SAND83-7451, 'Investigative Study of the Underground ... · !EE e HUTI ts S }]DUcted to...

CONTRACTOR REPORTSAND83-7451Unlimited ReleaseUC-70

-U

a * Nevada Nuclear Waste Storage Investigations Project

Investigative Study of theUnderground Excavations for aNuclear Waste Repository in Tuff

C. M. St. JohnJ. F. T. Agapito & Associates Inc.27520 Hawthorne Blvd., Suite 295Rolling Hills Estates, CA 90274

Prepared by Sandia National Laboratories Albuquerque. New Mexico 87185and Livermore, Cahifornia 94550 for the United States Department of Energyunder Contract DE-AC04-760P00789

Printed July 1987

SAND83-7451

Unlimited ReleaseJuly 1987

INVESTIGATIVE STUDY OF THE UNDERGROUNDEXCAVATIONS FOR A NUCLEAR WASTE REPOSITORY IN TUFF

by

C. M. St. John

J. F. T. Agapito & Associates Inc.27520 Hawthorne Blvd., Suite 295Rolling Hills Estates, CA 90274

for

Sandia National LaboratoriesP. 0. Box 5800

Albuquerque, New Mexico 87185

Under Sandia Contract 25-8908

Sandia Contract MonitorB. Ehgartner

Geotechnical Design Division 6314

ABSTRACT

The report documents the results of numerical studies of the behaviorof a tuff rock mass within which emplacement drifts for a nuclear wasterepository are excavated. The first study was performed to evaluatethe effects of rockbolting and excavation-induced damage on the be-havior of the rock mass around typical drifts. The second study wasperformed to provide a simple means of assessing the significance ofdrift shape, drift size, and in-situ state of stress on the deformationand stress in the vicinity of drifts for vertical and horizontalemplacement of waste. Neither study considered the effect of heatingof the rock mass after emplacement of the waste so the conclusionspertain only to the conditions immediately after excavation of theunder round openings. The result analyses of the rnekbojted exZ

jgf t~he states of detor or;6 streFss within the rocK mass-Kno that!EE e HUTI S ts }]DUcted to acceptGe----e- orsrT-vni

ccorarig rockbots were not consere e suy o rtt shape,an fMt size, and the in-situ state of stress. That study indicated thatstable openings of the dimensions investigated can be constructedwithin a tuff rock mass with the properties assumed. Of the parametersinvestigated, the in-situ state of stress appeared to be most impor-tant. Potentially adverse conditions were predicted if the in-situhorizontal stress is very low, but current indications are that it lieswithin a range which is consistent with good conditions and a stableroof.

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TABLE OF CONTENTS

Section Page

1. INTRODUCTION

1.1 Purpose and Justification .1.... . .......... . 11.2 Approach . . . . . . .... . . . . . . . . 11.3 Assumptions. . . . . . .. . . . . . . . . . . 2

2. PRELIMINARY ANALYSES OF HORIZONTAL EMPLACEMENT DRIFT

2.1 Introduction. . .. . 22.2 Problem Description. .. .. . . . . . . 2

2.2.1 General Description . .. . . . . . . . . . 22.2.2 Drift Geometries .. 42.2.3 Rock Mass Properties . ... . . . . . 52.2.4 Rock Bolt Properties . . . . . . . . . . . . . . . 5

2.3 -Method of Analysis . . . . . . . . . . . . . . . . . . . 62.3.1 Introduction . . . . .. . . . . 62.3.2 Boundary-Element Models . . . . .62.3.3 Finite-Element Models . . . . . . . . . . . . . 6

2.4 Results of Analyses . . . . . . . . . . . . . . . . . . . 72.4.1 Introduction . . . . . . 72.4.2 Analysis of Unsupported Drifts .82.4.3 Analysis of the Effects of Rockbolting

and Excavation-Induced Damage . . . . . . . . . . 82.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . 10

3. ANALYSIS OF VERTICAL AND HORIZONTAL EMPIACEMENT DRIFTS

3.1 Introduction . . . . . . . . . . . . . . . .. . . . . . . 113.2 Problem Description .. . . . 11

3.2.1 General Description . . . . . . . . . . . .. 113.2.2 Drift Dimensions .... ... .......... . 123.2.3 Rock Mass Properties . . . . 13

3.3 Method of Analysis. . . . . . . . 143.4 Results of Analyses .. 15

3.4.1 .Introduction . . . . . . . . . . 153.4.2 Vertical Emplacement . . .. . . . . 153.4.3 Horizontal Emplacement . . . . . . . . 15

3.5 Conclusions . . . . . . . . . . ... . . . . . . . . . . 17

4. ES.21.. ...... ... 21

APPENDICESA - Relationship of Data Used in this Analysis to

NNWSI Reference Information BaseB - Relationship of Data Used in this Analysis to SEPDBC - Distribution List

V

LIST OF ILLUSTRATIONS

Figure

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Geometry of Horizontal Emplacement DriftsAnalyzed Using Boundary-Element andFinite-Element Models ... . . . . . . . . . . . . . . . . . 34

Derivation of the Matrix Factor of Safety ... . . . . . . . . 35

Drift Shapes and Internal Sample Pointsfor Boundary-Element Analyses . . . . . . . . . . . . . . . . 36

Finite-Element Model for Analysis of an Arched,Horizontal Element Model . . . . . . . . . . . . . . . . . . 37

Boundary Displacements Computed by theBoundary-Element Analyses . . . . . . . . . . . . . . . . . . 38

Deformed Shapes Computed Using the Finite-ElementModels of Unsupported Drifts . . . . . . . . . . . . . . . . . 39

Matrix Strength Ratio Computed from the Resultsof Boundary-Element Analyses . . . . . . . . . . . . . . . . . 40

Matrix Strength Ratio for Unsupported Drifts,Computed from Results of Finite-Element Analyses . . . . . . . 41

Distribution of Axial Stress in RockboltsAround Drifts in Homogeneous Rock . . . . . . . . . . . . . . 42

Distribution of Bond Shear Stress atGrout/Rock Interface of Rockbolts AroundDrifts in Homogeneous Rock . . . . . . . . . . . . . . . . . 43

Results of Finite-Element Analysis of RockboltedDrift with an Annulus of Damaged Rock . . . . . . . . . . . . 44

Axial Stress Distributions for Rockbolts and ShearStress Distributions at Grout/Rock Interface Arounda Drift with an Annulus of Damaged Rock . . . . . . . . . . . 45

Parson's Design of Drift for VerticalEmplacement of Waste Canisters of Spent Fuel . . . . . . . . . 46

Parson's Design of Drift for HorizontalEmplacement of Waste Canisters of Spent Fuel . . . . . . . . . 47

Alternative Shapes and Sizes of Drifts AnalyzedDuring Parametric Study of Vertical Emplacement. . . . . . . . 48

Alternative Shapes and Sizes of Drifts AnalyzedDuring Parametric Study of Horizontal Emplacement. . . . . . . 49

Derivation of the Joint Factor of Safety . . . . . . . . . . . 50

Boundary-Element Models of Vertical EmplacementDrifts, Showing Internal Sampling Points . . . . . . . . . . . 51

Boundary-Element Models of Horizontal EmplacementDrifts, Showing Internal Sampling Points . . . . . . . . . . . 52

Boundary Displacements, Vertical Emplacement,Parson's Shapes . . . . . . . . . . . . . . . . . . . . . . . 53

vI

LIST OF ILLSTRATIONS

Figure

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age

Boundary Displacements, Vertical Emplacement,Horseshoe Shapes .................

Boundary Displacements, Vertical Emplacement,Continuous Miner Shapes

Principal Stresses, Vertical Emplacement,Parson s Shapes . . . . . . . . . . . . . . . . .

Principal Stresses, Vertical Emplacement,Horseshoe Shapes . . . . . . . . . . . . . . . . .

Principal Stresses, Vertical Emplacement,Continuous Miner Shapes . . . . . . . . . . . . .

Tangential Stresses, Vertical Emplacement,Parson's Shapes . . . . . . . . . . . . . . . . .

Tangential Stresses, Vertical Emplacement,Horseshoe Shapes . . . . . . . . . . . ... . . . .

Tangential Stresses, Vertical Emplacement,Continuous Miner Shapes . . . . . . . . . . . . .

Matrix Strength Ratio, Vertical Emplacement,Parson's Shapes . . . . . . . . . . . . . . . . .

Matrix Strength Ratio, Vertical Emplacement,Horseshoe Shapes . . . . . . . . . . . . . . . . .

Matrix Strength Ratio, Vertical Emplacement,Continuous Miner Shapes . . . . . . . . . . . ..

Joint Strength Ratio, Vertical Emplacement,Parson's Shapes . . . . . . . . ... . . . . . . .

Joint Strength Ratio, Vertical Emplacement,Horseshoe Shapes .................

Joint Strength Ratio, Vertical Emplacement,Continuous Miner Shapes . . . . . . . . . . . . .

Boundary Displacements, Horizontal Emplacement,Parson's Shapes . . . . . . . . . . . . . . . . .

Boundary Displacements, Horizontal Emplacement,Horseshoe Shapes .................

Boundary Displacements, Horizontal Emplacement,Continuous Miner Shapes . . . . . . . . . . . . .

Principal Stresses, Horizontal Emplacement,Parson s Shapes .................

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LIST OF IMUSTRATIONS

Figure Page

39 Principal Stresses, Horizontal EmplacementHorseshoe Shapes . . . . . . . . . . . . . ... . . . . . . . . 72

40 Principal Stresses, Horizontal Emplacement,Continuous Miner Shapes .... . . . . . . . . . . . . . . . 73

41 Tangential Stresses, Horizontal Emplacement,Parson's Shapes . . . . . . . . . . . . . . . . . . . . . . . 74

42 Tangential Stresses, Horizontal Emplacement,Horseshoe Shapes .... . . . . . . . . . . . . . . . . . . . 75

43 Tangential Stresses, Horizontal Emplacement,Continuous Miner Shapes .... . . . . . . . . . . . . . . . 76

44 Matrix Strength Ratio, Horizontal Emplacement,Parson's Shapes . . . . . . . . . . . . . . . . . . . . . . . 77

45 Matrix Strength Ratio, Horizontal Emplacement,Horseshoe Shapes . . . . . . . . . . . . . .. . . . . . . . . . 78

46 Matrix Strength Ratio, Horizontal Emplacement,Continuous Miner Shapes . . . . . . . . . . . . . . . . . . . 79

47 Joint Factor of Safety, Horizontal Emplacement,Parson's Shapes . . . . . . . . . . . . . . . . . . . . . . . 80

48 Joint Factor of Safety, Horizontal Emplacement,Horseshoe Shapes . . . . . . . . . . . . . . . . . . . . . . . 81

49 Joint Factor of Safety, Horizontal Emplacement,Continuous Miner Shapes .................. . 82

Vtt

LIST OF TABLES

Table PaRe

1 Material Properties of Tuff Rock Mass .. . . . . . . . . . 23

2 Rock Bolt Properties .. ... ... ......... 24

3 Drift Closures Computed Using Boundary-Elementand Finite-Element Models . . . . . . . . . . . . . . . . . . 25

4 Computed Closures of Bolted andUnbolted Excavations . . . . . . . . . . . .. . . . . . .. ., 26

5 Data for Analysis of Emplacement Drifts . . . . . . . . . ... 27

6 Results of Boundary-Element Calculations - Parson'sShape, Vertical Emplacement at Time of Excavation. . . . . . . 28

7 Results of Boundary-Element Calculations - HorseshoeShape, Vertical Emplacement at Time of Excavation. . . . . . . 29

8 Results of Boundary-Element Calculations - ContinuousMiner Shape, Vertical Emplacement at Time of Excavation. . . . 30

9 Results of Boundary-Element Calculations - Parson'sShape, Horizontal Eplacement at Time of Excavation. . . . . . 31

10 Results of Boundary-Element Calculations - HorseshoeShape, Horizontal Emplacement at Time of Excavation . .. . . 32

11 Results of Boundary-Element Calculations - ContinuousMiner Shape, Horizontal Emplacement at Time of Excavation. . . 33

ix

This study was initiated by Ken Beall of SNL at a time whenpreliminary repository designs were being prepared by the DravoCorporation. At that time, finite-element and boundary-elementanalyses of several different shapes for the vertical and horizontalemplacement options were completed by David Van Dillen and Tony Zahrah,both of Agbabian Associates. Selected results of the finite-elementcalculations are reproduced in this report. However, the boundary-element calculations were repeated using more recent design parametersand rock mass properties. This was done at the instigation of ArthurMansure, who recognized a need for an easily assimiIated presentationof the influence of design decisions impacting excavation shape anddimensions, and the importance of the initial state of stress. Therevised boundary-element calculations and assembly of the com positefigures were completed by Kandiah Arulmoli. Janis Goshi and KathyWright typed and assembled the report.

