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TitleStability Analysis and Modelling of Underground Excavations in Fractured Rocks
Tags Deformation (Engineering) Stress (Mechanics) Fracture Viscoelasticity
File Size4.6 MB
Total Pages309
Table of Contents
                            Front Cover
Stability Analysis and Modelling of Underground Excavations in Fractured Rocks
Copyright Page
Contents
Series Preface
Preface
About the Authors
CHAPTER 1. INTRODUCTION
	1.1. Rock Mechanics and Underground Excavation Stability
	1.2. Structure of the Book
CHAPTER 2. PHYSICAL MODELLING OF JOINTED ROCK MASS
	2.1. Modelling of Jointed Rock Masses Under Plane Stress State
	2.2. Model Test of Rock Mass with Rock Bridges
	2.3. Model Tests on Stability of Surrounding Rock of Large-scale Cavity
CHAPTER 3. NUMERICAL MODELLING OF JOINTED ROCK MASS
	3.1. Equivalent Continuum Model for Jointed Rock Masses
	3.2. Equivalent Analysis for Rock Masses Containing Thick Joints
	3.3. Strength Characteristics of Fractured Rock Mass
CHAPTER 4. SENSITIVITY ANALYSIS OF ROCK MASS PARAMETERS
	4.1. Sensitivity Analysis of Commonly Used Parameters
	4.2. Analysis of the Effect of Joint Parameters on Rock Mass Deformability
	4.3. Sensitivity Analysis of Rock Mass Parameters on Damage Zones
CHAPTER 5. STABILITY ANALYSIS OF RHEOLOGIC ROCK MASS
	5.1. Rheological Mechanical Models for Rocks and Rock Masses
	5.2. Visco-elastic Surrounding Rock Mass and Supporting Problem
	5.3. Interaction between the Visco-elastic–Plastic Surrounding Rock and Lining
	5.4. Stress State in Visco-elastic–Visco-plastic Surrounding Rock Masses
	5.5. Rheological Analysis with Dilation and Softening of the Rock Mass
	5.6. Effect of Bolt Reinforcement in Visco-elastic Rock Mass
	5.7. Rheological Damage Analysis of the Rock Mass Stability
CHAPTER 6. BACK ANALYSIS AND OBSERVATIONAL METHODS
	6.1. Elastic Back Analysis and Stress Distribution Analysis
	6.2. Visco-elastic Back Analysis and Its Engineering Applications
	6.3. Back Analysis and Optimised Methods in Transverse Isotropic Rock
	6.4. Back Analysis of Jointed Rock Mass and Stability Prediction
	6.5. Three-dimensional Back Analysis of Anisotropic Rock
	6.6. Three-dimensional Back Analysis of Jointed Rock Mass and Stability Analysis
	6.7. Applications of Statistics Model in Deformation Prediction
CHAPTER 7. CONSTRUCTION MECHANICS AND OPTIMISATION OF EXCAVATION SCHEMES
	7.1. Basic Principles of Interactive Construction Mechanics
	7.2. Applications of Interactive Programming in Optimisation of Cavern Construction
	7.3. Artificial Intelligence Techniques in Construction Optimisation
	7.4. Engineering Applications of Artificial Intelligence Optimisation Methods
CHAPTER 8. REINFORCEMENT MECHANISM OF ROCK BOLTS
	8.1. Effect of Bolts on Supporting the Rock Mass
	8.2. Physical Modelling of Rock Bolts
	8.3. Numerical Modelling of Bolt
	8.4. Scaled Engineering Model Test
REFERENCES
SUBJECT INDEX
                        
Document Text Contents
Page 2

ELSEVIER GEO-ENGINEERING BOOK SERIES
VOLUME 1

Stability Analysis and Modelling of

Underground Excavations in Fractured Rocks

Page 154

Multiplying the two sides of the above equation by eK3t, deriving the result with

respect to t and eliminating the term of eK3t, we have

a
2G3

ð1� 2nÞða� RÞ � K3T3

� �
_cc2ðtÞ þ

a
2G3

ð1� X2Þ þ K3T3Þ _bb2ðtÞ
� �

þ K3
a

2G3
ð1� 2nÞða� RÞ � 1

� �
c2ðtÞ þ K3

a
2G3

að1� X2Þ þ 1

� �
b2ðtÞ

¼
aPa
2G3

1�
1

K3T3

� �
ð1� X2Þ K3e

�t1=T3 � K3 �
1

T3

� �
e�t=T3

� �
� K3s0 ð5:122Þ

(iii) When r¼R, the displacement condition is

U ð2Þr ¼ U
ð3Þ
r

According to equations (5.54), (5.116) and (5.117), we have

b3ðtÞ ¼ ð1� 2nÞc2ðtÞ þ X
2
2b2ðtÞ ð5:123Þ

(iv) When r¼R, the stress condition is

sð3Þr¼a ¼ s
ð2Þ
r¼R � X2s

ð2Þ
r¼R

The last term in this equation reflects the action of the bolts. Substituting

equations (5.54), (5.114) and (5.117) into the above equation and interpreting the

results, we have

K3T3½ðX2 � 1Þ_cc2ðtÞ þ X2ðX2 � 1Þ _bb2ðtÞ � _bb3ðtÞ�

þ K3T3½ðX2 � 1Þc2ðtÞ þ X2ðX2 � 1Þb2ðtÞ � b3ðtÞ� ¼ 0

By solving this differential equation and substituting the result into equation

(5.123), we have

b2ðtÞ ¼ 1þ
2Rðn� 1Þ

a

� �
c2ðtÞ þ C 1e

�t=T3 ð5:124Þ

where C1 is an undetermined constant.

