UNDERGROUND RESEARCH LABORATORY ROOM 209 INSTRUMENT …

AECL-9566-2 ûfekATOMIC ENERGY &£& ENERGIE ATOMIQUEOF CANADA LIMITED \^Sj^ DU CANADA LIMITEEResearch Company ^^^^^ Societe de Recherche

UNDERGROUND RESEARCH LABORATORY ROOM 209 INSTRUMENT ARRAY:

NUMERICAL MODELLERS' PREDICTIONS

OF THE ROCK MASS RESPONSE TO EXCAVATION

RESEAU ÎNSTRUMENTS DE MESURE DE LA CHAMBRE 209

DU LABORATOIRE DE RECHERCHES SOUTERRAIN: PREDICTIONS NUMERIQUES

DES GROUPES DE MODELISATION DE LA REACTION

DE LA MASSE ROCHEUSE A L'EXCAVATION

Volume II

Compiled by / Compile et redige parP. A. Lang

Whiteshell Nuclear Research Etablissement de recherchesEstablishment nucleaires de Whiteshell

Pinawa, Manitoba ROE 1LOApril 1989 avril

Copyright •'<=) Atomic Energy of Canada Limited. 1989

ATOMIC ENERGY OF CANADA LIMITED

UNDERGROUND RESEARCH LABORATORY ROOM 209 INSTRUMENT ARRAY:NUMERICAL MODELLERS' PREDICTIONS

OF THE ROCK MASS RESPONSE TO EXCAVATION

VOLUME II

Compiled by

P.A. Lang

T. Chan, P. Griffiths, B. Nakka,P.K. Kaiser1, D.H. Chan1, D. Tannant1, F. Pelli1, C. Neville1,

Gen hua Shi2, R.E. Goodman2 and P.J. Perie2

1Department of Civil EngineeringUniversity of AlbertaEdmonton, Alberta T6G 2E1

2Lawrence Berkley LaboratoriesBerkley, California 94620

Vhiteshell Nuclear Research EstablishmentPinava, Manitoba ROE 1L0

1989AECL-9566-2

- 331 -,

CONTENTS

VOLUME II

APPENDIX B

Page

NUMERICAL SIMULATION OF ROOM 209 INSTRUMENT RING,by P.K. Kaiser, D.M. Chan, D. Tannant, F. Pelli andC. Neville; University of Alberta, Department of CivilEngineering. 333

APPENDIX C PREDICTION OF ROCK DEFORMATIONS FOR THE EXCAVATIONRESPONSE EXPERIMENT - ROOM 209 IN THE URL, LAC DU BONNET,MANITOBA, by Gen hua Shi, Richard E. Goodman and PierreJean Perie; Lawrence Berkley Laboratories, Earth SciencesDivision. 581

- 333 -

APPENDIX B

NUMERICAL SIMULATION OF ROOM 209 INSTRUMENT RING

by

P. K. Kaiser, D. M. Chan, D. Tannant, F. Pelli and C. Neville

University of AlbertaDepartment of Civil Engineering

- 335 -

CONTENTS*

Page

ERRATA 337

Data Presentation Clarifications (Addendum to Report) 338

LIST OF FIGURES 352

Table of Contents 365

INTRODUCTION 367

1.1 General 3671.2 Research Team 3681.3 Scope of Interim Technical Report 3681.4 Finite Element Program Descriptions 370

DESCRIPTION OF ROOM 209 EXPERIMENT AND AVAILABLE DATA 372

DEVELOPMENT OF THE FINITE ELEMENT MODEL 373

3.1 Finite Element Mesh and Coordinate System 3733.2 Approximation of In Situ Stress Tensor for

Finite Element Analysis 3763.2.1 Selection of Representative State of Stress 3763.2.2 Simplified State of Stress 377

3.3 Selection of Rock Mass Parameters 3793.4 Selection of Fracture Zone Parameters 380

(Joint Element) 3813.4.1 Joint Properties and Characterization 3813.4.2 Linear-Elastic Joint Model 3843.4.3 Hyperbolic Normal Closure of Joint 388

3.4.3.1 Barton-Bandis Joint Model 3883.4.3.2 Selected Hyperbolic Normal Closure

Parameters 3893.5 Seepage Analyses in Fracture Zone 390

3.5.1 Fracture Permeability Characterization 3903.5.2 Finite Element Representation of the

Fracture Zone 391

continued...

Table of Contents provided by Technical Information Services

- 336 -

CONTENTS (concluded)

3.6 Coupled Seepage-Deformation Analyses 3933.6.1 Overview 3933.6.2 Coupled Hydro-Mechanical Finite Element

Modelling of Fractured Rock Masses 393

4. RESULTS FROM FINITE ELEMENT SIMULATIONS 403

4.1 Introduction to Data Presentation 4034.2 Linear Elastic Rock Without Joint (I)

Uncoupled Analysis 4094.2.1 Assumed Parameters 4094.2.2 Comments to Figures 409

4.2.2.1 Displacements 4094.2.2.2 Stresses 410

4.3 Linear-Elastic Rock Mass with Fracture Zone (II)Uncoupled Analysis 4324.3.1 Assumed Parameters 4324.3.2 Comments to Figures 432

4.3.2.1 Displacements 4324.3.2.2 Stresses 433

4.3.3 Aperture of the Fracture Zone 4784.3.4 Uncoupled Pressure Head Distribution/Flow

Modelling 4784.4 Linear-Elastic Rock With Non-Linear Fracture

Zone (III) 493

5. LIMITATIONS OF APPLICABILITY 495

6. REFERENCES 497

7. Appendix A 501

8. Appendix B 505

9. Appendix C 531

10. Appendix D 569

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ERRflTR

Numerical Simulation of Room 209 Instrument Ring

by P.K. Kaiser et al. (1987)

Page *

382

383

386

386

397

404

406

406-407

409

433

531

571-578

Text

These data was averaged

make simlifying assumptions

mechanical behavior of the

represent the behavior of

CSIR Cell

CSIR Stress Cell

Location of ExtensometerAnchors and AssociatedFinite Element Nodes

Nodal Point

to the anchor heads.

steps where simulated

...EXCAVATION STEPS

CSIR

Correction

were

simplifying

behaviour

behaviour

CSIRO

CSIRO

Location ofExtensometer An

Back-RotatedAnchor Location

collars

were

EXCAVATION STEAND RELATIVESHEAR IN FRACTUI

CSIRO(not back-rotated)

579 0.50(aperture change, last entry)

1.50

* Page numbers were adjusted by Technical Information Services

- 338 -

Data Presentation Clarifications (Addendum to Report)

1. Converence Plots

All converence plots show inward radial displacement along the crown (roof), springline,and invert (floor) for the symmetrical displacement fields only; i.e., none of these plotshave been back-rotated. These converences represent predictions in the directions ofmaximum and minimum stress in the x-y plane. (Sign Convention: inward displacementpositive)

2. Extensometer Plots

All extensometer plots presented in Figures 4.8 to 4.21 and 4.25 to 4.38 are calculatedusing the back-rotated displacement fields and thus are directly comparable to plots ofmeasured responses. All extensometer plots for the excavation stages J-l and J+l arepresented in Appendix C and are calculated using the symmetrical displacement fields andcannot be compared directly with measured responses. (Sign Convention: extensionalstrain positive)Note: 1 The displacement at anchor #4 in extensometer EXT02 is incorrect for

Figures 4.8b, 4.15b, 4.25b, and 4.32b. (Replacement figures areattached.)

2 Extensometer data for the full section excavation, no joint analysis (Figures4.15 to 4.21) were calculated before submission of the report but weremistakenly replaced by repeated plots of the pilot excavation, no joint analysis;i.e., they are repeated plots of the earlier figures. (The original plots areattached, for replacement.)

3. Shear Displacement Plots

All plots of relative shear displacement in the fracture at the roof and springline arepresented in Appendix C. These are calculated using the symmetrical displacement field,thus they are plots of relative shear displacement in the directions of maximum andminimun stress in the x-y plane. Back-rotation is required for comparison with fieldmeasurements. (Sign Convention: radial displacement positive inwards)

4. Stress Profiles

All stress profiles in Figures 4.43 to 4.60 are taken from the springline and from theroof/floor in the symmetrical stress fields. These plots show the variation in the stressmagnitudes in the directions of maximum and minimum initial stresses in the x-y plane.Back-rotation is required for comparison with field measurements. (Sign Convention:tensile stress positive, shear stress follows right hand rule)

- 339 -

5. Aperture Profiles

All aperture profiles presented in Figures 4.61 to 4.66 are taken from the springline andfrom the roof/floor in the symmetrical displacement fields. These plots show the variationin fracture apertures in the directions of maximum and minimum initial stresses in the x-yplane. Back-rotation is required for comparison with field measurements.

6. Fracture Fluid Pressure Profiles

All fracture fluid pressure profiles are presented in Figures 4.67 to 4.74. These profiles aretaken from the springline and from the roof/floor. Figures 4.67 to 4.70 incorporated thesymmetrical variations in aperture when the seepage analyses were performed.

7. Principal Stress Changes

All plots of principal stress changes are presented in Appendix D. These are calculatedfrom the back-rotated stress fields and are directly comparable to the measured stresschanges and orientations. (Sign Convention: positive stress change indicates a reduction incompressive stress or an increase in tensile stress)

8. Hydraulic Apertures

Table D. 1 presents the predicted changes in hydraulic apertures at the back-rotated packed-off intervals and should be directly comparable to the measured changes.

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Roof Extensometer EXT02No Joint: Pilot Excavation

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Distance Along Extensometer (m)

Roof Extensometer EXT01No Joint: Full Section Excavation

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- 350 -

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Roof Extensometer EXT02Linear Joint 3x3: Full Section Excavation

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- 352 -

LIST OF FIGURES

General Figures Page'

Figure 3.1 Cross-Section of the Mesh 395

Figure 3.2 Enlarged Section of the Inner Mesh 396

Figure 3.3 Finite Element Mesh Near Instrumentation 397and Fracture Zone

Figure 3.4 Enlarged Section of the Altered Inner Mesh 398

Figure 3.5 Plan of Finite Element Model 399

Figure 3.6 Applied Initial Stresses and Coordinate System 400

Figure 3.7 Normal Stress - Normal Closure Relationship 401

Figure 3.8 Assumed Direction of Fluid Flow 402

Figure 4.1 Location of CSIRO Stress Cells 403

Figure 4.2 Location of Packed-Off Intervals 404

Figure 4.3 Location of Extensometer Anchors 405

Figure 4.4 Location of Convergence Measurement Points 408

Convergence Plots: No Joint (Non Back-Rotated)

Figure 4.5 No Joint : Development Room Excavation 411

Figure 4.6 No Joint : Pilot Excavation 412

Figure 4.7 No Joint : Full Section Excavation 413

Extensometer Plots: No Joint

Figure 4.8a Roof Extensometer EXT01 414No Joint: Pilot Excavation

* Page numbers were adjusted by Technical Information Services

- 353 -

Figure 4.8b

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 4.13a

Figure 4.13b

Figure 4.14

Figure 4.15a

Figure 4.15b

Figure 4.16

Figure 4.17

Figure 4.18

Figure 4.19

Figure 4.20a


Diagonal Extensometer EXT03No Joint: Pilot Excavation

SL Extensometer EXT04No Joint: Pilot Excavation

Floor Extensometer EXT05No Joint: Pilot Excavation







Diagonal Extensometer EXT03No Joint: Full Section Excavation



Diagonal Extensometer EXT06No Joint: Full Section Excavation


416

417

418

419

420

422

423

425

426

427

428

429

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Figure 4.20b SL Extensometer EXT08No Joint: Full Section Excavation

Figure 4.21 Diagonal Extensometer EXT09 431No Joint: Full Section Excavation

Convergence Plots: Linear Joint (Non Back-Rotated)

Figure 4.22 Linear Joint 3x3 : Development Room Excavation 435

Figure 4.23 Linear Joint 3x3 : Pilot Excavation 436

Figure 4.24 Linear Joint 3x3 : Full Section Excavation 437

Extensometer Plots: Linear Joint

Figure 4.25a Roof Extensometer EXT01 438Linear Joint 3x3 : Pilot Excavation

Figure 4.25b Roof Extensometer EXT02Linear Joint 3x3 : Pilot Excavation

Figure 4.26 Diagonal Extensometer EXT03 440Linear Joint 3x3 : Pilot Excavation

Figure 4.27 SL Extensometer EXT04 441Linear Joint 3x3 : Pilot Excavation

Figure 4.28 Floor Extensometer EXT05 442Linear Joint 3x3 : Pilot Excavation


Figure 4.30a SL Extensometer EXT07 444Linear Joint 3x3 : Pilot Excavation

Figure 4.30b SL Extensometer EXT08Linear Joint 3x3 : Pilot Excavation


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Figure 4.32a Roof Extensometer EXT01 447Linear Joint 3x3 : Full Section Excavation

Figure 4.32b Roof Extensometer EXT02Linear Joint 3x3 : Full Section Excavation

Figure 4.33 Diagonal Extensometer EXT03 449Linear Joint 3x3 : Full Section Excavation

Figure 4.34 SL Extensometer EXT04 450Linear Joint 3x3 : Full Section Excavation

Figure 4.35 Floor Extensometer EXT05 451Linear Joint 3x3 : Full Section Excavation


Figure 4.37a SL Extensometer EXT07 453Linear Joint 3x3 : Full Section Excavation

Figure 4.37b SL Extensometer EXT08Linear Joint 3x3 : Full Section Excavation


Convergence Plots (Non Back-Rotated)

Figure 4.39 Linear Joint 3x3 : Pilot Excavated to 23.5 m 4 5 6

Figure 4.40 Linear Joint 3x3 : Pilot Excavated to 25.2 m 457

Figure 4.41 Linear Joint 3x3 : Slash Excavated to 23.5 m 458

Figure 4.42 Linear Joint 3x3 : Slash Excavated to 25.2 m 459

Stress Profiles (Non Back-Rotated)

Figure 4.43 Stresses from Roof and Floor 460(Development Room 2x2)

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Figure 4.44 Shear Stresses from Roof and Floor 461(Development Room 2x2)

Figure 4.45 Stresses from Roof and Floor 462(Full Pilot 2x2)

Figure 4.46 Shear Stresses from Roof and Floor 463(Full Pilot 2x2)

Figure 4.47 Stresses from Roof and Floor 464(Full Excavation 2x2)

Figure 4.48 Shear Stresses from Roof and Floor 465(Full Excavation 2x2)

Figure 4.49 Stress Distribution from the Springline 466(Development Room N 2x2)

Figure 4.50 Shear Stress Distribution from the Springline 467(Development Room N 2x2)

Figure 4.51 Stress Distribution from the Springline 468(Development Room S 2x2)

Figure 4.52 Shear Stress Distribution from the Springline 469(Development Room S 2x2)

Figure 4.53 Stress Distribution from the Springline 470(Full Pilot N 2x2)

Figure 4.54 Shear Stress Distribution from the Springline 471(Full Pilot N 2x2)

Figure 4.55 Stress Distribution from the Springline 472(Full Pilot S 2x2)

Figure 4.56 Shear Stress Distribution from the Springline 473(Full Pilot S 2x2)

Figure 4.57 Stress Distribution from the Springline 474(Full Excavation N 2x2)

Figure 4.58 Shear Stress Distribution from the Springline 475(Full Excavation N 2x2)

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Figure 4.59 Stress Distribution from the Springline 476(Full Excavation S 2x2)

Figure 4.60 Shear Stress Distribution from the Springline 477(Full Excavation S 2x2)

Aperture Profiles (Non Back-Rotated)

Figure 4.61 Aperture Distribution from Roof & Floor 479(Development Room 3x3)

Figure 4.62 Aperture Distribution from Springline 480(Development Room 3x3)

Figure 4.63 Aperture Distribution from Roof & Floor 481(Full Pilot 3x3)

Figure 4.64 Aperture Distribution from Springline 4 8 2

(Full Pilot 3x3)

Figure 4.65 Aperture Distribution from Roof & Floor 483(Full Excavation 3x3)

Figure 4.66 Aperture Distribution from Springline 484(Full Excavation 3x3)

Fluid Pressure Distributions





Figure 4.71 Constant Aperture : Pilot Excavation 489

Figure 4.72 Constant Aperture : Pilot Excavation 490

Figure 4.73 Constant Aperture : Full Section Excavation 491

Figure 4.74 Constant Aperture : Full Section Excavation 492

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Joint Element Figures

Figure B.I Joint Element 516

Figure B.2 Mid-plane and Mid-nodes 516

Figure B.3 Global and Local Coordinate Systems 516

Figure B.4 Hyperbolic Cfn-V Relationship 517

Figure B.5 Yield Function 517

Figure B.6 Hardening-softening Law 518

Figure B.7 Plastic Potential Function 518

Figure B.8 io-x Relationship 519

Extensometer and Shear Displacement Plots: Linear Joint(Intermediate Excavation Stages: Non Back-Rotated)

Figure C.I Roof Extensometers EXT01-02 533Linear Joint 3x3 : Pilot Excavated to 23.5 m

Figure C.2 Diagonal Extensometers EXT03-09 534Linear Joint 3x3 : Pilot Excavated to 23.5 m

Figure C.3 SL Extensometers EXT07-08-04 535Linear Joint 3x3 : Pilot Excavated to 23.5 m

Figure C.4 Diagonal Extensometers EXT06 536Linear Joint 3x3 : Pilot Excavated to 23.5 m

Figure C.5 Floor Extensometers EXT05 537Linear Joint 3x3 : Pilot Excavated to 23.5 m

Figure C.6 Full Section Roof at the Fracture 538Linear Joint 3x3 : Pilot Excavated to 23.5 m

Figure C.7 Full Section SL at the Fracture 539Linear Joint 3x3 : Pilot Excavated to 23.5 m

- 359 -

Figure C.8

Figure C.9

Figure CIO

Figure C.ll

Figure C.I2

Figure C.I3

Figure C.14

Figure C.I5

Figure C.I6

Figure C.I7

Figure C.I8

Figure C.I9

Figure C.20

Figure C.21

Figure C.22

Roof Extensometers EXT01-02Linear Joint 3x3 : Pilot Excavated to 25.2 m

Diagonal Extensometers EXT03-09Linear Joint 3x3 : Pilot Excavated to 25.2 m

SL Extensometers EXT07-08-04Linear Joint 3x3 : Pilot Excavated to 25.2 m

Diagonal Extensometers EXT06Linear Joint 3x3 : Pilot Excavated to 25.2 m

Floor Extensometers EXT05Linear Joint 3x3 : Pilot Excavated to 25.2 m

Full Section Roof at the FractureLinear Joint 3x3 : Pilot Excavated to 25.2 m

Full Section SL at the FractureLinear Joint 3x3 : Pilot Excavated to 25.2 m

Roof Extensometers EXT01-02Linear Joint 3x3 : Slash Excavated to 23.5 m

Diagonal Extensometers EXT03-09Linear Joint 3x3 : Slash Excavated to 23.5 m

SL Extensometers EXT07-08-04Linear Joint 3x3 : Slash Excavated to 23.5 m

Diagonal Extensometers EXT06Linear Joint 3x3 : Slash Excavated to 23.5 m

Floor Extensometers EXT05Linear Joint 3x3 : Slash Excavated to 23.5 m

Full Section Roof at the FractureLinear Joint 3x3 : Slash Excavated to 23.5 m

Full Section SL at the FractureLinear Joint 3x3 : Slash Excavated to 23.5 m

Roof Extensometers EXT01-02Linear Joint 3x3 : Slash Excavated to 25.2 m

540

541

542

543

544

545

546

547

548

549

550

551

552

553

554

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Figure C.23

Figure C.24

Figure C.25

Figure C.26

Figure C.27

Figure C.28

Diagonal Extensometers EXT03-09Linear Joint 3x3 : Slash Excavated to 25.2 m

SL Extensometers EXT07-08-04Linear Joint 3x3 : Slash Excavated to 25.2 m

Diagonal Extensometers EXT06Linear Joint 3x3 : Slash Excavated to 25.2 m

Floor Extensometers EXT05Linear Joint 3x3 : Slash Excavated to 25.2 m

Full Section Roof at the FractureLinear Joint 3x3 : Slash Excavated to 25.2 m

Full Section SL at the FractureLinear Joint 3x3 : Slash Excavated to 25.2 m

555

556

557

558

559

560

Shear Displacement Plots (Non Back-Rotated)

Figure C.29

Figure C.30

Figure C.31

Full Section Roof at the FractureNo Joint : Pilot Excavation

Full Section SL at the FractureNo Joint : Pilot Excavation

Full Section Roof at the FractureNo Joint : Full Section Excavation

Figure C.32 Full Section SL at the FractureNo Joint : Full Section Excavation

Figure C.33 Full Section Roof at the FractureLinear Joint 3x3 : Pilot Excavation

Figure C.34 Full Section SL at the FractureLinear Joint 3x3 : Pilot Excavation

Figure C.35 Full Section Roof at the FractureLinear Joint 3x3 : Full Section Excavation

Figure C.36 Full Section SL at the FractureLinear Joint 3x3 : Full Section Excavation

561

562

563

564

565

566

567

568

Principal Stress Change Plots

Figure D.I Principal Stress Changes @ Nl vs Excavation Stage 571

Figure D.2 Principal Stress Changes @ N2 vs Excavation Stage 572

Figure D.3 Principal Stress Changes @ SI vs Excavation Stage 573

Figure D.4 Principal Stress Changes @ S2 vs Excavation Stage 574

Figure D.5 Principal Stress Changes @ Rl vs Excavation Stage 575

Figure D.6 Principal Stress Changes @ R2 vs Excavation Stage 576

Figure D.7 Principal Stress Changes @ Fl vs Excavation Stage 577

Figure D.8 Principal Stress Changes @ F2 vs Excavation Stage 578

- 363It

NUMERICAL SIMULATION OFROOM 209 INSTRUMENT RING

Interim Technical Reportfor Research Period

August 1986 to April 1987

prepared by

P.K. KaiserD.H. ChanD. TannantF. Pelli

C. Neville

Department of Civil EngineeringUniversity of Alberta

Edmonton, Alberta T6G 2G7

forAtomic Energy of Canada Ltd.