1.0 IETRODUCTION

1.1 Purpose and Justification

The work described in this report was performed for Sandia NationalLaboratories (SNL) as a part of the Nevada Nuclear Waste Storage Investigations(NNWSI) project. SNL is one of the principal organizations participating in theproject, which is managed by the U.S. Department of Energy's Nevada OperationsOffice. The project is part of the Department of Energy's program to developmethods to safely dispose of the radioactive waste from nuclear power plants.

The Department of Energy has determined that the safest and most feasiblemethod currently known for the disposal of such waste is to emplace it in minedgeologic repositories. The NNWSI project is conducting detailed studies of anarea on and adjacent to the Nevada Test Site (NTS) in southern Nevada to deter-mine the feasibility of developing a repository there.

This report documents the results of two numerical studies of the be-havior of a tuff rock mass within which emplacement drifts for a nuclear wasterepository are excavated. The first study was performed with the objective ofevaluating the effects of rockbolting and excavation-induced damage on the be-havior of the rock mass around typical drifts. It also served to provide datafor a comparison of the results of boundary-element and finite-element analysesof identical excavations in rock masses with the same properties. The secondstudy was performed with the objective of evaluating the influence of shape,dimensions, and in-situ state of stress on the predicted response of a tuff rockmass to excavation of emplacement drifts.

1.2 Approach.

For both portions of this study, excavation shapes were developed fromthen-current design concepts for the waste emplacement drifts. For the firstportion of this study, flat-roofed and arched drifts, with spans of approximately7.6 m (25 ft), were selected for analysis. Such spans are typical of those beingconsidered when employing the option of emplacing canisters in long, horizontalholes drilled into the emplacement drifts. These drifts were analyzed using theEMINES (Agbabian Associates, 1981) finite-element code and the HEFF (Brady, 1980)boundary-element code. The results of those analyses were subsequentlypostprocessed to prepare plots illustrating the deformation around the drift andthe ratio of the assumed rock matrix strength to the computed stresses. For thesecond portion of this study, nine alternative -drift profiles were prepared forboth vertical and horizontal emplacement. .,These drifts were then analyzed usingthe HEFF boundary-element code, and plots illustrating deformation, stress, andthe potential for inelastic behavior of the joint and rock matrix were prepared.

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1.3 Assumptions

Data for the analyses are discussed in detail in Sections 2.2 and 3.2.However, all analyses assumed that the tuff rock mass in which the drifts areexcavated can be characterized as a linearly elastic medium. The possibility ofrock mass failure or joint slip was evaluated by postprocessing the analysisresults. Also, only the mechanical response of the rock mass at the time ofexcavation was investigated. No consideration was given to changes that mightoccur as a result of drilling of the waste emplacement holes, disturbance of theoriginal thermal equilibrium of the host rock mass as a consequence of ventila-tion of the drift, and heating of the rock mass following waste emplacement.

2.0 PRELMIINARY ANALYSES OF HORIZONTAL EMPLACEKENT DRIFT

2.1 Introduction

This section describes a series of analyses of horizontal emplacementdrifts with nominal height and span of approximately 3.7 and 7.6 m (12 and 25ft), respectively. These calculations were performed with the objective ofinvestigating the influence of rockbolting and excavation-induced damage on thedeformation and stress in the vicinity of a typical emplacement drift. They alsoprovided an opportunity for comparison with the results of calculations performedusing finite-element and boundary-element models.

The preliminary analyses reported in this section were performed prior todevelopment of a comprehensive data base on the mechanical properties of tuff andat a time when concepts for repository design and siting were in their infancy.Accordingly, the basis for the calculations presented here differ substantiallyfrom those used for the parametric study that comprises Section 3. However, theresults of these analyses serve a useful function in providing a quantitativeassessment of the influence of rockbolting and excavation-induced damage, as wellas a justification for use of the simpler boundary-element models applied in thesubsequent parametric study.

2.2 Problem Description

2.2.1 Ceneral Description

The particular case considered here is that of excavation of a horizontalemplacement drift within a rock mass in which the vertical and horizontalstresses prior to disturbance are assumed to be 9.15 MPa (1,327 psi). Thesestresses are some 50% higher than those for the similar "isotropic" case con-sidered in Section 3 of this report and reflect early assumptions regardingrepository depth, the density of the overlying rock mass, and the ratio betweeninitial horizontal and vertical stresses. Two different shapes of excavation

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were considered: a conventional "horseshoe' shape and a rectangular shape withrounded corners. The horseshoe shape is typical of a drift with an arched roof,while the rectangular shape is typical of a drift with a flat roof.

For the boundary-element analyses, the emplacement drift was assumed tobe excavated within a linear elastic, homogeneous medium. The same assumptionwas made for the first finite-element calculations. Subsequently, rockbolts wereadded to the finite-element model and then an annulus of material with reducedmodulus was added to represent damage caused during excavation (i. e., blasting).Both the boundary-element and finite-element analyses considered a plane sectionof the drifts so the predicted responses are typical of portions of the excava-tion within the interior of a waste panel and remote from drift intersections.

In a two-dimensional model of the excavation, it is impossible todirectly account for the timing of installation of rockbolts as the drift isadvanced. This timing may be important if the rockbolts are not pretensionedafter installation, because the rockbolt loads will be determined entirely byinteraction between the rock mass and the rockbolts. For example, if the rock-bolts are installed several tunnel diameters back from the advancing face, alltime-independent deformation of the rock mass will have occurred prior to instal-lation. In such circumstances, the rockbolts will remain free of load unlesseither pretensioned or loaded as a result of time-dependent deformation of therock mass.

For the purposes of the present investigation, it was assumed that 25% ofthe excavation induced displacement of the rock mass would occur-before installa-tion of the rockbolts. This approximation was selected on the basis of resultspresented in several analytical studies of induced displacement and theredistribution of stress in the vicinity of an advancing tunnel (Van Dillen,1979; Einstein et al., 1980; John and Baudendistel, 1981). It corresponds toinstallation right at the advancing face and is intended to approximate a practi-cal upper limit on the interaction between rockbolt and rock mass (i.e.approximate the maximum rockbolt load).

Analysis of drifts with an annulus of excavation-induced damage requiredthat the extent and nature of any damage be approximated. Experimental evidenceindicates that there can be large variations in the extent of such damage,depending on the excavation technique used. For example, Agapito et al., (1984)describe significant differences in the extent of damage to pillars in an oilshale mine, depending upon whether excavation was performed using a mechanicalmining system or by drilling and blasting. Similar information is not currentlyavailable for the emplacement drifts of a repository constructed in tuff. In theabsence of such information some reasonable assumptions need to be made.

For the present study, it was assumed that the drifts would be excavatedusing conventional drill and blast techniques. It was further assumed that some

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type of controlled blasting method would be implemented. Presplitting and smoothwall blasting are the usual methods of controlling damage, with the latter themore common when blasting underground (Hoek and Brown, 1980). In either case,the spacing of the outermost drill holes, or trim holes, around the drift is ofthe order of 10 to 15 drill hole diameters. The extent of damage is related tothis spacing, the charge in the holes, and, in the case of smooth wall blasting,to the thickness of the annulus of rock removed when the trim holes aredetonated. Here it is assumed that the extent of damage will be approximately0.5 m (1.7 ft), which would be roughly equal to the spacing of the trim holes.Following review of discussions on the relationship between rock mass defor-mability and rock quality (Bieniawski, 1978; Hoek and Brown, 1980) it wasestimated that the elastic modulus of this blast damage zone would be about 20%of that of the undisturbed rock mass. Neither the assumption of the extent ofdamage nor its impact on the deformability of the rock mass is substantiated byany field data at present. However, these assumptions were considered ap-propriate for analyses intended to evaluate the potential significance of theseparameters.

2.2.2 Drift Geometries

Two drift geometries were investigated. In both cases, the nominal spanand height of the drift were 7.6 m (25 ft) and 3.7 m (12 ft), respectively. Thedrift geometries were designated "horseshoe-shaped" and "rectangular." For thehorseshoe-shaped drift, the span and height were increased slightly to accom-modate the curvature of the roof and sidewall without significant loss ofinternal clearance. The rectangular drift had the nominal dimensions, exceptthat a 1-m (3.3-ft) radius curve was added in the upper corners of the drift.Both shapes are illustrated in Figure 1.

In a nuclear waste repository utilizing a horizontal emplacement system,canisters of nuclear waste would be placed in horizontal holes bored from theemplacement drifts. One of the alternative concepts in the current design for arepository in tuff is the use of horizontal emplacement holes approximately 1 m(3.3 ft) in diameter, up to 200 m (656 ft) in length, and 30 m (98.4 ft) apart.Such length and spacing will ensure that the excavation-induced stresses anddisplacements around the emplacement drifts are not significantly influenced byeither adjacent emplacement drifts or the boreholes. Interactions between dif-ferent parts of the repository will begin after thermal loading of the repositoryby emplacement of the waste. Postemplacement conditions were not considered inthis investigation; hence, only a single drift was considered in any of theanalyses discussed in this part of the report.

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2.2.3 Rock Mass Properties

The data used for analysis of the emplacement drifts is listed in Table1, in which appropriate references are cited. The rationale for selection of themodulus of the annulus damaged rock considered in some of the finite-elementanalyses was given earlier.

For all analyses, it was assumed that the rock mass would behave as alinearly elastic medium. The results of analyses were subsequently postprocessedto determine the' potential for inducing failure of the rock mass. For thatpurpose, it was assumed that the rock mass strength could be described by alinear Mohr-Coulomb criterion, the parameters for which are listed in Table 1.The ratio of strength of the rock mass to the computed state of stress wasevaluated using the equations:

(°1 + 02) sinym + Vc (1 sin~m) :2 > aT (1)

FSm - 01-

FSmT ° 2 :0 > 2 (2)

in which a, and 02 are, respectively, the more compressive and less compressiveprincipal stresses in the plane of the section analyzed, and act 4m' and aT are,respectively, the uniaxial compressive strength, the angle of internal friction,and the tensile strength of the rock matrix. If °2 is tensile, then FSm is takenas lesser of the two given by the above equations. As illustrated in Figure 2,the strength ratio, or factor of safety, given by equation 1 is in fact the ratioof the permissible maximum shear stress, at the computed normal 'stress, to theactual maximum shear stress.

Although'the term "factor of safety" or "strength ratio" is usedthroughout this report, it is important to note that this is a quantity that iscomputed for a particular point within the rock mass. The fact that the factorof safety--or strength ratio may locally fall below 1.0, indicating that the rockmatrix does not have sufficient strength to withstand the applied stress, doesnot necessarily imply any large-scale instability. For example, local over-stressing around an excavation will usually result in local inelastic deformationof the rock mass and redistribution of stress until a sustainable stress state isachieved. Calculations in which such redistribution of stress is simulated arepossible but were not performed in the investigation reported here.

2.2.4 Rock Bolt Properties

Since data on rock support requirements were available, representativevalues were assumed. -These are listed in Table 2 and illustrated in Figure 1.The spacing of approximately 1.5 by 1.5 m (4.9 x 4.9 ft) is quite typical of

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medium rockbolting (Hoek and Brown, 1980). The length of 3 m (9.8 ft) is ap-proximately half the average dimensions of the tunnel, which, again, is typical.The rockbolt diameter corresponds to a #9 reinforcing bar, which is relativelylarge for medium rockbolting; 25-mm (1-inch) diameter would be more common. Thelarger size was selected to illustrate the greatest likely impact that rockboltsmight have on the deformations and stresses in the vicinity of the drift.

