SAND86- 1250 e UC-70Unlimited ReleasePrinted May 1987

Nevada Nuclear Waste Storage Investigations Project

Sensitivity Analyses of Underground Drift Temperature,Stresses, and Safety Factors to Variation in the RockMass Properties of Tuff for a Nuclear Waste RepositoryLocated at Yucca Mountain, Nevada

B. L. Ehgartner

Prepared bySandia National LaboratoriesAlbuquerque, New Mexico 87185 and Livermore, California 94550for the United States Department of Energyunder Contract DE-AC04-76DPO07B9

4 .

Di stributionCategory UC-70

SAND86-1250Unlimited Release

Printed May 1987

SENSITIVITY ANALYSES OF UNDERGROUND DRIFT TEMPERATURE, STRESSES, ANDSAFETY FACTORS TO VARIATION IN THE ROCK MASS PROPERTIES OF TUFF FOR ANUCLEAR WASTE REPOSITORY LOCATED AT YUCCA MOUNTAIN, NEVADA.

B. L. Ehgartner

Sandia National LaboratoriesAlbuquerque, New Mexico 87185

ABSTRACT

Preliminary two-dimensional thermal and thermal/mechanical sensitivityanalyses or the design of the nt drift wereperformed for times out to 100 years after waste emplacement. Thepurpose of the analyses is to provide insight into the relativeimnpo ce of the thermal and thermal/mechanical prop e thatimpact the stability of the emplacement drift- specifically, heatcapacity, conductivity, thermal expansion, insitu thermal gradient,insitu stress, joint cohesion and friction angle, elastic modulus,Poisson's ratio, rock friction angle, rock compressive and tensilestrength. This will help prlQr"itze future characters 7tivr andanalysis activities prior to development. The model input propertieswere varied over the expected range of their values and thecorresponding effect on the temperature, stresses, and safety factorsof the rock mass surrounding the drift were recorded. First, theproperties were varied individually to determine the independenteffects on drift performance. Second, select properties were variedsimuljtAnmusly to assess joint effects and estimate the probability ofundesired drift performance. The results represent a first attempt toestimate the variability of the properties and their effects on thedrift. Other sources of variability that can affect drift design arenot considered, hence the results are considered preliminary. As sitecharacterization proceedes, the enhanced understanding of propertyvariability will lead to updating the results and conclusions of thisreport. Results of the preliminary analyses indicate that the designof the horizontal emplacement drift can tolerate the expectedvariability in the thermal and thermal/mechanical properties.Conditions that may require supplemental ground support are predictedin these preliminary analyses to occur over approximately 20 percentof the horizontal emplacement drifting.

iil/iv

TABLE OF CONTENTS

Section Page

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

2 MODEL DESCRIPTION .... 4. .................... . .. 4

2.1 Thermal and Thermal/Mechanical Properties . 42.2 Geometric Parameters and Waste

Characteristics ..... 6..................... 62.3 Thermomechanical Code and Postprocessing .. 9

3 APPROACH ...................... 13

4 INDIVIDUAL VARIATION OF THERMAL ANDTHERMAL/MECHANICAL PROPERTIES .................... 14

5 SIMULTANEOUS VARIATION OF THERMAL ANDTHERMAL/MECHANICAL PROPERTIES ..................... 23

6 CONCLUSIONS ................... ...... ............ 29

REFERENCES ........................... ... ..... 33

APPENDIX -- Parameters Used in This Study andCorresponding NNWSI Reference Information BaseValues .. **.... ...... ..................... 35

LIST OF FIGURES

Figure Page

1 Design of Drift for Horizontal Emplacementof Waste Container of Spent Fuel .......... *.. 7

2 Boundary Element Model for Analysis of HorizontalEmplacement ............ 99906940 10

v

LIST OF TABLES

Table Page

1 Thermal and Thermal/Mechanical Properties .......... 6

2 Geometric Data for Horizontal Emplacement Option ... 8

3 Normalized Coefficients for the Power Decay Functionfor PWR and BWR Spent Fuel Mix ..................... 9

4 Expected Ranges, Sensitivities, and Design ImpactFactors of Floor Temperatures, Stresses, and Factorsof Safety at the Horizontal Emplacement Drift 50years after Waste Emplacement due to Variation inThermal/Mechanical Properties ...................... 17

5 Expected Ranges, Sensitivities, and Design ImpactFactors of Crown Stresses and Factors of Safety aboutthe Horizontal Emplacement Drift 50 years after WasteEmplacement due to Variation in the Elastic Modulus,Thermal Expansion, Compressive Strength, and JointCohesion 21

6 Expected Range of Rock Mass Safety Factor, DesignImpact Factor, and Probabilities of Failure due toJoint Variation of Selected Properties about theDrift 50 years after Waste Emplacement ............. 25

7 Expected Range in Rock Mass Safety Factor andProbability of Failure at 50 years after WasteEmplacement with Drift Removed ..................... 27

8 Probabilities of Rock Mass Failure at AlternativeEmplacement Times with the Drift Present in the Modeland with Drift Removed .............. 28

Vt

1. INTRODUCTION

The Nevada Nuclear Waste Storage Investigations (NNWSI) project is currently

assessing the feasibility of siting a high-level nuclear waste repository at

Yucca Mountain, Nevada. The purpose of the repository is to safely and

effectively dispose of spent fuel generated by nuclear reactors and high-

level radioactive waste resulting from plutonium production. The Department

of Energy (DOE) has determined that a geologic repository is the best means

of accomplishing the objective of waste disposal. Sandia National

Laboratories, a contractor to the DOE, is responsible for the conceptual

design of the waste repository.

