -1.00E+08 -3.97E+07 1.99E+07 -9.94E+06

7.65E+03 -1.00E+08 2.08E+07 8.26E-02 -7.11E-02 8.28E+00 8.64E+00 -1.00E+08 -4.16E+07 2.08E+07 -1.04E+07

8.05E+03 -1.00E+08 2.27E+07 9.05E-02 -7.83E-02 8.26E+00 8.64E+00 -1.00E+08 -4.54E+07 2.27E+07 -1.14E+07

8.25E+03 -1.00E+08 2.37E+07 9.44E-02 -8.18E-02 8.25E+00 8.65E+00 -1.00E+08 -4.73E+07 2.37E+07 -1.18E+07

8.45E+03 -1.00E+08 2.46E+07 9.83E-02 -8.54E-02 8.24E+00 8.65E+00 -1.00E+08 -4.92E+07 2.46E+07 -1.23E+07

8.65E+03 -1.00E+08 2.56E+07 1.02E-01 -8.90E-02 8.22E+00 8.65E+00 -1.00E+08 -5.12E+07 2.56E+07 -1.28E+07

8.85E+03 -1.00E+08 2.66E+07 1.06E-01 -9.26E-02 8.21E+00 8.65E+00 -1.00E+08 -5.31E+07 2.66E+07 -1.33E+07

9.25E+03 -1.00E+08 2.85E+07 1.14E-01 -9.97E-02 8.19E+00 8.65E+00 -1.00E+08 -5.70E+07 2.85E+07 -1.42E+07

9.45E+03 -1.00E+08 2.95E+07 1.18E-01 -1.03E-01 8.18E+00 8.66E+00 -1.00E+08 -5.90E+07 2.95E+07 -1.47E+07

9.65E+03 -1.00E+08 3.05E+07 1.22E-01 -1.07E-01 8.17E+00 8.66E+00 -1.00E+08 -6.09E+07 3.05E+07 -1.52E+07

9.85E+03 -1.00E+08 3.15E+07 1.26E-01 -1.10E-01 8.15E+00 8.66E+00 -1.00E+08 -6.29E+07 3.15E+07 -1.57E+07

1.01E+04 -1.00E+08 3.24E+07 1.30E-01 -1.14E-01 8.14E+00 8.66E+00 -1.00E+08 -6.49E+07 3.24E+07 -1.62E+07

1.03E+04 -1.00E+08 3.34E+07 1.34E-01 -1.18E-01 8.13E+00 8.66E+00 -1.00E+08 -6.69E+07 3.34E+07 -1.67E+07

1.05E+04 -1.00E+08 3.44E+07 1.38E-01 -1.21E-01 8.12E+00 8.66E+00 -1.00E+08 -6.89E+07 3.44E+07 -1.72E+07

1.07E+04 -1.00E+08 3.54E+07 1.42E-01 -1.25E-01 8.11E+00 8.67E+00 -1.00E+08 -7.09E+07 3.54E+07 -1.77E+07

1.09E+04 -1.00E+08 3.65E+07 1.46E-01 -1.28E-01 8.10E+00 8.67E+00 -1.00E+08 -7.29E+07 3.65E+07 -1.82E+07

1.11E+04 -1.00E+08 3.75E+07 1.49E-01 -1.32E-01 8.08E+00 8.67E+00 -1.00E+08 -7.50E+07 3.75E+07 -1.87E+07

1.13E+04 -1.00E+08 3.85E+07 1.53E-01 -1.35E-01 8.07E+00 8.67E+00 -1.00E+08 -7.70E+07 3.85E+07 -1.92E+07

1.15E+04 -1.00E+08 3.95E+07 1.57E-01 -1.39E-01 8.06E+00 8.67E+00 -1.00E+08 -7.90E+07 3.95E+07 -1.98E+07

1.17E+04 -1.00E+08 4.06E+07 1.61E-01 -1.43E-01 8.05E+00 8.67E+00 -1.00E+08 -8.11E+07 4.06E+07 -2.03E+07

1.19E+04 -1.00E+08 4.16E+07 1.65E-01 -1.46E-01 8.04E+00 8.68E+00 -1.00E+08 -8.32E+07 4.16E+07 -2.08E+07


74

Step Confining

Stress Deviatoric


Strain Distance

x Distance y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

1.21E+04 -1.00E+08 4.26E+07 1.69E-01 -1.50E-01 8.02E+00 8.68E+00 -1.00E+08 -8.52E+07 4.26E+07 -2.13E+07

1.23E+04 -1.00E+08 4.37E+07 1.73E-01 -1.53E-01 8.01E+00 8.68E+00 -1.00E+08 -8.73E+07 4.37E+07 -2.18E+07

1.25E+04 -1.00E+08 4.47E+07 1.77E-01 -1.57E-01 8.00E+00 8.68E+00 -1.00E+08 -8.94E+07 4.47E+07 -2.24E+07

1.27E+04 -1.00E+08 4.58E+07 1.81E-01 -1.60E-01 7.99E+00 8.68E+00 -1.00E+08 -9.15E+07 4.58E+07 -2.29E+07

1.29E+04 -1.00E+08 4.68E+07 1.85E-01 -1.64E-01 7.98E+00 8.68E+00 -1.00E+08 -9.36E+07 4.68E+07 -2.34E+07

1.31E+04 -1.00E+08 4.79E+07 1.89E-01 -1.68E-01 7.97E+00 8.69E+00 -1.00E+08 -9.57E+07 4.79E+07 -2.39E+07

1.33E+04 -1.00E+08 4.89E+07 1.93E-01 -1.71E-01 7.95E+00 8.69E+00 -1.00E+08 -9.79E+07 4.89E+07 -2.45E+07

1.35E+04 -1.00E+08 5.00E+07 1.97E-01 -1.75E-01 7.94E+00 8.69E+00 -1.00E+08 -1.00E+08 5.00E+07 -2.50E+07

1.37E+04 -1.00E+08 5.11E+07 2.01E-01 -1.78E-01 7.93E+00 8.69E+00 -1.00E+08 -1.02E+08 5.11E+07 -2.55E+07

1.39E+04 -1.00E+08 5.22E+07 2.05E-01 -1.82E-01 7.92E+00 8.69E+00 -1.00E+08 -1.04E+08 5.22E+07 -2.61E+07

1.41E+04 -1.00E+08 5.32E+07 2.09E-01 -1.85E-01 7.91E+00 8.69E+00 -1.00E+08 -1.06E+08 5.32E+07 -2.66E+07

1.43E+04 -1.00E+08 5.43E+07 2.12E-01 -1.89E-01 7.89E+00 8.70E+00 -1.00E+08 -1.09E+08 5.43E+07 -2.72E+07

1.45E+04 -1.00E+08 5.54E+07 2.16E-01 -1.92E-01 7.88E+00 8.70E+00 -1.00E+08 -1.11E+08 5.54E+07 -2.77E+07

1.47E+04 -1.00E+08 5.65E+07 2.20E-01 -1.96E-01 7.87E+00 8.70E+00 -1.00E+08 -1.13E+08 5.65E+07 -2.83E+07

1.49E+04 -1.00E+08 5.76E+07 2.24E-01 -2.00E-01 7.86E+00 8.70E+00 -1.00E+08 -1.15E+08 5.76E+07 -2.88E+07

1.51E+04 -1.00E+08 5.87E+07 2.28E-01 -2.03E-01 7.85E+00 8.70E+00 -1.00E+08 -1.17E+08 5.87E+07 -2.94E+07

1.53E+04 -1.00E+08 5.98E+07 2.32E-01 -2.07E-01 7.84E+00 8.70E+00 -1.00E+08 -1.20E+08 5.98E+07 -2.99E+07

1.55E+04 -1.00E+08 6.09E+07 2.36E-01 -2.10E-01 7.82E+00 8.71E+00 -1.00E+08 -1.22E+08 6.09E+07 -3.05E+07

1.57E+04 -1.00E+08 6.21E+07 2.40E-01 -2.14E-01 7.81E+00 8.71E+00 -1.00E+08 -1.24E+08 6.21E+07 -3.10E+07

1.59E+04 -1.00E+08 6.32E+07 2.44E-01 -2.17E-01 7.80E+00 8.71E+00 -1.00E+08 -1.26E+08 6.32E+07 -3.16E+07

1.61E+04 -1.00E+08 6.43E+07 2.48E-01 -2.21E-01 7.79E+00 8.71E+00 -1.00E+08 -1.29E+08 6.43E+07 -3.21E+07

1.63E+04 -1.00E+08 6.54E+07 2.52E-01 -2.24E-01 7.78E+00 8.71E+00 -1.00E+08 -1.31E+08 6.54E+07 -3.27E+07

1.65E+04 -1.00E+08 6.66E+07 2.56E-01 -2.28E-01 7.76E+00 8.71E+00 -1.00E+08 -1.33E+08 6.66E+07 -3.33E+07

1.67E+04 -1.00E+08 6.65E+07 2.56E-01 -2.28E-01 7.76E+00 8.72E+00 -1.00E+08 -1.33E+08 6.65E+07 -3.33E+07

1.69E+04 -1.00E+08 6.63E+07 2.55E-01 -2.27E-01 7.77E+00 8.72E+00 -1.00E+08 -1.33E+08 6.63E+07 -3.32E+07

1.71E+04 -1.00E+08 6.61E+07 2.54E-01 -2.26E-01 7.77E+00 8.71E+00 -1.00E+08 -1.32E+08 6.61E+07 -3.30E+07


75

Step Confining

Stress Deviatoric


Strain Distance

x Distance y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

1.75E+04 -1.00E+08 6.51E+07 2.51E-01 -2.23E-01 7.78E+00 8.71E+00 -1.00E+08 -1.30E+08 6.51E+07 -3.26E+07

1.77E+04 -1.00E+08 6.45E+07 2.49E-01 -2.21E-01 7.79E+00 8.71E+00 -1.00E+08 -1.29E+08 6.45E+07 -3.23E+07

1.79E+04 -1.00E+08 6.38E+07 2.46E-01 -2.19E-01 7.79E+00 8.71E+00 -1.00E+08 -1.28E+08 6.38E+07 -3.19E+07

1.81E+04 -1.00E+08 6.29E+07 2.43E-01 -2.16E-01 7.80E+00 8.71E+00 -1.00E+08 -1.26E+08 6.29E+07 -3.15E+07

1.83E+04 -1.00E+08 6.19E+07 2.40E-01 -2.13E-01 7.81E+00 8.71E+00 -1.00E+08 -1.24E+08 6.19E+07 -3.10E+07

1.85E+04 -1.00E+08 6.09E+07 2.36E-01 -2.10E-01 7.82E+00 8.71E+00 -1.00E+08 -1.22E+08 6.09E+07 -3.04E+07

1.87E+04 -1.00E+08 5.98E+07 2.32E-01 -2.06E-01 7.84E+00 8.71E+00 -1.00E+08 -1.20E+08 5.98E+07 -2.99E+07

1.89E+04 -1.00E+08 5.87E+07 2.28E-01 -2.03E-01 7.85E+00 8.70E+00 -1.00E+08 -1.17E+08 5.87E+07 -2.93E+07

1.91E+04 -1.00E+08 5.76E+07 2.24E-01 -1.99E-01 7.86E+00 8.70E+00 -1.00E+08 -1.15E+08 5.76E+07 -2.88E+07

1.93E+04 -1.00E+08 5.65E+07 2.20E-01 -1.96E-01 7.87E+00 8.70E+00 -1.00E+08 -1.13E+08 5.65E+07 -2.82E+07

1.95E+04 -1.00E+08 5.54E+07 2.16E-01 -1.92E-01 7.88E+00 8.70E+00 -1.00E+08 -1.11E+08 5.54E+07 -2.77E+07

1.97E+04 -1.00E+08 5.43E+07 2.12E-01 -1.88E-01 7.89E+00 8.70E+00 -1.00E+08 -1.09E+08 5.43E+07 -2.71E+07

1.99E+04 -1.00E+08 5.32E+07 2.08E-01 -1.85E-01 7.91E+00 8.70E+00 -1.00E+08 -1.06E+08 5.32E+07 -2.66E+07

2.01E+04 -1.00E+08 5.21E+07 2.04E-01 -1.81E-01 7.92E+00 8.69E+00 -1.00E+08 -1.04E+08 5.21E+07 -2.61E+07

2.03E+04 -1.00E+08 5.10E+07 2.00E-01 -1.78E-01 7.93E+00 8.69E+00 -1.00E+08 -1.02E+08 5.10E+07 -2.55E+07

2.05E+04 -1.00E+08 4.99E+07 1.97E-01 -1.74E-01 7.94E+00 8.69E+00 -1.00E+08 -9.99E+07 4.99E+07 -2.50E+07

2.07E+04 -1.00E+08 4.89E+07 1.93E-01 -1.71E-01 7.95E+00 8.69E+00 -1.00E+08 -9.78E+07 4.89E+07 -2.44E+07

2.09E+04 -1.00E+08 4.78E+07 1.89E-01 -1.67E-01 7.97E+00 8.69E+00 -1.00E+08 -9.56E+07 4.78E+07 -2.39E+07

2.11E+04 -1.00E+08 4.73E+07 1.87E-01 -1.65E-01 7.97E+00 8.69E+00 -1.00E+08 -9.46E+07 4.73E+07 -2.37E+07

2.13E+04 -1.00E+08 4.74E+07 1.87E-01 -1.66E-01 7.97E+00 8.69E+00 -1.00E+08 -9.48E+07 4.74E+07 -2.37E+07

2.15E+04 -1.00E+08 4.76E+07 1.88E-01 -1.67E-01 7.97E+00 8.69E+00 -1.00E+08 -9.53E+07 4.76E+07 -2.38E+07

2.17E+04 -1.00E+08 4.79E+07 1.89E-01 -1.68E-01 7.96E+00 8.69E+00 -1.00E+08 -9.59E+07 4.79E+07 -2.40E+07

2.19E+04 -1.00E+08 4.84E+07 1.91E-01 -1.69E-01 7.96E+00 8.69E+00 -1.00E+08 -9.67E+07 4.84E+07 -2.42E+07

2.21E+04 -1.00E+08 4.89E+07 1.93E-01 -1.71E-01 7.95E+00 8.69E+00 -1.00E+08 -9.78E+07 4.89E+07 -2.45E+07

2.23E+04 -1.00E+08 4.96E+07 1.95E-01 -1.73E-01 7.95E+00 8.69E+00 -1.00E+08 -9.91E+07 4.96E+07 -2.48E+07

2.25E+04 -1.00E+08 5.03E+07 1.98E-01 -1.76E-01 7.94E+00 8.69E+00 -1.00E+08 -1.01E+08 5.03E+07 -2.52E+07


76

Step Confining

Stress Deviatoric


Strain Distance

x Distance y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

2.27E+04 -1.00E+08 5.12E+07 2.01E-01 -1.79E-01 7.93E+00 8.69E+00 -1.00E+08 -1.02E+08 5.12E+07 -2.56E+07

2.29E+04 -1.00E+08 5.22E+07 2.05E-01 -1.82E-01 7.92E+00 8.69E+00 -1.00E+08 -1.04E+08 5.22E+07 -2.61E+07

2.31E+04 -1.00E+08 5.32E+07 2.09E-01 -1.85E-01 7.91E+00 8.69E+00 -1.00E+08 -1.06E+08 5.32E+07 -2.66E+07