Material properties of the rockbolts are listed in Table 2. In theanalyses performed it was assumed that the rockbolts were bonded to the rock massalong their entire length using a polyester resin. As for the rock mass, thebolts and resin were assumed to be linearly elastic; no attempt was made tosimulate failure of the rockbolts either by yield of the steel or failure of theresin bond.

2.3 Methods of Analysis

2.3.1 Introduction

As noted earlier, analyses were performed using both boundary-elementmodels and finite-element models. In this section, the various models and thetwo computer codes used for the analyses are described.

2.3.2 Boundary-Element Models

The boundary-element models of the flat-roofed and arched excavations areillustrated in Figure 3. In both cases, a total of 42 boundary elements wereused to define the perimeter of the excavation. Displacements and stresses arecomputed at the center point of each boundary element, and also at internalsample points. The internal sample points (Figure 3) were generated automati-cally along lines normal to each boundary element and originate at the centerpoint of the element. Accordingly, the division of the drift boundary intoelements can be inferred from these lines of sample points.

The boundary-element analyses were performed using the HEFF (HLeat withFictitious force) code (Brady, 1980). The code is based on an indirect formula-tion of the boundary-element method of stress analysis described by Crouch andStarfield (1983) and utilizes constant-stress, linear elements. In the presentinvestigation, the capability of the code to perform thermal and thermal-mechanical analyses was not exploited.

2.3.3 Finite-Element Models

The finite-element model for the arched excavation is illustrated inFigure 4. It employed 254 four-node continuum elements and 286 nodes. An addi-tional 20 elements and 25 nodes were used in the models that included rockbolts.The finite-element meshes for the rectangular-shaped excavation were similar to

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that for the arched excavation. In both cases, the number of finite elementsaround the drift boundary corresponds closely to the number of elements used inthe boundary-element analyses.

Unlike the boundary-element models in which only the perimeter of thedrift need be discretized, the finite-element models require discretization ofsome finite domain. The limits and boundary conditions of that domain are il-lustrated in Figure 4. Those limits were selected using a "rule of thumb" thatthe boundaries for linear elastic analyses should be at least four driftdiameters away from the excavation.

The finite-element analyses were performed using the BMINES code, whichis a general-purpose finite-element code for two- and three-dimensional linearand nonlinear analyses of solid structures. It was written by AgbabianAssociates for the U.S. Bureau of Mines (USBM) and has been used extensively forlarge-scale analyses of complex mining systems. User documentation and verifica-tion for the most recent public version of this code is contained within a reportto the USBM (Agbabian Associates, 1981). Since completion of that report,several significant modifications have been made to the code. These modifica-tions include addition of a new element, based on the usage of relative degreesof freedom, to model fully bonded rockbolts (St. John and Van Dillen, 1983). Itwas this element that was used during the present investigation.

The main application of BMINES, in the present study, was to investigatethe effect of rockbolting and excavation-induced damage on the stability of theemplacement drifts. Simulation of rockbolting was achieved by activating therockbolt elements after the stresses around the interior of the excavation hadbeen relaxed by 25%. These rockbolts spanned the first four rings of elementsaround the drift and were located as illustrated in Figure 1. Excavation-induceddamage was simulated by assigning the reduced modulus listed in Table 1 to theinnermost ring of elements.

2.4 Results of Analyses

2.4.1 Introduction

This section is divided into two parts. The first presents the resultsof boundary-element and finite-element analyses of identical configurations forthe horizontal emplacement drift. The second discusses the results of simulationof the effects of rockbolts and excavation-induced damage, using the finite-element models.

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2.4.2 Analysis of Unsupported Drifts

Analysis of the rectangular-shaped and horseshoe-shaped excavationswithin a homogeneous rock mass with a premining isotropic stress of 9.15 MPa(1307 psi) were performed using both boundary- and finite-element modelsdescribed in Section 2.3. Results of those analyses are presented in Table 3 andFigures 5 through 8.

Table 3 lists roof-to-floor and wall-to-wall closures computed using thetwo models. Differences between the results of the boundary-element and finite-element analyses are observed to be small; the displacements computed by bound-ary-element models exceed those of the finite-element models by approximately 2%in most cases. This type of difference is anticipated because the particularformulation of the boundary-element method used generally overestimates thedisplacements (Crouch and Starfield, 1980), while the displacement formulation ofthe finite-element method, on which the BHINES code is based, generally providesa lower-bound solution (Zienkiewicz, 1977).

The displacements induced as a result of excavation are also illustratedin Figures 5 and 6. In the case of the boundary element calculation (Figure 5),the deformed and undeformed boundaries are plotted, with vectors joining thecenter points of the elements in their deformed and undeformed locations. In thecase of the finite-element calculation (Figure 6), the deformed and undeformedlocations of the elements in the immediate vicinity of the drift have beenplotted. Taken together, Table 3 and Figures 5 and 6 indicate that the displace-ments predicted by the two different numerical procedures are in quantitative andqualitative agreement.

Figures 7 and 8 were prepared by postprocessing the results of theboundary-element and finite-element analyses to obtain contours of the matrixstrength ratio, as defined in Section 2.3.3. It may be observed that the matrixstrength ratio exceeds 1.0 at all points around the drift and within the rockmass. The shaded areas in those figures define the regions within which theratio of strength to stress is less than 5. They were added simply to facilitatecomparison between the several plots. Such comparison reveals substantial agree-ment between the models based on the two computer codes.

2.4.3 Analysis of the Effects of Rockbolting and Excavation-Induced Damage

The results of all the finite-element analyses are summarized in Table 4and illustrated in Figures 9 through 12. The data presented in the table indi-cates that rockbolts have a negligible influence on the computed closures of thedrifts in homogeneous rock. This result is anticipated because the stiffness ofthe rockbolts is insignificant relative to the stiffness of the rock mass it

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supports. (The cross-sectional area of rock "supported" by each bolt is ap-

proximately 3500 times greater than the cross-sectional area of bolt, so'the fact

that steel has a higher elastic modulus than the rock mass is relatively unimpor-

tant.) The influence of the rockbolts on the state'of stress in the rock mass is

also small. This suggests that the primary function of rockbolts is to preserve

the integrity of the rock mass, by maintaining individual blocks of rock in

place, rather than through modification of the stress state.

The results of these analyses also indicate that early installation of

rockbolts does not generate significant loads in the bolts. This is illustrated

in Figures 9 and 10, in which the distribution of axial stress in the bolt and

shear stress at the contact between the rock and resin at the perimeter of the

rockbolt holes are plotted. Axial stresses in the bolt are observed to peak in

the range of 50Oto 75 MPa (7252 to 10,878 psi); a level'much lower than the yield

stress of steel. The bond shear stresses are also very low, so debonding is not

generally anticipated.

When reviewing the plots of the bond shear stress (Figure 10), it may be

observed that the shear stress rises suddenly at the free end of the bolt. This

may be anticipated on practical grounds in that high stresses may be expected

where a bolt is being pulled out of its "socket". This phenomenon has been

observed in previous numerical simulations and was investigated by St. John

et.al. (1983). It's explanation lies in the fact that the shear stress in the

grout is proportional to the gradient of the axial stress. At the "free" end of

the bolt the axial stress decays from some finite value to zero over a short

distance, causing the predicted shear stress in the grout to rise sharply.

The arched tunnel configuration was reanalyzed with "damaged" material

properties assigned to the innermost ring of elements. The effect of the damaged

zone was to cause increased closures (Table 4), particularly at the springline

(Figure 11). Computed matrix strength ratio around the excavation (Figure 11)

tend to be higher because loads are transferred away from the softer'annulus into

the stiffer, undamaged rock. However, the loads experienced by the rockbolt are

significantly increased. This effect is illustrated in Figure 12, in which the

axial stress may be observed to change by a factor of 4 to 5 across the boundary

between damaged and undamaged regions. (In practice, there would be a gradual

transition from damaged to undamaged conditions.) The fact that the change in

axial stress corresponds to the difference between the damaged and undamaged rock

mass deformability confirms the observation that the rockbolt load is completely

determined by the rock mass deformation. As noted earlier, this occurs because

the rockbolt stiffness is low relative to the rock mass stiffness.

The bond shear stresses illustrated in Figure 12 do not display the same

sudden change at the boundary between damaged and undamaged regions as do the

axial stresses. However, they are much higher than in the homogeneous case anddo peak somewhere around the boundary between the two regions. The actual shape

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of the distribution of the bond shear stress can be explained by noting that theshear displacement, and hence the shear stress, must be zero at the head of thebolt, where it is assumed there is a face plate. Elastic unloading of the an-nulus of damaged rock is resisted by the rockbolts passing through that annulusand also by the remainder of each bolt, which is firmly anchored in undamagedmaterial. Accordingly, the distribution of bond shear stress along the portionof the rockbolt in undamaged material resembles that anticipated for a pullouttest.

2.5 Conclusions

The results of analyses reported in this section indicate that under theassumed set of conditions, the stresses around the arched and rectangular excava-tions are modest in comparison to the strength of the rock matrix. Despite thefact that data used for the analyses were not entirely consistent with currentdesign concepts (SCP-CDR, in preparation by MacDougall, 1987) or informationgiven in the Reference Information Base (RIB), which is also summarized inAppendix A, the results are generally pertinent to the subject of analysis of theunderground excavations of the repository. Specifically, it has beendemonstrated that:

o for simple linear analysis of unsupported drifts in homogeneous rock theresults of boundary-element and finite-element analyses are essentiallyidentical;

o rockbolts do not significantly influence the deformation or the state ofstress around an excavation in homogeneous, linearly elastic rock;

o relative values of the modulus of the rock bolt and rock are important incalculating stresses in rock bolt and shear stresses in grout/rock inter-face; and

o the effect of excavation-induced damage is to reduce the stress aroundthe periphery of a drift, and cause load to be transferred back into thesurrounding undamaged rock.

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3.0 ANALYSIS OF VERICAL AIMD HORIZONTAL PACEMENT DRIFTS

3.1 Introduction

Since completion of the analyses described in the previous section theconcepts for a repository at the site at Yucca Mountain have matured and con-siderable progress has been made in establishing an engineering data base on rockmass properties. The repository design studies have progressed to the pointwhere there are two different preliminary designs for a repository: one in whichthe nuclear waste canisters would be stored within the floor of the emplacementdrift and another in which the canisters would be stored in long, horizontalholes. Current designs for the emplacement drifts for the two cases are il-lustrated in Figures 13 and 14. These designs, which are analyzed in detail inanother report (St. John, 1987a), are based on a particular set of assumptionsregarding the dimensions of the waste canisters and the waste transporter, andthe method of excavation. Should the basis of any of these assumptions change,the emplacement drifts will need to be redesigned.

The purpose of the analyses documented in this section is to provide anunderstanding of the extent to which excavation dimensions and shape influencethe deformation and stress-around the emplacement drifts immediately after ex-cavation. Shape and dimension may thus be viewed as two variables of aparametric study of excavation behavior. In-situ stress is the third variableconsidered in this study.

There are several reasons why ratio of the horizontal to vertical in-situstress should be considered as a variable in such an investigation. First, it isan important parameter in determining the response of a rock mass to the creationof an excavation. Second, there is, as yet, relatively little field data for theYucca Mountain site on which to base estimates of the in-situ stress state (Baueret al., 1985).

In the following subsections, the bases for the analyses are describedand the results presented. Extensive use is made of tabulations and illustra-tions as convenient means of presenting the amount of information developed forthe 54 different cases investigated. Conclusions are restricted to comments onthe general trends of behavior predicted by the analyses.

3.2 Problem Description

3.2.1 General Description

Analyses were performed of drifts for emplacement of waste canisters ineither short vertical holes in the floor of the drifts or long horizontal holesin the pillars between drifts. Current design concepts for a repository provide

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for a number of essentially independent panels within which several emplacementdrifts would be excavated. For the vertical emplacement option, the drifts wouldbe relatively close together; 34.14 m (112 ft) in the design analyzed here(Mansure and Ortiz, 1984). This means there is a possibility of interactionbetween adjacent drifts. Hence, the numerical models of the vertical emplacementoption described below also consider drifts adjacent to the one under investiga-tion. In contrast, the drifts for the horizontal emplacement option would bevery widely spaced because it is proposed that each emplacement hole be ap-proximately 208 m (682 ft) long (Mansure and Stinebaugh, 1985). Accordingly,there will be little or no interaction between the horizontal emplacement drifts,and the numerical models of the horizontal emplacement option considered only asingle drift. In both cases, due to problem symmetry, only one half of thegeometry is considered during the analyses.