Whiteshell Nuclear Research EstablishmentPinawa, Manitoba ROE 1L0

April 1987

- 365 -

Table of Contents

INTRODUCTION 1

1 . 1 General 1

1. 2 Research Team 2

1.3 Scope of Interim Technical Report 2

1.4 Finite Element Program Descriptions 4

DESCRIPTION OF ROOM 209 EXPERIMENT AND AVAILABLE DATA 6

DEVELOPMENT OF THE FINITE ELEMENT MODEL 7

3.1 Finite Element Mesh and Coordinate System 7

3.2 Approximation of In Situ Stress Tensor for FiniteElement Analyses 10

3.2.1 Selection of Representative State ofStress 10

3.2.2 Simplified State of Stress 11

3.3 Selection of Rock Mass Parameters 13

3.4 Selection of Fracture Zone Parameters (JointElement) 15

3.4.1 Joint Properties and Characterization 15

3.4.2 Linear-Elastic Joint Model 18

3.4.3 Hyperbolic Normal Closure of Joint 22

3.4.3.1 Barton-Bandis Joint Model 22

3.4.3.2 Selected Hyperbolic NormalClosure Parameters 23

3.5 Seepage Analyses in Fracture Zone 24

3.5.1 Fracture Permeability Characterization ....24

3.5.2 Finite Element Representation of theFracture Zone 25

3.6 Coupled Seepage-Deformation Analyses 27

3.6.1 Overview 27

I I

- 366 -

3.6.2 Coupled Hydro-Mechanical Finite Element

Modelling of Fractured Rock Masses 27

4. RESULTS FROM FINITE ELEMENT SIMULATIONS 37

4.1 Introduction to Data Presentation 374.2 Linear Elastic Rock Without Joint (I);

Uncoupled Analysis 43

4.2.1 Assumed Parameters 43

4.2.2 Comments to Figures 43

4.2.2.1 Displacements 43

4.2.2.2 Stresses 44

4.3 Linear-Elastic Rock Mass with Fracture Zone (II);Uncoupled Analysis 62

4.3.1 Assumed Parameters 62

4.3.2 Comments to Figures 62

4.3.2.1 Displacements 6?

4.3.2.2 Stresses 63

4.3.3 Aperture of the Fracture Zone 104

4.3.4 Uncoupled Pressure Head Distribution/FlowModelling 104

4.4 Linear-Elastic Rock With Non-Linear Fracture Zone(III) 119

5. LIMITATIONS OF APPLICABILITY 121

6. REFERENCES 123

7. Appendix A 126

8. Appendix B 129

9. Appendix C 154

10. Appendix D 191

211

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1. INTRODUCTION

1. 1 General

This report deals with items of Stage 1, Phase 1 of the

research proposal submitted by Dr. P.K. Kaiser in May 1986. In

accordance with the objectives of the Excavation Response

Experiment, it was proposed to provide the following:

Item 1.3.a: Prediction of rock mass response to excavation of

Room 209 Instrument Ring.

Spec i f ically:

Item 2.1.i: Simulation of the three-dimensional geomechanics

response;

Item 2.1.ii: Prediction of the stress-dependent conductivity

change at specific locations; and

Item 2.1.iii: Simulation of the fracture flow response by

two-dimensional flow modelling.

For Stage 1 (August 1986 to April 1987), it was proposed:

to predict the geomechanical behaviour of Room 209

Instrument Ring;

to list the limitations or limits of applicability of

prediction;

to give an unconditional (most likely, average condition)

prediction; and

to provide some conditional predictions by variation of the

most dominant and the least reliable input parameters. (For

reasons given below, this aspect was not completed and

deferred to Stage 2).

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1.2 Research Team

The research was conducted and the report prepared by:

Principal Investigator: Dr. P.K. Kaiser

Technical Advisor: Dr. D.H. Chan

Research Engineer: F. Pelli

Graduate Research Student: D. Tannant

Research Assistant (Student): C. Neville

1.3 Scope of Interim Technical Report

According to the prime purpose of Stage 1, i.e., to

provide a 'blind1 prediction for comparison with field

observations, this report is intended primarily as a document

of our first prediction. This prediction does not reflect the

best possible prediction but rather what could be achieved with

limited computing funds in the limited time available.

While we attempted to predict the actual rock mass

response as closely and as accurately as possible, we realized

when selecting the design parameters that several dominating

parameters were not available, not sufficiently well defined,

or possibly not yet determinable. Hence, we proceeded with the

intent to provide a prediction which should primarily serve as

a basis for comparison with observations rather than as an

accurate prediction of the expected behaviour. In a major

effort, we attempted to select most representative parameters

to provide a forecast of average conditions. However, several

input parameters are expected to vary widely and so will the

expected rock mass response.

With these conditions, objectives and limitations in mind,

we concentrated on simulating the three-dimensional state of

stress and on predicting the response of the expected fracture

zone ahead of the extensometer ring. For this purpose we

- 369 -

conducted analyses of:

(I) a linear elastic rock mass without fracture zone;

(II) a linear elastic rock mass with a linear (joint)

fracture zone and uncoupled fracture pressure

predictions;

Furthermore, a non-linear joint element was developed and

tested (see later). One 3D-analysis has been completed and

further simulations of this kind will be conducted during Stage

2 for presentation in the final report:

(III) linear elastic rock mass with non-linear (joint)

fracture zone (uncoupled fracture pressure).

The procedure and programs for coupled fracture-pressure

displacement analyses were developed and tested (to be reported

in the final report) but no coupled 3D-analyses were completed.

They will be conducted during Stage 2 and presented in the

final report:

(IV) linear elastic rock mass with coupled (fracture

pressure) analyses.

While the latter two conditions reflect reality more closely,

results from Sections I and II indicate that little or no

yielding of the fracture zone is expected. This was confirmed

by the single Type-III-analysis. Coupled analyses may produce

significantly different results depending on the selected joint

parameters.

Considering the complex excavation sequence with

Development Room (DR), Pilot (P) and Slash (S) Excavation, as

well as 10 and 9 excavation steps, respectively, it was

impossible to predict the expected response at all excavation

stages. In an effort to make the 'blind' prediction as valuable

as possible, we concentrated:

a) on predicting the initial state (DR excavated) so that

- 370 -

displacement, stress and permeability changes could be

determined;

b) on predicting the final condition after pilot excavation;

and

c) on predicting the ultimate condition after slashing was

completed.

Results from analyses of intermediate excavation stages

(to be presented in the final report) should be considered as

'blind' predictions as long as the parameters and methods of

analysis are unchanged and the ultimate responses (reported in

this report) are matched.

In summary, this interim report presents uncoupled

analyses of the Room 209 Excavation in linear elastic rock with

and without a linear elastic fracture zone at three stages:

development room excavated, pilot completed, slashing

completed. Because of the almost ideal setting with a single

water-bearing fracture zone, our analyses contain only one

major discontinuity and fluid flow is only simulated in this

plane.

1.4 Finite Element Program Descriptions

The geomechanics simulations were conducted with the

program SAFE - Soil Analysis by Finite Elements developed by

Dr. D.H. Chan at the University of Alberta (Appendix A). All

modifications, e.g., joint element implementation, are made to

this program.

ADINAT (Adina Eng., 1984) was used for the fracture flow

modelling. As described later in Section 3.6, SAFE and ADINAT

- 371 -

were coupled to enable simulation of the effect of fracture

pressure changes on the response of the surrounding rock and

the fracture itself.

- 372 -

2. DESCRIPTION OF ROOM 209 EXPERIMENT AND AVAILABLE DATA

The location of all instrumentation, the excavation sequence

and the rock properties were made available in stages during

meetings at the URL or in several memoranda. The amount of

information provided is very large and cannot be summarized in

a meaningful manner. Hence, the reader is referred to the draft

report prepared by Lang et al. (February 12, 1987). All data

contained in that report constitutes part of this report.

Individual aspects which were used for our analyses will

be introduced and explained where appropriate.

- 373 -

3. DEVELOPMENT OF THE FINITE ELEMENT MODEL

3.1 Finite Element Mesh and Coordinate System

The finite element mesh configuration adopted for the 3-D

simulation of the Room 209 Excavation is shown in Figures 3.1

and 3.2. Although a full mesh analysis would have been

preferable, the economics of such a mesh was beyond the

available resources and was not justifiable for Phase 1 and

developmental work. The non-circular shape of the excavation

also meant that a quarter mesh could not adequately represent

the excavation geometry. Therefore, a half-mesh was utilized.

This mesh took advantage of a vertical plane of symmetry

passing through the axis of the tunnel.

A cross-section of the half-mesh is comprised of 93

elements and 219 nodes in one plane (Fig. 3.1), or 501 nodes in

a slice of elements. Most of the nodes are located on lines

which radiate from the excavation boundary. Some of these lines

were designed to correspond with che radial extensometers and

certain nodes were positioned at the approximate extensometer

anchor point locations (see later Figs. 4.3a and 4.3b).

The sizing of the elements was based on experience gained

during previous 2-D and 3-D finite element modelling of

circular excavations performed at the University of Alberta.

The mesh is terminated at about eight tunnel diameters (33 m)

from the excavation. Previous experience has shown that this

size of mesh adequately models the far-field conditions.

In the longitudinal direction (z-axis) the mesh is

comprised of 20 slices including one slice of joint elements

representing the fracture zone. Figure 3.3 shows a horizontal

section with the slices between, the Development Room and the

- 374 -

location of the stress change gauges. The thickness of the

slices varies throughout the mesh. The slices are narrowest

(0.5m) near the extensometer and fracture zone locations and

are widest (8.0m) at the margins of the mesh. Many of the

slices are designed to correspond with the excavation stages.

However, the actual excavation faces are approximated by a

vertical plane. The fracture zone was represented by a planar

slice of joint elements. The symmetry associated with the

half-mesh required that these joint elements be orientated

perpendicular to the tunnel axis. Fortunately, the actual

fracture zone is nearly perpendicular to the tunnel axis and,

hence, this approximation should yield reasonable results.

Three slices of the mesh were altered to better

approximate the shape of the development room. Some element

boundaries in the inner mesh were moved to allow for a smoother

representation of the wider section of the development room

(Fig. 3.4) and to generate more accurate stress conditions near

the extensometer locations.

The boundary conditions imposed upon the mesh are shown in

Figure 3.5 and consist of:

1. fixing the displacement in the z-direction at both

longitudinal margins of the mesh;

2. fixing the displacement in the x-direction along the

vertical plane of symmetry? and

3. fixing all degrees of freedom along the remaining boundary

of the mesh.

The effect of fixing the nodes along the cylindrical surface

was assessed by performing 2-D analyses using free nodes and

fixed nodes. The difference in radial displacements at the

extensometer anchor point locations between the fixed case and

the free case was found to be small (maximum of about 10%). The

- 375 -

two cases with fixed and free boundaries would give upper and

lower bounds on radial displacement but only the fixed boundary

was used.

The excavation of the development room, pilot and slash

was simulated by seven consecutive excavation stages:

1. excavation of the development room;

2. excavation of the pilot to within one slice (0.5 m) of the

joint (called J-1);

3. excavation of the pilot to one slice (1.10 m) past the

joint (called J+1);

4. excavation of the remaining pilot (full pilot);

5. excavation of the slash to within one slice of the joint

(called J-1);

6. excavation of the slash to one slice past the joint

(called J+1);

7. excavation of the remaining slash (full excavation).

The locations of the slices immediately before and after the

joint correspond to planned, actual excavation steps at these

locations. The finite element mesh allows for more detailed

simulation of the actual excavation sequence by modelling more

of the excavation steps, however, this was not completed in

this phase of the modelling.

Specific locations and directions of positive

displacements and stresses within the finite element mesh are

related to the mesh's cartesian coordinate system as shown in

Figures 3.5 and 3.6. The relationship between the finite

element mesh coordinate system and the coordinate system used

by AECL is as follows:

- 376 -

a) Elevations (Y) correspond

b) Z = (E-Eo)cos30° - (N-No)sin30°

c) X = (E~Eo)sin30° - (N-No)cos30°

where No = 5570543.87 and Eo = 295792.5 (in meters) and N and E

are the northing and easting.

3.2 Approximation of In Situ Stress Tensor for Finite Element

Analyses

3.2.1 Selection of Representative State of Stress

Memorandum GSEB-86-197 presented a summary of the in situ

stress testing in the Room 209 area. The results were grouped

according to the method of stress measurement; CSIR or USBM

technique. The principal stress orientations obtained from both

types of test methods agreed reasonably well with each other,

however the stress magnitudes from the CSIR tests were about

15% lower than those from the USBM tests. For the calculations

of Stage 1, we have chosen the stress magnitudes of the CSIR

tests because these values are partially verified by the USBM

tests and are measurements from Borehole 209-010-OC1 in the

immediate vicinity of Room 209. There was some doubt about the

reliability of the USBM results since the 3-D stress tensor was

calculated by combining measurements from locations 20 to 30 m

apart. Furthermore, these measurements were not from the

immediate vicinity of Room 209. Fortunately, the similiarity of

the CSIR and USBM stress tensors gives some confidence in

assuming that the measured CSIR stress tensor should be

applicable throughout the rock mass influenced by the

excavation experiment at Room 209.

Rather than using the average stress orientations given by

the CSIR tests, we have chosen the average orientation of all

- 377 -

measurements. In this manner, any localized effects that might

influence the point measurements of the CSIR method are

smoothed out. Consequently, the following in situ principal

stresses were assumed to be applicable throughout the zone of

influence:

a, = 26.6 MPa at 16°/222°;

o2 = 16.5 MPa at 35°/120°;

a3 = 9.0 MPa at 50°/332°.

The orientations provide dip relative to a horizontal plane and

dip direction of the stress vector. The corresponding principal

stress ratios are:

Kl2 = 1.61; K23 = 1.83; K,3 = 2.96.

3.2.2 Simplified State of Stress

Our 3-D finite element model consists of a half-mesh as

shown in Figure 3.1. Because of symmetry shear stresses can

only be applied as shown in Figure 3.6. This restriction

requires that two principal stress directions for the finite

element model must be within the vertical planes (x-y) which

are perpendicular to the tunnel axis (Figure 3.6), and,

furthermore, must be aligned in the horizontal and vertical

directions (x and y). Therefore, for finite element modelling

the stresses ox, ay, az and ryz are required. The shear stresses

rxy and rX2 had to be set to zero.

Since the existing in situ principal stress directions are

inclined with respect to all coordinate axes, the existing in

Situ stress tensor had to be transformed to the coordinate

system which corresponds to the tunnel coordinate system used

for the finite element analysis (Fig. 3.6). a2 was first

rotated to the tunnel axis as it was already in the vertical

plane containing the tunnel axis. This only required a vertical

rotation of 35" for it to become parallel to the z-axis. By

- 378 -

performing this transformation the new stress tensor reads:

(MPa)<\x T

Tyx °Tz* T

xy xz

yy yz

zy °zz

24

4 .

3 .

. 54

53

31

4 .

12.

- 2 .

53

73

54

3

- 2

14

. 3 1

. 5 4

.80

This tensor relates to the x,y,z tunnel coordinate axes.

Positive normal stresses are compressive.

The stresses axil and oyy are the horizontal and vertical

stresses in the x-y plane but they are not the maximum and

minimum stresses within this plane as rxy is not yet zero.

However, a simple angular rotation of the stress tensor in this

plane allows the determination of the principal stresses in the

x-y plane, o'x and o'y and their inclination, a (Fig. 3.6). These

stresses are o\ - 26.0 MPa and a'y = 11.0 MPa and are inclined

at a = 19° clockwise from the horizontal and vertical,

respectively, viewed in the direction of tunnel advance.

We elected to perform the finite element analyses by

applying these stresses (o'K and a'y) in the horizontal and

vertical directions; o' = o , a'« a y

reasons for making this approximation:

o . There are a number ofy

1. By using the values of o\ and o'y rather than ox and cy, the

true in situ stress ratio in the x-y plane is maintained at

2.36 rather than 1.93 (if the magnitudes of oxx and oyy were

used and shear was neglected).

2. The half-mesh cannot incorporate any shear stresses in the

y-z plane. By using the principal stresses in the x-y

plane, the effect of the shear stress rxy is not neglected.

3. The in situ stress ratio of 2.36 in the x-y plane may have

a significant influence on the deformation patterns around

the excavation. By maintaining this ratio, abeit in the

- 379 -

wrong orientation, it is possible to account for the

influence of this fairly high stress ratio by rotating the

calculated stress, displacement and strain field back by

19°. '

4. By using this technique of rotating back, a non-symmetric

stress and displacement field will evolve even though a

symmetric half-mesh was used. In this manner, it should be

possible to generate the expected non-symmetrical response,

The attempt to simulate the non-symmetric in situ stress

field with a half-mesh and rotation of the calculated

quantities relies on the assumption that the geometry of the

excavation has little effect on the displacement field. This

assumption would be valid for a cylindrical excavation but is

not exact for the Room 209 excavation. However, it is felt that

using the principal stresses o\ and a'y and thereby maintaining

the higher stress ratio was more important than properly

describing the excavation geometry. This compromise is

necessary because of computational cost restrictions. The

significance of this assumption could be tested if necessary.

The procedure described above also produces, as an intermediate

step, the symmetric displacement pattern, and therefore the

influence of the excavation geometry may be assessed before

back-rotation.

3.3 Selection of Rock Mass Parameters

The rock mass is assumed to behave as a linear elastic

material and one specific Young's modulus and Poisson's ratio

of the rock surrounding Room 209 had to be estimated. The

effect of possible blast damage was neglected for Stage 1. In

Memorandum GSEB-86-051 the rock mass was assumed to be best

'The influence of opening shape was considered to be of lessimportance (compared to the effect of stress ratio).