A fundamental concern in the design of a repository is the structural

stability of the underground waste emplacement drifts. Stability of the

drifts is required for worker safety and to allow for possible retrieval of

the waste up to 50 years following waste emplacement. The drifts must also

provide a usable environment in which temperatures are not too excessive to

prevent entry by personnel. Reference thermaltmechanical analyses of the

drifts using best estimates of the geologic and geometric properties have

been completed and are documented in SAND86-7005 (St. John, 1987). The

results of these preliminary analyses predict stable and usable openings

throughout the retreival period.

Because of the inherent variable nature of geologic properties and

limitations on the ability to measure accurately or predict the properties

of the emplacement horizon, uncertainty exists in the values of the ermal

and thermal/mechanical properties used in the modeling of the emplacement

drifts. The analytic results used to predict stable and usable drifts at

Yucca Mountain thus far were in general based on average values or best

estimates of the geologic properties, although some analyses have been

completed that used "limit properties". The effect of changes or

variability in the thermal and thermal/mechanical properties on the

stability and usability of the horizontal waste emplacement drifts is

discussed herein. This report does not consider the effects of uncertainty

-1-

in the abilty o predict drift stability from model results or the ability

of the model to simulate field conditions.

This report presents preliminary results of two types_of sensitivity studies

in which the rock mass thermal and thermal/mechanical properties were

varied. The effect or the variation of the geologic properties on selected

model outputs used to assess drift stability and usability was then

determined. The drift temperatures, stresses.-and factors of safety are

model outputs used in the determination of drift stability and usability.

Defgrmations were not considered because their predicted relative small

magnitudes are not likely to effect the usability of the drift. Maximum

drift closures do not exceed 0.2 percent of the horizontal emplacement drift

dimensions (St John, 1986). The horizontal waste emplacement drift was

modeled in both sensitivity studies, using a boundary element code that

provided a time-dependent, two-dimensional, thermoelastic solution. The use

of a linear elastic code is justified because this report represents a first

attempt at defining the variability of the thermal and thermal/mec ancial

properties and the effects of the variability on the performance of the

horizontal emplacement drift.

The first sensitivity study considered the effect of individual variations

of the model input properties on drift temperature, stresses, and rock mass

factors of safety. The thermal and thermal/mechanical properties were

singly varied over thir expected ran resulting in variations in the

temperatures, stresses, and factors of safety. The results of the study

were used to assess whether the horizontal waste emplacement drift design

could tolerate expected changes in geologic properties and remain stable and

usable. In addition, the results provided an i ortance ranking of the

individual properties to the success of the emplacement drift design. This

ranking will help guide and prioritize future experimental and analytical

work aimed at defining the expected vues and variances of thermal and

thermal/mechanical properties important to the design of the underground

drifts. Based on this ranking, some properties were selected~ tae second

sensitivity. study.

-2-

The second sensitivity study evaluated the effects of simultaneous property

variation on drift stability; hence, it is probabilistic in nature.

Stability in this study was assessed through the probability of failure or

the likelihood that the factor of safety of the rock mass hosting the drift

would be less . afety factors were based-on the estimated rock mass

strength and predicted stresses of the linear elastic model at various

points around the drift. The results of this study provided an estimate of

the probability that supplemental ground support would be required for the

emplacement drift. Baseline ground support consists of rockbolts an re

mesh to accommodate the anomalous pieces of rock that may dis 0ge-dueto

construction processes (MacDougall, 1986) or localized instabilities in the

rock mass that can be considered as skin effects. For purposes of this

report, supplemental ground support is assumed to be needed if therzei-

significant overstressing of the rock mass surrounding the drift.- The

addition of rock-bolts into a linear elastic model of the emplacement drifts

has been shown to result in small or insignificant changes in the stress

state surrounding waste emplacement drifts (St. John, 1987), therefore the

baseline ground support is not included in the model of the waste

emplacement drifts. This report attempts to define the potential need for

supplemental drift support, but not the amount. In practice, a range of

support requirements is expected to accommodate variability in actual ground

conditions and detailed evaluations of site-specific conditions are probably

warranted.

Section 2 describes the thermomechanical model and its inputs. Section 3

discusses the approach or the use of the thermomechanical model in the two

sensitivity studies. Section 4 presents results of the first sensitivity

study where the thermal and thermal/mechanical properties were individually

varied. Section 5 presents results of the second sensitivity study where

selected properties from the first study were varied simultaneously. The

report draws conclusions from the results of the two preliminary sensitivity

studies in Section 6.

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2. MODEL DESCRIPTION

The modeling of the horizontal emplacement drift required the following

elements: (1) the thermal and thermal/mechanical properties, (2) the

geametr-o-paramaters and waste characteristics, and (3) the thermomechanical

code and its postprocessing. Each of these elements of modeling are defined

in separate subsections below.

2.1 Thermal and Thermal/Mechanical Properties

Several geologic horizons compose the stratigraphy of Yucca Mountain.

However, two stratagraphic units influence the thermal and thermal/

mechanical response Of the waste emplacement drifts. They are defined as

the lithophysae rich (TSw-1) and lithophysae poor (TSw-2) units of the

welded, devitrified Topopah Spring Member tuff (Ortiz, et al., 1985).