For both the vertical and horizontal emplacement options, three differentshapes and three different dimensions were considered. Of these shapes, one wasselected to be similar to the designs illustrated in Figures 13 and 14 as takenfrom Parsons Brinckerhoff Quads & Douglas (1985). The other two shapes were atypical horseshoe profile, such as might be created using a conventional drilland blast method of excavation, and a flat roof shape, such as might be createdusing a continuous miner. The three shapes are referred to as 'Parsons,""Horseshoe" and "Continuous Miner' in the following discussions. The three sizesfor each shape cover the reasonable range of dimensions for each drift type, andinclude a case meeting clearance requirements for waste transportation andemplacement.

3.2.2 Drift Dimensions

The designs for the waste emplacement drifts for the vertical andhorizontal emplacement option that are modeled in this report are illustrated inFigures 13 and 14. These drifts have nominal dimensions of 6.7 x 4.9 m (22 by 16ft) and 4.0 x 6.1 m (13 by 20 ft), respectively. For the vertical drifts, thevertical dimension is primarily dictated by the length of the waste canisters.6.7 m (22 ft) is considered to be a reasonable upper limit on the vertical heightrequired in the drift so this was considered along with reduced vertical heightsof 5.5 m (18 ft) and 4.6 m (15 ft). The nominal span of 4.9 m (16 ft) was main-tained for all vertical emplacement drifts analyzed since the width of the wastetransporter is unlikely to be influenced markedly if the canister length changes.For the horizontal emplacement drifts the height was maintained at 4 m (13 ft),while varying the nominal span from 5.5 m (18 ft) to 7.9 m (26 ft), with the spanof 6.1 m (20 ft) as an intermediate case. The larger span reflects some earlierdesign concepts that incorporated an alcove at the entry to the borehole.

The full array of shapes and sizes investigated in this study is il-lustrated in Figures 15 and 16. These shapes generally conform to the nominaldimensions specified above and satisfy clearance requirements indicated in

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Figures 13 and 14. No attempt was made to optimize the profile to minimize theamount of excavation or meet any other design parameters, and the shapes are byno means unique. They were selected solely to provide a means of illustratingthe potential influence of alternative designs on the deformation and state ofstress around emplacement drifts.

3.2.3 Rock Mass Properties

The mechanical properties used during analyses of the vertical andhorizontal emplacement drifts are listed in Table 5, along with appropriatecitations. In that table, three categories of data are listed: rock mass, rockmatrix, and joints. The rock mass properties are used to describe the average,large-scale properties for the rock within which the drifts are excavated. Suchdata may be obtained by performing large-scale tests, to measure deformabilityfor example, or by inference from site characterization and laboratory testing ofthe rock matrix and the joints and other discontinuities in the rock mass. Therock mass properties were used during the boundary-element analyses. The matrixand joint properties were used during postprocessing to evaluate the potentialfor a matrix failure or joint activation.

The rock mass properties important to the boundary-element analyses arethe elastic constants, Young's modulus and Poisson's ratio, and the in-situstress state. The Young's modulus listed in Table 5 is an estimate based on theresults of limited field testing and laboratory testing. It is, in fact, ap-proximately 50% of the measured deformation modulus of the matrix of thelithophysae-poor, welded, divitrified tuff selected for repository construction(Nimick, Bauer, and Tillerson, 1984). The Poisson's Ratio listed in the table isbased on laboratory testing of the same material.

Selection of a different value of elastic modulus other than that givenin Table 5 would not significantly influence the findings of this investigation.The state of stress around an excavation in a linearly elastic, homogeneousmedium is independent of this parameter. (There is a linear dependence of thedisplacements upon the modulus, but this is relatively unimportant in this studysince the displacement predicted in these analyses are all relatively small.)The results of linear elastic analyses are influenced by the Poisson's ratio.However, the range of this parameter for the Topopah Spring Tuff is relativelysmall (Price, 1968), so the value given in Table 5 was used in all cases.

The other important parameter for the boundary-element analyses is thein-situ state of stress. For the analyses, an in-situ vertical stress gradientof 0.023 MPa/m (1.094 psi/ft) was inferred from the specific gravity listed inTable 5. It gives a vertical stress of 6.945 HPa (1007 psi) at the potentialrepository depth of 302 m (991 ft). The ratio between this vertical stress andthe horizontal stress in the plane of the cross section of the drifts analyzedwas one of the parameters investigated in this study. Values of 0.0, 0.5, and

-13-

1.0 were used. The stress normal to the plane of the drift section does notenter into the boundary-element calculations and was not accounted for duringevaluation of the potential for either matrix failure or joint activation.

The results of the boundary-element calculations were postprocessed in amanner similar to that described in Section 2.2.3. The matrix factor of safetywas evaluated at the midpoint of elements and internal sample points, usingequation 1, and contoured as before. The unconfined compressive strength usedfor that purpose is listed in Table 5 It was selected by reducing the laboratoryvalue by 50% (Nimick, Bauer, and Tillerson, 1984). For the joints, a linearCoulomb-Navier criterion was assumed. Specifically, if a. and a nare the com-puted shear and normal stresses on a plane of a given orientation, the factor ofsafety against slip, or joint activation, is defined by:

C, + ana*FS - nan| : a > 0 (3)

in which C and $ are, respectively, the cohesion and friction angle of thejoint. Since joints do not usually possess any strength in tension, the factorof safety is assumed to be zero if the normal stress, an, is zero.

In the present study, it was assumed that the joints in the tuff rockmass are vertical and strike parallel to the axis of the drifts analyzed. Underthese particular circumstances, an is the horizontal stress, axxt and a. is theshear stress, xay. The assumption that the joints are vertical is consistentwith the results of logging borehole cores from the candidate site at YuccaMountain (Bauer, 1986). Selection of a strike direction parallel to the driftaxis is believed to provide a conservative estimate of potential joint activa-tion. In a separate study (St. John, 1987b), it was concluded that the largestregions of potential activation of vertical joints around a drift generallyoccurs if the joints are parallel to the drift walls.

The method of calculation of the joint strength ratio defined by equation 3is also illustrated in Figure 17. As for the matrix strength ratio, the jointstrength ratio was evaluated at the center of each boundary element and at inter-nal sample points and then contoured. Once again, it is appropriate to emphasizethat these strength ratios refer to the local conditions rather than the entirestructure. Local overstressing of the matrix or joints around an undergroundexcavation does not necessarily imply that the excavation would be unstable.

3.3 Method of Analysis

Boundary-element analyses of the emplacement drifts were performed usingthe HEFF code, described briefly in Section 2.3.2. For the vertical emplacementdrifts, approximately 30 boundary elements were used to define each of the halfperimeters illustrated in Figure 15. An additional 16 boundary elements were

-14-

used to define the geometry of the nearest drift. With a vertical plane ofsymmetry, a model of the two adjacent drifts was thus defined. As with earlieranalyses, internal sample points were generated along lines normal to the mid-point of each boundary element. The locations of most of these sample points areillustrated in Figure 18.'

Between 30 and 40 boundary elements were used to define each of theprofiles for the horizontal emplacement drifts illustrated in Figure 16. Asdiscussed in Section 3.1, adjacent drifts were not analyzed because of the widespacing. Internal sample points for the horizontal emplacement drifts are il-lustrated in Figure 19.

3.4 Results of Analyses

3.4.1 Introduction

The results of all analyses of the vertical and horizontal emplacementdrifts are presented in a series of tables and figures. 'The tables list theroof-to-floor and sidewall-to-sidewall closures, and the tangential stress andmatrix and joint factors of safety in the roof of the drift. The figures consistof plots of deformed shape, principal stresses, tangential stress, and factors ofsafety for the matrix and the joints.

Since the purpose of these analyses was to provide data for a parametricstudy of the drifts, the plots for individual cases have been assembled tofacilitate visual comparison. Clearly there'is a practical limit on the amountof information that can be presented on a single 'page, so a selection of theparametric variables to be presented on each page has to be made. Here theoption of displaying the influence of in-situ stress state and size on drifts ofa particular shape was selected. Each page therefore contains nine plots, andthere are six pages for each type of plot, three shapes for vertical emplacementand three for horizontal emplacement.

3.4.2 Vertical Emplacement

The results of the analyses of the vertical emplacement option arepresented in Tables 6 though 8 and Figures 20 through 34. To facilitate com-parison between the different shapes, the plot types are grouped so that outputfor the "Parson's," "horseshoe," and "continuous miner" shapes are presented onconsecutive pages. Apart from that, the ordering of the plots is as follows:

o Figures 20 through 22: Boundary Displacement Plots

These illustrate the original shape of the drift, which is shown as adashed line, and a deformed shape, which is shown solid. The vectors

-15-

joining the original and deformed shape indicate the direction and mag-nitude of the displacements of the center of each boundary element. Thescale for the displacement vectors is given at the base of the figure.Note that the scale of the displacements is magnified relative to thedimensions of the drift.

o Figures 23 through 25: Principal Stress Vector Plots

These illustrate the magnitude and direction of the principal stressescomputed at selected sample points. (Vectors are not plotted at everysample point since that would result in excessive cluttering of thefigures.) The magnitude of the stress at each sample point can be deter-mined by comparing the total length (tip to tip) of each vector with thestress scale provided. Cases in which the principal stress is tensileare designated by plotting a "T." with the root of the "T" adjacent tothe vector representing the stress that is tensile. Note that there issometimes a "T" indicating tensile stresses at the boundary. This canoccur if the stress normal to the boundary of the drift is slightlynegative instead of zero. The presence of significant tensile stressesat the boundary is best judged from the tangential stress plots describedbelow.

o Figures 26 through 28: Tangential Stress Plots

These illustrate the distribution of stress in the wall, sidewall, andfloor of the drift. (The term "tangential stress" is used because thestress normal to the surface must be zero.) The magnitude of tangentialstresses can be determined from the vectors radiating from the midpointof each boundary element. The sign of these stresses is indicated by thedirection of the vectors. If the vectors point out of the drift, thenthe stress is compressive, while tensile stresses are denoted by inward-pointing vectors.

o Figures 29 through 31: Matrix Strength Ratio Plots

These illustrate the ratio between the computed state of stress and thematrix strength, as defined by the Mohr-Coulomb strength model (equation1). The key for the contours of this ratio is given at the base of eachfigure.

o Figures 32 through 34: Joint Strength Ratio Plots

These illustrate the ratio between the computed state of stress and thestrength of vertical joints assumed to exist at every point within therock mass. The model for the joint strength was defined by equation 3and discussed in Section 3.2.3. It is appropriate to note, however, that

-16-

the factor of safety at any point is assumed to be zero if the stressnormal to the selected joint direction is tensile. To facilitate iden-tification of regions of potential joint activation, these are identifiedon the plots by vertical hatching.

Conclusions that may be drawn through review of the results of analysesare presented in Section 3.5.

3.4.3 Horizontal Emplacenent

The results of analyses of horizontal emplacement are presented in Tables9 through 11 and Figures 35 through 49. With the sole exception of the displace-ment plots, the scales and keys for the figures are identical to those for thevertical emplacement drifts. The ordering of the plots is the same as before.Namely:

o Figure 35 through 37: Boundary Displacement Plots

o Figures 38 through 40: Principal Stress Vector Plots -

o Figures 41 through 43: Tangential Stress Plots

o Figures 44 through 46: Matrix Strength Ratio Plots

o Figures 47 through 49: Joint Strength Ratio Plots

Conclusions that may be drawn from review of these tables and figures arepresented below.