- 380 -

approximated as a homogeneous elastic medium with Young's

modulus, E = 40 GPa and Poisson's ratio, v = 0.2. These values

were recommended by AECL after consideration of the behavior of

the rock around instrumentation rings in the shaft where

back-calculations using observed displacements were performed.

These values may not be appropriate for the rock near Room 209.

Since Room 209 is at a greater depth and is located in

less fractured rock than the instrumentation rings in the

shaft, it seems probable that the Young's modulus would be in

excess of 40 GPa. Memorandum GSEB-86-260 provided results of

modulus determination for the pink and grey granite at various

stress levels. The results show an expected stress level

dependency of the modulus. Using Figure 1-2 (GSEB-86-260) and

assuming an average in situ stress level of about 20 MPa at

Room 209, the tangent modulus was found to be about 70 GPa. The

modulus values presented in Figures 1-1 and 1-2 were determined

from biaxial testing of overcored samples and probably

represent appropriate values for small intact rock samples.

However, the rock mass contains small fractures and

micro-cracks in varying concentrations which tend to reduce the

modulus. Thus 70 GPa appears to be a realistic upper bound and

40 GPa a reasonable lower bound for the Young's modulus of the

rock mass. Overcoring results in Borehole 209-010-OC1 presented

in GSEB-86-051 give an average E modulus of 53.5 GPa.

Considering this information, a Young's modulus of 50 GPa was

chosen for our initial simulations (Stage 1).

Figure 1-2 (GSEB-86-260) shows that there is practically

no difference in modulus between the pirk, grey, and

leucocratic granite. While some differentiation may be

justified later when the actual conditions are known, the

Stage 1 finite element simulation has been simplified by

modelling the entire rock mass as one material type regardless

of the actual rock types. Although data presented in

- 381 -

GSEB-86-260 also shows some anisotropy near Room 209, this

anisotropy had to be neglected for reasons of symmetry and the

rock mass was assumed to be an isotropic, linear-elastic

medium.

Values of Poisson's ratio, determined from uniaxial

testing of intact 45 mm diameter drill core (GSEB-86-260), vary

between 0.24 and 0.27 for grey and pink granite, respectively,

and an average of 0.18, determined from CSIR testing in

Borehole 209-010-OC1 (GSEB-86-197). A value of 0.2 was chosen

for our model as recommended in Memorandum GSEB-86-051.

3.4 Selection of Fracture Zone Parameters (Joint Element)

3.4.1 Joint Properties and Characterization

Many rock joints from the URL area have been sampled and

examined. The preliminary results on joint testing and

characterization were presented in Memorandum GSEB-86-260 and

the report by Jackson et al. (1985). The joints were

characterized using the method of Barton and Choubey (1977),

which allowed quantification of the joint surface roughness and

the joint wall strength based on the parameters, JRC (joint

roughness coefficient) and JCS (joint wall compressive

strength).

The data presented in GSEB-86-260 were obtained from tests

on joint samples collected from boreholes drilled from within

the shaft at depths of less than 100 m below ground surface.

These near surface joints tend to exhibit greater weathering

and alteration of infilling materials and often have different

characteristics from joints at greater depths. Since Room 209

is located approximately 240 m below ground surface, the data

from the relatively shallow joint samples may possibly not be

- 382 -

representative of the joint conditions in the Room 209 area.

For this reason the joint characterization data contained in

GSEB-86-260 was neglected and only the joint data provided in

the report by Jackson et al. (1985) were considered. This

report provides values for JRC0, JCSO and oc for rock joint

samples obtained at various depths (note: the subscript, 0,

refers to parameters obtained from laboratory size joint

samples). In an attempt to characterize the joints around Room

209, the data from all samples taken at depths greater than

about 100 m and less than 270 m were compiled for the URL

boreholes near the shaft location (URL1, URL5, URL6). These

data was averaged to obtain representative values of JCS0 and

JRC0 for joint characterization. Based on these data the

following values were assumed applicable to the joints in

question:

JCSo = 127 MPa

JRC0 = 6.6

oc = 184 MPa

Lo = 40 cm.

Some joint models require an estimate of the initial

mechanical joint aperture, Eo. This aperture could be estimated

by application of the empirical relationship provided by Barton

and Bakhtar (1983):

Eo st 3^± (0.2ac/jCSo " 0.1). [3.1]

However, it seemed more appropriate to utilize the borehole

fluid withdrawal test results which were performed on

packer-isolated intervals of the fracture system to estimate

the equivalent fracture aperture directly (Kozak and Davison,

1986). The equivalent rock mass permeability, Kerm was

determined from either multiple-step or single step fluid

withdrawal tests such that only small changes in hydraulic

pressure were generated (<200 kPa). A relationship between flow

rate, Q, and pressure drop, Ap, was established and Kerm was

- 383 -

determined from the linear portion of this relationship (Kozak

and Davison, 1986):

Kerm = (Q/Ap) 2^L ln(R/r) [3.2]

where L is the length of the test interval, r is the radius of

the borehole and R is the radius of influence of the pressure

drop (reach). The reach was assumed to be 15 m based on results

from pressure response tests in the same boreholes.

The equivalent single smooth-wall hydraulic aperture, e

(or conducting aperture) was then determined from Kerm:

e = "i (K 12MU1/3 [3.3]er

wheie u is the fluid viscosity, p is the fluid density and g is

the gravitational acceleration.

The results from Kozak and Davison (1986) show that the

hydraulic apertures vary greatly over short distances (2 to

10 m) ; the largest variation being from 14 nm to 155 /urn. Kozak

and Davison (1986) make simlifying assumptions and the

hydraulic apertures determined in this fashion are only rough

estimates.

The results are based on the assumption that the reach was

15 m, however, the interborehole pressure interference tests

gave rapid response times (<1 min). This indicates that larger

values for the reach might be more appropriate. Fortunately,

the magnitude of R does not greatly affect e. For example, with

an R of 100 m, e increases by only 10%. The interference tests

also indicated areas of poor interconnection. Hence, some of

the implicit assumptions for Equation 3.3, e.g., the fracture

representing a disc of infinite radius and constant aperture,

are not strictly valid.

- 384 -

Based on the results from Kozak and Davison (1986) an

average single conducting aperture of 50 Mm was chosen to

represent the initial conducting aperture throughout the

fracture zone. This conducting or hydraulic aperture provided

the starting point for the analysis of fluid flow and fluid

pressure in the fracture zone.

Joint models which utilize joint closure as a parameter

generally require an initial mechanical joint aperture, Eo.

This aperture is used as a referrence point from which changes

in joint closure and/or joint normal stress can be modelled.

Barton et al. (1985) found that the conducting aperture may not

necessarily be the same as the mechanical aperture. Therefore,

the equivalent single fracture apertures (conducting) obtained

from the pumping tests are converted to mechanical apertures

using the empirical equation developed by Barton et al. (1985):

e = E2/JRCo2'5 [3.4]

This equation predicts that the rougher joint surfaces (higher

JRC values) will show greater deviation from the case where the

conducting aperture is equivalent to the mechanical aperture.

Note that this equation is only valid for E > e.

In this fashion, the initial conducting aperture of 50 urn

was converted to an initial mechanical aperture of 75 *xm for

the normal and shear stiffness calculation. Equation 3.4 will

also be used when coupling closure, based on the finite element

analyses (using mechanical joint properties), to fluid flow

based on the hydraulic apertures,

3.4.2 Linear-Elastic Joint Model

The simplest joint model utilized in the finite element

simulation was a model with a constant normal stiffness, Kn,

and a constant shear stiffness, Ks. This model assumes a linear

- 385 -

variation of normal stress, on, with normal closure, V^, and a

linear relationship between shear stress and shear

displacement. The shear stiffness is assumed to be independent

of the normal stress.

Data from shear or closure tests was not provided. Values

of Kn and Ks had to be estimated, based on the empirical

formulae provided by Bandis et al. (1983), and Barton et al.

(1985). The JCS0, JRC0 and Eo values reported earlier were used

to calculate a hyperbolic normal stress versus closure curve

(see section 3.4.3.1) and a slightly non-linear shear stiffness

versus normal stress curve. In order to estimate a single value

for both the normal stiffness, Kn and shear stiffness, Ks, an

appropriate effective normal stress on the joint was required.

Prior to the Room 209 excavation the normal stress was assumed

to be 14.8 MPa. However, this is a total stress and the fluid

pressure in the joint is required in order to estimate the

effective normal stress.

The records from the pressure gauges installed in

packed-off intervals of the fracture (Kozak and Davison, 1986)

give an indication of the steady-state fluid pressures. Aside

from the perturbations caused by drilling activities in the

shaft and Room 209 area, there appears to be a consistent trend

of increasing piezometric pressure with time over the period of

April 1986 to the end of October 1986. The increase in pressure

was approximately 100 kPa. The changing piezometric pressures

may indicate that an equilibrium pressure has not yet been

reached or that the fluid pressures in the fractures are being

influenced by seasonal variations in the regional groundwater

flow pattern. In an attempt to choose a representative value of

the fluid pressure at the time of the excavation of Room 209,

the pressures recorded at the end of October 1986 were averaged

to yield a value of 1065 kPa. This value was employed to

determine the effective normal stress acting on the joint prior

- 386 -

to the Room 209 excavation.

In order to choose a representative value of Kn and Ks, an

estimation of the range in normal effective stresses at various

locations in the joint at various stages of the excavation was

also required. The fluid pressures were assumed to vary from 0

to 1065 KPa. The range in total normal stress was obtained by

performing a 2-D finite element analysis under plane strain

conditions with full tunnel excavation. This analysis showed

that the greatest fluctuations in normal stress occur

immediately around the opening. The variations in stress

quickly reduce to less than about 2 MPa at one meter from the

opening. The normal stress either increases or decreases from

the initial magnitude depending upon the location around the

opening. Considering the fluid pressures and expected range of

total normal stress, 14 MPa was taken as the repesentative

effective normal stress in the fracture, from which the

following Kn and Ks values were initially chosen:

Kn = 10000 MPa/mm and Ks = 4.6 MPa/mm.

These two stiffness parameters fully define the mechanical

behavior of the linear joint model.

The finite element mesh models the presence of one joint

which is assumed to represent the behavior of the water bearing

fracture zone. Since this zone is composed of more the one

discrete fracture (typically about four), the joint element

parameters must attempt to represent the behavior of a fracture

zone rather than a single fracture. The parameters for the

joint element were based on JRC and JCS values obtained from

single representative joints, and also on the estimate of the

initial conducting aperture.

The initial conducting aperture was determined from pump

tests performed on packed-off sections of the fracture zone

- 387 -

and, hence, provides a single value of initial aperture

representing the complete fracture zone.

The values of JRC and JCS should be modified to allow for

single joint representation of a fracture system, but this was

not performed for the Stage 1 simulations as no information was

available concerning the extrapolation of the empirical

relationships from discrete fractures to fracture systems

represented by equivalent single fracture properties. Rather

than modifying the joint parameters JRC, JCS and e, the normal

stiffness and shear stiffness of the joint element (which are

based on these parameters) can be altered in an attempt to

account for the presence of multiple fractures in the fracture

zone.

An initial set of finite element analyses of the

geomechanical response of the Room 209 Excavation was performed

using linear joint elements with the previously indicated

stiffness values. A preliminary analysis of these results

showed that there was little relative shear within the joint

and very small changes in normal closure. These analyses were

conducted using 2 x 2 Gaussian integration in the joint

elements. The aperture variations within these elements

(although very small) seemed to show unexpected fluctuations

near the tunnel. A single analysis using 3 x 3 Gaussian

integration showed improved response of the joint elements to

normal closure. Since the normal closure of the joint has a

dominant control on the hydraulic response of the joint, it was

necessary to repeat the linear joint analyses using 3 x 3

integration to obtain more reasonable aperture distributions.

However, rather than repeat the analyses with the orginal joint

stiffness values, the subsequent analyses were conducted with

reduced stiffnesses. The motivation for using a softer joint

element was twofold:

1. to account for the presence of multiple fractures in the

- 388 -

fracture zone and

2. to allow the joint to have greater influence on the

hydraulic response within the joint.

The normal stiffness was reduced to one half, from 10000 MPa/mm

to 5000 MPa/mm. The shear stiffness chosen for the initial

analyses was based on the shear stress required to reach peak

shear displacement, Ksp, using Barton and Bakhtar's (1983)

empirical curve (Fig. 3.7). The joint was assumed to have

sheared to approximately peak strength. However, the

preliminary analysis showed that much less than peak shear

displacement was achieved. Therefore the initial shear

stiffness at low shear displacement, Ksi, should have been used

(i.e. approximately 12 MPa/mm). Based on the assumption that

the fracture zone (composed of an average of four fractures) is

four times softer in shear than a single fracture, the shear

stiffness of 12 MPa/mm was reduced to 3 MPa/mm for the

subsequent (3 x 3) linear joint analyses.

3.4.3 Hyperbolic Normal Closure of Joint

3.4.3.1 Barton-Bandis Joint Model

Bandis (1980) found that the behaviour of natural, unfilled,

interlocked rock joints is described by a hyperbolic

stress-closure relationship. This hyperbolic joint model is

given as:AV,— i = a - bAVj [3.5]

n

where AV^ is the normal closure of the joint, <rn is the normal

effective stress applied to the joint, and a and b are

empirical constants. The asymptote to the hyperbola, (a/b) is

equal to the maximum joint closure, Vm. The constant, a, is

equal to the reciprocal of the initial normal stiffness Kni.

Therefore, knowledge of Kni and Vm completely defines the

- 389 -

hyperbolic model.

The values of Kni and Vm are dependent on a^, JCS0 and JRC0,

where a is the mechanical fracture aperture. The following two

equations present the empirical relationships developed by

Bandis (1980) to calculate Knl and Vm.

Kni = 0.02 (JCS0/a3) + 1.75 JRC0 - 7 [3.6]

Vm = A + B (JRC0) + C (JCS0/a:)D [3.7]

The constants A, B, C and D are given by Barton and Bakhtar

(1983) for different cycles of loading-unloading. Equation 3.7

was found applicable for describing the variation in the

maximum closure of unfilled, interlocked joints (Barton and

Bakhtar, 1983).

3.4.3.2 Selected Hyperbolic Normal Closure Parameters

The Bandis hyperbolic stress-closure joint model was

implemented as a non-linear normal closure model in the 3-D

joint element (refer to Appendix B). The required initial

stiffness Kni and the maximum joint closure Vm were calculated

by using the values of JCSOf JRC0 and Eo presented earlier:

1. the representative maximum closure was estimated to be

0.024 mm; and

2. the representative initial normal joint stiffness was

estimated to be 38 MPa/mm.

These two values fully define the normal closure relationship:

- 390 -

This hyperbolic normal closure relationship can be used

with linear or non-linear elastic or plastic constitutive

relationships for shear. The tangent to this curve at the

normal stress level of 14 MPa was used to estimate the initial

linear normal stiffness of 10000 MPa/mm.

3.5 Seepage Analyses in Fracture Zone

3.5.1 Fracture Permeability Characterization

Many researchers have used flow between smooth parallel

plates as a model for fluid flow in rock fractures. The

parallel plate solution is based on laminar flow through an

open fracture and the resulting constitutive equation can be

expressed as:

pg

This expression was found to be applicable for fracture

apertures as small as 0.2 urn (Witherspoon et a)., 1980). The

expression for permeability can then be incorporated into the

equation for fluid flow to yield:

pgQ = K i A = jj£ e* i t3'10

where i is the hydraulic gradient and A is the cross-sectional

area of flow (assumes unit width). This constitutes the well

known "cubic law" for fluid flow through parallel plates.

Fractures generally have uneven walls and variable

aperture and also involve contact between adjoining surfaces.

In order to account for flow in rough fractures many

researchers have modified the parallel plate relationship

(Eqn. 3.9) by either adding terms related to the relative

- 391 -

roughness of the fracture or by defining an effective hydraulic

aperture. This is in accordance with Gale (1977) who stated:

"One should not attempt to account for the reduced flow rates

in fractures where roughness is a significant factor by varying

the basic cubic relationship. Instead, one should either alter

the size of the aperture,, making it a function of the spatial

coordinates, or expand the basic parallel plate relationship by

adding a compatible term to compensate for the deviation of the

fracture in question from the concept of smooth parallel

walls." Following this logic the mechanical joint apertures

(nodal apertures) from the 3-D excavation response modelling

are converted to hydraulic (nodal) apertures via the empirical

relationship Equation 3.4. These apertures can then be

converted into nodal permeabilities using Equation 3.9.

3.5.2 Finite Element Representation of the Fracture Zone

The finite element mesh used for the 2-D simulation of

fluid flow in the fracture zone is identical to the

cross-section of the 3-D mesh employed for the 3D-modelling of

the geomechanics (Figs. 3.1 and 3.2). The seepage analyses were

performed using the computer code ADINAT. Although ADINAT

allows for transient flow analysis, only the ultimate

steady-state condition was established.

The boundary conditions assumed for the seepage analyses

consisted of:

1. Specifying constant nodal values of pressure head at the

outer mesh boundary. This implies that the initial in situ

hydraulic pressure is assumed to be constant over the

entire flow region (i.e. not hydrostatic). The

applicability of this assumption can best be assessed when

the actual observations are available.

2. Setting the head equal to zero at the inner boundary nodes.

- 392 -

The location of this inner boundary is dependent on which

excavation step is modelled.

3. The remaining boundary nodes, along the line of mesh

symmetry, are left free.

The initial piezometric pressure in the fracture zone (prior to

excavation) was assumed to be 1065 kPa.

The seepage analysis using ADINAT requires that a single

permeability (and aperture) be assigned to every element. The

results from the 3-D excavation response analysis using SAFE

provided the required hydraulic nodal apertures. The technique

utilized to convert nodal apertures into elemental apertures

consisted of averaging all nodal hydraulic apertures within a

particular element.

The technique for generating elemental permeabilities was

more complex and based on several important assumptions. While

more complex relationships have been developed, e.g., by Tsang

and Witherspoon (1981), we opted to determine the element

permeability by only considering 'serial' flow. Hence, the

directions of flow and permeability change were assumed to

correspond. This approach seemed appropriate considering the

geometry of the excavation and the assumed boundary conditions.

After excavation seepage must occur radially toward the tunnel

(Fig. 3.8). Furthermore, the rock mass and the fracture zone

respond to the excavation by deforming such that the greatest

variation in fracture aperture occurs near the opening.

Therefore, excavation effectively generates concentric rings of

different aperture around tunnel. The flow which is induced by

the head drop at the excavation must flow across these rings

and thus flow across a series of variable aperture zones.

The nodal permeabilities were converted into

representative elemental permeabilities using the following

- 393 -

r e l a t i o n s h i p based on ' s e r i a l ' f low:

Kelem = L / / Z K~ [ 3 . 1 1 ]i = 1

where lj are the lengths of the flow path through each band of

average permeability Ki {Fig. 3.8). The total number of bands

is n.

3.6 Coupled Seepage-Deformation Analyses

3.6.1 Overview

A numerical methodology for iterative coupling of the

computer codes SAFE and ADINAT was developed. This enables

coupled mechanical-hydrological modelling of fractured rock

masses. However, the technique has only been tested on single

2-D fractures and has not yet been applied to the 3-D modelling

of the Room 209 Excavations. The procedure and its verification

will be documented in our Stage 2 report.

3.6.2 Coupled Hydro-Mechanical Finite Element Modelling of

Fractured Rock Masses

The coupling technique that was developed and which will

be used to model the influence of rock deformation on fracture

seepage (if sufficiently deformable joint properties are

applicable) is briefly outlined below.

1. An initial aperture distribution and an initial

steady-state fluid pressure distribution are assumed for

the joint elements.

2. Geomechanical analyses are conducted which simulate the

excavation stages until the fracture zone is intersected.

The fluid pressures are assumed to remain unchanged up to

this point. The joint apertures are allowed to change in

- 394 -

response to the changing stress field.

3. When the excavation intersects the joint elements, the

boundary conditions on fluid pressure are altered and an

initial seepage analysis is conducted. A new steady-state

fluid pressure distribution is obtained.