2.33E+04 -1.00E+08 5.43E+07 2.13E-01 -1.89E-01 7.89E+00 8.70E+00 -1.00E+08 -1.09E+08 5.43E+07 -2.72E+07

2.35E+04 -1.00E+08 5.54E+07 2.16E-01 -1.92E-01 7.88E+00 8.70E+00 -1.00E+08 -1.11E+08 5.54E+07 -2.77E+07

2.37E+04 -1.00E+08 5.65E+07 2.20E-01 -1.96E-01 7.87E+00 8.70E+00 -1.00E+08 -1.13E+08 5.65E+07 -2.82E+07

2.39E+04 -1.00E+08 5.76E+07 2.24E-01 -2.00E-01 7.86E+00 8.70E+00 -1.00E+08 -1.15E+08 5.76E+07 -2.88E+07

2.41E+04 -1.00E+08 5.87E+07 2.28E-01 -2.03E-01 7.85E+00 8.70E+00 -1.00E+08 -1.17E+08 5.87E+07 -2.93E+07

2.43E+04 -1.00E+08 5.98E+07 2.32E-01 -2.07E-01 7.84E+00 8.70E+00 -1.00E+08 -1.20E+08 5.98E+07 -2.99E+07

2.45E+04 -1.00E+08 6.09E+07 2.36E-01 -2.10E-01 7.82E+00 8.71E+00 -1.00E+08 -1.22E+08 6.09E+07 -3.05E+07

2.47E+04 -1.00E+08 6.20E+07 2.40E-01 -2.14E-01 7.81E+00 8.71E+00 -1.00E+08 -1.24E+08 6.20E+07 -3.10E+07

2.49E+04 -1.00E+08 6.32E+07 2.44E-01 -2.17E-01 7.80E+00 8.71E+00 -1.00E+08 -1.26E+08 6.32E+07 -3.16E+07

2.51E+04 -1.00E+08 6.43E+07 2.48E-01 -2.21E-01 7.79E+00 8.71E+00 -1.00E+08 -1.29E+08 6.43E+07 -3.21E+07

2.53E+04 -1.00E+08 6.54E+07 2.52E-01 -2.24E-01 7.78E+00 8.71E+00 -1.00E+08 -1.31E+08 6.54E+07 -3.27E+07

2.55E+04 -1.00E+08 6.66E+07 2.56E-01 -2.28E-01 7.76E+00 8.71E+00 -1.00E+08 -1.33E+08 6.66E+07 -3.33E+07

2.57E+04 -1.00E+08 6.77E+07 2.60E-01 -2.32E-01 7.75E+00 8.72E+00 -1.00E+08 -1.35E+08 6.77E+07 -3.39E+07

2.59E+04 -1.00E+08 6.89E+07 2.64E-01 -2.35E-01 7.74E+00 8.72E+00 -1.00E+08 -1.38E+08 6.89E+07 -3.44E+07

2.61E+04 -1.00E+08 7.00E+07 2.68E-01 -2.39E-01 7.73E+00 8.72E+00 -1.00E+08 -1.40E+08 7.00E+07 -3.50E+07

2.63E+04 -1.00E+08 7.12E+07 2.72E-01 -2.42E-01 7.72E+00 8.72E+00 -1.00E+08 -1.42E+08 7.12E+07 -3.56E+07

2.65E+04 -1.00E+08 7.23E+07 2.76E-01 -2.46E-01 7.70E+00 8.72E+00 -1.00E+08 -1.45E+08 7.23E+07 -3.62E+07

2.67E+04 -1.00E+08 7.35E+07 2.80E-01 -2.49E-01 7.69E+00 8.73E+00 -1.00E+08 -1.47E+08 7.35E+07 -3.68E+07

2.69E+04 -1.00E+08 7.47E+07 2.84E-01 -2.53E-01 7.68E+00 8.73E+00 -1.00E+08 -1.49E+08 7.47E+07 -3.73E+07

2.71E+04 -1.00E+08 7.59E+07 2.87E-01 -2.56E-01 7.67E+00 8.73E+00 -1.00E+08 -1.52E+08 7.59E+07 -3.79E+07

2.73E+04 -1.00E+08 7.71E+07 2.91E-01 -2.60E-01 7.66E+00 8.73E+00 -1.00E+08 -1.54E+08 7.71E+07 -3.85E+07

2.75E+04 -1.00E+08 7.83E+07 2.95E-01 -2.64E-01 7.65E+00 8.73E+00 -1.00E+08 -1.57E+08 7.83E+07 -3.91E+07

2.77E+04 -1.00E+08 7.95E+07 2.99E-01 -2.67E-01 7.63E+00 8.73E+00 -1.00E+08 -1.59E+08 7.95E+07 -3.97E+07


77

Step Confining

Stress Deviatoric


Strain Distance

x Distance y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

2.79E+04 -1.00E+08 8.07E+07 3.03E-01 -2.71E-01 7.62E+00 8.74E+00 -1.00E+08 -1.61E+08 8.07E+07 -4.03E+07

2.81E+04 -1.00E+08 8.19E+07 3.07E-01 -2.74E-01 7.61E+00 8.74E+00 -1.00E+08 -1.64E+08 8.19E+07 -4.09E+07

2.83E+04 -1.00E+08 8.31E+07 3.11E-01 -2.78E-01 7.60E+00 8.74E+00 -1.00E+08 -1.66E+08 8.31E+07 -4.15E+07

2.85E+04 -1.00E+08 8.43E+07 3.15E-01 -2.81E-01 7.59E+00 8.74E+00 -1.00E+08 -1.69E+08 8.43E+07 -4.21E+07

2.87E+04 -1.00E+08 8.55E+07 3.19E-01 -2.85E-01 7.57E+00 8.74E+00 -1.00E+08 -1.71E+08 8.55E+07 -4.28E+07

2.89E+04 -1.00E+08 8.67E+07 3.23E-01 -2.88E-01 7.56E+00 8.75E+00 -1.00E+08 -1.74E+08 8.67E+07 -4.34E+07

2.91E+04 -1.00E+08 8.80E+07 3.27E-01 -2.92E-01 7.55E+00 8.75E+00 -1.00E+08 -1.76E+08 8.80E+07 -4.40E+07

2.93E+04 -1.00E+08 8.92E+07 3.31E-01 -2.95E-01 7.54E+00 8.75E+00 -1.00E+08 -1.78E+08 8.92E+07 -4.46E+07

2.95E+04 -1.00E+08 9.05E+07 3.35E-01 -2.99E-01 7.53E+00 8.75E+00 -1.00E+08 -1.81E+08 9.05E+07 -4.52E+07

2.97E+04 -1.00E+08 9.17E+07 3.39E-01 -3.02E-01 7.52E+00 8.75E+00 -1.00E+08 -1.83E+08 9.17E+07 -4.59E+07

2.99E+04 -1.00E+08 9.30E+07 3.43E-01 -3.06E-01 7.50E+00 8.76E+00 -1.00E+08 -1.86E+08 9.30E+07 -4.65E+07

3.01E+04 -1.00E+08 9.43E+07 3.47E-01 -3.10E-01 7.49E+00 8.76E+00 -1.00E+08 -1.89E+08 9.43E+07 -4.71E+07

3.03E+04 -1.00E+08 9.55E+07 3.51E-01 -3.13E-01 7.48E+00 8.76E+00 -1.00E+08 -1.91E+08 9.55E+07 -4.78E+07

3.05E+04 -1.00E+08 9.68E+07 3.55E-01 -3.17E-01 7.47E+00 8.76E+00 -1.00E+08 -1.94E+08 9.68E+07 -4.84E+07

3.07E+04 -1.00E+08 9.81E+07 3.59E-01 -3.20E-01 7.46E+00 8.76E+00 -1.00E+08 -1.96E+08 9.81E+07 -4.91E+07

3.11E+04 -1.00E+08 1.01E+08 3.67E-01 -3.27E-01 7.43E+00 8.77E+00 -1.00E+08 -2.01E+08 1.01E+08 -5.04E+07

3.13E+04 -1.00E+08 1.02E+08 3.71E-01 -3.31E-01 7.42E+00 8.77E+00 -1.00E+08 -2.04E+08 1.02E+08 -5.10E+07

3.15E+04 -1.00E+08 1.03E+08 3.75E-01 -3.34E-01 7.41E+00 8.77E+00 -1.00E+08 -2.07E+08 1.03E+08 -5.17E+07

3.17E+04 -1.00E+08 1.05E+08 3.78E-01 -3.38E-01 7.40E+00 8.77E+00 -1.00E+08 -2.09E+08 1.05E+08 -5.23E+07

3.19E+04 -1.00E+08 1.06E+08 3.82E-01 -3.41E-01 7.38E+00 8.78E+00 -1.00E+08 -2.12E+08 1.06E+08 -5.30E+07

3.21E+04 -1.00E+08 1.07E+08 3.86E-01 -3.45E-01 7.37E+00 8.78E+00 -1.00E+08 -2.15E+08 1.07E+08 -5.36E+07

3.23E+04 -1.00E+08 1.09E+08 3.90E-01 -3.48E-01 7.36E+00 8.78E+00 -1.00E+08 -2.17E+08 1.09E+08 -5.43E+07

3.25E+04 -1.00E+08 1.10E+08 3.94E-01 -3.52E-01 7.35E+00 8.78E+00 -1.00E+08 -2.20E+08 1.10E+08 -5.50E+07

3.27E+04 -1.00E+08 1.11E+08 3.98E-01 -3.55E-01 7.34E+00 8.78E+00 -1.00E+08 -2.23E+08 1.11E+08 -5.56E+07

3.29E+04 -1.00E+08 1.13E+08 4.02E-01 -3.59E-01 7.33E+00 8.79E+00 -1.00E+08 -2.25E+08 1.13E+08 -5.63E+07

3.31E+04 -1.00E+08 1.14E+08 4.06E-01 -3.62E-01 7.31E+00 8.79E+00 -1.00E+08 -2.28E+08 1.14E+08 -5.70E+07


78

Step Confining

Stress Deviatoric


Strain Distance

x Distance y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

3.33E+04 -1.00E+08 1.15E+08 4.10E-01 -3.66E-01 7.30E+00 8.79E+00 -1.00E+08 -2.31E+08 1.15E+08 -5.77E+07

3.35E+04 -1.00E+08 1.17E+08 4.14E-01 -3.69E-01 7.29E+00 8.79E+00 -1.00E+08 -2.33E+08 1.17E+08 -5.84E+07

3.37E+04 -1.00E+08 1.18E+08 4.18E-01 -3.73E-01 7.28E+00 8.79E+00 -1.00E+08 -2.36E+08 1.18E+08 -5.91E+07

3.39E+04 -1.00E+08 1.19E+08 4.22E-01 -3.76E-01 7.27E+00 8.80E+00 -1.00E+08 -2.39E+08 1.19E+08 -5.97E+07

3.41E+04 -1.00E+08 1.21E+08 4.26E-01 -3.80E-01 7.25E+00 8.80E+00 -1.00E+08 -2.41E+08 1.21E+08 -6.04E+07

3.43E+04 -1.00E+08 1.22E+08 4.30E-01 -3.83E-01 7.24E+00 8.80E+00 -1.00E+08 -2.44E+08 1.22E+08 -6.11E+07

3.45E+04 -1.00E+08 1.24E+08 4.34E-01 -3.87E-01 7.23E+00 8.80E+00 -1.00E+08 -2.47E+08 1.24E+08 -6.18E+07

3.47E+04 -1.00E+08 1.25E+08 4.38E-01 -3.90E-01 7.22E+00 8.81E+00 -1.00E+08 -2.50E+08 1.25E+08 -6.24E+07

3.49E+04 -1.00E+08 1.26E+08 4.42E-01 -3.94E-01 7.21E+00 8.81E+00 -1.00E+08 -2.53E+08 1.26E+08 -6.31E+07

3.51E+04 -1.00E+08 1.28E+08 4.46E-01 -3.97E-01 7.19E+00 8.81E+00 -1.00E+08 -2.55E+08 1.28E+08 -6.38E+07

3.57E+04 -1.00E+08 1.32E+08 4.58E-01 -4.07E-01 7.16E+00 8.82E+00 -1.00E+08 -2.64E+08 1.32E+08 -6.59E+07

3.59E+04 -1.00E+08 1.33E+08 4.62E-01 -4.11E-01 7.15E+00 8.82E+00 -1.00E+08 -2.66E+08 1.33E+08 -6.66E+07

3.61E+04 -1.00E+08 1.35E+08 4.66E-01 -4.14E-01 7.13E+00 8.82E+00 -1.00E+08 -2.69E+08 1.35E+08 -6.73E+07

3.63E+04 -1.00E+08 1.36E+08 4.70E-01 -4.18E-01 7.12E+00 8.82E+00 -1.00E+08 -2.72E+08 1.36E+08 -6.80E+07

3.65E+04 -1.00E+08 1.37E+08 4.74E-01 -4.21E-01 7.11E+00 8.83E+00 -1.00E+08 -2.75E+08 1.37E+08 -6.87E+07

3.67E+04 -1.00E+08 1.39E+08 4.78E-01 -4.24E-01 7.10E+00 8.83E+00 -1.00E+08 -2.78E+08 1.39E+08 -6.94E+07

3.69E+04 -1.00E+08 1.40E+08 4.82E-01 -4.28E-01 7.09E+00 8.83E+00 -1.00E+08 -2.81E+08 1.40E+08 -7.01E+07

3.71E+04 -1.00E+08 1.42E+08 4.85E-01 -4.31E-01 7.08E+00 8.83E+00 -1.00E+08 -2.83E+08 1.42E+08 -7.08E+07

3.73E+04 -1.00E+08 1.43E+08 4.89E-01 -4.35E-01 7.06E+00 8.84E+00 -1.00E+08 -2.86E+08 1.43E+08 -7.15E+07

3.75E+04 -1.00E+08 1.44E+08 4.93E-01 -4.38E-01 7.05E+00 8.84E+00 -1.00E+08 -2.89E+08 1.44E+08 -7.22E+07

3.77E+04 -1.00E+08 1.46E+08 4.97E-01 -4.42E-01 7.04E+00 8.84E+00 -1.00E+08 -2.91E+08 1.46E+08 -7.29E+07

3.79E+04 -1.00E+08 1.47E+08 5.01E-01 -4.45E-01 7.03E+00 8.84E+00 -1.00E+08 -2.94E+08 1.47E+08 -7.35E+07

3.81E+04 -1.00E+08 1.49E+08 5.05E-01 -4.48E-01 7.02E+00 8.85E+00 -1.00E+08 -2.97E+08 1.49E+08 -7.43E+07

3.83E+04 -1.00E+08 1.50E+08 5.09E-01 -4.52E-01 7.00E+00 8.85E+00 -1.00E+08 -3.00E+08 1.50E+08 -7.50E+07

3.87E+04 -1.00E+08 1.52E+08 5.17E-01 -4.58E-01 6.98E+00 8.86E+00 -1.00E+08 -3.05E+08 1.52E+08 -7.62E+07

3.89E+04 -1.00E+08 1.54E+08 5.21E-01 -4.62E-01 6.97E+00 8.86E+00 -1.00E+08 -3.08E+08 1.54E+08 -7.69E+07


79

Step # Microcracks # Microcracks(CNF) # Microcracks(CSF) # Microcracks(PNF) # Microcracks(PSF)