3.5 Conclusions

The variables of this parameter study were excavation shape, excavationdimensions, and in-situ state of stress. The effects of change in stress as-sociated with heating of the rock mass after emplacement of nuclear waste werenot considered. From data presented in Tables 6 through l1 and Figures 20through 49, the following conclusions are drawn in respect to the importance ofthe variables influencing the pre-emplacement condition.

o Of the three shapes investigated, the Parson's shape results in the mostmoderate stresses, displacements, and regions in which the matrix orjoint strengths are exceeded. This finding is attributed to the factthat the Parson's shape always has the minimum span, because additionalspan is necessary to provide the desired clearance for the two othershapes. However, the tangential stress around the horseshoe-shaped driftvaries most smoothly, a feature that would usually be consideredfavorable. The horseshoe shapes also exhibit higher tangential stresses

-17-

around the springline of the drifts. (This feature may prove to bebeneficial in reducing or eliminating tensile cracking in the sidewallsafter waste emplacement and thermal loading.) On the whole, the horse-shoe shape is considered preferable to the others, even though there is apotential for some activation of vertical or near vertical joints in theside wall. It is possible that such activation could result in limiteddevelopment of loose slabs of material, however these would normally becontrolled by roof support and routine maintenance.

o From the analyses of drifts of different dimensions, it is concluded thatthe rock mass response is relatively insensitive to the drift height,although the wall-to-wall closure of higher drifts does increase substan-tially if the initial horizontal stress is high. The results are muchmore sensitive to the excavation span. This is particularly noticeablein the plots of principal stress and joint activation for the horizontalemplacement drifts at low initial stress. Specifically, the larger spansresult in a much greater reduction of horizontal stress in the rock massabove the drift. This would usually be associated with poorer stability,because higher horizontal stresses in the roof will resist relativemovement along joints.

o Of the three different states of in-situ stress considered, the one withthe lowest horizontal stress results in the least favorable responses.Extensive regions of tension and joint activation are observed both inthe roof and floor of all drifts when there is no in-situ horizontalstress. It should be pointed out, however, the assumption that there isno in-situ horizontal stress is unrealistic. Bauer, Holland, and Parrish(1985) recommend that the ratio of horizontal to vertical in-situstresses be assumed to lie in the range of 0.3 to 0.8, and Nimick, Bauerand Tillerson (1984) recommend that a value of 0.25 be considered as alower bound for that ratio.

o For good roof stability it is generally considered to be desirable that acompressive state of stress be maintained in the rock mass above anunderground opening. The data presented in Tables 6 through 11 provide ameans of estimating the minimum in-situ stress state for this conditionto be satisfied. For vertical emplacement a minimum value of ap-proximately 0.3 is required for either of the drifts with an arched roof,and a value of 0.4 for the continuous miner shape. The correspondingvalues for the horizontal emplacement option are 0.4 and 0.6 respec-tively. This indicates that the extent of any region of tension in theroof will be small even if the in-situ horizontal stress approaches thecurrent lower bound estimates, providing the roof of the openings isappropriately arched. If an average value for the in-situ horizontalstress, in the range of 0.3 to 0.8 recommended by Bauer, Holland, andParrish (1985), pertains, then the roof stresses are compressive, or very

-18-

nearly compressive, for all the shapes investigated in this study.Further, limited regions of tension are not considered crucial to roofstability since a fractured rock mass may tend to form a stable arch,particularly if its integrity is maintained by rockbolts or some otherrock support system.

o Based on the results of the analyses performed in this study it is con-cluded that stable openings of the dimensions investigated can beconstructed within a tuff rock mass with the properties assumed. Of theparameters investigated, the in-situ state of stress appeared to be mostimportant. Stability problems might be encountered if the in-situhorizontal stress is very low, but current indications are that it lieswithin a range which is consistent with good roof conditions. Followingwaste emplacement the horizontal stresses will increase significantly.This will tend to further stabilize the roof, providing that the stressesdo not become sufficiently high to induce crushing, new fracturing orother potentially detrimental motion of the rock mass around the opening.

Finally, it is appropriate to note that the results of this parameterstudy have wider application than the specific set of conditions analyzed herebecause for the models used in these analyses:

o excavation-induced stresses and displacements around the drifts arelinearly dependent upon the in-situ horizontal stress (i.e., on the Kvalue);

o total stresses and displacements for any particular K value are linearlydependent on the in-situ vertical stress, which was assumed here to be6.945 MPa (1,000. psi), (See Section 3.2.3);

o excavation-induced and total stresses are independent of the elasticmodulus and only moderately dependent upon the Poisson's Ratio;

o excavation-induced displacements are linearly dependent upon the elasticmodulus and only moderately dependent upon the Poisson's Ratio;

o excavation-induced and total stresses (i.e. initial plus induced) are thesame for all drifts of identical shape (i.e., when the sizes but not theshapes are different); and

o induced displacements around drifts of the same shape are linearlyproportional to the dimensions of the drift.

These properties derive from the fact that the rock mass was assumed tobe linearly elastic and homogeneous and that gradient of the initial horizontaland vertical stress is insignificant. The distinction between induced and total

-19-

conditions has been drawn because the results of a linear elastic analysis areproportional to the change in boundary conditions, which in this case correspondsto relaxing the in-situ stresses along the boundary of the excavations.

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4.0 REFERENCES

Agapito, J. F. T. et al., "Impact of Excavation Technique on Strength of OilShale Pillars," International Journal of Mining Engineering, Vol. 2, pp 93-105,1984.

Agbabian Associates, "Modernization of the BMINES Computer Code Vol. 1:User's Guide (BMINES Computer Program for Analytical Modeling of Rock/StructureInteraction)," U-7910-5117, Agbabian Associates, El Segundo, CA, 1981.

Bauer, S. J., "Preliminary Report on Yucca Mountain FractureCharacteristics," Sandia National Laboratories Memorandum, Sandia NationalLaboratories, Albuquerque, NM, 1986.

Bauer, S. 3J. F. J. Holland, and D. K. Parrish, "Implications about In-SituStress at Yucca Mountain," 26th U.S. Symposium on Rock Mechanics, Rapid City,S.D., June, 1985.

Bieniawski, Z. T., "Determining Rock Mass Deformability: Experience fromCase Histories " International Journal Rock Mechanical and Mining Science, Vol.15, pp. 237-244, 1978.

Brady, B. H. G., HEFF, a Boundary-Element Code for Two-DimensionalThermoelastics Analysis of a Rock Mass Subject to Constant or Decaying ThermalLoading," User's Guide and Manual, RHO-BWI-C-80. . Prepared by the University ofMinnesota for Rockwell Hanford'Operations, Richland, WA, June, 1980.

Crouch, S. L. and A. M. Starfield, Boundarv-Element Methods in SolidMechanics, George Allen, and Unwin, London, 1983.

Einstein, H. H., C. W. Schwartz, W. Steiner, M. K. Baligh and R. E. Levitt,Improved Design for Tunnel Supports: Analysis Method and Ground StructureBehavior, Vol. 2," DOT/RSPA/DPB-50/79/10, pp. 236-244, 1980.

Hoek E. and E. T. Brown, Underground Excavations in Rock, Institution ofMining and Metallurgy, London, l9bU.

John, K. and M. Baudendistel, "A Compromise Approach to Tunnel Design,"Proceedings 22nd U.S. Symposium on Rock Mechanics, Massachusetts Institute ofTechnology, Boston, MA, June, pp. 313-321, 1981.

Johnstone, J. K., R. R. Peters, and P. F. Gnirk "Unit Evaluation at YuccaMountain, Nevada Test Site: Summary Report and Recommendation," SAND83-0372,1984.

Mansure, A. J. and T. S. Ortiz, "Preliminary Evaluation of the SubsurfaceArea Available for a Potential Nuclear Waste Repository at Yucca Mountain,"SAND84-0175, Division 6314, Sandia National Laboratories, NM, December, 1984.

Mansure, A. J. and R. E. Stinebaugh "Typical Excavation and AccessDimensions for the Underground Portion of tie Repository," memo S/PB-6314-103 toDick Harig, (See Appendix F of SAND86-7085, Reference Thermal andThermal/Mechanical Analyses of Drifts for Vertical and Horizontal Emplacement ofNuclear Waste in a Repository in Tuff, St. John, 1987) Sandia NationalLaboratories, Albuquerque, NM, April, 1985.

MacDougall, H. R. (Compiler), "Site Characterization Plan Conceptual DesignReport," SAND84-2641, Sandia National Laboratories, Albuquerque, N.M., 1987

Nimick, F. B., S. J. Bauer and J. R. Tillerson, "Recommended Matrix and RockMass Bulk, Mechanical, and Thermal Properties for Thermomechanical Stratigraphyof Yucca Mountain," Version 1, Keystone Document Number 6310-85-1, SandiaNational Laboratories, Albuquerque, NM, October, 1984.

Parsons Brinckerhoff Quade and Douglas, Inc "Ground Support Cross-Sections," SNL drawing number R06950, San Francisco, dA, May, 1985.

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Price R. H "Effects of Sample Size on the Mechanical Behavior of TopopahSpring Tufk, SANf85-0709, Sandia National Laboratories, Albuquerque, NM , August.1986,

St. John, C. M., "Reference Thermal and Thermal/Mechanical Analyses ofDrifts for Vertical and Horizontal Emplacement of Nuclear Waste in a Repositoryin Tuff,' SAND86-7005, Sandia National Laboratories, Albuquerque, NM, 1987a.

St. John C. M., "An Investigation of Excavation Stability in a FiniteRepository," SAND86-7001, Sandia National Laboratories, Albuquerque, NM, 1987.

St. John, C. 1. and D. E. Van Dillen 'Rockbolts: A New NumericalRepresentation and Its Application in Tunnel design * 24th U.S. Symposium on RockMechanics, Texas A&M University, College Station, , June, pp. 13-25, 1983.

St. John, C. M., Van Dillen, D. E., and Detournay E. 'An Investigation ofthe Failure Resistance of Rockbolted Tunnels for Deep Aissile Basins," R-8227-5534, Prepared for Defense Nuclear Agency by Agbabian Associates, El Segundo, CA,September, 1983.

Tillerson, J. R. and F. B. Nimick 'Geoengineering Properties of PotentialRepository Units at Yucca Mountain Southern Nevada," SAND84-0221, SandiaNational Laboratories, Albuquerque, Nh, 1984.

Van Dillen D E., EA Two-Dimensional Finite-Element Technique for ModellingRock/Structure interaction of a Lined Underground Opening," Proceedings 20th U.S.Svm osium on Rock Mechanics, University of Texas, Austin, TX, June, pp. 251-258,

iFc.

Zienkievicz, O. C., The Finite-Element Method, McGraw-Hill, London, 1977.

-22-

St 83 - 7+5

TABLE 1. MATERIAL PROPERTIES OF TuFF ROCK MASS

Property Value

Elastic Modulus 26.7 CPal (3.87*106 psi)

Elastic Modulus of Damaged Rock 5.54 GPa2 (0.80*106 psi)

Poisson's Ratio 0.141

Uniaxial CompressiveStrength (ac) 91.1 MPa3 (13,212 psi)

Tensile Strength (OT) 12.8 MPal (1856 psi)1

Angle of Internal Friction ()260

Notes: 1.2.3.

Johnstone et al., (1984).Estimated by Author.Tillerson and Nimick (1984) give a value of 95.9 MPa.The value of 91.1 MPa used in this study appeared in an earlierdraft of that reference.

-23-

-I

TABLE 2. ROCK BOLT PROPERTIES

Rockbolt Diameter' 2.87 cm (1 1/8 in.)

Rockbolt Spacing 1.5 by 1.5m (4.9 by 4.9 ft)

Rockbolt Length 3m (9.8 ft)

Rockbolt Hole Diameter 3.5cm (1 3/8 in.)

Elastic Modulus of Steel 207 GPa (30*106 psi)

Tensile Strength of Steel 550 MPa (80,000 psi)

Shear Modulus of Resin2 3.71 GPa (0.538*106 psi)

Notes: 1.

2.