4. The total stresses within the rock mass are assumed to

remain constant and any change in fluid pressure causes a

change in effective stress. Therefore the change in fluid

pressure distribution generates force contributions which

are applied at the nodal points of the joint elements.

5. A new geomechanical analysis is conducted with these

modified forces and the related joint aperture change (and

permeability change) is calculated.

6. The steady-state seepage analysis is repeated with these

new apertures and the revised fluid pressure distribution

is used as input for Step 5. This procedure is repeated

until convergence is achieved.

7. Additional excavation stages can then be modelled by

following the same rationale.

This procedure was tested on a 2D-joint and showed rapid

convergence.

- 395 -

10 IS ?0 25DISTANCE ( m )

30

Figure 3.1 Cross-Section of the Mesh

- 396 -

0 2 4 6

DISTANCE (m)

ENLARGED SECTION OF THEINNER MESH

Figure 3.2

i m

ExtensometerLocations

VI

I Development j Room

Slice Boundaries

10

JointElements)

|

12

j * i

13

i CSIRi Cell

Locationsa

io

14 15

Plane of Mesh Symmetry—-'

Figure 3.3 Finite Element Mesh Near

Instrumentation and Fracture Zone

l i

- 398 -

CD

2 4 6

DISTANCE (m)

ENLARGED SECTION OF THEALTERED INNER MESH

Figure 3.4

t 52m

Development, Room

Joint

Elements

?\\o\/-nioi oiusn-v

Em

I

Figure 3.5 Plan of Finite Element Model

- 400 -

Direction ofTunnel Advance

Mesh Coordinate Systen

Figure 3.6 Applied Initial Stresses

and Coordinate System

- 401 -

Peak

-1.0-

-2.0-1

o£

Ctl - 3 . 0 -

-4 .0 -

- 5 . 0 -

-6 .0

Figure 3.7

Normal Stress - Normal Closure Relationship

- 402 -

Figure 3.8 Assumed Direction of Fluid Flow

- 403 -

4. RESULTS FROM FINITE ELEMENT SIMULATIONS

4.1 Introduction to Data Presentation

According to the intent of this interim report, this

section presents the results of our prediction without any data

interpretations. Limitations are discussed under a separate

heading.

Stresses are calculated and plotted at the Gaussian Points

of the elements. These do not necessarily correspond with the

instrument locations and interpolation is required when

predictions are to be compared with observations. For example,

as shown by Figure 4.1, Stress Cell S1 falls on a node rather

than on an integration point. If instrument locations are shown

on plots of stresses, they are projected onto the line

connecting integration points. Note that the stress profiles

are for the symmetric stress field only.

Additional figures are presented in Appendix D which

incorporate the back-rotated principal stress changes at the

stress cell locations (Fig. 4.1). Appendix D also contains a

table of back-rotated hydraulic apertures. Figure 4.2 shows the

locations of the packed-off intervals relative to our mesh.

Figures 4.3a and b, present the location of the

multi-point extensometers anchors. These points were

back-rotated to determine the locations in the non-symmetric

stress field and the displacements at these specific locations

were used to generate the extensometer plots. The same

transformation is also required for direct comparison of stress

and fracture-pressure profiles with non-symmetric results.

- 404 -

CMCO

back—rotatedlocations

0 2 4 6

DISTANCE (m)

Figure 4.1

Location of CSIR Stress Cells

- 405 -

back—rotatedlocations

0 7 i li 0

DISTANCE (m)

Figure 4.2

Location of Packed—Off Intervals

- 406 -

9

— EXTENSOMETER POINT

O NODAL POINT

s• - ? . 9 01*

Figure 4.3aLocation of Extensometer Anchors

andAssociated Finite Element Nodes

6

- 407 -

•1 01 »

o- 'a

— EXTENSOMETER POINT

O NODAL POINT

J.50t«>' 4 / 3 01 J 5 l « l i » t O V "

Figure 4.3b

- 408 -

O

t

t

• = Pilot Crowno = Full Section Crown• = Pilot Springlineo = Full Section SpringlineA = Invert

Figure 4.4Location of Convergence Measurement Points

- 409 -

4.2 Linear Elastic Rock Without Joint (I)

Uncoupled Analysis

4.2.1 Assumed Parameters

Field Stress: ax = -26.0 MPa

oy = - 1 1 . 0 MPa

oz = -14.8 MPa

ryz = 2 . 5 4 MPa

Rock Mass: E = 5 0 MPa

v = 0.2

4.2.2 Comments to Figures

4.2.2.1 Displacements

a) Convergence

The location of the convergence points and the

corresponding symbols are shown on Figure 4.4. The radial

convergences of Crown, Springline and Invert along the

tunnel are presented in Figures 4.5 to 4.7. Inward movement

is positive.

b) Multi-Point Extensometer Movements

Full Pilot:

Figures 4.8 to 4.14 represent displacements relative to the

anchor heads. The rotated anchor positions are shown on

Figures 4.3a and 4.3b. Positive displacements indicate

extension between anchor points. For comparison with

results presented later in Section 4.3, the displacements

on either side of the joint (fracture zone) are shown for

the crown in Appendix C, Figure C.29 and for the springline

in Figure C.30 together with the relative displacements (or

displacement differential).

- 410 -

Full Excavation (after slashing):

Correspondingly, Figures 4.15 to 4.21 represent predictions

at the extensometer ring and Figures C.31 and C.32 at the

fracture zone.

4.2.2.2 Stresses

Stresses have been calculated and are available on tape for

these cases but are not included because they differ little

from those calculated for the case with a linear elastic

fracture zone after complete excavation of pilot or slash.

E 2

a>EO

Q

T3oct:

-1

-•®. \

vs

' ' 1 ' ' - ^ ^ ^ ^ ^ ^

1

(

onA

1 1 '

= Full Section= Full Section= Invert

• h i i ^ ^ ^ BM f ^

LJ LJ LJ U t-l U

1 • ' I 1 ' "

CrownSpringline

1 * • • I I "

10 15 20 25 30 35 40

Distance Along Axis of Excavation (m)45 50 55

Figure 4.5 No Joint : Development Room Excavation

oPilot CrownFull Section CrownPilot SpringlineFull Section SpringlineInvert

15 20 25 30 35 40Distance Along Axis of Excavation (m)

Figure 4.6 No Joint : Pilot Excavation

ca>Ea>o

"Q.w

Q

~UT>O

2H

- 10

o = Full Section Crownu = Full Section SpringlineA = Invert

I I

B

10 15 20 25 30 35 40Distance Along Axis of Excavation (m)

45 50

I

55

Figure 4.7 No Joint : Full Section Excavation

£

oo

c

£

oV)c<u

-•—X

Ld

0.30

0.25

0.20

0.05

0.00

Figure 4.8a

5 10 15



20

0.30

0.25

o•••

emen

tfe

r M

ov

enso

mel

O.2O

0.15

0.10

0.05

0.00

Figure 4.8b



20

Figure 4.9 Diagonal Extensometer EXT03Nn .Inint* Pilot Fyr.nvntinn

£ 0.7-

D 0.6-ou

0.5-

Figure 4.10

-vj

I



20

E

ou

c0)

<D

O

v_<D

••—<DEo

<LJ

0.30

0.25

0.20

0.15 :

0.10

0.05

0.00

00I

Figure 4.11


Floor Extensometer EXT05No Joint: Pilot Excavation

20

0.45

E

Col

lar

••*

0.40

0.35

0.30

0.25-

0.20

0.15

E o.ioo

LxJ

0.05

0.00

Figure 4.12

5 10 15



v©

20

Figure 4.13a SL Extensometer EXT07No Joint: Pilot Excavation

Figure 4.13b SL Extensometer EXT08No Joint: Pilot Excavation

5 tO 15


Figure 4.14 Diagonal Extensometer EXT09No Joint: Pilot Excavation

0.30

0.00

Figure 4.15a



I

* -

I

20

EE

oo

I

ocQ)

"xLJ

0.30

0.25

0.20

0.15

0.10

0.05

0.00

Figure 4.15b



I

20

0.45

LULU

)

Co

llar

•

/em

ent

w

o

jom

et<

Ext

en!

0.40-

0.35-

0.30

0.25

0.20

0.15

0.10

0.05

0.00

I

to

I

5 10Distance Along Extensometer (m)

20


D 0.6-

<S0.5

Figure 4.17



i

20

0.30

0.00

Figure 4.18



I

I

20

?E,V.

"oo•••

<uEQ>>O2v_

"Q>

Eo<ncQ)

0.45-

0.40

0.35

0.30-

0.25

0.20-

0.15

0.10

0.05

LJ

0.00

tooo



E

oo

0)

"5£owcd)

~xLd

Figure 4.20a

5 10Distance Along Extensometer (m)

5L Extensometer EXT07No Joint: Full Section Excavation

Figure 4.20b



O

20

0.45

E

liar

oo

•

EQ)

O

%EoV)ca>

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.005 10 15


u>

20


- 432 -

4.3 Linear-Elastic Rock Mass with Fracture Zone (II)

Uncoupled Analysis

4.3.1 Assumed Parameters

Field Stress:

Rock Mass:

Fracture zone:

ax = - 2 6 . 0 MPa

ay = * 1 1 . 0 MPa

az = - 1 4 . 8 MPa

r y z = 2 . 5 4 MPa

E = 5 0 MPa

v = 0 . 2

i) 2 x 2 integration:

Kn = 10000 MPa/mm

Ks =4.6 MPa/mm

e = 50 um (hydraulic aperture)

ii) 3 x 3 integration:

Kn =5000 MPa/mm

Ks =3.0 MPa/mm

e = 50 Mm (hydraulic aperture)

4.3.2 Comments to Figures

4.3.2.1 Displacements

a) Convergence

Radial convergences for the Crown, Springline and Invert

are shown in Figures 4.22 to 4.24. The location of the

convergence points and the corresponding symbols are

indicated on Figure 4.4. Inward movement is positive.

b) Multi-Point Extensometer Movements

Full Pilot:

Figures 4.25 to 4.31 present the radial displacement

distributions at the extensometer ring and Figures C.33 and

C.34 on either side of the fracture zone for crown and

- 433 -

springline. The differential movement predicted for the

fracture zone is also shown. Extension is positive.

Full Excavation (after slashing):

Figures 4.32 to 4.38 and Figures C.35 and C.36 represent

the corresponding figures for the conditions after slashing

to the full excavation.

c) Intermediate Excavation Steps

As outlined in Section 3.1, intermediate excavation steps

where simulated with pilot or slashing stopping immediately

before (J-1; Z = 23.5m) or after (J+1; Z = 25.2m) the

fracture zone. The corresponding convergence profiles are

summarized in Figures 4.39 to 4.42 for pilot and full

excavation, respectively. The displacement profiles at the

multi-point extensometer ring and plots of differential

movement at the fracture zone are presented in Appendix Cr

Figures C.1 to C.28 (for the symmetric case).

4.3.2.2 Stresses

Stresses are expected to vary significantly in the vicinity of

the excavation and, hence, readings are extremely sensitive to

the exact instrument location. Furthermore, we are not certain

in which form the observed stresses or stress changes will be

presented. For these reasons, we decided to provide stress (not

stress change) profiles for the stress gauge ring after

development room, full pilot and full slash excavations (for

the symmetric stress field). The normal and shear stress

profiles for these excavation stages are presented in Figures

4.43 to 4.48 for roof and floor. The corresponding stress

profiles for the springline are given in Figures 4.49 to 4.59

for the north (N) side and south (S) side. (Compression is

negative for these figures).

Stresses for the intermediate stages have been calculated

but not yet plotted and could be provided as a supplement if

- 434 -

required.

It is important to note that a direct comparison between

observed stress changes and stresses presented in these figures

is not possible for several reasons:

sensitivity to instrument location;

need for back-rotation because of assumed horizontal

principal stresses; and

extreme variations in shear stresses near springline

(compare Figs. 4.58 and 4.60 for north and south side

locations).

It may prove to be more useful to generate normalized stress

change versus time profiles to compare relative stress changes

between excavation stages rather than absolute values. This

aspect will be covered in our Stage 2 report.

The principal stress changes at each stress cell location

(back-rotated) are presented in Appendix D, Figures D.1 to D.8

for six excavation stages.

E 2E

c

ujoa.V)

Q

O

- 1

o = Full Section Crown• = Full Section Springline^ = Invert

43 H (3 -e- -e- -B-

0 10 15 20 25 30 35 40Distance Along Axis of Excavation (m)

45 50 55

Figure 4.22 Linear Joint 3x3 : Development Room Excavation

= Pilot Crown= Full Section Crown= Pilot Springline= Full Section Springline= Invert


Figure 4.23 Linear Joint 3x3 : Pilot Excavation

EE

c

Eo

2-

o o

- 1

o = Full Section Crownn = Full Section SpringlineA = Invert

I i-u-Q'Hjil Li Q '

• & - - •

o1 I i •


45 50 55

Figure 4.24 Linear Joint 3x3 : Full Section Excavation

£

oo

*

a>

oV)ca>

~x

0.30

0.25

0.20

0.15

0.10-

0.05

0.00

Figure 4.25a


Roof Extensometer EXT01Linear Joint 3x3: Pilot Excavation

a>

20

0.30

0.25

0.20

0.15

0.10

0.05

0.00

Figure 4.25b


Roof Extensometer EXT02Linear Joint 3x3: Pilot Excavation

u>

20

Col

lar

m

I.>

cem

ent v

iter

Mo\

SLU

OS

Ca>

"xLJ

0.40-

0.35

0.30-

0.25

0.20-

0.15-

0.10

0.05

0.00

i i

3

i

1

_ — . e- •

2

. ©

1

i . . .


oI

20

Figure 4.26 Diagonal Extensometer EXT03Linear Joint 3x3: Pilot Excavation

E 0.7 A

Figure 4.27


SL Extensometer EXT04Linear Joint 3x3: Pilot Excavation

20

0.30

0.25

0.00

Figure 4.28


Floor Extensometer EXT05Linear Joint 3x3: Pilot Excavation

I

*»

10

20

£E

oo

E>Ok.<D

%Eo(/>c

Figure 4.29

5 10 15Distance Along Extensorneter (m)

Diagonal Extensometer EXT06Linear Joint 3x3: Pilot Excavation

20

- 444 -

qc

cLX

LJ aQ> N"

o "c^ '"x r

DO

I

(LULU) JD||03 'j'J'M |U9LU8A0|^ J8|9UJ0SU9|X3


i

20

Figure 4.30b SL Extensometer EXT08Linear Joint 3x3: Pilot Excavation


20

Figure 4.31 Diagonal Extensometer EXT09Linear Joint 3x3: Pilot Excavation

E

"oO

cQ>

Q>>O

Eoc0)

X

0.30

0.25

0.20

0.15

0.10

0.05

0.00

Figure 4.32a



I

•IN

20

0.30

0.25-

0.20

0.15

0.10

0.05

0.00

Figure 4.32b



oo

20


20

Figure 4.33 Diagonal Extensometer EXT03Linear Joint 3x3: Full Section Excavation

0.7-

0.2-

0.1-

0.0

Figure 4.34


5L Extensometer EXT04Linear Joint 3x3: Full Section Excavation

O

20

0.30

0.25

0.20

0.15

0.10

0.05

0.00

Figure 4.35

5 10 15


Floor Extensometer EXT05Linear Joint 3x3: Full Section Excavation

U l

20

Figure 4.36 Diagonal Extensometer EXT06

E0.7:

O 0.6-OO

—. 0.5-

0.4

0.3-

0.2-

0.1

o.o-t

Figure 4.37a

5 10 15


SL Extensometer EXT07Linear Joint 3x3: Full Section Excavation

I

20

- 454 -

00oXLJ

CD

O(/>

cQ>

"xLU

3

en

(UJLU) JD||OQ " I '


20

Figure 4.38 Diagonal Extensometer EXT09Linear Joint 3x3: Full Section Excavation

Pilot CrownFull Section CrownPilot SpringlineFull Section SpringlineInvert


Figure 4.39 Linear Joint 3x3 : Pilot Excavated to 23.5 m

E 2E

ca>E

a.V)

Oa:

- 1

• = Pilot Crowno = Full Section Crown• = Pilot Springlineci = Full Section Sprir glineA = Invert

k

0 10 15 20 25 30 35 40Distance Along Axis of Excavation (m)

50 55

Figure 4.40 Linear Joint 3x3 : Pilot Excavated to 25.2 m

= Pilot Crown= Full Section Crown= Pilot Springline= Full Section Springline= Invert

-O -O -Q -Q -Q -

- 115 20 25 30 35 40

Distance Along Axis of Excavation (m)

Figure 4.41 Linear Joint 3x3 : Slash Excavated to 23.5 m

E 2E

c

E

Q

- 1i i • •

i

, . ."^^^^"^^^

i

i

• = Pilot Crowno = Full Section Crown• = Pilot Springline11 = Full Section SpringlineA = Invert

" * > i B l l ••—• • - « _ •. . . . • -« . ,_


45 50 55

Figure 4.42 Linear Joint 3x3 : Slash Excavated to 25.2 m

- 460 -

oCO

o

c2

in

Ld

8-

IR1

F1& F2

9

6

©

iCD

i

6

CD

©

A

AA

AA

4

4 D

0

A

ax

ay

az

- 5 -10 -15 -20 -25 - 3 0Stress (MPa)

Figure 4.43Stresses from Roof and Floor(Development Room 2X2)

-35 -40

- 461 -

O00

o_

o

IT)

bJ

R2

F1& F2

oiii•i

©

o

©

i6

c

CD

D rxy

o ryz

^ TXZ

- 2 - 1 0 1 2 3 4

Stress (MPa)Figure 4.44Shear Stresses from Roof and Floor(Development Room 2X2)

- 462 -

OCO

o_

co

> o_Q) IT

o

R2

F1& F2

O &

i

4

© A

A

© A

?

6 Ai i

7

n

u

[3

D

O

A

ax

cry

5 0 - 5 -10 -15 - 2 0 - 2 5 - 3 0 - 3 5

Stress (MPa)Figure 4.45Stresses from Roof and Floor(Full Pilot 2X2)

-40 -45 -50

- 463 -

- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5Stress (MPa)

Figure 4.46Shear Stresses from Roof and Floor(Full Pilot 2X2)

- 464 -

ooo

o_

oID

o

> 9

R2

R1

F1& F2

CDii

6 A

0 A

J

i

©

©

[]

C3

[]

[)

[I

D

O

A

ax

cry

crz

CM

5 0 - 5 -10. -15 -20 -25 -30 -35Stress (MPa)

Figure 4.47Stresses from Roof and Floor(Full Excavation 2X2)

-40 -45 -50

- 465 -

- 3 - 2 - 1 0 1 2Stress (MPa)

Figure 4.48Shear Stresses from Roof and Floor(Full Excavation 2X2)

• — \

Q_

V)

<D\_

(/)

1

<N -1 .

O

1 .

in

7"

o1

in1 ~

o -

1 1

AyvxxvvA- A* A' A* A* *

GCSBGQOO0-G-

N2 N1

I ii

n n

• • A A'

- -O - - 0

n

•••A-

- - G

LJ

A

©

A

ra

I

LJ

-A

9

i

LJ

A-

g

• - —H

& • • • • •

•€>-•

I

G

O

A

A

ax

ay

az

- ©

0 10 15 20Distance (m)

25 30

Figure 4.49 Stress Distribution from the Springline(Development Room N 2x2)

S1 S2

r o H

CL «N -1

o H

OCHROO OO 0-G - - G - - Q O ©- 'Q e— Q

s*- •ift a fr •A A -&

i

51

10 15 20

Distance (m)25

D rxyI

o T y Z

A TXZ

^

30

Figure 4.50 Shear Stress Distribution from the Springline(Development Room N 2x2)

o

oQ_s •

( / )in

i

-25

oC M -

1 .