Current conceptual designs for the repository locate the underground

facility in TSw-2;,therefore, TSw-2 will be expected to most significantly

influence the thermal/mechanical response of the emplacement drifts.

The average or recommended thermal and thermal/mechanical properties for

TSw-2 are defined in the NNWSI Reference Informallon-aase (Zeuch and

Eatough, 1986), and the rationale for deriving the rock mass properties from

laboratory values is discussed in Keystone Document Number 6310-86 (Nimick,

Bauer, and Tillerson, 1984). The Reference Information Base (RIB) values

for the recommended rock mass properties of TSw-2 were used as the average

values in this report. The rock mass properties were based on the combined

behavior of both intact rock and fractures.

The variations of the thermal and thermal/mechanical properties used in this

report are based on combined data from both TSw-1 and TSw-2. This will add

a degree of conservatism to the results Of the analyses because the

variability of the combined TSw-1 and TSw-2 data is greater than the

variability resulting solely from TSw-2 data. Because uncertainty exists in

spatially defining the lithophysae content throughout the Topopah Spring

Member tuff, combined TSw-1 and TSw-2 data will be used to define the

-4-

variation in the thermal and thermal/mechanical properties. However, the

use of combined data will provide a conservative estimate of variability

because the properties of the two units are significantly different (Nimick,

1987).

Raw data characterizing the geology of the emplacement horizon was obtained

from a data base (NNWSI Tuff Data Base, 3/22/85) that includes the results

of tests and measurements performed on core samples from the repository

site. TSw-l and TSw-2 data were statistically analyzed from boreholesUE%-

25A#1, USW G-1, USW GU-3, USW H-1, and USW G-4 to determine the coefficient

of variation of several thermal/mechanical properties.

Table 1 provides the properties used in the sensitivity studies. The

average values reflect the rock mass properties of TSw-2. The coefficients

of variation are a result of the statistical analyses on combined TSl and

TSw-2 data. The standard deviations were obtained by multiplication of the

average values by the coefficients of varia ion.

The results represent a preliminary statistical analysis of the data, and

caution should be exercised in the future use of data presented in Table 1

because the Tuff Data Base is updated periodically. Currently, the Tuff

Data Base is included in the RIB under Chapter 1 - Site Characteristics.

Future studies or analyses should use the RIB to obtain the thermal and

thermal/mechanical properties of TSw-1 and TSw-2.

The surface temperature was not varied in any of the sensitivity studies

because seasonal variations in the ambient temperature of the air at the

surface do not influence the in situ rock temperatures at 300 m below the

surface--the average depth of the underground repository facilities.

-5-

Table 1

Thermal and Thermal/Mechanical Properties

v V d

Average ,z C. V. (%) - Std. Dev.Property 1'I !

Overburden density, S/cm3

Young's modulus, GPa

Poisson's ratio

Hor/ver in situ stress

Thermal conductivity, W/m-0C

Heat capacity, J/cm 3C

v Thermal expansion, 1/aC

Surface temperature, OC

In situ thermal gradient,OC/m

lJoint cohesion, MPa

lRock friction angle, deg

Joint friction angle, deg

Compressive strength, MPa

Tensile strength, MPa

r,34&

15 1

0.2

-0.55,

2. 7

2.25

10.7 E-6

16.

0.0239

1 .0

29.2

38.7

75.4

9.0

2.94

34.1

21.8

45.4

22.2

5.08

15.2

not varied

38.9

38.3

11.0

11.0

58.3

14.7

0.07

5.1

0.04

0.25

0.46

0.11

1.6 E-6

0.0093

0.38

3.2

4.25

44.0

1.3

I I

I/

2.2 Geometric Parameters and Waste Characteristics

The horizontal emplacement drift dimensions and characteristics of the

emplaced waste are listed in Tables 2 and 3, respectively. The geometric

data and waste characteristics are also documented in the RIB.

The drift was a modified horseshoe shape with flat sidewalls and floor. The

crown or arch of the roof was circular. Figure 1 shows the excavated and

finished dimensions Of the drift. The excavated dimiensions were used in

this study as ground support structures or the systems were not modeled.

The waste is emplaced in ong, horizontal boreholes extending from both

sides of the drift.

S P

-6-

18' EXCAVATED WIDTH(35.49 )

CLEARANCE =17'(5s1l")

DRIFT CENTERLINE

U,do

UV

I

I * 4� 4. -- 1.4 4-

.1=

N~~~~~~~

III

I

wu

U.

IC

A

I T0.

oil A^A-VIN III I ypp III

Figure 1 Design of Drift for Horizontal Emplacementof Waste Container of Spent Fuel

-7-

Table 2

Geometric Data for Horizontal Emplacement Option

Geometry meters

Drift height 3.96

Drift width 5.49

Panel width 427.

Radius of roof arch 3.25

Waste standoff from drift center line 35.8

Waste emplacement borehole spacing 31.1

Depth of drift below ground surface 300.