The rockbolt parameters are typical for mediumbolting (Hoek and Brown, 1980).TypicaL value for Celtite Resin

-24-

i

TABLE 3. DRIFT CLOSURES COMPUTED USING BOUNDARY-ELEMENTAND FINITE-ELEMENT KODELS

Roof-to-Floor Closure Boundary Element Finite Element DifferenceExcavation Shape ( lme) (mm) Ef

Roof-to-Floor Closure

Rectangular 4.87 4.76 2.3

Horseshoe 4.65 4.55 2.2

Wall-to-Wall Closure

Rectangular 1.68 1.65 1.8

Horseshoe 1.20 1.17 2.5

-25-

TABLR 4. COMPUTED CIDSURES OF BOLTED AND UNBOLTED EXCAVATIONS

Excavation Roof-to-Floor SpringlineShape Closure (mm) Closure (mm)

Rectangular Excavation

7.6 by 3.7 a unbolted 4.757 1.6507.6 by 3.7 m bolted 4.757 1.650

Arched Excavation

7.6 by 3.7 m unbolted 4.548 1.1667.6 by 3.7 m bolted 4.546 1.1657.6 by 3.7 D bolted 6.431 2.731w/damaged annulus

-26-

TABLE 5. DATA FOR ANALYSIS OF EMQ'1AEKET DRIFTS

Property Value Reference

Rock Mass

Specific Gravity 2.34 g/cm3 1Young's Modulus -15.1 NPa 2Poisson's Ratio 0.2 2

Rock Matrix

Unconfined CompressiveStrength of Rock 75.4 MPa 2

Tensile Strength -9.0 MPa 2Angle of Internal Friction 29.2 2

Joints

Joint Cohesion 1.0 MPa 2Joint Coefficient of Friction 0.8 (38.7a) 2Joint Angle 90- 2

References:1. Johnstone,, et al (1984)2. Nimick, et al., (i984)

-27-

TABLE 6. RESULTS OF BOUNDARY-ELEMENT CALCULATIONSPARSON'S SHAPE, VERTICAL EMPACEMiT AT TIME OF EXCAVATION

Closure (ma) F.S.1 at RoofCrown axiMum Tangential

Stress Condition Floor Closure Stress at Matrix Jointto Floor on Sidewall Roof (MPa) FSM FS1

Height - 22 ft

K2 - 0.0 5.11 -1.00 -6.03 L.493 0.00

K - 0.5 4.37 2.05 4.45 9.16 17.58

K - 1.0 3.63 5.09 14.94 3.07 14.87

Height - 18 ft

K - 0.0 4.99 -1.04 -6.11 1.473 0.00

K - 0.5 4.35 1.48 3.76 10.74 18.28

K - 1.0 3.72 4.01 13.64 3.29 2.93

Height - 15 ft

K - 0.0 4.88 -1.02 -3.86 2.333 0.00

K - 0.5 4.32 1.04 3.20 12.54 19.08

K - 1.0 3.77 3.17 12.58 3.56 15.08

Notes: 1. F.S. is the factor of safety asand Figure 17 for the joint.

defined in Figure 2 for the matrix

2. K is the ratio between the in-situ horizontal and vertical stresses(i.e., ax/°yy)

3. Ratio of tensile strength (i.e., -9 MPa) to tangential stress at roof(see eq. (2)). The plots are derived using eq. (1).

-28-

TABLE 7. RESULTS OF BOUNDARY-ELEHENT CALCUILATIONSHORSESHOE SHAPE, VERTICAL EMPIACEHENT AT TINE OF EKCAVATION

Closure (FrMn) F.S.3 at RoofCrown Maximum Tangential

Stress Condition Floor Closure Stress at Matrix Jointto Floor on Sidewall Roof (HPa) FSm FS-

Height - 22 ft

K2 - 0.0 5.41 -1.39 -6.16 1.465 0.00

K - 0.5 4.60 1.59 4.31 9.39 17.42

K - 1.0 3.78 4.57 14.78 3.08 14.66

Height - 18 ft

K - 0.0 5.31 -1.59 -6.22 1,453 0.00

K - 0.5 4.61 0.88 3.64 11.09 18.63

K - 1.0 3.91 3.35 13.51 3.35 15.15

Height - 15 ft

K - 0.0 5.09 -1.49 -6.32 1.423 0.00

K - 0.5 4.49 0.59 3.06 13.09 19.94

K - 1.0 3.89 2.67 12.44 3.59 15.58

Notes: 1. F.S. is the factor of safety as defined in Figure 2 for the matrixand Figure 17 for the joint.

2. K is the ratio between the in-situ horizontal and vertical stresses(i.e. , a /. )'


-29-

TABLE 8X' RESUlTS OF BOUNDARY-ELEMENT CALCULATIONSCONTINUOUS MINER SHAPE, VETCAL EMPLACEMENT AT TIME OF EXCAVATION

Closure (ma) F.S. 1 at RoofCrown Maximum Tangential

Stress Condition Floor Closure Stress at Matrix Jointto Floor on Sidewall Roof (MPa) FMm FS1

Height - 22 ft

K2 - 0.0 5.73 -1.23 -5.43 1.663 0.00

K - 0.5 5.06 1.97 0.76 51.61 35.100

K - 1.0 4.41 5.17 6.94 6.05 15.800

Height - 18 ft

K - 0.0 5.72 -1.25 -5.49 1.643 0.00

K - 0.5 5.17 1.43 0.38 102.8 53.500

K - 1.0 4.61 4.12 6.25 6.67 16.000

Height - 15 ft

K - 0.0 5.49 -1.18 -5.70 1.583 0.00

K - 0.5 5.05 1.11 -0.13 69.233 0.00

K - 1.0 4.60 3.39 5.45 7.58 16.400

Notes: 1. F.S. is the factor of safety as defined- in Figure 2 for the matrixand Figure 17 for the joint.

2. K is the ratio between the in-situ horizontal and vertical stresses(i.e., 0xx/°yy)-

3. Ratio of tensile strength (i.e., -9 MPa) to tangential stress at roof(see eq. (2)). The plots are derived using eq. (1). -

-30-

TABLE 9. RESULTS OF BOUNDARY-ELEHENT CALICULATIONSPARSON'S SHAPE, HORIZONTAL EMPIACEKENT AT TIDNE OF EXCAVATION

C Closure X(FM) F.S.' at Roofrown Tangential

Stress Condition Floor Closure Stress at Matrix Jointto Floor on Sidewall Roof (MPa) FSm FS

Span - 20 ft

K2 - 0.0 5.80 -1.56 -6.47 1.393 0.00

K - 0.5 5.24 0.42 2.25 17.65 30.03

K - 1.0 4.68 2.39 10.97 4.01 21.50

Span - 18 ft-

K - 0.0 5.24 -1.41 -6.40 1.633 0.00

K - 0.5 4.69 0.54 2.78 14.36 20.14

K - 1.0 4.13 2.50 11.97 3.71 15.35

Span - 26 ft

K - 0.0 7.44 -1.93 -6.63 1. 36S 0.00

K - 0.5 6.88 0.05 1.00 39.03 70.87

K - 1.0 6.32 2.03 8.64 4.96 36.11

Notes: 1.

2.

3.

F.S. is the factor of safety as defined in Figure 2 for the matrixand Figure 17 for the joint.

K is the ratio between the in-situ horizontal and vertical stresses(i.e., a /0'').

Ratio of tensile strength (i.e., -9 MPa) to tangential stress at roof(see eq. (2)). The plots are derived using eq. (1).

-31-

TABLE 10. RESULTS OF BOUNDARY-ELEKENT CALCULATIONSHORSMESHO SHAPE, HORIZONAL EHPLAEKENT AT TIES OF EXCAVTION

Closure Ems) F.S.1 at RoofCrw aiu Tangential

Stress Condition Floor Closure Stress at Matrix Jointto Floor on Sidewall Roof (MPa)

Nominal Span - 20 ft

K2 - 0.0 5.87 -1.85 -6.64 1.363 0.00

K - 0.5 5.30 0.06 2.00 19.81 31.78

K - 1.0 4.73 1.96 10.63 4.12 21.85


K - 0.0 5.36 -1.80 -6.56 1.373 0.00

K - 0.5 4.78 0.13 2.63 15.15 24.43

K - 1.0 4.20 2.06 11.83 3.75 18.32


K - 0.0 7.62 -2.41 -6.68 1.353 0.00

K - 0.5 7.04 -0.45 0.93 41.89 70.73

K - 1.0 6.45 1.52 8.55 5.01 34.65

Note: 1. F.S. is the factor of safety as defined in Figure 2 for the matrix andFigure 17 for the joint.

2. K is the ratio between the in-situ horizontal and vertical stresses(i.e., axxlayy).


-32-

TABLE 11. RESULTS OF BOUNDARY-ELEMENT CALCUILATIONSCONTINUOUS MINER SHAPE, HORIZONTAL AMPLACEIENT hI TIME OF EIC&VATION

Closure (Mm) F.S.' at RoofCrown Maximum Tangential

Stress Condition Floor Closure Stress at Matrix Jointto Floor on Sidewall Roof (MPa)


K2 - 0.0 6.24 -1.38 -6.07 1.48' 0.00

K - 0.5 5.83 0.80 -0.88 43.52 0.00

K - 1.0 5.41 2.98 4.32 9.43 17.200

Nominal Span -18 ft

K - 0.0 5.62 -1.19 -5.93 1.528 0.00

K - 0.5 5.17 1.01 -0.48 79.15 0.00

K - 1.0 4.72 3.20 4.96 8.27 16.700


K - 0.0 8.16 -1.88 -6.04 1.493 0.00

K - 0.5 7.71 0.38 -1.15 7.83i - 0.00

K - 1.0 7.26 2.64 3.74 10.80 17.800

Note: 1. F.S. is the factor of safety as defined in Figure 2 for the matrix andFigure 17 for the joint.

2. K is the ratio between the in-situ horizontal and vertical stresses(i.e., Oxx/OYY)-


'-33-

en

w

C'

LULU

METERS

Figure 1. Geometry of Horizontal Emplacement Drifts AnalyzedUsing Boundary-Element and Finite-Element Models

-34-

SHEARSTRESS B

(IT

TENSIONCUT- OFF

a, i+a'.2 )

FSm OACm/taNm sin#

2

"Cohesion"a

Cm 2/KP : Kp - (l+sin~m)/(l-sin#m)

Hence: FS -(or1+o2)sino + ac(l-sin~m)

(a1- a 2 )

Figure 2. Derivation of the Hatrix Factor of Safety

-35-

5

4 -

2

Di

..... oo .

O l a t Psoo

. . ..... .

. . .. ...

Hosso . . .. Drf.

. . . .- . .

a

4

2

0

-2

-4

-6

-2

-4

-8 LaI 2 4

Meters5 0 2 4

Meters6 8

Figure 3. Drift Shapes and Internal Sample PointsFor Boundary-Element Analyses

-36-

APPLIED VERTICAL STRESS

Figure 4. Finite-Element Model for Analysis of an Arched,Horizontal Emplacement Drift-

I

-37-

4

2 .

-2 .I-.J

-4

0 2 4 6 0Meters

For presentation purposes the displacementshave been magnified approximately 160x relativeto the geometric dimensions

4

2

0 O

-2

-4

. ~~-6B 8

Displacement

0 20 mm

Meters

Figure 5. Boundary Displacements Computed by theBoundary-Element Analyses

-38-

CD

F 2- DISPLACEMENT DISPLACEMENT

0 0mon 0 _mM 1

-2

0 2 4 6 02 4 6

METERS

For presentation purposes the displacementhave been magnified approximately 150x relativeto the geometric dimension

Figure 6. Deformed Shapes Computed Using the Finite-Element Models of Unsupported Drifts

-39-

8

4

2

0

-2

-4

-8

a

4

2

0

-2

-4

-64

Meters Meters

Matrix Strength Ratio

ABC0E

1.03.05.07.09. 0

E Ratio i 5.O

Figure 7. Matrix Strength Ratio Computed from the Resultsof Boundary-Element Analyses

-40-

Uea:w

LL

METERS

Figure 8. Matrix Strength Ratio for Unsupported Drifts,Computed from Results of Finite-Element Analyses

-41-

6- -6

4- -4

co

2

21 -2

0- -o

-2- -- 2

.~~~~~ I I~ II- " - -Z

0 2 4 6 0 2 4 6

METERS

8

Figure 9. Distribution of Axial Stress in RockboltsAround Drifts in Homogeneous Rock

-42-

M - w~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I4~~~~~~~~~~-I

6

4

CA

- 2-Iw

-6

-4

-2

-o

-- 2-2-

I. I4- .I. .. I -4

0 2 4 6 0

METERS

I I I2 4 6 8

Figure 10. Distribution of Bond Shear Stress at Grout/RockInterface for Perimeter of Rockbolts AroundDrifts in Homogeneous Rock

-43-

U)

W 7

0 2 60 46KEY

2- ~~~~~~~~~~~~C-5D-7E-9F-Il

METERS

For presentation purposes the displacementshave been magnified approximately 150x relativeto the geometric dimension

Figure 11. Results of Finite Element Analysis of RockboltedDrift with an Annulus of Damaged Rock

-44-

j } | +s

8 heY -

Co

5:'a

-6

-4

-2

-o

-- 2

-- AI \-LIMIT OFDAMAGE

"-LIMIT OFDAMAGE

I U 4* I dI 6 0 2METERS

I 64 6 8

Figure 12. Axial Stress Distributions for Rockbolts and ShearStress Distributions at Grout/Rock Interface Arounda Drift with an Annulus of Damaged Rock

-45-

to

lii

-J

C-)l

.--= I I ~ . j I, I

16' EXCAVATED(TYP.)

