far-field rock mechanics modelling for nuclear waste disposal
TRANSCRIPT
SKI Report 95:40
SITE-94
Far-field Rock Mechanics Modellingfor Nuclear Waste Disposal
Hakan HanssonOve StephanssonBaotang Shen
July 1995
ISSN 1104-1374ISRN SKI-R--95/40--SE
STATENS KARNKRAFTINSPEKTIONSwedish Nuclear Power Inspectorate
VOL 2 a Hi 1 2
SKI Report 95:40
SITE-94
Far-field Rock Mechanics Modellingfor Nuclear Waste Disposal
Hakan Hansson 1
Ove Stephansson 1
Baotang Shen2
1 Division of Engineering Geology, Department of Civil Engineering,Royal Institute of Technology, SE-100 44 Stockholm, Sweden
2 Current address: Division of Exploration and Mining, CSIRO,P.O. Box 883, Kenmore, Queensland 4069, Australia
July 1995
SKI Project Number 93086
This report concerns a study which has been conducted for the Swedish NuclearPower Inspectorate (SKI). The conclusions and viewpoints presented in the report
are those of the authors and do not necessarily coincide with those of SKI.
NORSTEDTS TRYCKERI ABStockholm 1997
PREFACE
This report concerns a study which is part of the SKI performance assessment projectSITE-94. SITE-94 is a performance assessment of a hypothetical repository at a real site.The main objective of the project is to determine how site specific data should beassimilated into the performance assessment process and to evaluate how uncertaintiesinherent in site characterization will influence performance assessment results. Otherimportant elements of SITE-94 are the development of a practical and defensiblemethodology for defining, constructing and analysing scenarios, the development ofapproaches for treatment of uncertainties and evaluation of canister integrity. Further,crucial components of an Quality Assurance program for Performance Assessmentswere developed and applied, including a technique for clear documentation of theProcess System, the data and the models employed in the analyses, and of the flow ofinformation between different analyses and models.
Bjorn DverstorpProject Manager
SUMMARY
This document is a report covering the far-field part of a rock mechanics studyperformed for the SITE-94 project, initiated by the Swedish Nuclear Power Inspectorate(SKI). The rock mechanics study was carried out by the Division of EngineeringGeology, Department of Civil and Environmental Engineering, Royal Institute ofTechnology, Stockholm, between 1993 and 1995.
The objectives of the far-field rock mechanics study for project SITE-94 were toinvestigate the mechanical influence of thermal loading and glaciation on the stabilityand safety of a hypothetical nuclear waste repository. The Aspo Hard Rock Laboratorytest site was used as the target site for regional and local geology, in situ stress data andmaterial properties.
The far-field study treated the rock mass as an assembly of discrete blocks defined by anumber of major faults and fracture zones. Two computational models with 15 and 23major faults and fracture zones were constructed and studied. Thermal loading due towaste emplacement and mechanical loading from a hypothetical glaciation/deglaciationcycle was applied in order to examine the global behaviour of the rock mass under suchloading conditions. The problem was treated as a three-dimensional one, simulated byusing the three-dimensional distinct element method code 3DEC. From the numericalresults, it was found that a maximum temperature of 48°C would be reached 200 yearsafter the emplacement of the waste canisters. The average increase of maximumprincipal stress due to thermal loading is 9.5 MPa horizontally and 20.2 MPa invertically due to glaciation. The maximum shear displacement induced by thermalloading is 25 mm, and 81.9 mm by glaciation.
11
SAMMANFATTNING
Denna rapport behandlar den storskaliga delen av en bergmekanisk studie initierad avStatens kärnkraftinspektion (SKI). Denna studie ingår i projektet SITE-94 och ärgenomförd vid Avdelningen för Teknisk geologi, Institutionen för anläggning och miljö,Kungliga tekniska högskolan, Stockholm. Projektet har pågått från 1993 till 1995.
Målet med den storskaliga bergmekaniska studien av SITE-94 var att undersökapåverkan på ett fiktivt slutförvar för kärnavfall från uppvärmning och glaciation. DettaGeologin och övriga förhållanden vid Äspö berglaboratorium har använts i störstamöjliga utsträckning som ingångsdata för studien.