The power output of the waste is characterized according to a normalized

thermal decay curve described by the following equation,

Power- Pl*exp(-A*t) + P2*exp(-B*t) + P3*exp(-C*t) + P4*exp(-B*t)

where P1, P2, P3, and P4 are proportions of the gross thermal loading of the

waste, and A, B, C, and D are constants that control the decay of the

thermal load, t is the time in years since the waste was emplaced in the

repository. A 60/40-percent mixture of pressurized-water reactor (PWR) and

boiling-water reactor (BWR) spent fuel 8.55 years out of the reactor was

modeled. The normalized components of the power decay curve, listed in

Table 3, are valid for waste 5 years to 500 years out of the reactor

(Mansure, 1985).

The gross thermal loading of the waste was 57 kW/acre (Johnstone, Peters,

and Gnirk. 19 4). The loading was assumed instantaneous, and a series of

linear heat sources modeled the waste emplacement regions about the drift.

The waste emplacement regions ot line heat

7 sources that extend infin~t-j.4-4nto and out of the plane of analysis

containing the drift. The spacing of the heat sources was the same as the

-8-

I *

borehole spacing. The areal power density or gross thermal loading of the

repository (57 kW/acre) was used to determine the strefngtth-ofte-1ine heat

sources based on geometries ln-lAhle.2. A symmetric view of the repository

model is shown in Figure 2a. Figure 2a shows the location of the drift in

the repository model and an enlargement of the --- s prov in Figure

2b. The symmetric view of the drift shown in Figure 2b indicates the number

of boundary elements that modeled the drift.

Table 3

Normalized Coefficient for the Power Decay Function

for PWR and BWR Spent Fuel Mix

Series Proportion of Time

Component Normalized Strength Component

1 P1 - 0.1560 A - 0.001354

2 P2 * 0.5979 B - 0.01914

3 P3 * 0.1523 C - 0.05189

4 P4 - 0.09384 D - 0.4377

2.3 Thermomechanical Code and Postprocessing

The above thermal and thermal/mechanical properties, geometries, and thermal

characteristics and loading were input into the boundary element code HEFF

(HEat with Fictitious Force), which performed the thermomechanical analyses

of the horizontal emplacement drifts. The code (Brady, 1980) assumes a

linear elastic med T "+& iheat sour- o. The code calculates

temperatures and stresses at selected points in the elastic medium. It was

then necessary to postprocess the stresses to determine factors of safety

for the rock mass and joints.

The rock mass safety factor was based on the ength of the rock matrix,

-which was degraded to account for the presence of pints. The safety factor

is the ratio of rock mass strength to stress. The Coulomb failure criterion

was used where the safetyfactor is defined as:

-9-

a

-200w

-400

Meters

-204

I

a) Repository Model (above)

b) Drift Detail andSample Points (left)

FXe 2 ou da y lemen Modsampl p o int

-302I.\_S emI entj

-305048

Figure 2 Boundary Element Model for Analysis of Horizontal Emplacement

-10-

from the wall increased. The joint slip safety factor increased above 1

at 1 m into the drift wall rock. In general the stress and safety factor at

the crown changed by a factor of 2 to favor drift stability over the 3-m

distance into the host rock. Even greater changes in the magnitude of the

joint safety factor are noted over the 3-m distance from the wall. This

implies that conservative estimates of safety factors are found at the drift

boundaries as they are lower than those found out in the rock mass. More

representative factor-of-safety values can be obtained by integrating or

averaging over a volume extending 3 m into the drift host rock. An

integrated safety factor, representing a volume of rock mass, would be a

better indicator of drift stability since volumetric not localized failure

will control drift stability.

Table 5

Expected Ranges, Sensitivities, and Design Impact Factors of Crown Stressesand Factors of Safety about the Horizontal Emplacement Drift 50 Years afterWaste Emplacement due to Variation in Elastic Modulus, Thermal Expansion,Compressive Strength, and Joint Cohesion.

PropertyDistance ExpectedFrom Drift(m) Rge

Design ImpactFactorSensitivity

Elastic modulus

Thermal expansion

Of Crown Stresses, MPa:0 20.3 to 37.2I 13.9 to 23.02 11.6 to 18.63 10.6 to 13.70 25.0 to 32.51 16.4 to 20.52 13.6 to 16.63 12.3 to 15.0

1.660.8950.6760.5972.341.260.950.84

0.1810.0800.0580.0250.0800.0360.0250.022

Compressive strengthOf Rock Mass Safety Factors (at crown):0 1.05 to 2.61 0.0181 1.84 to 44.93 0.02292 2.35 to 6.50 0.02653 2.58 to 7.27 0.0289

0.9400.6490.6070.598

Joint cohesionOf Joint Safety0 0.221 1.872 3.943 7.148

Factorsto 0.50to 2.37to 4.48to 8.29

(at wall):0.3680.14530. 4890.734

0.2190.2230.0840.059

-21 -

The sensitivity of crown stress to elastic modulus and thermal expansior

decrease as distance from the crown increases. This is a result Of the

expected range in crown stresses narrowing as the distance from the crown

increases. Consequently, the safety factor sensitivities increase as

distance from the crown increases. The same trend is noted in the joint

safety factors in the drift wall area. However, the design impact factordecreases for all properties as distance from the the drift increases.

Thus, the trend in the design impact factor agrees with what is intuitively

expected; that is, the influence of property variability on design lessens

as distance from the drift increases. This again demonstrates the correct-

ness of using design impact factors rather than sensitivity factors to

indicate the sensitivity of the design of the drift to property variability.