Figure 13. Parson's Design of Drift for Vertical Emplacement of WasteCanisters of Spent Fuel

-46-

Figure 14. Parson's Design of Drift for Horizontal .Emplacement of Waste Canisters of Spent Fuel

-47-

Figure 15. Alternative Shapes and Sizes of Drifts AnalyzedDuring Parametric Study of Vertical Emplacement

-48-

Figure 16. Alternative Shapes and Sizes of Drifts AnalyzedDuring Parametric Study of Horizontal Emplacement

-49-

SHEARSTRESS

Cj

CENTER OFNORMALS (Tn

(Ts

FS- AC -AB

C, + aotane N

° nl n

C+ axxtanoa

For vertical joints FSc - l xy >0i TXTx

Figure 17. Derivation of the Joint Factor of Safety

-50-

p 1

8

4

Oi

18

......

......

......------

...... .

...... I...................

............

......

4

0

_ . * , I * V *

8

4

0

::-:-. - -.A; 1 ::I

... . . .

I ,

. . . . . . .

. .. . . . .

I. . . . .

. . . . . . . .

- I

II

I. . . . .

I. . . . .

8

4

0

- ----- ~~~~~~~~~~ 4

8

41

::., .. , 1.

............

......

...... I

. . -

..... . . .*. .... .

. .. . .. .

. . . . .

. . . . . .

. . . . . . .I

I .

II

I

. . . . . .

. . . . . .

I

II

I

8

4

00 I

.. 4 a . .. . . . ... . fi ._o 0 468 g 4 8 0 48 81__ ~~~~~~~~~~meters _

Figure 18. Boundary-Element Models of Vertical EmplacementDrifts, Showing Internal Sampling Points

-51-

- I I I

8

4

0

.........

....

A:''''-w-. -

: :. . .

:-.......... ....... .

.........

.........

.........

.........

.........

8

4

0

-4 I I * I. * 1....

8 -....

4

0 ....................

I . .

............................

............................

8

4

0

I 4' * 1.

at'...

4

0 .......................................

- ...... . .

.......................... . - .

..........................

a

4

0

_ -. ... _0 4 18 0 4 8 0 4 a__ meters I

Figure 19. Boundary-Element Models of Horizontal EmplacementDrifts, Showing Internal Sampling Points

-52-

I- metersFor nresentation ~nurnoses the dtgnTAneM~ntR hA-vA 'hPnmagnified apprdimensions

7oximately 600x relative to the geometric Displacement Scale

0 1cm

Figure 20. Boundary Displacements, Vertical Emplacement,Parson's Shapes

-53-

0 4_a 0 4 8 0 4 84 meters

For presentation purposes the displacements have beenmagnified approximately 600x relative to the geometric Displacement Scadimensions I

Ile

0 1 cm

Figure 21. Boundary Displacements, Vertical Emplacement,Horseshoe Shapes

-54-

Lon purposes tne displacements have been:oximately 600x relative to the geometric Displacement Scale

0 1 cm

Figure 22. Boundary Displacements, Vertical Emplacement,Continuous Miner Shapes

-55-

Principal Stress

0 50 MPa

Figure 23. Principal Stresses, Vertical Emplacement,Parson's Shapes

-56-

4

I I +1 *1x -% N

k+Jr

iI II

4-I.+ t1

F I

l I 4 +I. + +

I I 4-

IIII I t I"

4+

II I~~~

fIII 'I

4 A.*

4*1 I.

+

Principal Stress0 M

o 50 lPa

Figure 24. Principal Stress, Vertical Emplacement,Horseshoe Shapes

-57-

I -%"4lii - i *1

I I +I ~I 0+

Jr

I. IT 4

IIII

' I

t 44 4

+

N Ar

I -7L

IIII

I II'I

I I II

t- 4I. +f +

$ +

k

k++

i$1.k

Principal Stress

0 50 MPa

Figure 25. Principal Stresses, Vertical Emplacement,Continuous Miner Shapes

-58-

Tangential Stress

0 50 MPa

Figure 26. Tangential Stresses, Vertical Emplacement,Parson's Shapes

-59-

Tangential Stress0 I0 50 MPa

Figure 27. Tangential Stresses, Vertical Emplacement,Horseshoe Shapes

-60-

Tangential Stress

0 50 MPa

Figure 28. Tangential Stresses, Vertical Emplacement,Continuous Miner Shapes

-61-

Matrix Strength Ratio: A - 1.0 ; B - 3.0 ; C - 5.0 ; 0 - 7.0 ; E - 9.0

Figure 29. Matrix StrengthParson's Shapes

Ratio, Vertical Emplacement,

-62-

Matrix Strength Ratio:: A - 1.0; B - 3.0; C - 5.0; D - 7.0; E - 9.0

Figure 30.. Matrix Strength Ratio, Vertical Emplacement,- :Horseshoe Shapes

-63-

Matrix Strength Ratio: A - 1.0; a - 3.0; C - 5.0; D - 7.0; E - 9.0

Figure 31. Matrix Strength Ratio, Vertical Emplacement,Continuous Miner Shapes

-64-

r.

Joint Stress Ratio: R - 1.0 ; B - 3.0 ; C - 5.0 ; D - 7.0 ; E - 9.0

Region of Joint Activation

Figure 32. Joint Strength Ratio, Vertical EmplacementParson's Shapes

-65-

Joint Stress Ratio A - 1.0; B - 3.0; C - 5.0; D - 7.0; E - 9.0

MM Region of Joint Activation

Figure 33. Joint Strength Ratio, Vertical Emplacement,Horseshoe Shapes

-66-

r" '

Joint Stress RatIo: A - 1.0; B - 3.0; C - 5.0; D - 7.0; E - 9.0

E Region of Joint Aictivation

Figure 34. Joint Strength Ratio, Vertical Emplacement,Continuous Miner Shapes

-67-

For presentation purposes the displacementshave been magnified approximately 300x relativeto the geometric dimensions.

Displacement Scale

0 2 cm

Figure 35. Boundary Displacements, Horizontal Emplacement,Parson's Shapes

-68-

r

Displacement ScaleFor presentation purposes the displacementshave been magnified approximately 300x relativeto the geometric dimensions.

'0 2 cm

Figure 36. Boundary Displacement, Horizontal Emplacement,Horseshoe Shapes

-69-

Displacement Scale

For presentation purposes the displacementshave been magnified approximately 300x relativeto the geometric dimensions.

0 2 cm

Figure 37. Boundary Displacement, Horizontal Emplacement,Continuous Miner Shapes

-70-

c

Principal Stress

0 50 MPa

Figure 38. Principal Stresses, Horizontal Emplacement,Parson's Shapes

-71-

Principal Stress

0 50 MPa

Figure 39. Principal Stresses, Horizontal EmplacementHorseshoe Shapes

-72-

^ Principal Stress

0 50 MPa

Figure 40. Principal Stresses, Horizontal Emplacement,Parson's Shapes

-73-

J

Tangential Stress

o 50 MOP

Figure 41. Tangential Stresses, Horizontal Emplacement,Parson's Shapes

-74-

Tangential Stress

° 50 MPa

Figure 42. Tangential Stresses, Horizontal EmplacementHorseshoe Shapes

-75-

T

Tangential Stress

0 50 MPa

Figure 43. Tangential Stresses, Horizontal Emplacement,Continuous Miner Shapes

-76 -

-U

.4

Matrix Strength Ratio: A - 1.0; B - 3.0; C - 5.0, D - 7.0; E - 9.0

Figure 44. Matrix Strength Ratio, Horizontal Emplacement,Parson's Shapes

-77-

Matrix Strength Ratio: A - 1.0; B - 3.0; C - 5.0; D - 7.0; E - 9.0

Figure 45. Matrix Strength Ratio, Horizontal Emplacement,Horseshoe Shapes

-78-

Matrix Strength Ratio: A - 1.0; B - 3.0; C - 5.0; D - 7.0; E - 9.0

Figure 46. Matrix Strength Ratio, Horizontal Emplacement,Continuous Hiner Shapes

-79-

4 8 0 4 a 0 4meters

Joint Stress Ratio: A - 1.0; B - 3.0; C - 5.0; D - 7.0; E - 9.0

Region of Joint Activation

Figure 47. Joint Factor of Safety, Horizontal Emplacement,Parson's Shapes

-80-

tl � � .. . ... . ..I. ...

a .

a.

Joint Stress Ratio: A - 1.0; B - 3.0; C - 5.0; D - 7.0; E - 9.0

DiM Region of Joint Activation

Figure 48. Joint Factor of Safety, Horizontal Emplacement,Horseshoe Shapes

I -81-

Joint Stress Ratio: A - 1.0; 8 - 3.0; C - 5.0; D - 7.0; E - 9.0

E l Region of Joint Activation

Figure 49. Joint Factor of Safety, Horizontal Emplacement,Continuous Miner Shapes

-82-

r

APPENDIX A

Relationship of Data Used in This Analysis toNNWSI Reference Information Base

A-1

This preliminary design analysis was done to determine if significantdifferences exist in the response of drifts of various shapes and sizes toexcavation-induced stresses and to determine how rock bolts will effect driftresponse. As such, it is the comparison between the responses that is importantrather than the absolute response of a particular drift. Differences between thedata used in this report and reference data should effect the response of all thecalculations similarly and should not change the conclusions of this report.

This analysis was initiated before baseline project data was established(Zeuch and Eatough, 1986). The data used includes data from the unit evaluationstudies as well as more recent data. Differences do exist between the data usedand current reference data. Key data used are given in Table A-1 together withthe reference data.

None of the data used by this report that is not already in the RIB iscandidate information for inclusion in the RIB and none of the results of thiswork is candidate information for inclusion in the RIB. This report also does notpresent any new data to be input into the DRMS.

A-2

V

a .

Table A-1Material Properties Data Used for this Analysis and RIB Data.

RIB DATA' Rock Bolt Size andProperty TSw2 Value Section Analyses Shape Analyses

(Current Study) (Current Study)

Density 2.34 1.3.1.5 2.34 (3) g/cu.cmPoisson's Ratio 0.20 1.3.1.7 0.14 (2) 0.20 (3)Elastic Modulus 15.1 1.3.1.7 26.7 (2) 15.1 (3) GPaCompressive Strength 75.4 1.3.1.7 91.1 (2) 75.4 (3) HPaMatrix Friction Angle 29.2 1.3.1.7 26.0 (2) 29.2 (3) deg.Tensile Strength -9.0 1.3.1.7 -12.8 (2) -9.0 (3) MPaJoint Cohesion 1.0 1.3.1.8 1.0 (3) MPaJoint Friction Angle 38.7 1.3.1.8 38.7 (3) deg.Joint Orientation V (4) deg.

Notes: (1) Zeuch and Eatough (1986).

(2) These data were in general taken from the unit evaluation and predatethe RIB. Unit evaluation data are documented in Tillerson and Nimick(1984).

(3) Data from Nimick et al., (1984).

(4) Vertical joint orientation (Johnstone, et al., 1984).

A-3

REFERENCES FOR APPENDIX A

Johnstone, J. K., R. R. Peters, and P. F.Gnirk, "Unit Evaluation at YuccaMountain, Nevada Test Site: Summary Report and Recommendation," SAND83-0372,Sandia National Laboratories, Albuquerque, NM, 1984.

Nimick, F. B., S. J. Bauer and J. R. Tillerson, "Recommended Matrix and RockMass Bulk, Mechanical, and Thermal Properties for Thermo-mechanical Stratigraphyof Yucca Mountain,' Version 1, Keystone Document Number 6310-85-1, Sandia NationalLaboratories, Albuquerque, NM, 1984.