1

o1

mI

o -

1 I

GCBXBGQ O O ©-O - O -

S1 S2

l i

n

•A- —

-0--

n

— &• • • •

- - - O - -

I

—A

- - B

&

r3

l

Cj

I

LJ

A . • • • •

g__

• G

o-

i

A

u crx

° cry

A az

• i

0 10 15 20

Distance (m)25 30

Figure 4.51 Stress Distribution from the Springline(Development Room S 2x2)

CD

••—soCL

ess

(

o -

t

1(

1 1S1 S2

GCHI8GO €K> ©-O - -O - -Q - -

fHHH"!"! WW VI W • • • ft • • ' f}—'-

I I) 5

. . . . A . . •B

1

10

A

1

15

• A,

20 25

t.j

o

rxy

Tyz

TXZ

30

Distance (m)

Figure 4.52 Shear Stress Distribution from the Springline(Development Room S 2x2)

1

mCM -

I .

oCM -

a.

"""" in

in 1<na)

(/) oi

mI

r~iN2 N1

/

PI> J\7

LIA i |

1 •

S A - -

1

,^-B

• A

- - ©

A

e —

i

A

O

1

I—,

A

©

B—

A •

O-

I

— — El

A

n ax

° ay

A az

- ©

10 15 20

Distance (m)25

oI

30

Figure 4.53 Stress Distribution from the Springline(Full Pilot N 2x2)

m -

- < * • -

DQ_

<DI.

o -

--G--0 Q Q Ô 9 O >

N2 N1

B-

G

O

A

rxy

ryz

T X Z

0 5 10 15 20

Distance (m)25 30

Figure 4.54 Shear Stress Distribution from the Springline(Full Pilot N 2x2)

otoI

S1 S2

DCL

I

oI

- a - -e-

inV) 7toa>\-

in oI

IDI

O -

•A A u-

- © - - • € > r> n

0

A

ax

ay

az

•A

- -O

0 10 15 20

Distance (m)25 30

Figure 4.55 Stress Distribution from the Springline(Full Pilot S 2x2)

0 0 -

IO -

in -

O

°- •*-ro -

V)V)

o -

7-(M _

to

1 ' '

ftiv\r

S1 S2

I I1

-r\ jy —

^—s_

I

- _R

B— A 25

1 i

Q •

L1 Txy

o T y Z

A TXZ

a

1 '

I

10 15 20

Distance (m)25 30

Figure 4.56 Shear Stress Distribution from the Springline(Full Pilot S 2x2)

oQ_

otoI

mCM -

oCMI

in

7(D

00 o

7

inI

o -

N2 N1

& • & • • * •

JB-

A

-© o

• A -

© 1? —

-e-

D

-•

- • o

ay

az

oi

5 10 15 20

Distance (m)25 30

Figure 4.57 Stress Distribution from the Springline(Full Excavation N 2x2)

15 20

Distance (m)25 30

Figure 4.58 Shear Stress Distribution from the Springline(Full Excavation N 2x2)

O

I

inCM

I

oI

i/i oT

I

DQ_

S1 S2

JB-

A- •

- -e o- o

• t v

-B-

- -o 9 -

- Q

u

o

A

ax

ay

az

•A

- Q


25 30

Figure 4.59 Stress Distribution from the Springline(Full Excavation S 2x2)

OQ-

(N -

o -

I

I

. . A . A - A - A - - - - A ^

3 e 9 O O

a

o

A

Txy

ryz

TXZ

I I


25 30

Figure 4.60 Shear Stress Distribution from the Springline(Full Excavation S 2x2)

- 478 -

4.3.3 Aperture of the Fracture Zone

Since fracture permeability and fracture aperture are

related, but only empirical or simplistic relationships (e.g.,

parallel plate or cubic law, Eqn. 3.6) are available, we have

presented our prediction in terms of equivalent fracture

aperture for a fracture with an assumed initial aperture of

50 Mm. Aperture profiles for roof/floor and springline are

presented in Figures 4.61 to 4.66 for development room, pilot

and full excavation. The hydraulic apertures at specific

locations in the fracture zone corresponding to the location of

the packed-off intervals (back-rotated) are presented in

Appendix D, Table D.1 for the excavation of the development

room, full pilot and full slash.

4.3.4 Uncoupled Pressure Head Distribution/Flow Modelling

Based on the procedure outlined in Section 3.5, the

pressure distribution and flow was calculated in an uncoupled

manner and the results are presented in Figures 4.67 to 4.70.

Fluid pressure profiles for roof/floor and springline, arising

from the pilot and full excavations are given. For comparison,

profiles for constant fracture aperture are presented in

Figures 4.71 to 4.74. Note that there is virtually no

difference between the two sets of figures.

- 479 -

49 49.5 50 50.5Aperture (yum)

Figure 4.61Aperture Distribution from Roof & Floor(Development Room 3x3)

51

0 5 10 15 20Distance (m)

Figure 4.62 Aperture Distribution from Springline(Development Room 3x3)

- 481 -

49 49.5 50 50.5Aperture (//m)

Figure 4.63Aperture Distribution from Roof & Floor(Full Pilot 3x3)

51

O>

10 15Distance (m)

20

Figure 4.64 Aperture Distribution from Springline(Full Pilot 3x3)

- 483 -

49.5 50 50.5Aperture (/xm)

Figure 4.65Aperture Distribution from Roof & Floor(Full Excavation 3x3)

51

en

oo

10 15Distance (m)

20 25

Figure 4.66 Aperture Distribution from Springline(Full Excavation 3x3)

- 485 -

85-

75-

6 5 -

o

>LJ

55 -<

4 5 -

10 20 30 40 50 60 70 80 90 100Normalized Water Pressure (%)

Figure4.67Linear Joint 3x3 : Pilot Excavation

100

<D

10 15 20Springline Coordinate (m)

25

00

30 35

Figure 4.68 Linear Joint 3x3 : Pilot Excavation

- 487 -

C

o

LJJ

15-»10 20 30 40 50 60 70 80 90 100

Normalized Water Pressure (%)

Figure4.69Linear Joint 3x3 : Full Section Excavation

• V

Q>

DV)V)Q>

Ql

(D

"o

0>N

"6Eoz:

90 :

so :

70-

60

50

40

30

20

10

0

^ ^ ^ ^

yS

yS

r

Il"*** i • i

1 1 1 i • • • * i • i ' i

10 15 20Springline Coordinate (m)

25

0000

30 35

Figure 4.70 Linear Joint 3x3 : Full Section Excavation

- 489 -

>CD

1510 20 30 40 50 60 70 80 90 100

Normalized Water Pressure (%)

Figure 4.71 Constant Aperture : Pilot Excavation

<D

100

90

80

7 0 ,

Pre

ssV

oter

<DM

*mal

i;

o

60

50

40

30

20

\0

010 15 20 25

Springline Coordinate (m)

oI

30

Figure 4.72 Constant Aperture : Pilot Excavation

- 491 -

C

o"5>

10 20 30 40 50 60 70 80 90 100Normalized Water Pressure (%)

Figure4.73Constant Aperture : Full Section Excavation

100

15 20Springline Coordinate (m)

25

to

30 35

Figure 4.74 Constant Aperture : Full Section Excavation

- 493 -

4.4 Linear-Elastic Rock With Non-Linear Fracture Zone (III)

A non-linear finite element analysis was carried out in

order to study the effect of yielding in the fracture zone on

the tunnel behaviour. The rock mass was assumed to be linear

elastic with the same parameters as used in earlier analyses.

The following parameters were selected for the elasto-plastic

joint:

Ks1 = 4.6 MPa/mm

Ks2 = 4.6 MPa/mm

Kn = 10000 MPa/mm

f0 = 0.0

fr = 0.0

fp = 3.0 MPa

x = 1.5 mm

xr = 6.0 mm

<t> = 30°

i0 = 5.1°

oc = 127 MPa

where Ks1, Ks2 and Kn are shear and normal stiffnesses in the

linear elastic range; f0, fp and fr are parameters controlling

the position of the yield function at peak or in the post-peak

region; xp and xr represent the total accumulated plastic

relative shear displacement at peak and in the post peak

region; <j> is the friction angle; i0 is the dilation angle for

zero normal stress and oc is the unconfined compressive

strength of the joint asperities. The joint was assumed to be

linear elastic in the normal direction. This is because no

significant normal stiffness variation was expected in the

stress range of interest.

The pilot tunnel was excavated to one element slice before

the joint and one immediately after it. These two steps were

considered to be the most critical in terms of possible

- 494 -

yielding in the joint. However, no yielding was observed

because, for the given parameters, the linear elastic range was

not exceeded. The validity of these parameters and the

practical implications will have to be evaluated by comparison

with field observations.

- 495 -

5. LIMITATIONS OF APPLICABILITY

As outlined earlier, because of time and computing fund

limitations, only very selective cases were analyzed. While an

attempt was made to select the most appropriate rock mass

properties, it was found that insufficient data were available

to make an unconditional prediction. Hence, the results

presented must be viewed as a first approximation for

comparison with field observations. Many extreme

simplifications had to be made and further program development

and parametric studies will be required before an assessment of

our predictive capability can be made. For these reasons, we

cannot foresee that our predictions will agree accurately with

all field observations.

Our prediction is extremely limited and intended as a

basis for an evaluation of where further improvements are

needed.

The following specific examples are intended in support of

this statement:

a) The stress state could only be approximated;

b) Anisotropy was neglected;

c) The single fracture zone could not be orientated

accurately;

d) Effects of blast damage were neglected;

e) The influence of potential temperature changes was not

considered;

f) Only uncoupled analyses could be completed during Stage 1,

g) A single, constant pressure boundary was assumed for the

flow analyses ; and

- 496 -

h) A single, uniformly distributed, initial fracture aperture

was assumed.

Furthermore, in the late stages of our research effort, it

was realized that 3 x 3 instead of 2 x 2 integration schemes

were required for stable fracture zone aperture predictions.

This required a complete re-analysis during April 1987. No

critical data evaluation could be completed before the deadline

for this report. This will be undertaken in Stage 2 when

results are compared with field data. The final technical

report will present the verification of our prediction.

- 497 -

6. REFERENCES

Adina Eng., 1984. ADINAT - A finite Element Program for

Automatic Dynamic Incremental Nonlinear Analysis of

Tempertures. Adina Engineering, Inc. 71 Elton Avenue

Watertown, MA.

Bandis, S. 1980. Experimental Studies of Scale Effecects on

Shear Strength and Deformation of Rock Joints. Ph.D Thesis.

The University of Leeds.

Bandis, S.C., Lumsden, A.C., and Barton, N.R., 1983.

Fundamentals of rock deformation. International Journal of

Rock Mechanics and Mining Sciences & GeomechanicsAbstracts, 20, No. 6, pp. 249-268.

Barton, N. and Bakhtar, K. 1983. Rock joint description and

modeling for the hydrothermomechanical design of nuclear

waste repositories. CANMET, Mining Research Laboratories,

TRE83-10, 258p.

Barton, N., Bandis, S., and Bakhtar, K. 1985. Strength,

deformation and conductivity coupling of rock joints.

International Journal of Rock Mechanics and Mining Sciences

& Geomechanics Abstracts, 22, No. 3, pp. 121-140.

Barton, N. and Choubey, V. 1977. The shear strength of rock

joints in theory and practice. Rock Mechanics, 10, No. 1-2,

pp. 1-54.

Barton, N., Makurat, A., Vik, G., and Loset, F. 1985. The

modelling and measurement of super-conducting rock joints.

26th U.S. Symposium on Rock Mechanics, Rapid city, 1, pp.

487-495.

Carol, I. and Alonso, E.E. 1983. A new joint element for the

analysis of fractured rock. 5th Congress of the

International Society for Rock Mechanics, Melbourne, 2, pp.F147-F151.

- 498 -

Carol, I., Gens, A., and Alonso, E.E. 1985. A three dimensional

elastoplastic joint element. Proceedings of the

International Symposium on Fundamentals of Rock Joints,Bjorkliden, pp. 441-451.

Carol, I., Gens, A., and Alonso, E.E. 1986. Three dimensional

model for rock joints. 2nd International Symposium on

Numerical Models in Geomechanics, Ghent, pp. 179-189.

Gale, J.E., 1977. A numerical, field and laboratory study of

flow in rocks with deformable fractures. Inland Waters

Directorate, Water Resources Branch, Ottawa, 72, 145 p.

Jackson, R., Annor A., Wong, A.S. and Betournay, M., 1985.

Preliminary Results of Rock Joint Testing on URL Core.

Canmet - Energy Research Program, Mining Research

Laboratories, Division Report ERP/MRL 85-14(TR)

Kozak, E.T. and Davison, C.C., 1986. Hydrogeological Conditions

in a Vertical Fracture Intersecting Room 209 of the 240 m

level of the Underground Research Laboratory - 1.

Pre-excavation Conditions. AECL internal report.

Lang, P. A., Everitt, R. A., Kozak, E. T., Davison, C. C ,

1987. Room 209 Instrument Array - 1. Pre Excavation

Information for Modellers. AECL Report.

Tsang, Y.W. and Witherspoon, P.A. 1981. Hydromechanical

behavior of a deformable rock fracture subject to normal

stress. Journal of Geophysical Research, 86, No. B10, pp.

9287-9298.

Wilson, C.R. and Witherspoon, P.A. 1970. An investigation of

laminar flow in fractured porous rocks. Dept. of Civil

Engineering, Institute of Transportation and Traffic

Engineering, University of California, Berkeley, 178 p.

Witherspoon, P.A., Wang, J.S.Y., Iwai, K., and Gale, J.E.,

1980. Validity of cubic law for fluid flow in a deformable

rock fracture. Water Resources Research, 16, No. 6, pp.

1016-1024.

- 501 -

7. Appendix A

SAFE - Soil Analysis by Finite Elementdeveloped byD.H. Chan


Edmonton, AlbertaT6G 2G7

- 503 -

SAFE

SAFE (Soil Analysis by Finite Element) is a computer program developed at the University ofAlberta to analyze deformation of soil and rock structures. The program is written in FORTRAN IVlanguage and has been installed on different types of computer systems including the IBMsystem, the Amdahl MTS system and the CDC Cyber 205 vector computer system. The programhas been applied in analyzing a wide variety of geotechnical problems such as excavation, dam,shaft and tunnel constructions.

The initial development of the program was to analyze the post peak deformation of strainsoftening soil. But the program has now been extended to include 2 and 3 dimensional analysisusing total and effective stress formulation for fully undrained and drained conditions. A variety ofnon-linear elastic and plastic models with associated and non-associated flow rules are alsoavailable. Localized shear zone deformation can be modelled using the program and furtherdevelopments of the program are currently in progress.

The following is a list of the main features of the program SAFE.

Basic FormulationDisplacement finite element formulation assuming small strain and small deformation.

Element TypesTwo dimensional 3 to 6 nodes triangular, 4 to 8 nodes rectangular and three dimensional8 to 20 nodes solid elements.

Type of Analysis1. Plane stress, plane strain, axisymmetric and three dimensional analysis.2. Non-linear elastic hyperbolic model.3. Elastic perfectly or brittle plastic model using von-Mises, Tresca, Drucker-Prager,and Mohr-Coulomb yield criteria with associated or non-associated flow rule.4. Elastic plastic strain hardening and softening (weakening) model5. Elastic hyperbolic softening model.

Drainage Condition1. Total stress analysis.2. Fully undrained effective stress analysis.3. Fully drained effective stress analysis.

Standard Features1. Prescribed concentrated point force or distributed pressure boundary condition.2. Prescribed displacement boundary condition.3. Changing material properties at any stage of the analysis.4. Program restart at any stage of the analysis.5. Newton Raphson and Modified Newton Raphson iterative scheme for non-linearanalysis.

- 50A -

6. Choice of 2 x 2 , 3 x 3 , 2 x 2 x 2 , and 3 x 3 x 3 integration scheme.7. Load increment subdivision for non-linear analysis.

Special Features1. Element birth and death option.2. Automatic application of stress relieve due to excavation.3. Skyline and extended skyline matrix equation solver.4. Choice of stress calculation for non-linear analysis:

(i) Euler forward integration scheme;(ii) Improved Euler scheme;(Hi) Runge-Kutta scheme.

Post Processing Programs for SAFE1. Finite element mesh and deformed mesh plotting.2. Stress and strain contour plotting.3. Displacement arrow plotting.

Current Development1. Improved undrained analysis.2. No tension analysis with crack model.3. Geogrid element and soil geogrkJ interface element.4. Anisotropic plasticity.5. Special shear band element with discontinuous shape function.6. Time depending strain softening.

- 5 0 5 -

8. Appendix B

DESCRIPTION OF JOINT ELEMENTimplemented and tested

byF. Pelli


Edmonton, AlbertaT6G 2G7

- 507 -

APPENDIX BDESCRIPTION OF THE JOINT ELEMENT

B.I Introduction

For the purpose of modelling the behaviour of the discontinuous rock mass

a three dimensional isoparametric joint element was implemented into the

finite element computer program SAFE. The element is capable of modelling

several relevant features of rock joints such as dilatancy due to relative

shear displacement, opening-closure of the joint, non-linear normal and shear

behaviour (in pre- and post-peak region). The constitutive law implemented in

conjunction with the element is based on non-associated flow plasticity and

includes a strain-hardening/softening law.

The program SAFE (Soil Analysis by Finite Elements) was selected for the

implementation.

In the following paragraphs both element formulation and constitutive law

are described.

B.2 Element Formulation

The 3-D isoparametric joint element developed by Carol et ai. (1985) was

selected. The element (Fig. B.1) is defined by a variable number of nodal

points (8 to 16) and can be coupled with 3-D isoparametric solid elements.

The average position of the joint contact surface is described by a set

of 'mid-plane' points (4 to 8) located between each pair of nodes (Fig. B.2).

The relative displacement occurring at each of the mid-plane points is taken

to be equal to the difference of the displacements of the two adjacent nodes.

Geometry and relative displacements are interpolated between mid-plane

nodes by means of standard two dimensional isoparametric shape functions. Two

typical expressions for a corner and side node are:

- 508 -

N1 = 0.25 (1 - r) (1 - s) (-1 - r - s)

(B.1)

N 5 = 0.5 (1 - rz) (1 - s)

where: N^ ... shape function at node i

r,s,t ... local curvilinear coordinate system.

The orientation of the local axes (r,s,t) with respect of the global

coordinate system (x,y,z) can be established.

Two vectors, tangent to the element surface at a certain location are defined

as:

5r

5z5r

3s

as

ds

(B.2)

A third vector V^' perpendicular to the surface, can be found as the cross

product of V^ and V-,:

Dividing each of the vectors by its own magnitude results in three unit

vectors (v-, v~, _v,) (Fig. B.3).

The B matrix relating relative displacements to nodal displacements can

- 509 -

now be written as:

B = IB 1|B 2|B 3|B 4|-B 1|-B 2|-B 3|-B 4|B 5|B 6|B 7|B 8|-B 5|-B 6|-B 7|-B 8]

where: [B.J = N. [G] (B.3)

N• ... shape function at node i

[G] ... matrix containing the components of v_f, v~, _v.

The element stiffness matrix can then be established:

[K] = / [B]T[C] [B] ds (B.4)

where: [C] ... stress-relative displacement matrix.

The element nodal force vector induced by initial stresses {a } can alsoo'

be written:

{F } = / [B] {a } dS (B.5)o o

s

Using the virtual work approach the following load-displacement relationship

is found:

- {FQ} - tK] {Au} (B.6)

where: {R} . . . externally applied load vector

. • . incremental displacement vector

For each load increment a series of equilibrium iterations is performed by the

- 510 -

program until the specified convergence criteria are met. The iterative

procedure used by the program SAFE is based on the Newton-Raphson method and

allows stiffness matrix updating after any iteration (i.e. as often as

specified by the user).

B.3 Behaviour in Compression

The behaviour of a real rock joint under normal compressive load was

approximated by a non-linear, elastic constitutive relationship. The

hyperbolic function proposed by Bandis et al (1983) was selected to relate

normal stress (o ) to normal relative displacement (V•)•

The hyperbolic function, graphically shown in Fig. B.4, takes the

following analytical form:

V .— 3 (B.7)

a - b A V.

where: a and b are function parameters.