Sprickzonerna i den storskaliga modellen definierar bergmassan. I modellerna har 15respektive 23 sprickzoner använts. Uppvärmning orsakad av sönderfall av radioaktivtmaterial samt belastningstillskott på ytan från inlandsis simulerades för att bestämmadet storskaliga betendet hos bergmassan. De tredimensionella modellerna simuleradesmed den diskreta elementkoden 3DEC. Den maximala temperaturen är 48°C och uppnåsefter 200 år. Medelvärdet på spänningsökningen för maximala huvudspänningen,orsakad av uppvärmning är 9,5 MPa i horizontell riktning och under glaciation ärmedelvärdet av spänningsökningen 20,2 MPa i vertikal riktning. Den maximalaskjuvdeformationen för en sprickzon är 25 mm under uppvärmningasfasen och 82 mmvid maximala islasten.
Ill
CONTENTS
SUMMARY i
SAMMANFATTNING ii
1 INTRODUCTION 1
2 GEOLOGICAL MODELS AND DATA 12.1 Geological models 3
2.1.1 The SKB geological model 32.1.2 The SKN geological model 32.1.3 The SKI geological model 6
2.2 Material models and properties 112.2.1 Material models 112.2.2 Properties of rock mass, ice and water 112.2.3 Properties of fracture zones 12
3 LOADING SCENARIOS 163.1 Thermal loading 163.2 Glaciation 19
4 COMPUTATIONAL METHOD 22
5 COMPUTATIONAL MODELS 235.1 Criteria for reducing the number of fracture zones 235.2 Model orientation and boundary conditions 255.3 Geometry of the models 28
5.3.1 Model geometry for SKI model with 23 fracture zones 285.3.2 Model geometry for SKI models with 15 fracture zones 33
6 MODELLING RESULTS FOR THE SKI MODELS 376.1 Introduction 376.2 Temperature distributions 386.3 SKI model with 23 fracture zones 41
6.3.1 Loading sequence 416.3.2 Calculated stresses and comparison with measured values 416.3.3 Deformations 53
6.4 SKI models with 15 fracture zones 566.4.1 Loading sequences 566.4.2 Stresses 586.4.3 Deformations 68
IV
7 DISCUSSION 727.1 Geological interpretations for the Aspo area 727.2 Computational models 727.3 Material models and properties 757.4 Boundary stress conditions 767.5 Excavation of a repository 767.6 Effect of thermal loading 777.7 Effect of glacial loading 777.8 Other factors 78
8 CONCLUSION 79
9 RECOMMENDATIONS 81
10 ACKNOWLEDGEMENTS 82
11 REFERENCES 82
1 INTRODUCTION
SITE-94 is a research project initiated by the Swedish Nuclear Power Inspectorate (SKI).The project is a post closure performance assessment of a hypothetical repository for spentnuclear fuel placed at the Aspo Hard Rock Laboratory (HRL). The HRL is operated by theimplementor, the Swedish Nuclear and Waste Management Company (SKB). Basically alldata from the pre-investigation phase of the HRL have been made available to the project.The data have been independently re-interpreted as part of the project.The present reportis part of the SITE-94 repository performance assessment research project.
Within the SITE-94 subproject site evaluation, four fields were identified to be of majorconcern in the assessment, namely, geology, geochemistry, hydrogeology and rockmechanics. Specific studies in each field will provide information about geologicalstructures, hydrological parameters, transport paths for radio-nuclides and mechanicalstability of rock mass in the Aspo area.
Rock mechanics analysis of a repository was one of the major aspects of site evaluationin the SITE-94 project. Previous studies related to this field were presented in Shen andStephansson (1990), Stephansson and Shen (1991) and Rosengren and Stephansson(1990). Rock mechanics studies will provide information about repository stability, andmovement and propagation of fractures with respect to heat release of waste and futureglaciation. The study was carried out in two different models scales: i) a far-field modelof the approximate size of the Aspo island and ii) a near-field model of the size of atunnel and a deposition hole. The rock structures (fracture zones, faults) for the far-fieldmodelling supplied by SKI (Tiren et al, 1996b) for the Aspo site were used.. The majorresults from this rock mechanics study are the stress distributions, rock mass movement,fracture initiation and fracture propagation. These results can be used for an estimate ofthe mechanical stability of the repository and also as input data for the hydrogeologicalstudies and safety analysis.