2.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

6.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

6.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

6.45E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

6.65E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

6.85E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

7.05E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

7.25E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

7.45E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00


80


7.65E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

7.85E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

8.05E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

8.25E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

8.45E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

8.65E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

8.85E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

9.05E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

9.25E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

9.45E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

9.65E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

9.85E+03 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.01E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.03E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.05E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.07E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.09E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.11E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.13E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.15E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.17E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.19E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.21E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.23E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.25E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.27E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00


81


1.29E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.31E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

1.33E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

1.35E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

1.37E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

1.39E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

1.41E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

1.43E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

1.45E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

1.47E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

1.49E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

1.51E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

1.53E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

1.55E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

1.57E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

1.59E+04 4.00E+00 0.00E+00 4.00E+00 0.00E+00 0.00E+00

1.61E+04 4.00E+00 0.00E+00 4.00E+00 0.00E+00 0.00E+00

1.63E+04 7.00E+00 0.00E+00 7.00E+00 0.00E+00 0.00E+00

1.65E+04 7.00E+00 0.00E+00 7.00E+00 0.00E+00 0.00E+00

1.67E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.69E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.71E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.73E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.75E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.77E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.79E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00


82


1.81E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.83E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.85E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.87E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.89E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.91E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.93E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.95E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.97E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

1.99E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.01E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.03E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.05E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.07E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.09E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.11E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.13E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.15E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.17E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.19E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.21E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.23E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.25E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.27E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.29E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.31E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00


83


2.33E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.35E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.37E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.39E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.41E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.43E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.45E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.47E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.49E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.51E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.53E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.55E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