Physical properties of the joint such as maximum closure (V) and initial

tangent modulus (K •) can be expressed in terms of a and b as follows:

Vm

(B.8)

Kni a

The slope of the curve at any of its points can be calculated by

differentiating Eqn. B.7 and the following expression is found:

-2

- 511 -

In the current version of the program the same curve is used to describe

loading and unloading. This is a reasonable assumption for the stress

conditions and stress history considered to be applicable in the area of

Room 209.

B.4 Behaviour in Shear

The constitutive law governing shear behaviour as well as dilatancy due

to shear relative displacement is based on non-associated flow plasticity

(Note: no dilation is assumed to occur as long as the shear stresses do not

exceed the elastic range).

Fornulation of the elasto-plastic model requires the definition of a

yield surface, a hardening law and a flow rule.

The hyperbolic yield function proposed by Carol et al. (1985) was

selected. The family of yield surfaces, schematically depicted in Fig. B.5,

can be expressed in the following form:

1 + T2

where: x , x ... shear stress components;

<t> . . . friction angle;

an . . . normal stress;

f . . . function parameter (Fig. B.5).

In order to follow the hardening/softening history of the joint the

parameter f (see yield function) is assumed to be a function of x, where x is

the total accumulated plastic rels. ~.ve shear displacement. Two polynomial

functions (2nd order up to the peak strength and 3rd order in the post-peak

- 512 -

range) were selected to describe the f - x relationship (Fig. B.6). The

hardening/softening law is defined by five parameters:

f 0 ' fp' fr' xp' xr

The plastic potential function (Q) was selected such as to have the following

partial derivatives:

2 n

where: i = dilation angle.

Note: the increment of plastic shear deformation is assumed to have the same

direction as the shear stress.

The dilation angle is expressed, to account for normal stress dependency

as follows:

tan i = tan iQ (1 - on/a )4 (B.12)

where: ±Q . . . dilation angle for an = 0

q . . . unconfined compressive strength of the rock irregularities

in the joint.

Eqn. B.12 given by Ladanyi and Archambault (1970), is graphically depicted in

Fig. B.7.

The parameter iQ is also a function of the total accumulated plastic

shear relative displacement. The iQ - x relationship is shown in Fig. B.8.

The dilation angle (iQ) decreases linearly with plastic deformation until the

- 513 -

ultimate strength is reached. After further straining, it remains constant.

B.5 Opening and Closure of Joint.

If the stress normal to the rock joint becomes tensile, joint opening is

expected to occur. An effective model must be able to simulate stress release

due to opening of the joint, open joint properties, and joint closure. The

isoparametric element simulates joint opening by completely releasing normal

and shear stresses if normal tensile stresses occur. The open joint is

assumed to be linear elastic having normal and shear stiffnesses close to

zero.

The normal relative displacement value at which opening occurs is stored

by the program. This value is then used as criterion to evaluate if the joint

is still open or closing. The closing joint resumes its elastic-plastic

properties as they were before opening occurred.

B.6 Testing of Joint Element

The element was tested to verify its behaviour under various loading

conditions:

(a) Tests on the linear elastic element were carried out by applying shear

and normal external loads. The results were found to be consistent with

the adopted linear elastic consitutive law.

(b) The non-linear elastic normal behaviour was tested by applying a normal

compressive load on the element. The results were compared with hand

calculations and were found to be consistent with the hyperbolic

stress-relative displacement relationship used. Both loading and

- 514 -

unloading conditions were considered. Convergence was achieved easily

except for those cases where high normal displacements (close to max

closure) were reached.

(c) The element was tested in the plastic range by applying initial normal

stress (in equilibrium with an external normal load) and shear relative

displacements. An elastic, perfectly plastic constitutive relationship

with constant initial dilation angle (ig) w a s assumed and the shear

stress and the normal dilation as calculated by the program were found to

correspond to those calculated by hand.

(d) Hie strain hardening-softening law with variable iQ was included in the

program and also tested. For this case, the shear stress was found to be

consistent with the final f value (in the post-peak region) and with the

accumulated plastic strain.

(e) Finally, the opening/closure feature was tested. The joint was opened

and then closed by means of applied nodal displacements in the normal

direction. The element was found to perform well under these conditions

but convergence during closure tended to be relatively slow.

B.7 References

Bandis, S.C., Lumsden, A.C., and Barton, N.R. (1983). Fundamentals of rock

joint deformation. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.

Vol. 20, No. 6, pp. 249-268.

- 515 -

Carol, I., Gens, A., and Alonso, E.E. (1985). A three dimensional

elastoplastic joint element. Proc. Int. Symp. Fundam. of Rock Joints,

Bjorkliden, pp. 441-451.

Ladanyi, B. and Archambault, G.A. (1970). Simulation of shear behaviour of a

jointed rock mass. Proc. 11th Symp. Rock Mech. AIME, pp. 105-125.

B.8 Oopy of Paper by Carol et al. (1985)

- 516 -

Figure B.1 Joint Element

mid-plane

mid-nodes

Figure B.2 Mid-plane and Mid-nodes

mid-plane

Figure B.3 Global and Local Coordinate Systems

- 517 -

Figure B.4 Hyperbolic o -v Relationship

Figure B.5 Yield Function

- 518 -

Figure B.6 Hardening-softening Law

Figure B.7 Plastic Potential Function

- 519 -

Figure B.8 i 0 - * Relationship

- 520 -

Proceedings ol the international Symposium on Fundamentals of Rock Joints / B/orkltden / 15-20 September 1985

A three dimensional elastoplastic joint elementI. CAROLA GENSE.E. Al.ONSOUniversiim Politecnica tie Barcelona, Spain

ABSTRACT: A nt-w elastoplastic joint model for three-dimensional analysis has. beendeveloped. Firstly an elastoplastic constitutive law that incorporates wellaccepted empirical properties of joints is presented. The model prediction:; art*compared with published results and some field shear test data. A 16 node isoparametrie is then described and applied to the modelling of one of the field shear tests.

1.INTRODUCTION

In order to obtain a good estimate of tin-.k-fornaLii li ty an-: s.ifety conditions ofm<iny large structures, such as archdams, on fractured rock it is imperativeto iiiodc-l threedimensional effects. Inthis type of problems finite elementmethods, which combine continuum elementswith joint elements representing surfacesof discontinuity provide a powerfulanalysis tool.

The authors are currently involved inthe safety evaluation of a large archdam in the Pyrinean area (Canelles dam)and have already used a jointed finiteelement model under plane strainconditions to explore its possibilities(Alonso and Carol, 1985). The resultsof this previous work and the markedthreedimensional effects of the dam-rockinteraction prompted the development ofa surface type joint element to be usedin conjunction with available three-dimensional finite element computercodes.

This development, which is reported inthis paper, required the considerationof two different aspects: 1) The selec-tion of a realistic constitutive lawincorporating relevant and well acceptedexperimental facts and ?) The develop-ment of a threodimensional joint elementcompatible with existing computers codesinndl inij isoparametric "brick" elements.

A literature rcvi •••-• revealed that very

few threcdimensional elements have beendeveloped. Its application to r-.W prol-lems seems also to be very lir.itc:. WinDillon and Ewing (1981) concisely J^crina plastic threedimensional joint elemenrbut no details are available concerningits formulation and its use in boundaryvalue problems. Heuze and Barbour (1982)develop an axisymmetric joint element asan extension of a twodimensional formula-tion. It was concluded that the develop-ment of the proposed surface jointelement should start from basic consid-erations of joint behaviour in order togeneralize them and be able, finally, tointegrate them in a properly definedsurface element.

2.CONSTITUTIVE LAWA primary objective was to incorporate,within a rigorous elastoplastic frame-work, the accepted empirical behaviourof rock joints. In order Co build anelastoplastic model it is necessary toestablish:

a) The elastic behaviour

b) The yield surfacec) The hardening lawd) The flow rule

2.1.Elastic behaviourConcerning the elastic behaviour boththe normal (to the joint) behaviour andthe shear behaviour should be defined.The normal displacement u was splitted

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in two parts: an stress-relate.) compo-nents ( u* ) .mi a .|i.un,.-t r lei 1 term,associated to di latency effects (uP| :

u - u e l • UP (1}

The dilatancy term uP is describedby means of the plastic formulationdeveloped later on.

The u e l term may be analyzed fromnormal compression tests. Availableresults indicate a nonlinear ;-u°lrelationship with a marked "locking"character (the joint tends to be infinitely rigid for increasing nor~.il stress, ~;) . A relationship propose! by Goodmanand St. John (1977), somewhat simpli-fied,

" " C ''u *uc-l' (2)

rocw a s u s e d , a s a s t a r t i n g p o i n t . , t - j

d o r c r i b e t h e n o r m . i l c o m p r e s s i o n o f '.;•:•

T o m t . I r . t i n : , o q u . i t . i o n u,,,,. i s t h<

r i . i x i m u r . s h r t e n i n ; o f t h e l o i r . : i n . i u - - . ' - i

b y t h-. i: i- •.: . t i e . • . : . . ; .- l t . • • l r , -< .>.,!. , t . l ! l ! • . Til- •. ) . ' f f : . . ' l . - , : - ' 1- . . J ! ' . u . i l ly

f - u n i i '.<.• :,•• ::, i l l e r b u t ~lz'< • • o n e ,

a n ! : r . : ) , : • v • t h - r - - l . i ' i :. ' . ; : '-:!*•'•: I ;;. t..

wii: c h

• • iifrn i

T h i " i s i l l u s t r a t e d in Fi'J-

•>liow;. ,I pi M -j{ r h " 'iiri"ii' : .:.

for 5-..-V. u l v.'ili.o:- •..: t ('.. : ! .. .

tin.: u,.c • ! r-:. Th:\. t a c t or I iit.i--

n'jjnerical 3i f f I C J 11 les siiic*1 th<- u ' *

i n t e r c e p t o f t h e t-inger.t tc; t h e • - i" •

c u r v e ( w h i c h is u s e d l n t h e i t e r a t i v e

folution process di".;cr ibc.J I J V I I -aybfco:::e ^cîtivo (joint open.';1. Forthis rea — ri n two parameter law (t=l)

was selected in this work. It is be-lieved that it provides a sufficientlygood description of normal (elastic)behaviour for practical purposes.

With regard to the elastic shearstiffness terms, constant, or stressdependent moduli may be specified.Accordingly, the elastic matrix Erelating the stress vector acting on

the joint (see f i g .

and the r e l a t i v e el.ist

vector ("s t ra in")

is given by

v '

(u<-J) 0

K.,

'::.- : l.iy. -merit1 ' 1 . V j ' 1 , v ^ 1 !

(•1)

Fig. 1- ExaiTiple plor of t h erelationship showing a "tadjle" ;.»Jir,tfor value; of t less thian 1

where K,r i:> the shear stiffnei.i, and Kr.

l s obt .J l n<- 1 i ro;:: cûdt lor. ' 3 :

Fit,- - r ~ !_ . -*»•"Y.

It is- possible, by changing t.".e matrixn, to uso more complex elastic behaviourincorporating, for instance, shear andnormal behaviour coupling, anisotropyor nonlinearity.

2.2.Yield surfaceIt has been found that a simple two-parameter hyperbolic yield function fitswith acceptable accuracy the shearstrength of natural and artificial joints.For a single shear component the law isgiven by.

t = B • " ' •2-a-C (6)

where a and B are constants. The constantB happens to be the slope of theassymptote when o•*>••. On the other handa gives the distance between theorigin and the C-axis intercept of theassymptote (see Fig.4).

A few comparisons between jointstrength data and the proposed envelope

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are shown in Fig. 3. Fig 3a. reproducesthe results used by Hoek (1983) tosubstantiate his proposal of a jointstrength criterium and shows the compa£ison between the Barton and Hoek crite-ria and the equation (6) to a number ofstrength data points of moderatelyweathered greywacke (15x15 cms samples)

tested by Martin and Millar (1974).Any of the three mentioned criteria aregood enough for practical purposes. InFig. 3b. the results of several testson 13x10 cms plaster replicas tested byPeek (1981) are presented together withthe best approximation of the law givenby equation (6).

o)Stresses

blrelotive displacements

Fig.2-Definition of stresses and "strains"

in the joint.

The range of normal stresses is verysmall but unlike the Martin and Millar(1974) results, multistage testing couldbe avoided in this case. Again the compa£lr.on is judged quite acceptable. Finally,Fig. Jo shows unpubll sir; ! shear strengthdata obtained in the Hcx-k portable iristru'•nt (Houk <IIK1 Uray, 1974) on 0 11,6 cms

sampler of clay-banded tertiary marlsin the vicinity of Caspc Jam, Spain.Curve (1) shows the test results of apreviously induced tension fracturethrough the intact material. Curve (2)reflects the strength of the clayeybands, again in a pre-splitted joint.The test followed a multistage techniquesimilar to the one described by Martinand Millar (1974).

Fig. 3-Comparit,on of equation (6) withjoint strength data, a) Moderatelyweathered greyvacko. Grade 3, Test sample7 (Martin and Millar, 1974). b) Plasterreplicas of a natural joint (Peek, 1981).c) Tertiary clay banded marls of Caspedam, Spain.

In all the caws presented the fit wasobtained by moans of a minimun squareliiii'iir rogr'bsion between T'/" and 0(set1 equation 0 ) . It is concluded thatthe proposed '.lio/ir strength equation is•is <JOCK1 .f. otliT;-. already existing, nutit offer:. ';oirio ri'lviintageo. Fif-t of all

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it bears a direct- relatlonship with theMoht-Coulomb linear criteria and its twuparameters tg0 and a have equivalentmeanings. Unlike Mohr-Coulomb, law,however, equation (6) shows a continuous,first derivative in the origin and thisis an advantage if it is to be used asa yield function in a numerical model.On the other hand the Barton (1974) wellknown relationship presents rapidoscillations for small values of ; winchis an undesirable situation for numericalmoit.-1 ling- Finally, the criteria propose,jby Hoek (lrJ03) is perhaps too compl ieatf-,3anj, for large value;;, tends to a non~rejii.tic jcrj (tangent) friction angle(horizontal ainjTiptotf) .Frun t rto numerical point of view,

equation (C) offers an additional advan-)••: There exists analytical solution for

point of intersection between the1 : f ' i n : l ; •-:: ''.-j'j-jt i u n fi- ai,-\ t 11- -

;• i'. :,. I r. t h i s w j y \ !.>• i .i:.il

v seir :. t .r I h' ;..:n' :r.

d .", (d (8)

th--

. ' . i •

b- -I;.iv b>.

a v j i i < ? : an:! s ' ± : . ; i ' u t ' - J by a f a : t .m<jl<-o p e r a t i o n . B ' i s e j on e q u a t i o n J.) th<-f o l l o w i n g y i e l ' i f u n c t i o n h a s ( n

•->'

Tht zones F '0, F 0 and the bouniaryF=0 are represented in fig. 4. Theconstants a ani tg*l were selected asthe hardening paranc-ters of the model.

K m . •J-Vn-1

-'. i .Hardening lawIn order to fellow the h.iriienin; Inof the joint the following mfertiilplastic vari.ille was chosen

where dv\ and dv . arc the plasticcomponents of the two shear relativedisplacements. Any function relatinga and tg 0 with C may be used, bearingalways in mind the adaptability toexperimental results.

In the present work the- polynomialvariations, shown in Fig. 0 for a, havebeen used. They allow the modelling of,i peak shear strength for total accumu-lated "strains" given by r,p and a strainsoftening behaviour up to residual conthtion.i for a plastic "strain" given byC . The proposed formulation may beextended to include amsotropic effectsand to model reversal effects.

Fig. rj-Definifion of hardening l.jv forparameter a.

i.4.Flow ruleThe plastic potential muit be able tomodel twu distinct effects: the influ-ence of norrnal stress on the intensityof dilatancy and its variation withplastic deformation.

On the other hand it has been acceptedthat the increment of plastic deformationin tanqenti.il direction follows thedirection of the shear stress. Howevera dilatancy angle i is defined to modelpl.istic dilat.incy effects. Therefore,i! y V ,". ] , " j) is the plastic potentialit gradient along *.,Tn and : mustit l sf y:

8o . 3p J . t g i (9)1

Tli>- v.in.ition of cillatancy ,inqle withrnMl Lre.-, n..iy lie specified hy some(•') f unct ion . The Laiianyi nr>.I

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Archambault (1970) expression gives

tgi=tgic. (l-j/qu) * (jo)

where l; is the dilatancy angle for0 = o and q u the unconfined compressivestrength of the rock irregularitiesdescribing the joint.

Fig. 6-Variation of initial diljtancyingle with the lntprna) plastic vari.i-

In or:i"r to introduce tin.- influence ofaccumulated plastic deformation, theangle iQ was assumed to decreaselinearly with Cup to a constant "resid

ual" value (see Fig. 6i. The .ihapetnc {• ti-ntial O in th'.C" i '• shown it1. Fig. 7.

Fig. 7-Plaitic potential

?.NUMERICAL IMPLEMENTATION OF THECONSTITUTIVE LAW

In tlii implementation of a constitutivelaw in a general numerical procedure,situations may arise that have not beenspecifically contemplated in the formu-

lation of the model or that requiresome specifical numerical treatment.In the case of the rock joint model itis necessary to distinguish, firstlywhether the joint is open or closed.In fact, the constitutive law describedabove is only valid for a closed joint.If the joint is open it will be neces-sary to ensure that no stresses aretransmitted across it.

In the case of a closed joint it isnecessary again to distinguish betweentwo cases; an opening joint or a closingjoint, since they require differentnumerical treatment. If the joint isin the process of opening an "initialstress" approach can he used directly.However, if thejoint is closing thereis the possibility that thenormal dis-placement imposed by the "initialstress" ni'-thod is larger (in absolutet-.T'v.; th.jn t h' • trKiXiriU.". ii i splaceniontuivii :.••/ th' ii:r;-..il stress - norm-ilil :,pld' e::i.-nt r< lationshlp (eq. i). Il,trial case tliv corivorg'-nco can notbe achieved. The u»e of a conventional"initial deforir.dtion" procedure is notacceptable either because it couldlead to difficulties if a tangentialstress higher than the peak tangentialstress was imposed at some stage. Toovercome' this difficulty a "xixed"procedure is adopted in which thevariables imposed in each incrementcirv t Sie normal stress an-i the two' an:jent i .11 "strains", '. , ' v i ait i' vFinjlJy, in c-v:r\on with all ••Irtst"-

pl.is!;/.- -..:'•:•, it is also n e c s : J: yto Jist i r.-j.ji«ifi elastic stress incrementsfr-ori e lastoplast I C ones.

In Fig. H, a flow chart is presentedshowing the various paths that can befoll'.jwe.-j by the analysis depending onth< lifferent states of the joint.

4.APPLICATION OF THE CONSTITUTIVh LAW

TO FIKLD TKST DATATli'.- ,iv,ii labi 1 l ty of 3o:n<- g->..J qiiiilityfield test results has al lewe.' to checkthe usefulness of the constitutive lawdescribed above for modelling adequatelythe actual behaviour of joints. Thetests were performed on '.he beddingplfiries of 'i fairly massive limestoneusing the ,iri ing'.-ment depicted in I'm.9. There was .i especial intercut inmodelling the behaviour of this discon-

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t inuities because th<> arch Jari to beanalyzed is founded in this limestone

( " n . H j .

us» Homes atucs 1

TCP 9 THE Ci.*S !I t MUCHCNI Of 6" v' t !

x it..141" i

r..r..«•Situ, sac siacss «.ms j

S. .e

Kig. fl b.

Th'_' parajaoters defining the normalstress/normal displacement elasticrelationship (eq. 3) can be independently determined from the appropiate expo£imentai curves. The values of umc =0.9x 10-3m and c = -98 KN/m2 yieldeda sufficient approximation to the fieldtest d.ita.