The study was performed by using the three-dimensional distinct element code 3 DEC(ITASCA,1994) and a boundary element method code (Shen, 1993). The object of thisreport is to investigate the mechanical behaviour of the rocks in the far-field scale byusing the 3DEC code. Results of the near-field studies are discussed in two separatereports (Shen and Stephansson, 1996 a, b).
The overall task of the far-field study is to provide a comprehensive understanding ofthe impact of thermal loading and glaciation on the rock masses surrounding therepository at Aspo. Due to the existence of fracture zones, faults and otherdiscontinuities at Aspo, the large scale rock mass movement and the stability of therepository will depend on the response of these discontinuities to the loading from heatand glaciation.
The main part of this report is divided into nine chapters. Chapter 1 is an introduction tothe background and objectives of the project. Chapter 2 is devoted to the regional
geology at the Aspo site, material properties and boundary conditions. The loadingscenarios are described in chapter 3. The 3DEC code is described in chapter 4. Thesetting up and descriptions of the computational models are presented in Chapter 5. Themajor results are summarised in Chapter 6, followed by discussions (Chapter 7) andconclusions (Chapter 8). The recommendations are presented in Chapter 9.
2 GEOLOGICAL MODELS AND DATA
2.1 Geological models
There exist several interpretations and models of the geological structures at the islandof Aspo. Considering information from surface mapping, drill holes and seismic data atAspo island SKB presented the first structural map containing 8 major fracture zonesand 15 minor fracture zones (Gustafson et al, 1991). SKN later made their interpretationfrom the existing data and presented an alternative model (Palmqvist et al, 1992). Thismodel contains fewer fracture zones than the SKB model, although the major structuresare similar to the SKB model. SKI later collected more data from surface mapping,seismic reflection, bore hole geophysics and hydrogeological testing in boreholes andpresented a new structural model for Aspo. It contains about 30 major and 25 minorfracture zones. Later Tiren presented a modified SKI model that consists of 52 fracturezones (Tiren et al, 1996b). This model was used for the major part of the simulations inthis study.
2.1.1 The SKB geological model
The SKB model, see figure 2.1, is based on the pre-investigation phase for the AspoHard Rock Laboratory conducted between 1986 and 1990. The purpose of the modelwas to characterise the island of Aspo for the construction of the Aspo Hard RockLaboratory (Gustafson et al, 1991).
2.1.2 The SKN geological model
The SKN model was based on data from SKB and is an alternative interpretation of thegeology in the area (Palmqvist et al, 1992), see figure 2.2. The author also presented acomparison between the SKB and SKN models.
LEGEND
Fracture zones confirmed bydrilling or surface Investigations:f^«» Major fracture zone (width > 5m)
Minor -"- -"- (width < 5m)
TopographIcaI Iy/geophys i caI Iy„-.— indlooted zones
HydraulIc conductorPossible hydraulic conductor
Core drlIIholePercuss i on drI I I ho Ie
Tunnel .n-.o-,,
Figure 2.1 View of the SKB geological model at ground surface( Gustafson et al, 1991).
Aspo
0 100m1 i i
Figure 2.2. The geological prediction model for the Aspo Hard Rock Laboratory(Palmqvist et al, 1992).
2.1.3 The SKI geological model
The first model (January 1993) has been used for the determination of properties forfracture zones at Aspo. The model was updated in February 1994, see figures 2.3 to 2.5.Figure 2.3 is a structural map at the ground surface and figure 2.4 is a structural map atthe depth of 500 m. Figure 2.5 presents a cross section intersecting borehole KAS 02and KAS 03. Measured stresses from these boreholes were later used as boundarystresses in the modelling and for comparison with calculated stresses. The updatedmodel was used for the major part of the study, but the determination of the propertiesof the fracture zones was done with the first structural model. The model was based oncore mapping and interpretation of geophysical data without incorporating data from theconstruction of the Aspo Hard Rock Laboratory (Tiren et al, \996b).