Stability Analysis of Rheologic Rock Mass 135

Page 155

Substituting equation (5.124) back into equation (5.122) gives

a
2G3

ð1� X2Þðaþ 4nR� 3RÞ þ
2R

a
K3T3ðn� 1Þ

� �
_cc2ðtÞ

þ K3
a

2G3
ð1� X2Þ


ðaþ 4nR� 3RÞ þ

2R

a
ðn� 1Þ


c2ðtÞ

¼
aPa
2G3

1�
1

K3T3

� �
ð1� X2Þ K3e

�t=T3 � K3 �
1

T3

� �
e�t=T3

� �

� K3s0 þ
aa
2G3

ð1� X2Þ
1

T3
� K3

� �
C 1e

�t=T3

then solving this equation gives

c2ðtÞ ¼ C 2e
�ðN2=N1Þt þ

a

3R� a� 4nR
C 1e

�t=T3 �
PaðK3T3 � 1Þ

K3T3ðaþ 4nR� 3RÞ
e�t=T3

þ
ð1� X2ÞaPK3a2

N2
1�

1

K3T3

� �
e�t1=T3 �

2K3G3a

N2
s0 ð5:125Þ

where

N1 ¼ aað1� X2Þðaþ 4nR� 3RÞ þ 4G3K3T3ðn� 1ÞR

N2 ¼ K3aað1� X2Þðaþ 4nR� 3RÞ þ 4G3RK3ðn� 1Þ

)
ð5:126Þ

and C1, C2 are undetermined constants.

For equation (5.114), when t¼ t1, r¼ a and r¼R, we have respectively

c2ðt1Þ � b2ðt1Þ ¼ 0 and c2ðt1Þ � X
2
2b2ðt1Þ ¼ 0

From this relation, we have

c2ðt1Þ ¼ b2ðt1Þ ¼ 0

If we substitute this result back into equations (5.124) and (5.125), then the

undetermined constants of C1 and C2 can be obtained:

C 1 ¼ 0

C 2 ¼
PaðK3T3 � 1Þ

K3T3ðaþ 4nR� 3RÞ

aPK3a2ð1� X2Þ

N2
1�

1

K3T3

� �� �

� e ðN2=N1Þ�ð1=T3Þð Þt þ
2K3G3as0

N2
eðN2=N1Þt1

9>>>>=
>>>>;

ð5:127Þ

136 Chapter 5

Page 308

R

reinforcement mechanism 4, 247, 248

relative convergence 77

relative error 37�39, 68, 69, 74, 75, 78, 82,

87

residual strength zone 127�129, 132

rheologic behaviour 3, 89

rock bridge 14, 16, 18, 20, 54, 56, 57

rock engineering system 74, 83

rock mass cohesion 14, 20

rock mass dimension 6

rock mass friction angle 14

rock mass strength 9, 11�13, 36, 43, 51,

54, 66, 87, 216, 248, 249, 251, 255

rock reinforcement 3, 212, 215, 247

roughness 30

S

scale e�ect 27, 37�39, 192

secondary tensile crack 9

sensitivity analysis 2, 3, 67, 68, 70, 74�77,

83, 84

sensitivity factor 68, 73, 74, 81, 82, 84, 86

sensitivity function 68, 69, 71, 73

sensitivity order 82

shear dilation 17

shear failure 9, 18, 22, 58, 83, 189, 200

shear failure plane 9

shear sliding 9

shear strength 14, 18, 19, 20, 22, 35,

54�59, 61, 248, 249, 255

shotcrete 52, 132, 150, 153, 191, 215, 221,

247, 248

sidewall 24, 25, 142, 155, 160, 189, 228,

262

similarity 5, 6, 24, 25, 250

similarity ratio 6

size e�ect 6, 14

softening 122, 124, 250, 253, 255

spacing 4, 6, 30, 39, 40, 53, 175, 181, 220,

221, 252

St. Venant medium 117

stability analysis 3�5, 42, 67, 70, 89, 96,

150, 157, 160, 194

statistic method 201

sti�ness-reduction method 71

strength equivalence 3, 29, 33, 35, 36, 41,

50

stress back analysis 2, 157

stress concentration 55, 142, 158

stress intensity factor 56

stress-volumetric strain curve 152

structural loosening 25

superposition theorem 89

swelling 152

system character 67, 68, 71

T

tensile crack 9, 16, 17

tensile rupture 25

tensile�compressive strength ratio 19

threshold stress 55

time series 201, 205

time series analysis 201

time-dependent characteristics 89

torsional tensile shear failure 18

transversal compressive crack 17

transverse deformation 8

transverse isotropic 4, 172, 174

U

unloading process 71

V

visco-elastic back analysis 4, 166, 170

visco-elastic deformation 89, 151

visco-elastic zone 115, 116, 118, 122, 123,

126, 127, 129, 133, 138, 140, 144

visco-plastic deformation 89, 151

visco-plastic zone 117, 118, 121�129, 131,

132

Y

yield zone 53

Index 289

Page 309

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