Tillerson, J. R. and F. B. Nimick, "Geoengineering Properties of PotentialRepository Units at Yucca Mountain, Southern Nevada," SAND84-0221, Sandia NationalLaboratories, Albuquerque, NM, 1984.

Zeuch, D. H. and M. J. Eatough, "Draft Reference Information Base for theNevada Nuclear Waste Storage Investigations Project," Sandia NationalLaboratories, Albuquerque, NM, April, 1986.

A-4

APPENDIX B

Relationship of Data Used In this Analysis to SEPDB

BE1

No data contained in this report is candidate information for the Site andEngineering Properties Data Base.

B-2

APPENDIX C

.Distribution List

C-1

V

DISTRIBUTION LIST

D. H. Alexander (RW-232)Office of Civilian RadioactiveWaste Management

U.S. Department of EnergyForrestal BuildingWashington, DC 20585

Eric AndersonMountain West Research-Southwest, Inc.398 South Mill Avenue, Suite 300Tempe, AZ 85281

J. H. AnttonenDeputy Assistant Manager forCommercial Nuclear Waste

Basalt Waste Isolation Project OfficeU.S. Department of EnergyP.O. Box 550Richland, WA 99352

Timothy C. BarbourScience Applications

International Corporation1626 Cole Boulevard, Suite 270Golden, CO 80401

E. P. BinnallField Systems Group LeaderBuilding 50B/4235Lawrence Berkeley LaboratoryBerkeley, CA 94720

R. J. Blaney (RW-22)Office of Geologic RepositoriesU.S. Department of EnergyForrestal BuildingWashington, DC 20585

P.M. Bodin (12)Office of Public AffairsU.S. Department of EnergyP.O. Box 98518Las Vegas, NV 89193-8518

E. S. Burton (RW-25)Siting DivisionOffice of Geologic RepositoriesU.S. Department of EnergyForrestal BuildingWashington, DC 20585

Flo ButlerLos Alamos Technical Associates1650 Trinity DriveLos Alamos, New Mexico 87544

V. J. Cassella (RW-222)Office of Civilian RadioactiveWaste Management


B. W. ChurchDirectorHealth Physics DivisionU.S. Department of EnergyP.O. Box 14100Las Vegas, NV 89114

C. R. Cooley (RW-24)Geosciences & Technology DivisionOffice of Geologic RepositoriesU.S. Department of EnergyForrestal BuildingWashington, DC 20585

J. A. CrossManagerLas Vegas BranchFenix & Scisson, Inc.P.O. Box 14308Mail Stop 514Las Vegas, NV 87114

H. D. CunninghamGeneral ManagerReynolds Electrical &

Engineering Co., Inc.P.O. Box 14400Mail Stop 555Las Vegas, NV 89114

Neal Duncan (RW-44)Office of Policy, Integration, andOutreach


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J. J. Fiore (RW-221)Office of Civilian Radioactive

Waste Management IU.S. Department of EnergyForrestal BuildingWashington, DC 20585

John FordhamDesert Research InstituteWater Resource CenterP.O. Box 60220Reno, NV 89506

Judy Foremaster (5)City of CalienteP.O. Box 158Caliente, NV 89008

D. L. FraserGeneral ManagerReynolds Electrical & Engineering

Co., Inc.P.O. Box 14400Hail Stop 555Las Vegas, NV 89114-4400

M. W. Frei (RW-231)Office of Civilian RadioactiveWaste Management


B. G. Gale (RW-223)Office of Civilian RadioactiveWaste Management


R. V. Gale (RW-40)Office of Civilian RadioactiveWaste Management

U.S. Department of EnergyForrestal'BuildLngWashington, DC 20585

V. H. GlanzmanU.S. Geological Survey913 Federal CenterP.O. Box 25046Denver, CO 80225

Vincent GongTechnical Project Officer for NNWSIReynolds Electrical & Engineering

Co., Inc.P.O. Box 14400Mail Stop 615Las Vegas, NV 89114-4400

A. E. GurrolaGeneral ManagerEnergy Support DivisionHolmes & Narver, Inc.P.O. Box 14340Mail Stop 580Las Vegas, NV 89114

R. HarigParsons Brinckerhoff Quade &Douglas, Inc.

1625 Van Ness AvenueSan Franciso, CA 94109-3678

Roger HartItasca Consulting Group, Inc.P.O. Box 14806Minneapolis, Minnesota 55414

T. HayExecutive AssistanceOffice of the GovernorState of NevadaCapitol ComplexCarson City, NV'89710

L. R. Hayes (3)Technical Project Officer for NNWSIU.S. Geological Survey421 Federal Center-P.O. Box 25046Denver, CO 80225

W.M. HewittProgram ManagerRoy F. Weston, Inc.955 L'Enfant Plaza, SouthwestSuite 800Washington, DC 20024

T. H. Isaacs (RW-22)Office of Civilian RadioactiveWaste Management

U.S. Department of Energy'Forrestal BuildingWashington, DC 20585

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Allen Jelacic (RW-233)Office of Civilian RadioactiveWaste Management


C. H. JohnsonTechnical Program ManagerNuclear Waste Project OfficeState of NevadaEvergreen Center, Suite 2521802 North Carson StreetCarson City, NV 89701

S. H. Kale (RW-20)Office of Civilian RadioactiveWaste Management


B. J. King (2)LibrarianBasalt Waste Isolation Project

LibraryRockwell Hanford OperationsP.O. Box 800Richland, WA 99352

Cy Klingsberg (RW-24)Office of Geologic RepositoriesGeosciences and Technology DivisionU.S. Department of EnergyForrestal BuildingWashington, DC 20585

J. P. Knight (RW-24)Office of Civilian RadioactiveWaste Management

U.S. Department of EnergyForrestal BuildingWashington DC 20585

T. P. Longo (RW-25)Office of Geologic RepositoriesU.S. Department of EnergyForrestal BuildingWashington, DC 20585

R.R. Loux, Jr. (3)Executive DirectorNuclear Waste Project OfficeState of NevadaEvergreen Center, Suite 2521802 North Carson StreetCarson City, NV 89701

S. A. MannManagerCrystalline Rock Project OfficeU.S. Department of Energy9800 South Cass AvenueArgonne, IL 60439

Dr. Martin MifflinDesert Research InstituteWater Resources Center2505 Chandler AvenueSuite 1Las Vegas, NV 89120

D. F. MillerDirectorOffice of Public AffairsU.S. Department of EnergyP.O. Box 98518Las Vegas, NV 89193-8518

R. Lindsay MundellU.S. Bureau of MinesDenver Federal CenterP.O. Box 25086Building 20Denver, Colorado 80225

S. D. MurphyTechnical Project OfficerFenix & Scisson, Inc.P.O. Box 15408Mail Stop 514Las Vegas, NV 89114

for NNWSI

J. 0. NeffManagerSalt Repository Project OfficeU.S. Department of Energy505 King AvenueColumbus, OH 43201

D. C. Newton (RW-23)Engineering & Licensing DivisionU.S. Department of EnergyForrestal BuildingWashington, DC 20585

N.A. NormanProject ManagerBechtel National Inc.P.O. Box 3965San Francisco, CA 94119

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D. T. Oakley (4)Technical Project Officer for NNWSILos Alamos National LaboratoryP.O. Box 1663Mail Stop F-619Los Alamos, NM 87545

0. L. OlsonManagerBasalt Waste Isolation Project OfficeRichland Operations OfficeU.S. Department of EnergyP.O. Box 550Richland, WA 99352

Gerald Parker (RW-241)Office of Civilian RadioactiveWaste Management


David K. ParrishRE/SPEC Inc.3815 Eubank, N.E.Albuquerque, NM 87191

J. P. PedalinoTechnical Project Officer for NNWSIHolmes & Narver, Inc.P.O. Box 14340Mail Stop 605Las Vegas, NV 89114

P. T. PrestholtNRC Site Representative1050 East Flamingo RoadSuite 319Las Vegas, NV 89109

W. J. Purcell (RW-20)Associate DirectorOffice of Civilian RadioactiveWaste Management


L. D. Ramspott (3)Technical Project Officer for NNWSILawrence Livermore NationalLaboratory

P.O. Box 808Mail Stop L-204Livermore, CA 94550

J. R. RolloDeputy Assistant Director

for Engineering GeologyU.S. Geological Survey106 National Center12201 Sunrise Valley DriveReston, VA 22092

B. C. Rusche (RW-l)DirectorOffice of Civilian RadioactiveWaste Management


J. E. Shaheen (RW-44)Outreach ProgramsOffice of Policy, Integration and

OutreachU.S. Department of EnergyForrestal BuildingWashington, DC 20585

Dr. Madan N. SinghPresidentEngineers International,98 East Naperville RoadWestmont, IL 60559-1595

Inc.

M. E. SpaethTechnical Project Officer for NNWSIScience ApplicationsInternational Corporation101 Convention Center DriveSuite 407Las Vegas, NV 89109

Christopher N. St. JohnJ.F.T. Agapito & Associates, Inc.27520 Hawthorne Blvd., Suite 295Rolling Hills Estates, CA 90274

Ralph Stein (RW-23)Office of Civilian RadioactiveWaste Management

U. S. Department of EnergyForrestal BuildingWashington, DC 20585

K. Street, Jr.Lawrence Livermore NationalLaboratory -

P.O. Box 808Mail Stop L-209Livermore, CA 94550

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W. S. TwenhofelConsultantScience Applications

International Corp.820 Estes StreetLakewood, CO 89215

D. L. Vieth (4)DirectorWaste Management Project OfficeU.S. Department of EnergyP.O. Box 98518Las Vegas, NV 89193-8518

J. S. WrightTechnical Project Officer for NNWSIWaste Technology Services DivisionWestinghouse Electric CorporationNevada OperationsP.O. Box 708Mail Strop 703Mercury, NV 89023

ChiefRepository Projects BranchDivision of Waste ManagementU.S. Nuclear Regulatory CommissionWashington, DC 20555

Document Control CenterDivision of Waste ManagementU.S. Nuclear Regulatory CommissionWashington, DC 20555

NTS Section LeaderRepository Project BranchDivision of Waste ManagementU.S. Nuclear Regulatory CommissionWashington, DC 20555

SAIC-T&MSS Library (2)Science Applications

International Corporation101 Convention Center DriveSuite 407Las Vegas, NV 89109

ONWI LibraryBattelle Columbus LaboratoryOffice of Nuclear Waste Isolation505 King AvenueColumbus, OH 43201

Department of ComprehensivePlanning

Clark County225 Bridger Avenue, 7th FloorLas Vegas, NV 89155

Lincoln County CommissionLincoln CountyP.O. Box 90Pioche, NV 89043

Community Planning andDevelopment

City of North Las VegasP.O. Box 4086North Las Vegas, NV 89030

City ManagerCity of HendersonHenderson, NV 89015

Planning DepartmentNye CountyP.O. Box 153Tonopah, NV 89049

Economic DevelopmentDepartment

City of Las Vegas400 East Stewart AvenueLas Vegas, NV 89101

Director of Community PlanningCity of Boulder CityP.O. Box 367Boulder City, NV 89005

Technical Information CenterRoy F. Weston, Inc.955 L'Enfant Plaza, SouthwestSuite 800Washington, DC 20024

Commission of theEuropean Communities

200 Rue de la LoiB-1049 BrusselsBELGIUM

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6300 R. W. Lynch6310 T. 0. Hunter6310 NNWSI CF6310 75/12462/0/Q36311 A. L. Stevens6311 C. Mora6311 V. Hinkel (2)6312 F. W. Bingham6313 T. E. Blejwas6314 J. R. Tillerson6314 S. J. Bauer6314 L. S. Costin6314 B. L. Ehgartner (10)6314 R. J. Flores6314 A. J. Mansure6314 R. M. Robb6314 R. E. Stinebaugh6315 S. Sinnock6316 R. B. Pope6332 WMT Library (20)6430 N. R. Ortiz3141 S. A. Landenberger (5)3151 W. L. Garner (3)8024 P. W. Dean3154-3 C. H. Dalin (28)

for DOE/OSTI

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