Of more interest is the definitionof the shear stress/shear displacementbehaviour because the behaviour at dif-

Kig. c<-Conputation flow chart for thepropo'-'.1!: constitutive law. a) Open joint.,b) Closed joint, "mixed" procedure, c!Closei joint "initial stress" procedure.

ffroiu jtrcsa levels has to be adequate-ly uri/dictei. Firstly, the elastic partot thi-- iy.o<iel must be completed by th"dcten::inantion of IC, the shear stressshear displacement elastic modulus. Avalue of ICj. = 473OOOKN/m3 was dJopte.ibased on the mean slope of the earlyparts of the test curves of Fig. 11.

The definition of the family ofyield surfaces and the hardening lawrequires the determination of

- initial yield surface (ao, 0O)

- peak yield surface (ap# 0_)

- residual yield surface (ar, t*r)- residual plastic variable at peak f.p- internal plastic variable at residual

state ; r.

The values for ap, 0p, ar and (!r wereobtained by imposing the best possiblefit between tin1 constitutive lawhyperbolic functions (eq. 7) and themeasured peak and residual strengthvalues. The parameters thus determinedwere:

l<(0.i» KN/mJ C , 3r>.2i%"M i \ ( , KN/m:! fir - \'-.?(,o

i tit iTi'st lnrj t<-> not" th.it I Iv

;,-Milfll da',1 all«wi»! ,'.., -n (••• JI.I ic

ap

a,-It is

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equal to 0r without loss of accuracy.This appears to imply that for thejoints studied, the strain-softeningprocess did not affect the frictionangle defined according to equation 7.

Fig. 3-Arr<inge.i>ent for field sheartest.

It was attractive to make theassumption that 0 did not change duringstrain hardening either and that onlythe degree of mobilization of the parameter a varied. Therefore, the a valuesof ao=o and 0O=35,26° were selected todefine the initial yield surface. InFig. 10 the initial, peak and residualyield surfaces are shown.The values of the internal plastic

variable at peak and residual states(Op and ',r) were fixed at 3 mm and9 mm respectively. They were based onthe displacement required to achievepeak and residual conditions in thefield tests.In Fig. II the very good agreement

between the model prediction and thetest results can be observed.Unfortunately the data concerning

the normal displacements during shear,necessary to obtain dilatancy parame-

ters, was not quoted in the originalreport presenting the field test data.A conservative value of io=9° wasadopted, which was the same one usedin the previous analysis (Alonso andCarol, 190S). Finally compression teston rock specimens gave an averagecompression strength of 50 MPa.

Fig. 10-Initial, peak and residualyield surfaces of limestone beddingplane (Canelles dam).

5.THE JOINT ELEMENT

5.1.GeometryA 16-node isoparametric joint elementhas been developed (Fig. 12). Eight"midplane" points, PMt, located betweeneach pair of opposite joint nodes definethe average position of the jointcontact surface (Fig. 13). A curvilinearcoordinate system (s,t) is defined inthis average surface by means ofquadratic twodimensional shape functionsNi. Two typical expressions for corner(Nj) and side (N5) nodes arc

1/4 -d-s) • (l-t)-(-l-s-t)

$= 1/2 (II)

The global coordinates of any pointin the joint surface arc then definedby the vector r(s,t)*(x(s.t), y(s,t),z(s,t)) where

sx(s.t)xyN.(s.t).xPMi n ; )

and y and z have^similar expressions.The vectors it and -j£ define a

tangent plane at any joint in the joint

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Model predictions

Actual measurements

< 4 6 7 8 9Refcitn* horizontal displacement (mm)

Fig. 11-Experimental results and rôdcl predictions for the shear behaviour of

limestone- b.riding plan* 'Candles 3an) .

surface (Fig. !••,. Thes-= two vectorsallow the determination of th' n:.'rr::j:vector n and the parameter J, necessaryto perform the numerical integration.The following expressions hold

G =

nx "y nz

[ t2x C2y C2

(16!

J =•dsdt

- 1n = T

(13)

(14)

where

JL 3?

3s

and dA is the differential vector ofjoint surface area. Knowing it andselecting a tangential to the surfaceunit vector T\ it is possible tocompute the third reference vectort2 = rf -~t, and to establish a local refe£ence system at any point in the surface.The following matrix characterizes thissystem

Fig. 12-Three dimensional joint element

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Fig. 13-Definition of mid-surface points(PMi). Local and global coordinates.

5.2.Linear formulationKnowing the relative displacements

'*xPMi# 'vPMi' '*zPMi' at t n e mldsur£'iCC

points of the joint, PMi, it is possibleto obtain the relative displacements atany point in the midsurface by means ofisoparametric interpolation. For instance

( s , t > =8

(s,t)-'xPMi (I7)

and similarly for the remaining twocomponents. The vector of relativedisplacements is then given by

Txyz(s,t) = (fx(s,t), iy(s,t>, Vs,t)>-

= N(s,t>- *el (18)

where the matrix N contains the shapefunctions and oe| is the element nodaldisplacement vector. The vector ofrelative displacement in the localcoordinate system, C^, is needed todescribe constitutive behaviour. It isgiven by

*j(s, t) = B (s, t) • ?el (19)where the geometric matrix B is givenby

B «{ - B , | - B 2 | - B 3 | - B 4 | B , | B 2 | B 3 | B 4 |

I - 5 s I - » e I - S T I - 5 e I » s l s 6

where

(20)

(21)

Fig. 14-Local reference coordinatesystem.

Using the standard virtual work approachthe element nodal force vector ? ej, cannow be established:

«„el -cel+ Fel (22)

where Kej is the element stiffnes matrixwhich can be obtained if an "elastic"constitutive matrix D is defined in thejoint and Fej is the element nodal forcevector induced by initial stresses ^y.

?el = 'el 5* • * ] • " * (23!

5. 3.Extension to nonlinear behaviourAn iterative procedure is needed tctake into account the nonlinear jointbehaviour. The method adopted is indi-cated in Fig. IS in terms of twogeneralized stress and "strain" axis?j and U . Beginning with an initialelastic p matrix a stress-strain statelike 1 {ifj1,!^1) is obtained in anypoint within the joints. The integrationof the constitutive model using the"initial stress" or "mixed" proceduresdescribed previously, leads to a dif-ferent stress strain state (I'). The"initi.il" stress to be relaxed in thenext iteration is givi>n by

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,01 o-a, oi - '- Di

(24)

where the matrix D l can be computed indifferent ways (initial, tangent, secantor any suitable combination). A newlinear solution takes the joint stressesand strains to a state like 2 and fromthen on the iterative procedure isrepeated until convergence is finallyreached.

Fig. 15-IteraLivt- procos? ;n th" t. -• j spac-

6.MODELLING LARGE SCALE FIELD SHEAR TESTSWhen checking the usefulness of theconstitutive laws against some fieldtest results, the assumption was madethat those results represented the actualbehaviour of an clement of joint subjectto uniform stresses and displacements.In fact, the test was performed usingthe arrangement of Fig. 9 in whichuniforms conditions do not necessarilyprevail. Taking advantage of theincorporation of the joint element in a3-Dimensional Finite Element Programmeit is possible to analize the actualtests and compare the predicted resultswith the experimental data.

The test was modelled as an clasticbrick element resting on a jointelement (Fig. 16). The selected dimen-sions wore the saim; as in tho actualfield test.

It was subject first to a normalload of fij';KN, •"-t.ing uniformly on the

top face of the brick element. Afterwardsa uniform horizontal displacement wasapplied to the vertical face (5-7-9-11)of the same element. The parameters ofthe joint model were those determined insection 4 whereas the intact rock wasmodelled elastically with E « 10000 MP a

and v = 0.2.

Fig. 16-Discretization of field sheartest.

The predicted load-horizontal displace-ment curve is presented in Fig. 17together with the field result. Againthe agreement is very good demonstratingthat the sample dimensions chosen forthe test were adequate.

7.CONCLUSIONSAn elastoplastic three dimensionalconstitutive law to model the behaviourof joints has been developed. It incor-porates some well accepted empiricalfacts of joint behaviour.

A new equation for the definition ofthe yield surfaces is proposed. In ad-dition to some numerical advantages, itfits very well available experimentaldata.

The proposed constitutive law yieldspredictions in good agreement withexperimental data from field sheartests.

A 16-node isoparametric joint element,for use in three-dimensional finiteelement programs, is developed. Whenapplied to the modelling of one largescale shear test it shows a goodagreement between computed and experi-

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mental results. Joint strength characteristics of aweathered rock. Proceedings of the3rd Congress of the ISRM, Denver, vol.2A, pp. 263-270.

Peek, R. (1981). Roughness - shearstrength relationship. Jnl. of theGeot. Engng. Div. Tech. Note, vol.107, n? GT5, pp. 672-677.

Van Dillen, D.E. and Ewing, R.D. (1901).EMI-IES: A Finite Element Code for RockMechanics Applications. Proc. of the22nd Syrap. on Rock Much. MIT, pp.373-37?.

Fig. 17-Coroparison of computed andexperimental results of field shear test.

REFERENCES

Alonso, E.E. and Carol, I. (19B5).Foundation analisis of an arch da.T..Comparison of two modelling techniques:No tension and jointed rock material.

Rock Mechanics and Rock Engineering.

In press.

Barton, N. (1974). Estimating the shearstrength of rock joints. Proc. ofthe 3rd Congress of the ISRM, Denver,vol. 2A, pp. 219-220.

Goodman, R.E. and C. St. John (1977).Finite element analysis for discont^nuous rocks. In "Numerical Methods inGeotechnical Engineering". Ed. by C.S. Desai and J.T. Christian. McGraw-Hill.

Heuzc, F.E. and Barbour, T.G. (1982).

New models for rock joints and inter-

faces. Jnl. of Geot. Engng. Div.,

vol. 108, n? GTS, pp. 757-776.

Hoek, E. (1983). Strength of jointed

rock masses. Twenty third Rankine

Lecture, Geotechnique, vol. 23, n? 3,

pp. 185-224.

Hoek, E. and Bray, J.W. (1974). RockSlope Engineering. The Institutionof Mining and Metallurgy. London.

Ladanyi, B. and Archambault, G.A. (1970)Simulation of shear behaviour of ajointed rock mass. Proc. llth Symp.Rock Mech. AIME, pp. 105-125.-

Martin, G.R. and Millar, P.J. (1974).

-M1 (six

9. Appendix C

SUPPLEMENTAL EXTENSOMETER DATAFOR

INTERMEDIATE EXCAVATION STEPS

0.30

10 15 20 25Distance Along Extensometer from Collar (m)

30

u>I

Figure C.1 Roof Extensometers EXT01-02Linear Joint 3x3 : Pilot Excavated to 23.5 m

E

oo

c

Q>>O

5oCO

c

"x

to


Figure C.2 Diagonal Extensometers EXT03-09Linear Joint 3x3 : Pilot Excavated to 23.5 m

EE

oo

Q)

Q>

%

EoW

c<D

~xLU

0.7-

0.6-

- 0 .1 -10 15 20 25

Distance Along Extensometer from Collar (m)

Figure C.3 SL Extensometers EXT07-08-04Linear Joint 3x3 : Pilot Excavated to 23.5 m

30

U>

35

0.45 J

"oo

cEQ>

%EoW

c<D

-0 .10-

i

10 15 20 25

Distance Along Extensometer from Collar (m)30 35

Figure C.4 Diagonal Extensometer EXT06Linear Joint 3x3 : Pilot Excavated to 23.5 m

0.30-


30 35

Figure C.5 Floor Extensometer EXT05Linear Joint 3x3 : Pilot Excavated to 23.5 m

0.5-

0.4

0.3

E 0.2^

1 o.HE0)O 0.0QLOT

Q.2 -0.1-

| -O2-Da:

-0.3-

-0.4

-0.5

o = Displacement @ Z = 24.0 mA = Displacement @ Z = 24.1 mo = Relative Displacement

0 5 10 15 20 25Distance from the Tunnel Wall (m)

Figure C.6 Full Section Roof at the FractureLinear Joint 3x3 : Pilot Excavated to 23.5

30 35

1.75

1.50

1.25E

jment

on

spl<

Q

oa:

i

0.75

0.50

0.25

n

-0.25-

-0.50


Figure C.7

10 15 20 25

Distance from the Tunnel Wall (m)

Full Section SL at the FractureLinear Joint 3x3 : Pilot Excavated to 23.5 m

30

Cn

i

35

0.30


30

s

35

Figure C.8 Roof Extensometers EXT01-02Linear Joint 3x3 : Pilot Excavated to 25.2 m

E

oo

0)

Q)

O

c


30 35

Figure C.9 Diagonal Extensometers EXT03-09Linear Joint 3x3 : Pilot Excavated to 25.2 m

1 J0\

.t. C

olw

.r,em

ent

o

"5C

0.7-

0.6-

0.5-

0.4-

0.3-

0.2-

0.1-

oV)

S o.o

-0.110 15 20 25

Distance Along Extensometer from Collar (m)30

Figure C.10 SL Extensometers EXT07-08-04Linear Joint 3x3 : Pilot Excavated to 25.2 m

E

oo

otoc

"x


30

i

35

Figure C.11 Diagonal Extensometer EXT06Linear Joint 3x3 : Pilot Excavated to 25.2 m

0.30

E

jg"oo

c

a>

"5o(0

cUJ

o.oo

-0.05-

-0.10-10 15 20 25


I

35

Figure C.12 Floor Extensometer EXT05Linear Joint 3x3 : Pilot Excavated to 25.2 m

0.5

0.4-

0.3

-0.5

o = Displacement @ Z = 24.0 m^ = Displacement @ Z = 24.1 mo = Relative Displacement

10 15 20 25Distance from the Tunnel Wall (m)

30 35

Figure C.13 Full Section Roof at the FractureLinear Joint 3x3 : Pilot Excavated to 25.2 m

1.75 -J

E

0)O

_gQ.OT

o

oQ:

o = Displacement @ Z = 24.0 m= Displacement @ Z = 24.1 m

o = Relative Displacement

-0.25

- 0 . 5 0 -10 15 20 25


Figure C.14 Full Section SL at the FractureLinear Joint 3x3 : Pilot Excavated to 25.2 m

0.30

E

ou

Q)

0)"5OCOc©"xUJ

0.00

-0.05

-0.10 -1


Figure C.15 Roof Extensometers EXT01-02Linear Joint 3x3 : Slash Excavated to 23.5 m

30 35

J,

"oo

c<D

oCOc0)

00


30 35

Figure C.16 Diagonal Extensometers EXT03-09Linear Joint 3x3 : Slash Excavated to 23.5 m

I

in

i


30 35

Figure C.17 SL Extensometers EXT07-08-04Linear Joint 3x3 : Slash Excavated to 23.5 m

E

oo

c

Q>

0)

oincQ)

UJ

i


30 35

Figure C.18 Diagonal Extensometer EXT06Linear Joint 3x3 : Slash Excavated to 23.5 m

0.30


30 35

Figure C.19 Floor Extensometer EXT05Linear Joint 3x3 : Slash Excavated to 23.5 m



t

30 35

Figure C.20 Full Section Roof at the FractureLinear Joint 3x3 : Slash Excavated to 23.5 m

E

0>O

"5.CO

b"6T3O

-0.25

-0.50



30 35

Figure C.21 Full Section SL at the FractureLinear Joint 3x3 : Slash Excavated to 23.5 m

u.ou-

J , 0.25 -i

^ 0.20-O

•

^ 0.15-

| 0.10-0) :

2 0.05-V .0)

g 0.00ôw£ -0.05-"x :Ul :

-0.10

r0 5 10 15 20 25


Figure C.22 Roof Extensometers EXT01-02Linear Joint 3x3 : Slash Excavated to 25.2 m

30

I

Ul

I

35

0.45

"5O

c

O(OCQ>

"xUl

LnUitn


30 35

Figure C.23 Diagonal Extensometers EXT03-09Linear Joint 3x3 : Slash Excavated to 25.2 m

-0.110 15 20 25


Figure C.24 SL Extensometers EXT07-08-04Linear Joint 3x3 : Slash Excavated to 25.2 m

E

oo

Q)

o

Eowc0)

en

10


Figure C.25 Diagonal Extensometer EXT06Linear Joint 3x3 : Slash Excavated to 25.2 m

E

oo

c<D

EQ)>O

"5oCO

c

~xUl

0.05-

0.00

-0.05-

-0.1010 15 20 25


I *Ln09

35

Figure C.26 Floor Extensometer EXT05Linear Joint 3x3 : Slash Excavated to 25.2 m



30 35

Figure C.27 Full Section Roof at the FractureLinear Joint 3x3 : Slash Excavated to 25.2 m

1.75

1.50

1.25

1-

0.75-

0.50

E

cq>

o>o_go.CO

QTi 0.25T3Oa:

-0 .25-

-0.50

h

Ab.


0 5 10 15 20 25

Distance trom the Tunnel Wall (m)

Figure C.28 Full Section SL at the FractureLinear Joint 3x3 : Slash Excavated to 25.2 m

30 35

00rsj

0.5

(LU

LU

)

jmen

t

oo

Dis

plR

adia

l

0.4

0.3

0.2

0.1

0.0

-0.1

-0.2

-0.3

-0.4

-0.5



Figure C.29 Full Section Roof at the FractureNo Joint : Pilot Excavation

1.75

= Displacement @ Z = 24.0 m= Displacement @ Z = 24.1 m

o = Relative Displacement

-0.5010 15 20 25


Figure C.30 Full Section SL at the FractureNo Joint : Pilot Excavation

0.5



Figure C.31 Full Section Roof at the FractureNo Joint : Full Section Excavation

?

c

EQ>UDQ.10

b

Radi

al

u .

1.75

1.50 J

4 OC

1.Z5 -

1

0.75

0.50

0.25

0

-0.25

-0.50

1i«

%\\

«l),\

" * ^ m+ __^ ^ ^

t o o o O O O O O 0 0

1 ' " . » • • • ! I ' 1


-o----9 s r — - • ? • • - • • • i g


in

30 35

Figure C.32 Full Section SL at the FractureNo Joint : Full Section Excavation

0.5

0.4

0.3

E

"cQ>E<UOOQ.W

Q

dial

o

0.2

0.1

0.0

-0.1

-0.2

-0.3

-0.4

-0.5


o 5 10 15 20 25Distance from the Tunnel Wall (m)

Figure C.33 Full Section Roof at the FractureLinear Joint 3x3 : Pilot Excavation

ini

30 35

E

c

<D

<DQ.

b"oO

OH

1.75

1.50

1.25

1

0.75

0.50

0.25

0

-0.25

-0.50

'&.

oA

Displacement @ Z = 24.0 mDisplacement @ Z = 24.1 mRelative Displacement

0 5 10 15 20 25Distance from the Tunnel Wall (m)

Figure C.34 Fuii Section SL at the FractureLinear Joint 3x3 : Pilot Excavation

35



30 35

Figure C.35 Full Section Roof at the FractureLinear Joint 3x3 : Full Section Excavation

E

1.50

1.25

1ca>E 0.75uoH 0.50

-R 0.25ooon

-0.25

-0.50

*

V


o 5 10 15 20 25


Figure C.36 Full Section SL at the FractureLinear Joint 3x3 : Full Section Excavation

30 35

10. Appendix D

PRINCIPAL STRESS CHANGES AND HYDRAULIC APERTURESAT STRESS CELL AND PACKER LOCATIONS

N

i -

J-1

\\-

Pilot

• MeshCoerdinott Sysftm

Slosh

Jnt

lCSIR

t

Pilota = a1A =cr2

o = cr3

Slash• = a1o = a2• = a3

8 18 20 22 2410 12 14 16

Distance (m)

Figure D.1 Principal Stress Changes @ N1 vs Excavation Stage

26

N

0 0 -

Q)CDC

oCOV)

CM-

O- l

J-1 J+1

toI

COI

Jnt

lCSIR

t

PilotD = a1

A = a2

O = CT3

Slash• = cr1

o = c r 2

• = cr3

8 10 12 14 16 18 20 22 24

Distance (m)

Figure D.2 Principal Stress Changes @ N2 vs Excavation Stage

26

J-1 J+1

.. „Pilot

Coordinol* System

Slosh

Full

Jnt CSIRt

Pilot

A = ( 7 2

o = CT3

Slash

o = (72

• = (73

6 8 20 22 2410 12 14 16 18

Distance (m)

Figure D.3 Principal Stress Changes @ S1 vs Excavation Stage

26

J-1

-II-

J+1

••

Pilot

Coordinate Sy$l«m

Slosh

Jnt

tCSIR

t

Pilota = a1A =cr2

o = cr3

Slash• = a1o = cr2

• = CT3

8 18 20 22 2410 12 14 16

Distance (m)

Figure D.4 Principal Stress Changes @ S2 vs Excavation Stage

26

0 0 -

t o -

Q)CM-

J-1 J+1Pilot

• MtshCoordinote Sytlcm

Slosh

2!