2.57E+04 9.00E+00 0.00E+00 9.00E+00 0.00E+00 0.00E+00

2.59E+04 1.00E+01 0.00E+00 1.00E+01 0.00E+00 0.00E+00

2.61E+04 1.00E+01 0.00E+00 1.00E+01 0.00E+00 0.00E+00

2.63E+04 1.00E+01 0.00E+00 1.00E+01 0.00E+00 0.00E+00

2.65E+04 1.00E+01 0.00E+00 1.00E+01 0.00E+00 0.00E+00

2.67E+04 1.10E+01 0.00E+00 1.10E+01 0.00E+00 0.00E+00

2.69E+04 1.30E+01 0.00E+00 1.30E+01 0.00E+00 0.00E+00

2.71E+04 1.30E+01 0.00E+00 1.30E+01 0.00E+00 0.00E+00

2.73E+04 1.50E+01 0.00E+00 1.50E+01 0.00E+00 0.00E+00

2.75E+04 1.70E+01 0.00E+00 1.70E+01 0.00E+00 0.00E+00

2.77E+04 1.70E+01 0.00E+00 1.70E+01 0.00E+00 0.00E+00

2.79E+04 1.70E+01 0.00E+00 1.70E+01 0.00E+00 0.00E+00

2.81E+04 1.90E+01 0.00E+00 1.90E+01 0.00E+00 0.00E+00

2.83E+04 1.90E+01 0.00E+00 1.90E+01 0.00E+00 0.00E+00


84


2.85E+04 1.90E+01 0.00E+00 1.90E+01 0.00E+00 0.00E+00

2.87E+04 2.10E+01 0.00E+00 2.10E+01 0.00E+00 0.00E+00

2.89E+04 2.10E+01 0.00E+00 2.10E+01 0.00E+00 0.00E+00

2.91E+04 2.30E+01 0.00E+00 2.30E+01 0.00E+00 0.00E+00

2.93E+04 2.60E+01 0.00E+00 2.60E+01 0.00E+00 0.00E+00

2.95E+04 2.60E+01 0.00E+00 2.60E+01 0.00E+00 0.00E+00

2.97E+04 2.70E+01 0.00E+00 2.70E+01 0.00E+00 0.00E+00

2.99E+04 2.80E+01 0.00E+00 2.80E+01 0.00E+00 0.00E+00

3.01E+04 2.90E+01 0.00E+00 2.90E+01 0.00E+00 0.00E+00

3.03E+04 3.10E+01 0.00E+00 3.10E+01 0.00E+00 0.00E+00

3.05E+04 3.30E+01 0.00E+00 3.30E+01 0.00E+00 0.00E+00

3.07E+04 3.30E+01 0.00E+00 3.30E+01 0.00E+00 0.00E+00

3.09E+04 3.40E+01 0.00E+00 3.40E+01 0.00E+00 0.00E+00

3.11E+04 3.50E+01 0.00E+00 3.50E+01 0.00E+00 0.00E+00

3.13E+04 3.60E+01 0.00E+00 3.60E+01 0.00E+00 0.00E+00

3.15E+04 3.60E+01 0.00E+00 3.60E+01 0.00E+00 0.00E+00

3.17E+04 3.90E+01 0.00E+00 3.90E+01 0.00E+00 0.00E+00

3.19E+04 4.20E+01 0.00E+00 4.20E+01 0.00E+00 0.00E+00

3.21E+04 4.50E+01 0.00E+00 4.50E+01 0.00E+00 0.00E+00

3.23E+04 5.00E+01 0.00E+00 5.00E+01 0.00E+00 0.00E+00

3.25E+04 5.40E+01 0.00E+00 5.40E+01 0.00E+00 0.00E+00

3.27E+04 5.60E+01 0.00E+00 5.60E+01 0.00E+00 0.00E+00

3.29E+04 5.90E+01 0.00E+00 5.90E+01 0.00E+00 0.00E+00

3.31E+04 6.50E+01 0.00E+00 6.50E+01 0.00E+00 0.00E+00

3.33E+04 6.80E+01 0.00E+00 6.80E+01 0.00E+00 0.00E+00

3.35E+04 7.20E+01 0.00E+00 7.20E+01 0.00E+00 0.00E+00


85


3.37E+04 7.80E+01 0.00E+00 7.80E+01 0.00E+00 0.00E+00

3.39E+04 8.40E+01 0.00E+00 8.40E+01 0.00E+00 0.00E+00

3.41E+04 8.70E+01 0.00E+00 8.70E+01 0.00E+00 0.00E+00

3.43E+04 8.90E+01 0.00E+00 8.90E+01 0.00E+00 0.00E+00

3.45E+04 1.01E+02 0.00E+00 1.01E+02 0.00E+00 0.00E+00

3.47E+04 1.12E+02 0.00E+00 1.12E+02 0.00E+00 0.00E+00

3.51E+04 1.27E+02 0.00E+00 1.27E+02 0.00E+00 0.00E+00

3.53E+04 1.34E+02 0.00E+00 1.34E+02 0.00E+00 0.00E+00

3.57E+04 1.44E+02 0.00E+00 1.44E+02 0.00E+00 0.00E+00

3.59E+04 1.53E+02 0.00E+00 1.53E+02 0.00E+00 0.00E+00

3.61E+04 1.63E+02 0.00E+00 1.63E+02 0.00E+00 0.00E+00

3.65E+04 1.77E+02 0.00E+00 1.77E+02 0.00E+00 0.00E+00

3.67E+04 1.87E+02 0.00E+00 1.87E+02 0.00E+00 0.00E+00

3.69E+04 1.95E+02 0.00E+00 1.95E+02 0.00E+00 0.00E+00

3.71E+04 2.06E+02 0.00E+00 2.06E+02 0.00E+00 0.00E+00

3.73E+04 2.13E+02 0.00E+00 2.13E+02 0.00E+00 0.00E+00

3.75E+04 2.25E+02 0.00E+00 2.25E+02 0.00E+00 0.00E+00

3.77E+04 2.33E+02 0.00E+00 2.33E+02 0.00E+00 0.00E+00

3.79E+04 2.41E+02 0.00E+00 2.41E+02 0.00E+00 0.00E+00

3.81E+04 2.53E+02 0.00E+00 2.53E+02 0.00E+00 0.00E+00

3.83E+04 2.60E+02 0.00E+00 2.60E+02 0.00E+00 0.00E+00

3.85E+04 2.70E+02 0.00E+00 2.70E+02 0.00E+00 0.00E+00

3.87E+04 2.75E+02 0.00E+00 2.75E+02 0.00E+00 0.00E+00

3.89E+04 2.83E+02 0.00E+00 2.83E+02 0.00E+00 0.00E+00

CNF = Contact bond normal failure CSF = Contact bond shear failure

PNF = Parallel bond normal failure PSF = Parallel bond shear failure


86

APPENDIX B

DATA SET FOR FAILURE TEST 10 MPA

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

3.65E+03 -1.00E+07 9.33E+04 2.11E-04 -4.26E-05 1.07E+01 1.08E+01 -1.00E+07 -1.87E+05 9.33E+04 -4.66E+04

3.85E+03 -1.00E+07 1.36E+05 8.11E-04 -4.88E-04 1.07E+01 1.08E+01 -1.00E+07 -2.71E+05 1.36E+05 -6.78E+04

4.25E+03 -1.00E+07 3.06E+05 3.17E-03 -2.69E-03 1.07E+01 1.08E+01 -1.00E+07 -6.13E+05 3.06E+05 -1.53E+05

4.45E+03 -1.00E+07 4.40E+05 4.92E-03 -4.35E-03 1.07E+01 1.08E+01 -1.00E+07 -8.80E+05 4.40E+05 -2.20E+05

4.85E+03 -1.00E+07 7.85E+05 9.59E-03 -8.75E-03 1.07E+01 1.08E+01 -1.00E+07 -1.57E+06 7.85E+05 -3.93E+05

5.05E+03 -1.00E+07 9.97E+05 1.25E-02 -1.15E-02 1.07E+01 1.08E+01 -1.00E+07 -1.99E+06 9.97E+05 -4.99E+05

5.25E+03 -1.00E+07 1.25E+06 1.58E-02 -1.46E-02 1.07E+01 1.09E+01 -1.00E+07 -2.50E+06 1.25E+06 -6.24E+05

5.45E+03 -1.00E+07 1.53E+06 1.95E-02 -1.81E-02 1.07E+01 1.09E+01 -1.00E+07 -3.05E+06 1.53E+06 -7.64E+05

5.65E+03 -1.00E+07 1.81E+06 2.33E-02 -2.17E-02 1.07E+01 1.09E+01 -1.00E+07 -3.62E+06 1.81E+06 -9.05E+05

5.85E+03 -1.00E+07 2.11E+06 2.72E-02 -2.53E-02 1.07E+01 1.09E+01 -1.00E+07 -4.23E+06 2.11E+06 -1.06E+06

6.05E+03 -1.00E+07 2.42E+06 3.11E-02 -2.89E-02 1.06E+01 1.09E+01 -1.00E+07 -4.83E+06 2.42E+06 -1.21E+06

6.25E+03 -1.00E+07 2.72E+06 3.49E-02 -3.25E-02 1.06E+01 1.09E+01 -1.00E+07 -5.43E+06 2.72E+06 -1.36E+06

6.65E+03 -1.00E+07 3.33E+06 4.26E-02 -3.97E-02 1.06E+01 1.09E+01 -1.00E+07 -6.66E+06 3.33E+06 -1.67E+06

6.85E+03 -1.00E+07 3.64E+06 4.65E-02 -4.33E-02 1.06E+01 1.09E+01 -1.00E+07 -7.28E+06 3.64E+06 -1.82E+06

7.05E+03 -1.00E+07 3.95E+06 5.03E-02 -4.69E-02 1.06E+01 1.09E+01 -1.00E+07 -7.91E+06 3.95E+06 -1.98E+06

7.25E+03 -1.00E+07 4.27E+06 5.42E-02 -5.05E-02 1.06E+01 1.09E+01 -1.00E+07 -8.54E+06 4.27E+06 -2.13E+06

7.45E+03 -1.00E+07 4.58E+06 5.81E-02 -5.41E-02 1.06E+01 1.09E+01 -1.00E+07 -9.17E+06 4.58E+06 -2.29E+06

7.65E+03 -1.00E+07 4.90E+06 6.19E-02 -5.77E-02 1.06E+01 1.09E+01 -1.00E+07 -9.80E+06 4.90E+06 -2.45E+06

8.05E+03 -1.00E+07 5.54E+06 6.96E-02 -6.49E-02 1.05E+01 1.09E+01 -1.00E+07 -1.11E+07 5.54E+06 -2.77E+06

8.25E+03 -1.00E+07 5.86E+06 7.35E-02 -6.85E-02 1.05E+01 1.09E+01 -1.00E+07 -1.17E+07 5.86E+06 -2.93E+06


87

8.25E+03 -1.00E+07 5.86E+06 7.35E-02 -6.85E-02 1.05E+01 1.09E+01 -1.00E+07 -1.17E+07 5.86E+06 -2.93E+06

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

8.45E+03 -1.00E+07 6.18E+06 7.73E-02 -7.21E-02 1.05E+01 1.09E+01 -1.00E+07 -1.24E+07 6.18E+06 -3.09E+06

8.65E+03 -1.00E+07 6.51E+06 8.12E-02 -7.58E-02 1.05E+01 1.09E+01 -1.00E+07 -1.30E+07 6.51E+06 -3.26E+06

8.85E+03 -1.00E+07 6.84E+06 8.51E-02 -7.94E-02 1.05E+01 1.09E+01 -1.00E+07 -1.37E+07 6.84E+06 -3.42E+06

9.05E+03 -1.00E+07 7.17E+06 8.89E-02 -8.30E-02 1.05E+01 1.09E+01 -1.00E+07 -1.43E+07 7.17E+06 -3.58E+06

9.25E+03 -1.00E+07 7.50E+06 9.28E-02 -8.66E-02 1.05E+01 1.09E+01 -1.00E+07 -1.50E+07 7.50E+06 -3.75E+06

9.45E+03 -1.00E+07 7.84E+06 9.66E-02 -9.02E-02 1.05E+01 1.09E+01 -1.00E+07 -1.57E+07 7.84E+06 -3.92E+06

9.65E+03 -1.00E+07 8.17E+06 1.01E-01 -9.38E-02 1.04E+01 1.09E+01 -1.00E+07 -1.63E+07 8.17E+06 -4.09E+06

9.85E+03 -1.00E+07 8.51E+06 1.04E-01 -9.74E-02 1.04E+01 1.09E+01 -1.00E+07 -1.70E+07 8.51E+06 -4.25E+06

1.01E+04 -1.00E+07 8.85E+06 1.08E-01 -1.01E-01 1.04E+01 1.09E+01 -1.00E+07 -1.77E+07 8.85E+06 -4.42E+06

1.03E+04 -1.00E+07 9.19E+06 1.12E-01 -1.05E-01 1.04E+01 1.09E+01 -1.00E+07 -1.84E+07 9.19E+06 -4.60E+06

1.05E+04 -1.00E+07 9.53E+06 1.16E-01 -1.08E-01 1.04E+01 1.09E+01 -1.00E+07 -1.91E+07 9.53E+06 -4.76E+06

1.07E+04 -1.00E+07 9.88E+06 1.20E-01 -1.12E-01 1.04E+01 1.09E+01 -1.00E+07 -1.98E+07 9.88E+06 -4.94E+06

1.09E+04 -1.00E+07 1.02E+07 1.24E-01 -1.15E-01 1.04E+01 1.09E+01 -1.00E+07 -2.04E+07 1.02E+07 -5.11E+06

1.11E+04 -1.00E+07 1.06E+07 1.28E-01 -1.19E-01 1.04E+01 1.09E+01 -1.00E+07 -2.11E+07 1.06E+07 -5.28E+06

1.13E+04 -1.00E+07 1.09E+07 1.31E-01 -1.23E-01 1.03E+01 1.09E+01 -1.00E+07 -2.18E+07 1.09E+07 -5.46E+06

1.15E+04 -1.00E+07 1.13E+07 1.35E-01 -1.26E-01 1.03E+01 1.09E+01 -1.00E+07 -2.25E+07 1.13E+07 -5.63E+06

1.17E+04 -1.00E+07 1.16E+07 1.39E-01 -1.30E-01 1.03E+01 1.09E+01 -1.00E+07 -2.32E+07 1.16E+07 -5.81E+06

1.19E+04 -1.00E+07 1.20E+07 1.43E-01 -1.33E-01 1.03E+01 1.09E+01 -1.00E+07 -2.39E+07 1.20E+07 -5.99E+06

1.21E+04 -1.00E+07 1.23E+07 1.47E-01 -1.37E-01 1.03E+01 1.09E+01 -1.00E+07 -2.46E+07 1.23E+07 -6.16E+06

1.23E+04 -1.00E+07 1.27E+07 1.51E-01 -1.41E-01 1.03E+01 1.09E+01 -1.00E+07 -2.54E+07 1.27E+07 -6.34E+06

1.25E+04 -1.00E+07 1.30E+07 1.55E-01 -1.44E-01 1.03E+01 1.09E+01 -1.00E+07 -2.61E+07 1.30E+07 -6.52E+06

1.27E+04 -1.00E+07 1.34E+07 1.58E-01 -1.48E-01 1.03E+01 1.09E+01 -1.00E+07 -2.68E+07 1.34E+07 -6.70E+06

1.29E+04 -1.00E+07 1.38E+07 1.62E-01 -1.51E-01 1.03E+01 1.09E+01 -1.00E+07 -2.75E+07 1.38E+07 -6.88E+06

1.31E+04 -1.00E+07 1.41E+07 1.66E-01 -1.55E-01 1.02E+01 1.09E+01 -1.00E+07 -2.83E+07 1.41E+07 -7.06E+06

1.33E+04 -1.00E+07 1.45E+07 1.70E-01 -1.59E-01 1.02E+01 1.09E+01 -1.00E+07 -2.90E+07 1.45E+07 -7.25E+06


88

1.35E+04 -1.00E+07 1.49E+07 1.74E-01 -1.62E-01 1.02E+01 1.09E+01 -1.00E+07 -2.97E+07 1.49E+07 -7.43E+06

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

1.37E+04 -1.00E+07 1.52E+07 1.78E-01 -1.66E-01 1.02E+01 1.09E+01 -1.00E+07 -3.05E+07 1.52E+07 -7.62E+06

1.39E+04 -1.00E+07 1.56E+07 1.82E-01 -1.69E-01 1.02E+01 1.09E+01 -1.00E+07 -3.12E+07 1.56E+07 -7.80E+06

1.41E+04 -1.00E+07 1.60E+07 1.85E-01 -1.73E-01 1.02E+01 1.09E+01 -1.00E+07 -3.19E+07 1.60E+07 -7.99E+06

1.43E+04 -1.00E+07 1.64E+07 1.89E-01 -1.77E-01 1.02E+01 1.09E+01 -1.00E+07 -3.27E+07 1.64E+07 -8.18E+06

1.45E+04 -1.00E+07 1.67E+07 1.93E-01 -1.80E-01 1.02E+01 1.09E+01 -1.00E+07 -3.35E+07 1.67E+07 -8.36E+06

1.47E+04 -1.00E+07 1.71E+07 1.97E-01 -1.84E-01 1.01E+01 1.09E+01 -1.00E+07 -3.42E+07 1.71E+07 -8.55E+06

1.49E+04 -1.00E+07 1.75E+07 2.01E-01 -1.87E-01 1.01E+01 1.09E+01 -1.00E+07 -3.50E+07 1.75E+07 -8.74E+06

1.51E+04 -1.00E+07 1.79E+07 2.05E-01 -1.91E-01 1.01E+01 1.09E+01 -1.00E+07 -3.57E+07 1.79E+07 -8.93E+06

1.53E+04 -1.00E+07 1.82E+07 2.09E-01 -1.95E-01 1.01E+01 1.09E+01 -1.00E+07 -3.65E+07 1.82E+07 -9.12E+06

1.55E+04 -1.00E+07 1.86E+07 2.13E-01 -1.98E-01 1.01E+01 1.09E+01 -1.00E+07 -3.73E+07 1.86E+07 -9.31E+06

1.57E+04 -1.00E+07 1.90E+07 2.16E-01 -2.02E-01 1.01E+01 1.09E+01 -1.00E+07 -3.80E+07 1.90E+07 -9.51E+06

1.59E+04 -1.00E+07 1.94E+07 2.20E-01 -2.05E-01 1.01E+01 1.09E+01 -1.00E+07 -3.88E+07 1.94E+07 -9.70E+06

1.61E+04 -1.00E+07 1.98E+07 2.24E-01 -2.09E-01 1.01E+01 1.09E+01 -1.00E+07 -3.96E+07 1.98E+07 -9.90E+06

1.63E+04 -1.00E+07 2.02E+07 2.28E-01 -2.13E-01 1.01E+01 1.09E+01 -1.00E+07 -4.04E+07 2.02E+07 -1.01E+07

1.65E+04 -1.00E+07 2.06E+07 2.32E-01 -2.16E-01 1.00E+01 1.09E+01 -1.00E+07 -4.12E+07 2.06E+07 -1.03E+07

1.67E+04 -1.00E+07 2.10E+07 2.36E-01 -2.20E-01 1.00E+01 1.09E+01 -1.00E+07 -4.19E+07 2.10E+07 -1.05E+07

1.69E+04 -1.00E+07 2.14E+07 2.40E-01 -2.24E-01 1.00E+01 1.09E+01 -1.00E+07 -4.28E+07 2.14E+07 -1.07E+07

1.71E+04 -1.00E+07 2.18E+07 2.43E-01 -2.27E-01 1.00E+01 1.09E+01 -1.00E+07 -4.36E+07 2.18E+07 -1.09E+07

1.73E+04 -1.00E+07 2.22E+07 2.47E-01 -2.31E-01 1.00E+01 1.09E+01 -1.00E+07 -4.44E+07 2.22E+07 -1.11E+07

1.75E+04 -1.00E+07 2.26E+07 2.51E-01 -2.34E-01 9.99E+00 1.09E+01 -1.00E+07 -4.52E+07 2.26E+07 -1.13E+07

1.77E+04 -1.00E+07 2.25E+07 2.51E-01 -2.34E-01 9.99E+00 1.09E+01 -1.00E+07 -4.51E+07 2.25E+07 -1.13E+07

1.79E+04 -1.00E+07 2.25E+07 2.50E-01 -2.33E-01 9.99E+00 1.09E+01 -1.00E+07 -4.50E+07 2.25E+07 -1.13E+07

1.81E+04 -1.00E+07 2.24E+07 2.49E-01 -2.32E-01 9.99E+00 1.09E+01 -1.00E+07 -4.48E+07 2.24E+07 -1.12E+07

1.83E+04 -9.99E+06 2.23E+07 2.48E-01 -2.31E-01 1.00E+01 1.09E+01 -9.99E+06 -4.45E+07 2.23E+07 -1.11E+07

1.85E+04 -9.99E+06 2.21E+07 2.46E-01 -2.29E-01 1.00E+01 1.09E+01 -9.99E+06 -4.41E+07 2.21E+07 -1.10E+07


89

1.87E+04 -9.99E+06 2.18E+07 2.44E-01 -2.27E-01 1.00E+01 1.09E+01 -9.99E+06 -4.37E+07 2.18E+07 -1.09E+07

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

1.89E+04 -9.99E+06 2.16E+07 2.42E-01 -2.25E-01 1.00E+01 1.09E+01 -9.99E+06 -4.31E+07 2.16E+07 -1.08E+07

1.91E+04 -9.98E+06 2.13E+07 2.39E-01 -2.22E-01 1.00E+01 1.09E+01 -9.98E+06 -4.25E+07 2.13E+07 -1.06E+07

1.93E+04 -9.98E+06 2.09E+07 2.35E-01 -2.19E-01 1.00E+01 1.09E+01 -9.98E+06 -4.18E+07 2.09E+07 -1.05E+07

1.95E+04 -9.98E+06 2.05E+07 2.32E-01 -2.16E-01 1.00E+01 1.09E+01 -9.98E+06 -4.10E+07 2.05E+07 -1.03E+07

1.97E+04 -9.98E+06 2.01E+07 2.28E-01 -2.12E-01 1.01E+01 1.09E+01 -9.98E+06 -4.03E+07 2.01E+07 -1.01E+07