The design impact factors of the properties decreased as the distance from

the excavation boundary increased. Because the design impact factors are

highest at the boundaries of the drift, boundary values are conservative

when used to determine the impact of property variability on design. This

adds a degree of confidence to the above conclusions that were reached by

examining the boundary values of the design impact factors, specifically,

that (1) the drift design can tolerate the expected variability in the

properties and (2) only variability in unconfined compressive strength,

elastic modulus, and thermal expansion significantly effect the mechanical

response of the drift.

The integrated average of safety factors and design impact factors over a

volume of rock, rather than peak boundary values, better represent the

condition of the rock mass surrounding the drift. Therefore, the joint

sensitivity studies presented in Section 5 consider a volume of rock

extending 3 m into the drift crown and wall. This volume of rock mass is

considered appropriate to represent the condition or stability of the drift.

-22-

5. SIMULTANEOUS VARIATION OF THERMAL AND THERMAL/MECHANICAL PROPERTIES

Section 4 considered changes in drift response caused by individual property

changes. This section analyses changes in drift response caused by the

simultaneous change in selected thermal and thermal/mechanical properties.

The sensitivities and design impact factors of Section 4 were used in

selecting the properties that were to be simultaneously varied. The most

sensitive properties to stresses and rock mass safety factors were used;

Specifically, the elastic modulus, thermal expansion, thermal conductivity,

compressive and tensile strengths, and the ratio of horizontal to vertical

in situ stress were selected. Even though the most design sensitive

properties were selected, some of the properties were considered to have an

insignificant impact on the response of the drift. Therefore, an adequate

number of properties were jointly varied in this study.

The selected properties were varied over the expected ranges listed in Table

1, and the same geometries and waste characteristics as used in Section 4

and described in Tables 2 and 3 were used. The horizontal emplacement drift

was modeled at 50 years, varying the elastic modulus, thermal expansion,

thermal conductivity, and compressive and tensile strengths. Also, the

horizontal emplacement drift was modeled at 0, 10, 35, and 100 years after

waste emplacement, varying the same properties with the exception that the

ratio of horizontal to vertical in situ stress replaced the thermal conduc-

tivity. This substitution is considered appropriate because the drift is

not sensitive to the thermal properties at the time of excavation since the

waste has not yet been emplaced. Selected output points at the drift crown

and wall, extending 1, 2, and 3 m into the drift host rock, were analyzed

with respect to factors of safety for the rock mass.

A probabilistic method was used to determine the expected range in safety

factors. The design impact factors were calculated as in Section 4, based

on the applicable design limits. Also, the probability of the rock mass

safety factors exceding the design'limits was determined. The design limit,

as used and defined in Section 4, for rock mass safety factor is 1.0. This

-23-

design limit is based on an unconfined compressive strength or 75.4 MPa for

the rock mass. The probability of exceding the design limits was expressed

as a percent value in the probability of failure.

The point estimate method (Rosenblueth, 1975) was used. The advantages of

the point estimate method over other methods commonly employed in

probabilistic geotechnical engineering has been established (McGuffy, et.

al., 1981). The simultaneous variation or properties is described in a

joint probability distribution of the properties. Joint property

distributions are modeled by selecting point values and assigning

appropriate weighting factors to them. The joint probability density

distribution is approximated by a discrete multipoint probability mass

uunction.

The number of points needed to model a joint distribution depends on the

number or properties being varied. The number of points required is equal

to 2 exp(n), where n is the number of properties being jointly varied.

Weighting factors assigned to the point locations approximate the total mass

or the joint density distribution. Therefore, the weighting factors are

lumped probabilities that must sum to 1. This is the first condition

required by the point estimate method. Other requirements stem from

satisfying moment criteria. The moments of the joint probability mass

function must approximate those of the joint probability density distri-

bution. This is accomplished by the location and relative probabilities

assigned to the point estimates. The first moment is equivalent to the mean

of the joint density distribution. The second moment is the variance.

Additional moments can be used to better define the joint mass function of

the properties, such as skewness and kurtosis. Skewness and kurtosis are

products of the distribution shape, whereas the first and second moments

center and describe the spread of the distribution, respectively. If all or

most of the above moments are satisfied in the multipoint distribution, then

the approximation of the joint density distribution will be adequate.

Often, the higher order moments Of the joint density distribution are not

well known. Therefore, the assumption of normality is often used. The

joint probability density distribution used in this study was assumed to be

normal.

-24-

I

The points values were calculated using the above methodology and input into

the thermomechanical model of the drift. A series of analyses were required

and the results were postprocessed to determine the expected range, design

impact factor, and probability of failure at various distances into the

drift host rock for 50 years after waste emplacement. The probability of

failure or the probability that the factor of safety for the rock mass is

less than 1 is applicable only to a point in the rock mass. Point or

localized failure in the rock mass is not to be interpreted as drift

instability. For an underground opening, a substantial portion of the rock

mass surrounding the drift would have to undergo failure before the drift

would be unstable. Therefore the probability of failure, as reported in

Table 6, refers to the point in the rock mass being analyzed and not to

failure of the drift.