I

00I

O

Jnt CSIR

l t

Pilota = a1A = a2o = a3

Slash- = cr1o = a 2• = cr3

8 10 12 14 16 18 20 22 24 26

Distance (m)

Figure D.5 Principal Stress Changes @ R1 vs Excavation Stage

CO-

f

Q>

C

0)

CM -

O-l h

toI

I

J-1 J+1Pilot

• MeihCoordinol*

Slosh

Jnt

lCSIR

t

Pilota = <J1

A = ( 7 2

o = cr3

Slash• = a1o = a2• = (73

8 18'

I

20 22 24 26

Figure D.6

10 12 14 16

Distance (m)

Principal Stress Changes @ R2 vs Excavation Stage

N

8 10 12 14 16 18 20 22 24 w 26

Distance (m)

Figure D.7 Principal Stress Changes @ F1 vs Excavation Stage

0 0 -

t o -

Q_

Q>

OinV)

CM-

J-1 J+1

-II-

Pilot

* MtshCoordinol* Sytltm

Slosh

00I

Jnt CSIR

t

Pilota = <J1

A = c r 2

o = a 3

Slash• = a1o = CT2

• = cr3

8 10 12 14 16 18 20 22 24 26

Distance (m)

Figure D.8 Principal Stress Changes @ F2 vs Excavation Stage

- 579• / .520

Table 0.1 Hydraulic Apertures

Packed-offInterval

F1§ F2ou *2 RIS • R2| S si

•S N1N2

F1F2

O "g R1

•Q.« R 2>

J « S1^ S S2

N1N2

F1F2

« 5 R2

3 2 si•M • S2

N1N2

Hydraulic Aperture'(um)

50.1050.20

49.9249.90

50.1750.04

50.0050.34

49.0948.64

49.5949.76

50.3750.23

50.4150.26

48.7748.97

49.4249.63

50.6850.34

50.3551.50

Aperture Change

(wn>

0.100.20

-0.09-0.10

0.170.04

0.00.34

-0.91-1.36

-0.41-0.24

0.370.23

0.410.26

-1.23-1.03

-0.58-0.37

0.680.34

0.350.50

'The initial aperture prior to excavation of thedevelopment room was assumed to be 50 urn.

- 581 - 58a,

APPENDIX C

PREDICTION OF ROCK DEFORHATIONS FOR THE

EXCAVATION RESPONSE EXPERIMENT - ROOM 209 IN THE

URL, LAC DU BONNET, MANITOBA

by

Gen hua Shi, Richard E. Goodman, Pierre Jean Perie

Lawrence Berkley LaboratoriesEarth Sciences Division

- 5 8 3

CONTENTS*

Page

Introduction 585

Predictions of Response - Extensometers: 585

Prediction of response - strain changes 586

Prediction of Response - Fluid Pressure Test in Hole Rl 587

The Discontinuous Deformation Analysis 587

Analysis of Face Advance Coefficients 588

Analysis of fluid flow in the water-filled fracture 589

Discussion 590

References 591

Figures 592

Appendices 606

* Table of Contents provided by Technical Inforaation Services

- 585 -

PREDICTION OF ROCK DEFORMATIONS FOR THE EXCAVATION RESPONSEEXPERIMENT - ROOM 209 IN THE UNDERGROUND RESEARCH LABORATORY, LACDU BONNET, MANITOBA.

by: Gen hua Shi, Richard E. Goodman, and Pierre Jean Perie,Earth Sciences Division, Lawrence Berkeley Laboratory

June 8, 1987

Introduction

As part of the excavation response experiment at theUnderground Research Laboratory, a series of extensometers,stress meters, and other instruments were set in place andmonitored as the 209 room was advanced. This group was involvedin the planning of the experiment and was asked to provide aprediction of instrumental readings. The expertise beingdeveloped in the group relates to the mechaui.es of discontinuousrocks. Although the experiment in question involves mining inrock relatively free of joints, some slabbing has beenexperienced following advance of the face in the URL so thebehaviour does not qualify as purely linear elastic andcontinuous. While the discontinuous deformation analysis methodthat was used for this work is intended for blocky rock, it didprove possible to apply it to this experiment. This predictionreport 'is intended to convey an experiment with a new andpromising type of model, rather than as a test of the capacity topredict rock response with the best available techniques.

The development of discontinuous deformation analysis isvery recent and, in fact, this document reports its first use inforward modelling on any real project. The recency of itsdevelopment to this stage limited the kinds of instrumentalresponses it could address. A prediction was made for theextensometers radiating in the plane perpendicular to the 209room at chainage 17.85m, and to the final readings of the stressmonitors in a plane perpendicular to the room axis at chainage27.2. Further a prediction was made of water flow in the fracturethat would be measured by water injection in borehole Rl aftercompletion of mining through the fracture.

The report first presents the predictions for eachextensometer, for the stress monitors, and for the pump test.Then it describes the analytical methods and assumptions thatwere introduced, followed by general comments and observations.Output listings of displacements and stresses and other workingmaterials are appended to the report.

Predictions of Response Extensometers:

The extensometer readings are predicted in Figures 1 through7. Each figure presents the relative displacement, in mm, betweenthe farthest anchor position and each of the other five anchors,corresponding to advance of the face. It was assumed that theextensometers were installed when the face was an average of 0.61

- 586 -

meters ahead of the extensometer ring. We treated the crosssection as circular with an average radius of 1.8 meters; thusthe initial position, describing zero response, was at z/a =0.17, where z is the longitudinal distance from the extensometerring to the face at any time. The curve of relative displacementversus face advance is based on calculations for successiverounds corresponding to the advance of the central bore, andtherefore the curves are continuous with discontinuous slopes.The response to excavation of the annular enlargement around thiscentral pilot drift - - the "slash" was not modelled. If ourpredictions were accurate in total displacement, their paths tothat final value should be initially too high and then too flat.

Each Figure of the extensometer predictions has five curves,corresponding to the first five anchor positions. The highest ofthe curves gives the relative displacement between the collar andthe end anchor (#1); the second highest curve gives relativedisplacement between anchors #5 and #1; the next highest curvedescribes relative displacements between anchors #4 and #1,followed by #3 and #1. Finally the relative displacement betweenanchors #2 and #1 are given by the lowest of the five curves.The depths of these anchors for each extensometer are listed inTable 1. The analysis used uniform, average anchor positionsrather than the actual values of each anchor.

TABLE 1Actual anchor depths corresponding to each of Figures 1 - 7 andanchor depths used to develop the points plotted on the curves

Figure Extensometer Anchor

123456

2O9-O18-ExtO4II II II QO

II II II Q 1

• I tl II QQ

• I 05 0.30

16.03 *15.8114.95 *15.0115.0115.04

9.01 15.01

All Values used: 0.20 1.50 3.00 5.00 9.00 15.00

* note renumbering of certain anchors

Prediction of response strain changes

Triaxial strain cells were embedded in the rock in boreholesahead of the face. These instruments lie in the planeperpendicular to the axis of the 209 room at chainage 27.2,beyond the fracture. The strain cells respond to changes instrain from their initial condition. These strain changes canthen be converted to stress changes. The predicted strainchanges in each triaxial strain cell are referred to coordinatesas follows: x is horizontal and y is upward in the planeperpendicular to the tunnel axis (section C-C in Figure 3-5 of

37-194-161-150-679-147-681-131

-73-68

-115-115-262-21

-470-55

- 587 -

the furnished documents). The predicted strain changes relatedto mining of the room completely past the instrument station. Thepredictions are listed in Table 2.

TABLE 2Predicted strain changes for complete mining past

the strain cells at chainage 27.2 in Room 209.

Strain change (microstrain)Strain Cell x^ strain _y_ strain xy strain

209-015-SM-R2 21209-015-SM-R1 77209-017-SM-F2 -18209-017-SM-F1 -17209-009-SM-S1 986209-009-SM-S2 1992O9-O1O-SM-N2 953209-010-SM-N1 210

Sign Convention: positive normal strain is extensile;negative normal strain is contractive; shear strain isconsistent with this convention (as for example, inTheory of Elasticity, by Timoshenko and Goodier).

Prediction of Response - Fluid Pressure Test in Hole Rl

Hole Rl pierces the water-filled fracture crossing room 209between approximate chainages 21 to 23. This hole was tested todetermine the permeability before mining through the fracture.The fluid flow was found to be 2.05 L/min. Figure 8 showsequipotential lines and flow directions for flow from borehole Rlinto the fracture, with discharge into the tunnel. Thepermeability was calculated from reported results of flow testsprior to mining. This Figure allowed calculation of the totalflow from the hole at a pressure of 1000 kPa in the hole andatmospheric pressure in the tunnel. The discharge amounts to 2.4L/min.

The Discontinuous Deformation Analysis

Discontinuous deformation analysis was originally developedby Shi and Goodman for back calculation of a blocky rock masswhose displacements were measured at discrete points.Displacements, rotations, and strains were found for each blocksuch that the indicated measurements were matched with minimumerror. Interpenetrations of one block by another were disallowedby a numerical process based upon kinematic rules. In a thesis inpreparation, Shi has advanced this method for forward calculationusing constitutive relations within the blocks. At present,friction and cohesion are zero between blocks. Each block canstrain, rotate and displace and the balance of forces and momentsin each block is established. Interpenetrations of blocks areprohibited. The solution is achieved iteratively. The entire load

- 588 -

is achieved in a number of load steps. In the present problem,the loads, derived from the initial stress state, were applied inten steps. To achieve force and moment equilibrium without anyinterpenetration of blocks, and without any tension betweenblocks, each load step required an average of four iterations.

The mesh used for the computation of the 209 room is shownin Figure 9. Four rings of blocks, delimited by radial andtangential joints, surround the excavation. The annular jointsbetween each ring are intended to model slabbing joints formed asa result of excavation. This idealized discontinuous medium isplaced in a state of initial stress with Sigma 1 equal to 31.4MPa directed clockwise 17.4 degrees from horizontal, and Sigma 3equal to 15.2 MPa (both compressive) as shown on Figure 3-3 ofthe furnished documents. The region was assumed to be in a stateof plane strain. To initiate the computation, the outer boundarywas fixed and the inner boundary was freed.

Figure 10 shows the deformed shape of the mesh after allload steps. Figure 11 compares the final and the initial blockcorner positions. On these figures, the deformations are drawnwith a fifty-fold exaggeration of scale. The numerical values ofthe x and y displacements of every corner are listed in theoutput, which is appended. On the basis of this information, thex and y displacements of each extensometer anchor position weredetermined and then rotated into the direction along the lengthof the extensometer. The resulting values represent the totaldisplacement associated with changing the region from one withouta tunnel to one with a tunnel. In order to consider the effectof face advance, the displacements were multiplied by faceadvance coefficients determined independently, as described below.

Analysis of Face Advance Coefficients

In the Proceedings of the 11th Symposium on Rock Mechanics,De la Cruz and Goodman presented mathematical results developingthe relationships between face advance and radial displacement,as a function of theta, for a linearly elastic and continuousmedium. If an instrument capable of measuring radialdisplacements is placed near the face of a tunnel and the tunnelface is then advanced more than four radii ahead, the instrumentwill record displacments amounting to something less than half ofthe total displacements associated with the plain strainsolution. De la Cruz and Goodman's formula is expressed in termsof a parameter, Z (=z/a), expressing the ratio of the initialdistance from the instrument to the tunnel face. The formulaextends only from Z equal zero to Z » 0.5. To express the fullrange of the displacement/advance relationship, a logarithmicextrapolation was performed. The results were then combined withthose from the published paper to yield Figure 12, computed forthe conditions of room 209. Figure 13 shows the same dataplotted on a logarithmic scale for Z. This establishes thejustification for the logarithmic extrapolation from Z of 0.5 togreater values. Figure 12 expresses the radial deformation in mm.for values of Z from .17 to 4, from which value onward, the

- 589 -

deformation is zero. Since this computation was made for alinearly elastic material, the proportion of total displacementcannot be determined with reference to Figure 11, as thatcomputation is for a discontinuous material. Consequently, thetotal displacement for creating the excavation was computed fromthe Kirsch Solution (using the formula presented by Goodman in"Introduction to Rock Mechanics". This amount of totaldisplacement, which is less than that given by the discontinuousdeformation analysis, is presented for each extensometerorientation in Figure 11. For a given value of Z, each curve willhave undergone a difference in radial displacement indicated bysubtracting the abscissa corresponding to Z from the initialabscissa at Z = 0.17. The ratio of this displacement differenceto the total radial displacement, given by the appropriatestraight line, establishes the proportion of total displacementwhich would be measured by an extensometer when the face hadadvanced to position Z.

Figure 14 shows the ratios as computed in this way as afunction of the face position. These curves establish thecoefficient multipliers to convert the computed discontinuousdeformation results to a three dimensional solution. Theincrements of face advance established the coefficientmultipliers given in Table 3.

TABLE 3EXCAVATION ADVANCE MULTIPLIERS

Proportion of total displacementtheta = 0,180 45,225 90,180 135,315

Stage

01234 etc

distance(m)

0.311.22.75.6

>7.2

Z

13

>4

(=z

.17

.67

.50

.11

.00

0.185.295.393.413

0.221.352.407.407

0.246.391.403.403

0.188.299.399.413

Analysis of fluid flow in the water-filled fracture

The finite difference method was used to create a mesh inthe plane of the fracture. All flow is confined to this plane.The flow is generalized LaPlacian in the plane, with theconductivity varying from point to point. The conductivity wasback-calculated from the flow experiments by running the programwith a mesh representative of the conditions of the flowexperiments. The boundary conditions were then changed to thoseshown in Figure 8 and the flow balance established. In principle,it is possible to input varying conductivity according to thestresses derived from the stress/deformation analysis of thesurrounding rock but no such runs were completed for this effort.

- 590 -Discussion

The methods used are intended for discontinuous rock. Thismedium is not really optimum for testing such techniques but itwill be interesting to see how these predictions compare withconventional finite element analyses using linear elasticity. Asnoted, the real case is neither linearly elastic and continuous,nor truly discontinuous so every method represents a compromise.

The discontinuous deformation analysis used here is adeveloping technique which is very new. It is in a primitivestate here and is not realizing its full potential. It is hopedthat a more complete analysis by this technique will be possibleat the time of further excavation response experiment stages.

The problem faced by the excavation advance is threedimensional. A two dimensional approach has been adapted byadjustments with coefficient derived from a generic threedimensional study by de la Cruz and Goodman made 17 years ago.The use of this method is premised on the assumption that thesame coefficients apply to all values of the radial distanceequally; it is not known if this is a valid assumption. It isalso assumed that the coefficients can be applied withoutmodification to a non-linear, non-elastic, discontinuousanalysis; this may also be questionable.

The introduction of water in the crack was done at theeleventh hour, as most of the energies of the modellers weredevoted to completion of the discontinuous deformation analysis.A more comprehensive effort at hydraulic modelling, coupled withthe discontinuous deformation analysis, will be directed tofuture modelling problems.

- 591 -

References

de la Cruz, Rodolfo, and Goodman, R.E., (1970), Theoretical basisof the borehole deepening method of absolute stress measurement,Proc. 11th Symp. on Rock Mechanics (AIME), pp. 353 - 375/

Goodman, R.E. (1980), Introduction to Rock Mechanics,(John Wiley)(Equation 7.2a and its derivation).

Shi, Gen-hua, and Goodman, R.E. (1986) Two-dimensionaldiscontinuous deformation analysis, International Journal ofNumerical and Analytical Methods in Geomechanics, (John Wiley)

DISPLACEMENT: MM

to

I

10 10

TUNNEL ADVANCE: M

Fig.l DISPLACEMENT OF 209-018-EXT04

DISPLACEMENT: MM

1 -

.8 .

10 IB

TUNNEL ADVANCE: M

Fig.2 DISPLACEMENT OF 209-018-EXT03

DISPLACEMENT: MM

1 .

.B .

I

10r IIB 20

TUNNEL ADVANCE: M

F i g . 3 DISPLACEMENT OF 209>-018-EXT01

DISPLACEMENT: HM

.B ,

I

10 IS 20

TUNNEL ADVANCE: M


DISPLACEMENT: MH

.8 .

T I10 15 20

TUNNEL ADVANCE: H

Fifl.5 DISPLACEMENT OF 209-018-EXT07

DISPLACEMENT: MM

1 .

.0 .

IB IB 20

TUNNEL ADVANCE: M

Fig.6 DISPLACEMENT OF 209-01B-EXT06

DISPLACEMENT: HH

t J

.8 .

I

to ts

TUNNEL ADVANCE: M


- 599 -

- 600 -

O)

- 601 -

- 602 -

2.0 -i

total displacement: theta - 0 deg.

135 deg

oOu>

Fig. 12

Z = * / a (dimensionless)

2.0 -i

total displacement, theta = 0 deg.

135 deg

45 deg.

10 z = / a (log scale)

oo

Fig. 13

0.50 -i

c0)

.2Q.

'"5 0.30 -iO

o0.20 :

0 0.10 -

OCL2 0.00CL 0.00

90

o

Face advance functionURL excavation response experimentroom 209

Fig. 141.00 2.00

m/a3.00 4.00

i5,00

- 606 -

Appendices

Output of discontinuous deformation analysis: The blocknumbers are defined on Figure 9 in the main report. The cornernumbers in each block are defined in the first figure of theappendix. Following that is a deformed mesh for each of the firstnine iterations. The results at the end of the tenth iterationare given in Figure 10 in the main report. Tables of values fordisplacements, strains, and stresses, are given for corner ineach block.

In these listings of output numbers, the symbols are asfollows: Uo, Vo, AZ are respectively the x and y displacement androtation pf, the block centroid. EX, EY, and GXY are respectivelythe x, y, and xy strains in the block. Strains are constantthroughout each block. CX, CY, and TXY are respectively thenormal stress parallel to x, the normal stress parallel to y, andthe shear stress x,y. The displacements of the corners of eachblock are given with the following symbols: X and Y arerespectively the x and y coordinates of the corner; U and V arerespectively the x and y displacements of the corner. The cornersare listed numerically in each block. The dimensions of theoutput are meters and MPa.

- 607 -

- 608 -

- 609 -

&

- 610 -

- 611 -

- 612 -

in

- 613 -

(0

I

_ 614 -

\

\\

XT

l

- 615 -

\

bSi

. 616 -

o>

(0

NUMBER OF BLOCKS:48NUMBER OF MEASURED POINTS:24NUMBER OF CONTACT POSITIONS:480NUMBER OF 6*6 SUBMATRICES:369NUMBER OF MEASURED STRAINS0TOTAL ITERATION NUMBER:42YONG'S MODULUS & POISSON RATIO:50000INITIAL STRESS:-30.8-163TOTAL DEFORMATION AND STRESS OF

- 617 -

BLOCKSUO VOEX EYCX CYBLOCK NO:

-0.0021370560.000836739'8.005008000

BLOCK NO:2-0.001184252-0.000670962

-57.440360000BLOCK NO:3-0.000076217-0.000721153

-61.221650000BLOCK NO:

-0.0024788660.001606964

43.242400000BLOCK NO:

-0.0023128040.001358044

31.495960000BLOCK NO:

-0.0007785360.000213276

-19.852500000BLOCK NO:

-0.000024295

AZGXYTXY

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