1.99E+04 -9.98E+06 1.97E+07 2.24E-01 -2.08E-01 1.01E+01 1.09E+01 -9.98E+06 -3.95E+07 1.97E+07 -9.86E+06

2.01E+04 -9.98E+06 1.93E+07 2.20E-01 -2.05E-01 1.01E+01 1.09E+01 -9.98E+06 -3.87E+07 1.93E+07 -9.67E+06

2.03E+04 -9.98E+06 1.89E+07 2.16E-01 -2.01E-01 1.01E+01 1.09E+01 -9.98E+06 -3.79E+07 1.89E+07 -9.47E+06

2.05E+04 -9.98E+06 1.85E+07 2.12E-01 -1.97E-01 1.01E+01 1.09E+01 -9.98E+06 -3.71E+07 1.85E+07 -9.27E+06

2.07E+04 -9.98E+06 1.82E+07 2.08E-01 -1.94E-01 1.01E+01 1.09E+01 -9.98E+06 -3.63E+07 1.82E+07 -9.08E+06

2.09E+04 -9.98E+06 1.78E+07 2.05E-01 -1.90E-01 1.01E+01 1.09E+01 -9.98E+06 -3.55E+07 1.78E+07 -8.89E+06

2.11E+04 -9.98E+06 1.74E+07 2.01E-01 -1.87E-01 1.01E+01 1.09E+01 -9.98E+06 -3.48E+07 1.74E+07 -8.69E+06

2.13E+04 -9.98E+06 1.70E+07 1.97E-01 -1.83E-01 1.01E+01 1.09E+01 -9.98E+06 -3.40E+07 1.70E+07 -8.50E+06

2.15E+04 -9.98E+06 1.66E+07 1.93E-01 -1.79E-01 1.02E+01 1.09E+01 -9.98E+06 -3.32E+07 1.66E+07 -8.31E+06

2.17E+04 -9.98E+06 1.62E+07 1.89E-01 -1.76E-01 1.02E+01 1.09E+01 -9.98E+06 -3.25E+07 1.62E+07 -8.12E+06

2.19E+04 -9.98E+06 1.59E+07 1.85E-01 -1.72E-01 1.02E+01 1.09E+01 -9.98E+06 -3.17E+07 1.59E+07 -7.93E+06

2.21E+04 -9.99E+06 1.57E+07 1.83E-01 -1.70E-01 1.02E+01 1.09E+01 -9.99E+06 -3.13E+07 1.57E+07 -7.84E+06

2.23E+04 -9.99E+06 1.57E+07 1.84E-01 -1.71E-01 1.02E+01 1.09E+01 -9.99E+06 -3.14E+07 1.57E+07 -7.86E+06

2.25E+04 -1.00E+07 1.58E+07 1.85E-01 -1.72E-01 1.02E+01 1.09E+01 -1.00E+07 -3.16E+07 1.58E+07 -7.89E+06

2.27E+04 -1.00E+07 1.59E+07 1.86E-01 -1.73E-01 1.02E+01 1.09E+01 -1.00E+07 -3.18E+07 1.59E+07 -7.95E+06

2.29E+04 -1.00E+07 1.60E+07 1.87E-01 -1.74E-01 1.02E+01 1.09E+01 -1.00E+07 -3.21E+07 1.60E+07 -8.02E+06

2.31E+04 -1.00E+07 1.62E+07 1.89E-01 -1.76E-01 1.02E+01 1.09E+01 -1.00E+07 -3.25E+07 1.62E+07 -8.12E+06

2.33E+04 -1.00E+07 1.65E+07 1.92E-01 -1.78E-01 1.02E+01 1.09E+01 -1.00E+07 -3.29E+07 1.65E+07 -8.24E+06

2.35E+04 -1.00E+07 1.67E+07 1.94E-01 -1.81E-01 1.02E+01 1.09E+01 -1.00E+07 -3.35E+07 1.67E+07 -8.37E+06

2.37E+04 -1.00E+07 1.71E+07 1.97E-01 -1.84E-01 1.01E+01 1.09E+01 -1.00E+07 -3.41E+07 1.71E+07 -8.53E+06


90

2.39E+04 -1.00E+07 1.74E+07 2.01E-01 -1.87E-01 1.01E+01 1.09E+01 -1.00E+07 -3.48E+07 1.74E+07 -8.70E+06

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

2.41E+04 -1.00E+07 1.78E+07 2.05E-01 -1.91E-01 1.01E+01 1.09E+01 -1.00E+07 -3.56E+07 1.78E+07 -8.89E+06

2.43E+04 -1.00E+07 1.82E+07 2.09E-01 -1.94E-01 1.01E+01 1.09E+01 -1.00E+07 -3.63E+07 1.82E+07 -9.08E+06

2.45E+04 -1.00E+07 1.86E+07 2.13E-01 -1.98E-01 1.01E+01 1.09E+01 -1.00E+07 -3.71E+07 1.86E+07 -9.28E+06

2.47E+04 -1.00E+07 1.89E+07 2.16E-01 -2.02E-01 1.01E+01 1.09E+01 -1.00E+07 -3.79E+07 1.89E+07 -9.47E+06

2.49E+04 -1.00E+07 1.93E+07 2.20E-01 -2.05E-01 1.01E+01 1.09E+01 -1.00E+07 -3.87E+07 1.93E+07 -9.67E+06

2.51E+04 -1.00E+07 1.97E+07 2.24E-01 -2.09E-01 1.01E+01 1.09E+01 -1.00E+07 -3.95E+07 1.97E+07 -9.87E+06

2.53E+04 -1.00E+07 2.01E+07 2.28E-01 -2.13E-01 1.01E+01 1.09E+01 -1.00E+07 -4.03E+07 2.01E+07 -1.01E+07

2.55E+04 -1.00E+07 2.05E+07 2.32E-01 -2.16E-01 1.00E+01 1.09E+01 -1.00E+07 -4.11E+07 2.05E+07 -1.03E+07

2.57E+04 -1.00E+07 2.09E+07 2.36E-01 -2.20E-01 1.00E+01 1.09E+01 -1.00E+07 -4.19E+07 2.09E+07 -1.05E+07

2.59E+04 -1.00E+07 2.14E+07 2.40E-01 -2.23E-01 1.00E+01 1.09E+01 -1.00E+07 -4.27E+07 2.14E+07 -1.07E+07

2.61E+04 -1.00E+07 2.18E+07 2.43E-01 -2.27E-01 1.00E+01 1.09E+01 -1.00E+07 -4.35E+07 2.18E+07 -1.09E+07

2.63E+04 -1.00E+07 2.22E+07 2.47E-01 -2.31E-01 1.00E+01 1.09E+01 -1.00E+07 -4.43E+07 2.22E+07 -1.11E+07

2.65E+04 -1.00E+07 2.26E+07 2.51E-01 -2.34E-01 9.99E+00 1.09E+01 -1.00E+07 -4.52E+07 2.26E+07 -1.13E+07

2.67E+04 -1.00E+07 2.30E+07 2.55E-01 -2.38E-01 9.97E+00 1.09E+01 -1.00E+07 -4.60E+07 2.30E+07 -1.15E+07

2.69E+04 -1.00E+07 2.34E+07 2.59E-01 -2.42E-01 9.96E+00 1.09E+01 -1.00E+07 -4.68E+07 2.34E+07 -1.17E+07

2.71E+04 -1.00E+07 2.38E+07 2.63E-01 -2.45E-01 9.95E+00 1.09E+01 -1.00E+07 -4.76E+07 2.38E+07 -1.19E+07

2.73E+04 -1.00E+07 2.42E+07 2.67E-01 -2.49E-01 9.94E+00 1.10E+01 -1.00E+07 -4.84E+07 2.42E+07 -1.21E+07

2.75E+04 -1.00E+07 2.46E+07 2.71E-01 -2.52E-01 9.93E+00 1.10E+01 -1.00E+07 -4.92E+07 2.46E+07 -1.23E+07

2.77E+04 -1.00E+07 2.50E+07 2.74E-01 -2.56E-01 9.92E+00 1.10E+01 -1.00E+07 -5.01E+07 2.50E+07 -1.25E+07

2.79E+04 -1.00E+07 2.54E+07 2.78E-01 -2.60E-01 9.91E+00 1.10E+01 -1.00E+07 -5.09E+07 2.54E+07 -1.27E+07

2.81E+04 -1.00E+07 2.59E+07 2.82E-01 -2.63E-01 9.89E+00 1.10E+01 -1.00E+07 -5.17E+07 2.59E+07 -1.29E+07

2.83E+04 -1.00E+07 2.63E+07 2.86E-01 -2.67E-01 9.88E+00 1.10E+01 -1.00E+07 -5.25E+07 2.63E+07 -1.31E+07

2.85E+04 -1.00E+07 2.67E+07 2.90E-01 -2.70E-01 9.87E+00 1.10E+01 -1.00E+07 -5.34E+07 2.67E+07 -1.33E+07

2.87E+04 -1.00E+07 2.71E+07 2.94E-01 -2.74E-01 9.86E+00 1.10E+01 -1.00E+07 -5.42E+07 2.71E+07 -1.36E+07

2.89E+04 -1.00E+07 2.75E+07 2.98E-01 -2.78E-01 9.85E+00 1.10E+01 -1.00E+07 -5.51E+07 2.75E+07 -1.38E+07


91

2.91E+04 -1.00E+07 2.80E+07 3.02E-01 -2.81E-01 9.84E+00 1.10E+01 -1.00E+07 -5.59E+07 2.80E+07 -1.40E+07

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

2.93E+04 -1.00E+07 2.84E+07 3.05E-01 -2.85E-01 9.82E+00 1.10E+01 -1.00E+07 -5.68E+07 2.84E+07 -1.42E+07

2.95E+04 -1.00E+07 2.88E+07 3.09E-01 -2.88E-01 9.81E+00 1.10E+01 -1.00E+07 -5.76E+07 2.88E+07 -1.44E+07

2.97E+04 -1.00E+07 2.92E+07 3.13E-01 -2.92E-01 9.80E+00 1.10E+01 -1.00E+07 -5.85E+07 2.92E+07 -1.46E+07

2.99E+04 -1.00E+07 2.97E+07 3.17E-01 -2.96E-01 9.79E+00 1.10E+01 -1.00E+07 -5.93E+07 2.97E+07 -1.48E+07

3.01E+04 -1.00E+07 3.01E+07 3.21E-01 -2.99E-01 9.78E+00 1.10E+01 -1.00E+07 -6.02E+07 3.01E+07 -1.51E+07

3.03E+04 -1.00E+07 3.05E+07 3.25E-01 -3.03E-01 9.77E+00 1.10E+01 -1.00E+07 -6.11E+07 3.05E+07 -1.53E+07

3.05E+04 -1.00E+07 3.10E+07 3.29E-01 -3.06E-01 9.75E+00 1.10E+01 -1.00E+07 -6.20E+07 3.10E+07 -1.55E+07

3.07E+04 -1.00E+07 3.14E+07 3.32E-01 -3.10E-01 9.74E+00 1.10E+01 -1.00E+07 -6.28E+07 3.14E+07 -1.57E+07

3.09E+04 -1.00E+07 3.19E+07 3.36E-01 -3.14E-01 9.73E+00 1.10E+01 -1.00E+07 -6.37E+07 3.19E+07 -1.59E+07

3.11E+04 -1.00E+07 3.23E+07 3.40E-01 -3.17E-01 9.72E+00 1.10E+01 -1.00E+07 -6.46E+07 3.23E+07 -1.62E+07

3.13E+04 -1.00E+07 3.28E+07 3.44E-01 -3.21E-01 9.71E+00 1.10E+01 -1.00E+07 -6.55E+07 3.28E+07 -1.64E+07

3.15E+04 -1.00E+07 3.32E+07 3.48E-01 -3.24E-01 9.70E+00 1.10E+01 -1.00E+07 -6.64E+07 3.32E+07 -1.66E+07

3.17E+04 -1.00E+07 3.37E+07 3.52E-01 -3.28E-01 9.68E+00 1.10E+01 -1.00E+07 -6.73E+07 3.37E+07 -1.68E+07

3.19E+04 -1.00E+07 3.41E+07 3.56E-01 -3.32E-01 9.67E+00 1.10E+01 -1.00E+07 -6.82E+07 3.41E+07 -1.71E+07

3.21E+04 -1.00E+07 3.46E+07 3.60E-01 -3.35E-01 9.66E+00 1.10E+01 -1.00E+07 -6.91E+07 3.46E+07 -1.73E+07

3.23E+04 -1.00E+07 3.50E+07 3.63E-01 -3.39E-01 9.65E+00 1.10E+01 -1.00E+07 -7.00E+07 3.50E+07 -1.75E+07

3.25E+04 -1.00E+07 3.55E+07 3.67E-01 -3.42E-01 9.64E+00 1.10E+01 -1.00E+07 -7.09E+07 3.55E+07 -1.77E+07

3.27E+04 -1.00E+07 3.60E+07 3.71E-01 -3.46E-01 9.63E+00 1.10E+01 -1.00E+07 -7.19E+07 3.60E+07 -1.80E+07

3.29E+04 -1.00E+07 3.64E+07 3.75E-01 -3.49E-01 9.61E+00 1.10E+01 -1.00E+07 -7.27E+07 3.64E+07 -1.82E+07

3.31E+04 -1.00E+07 3.68E+07 3.79E-01 -3.53E-01 9.60E+00 1.10E+01 -1.00E+07 -7.37E+07 3.68E+07 -1.84E+07

3.33E+04 -1.00E+07 3.72E+07 3.83E-01 -3.56E-01 9.59E+00 1.10E+01 -1.00E+07 -7.45E+07 3.72E+07 -1.86E+07

3.35E+04 -1.00E+07 3.77E+07 3.87E-01 -3.60E-01 9.58E+00 1.10E+01 -1.00E+07 -7.54E+07 3.77E+07 -1.89E+07

3.37E+04 -1.00E+07 3.82E+07 3.91E-01 -3.63E-01 9.57E+00 1.10E+01 -1.00E+07 -7.64E+07 3.82E+07 -1.91E+07

3.39E+04 -1.00E+07 3.86E+07 3.94E-01 -3.67E-01 9.56E+00 1.10E+01 -1.00E+07 -7.72E+07 3.86E+07 -1.93E+07

3.41E+04 -1.00E+07 3.91E+07 3.98E-01 -3.71E-01 9.54E+00 1.10E+01 -1.00E+07 -7.81E+07 3.91E+07 -1.95E+07


92

3.43E+04 -1.00E+07 3.96E+07 4.02E-01 -3.74E-01 9.53E+00 1.10E+01 -1.00E+07 -7.91E+07 3.96E+07 -1.98E+07

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear

Stress

3.45E+04 -1.00E+07 4.01E+07 4.06E-01 -3.78E-01 9.52E+00 1.10E+01 -1.00E+07 -8.01E+07 4.01E+07 -2.00E+07

3.47E+04 -1.00E+07 4.05E+07 4.10E-01 -3.81E-01 9.51E+00 1.10E+01 -1.00E+07 -8.09E+07 4.05E+07 -2.02E+07

3.49E+04 -1.00E+07 4.08E+07 4.14E-01 -3.85E-01 9.50E+00 1.10E+01 -1.00E+07 -8.16E+07 4.08E+07 -2.04E+07

3.51E+04 -1.00E+07 4.13E+07 4.18E-01 -3.88E-01 9.49E+00 1.10E+01 -1.00E+07 -8.25E+07 4.13E+07 -2.06E+07

3.53E+04 -1.00E+07 4.18E+07 4.22E-01 -3.92E-01 9.48E+00 1.10E+01 -1.00E+07 -8.35E+07 4.18E+07 -2.09E+07

3.57E+04 -1.00E+07 4.26E+07 4.29E-01 -3.99E-01 9.45E+00 1.10E+01 -1.00E+07 -8.53E+07 4.26E+07 -2.13E+07

3.59E+04 -1.00E+07 4.30E+07 4.33E-01 -4.02E-01 9.44E+00 1.10E+01 -1.00E+07 -8.61E+07 4.30E+07 -2.15E+07

3.61E+04 -1.00E+07 4.35E+07 4.37E-01 -4.06E-01 9.43E+00 1.10E+01 -1.00E+07 -8.69E+07 4.35E+07 -2.17E+07

3.63E+04 -1.00E+07 4.39E+07 4.41E-01 -4.09E-01 9.42E+00 1.10E+01 -1.00E+07 -8.79E+07 4.39E+07 -2.20E+07

3.65E+04 -1.00E+07 4.44E+07 4.45E-01 -4.13E-01 9.41E+00 1.10E+01 -1.00E+07 -8.89E+07 4.44E+07 -2.22E+07

3.67E+04 -1.00E+07 4.49E+07 4.49E-01 -4.16E-01 9.39E+00 1.10E+01 -1.00E+07 -8.98E+07 4.49E+07 -2.24E+07

3.69E+04 -1.00E+07 4.54E+07 4.53E-01 -4.20E-01 9.38E+00 1.10E+01 -1.00E+07 -9.08E+07 4.54E+07 -2.27E+07

3.71E+04 -1.00E+07 4.59E+07 4.56E-01 -4.23E-01 9.37E+00 1.10E+01 -1.00E+07 -9.17E+07 4.59E+07 -2.29E+07

3.73E+04 -1.00E+07 4.64E+07 4.60E-01 -4.27E-01 9.36E+00 1.10E+01 -1.00E+07 -9.27E+07 4.64E+07 -2.32E+07

3.77E+04 -1.00E+07 4.74E+07 4.68E-01 -4.34E-01 9.34E+00 1.10E+01 -1.00E+07 -9.48E+07 4.74E+07 -2.37E+07

3.79E+04 -1.00E+07 4.79E+07 4.72E-01 -4.38E-01 9.32E+00 1.10E+01 -1.00E+07 -9.58E+07 4.79E+07 -2.39E+07

3.81E+04 -1.00E+07 4.84E+07 4.76E-01 -4.41E-01 9.31E+00 1.11E+01 -1.00E+07 -9.68E+07 4.84E+07 -2.42E+07

3.83E+04 -1.00E+07 4.87E+07 4.80E-01 -4.45E-01 9.30E+00 1.11E+01 -1.00E+07 -9.75E+07 4.87E+07 -2.44E+07

3.85E+04 -1.01E+07 4.90E+07 4.84E-01 -4.48E-01 9.29E+00 1.11E+01 -1.01E+07 -9.81E+07 4.90E+07 -2.45E+07

3.87E+04 -1.01E+07 4.95E+07 4.87E-01 -4.51E-01 9.28E+00 1.11E+01 -1.01E+07 -9.90E+07 4.95E+07 -2.48E+07

3.89E+04 -1.00E+07 5.00E+07 4.91E-01 -4.55E-01 9.27E+00 1.11E+01 -1.00E+07 -1.00E+08 5.00E+07 -2.50E+07

3.91E+04 -1.00E+07 5.06E+07 4.95E-01 -4.58E-01 9.25E+00 1.11E+01 -1.00E+07 -1.01E+08 5.06E+07 -2.53E+07

3.93E+04 -1.00E+07 5.10E+07 4.99E-01 -4.62E-01 9.24E+00 1.11E+01 -1.00E+07 -1.02E+08 5.10E+07 -2.55E+07

3.95E+04 -1.00E+07 5.11E+07 5.03E-01 -4.66E-01 9.23E+00 1.11E+01 -1.00E+07 -1.02E+08 5.11E+07 -2.56E+07

3.97E+04 -1.01E+07 5.16E+07 5.07E-01 -4.69E-01 9.22E+00 1.11E+01 -1.01E+07 -1.03E+08 5.16E+07 -2.58E+07


93


3.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

4.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

6.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

6.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

6.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

6.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

6.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

8.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

8.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


94


8.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

8.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

8.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.01E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.03E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.05E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.07E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.09E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.11E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.13E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.15E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.17E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.19E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.21E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.23E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.25E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.27E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.29E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.31E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.33E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.35E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