Table 6

Expected Range of Rock Mass Safety Factor, Design Impact Factor, and

Probabilities of Failure due to Joint Variation of Selected Properties about

the Drift 50 years after Waste Emplacement

Distance from Expected Design Impact Probability of

Drift(m) Range Factor Failure C%)

Crown:

0 0.95 to 3.05 1.05 16.9

1 1.69 to 5.49 0.73 8.64

2 2.09 to 7.43 0.71 7.94

3 2.19 to 8.69 0.73 8.59

Wall:

0 1.09 to 3.79 0.94 14.2

1 2.69 to 3.83 0.25 0.0042

2 3.14 to 4.34 0.22 0.0001

3 3.26 to 4.48 0.21 0.0001

-25-

As expected and similar to results from Section 4, the rock mass safety

factor increases for locations removed from the drift boundary. However,

the expected range of safety factors in the crown region increases for

points farther removed from the drift boundary. The two trends result in

off-setting infuences on the design impact factor and probability of

failure. This is reflected in the lack of trend in design impact factor and

probability of failure. Generally, though, the highest design impact

factors and probabilities of failure occur near the drift crown. The only

significant design impact factors and probabilities Of failure in the drift

wall rock occur at the drift wall.

As expected, the ranges in the safety factor are greater than those

resulting from variation in any single property (Section 4). Also the

design impact factors and probabilities of failure are greater than those

obtained from any individual property variation. Hence, the design can

still tolerate the expected changes in the thermal and thermal/mechanical

properties without the addition Of supplemental ground support. The factor

Of safety for the rock mass falls below 1 at an extreme bound of the

expected range resulting in a design impact factor exceeding 1 at the

boundary. This indicates that the design limit (i.e., stresses were greater

than rock mass strength) was exceded and that localized failure may occur.

Localized failure of the rock will likely result in the formation of a

fracture with the possibility of some rubblized rock. The consequences of

this skin effect would likely be controlled by the baseline ground support

system (i.e., roof bolts and wire mesh).

Although the expected variation in properties results in stable drift

conditions, there is still a finite probability that the design limits can

be exceded. This is indicated in the probability of failure. To evaluate

whether or not the probabilities Of failure shown in Table 6 are relatively

high, the calculations that generated the above results were redone without

the drift present. The rock mass was still subjected to the thermally

induced stresses resulting from waste emplacement at 50 years. This allowed

the excavation-induced effects to be compared to those that would occur if

no drift were present. The expected ranges and probabilities of failure,

based on tensile and compressive failure criteria, are presented in Table 7.

-26-

The compressive failure criterion is applicable to the drift crown area

because the stress state is compressive. Tensile stresses occur in the

drift wall rock; therefore, the tensile strength criterion determines the

lowest rock mass factor of safety in the drift wall area.

Table 7

Expected Range in Rock Mass Safety Factor and Probability of Failure at 50

years after Waste Emplacement with Drift Removed

Failure Criterion Expected Range Probability of Failure (%)

Compressive 1.10 to 12.4 15.4

Tensile 3.09 to 4.27 0.0001

Comparison of the results in Tables 6 and 7 show that the presence of the

drift can enhance the rocks resistance to fracture at certain locations

surrounding the drift. The probabilities of failure for the analyses

including the drift are lower for the regions of rock mass extending more

than 1 m beyond the drift boundary. The probabilities of failure at the

boundary are not significantly higher than the probabilities resulting from

the analyses that do not include the drift. Thus it is concluded that the

probabilities of failure of the rock mass surrounding the drift are not high

relative to the conditions that would occur in the rock mass absent of the

drift.

To determine whether or not the above conclusion holds for alternative

emplacement times, the analyses were performed at 0, 10, 35, and 100 years.

Because the drift crown showed the highest probability of failure, and

failure located in the crown is considered more detrimental than rock mass

failure in the wall, only results for the crown are discussed. As above,

the analyses were also performed leaving the drift out of the model. The

same properties were varied as before with the exception of the in situ

horizontal-to-vertical stress ratio replacing the thermal conductivity.

This change allowed the drift to be sensitive at excavation time when the

drift response is independent of the thermal properties. The thermal

conductivity was chosen before, based on its sensitivity to wall stresses.

"27-

The crown stresses are more sensitive to the in situ stress ratio than the

thermal conductivity.

The properties were simultaneously varied to result in the probabilities Of

rock mass failure for analyses that included and removed the drift. The

results at the crown are shown in Table 8.

Table 8

Probabilities of Rock Mass Failure at Alternative Emplacement Times with the

Drift Present in the Model and with Drift Removed

Probability of Failure (%)

Time (yr) Drift Modeled Drift Removed

0 19.1 12.1

10 17.6 14.5

35 17.3 21.3

100 18.8 18.3

Comparison of the above probabilities of failure demonstrate again that the

probabilities Of failure at the drift are not significantly higher than

those expected if the drift were not present. The results above are at the

drift crown and are therefore not representative of the rock mass above the

crown, which is expected to have a lower probability of failure. However,

it is conservative to conclude in this preliminary analysis that the

probability Of significant rock mass failure about the drift is 20 percent.

This value agrees with the maximum probabilty of failure over time when the

drift effects are not included. Therefore, the preliminary estimate of the

probability of horizontal emplacement drift failure due to the uncertainties

associated in defining the thermal and thermal/mechanical properties is

approximately 20 percent.

-28-

6. CONCLUSIONS

Conclusions reached in this study should be considered as preliminary for

two reasons. First, this is the first attempt to define the variability in

the thermal and thermal/mechanical properties and apply a probabilistic

technique to assess the effects of the variability on emplacement design.

Subsequent refinement in the statistics that characterize the variability of

the properties and in the probabilistic technique will enhance the accurracy

of the results and may alter the conclusions reached. Second, only the

estimated effects of the variability in the thermal and thermal/mechanical

properties were considered in this study. Many other uncertainties exist

that contribute to providing a definitive statement on drift stability.

From the data aquistion phase to final interpretations of drift stability,

there exists many causes of variability that result in uncertainty in the

final conclusions, some of which are found in: sample disturbance, data

gathering and testing techniques; data reduction; scaling relationships from

laboratory data to field or rock mass properties; spatial variability of

properties; anisotropy, nonhomogeneous, and nonlinear material

characteristics; code numerics and mathematics; the ability of the model to

simulate field behavior; the modeling of the single and joint probability

distributions for the properties and thermomechanical reponses; predicting

the failure mechanism, defining the failure criteria, and predicting the

consequences of rock mass failure on drift stability; design geometries,

waste characteristics, and other quantities needed to define the model. Many

uncertainties are difficult to quantify, however the enforcing of quality

assurance procedures helps reduce or eliminate the uncertainties associated

with personnel performance. Although the data used in this report reflects

several of the possible causes of variability, many important sources were

not considered. For this reason, the conclusions presented below are

considered preliminary.

Results from sensitivity analyses that individually and simultaneously

-varied the thermal and thermal/mechanical properties of a horizontal

emplacement drift model over 100 years following waste emplacement enable

the following preliminary conclusions to be made.

-29-

- The horizontal emplacement drift can tolerate the expected

range in the thermal and thermal/mechanlcal properties.

This preliminary conclusion is reached after examining the expected ranges

in temperature, stresses, and safety factors of the drift that result from

individually varying the following properties of the rock mass over their

expected ranges: overburden density, Young's modulus, ratio of the

horizontal-to-vertical insitu stresses, Poisson's ratio, thermal conduc-

tivity, heat capacity, in situ temperature gradient, joint cohesion, rock

mass friction angle, joint friction angle, compressive strength, and tensile

strength. The resulting ranges in temperature, stresses, and safety factors

were within the limits allowed by the design of the drift 50 years after

waste emplacement. The upper temperature limit was defined as 50 OC, the

maximum stresseses allowed were limited to the strength of the rock mass

(i.e., 75 MPa in compression, 9.0 MPa in tension), and the lower limit for

factor of safety was 1.0.

Supporting the above conclusion are the results from the studies that

Jointly varied the properties that significantly influence the design of the

empacement drift over time, from excavation to 100 years after waste

emplacement. The studies showed the probability that detrimental effects on

the drift would occur outside the region of expected occurence.

The probability of encountering poor ground conditions that

may require supplemental ground support for the horizontal

emplacement drift is approximately 20 percent.

This preliminary conclusion is reached after examining the probabilities of

failure for the rock mass surrounding the horizontal emplacement drift at

the time of excavation and up to 100 years after waste emplacement. The

thermal and thermal/mechanical properties that significantly influence the

mechanical behavior of the rock surrounding the drift were simultaneously

varied, and the resulting rock mass safety factors with magnitudes less than

1 enabled the determination of the probabilities of failure at various

locations around the drift. The probability of failure results from

-30-

uncertainty in defining the rock mass properties that influence the drift

design (especially the compressive strength of the rock mass).

Approximately 20 percent of the possible values for the thermal and

thermal/mechanical properties result in rock mass safety factors less than

1 . This was observed in models that included and excluded the presence of

the emplacement drift. Factors of safety less than I imply localized

failure of the rock mass. This is compensated for by adding ground support

that will either inhibit or prevent fracturing of the rook mass in

significant amounts that may cause the drift to become unstable (i.e., poor

ground conditions).

Interpretation of the probability of failure is related to the cause(s) of

variability in the data used to estimate the rock mass properties. The

variability may result from real or spatial variation in the rock mass

properties over the emplacement horizon, or the cause of variation may be

caused by test and measurement errors in the data. The variation of the

properties used in this study is probably due to a combination of the two

causes.

The variability in rock mass data is most likely attributed to real

variation in the emplacement horizon properties. This is based on the data

being obtained from multiple widely spread boreholes and elevations. The

contribution of test and measurement errors to data variation is most likely

minor because the majority of data was derived through controlled laboratory

experiments. Therefore, the variability used in this study is considered

to partially include the spatial variability of the rock mass properties

over the emplacement horizon. Accordingly, the prediction of the

preliminary analysis is that approximately 20 percent of the underground

emplacement drifting may require ground support in addition to the support

requirements for expected ground conditions.

The alternative interpretation of probability of failure would result if no

spatial variability of the properties existed. In this case, the vari-

ability in the data would be soley attributed to test and measurement

errors. As such, the probability of the baseline ground support being

adequate for all of the emplacement drifting would be 80 percent. In other

-31-

words, the probability that additional or supplemental ground support will

be required in all the horizontal emplacement drifts because Of poor ground

conditions would be approximately 20 percent. This interpretation is not as

applicable as the above interpretation of probability of failure; however,

it is included to show the bounds on possible interpretations resulting from

studies such as this one.

The preliminary conclusion that supplemental ground support will be required

in certain areas of the underground facility because of variability in the

rock mass properties is empirically supported by the results of application

of two rock mass classification systems. The South African Council for

Scientific and Industrial Research (CSIR) and Norwegian Geotechnical

Institute (NGI) rock mass classification systems were applied to the Topopah

Spring tuff (Langkopf and Gnirk, 1986). The results classified the rock

mass as ranging from "poor" to "very good" based on empirically derived

criteria that relate geologic characteristics and properties to expected

ground conditions.