95


1.37E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.39E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.41E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.43E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.45E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.47E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.49E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.51E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.53E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.55E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.57E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.59E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.61E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.63E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.65E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.67E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.69E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.71E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.73E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.75E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.77E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.79E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.81E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.83E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.85E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.87E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


96


1.89E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.91E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.93E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.95E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.97E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.99E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.01E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.03E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.05E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.07E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.09E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.11E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.13E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.15E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.17E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.19E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.21E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.23E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.25E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.27E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.29E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.31E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.33E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.35E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.37E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.39E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


97


2.41E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.43E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.45E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.47E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.49E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.51E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.53E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.55E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.57E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.59E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.61E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.63E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.65E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.67E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.69E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.71E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.73E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.75E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.77E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.79E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.81E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.83E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.85E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.87E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.89E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.91E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


98


2.93E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.95E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.97E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.01E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.03E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.05E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.07E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.13E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.15E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.17E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.19E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.21E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.23E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.25E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.27E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

3.29E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

3.31E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

3.33E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

3.35E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.37E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.39E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.41E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.43E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.45E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

3.47E+04 5.00E+00 0.00E+00 5.00E+00 0.00E+00 0.00E+00

3.49E+04 5.00E+00 0.00E+00 5.00E+00 0.00E+00 0.00E+00


99


3.51E+04 5.00E+00 0.00E+00 5.00E+00 0.00E+00 0.00E+00

3.53E+04 7.00E+00 0.00E+00 7.00E+00 0.00E+00 0.00E+00

3.55E+04 8.00E+00 0.00E+00 8.00E+00 0.00E+00 0.00E+00

3.57E+04 1.00E+01 0.00E+00 1.00E+01 0.00E+00 0.00E+00

3.59E+04 1.10E+01 0.00E+00 1.10E+01 0.00E+00 0.00E+00

3.61E+04 1.10E+01 0.00E+00 1.10E+01 0.00E+00 0.00E+00

3.63E+04 1.20E+01 0.00E+00 1.20E+01 0.00E+00 0.00E+00

3.65E+04 1.20E+01 0.00E+00 1.20E+01 0.00E+00 0.00E+00

3.67E+04 1.20E+01 0.00E+00 1.20E+01 0.00E+00 0.00E+00

3.69E+04 1.30E+01 0.00E+00 1.30E+01 0.00E+00 0.00E+00

3.71E+04 1.30E+01 0.00E+00 1.30E+01 0.00E+00 0.00E+00

3.73E+04 1.30E+01 0.00E+00 1.30E+01 0.00E+00 0.00E+00

3.75E+04 1.30E+01 0.00E+00 1.30E+01 0.00E+00 0.00E+00

3.77E+04 1.40E+01 0.00E+00 1.40E+01 0.00E+00 0.00E+00

3.79E+04 1.40E+01 0.00E+00 1.40E+01 0.00E+00 0.00E+00

3.81E+04 1.60E+01 0.00E+00 1.60E+01 0.00E+00 0.00E+00

3.83E+04 2.00E+01 0.00E+00 2.00E+01 0.00E+00 0.00E+00

3.85E+04 2.00E+01 0.00E+00 2.00E+01 0.00E+00 0.00E+00

3.87E+04 2.10E+01 0.00E+00 2.10E+01 0.00E+00 0.00E+00

3.89E+04 2.10E+01 0.00E+00 2.10E+01 0.00E+00 0.00E+00

3.91E+04 2.40E+01 0.00E+00 2.40E+01 0.00E+00 0.00E+00

3.93E+04 2.50E+01 0.00E+00 2.50E+01 0.00E+00 0.00E+00

3.95E+04 2.80E+01 0.00E+00 2.80E+01 0.00E+00 0.00E+00

3.97E+04 2.80E+01 0.00E+00 2.80E+01 0.00E+00 0.00E+00

3.99E+04 3.20E+01 0.00E+00 3.20E+01 0.00E+00 0.00E+00


100

APPENDIX C

DATA SET FOR FAILURE TEST 1MPA

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear Stress

6.65E+03 -9.97E+05 2.36E+04 2.15E-04 -2.41E-04 1.11E+01 1.14E+01 -9.97E+05 -4.72E+04 2.36E+04 -1.18E+04

6.85E+03 -1.00E+06 4.63E+04 8.15E-04 -8.51E-04 1.11E+01 1.14E+01 -1.00E+06 -9.26E+04 4.63E+04 -2.31E+04

7.05E+03 -1.01E+06 8.01E+04 1.80E-03 -1.80E-03 1.11E+01 1.14E+01 -1.01E+06 -1.60E+05 8.01E+04 -4.01E+04

7.25E+03 -1.01E+06 1.45E+05 3.17E-03 -3.09E-03 1.11E+01 1.14E+01 -1.01E+06 -2.91E+05 1.45E+05 -7.27E+04

7.65E+03 -1.02E+06 3.00E+05 7.07E-03 -6.65E-03 1.11E+01 1.14E+01 -1.02E+06 -5.99E+05 3.00E+05 -1.50E+05

7.85E+03 -1.03E+06 4.21E+05 9.59E-03 -8.92E-03 1.11E+01 1.14E+01 -1.03E+06 -8.42E+05 4.21E+05 -2.11E+05

8.05E+03 -1.03E+06 5.49E+05 1.25E-02 -1.16E-02 1.11E+01 1.14E+01 -1.03E+06 -1.10E+06 5.49E+05 -2.75E+05

8.25E+03 -1.04E+06 6.84E+05 1.58E-02 -1.45E-02 1.11E+01 1.14E+01 -1.04E+06 -1.37E+06 6.84E+05 -3.42E+05

8.65E+03 -1.05E+06 1.01E+06 2.33E-02 -2.11E-02 1.11E+01 1.14E+01 -1.05E+06 -2.02E+06 1.01E+06 -5.04E+05

8.85E+03 -1.05E+06 1.19E+06 2.72E-02 -2.45E-02 1.11E+01 1.14E+01 -1.05E+06 -2.38E+06 1.19E+06 -5.94E+05

9.05E+03 -1.05E+06 1.37E+06 3.10E-02 -2.79E-02 1.10E+01 1.14E+01 -1.05E+06 -2.74E+06 1.37E+06 -6.86E+05

9.25E+03 -1.05E+06 1.54E+06 3.49E-02 -3.12E-02 1.10E+01 1.14E+01 -1.05E+06 -3.08E+06 1.54E+06 -7.70E+05

9.45E+03 -1.05E+06 1.72E+06 3.87E-02 -3.46E-02 1.10E+01 1.14E+01 -1.05E+06 -3.44E+06 1.72E+06 -8.60E+05

9.65E+03 -1.05E+06 1.91E+06 4.26E-02 -3.79E-02 1.10E+01 1.14E+01 -1.05E+06 -3.82E+06 1.91E+06 -9.54E+05

9.85E+03 -1.05E+06 2.10E+06 4.64E-02 -4.13E-02 1.10E+01 1.14E+01 -1.05E+06 -4.21E+06 2.10E+06 -1.05E+06

1.03E+04 -1.05E+06 2.48E+06 5.42E-02 -4.80E-02 1.10E+01 1.14E+01 -1.05E+06 -4.97E+06 2.48E+06 -1.24E+06

1.05E+04 -1.05E+06 2.68E+06 5.80E-02 -5.14E-02 1.10E+01 1.14E+01 -1.05E+06 -5.37E+06 2.68E+06 -1.34E+06

1.07E+04 -1.05E+06 2.88E+06 6.19E-02 -5.48E-02 1.10E+01 1.14E+01 -1.05E+06 -5.75E+06 2.88E+06 -1.44E+06

1.09E+04 -1.05E+06 3.07E+06 6.57E-02 -5.81E-02 1.09E+01 1.14E+01 -1.05E+06 -6.15E+06 3.07E+06 -1.54E+06

1.11E+04 -1.05E+06 3.27E+06 6.96E-02 -6.15E-02 1.09E+01 1.14E+01 -1.05E+06 -6.54E+06 3.27E+06 -1.63E+06

1.11E+04 -1.05E+06 3.27E+06 6.96E-02 -6.15E-02 1.09E+01 1.14E+01 -1.05E+06 -6.54E+06 3.27E+06 -1.63E+06


101

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear Stress

1.15E+04 -1.05E+06 3.67E+06 7.73E-02 -6.82E-02 1.09E+01 1.14E+01 -1.05E+06 -7.34E+06 3.67E+06 -1.83E+06

1.17E+04 -1.05E+06 3.87E+06 8.11E-02 -7.15E-02 1.09E+01 1.14E+01 -1.05E+06 -7.75E+06 3.87E+06 -1.94E+06

1.19E+04 -1.05E+06 4.08E+06 8.50E-02 -7.49E-02 1.09E+01 1.14E+01 -1.05E+06 -8.15E+06 4.08E+06 -2.04E+06

1.21E+04 -1.05E+06 4.29E+06 8.88E-02 -7.83E-02 1.09E+01 1.14E+01 -1.05E+06 -8.59E+06 4.29E+06 -2.15E+06

1.23E+04 -1.05E+06 4.50E+06 9.27E-02 -8.16E-02 1.09E+01 1.14E+01 -1.05E+06 -9.00E+06 4.50E+06 -2.25E+06

1.27E+04 -1.05E+06 4.92E+06 1.00E-01 -8.84E-02 1.08E+01 1.14E+01 -1.05E+06 -9.84E+06 4.92E+06 -2.46E+06

1.29E+04 -1.05E+06 5.13E+06 1.04E-01 -9.17E-02 1.08E+01 1.14E+01 -1.05E+06 -1.03E+07 5.13E+06 -2.56E+06

1.31E+04 -1.05E+06 5.35E+06 1.08E-01 -9.51E-02 1.08E+01 1.14E+01 -1.05E+06 -1.07E+07 5.35E+06 -2.67E+06

1.33E+04 -1.05E+06 5.57E+06 1.12E-01 -9.85E-02 1.08E+01 1.14E+01 -1.05E+06 -1.11E+07 5.57E+06 -2.78E+06

1.35E+04 -1.05E+06 5.79E+06 1.16E-01 -1.02E-01 1.08E+01 1.15E+01 -1.05E+06 -1.16E+07 5.79E+06 -2.89E+06

1.37E+04 -1.05E+06 6.01E+06 1.20E-01 -1.05E-01 1.08E+01 1.15E+01 -1.05E+06 -1.20E+07 6.01E+06 -3.01E+06

1.39E+04 -1.05E+06 6.24E+06 1.24E-01 -1.09E-01 1.08E+01 1.15E+01 -1.05E+06 -1.25E+07 6.24E+06 -3.12E+06

1.41E+04 -1.05E+06 6.47E+06 1.27E-01 -1.12E-01 1.08E+01 1.15E+01 -1.05E+06 -1.29E+07 6.47E+06 -3.23E+06

1.45E+04 -1.05E+06 6.93E+06 1.35E-01 -1.19E-01 1.07E+01 1.15E+01 -1.05E+06 -1.39E+07 6.93E+06 -3.47E+06

1.47E+04 -1.05E+06 7.17E+06 1.39E-01 -1.22E-01 1.07E+01 1.15E+01 -1.05E+06 -1.43E+07 7.17E+06 -3.59E+06

1.49E+04 -1.05E+06 7.41E+06 1.43E-01 -1.26E-01 1.07E+01 1.15E+01 -1.05E+06 -1.48E+07 7.41E+06 -3.70E+06

1.51E+04 -1.05E+06 7.65E+06 1.47E-01 -1.29E-01 1.07E+01 1.15E+01 -1.05E+06 -1.53E+07 7.65E+06 -3.82E+06

1.53E+04 -1.05E+06 7.88E+06 1.51E-01 -1.32E-01 1.07E+01 1.15E+01 -1.05E+06 -1.58E+07 7.88E+06 -3.94E+06

1.55E+04 -1.05E+06 8.13E+06 1.54E-01 -1.36E-01 1.07E+01 1.15E+01 -1.05E+06 -1.63E+07 8.13E+06 -4.06E+06

1.57E+04 -1.05E+06 8.37E+06 1.58E-01 -1.39E-01 1.07E+01 1.15E+01 -1.05E+06 -1.67E+07 8.37E+06 -4.19E+06

1.59E+04 -1.05E+06 8.62E+06 1.62E-01 -1.43E-01 1.06E+01 1.15E+01 -1.05E+06 -1.72E+07 8.62E+06 -4.31E+06

1.61E+04 -1.05E+06 8.88E+06 1.66E-01 -1.46E-01 1.06E+01 1.15E+01 -1.05E+06 -1.78E+07 8.88E+06 -4.44E+06

1.63E+04 -1.04E+06 9.13E+06 1.70E-01 -1.49E-01 1.06E+01 1.15E+01 -1.04E+06 -1.83E+07 9.13E+06 -4.57E+06