-32-

a .

REFERENCES

Brady, B. H. G., "HEFF, A Boundary Element Code for Two-DimensionalThermoelastics Analysis of a Rock Mass Subject to Constant or DecayingThermal Loading," User's Guide and Manual, RHO-BWI-C-80. Prepared by theUniversity of Minnesota for Rockwell Handford Operations, Richland, WA, June1980.

Hill, R. R., "Subsystem Design Requirements to Support the AdvancedConceptual Design Studies for the Yucca Mountain Mined Geological DisposalSystem," SAND85-0260, Sandia National Laboratories, Albuquerque, NM,February 24, 1986.

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

Langkopf, B. S., and P. R. Gnirk, "Rock-Mass Classification of CandidateRepository Units at Yucca Mountain, Nye County, Nevada," SAND82-2034,Sandia National Laboratories, Albuquerque, NM, February 1986.

MacDougall, H. R. (Compiler), "Site Characterization Plan Conceptual DesignReport," SAND84-2641, Sandia National Laboratories, Albuquerque, NM,November 1986.

Mansure, A. J., "Allowable Thermal Loading as a Function of Waste Age,"Letter Report to R. Hill, Division 6314, Sandia National Laboratories,Albuquerque, NM, February 13, 1985.

McGuffy, V., J. Iori, Z. Kyfor, and D. Athanasiou-Grivas, "Use of PointEstimates for Probability Moments in Geotechnical Engineering,"Transportation Research Record, 809, Department of Transportation, NY, 1981.

Nimick, F. B., "Bulk, Thermal, and Mechanical Properties of the TopopahSpring Member of the Paintbrush Tuff, Yucca Mountain, Nevada," SAND85-0762,Sandia National Laboratories, Albuquerque, NM, estimate May 1987.

Nimick, F. B., S. J. Bauer, and J. R. Tillerson, "Recommended Matrix andRock Mass Bulk, Mechanical, and Thermal Properties for ThermomechanicalStratigraphy of Yucca Mountain," Version 1, Keystone Document Number 6310-86, Division 6314, Sandia National Laboratories, Albuquerque, NM, October1984.

NNWSI Tuff Data Base, Version 3/22/85, Division 6315, Sandia NationalLaboratories, Albuquerque, NM, March 1985.

Ortiz, T.S., R.L. Williams, F.B. Nimick, B.C. Whittet, and D.L. South, "AThree-Dimensional Model of Reference Thermal/Mechanical and HydrologicStratigraphy at Yucca Mountain, South Nevada," SAND84-1076, Sandia NationalLaboratories, Albuquerque, NM, 1985

Rosenblueth, E., "Point Estimates for Probability Moments," Proceedings ofNational Academy of Sciences, Vol 72, No 10, October 1975.

St. John, C. H., "Investigative Study of the Underground Excavations for aNuclear Waste Repository in Tuff," SAND8-7451, Sandia National Laboratories,Albuquerque, NH, May 1987.

St. John, C. M,, "Reference Analyses of the Design of Drifts for Verticaland Horizontal Emplacement of Nuclear Waste in a Repository in Turf,"SAND86-7005, Sandia National Laboratories, Albuquerque, NM, May 1987.

Zeuch, D. H. and M. J. Eatough, "Reference Information Base for the NevadaNuclear Waste Storage Investigations Project," SLTR86-5005, Sandia NationalLaboratories, Albuquerque, NM, April 1986.

-34-

APPENDIX

Parameters Used in This Study and CorrespondingNNWSI Reference Information Base Values

Table A-1

Material Property Data Compared to RIB Values

Material Property

Thermal conductivity

Heat capacity

Density

Elastic modulus

Poisson's ratio

Coefficient ofthermal expansion

Uniaxial compressivestrength

Tensile strength

Friction angle

Cohesion (joint)

Friction coefficient(joint)

Value Used

2.07

2.25

2.34

15.1

0.2

W/m-1C

J/cm3-O0C

S/cm3

GPa

RIB Value

2.07 W/m-OC

2.25 J/cm3 _,C

2.34 g/cm3

15.1 GPa

0.2

10.7 E-6 1/0C

75.4 MPa

9.0 MPa

29.2 deg

1.0 MPa

0.8

RIB Reference

1/3/1/6/1-5

1/3/1/6/1-5

1/3/1/5/1-3

1/3/1/7/1-6

1/3/1/7/1-6

1/3/1/6/1-5

1/3/1/6/1-5

1/3/1/6/1-5

1/3/1/8/1-5

1/3/1/8/1-2

1/3/1/8/1-2

10.7 E-6 1/°C

75.4 MPa

9.0 MPa

29.2 deg

1.0 MPa

0.8

-36-

Table A-2

RIB ValuesGeometric Data Compared to

Geometric Data Value Used(m) RIB Value(m) RIB Reference

Depth below surface(average)

Drift height

Drift width

Radius of roof arch

Panel width

Emplacement driftstandoff

Borehole spacing

300

3.96

5.49

3.25

427

31.1

31.1

*

3.96

5.49

426.7

31.1

31.1

N.A.

2/2/1/1-15

2/2/1/1-15

N.A.

2/2/1/1

2/2/1/14

2/2/1/15

-37-/-38-

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