1.65E+04 -1.05E+06 9.39E+06 1.74E-01 -1.53E-01 1.06E+01 1.15E+01 -1.05E+06 -1.88E+07 9.39E+06 -4.69E+06

1.67E+04 -1.04E+06 9.65E+06 1.78E-01 -1.56E-01 1.06E+01 1.15E+01 -1.04E+06 -1.93E+07 9.65E+06 -4.82E+06

1.69E+04 -1.04E+06 9.91E+06 1.81E-01 -1.60E-01 1.06E+01 1.15E+01 -1.04E+06 -1.98E+07 9.91E+06 -4.95E+06


102

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear Stress

1.71E+04 -1.05E+06 1.02E+07 1.85E-01 -1.63E-01 1.06E+01 1.15E+01 -1.05E+06 -2.03E+07 1.02E+07 -5.09E+06

1.73E+04 -1.05E+06 1.04E+07 1.89E-01 -1.66E-01 1.06E+01 1.15E+01 -1.05E+06 -2.09E+07 1.04E+07 -5.22E+06

1.75E+04 -1.04E+06 1.07E+07 1.93E-01 -1.70E-01 1.06E+01 1.15E+01 -1.04E+06 -2.14E+07 1.07E+07 -5.35E+06

1.77E+04 -1.05E+06 1.10E+07 1.97E-01 -1.73E-01 1.05E+01 1.15E+01 -1.05E+06 -2.19E+07 1.10E+07 -5.48E+06

1.79E+04 -1.04E+06 1.12E+07 2.01E-01 -1.77E-01 1.05E+01 1.15E+01 -1.04E+06 -2.25E+07 1.12E+07 -5.62E+06

1.81E+04 -1.05E+06 1.15E+07 2.05E-01 -1.80E-01 1.05E+01 1.15E+01 -1.05E+06 -2.30E+07 1.15E+07 -5.75E+06

1.83E+04 -1.05E+06 1.18E+07 2.08E-01 -1.83E-01 1.05E+01 1.15E+01 -1.05E+06 -2.36E+07 1.18E+07 -5.89E+06

1.85E+04 -1.04E+06 1.21E+07 2.12E-01 -1.87E-01 1.05E+01 1.15E+01 -1.04E+06 -2.41E+07 1.21E+07 -6.03E+06

1.87E+04 -1.05E+06 1.23E+07 2.16E-01 -1.90E-01 1.05E+01 1.15E+01 -1.05E+06 -2.47E+07 1.23E+07 -6.17E+06

1.89E+04 -1.04E+06 1.26E+07 2.20E-01 -1.94E-01 1.05E+01 1.15E+01 -1.04E+06 -2.52E+07 1.26E+07 -6.30E+06

1.95E+04 -1.04E+06 1.34E+07 2.32E-01 -2.04E-01 1.04E+01 1.15E+01 -1.04E+06 -2.69E+07 1.34E+07 -6.72E+06

1.97E+04 -1.05E+06 1.37E+07 2.36E-01 -2.07E-01 1.04E+01 1.15E+01 -1.05E+06 -2.74E+07 1.37E+07 -6.86E+06

1.99E+04 -1.05E+06 1.40E+07 2.39E-01 -2.11E-01 1.04E+01 1.15E+01 -1.05E+06 -2.80E+07 1.40E+07 -7.00E+06

2.01E+04 -1.05E+06 1.43E+07 2.43E-01 -2.14E-01 1.04E+01 1.15E+01 -1.05E+06 -2.86E+07 1.43E+07 -7.14E+06

2.03E+04 -1.05E+06 1.46E+07 2.47E-01 -2.18E-01 1.04E+01 1.16E+01 -1.05E+06 -2.91E+07 1.46E+07 -7.28E+06

2.05E+04 -1.05E+06 1.49E+07 2.51E-01 -2.21E-01 1.04E+01 1.16E+01 -1.05E+06 -2.97E+07 1.49E+07 -7.43E+06

2.07E+04 -1.02E+06 1.48E+07 2.51E-01 -2.21E-01 1.04E+01 1.16E+01 -1.02E+06 -2.96E+07 1.48E+07 -7.41E+06

2.09E+04 -1.02E+06 1.48E+07 2.50E-01 -2.20E-01 1.04E+01 1.16E+01 -1.02E+06 -2.96E+07 1.48E+07 -7.39E+06

2.11E+04 -1.00E+06 1.47E+07 2.49E-01 -2.19E-01 1.04E+01 1.16E+01 -1.00E+06 -2.94E+07 1.47E+07 -7.36E+06

2.13E+04 -9.95E+05 1.46E+07 2.48E-01 -2.17E-01 1.04E+01 1.16E+01 -9.95E+05 -2.92E+07 1.46E+07 -7.30E+06

2.15E+04 -9.88E+05 1.45E+07 2.46E-01 -2.16E-01 1.04E+01 1.16E+01 -9.88E+05 -2.89E+07 1.45E+07 -7.24E+06

2.17E+04 -9.83E+05 1.43E+07 2.44E-01 -2.14E-01 1.04E+01 1.16E+01 -9.83E+05 -2.86E+07 1.43E+07 -7.15E+06

2.19E+04 -9.79E+05 1.41E+07 2.41E-01 -2.11E-01 1.04E+01 1.16E+01 -9.79E+05 -2.82E+07 1.41E+07 -7.06E+06

2.21E+04 -9.77E+05 1.39E+07 2.38E-01 -2.09E-01 1.04E+01 1.16E+01 -9.77E+05 -2.78E+07 1.39E+07 -6.94E+06

2.23E+04 -9.74E+05 1.36E+07 2.35E-01 -2.06E-01 1.04E+01 1.16E+01 -9.74E+05 -2.72E+07 1.36E+07 -6.81E+06

2.25E+04 -9.66E+05 1.33E+07 2.31E-01 -2.02E-01 1.04E+01 1.15E+01 -9.66E+05 -2.67E+07 1.33E+07 -6.67E+06


103

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear Stress

2.27E+04 -9.62E+05 1.31E+07 2.28E-01 -1.99E-01 1.05E+01 1.15E+01 -9.62E+05 -2.61E+07 1.31E+07 -6.53E+06

2.29E+04 -9.61E+05 1.28E+07 2.24E-01 -1.95E-01 1.05E+01 1.15E+01 -9.61E+05 -2.55E+07 1.28E+07 -6.38E+06

2.31E+04 -9.61E+05 1.25E+07 2.20E-01 -1.92E-01 1.05E+01 1.15E+01 -9.61E+05 -2.50E+07 1.25E+07 -6.24E+06

2.33E+04 -9.61E+05 1.22E+07 2.16E-01 -1.88E-01 1.05E+01 1.15E+01 -9.61E+05 -2.44E+07 1.22E+07 -6.09E+06

2.35E+04 -9.62E+05 1.19E+07 2.12E-01 -1.85E-01 1.05E+01 1.15E+01 -9.62E+05 -2.38E+07 1.19E+07 -5.95E+06

2.37E+04 -9.62E+05 1.16E+07 2.08E-01 -1.81E-01 1.05E+01 1.15E+01 -9.62E+05 -2.32E+07 1.16E+07 -5.81E+06

2.39E+04 -9.59E+05 1.13E+07 2.04E-01 -1.78E-01 1.05E+01 1.15E+01 -9.59E+05 -2.27E+07 1.13E+07 -5.67E+06

2.41E+04 -9.60E+05 1.11E+07 2.01E-01 -1.74E-01 1.05E+01 1.15E+01 -9.60E+05 -2.21E+07 1.11E+07 -5.53E+06

2.43E+04 -9.61E+05 1.08E+07 1.97E-01 -1.71E-01 1.05E+01 1.15E+01 -9.61E+05 -2.16E+07 1.08E+07 -5.39E+06

2.45E+04 -9.59E+05 1.05E+07 1.93E-01 -1.67E-01 1.06E+01 1.15E+01 -9.59E+05 -2.10E+07 1.05E+07 -5.25E+06

2.47E+04 -9.60E+05 1.02E+07 1.89E-01 -1.64E-01 1.06E+01 1.15E+01 -9.60E+05 -2.05E+07 1.02E+07 -5.12E+06

2.49E+04 -9.57E+05 9.97E+06 1.85E-01 -1.61E-01 1.06E+01 1.15E+01 -9.57E+05 -1.99E+07 9.97E+06 -4.99E+06

2.51E+04 -9.83E+05 9.84E+06 1.83E-01 -1.59E-01 1.06E+01 1.15E+01 -9.83E+05 -1.97E+07 9.84E+06 -4.92E+06

2.53E+04 -9.83E+05 9.88E+06 1.84E-01 -1.60E-01 1.06E+01 1.15E+01 -9.83E+05 -1.98E+07 9.88E+06 -4.94E+06

2.55E+04 -9.98E+05 9.92E+06 1.84E-01 -1.60E-01 1.06E+01 1.15E+01 -9.98E+05 -1.98E+07 9.92E+06 -4.96E+06

2.57E+04 -1.00E+06 1.00E+07 1.86E-01 -1.62E-01 1.06E+01 1.15E+01 -1.00E+06 -2.00E+07 1.00E+07 -5.00E+06

2.59E+04 -1.01E+06 1.01E+07 1.87E-01 -1.63E-01 1.06E+01 1.15E+01 -1.01E+06 -2.02E+07 1.01E+07 -5.06E+06

2.61E+04 -1.01E+06 1.03E+07 1.89E-01 -1.65E-01 1.06E+01 1.15E+01 -1.01E+06 -2.05E+07 1.03E+07 -5.13E+06

2.63E+04 -1.02E+06 1.04E+07 1.91E-01 -1.67E-01 1.06E+01 1.15E+01 -1.02E+06 -2.08E+07 1.04E+07 -5.21E+06

2.65E+04 -1.02E+06 1.06E+07 1.94E-01 -1.70E-01 1.06E+01 1.15E+01 -1.02E+06 -2.12E+07 1.06E+07 -5.31E+06

2.67E+04 -1.03E+06 1.08E+07 1.97E-01 -1.72E-01 1.05E+01 1.15E+01 -1.03E+06 -2.17E+07 1.08E+07 -5.42E+06

2.69E+04 -1.03E+06 1.11E+07 2.01E-01 -1.76E-01 1.05E+01 1.15E+01 -1.03E+06 -2.22E+07 1.11E+07 -5.55E+06

2.71E+04 -1.03E+06 1.14E+07 2.05E-01 -1.79E-01 1.05E+01 1.15E+01 -1.03E+06 -2.27E+07 1.14E+07 -5.68E+06

2.73E+04 -1.04E+06 1.17E+07 2.08E-01 -1.83E-01 1.05E+01 1.15E+01 -1.04E+06 -2.33E+07 1.17E+07 -5.83E+06

2.75E+04 -1.04E+06 1.19E+07 2.12E-01 -1.86E-01 1.05E+01 1.15E+01 -1.04E+06 -2.39E+07 1.19E+07 -5.97E+06

2.77E+04 -1.04E+06 1.22E+07 2.16E-01 -1.90E-01 1.05E+01 1.15E+01 -1.04E+06 -2.44E+07 1.22E+07 -6.11E+06


104

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear Stress

2.79E+04 -1.04E+06 1.25E+07 2.20E-01 -1.93E-01 1.05E+01 1.15E+01 -1.04E+06 -2.50E+07 1.25E+07 -6.26E+06

2.81E+04 -1.04E+06 1.28E+07 2.24E-01 -1.97E-01 1.05E+01 1.15E+01 -1.04E+06 -2.56E+07 1.28E+07 -6.40E+06

2.83E+04 -1.04E+06 1.31E+07 2.28E-01 -2.00E-01 1.05E+01 1.15E+01 -1.04E+06 -2.62E+07 1.31E+07 -6.54E+06

2.85E+04 -1.04E+06 1.34E+07 2.32E-01 -2.04E-01 1.04E+01 1.15E+01 -1.04E+06 -2.68E+07 1.34E+07 -6.69E+06

2.87E+04 -1.04E+06 1.37E+07 2.36E-01 -2.07E-01 1.04E+01 1.15E+01 -1.04E+06 -2.73E+07 1.37E+07 -6.84E+06

2.89E+04 -1.04E+06 1.40E+07 2.39E-01 -2.11E-01 1.04E+01 1.15E+01 -1.04E+06 -2.79E+07 1.40E+07 -6.98E+06

2.91E+04 -1.04E+06 1.42E+07 2.43E-01 -2.14E-01 1.04E+01 1.15E+01 -1.04E+06 -2.85E+07 1.42E+07 -7.12E+06

2.93E+04 -1.04E+06 1.45E+07 2.47E-01 -2.17E-01 1.04E+01 1.16E+01 -1.04E+06 -2.91E+07 1.45E+07 -7.27E+06

2.95E+04 -1.04E+06 1.48E+07 2.51E-01 -2.21E-01 1.04E+01 1.16E+01 -1.04E+06 -2.97E+07 1.48E+07 -7.42E+06

2.97E+04 -1.04E+06 1.51E+07 2.55E-01 -2.24E-01 1.04E+01 1.16E+01 -1.04E+06 -3.03E+07 1.51E+07 -7.57E+06

2.99E+04 -1.05E+06 1.54E+07 2.59E-01 -2.28E-01 1.04E+01 1.16E+01 -1.05E+06 -3.08E+07 1.54E+07 -7.71E+06

3.01E+04 -1.05E+06 1.57E+07 2.63E-01 -2.31E-01 1.03E+01 1.16E+01 -1.05E+06 -3.14E+07 1.57E+07 -7.85E+06

3.03E+04 -1.05E+06 1.60E+07 2.66E-01 -2.35E-01 1.03E+01 1.16E+01 -1.05E+06 -3.20E+07 1.60E+07 -7.99E+06

3.05E+04 -1.05E+06 1.63E+07 2.70E-01 -2.38E-01 1.03E+01 1.16E+01 -1.05E+06 -3.26E+07 1.63E+07 -8.14E+06

3.07E+04 -1.05E+06 1.66E+07 2.74E-01 -2.41E-01 1.03E+01 1.16E+01 -1.05E+06 -3.31E+07 1.66E+07 -8.29E+06

3.09E+04 -1.05E+06 1.69E+07 2.78E-01 -2.45E-01 1.03E+01 1.16E+01 -1.05E+06 -3.37E+07 1.69E+07 -8.43E+06

3.11E+04 -1.05E+06 1.72E+07 2.82E-01 -2.48E-01 1.03E+01 1.16E+01 -1.05E+06 -3.43E+07 1.72E+07 -8.58E+06

3.13E+04 -1.05E+06 1.75E+07 2.86E-01 -2.52E-01 1.03E+01 1.16E+01 -1.05E+06 -3.49E+07 1.75E+07 -8.73E+06

3.19E+04 -1.04E+06 1.84E+07 2.97E-01 -2.62E-01 1.02E+01 1.16E+01 -1.04E+06 -3.67E+07 1.84E+07 -9.18E+06

3.21E+04 -1.04E+06 1.87E+07 3.01E-01 -2.65E-01 1.02E+01 1.16E+01 -1.04E+06 -3.74E+07 1.87E+07 -9.34E+06

3.23E+04 -1.05E+06 1.90E+07 3.05E-01 -2.69E-01 1.02E+01 1.16E+01 -1.05E+06 -3.79E+07 1.90E+07 -9.48E+06

3.25E+04 -1.05E+06 1.93E+07 3.09E-01 -2.72E-01 1.02E+01 1.16E+01 -1.05E+06 -3.86E+07 1.93E+07 -9.64E+06

3.27E+04 -1.05E+06 1.96E+07 3.13E-01 -2.75E-01 1.02E+01 1.16E+01 -1.05E+06 -3.92E+07 1.96E+07 -9.79E+06

3.29E+04 -1.05E+06 1.99E+07 3.17E-01 -2.79E-01 1.02E+01 1.16E+01 -1.05E+06 -3.98E+07 1.99E+07 -9.94E+06

3.31E+04 -1.05E+06 2.02E+07 3.21E-01 -2.82E-01 1.02E+01 1.16E+01 -1.05E+06 -4.04E+07 2.02E+07 -1.01E+07

3.33E+04 -1.06E+06 2.05E+07 3.25E-01 -2.85E-01 1.02E+01 1.16E+01 -1.06E+06 -4.10E+07 2.05E+07 -1.03E+07


105

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear Stress

3.35E+04 -1.05E+06 2.08E+07 3.28E-01 -2.89E-01 1.02E+01 1.16E+01 -1.05E+06 -4.16E+07 2.08E+07 -1.04E+07

3.37E+04 -1.05E+06 2.11E+07 3.32E-01 -2.92E-01 1.01E+01 1.16E+01 -1.05E+06 -4.22E+07 2.11E+07 -1.06E+07

3.39E+04 -1.06E+06 2.14E+07 3.36E-01 -2.95E-01 1.01E+01 1.16E+01 -1.06E+06 -4.29E+07 2.14E+07 -1.07E+07

3.41E+04 -1.05E+06 2.18E+07 3.40E-01 -2.99E-01 1.01E+01 1.16E+01 -1.05E+06 -4.35E+07 2.18E+07 -1.09E+07

3.43E+04 -1.05E+06 2.21E+07 3.44E-01 -3.02E-01 1.01E+01 1.16E+01 -1.05E+06 -4.41E+07 2.21E+07 -1.10E+07

3.45E+04 -1.05E+06 2.24E+07 3.48E-01 -3.05E-01 1.01E+01 1.16E+01 -1.05E+06 -4.48E+07 2.24E+07 -1.12E+07

3.47E+04 -1.05E+06 2.27E+07 3.52E-01 -3.09E-01 1.01E+01 1.16E+01 -1.05E+06 -4.54E+07 2.27E+07 -1.14E+07

3.49E+04 -1.05E+06 2.30E+07 3.56E-01 -3.12E-01 1.01E+01 1.16E+01 -1.05E+06 -4.61E+07 2.30E+07 -1.15E+07

3.51E+04 -1.05E+06 2.34E+07 3.59E-01 -3.16E-01 1.01E+01 1.16E+01 -1.05E+06 -4.67E+07 2.34E+07 -1.17E+07

3.53E+04 -1.05E+06 2.37E+07 3.63E-01 -3.19E-01 1.00E+01 1.16E+01 -1.05E+06 -4.73E+07 2.37E+07 -1.18E+07

3.55E+04 -1.06E+06 2.40E+07 3.67E-01 -3.22E-01 1.00E+01 1.17E+01 -1.06E+06 -4.80E+07 2.40E+07 -1.20E+07

3.57E+04 -1.06E+06 2.43E+07 3.71E-01 -3.26E-01 1.00E+01 1.17E+01 -1.06E+06 -4.86E+07 2.43E+07 -1.22E+07

3.59E+04 -1.06E+06 2.47E+07 3.75E-01 -3.29E-01 1.00E+01 1.17E+01 -1.06E+06 -4.93E+07 2.47E+07 -1.23E+07

3.61E+04 -1.06E+06 2.49E+07 3.79E-01 -3.32E-01 1.00E+01 1.17E+01 -1.06E+06 -4.99E+07 2.49E+07 -1.25E+07

3.63E+04 -1.06E+06 2.53E+07 3.83E-01 -3.36E-01 9.99E+00 1.17E+01 -1.06E+06 -5.05E+07 2.53E+07 -1.26E+07

3.65E+04 -1.06E+06 2.56E+07 3.87E-01 -3.39E-01 9.98E+00 1.17E+01 -1.06E+06 -5.12E+07 2.56E+07 -1.28E+07

3.67E+04 -1.06E+06 2.59E+07 3.90E-01 -3.42E-01 9.96E+00 1.17E+01 -1.06E+06 -5.18E+07 2.59E+07 -1.30E+07

3.69E+04 -1.06E+06 2.62E+07 3.94E-01 -3.45E-01 9.95E+00 1.17E+01 -1.06E+06 -5.24E+07 2.62E+07 -1.31E+07

3.71E+04 -1.05E+06 2.65E+07 3.98E-01 -3.49E-01 9.94E+00 1.17E+01 -1.05E+06 -5.31E+07 2.65E+07 -1.33E+07

3.73E+04 -1.06E+06 2.69E+07 4.02E-01 -3.52E-01 9.93E+00 1.17E+01 -1.06E+06 -5.37E+07 2.69E+07 -1.34E+07

3.75E+04 -1.06E+06 2.72E+07 4.06E-01 -3.56E-01 9.92E+00 1.17E+01 -1.06E+06 -5.44E+07 2.72E+07 -1.36E+07

3.77E+04 -1.06E+06 2.75E+07 4.10E-01 -3.59E-01 9.91E+00 1.17E+01 -1.06E+06 -5.51E+07 2.75E+07 -1.38E+07

3.79E+04 -1.06E+06 2.79E+07 4.14E-01 -3.62E-01 9.89E+00 1.17E+01 -1.06E+06 -5.57E+07 2.79E+07 -1.39E+07

3.81E+04 -1.06E+06 2.82E+07 4.18E-01 -3.66E-01 9.88E+00 1.17E+01 -1.06E+06 -5.64E+07 2.82E+07 -1.41E+07

3.83E+04 -1.06E+06 2.86E+07 4.21E-01 -3.69E-01 9.87E+00 1.17E+01 -1.06E+06 -5.71E+07 2.86E+07 -1.43E+07

3.85E+04 -1.06E+06 2.89E+07 4.25E-01 -3.72E-01 9.86E+00 1.17E+01 -1.06E+06 -5.78E+07 2.89E+07 -1.44E+07


106

Step Confining

Stress Deviatoric

Stress Axial

Strain Volumetric

Strain Distance

x Distance

y Normal

Stress Hoop

Stress Radial

Stress Shear Stress

3.87E+04 -1.06E+06 2.92E+07 4.29E-01 -3.75E-01 9.85E+00 1.17E+01 -1.06E+06 -5.85E+07 2.92E+07 -1.46E+07

3.89E+04 -1.06E+06 2.96E+07 4.33E-01 -3.79E-01 9.84E+00 1.17E+01 -1.06E+06 -5.92E+07 2.96E+07 -1.48E+07

3.91E+04 -1.06E+06 2.99E+07 4.37E-01 -3.82E-01 9.82E+00 1.17E+01 -1.06E+06 -5.99E+07 2.99E+07 -1.50E+07

3.93E+04 -1.07E+06 3.03E+07 4.41E-01 -3.85E-01 9.81E+00 1.17E+01 -1.07E+06 -6.06E+07 3.03E+07 -1.51E+07

3.95E+04 -1.07E+06 3.06E+07 4.45E-01 -3.88E-01 9.80E+00 1.17E+01 -1.07E+06 -6.12E+07 3.06E+07 -1.53E+07

3.97E+04 -1.07E+06 3.10E+07 4.49E-01 -3.92E-01 9.79E+00 1.17E+01 -1.07E+06 -6.19E+07 3.10E+07 -1.55E+07

3.99E+04 -1.07E+06 3.13E+07 4.53E-01 -3.95E-01 9.78E+00 1.17E+01 -1.07E+06 -6.26E+07 3.13E+07 -1.56E+07

4.01E+04 -1.07E+06 3.16E+07 4.56E-01 -3.98E-01 9.77E+00 1.17E+01 -1.07E+06 -6.33E+07 3.16E+07 -1.58E+07

4.03E+04 -1.07E+06 3.20E+07 4.60E-01 -4.01E-01 9.75E+00 1.17E+01 -1.07E+06 -6.39E+07 3.20E+07 -1.60E+07

4.05E+04 -1.07E+06 3.24E+07 4.64E-01 -4.05E-01 9.74E+00 1.17E+01 -1.07E+06 -6.48E+07 3.24E+07 -1.62E+07

4.07E+04 -1.08E+06 3.27E+07 4.68E-01 -4.08E-01 9.73E+00 1.18E+01 -1.08E+06 -6.53E+07 3.27E+07 -1.63E+07

4.09E+04 -1.09E+06 3.30E+07 4.72E-01 -4.11E-01 9.72E+00 1.18E+01 -1.09E+06 -6.60E+07 3.30E+07 -1.65E+07

4.11E+04 -1.08E+06 3.34E+07 4.76E-01 -4.14E-01 9.71E+00 1.18E+01 -1.08E+06 -6.68E+07 3.34E+07 -1.67E+07

4.13E+04 -1.13E+06 3.37E+07 4.80E-01 -4.17E-01 9.70E+00 1.18E+01 -1.13E+06 -6.74E+07 3.37E+07 -1.68E+07

4.15E+04 -1.11E+06 3.40E+07 4.84E-01 -4.19E-01 9.68E+00 1.18E+01 -1.11E+06 -6.80E+07 3.40E+07 -1.70E+07

4.17E+04 -1.08E+06 3.44E+07 4.88E-01 -4.22E-01 9.67E+00 1.18E+01 -1.08E+06 -6.88E+07 3.44E+07 -1.72E+07

4.19E+04 -1.09E+06 3.47E+07 4.91E-01 -4.25E-01 9.66E+00 1.18E+01 -1.09E+06 -6.94E+07 3.47E+07 -1.74E+07

4.21E+04 -1.08E+06 3.50E+07 4.95E-01 -4.28E-01 9.65E+00 1.18E+01 -1.08E+06 -7.00E+07 3.50E+07 -1.75E+07

4.23E+04 -1.07E+06 3.54E+07 4.99E-01 -4.32E-01 9.64E+00 1.18E+01 -1.07E+06 -7.08E+07 3.54E+07 -1.77E+07

4.25E+04 -1.08E+06 3.57E+07 5.03E-01 -4.35E-01 9.63E+00 1.18E+01 -1.08E+06 -7.14E+07 3.57E+07 -1.79E+07

4.27E+04 -1.10E+06 3.60E+07 5.07E-01 -4.38E-01 9.61E+00 1.18E+01 -1.10E+06 -7.20E+07 3.60E+07 -1.80E+07

4.29E+04 -1.11E+06 3.61E+07 5.11E-01 -4.41E-01 9.60E+00 1.18E+01 -1.11E+06 -7.22E+07 3.61E+07 -1.80E+07


107


6.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

6.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

7.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

8.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

8.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

8.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

8.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

8.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.05E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.25E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.45E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.65E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

9.85E+03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.01E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.03E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.05E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.07E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.09E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.11E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.13E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.15E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


108


1.17E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.19E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.21E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.23E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.25E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.27E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.29E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.31E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.33E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.35E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.37E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.39E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.41E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.43E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.45E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.47E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.49E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.51E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.53E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.55E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.57E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.59E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.61E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.63E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.65E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.67E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


109


1.69E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.71E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.73E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.75E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.77E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.79E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.81E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.83E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.85E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.87E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.89E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.91E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.93E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.95E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.97E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

1.99E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.01E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.03E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.05E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.07E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.09E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.11E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.13E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.15E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.17E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.19E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


110


2.21E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.23E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.25E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.27E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.29E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.31E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.33E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.35E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.37E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.39E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.41E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.43E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.45E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.47E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.49E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.51E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.53E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.55E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.57E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.59E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.61E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.63E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.65E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.67E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.69E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.71E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


111


2.73E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.75E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.77E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.79E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.81E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.83E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.85E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.87E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.89E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.91E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.93E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.95E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.97E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

2.99E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.01E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.03E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.05E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.07E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.09E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.11E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.13E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.15E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.17E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.19E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.21E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.23E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00


112


3.25E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.27E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.29E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.31E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.33E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.35E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.37E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.39E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.41E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.43E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.45E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.47E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.49E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.51E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.53E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.55E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.57E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

3.59E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

3.61E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

3.63E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

3.65E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

3.67E+04 1.00E+00 0.00E+00 1.00E+00 0.00E+00 0.00E+00

3.69E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.71E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.73E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.75E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00


113


3.79E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.81E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.83E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.85E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.87E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.89E+04 2.00E+00 0.00E+00 2.00E+00 0.00E+00 0.00E+00

3.91E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

3.93E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

3.95E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

3.99E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

4.01E+04 3.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00

4.03E+04 4.00E+00 0.00E+00 4.00E+00 0.00E+00 0.00E+00

4.05E+04 4.00E+00 0.00E+00 4.00E+00 0.00E+00 0.00E+00

4.07E+04 4.00E+00 0.00E+00 4.00E+00 0.00E+00 0.00E+00

4.09E+04 4.00E+00 0.00E+00 4.00E+00 0.00E+00 0.00E+00

4.11E+04 5.00E+00 0.00E+00 5.00E+00 0.00E+00 0.00E+00

4.13E+04 5.00E+00 0.00E+00 5.00E+00 0.00E+00 0.00E+00

4.15E+04 5.00E+00 0.00E+00 5.00E+00 0.00E+00 0.00E+00

4.17E+04 6.00E+00 0.00E+00 6.00E+00 0.00E+00 0.00E+00

4.19E+04 6.00E+00 0.00E+00 6.00E+00 0.00E+00 0.00E+00

4.21E+04 7.00E+00 0.00E+00 7.00E+00 0.00E+00 0.00E+00

4.23E+04 7.00E+00 0.00E+00 7.00E+00 0.00E+00 0.00E+00

4.25E+04 9.00E+00 1.00E+00 8.00E+00 0.00E+00 0.00E+00

4.27E+04 1.00E+01 2.00E+00 8.00E+00 0.00E+00 0.00E+00

4.29E+04 1.20E+01 4.00E+00 8.00E+00 0.00E+00 0.00E+00

Date post:	02-May-2017
Category:	Documents
Upload:	nizam144
View:	220 times
Download:	1 times

Master Thesis 2012 Analysis of High Pressure Effects on Wellbore Integrity Using the Distinct...

Documents