According to Tiren et al (1996b) interpretations of the widths of the fracture zones arebased on the following observations.
The widths of the structures were determined based on to the fracture frequencyrecorded in the cores. The parts of the core with at least two to three times higherconcentrations of fractures than the average fracture concentration in the rock mass,defined the fracture width. The resolution of the width of the fracture zones was onemeter. For fracture zones that are 1-2 m wide, the notations of crushed rock in the coresand geophysical measurements have been used. The large number of fracture zones (52zones), with different strike and dip angle, in the Aspo area results in a large number ofintersections. In the areas close to these intersections there a higher concentration offractures. Therefore, the cores from the intersections were not used to determine thewidths of the fracture zones. Fracture widths that were not confirmed by core drillingwas estimated from other structures within the same set of fracture zones.
Estimates of the fracture widths are listed in Table 2.1. The estimates are rough and thefracture zone widths with a question mark in the table show the greatest uncertainty.The dip direction and dip angle of the fracture zones are also listed in the table.
Almost all the zones, except zone 21, were considered to intersect the geological model.Fracture zone 21 ends at fracture zone 36. The structures that are traceable over Aspoare the following: 1, 2, 3, 5, 6, 7, 14, 16, 17, 19, 20, 24, 27, 28, 29, 30, 31, 32, 33, 34,36, 37, 40, 43, 45, 47, 48, 49 and 51. The lengths of the other structures exceed fivehundred meters. The vertical extensions of fracture zones were estimated to beapproximately of the same magnitude as their lengths. In the modelling the verticalextension of fracture zones was taken to be 1.5 km, except for the largest structures. Thelargest structures intersect the whole computational model.
B8500
toooo
CO
oo
uooo
6000
7500
7000
6500
6500
8000
- 7500
- 7000
6500
SKI modelFracture zonesat Aspb surface
) / Aspo contourat surface
40 Zone id-code
0 500m
Figure 2.3. The SKI structural model with fracture zones in the Aspo area. Horizontal section at ground surface (Tiren et al, 1996b). Thelocations of borehole KAS 02 and KAS 03 are marked.
8500
8000 -
7500
oo1
oo
121152 | 8500
- 7500
7000
SKI-modelZones at -500 m
8000 Ff /
1/ 'Repositoryat -500m
,•• Aspo contour':;...-' at surface
40 Zone id-code
6500 0 500m
oo
CEOSICMA AB/PA 840806
Figure 2.4. The SKI structural, horizontal section at 500 m depth (Tire"n et al. 1996b).
Figure 2.5. Cross section (B-B') intersecting borehole KAS 02 and KAS 03 for the SKI structural model (Tiren et al, 1996b), seefigure 2.3.
10
Table 2.1. The data used for location andmodel in the AspQ area (Tire"n
orientation of fracture zones for theetal, 1996).
SKI
No.
l23456789
10111213141516171819202122232425262728293031323334353637383940414243444546474849505152
Name
NW-lNW-2NW-3NW-4NW-5NW-6NW-7NW-8NNW-1NNW-2NNW-3NNW-4NNW-5NNW-6NNE-E1NNE-E2NNE-E3NNE-E4NNE-W1NNE-W2NNE-W3NNE-W4NNE-W5NNE-W6NNE-W7NNE-LO1E-HI1E-HI2E-HI3E-HI4E-HI5E-HI6E-LO1E-LO2E-LO3ENE-1ENE-2ENE-3ENE-4ENE-5ENE-6ENE-7ENE-8ENE-9ENE-10N-HI1N-HI2N-HI3N-HI4N-HI5N-LO1N-LO2
Strike
(°)30430129829430230830728816134015633816433820520326
194235223
5922024
228238204268
28253265259257268255256249247255243233220243242227222182346350358341351162
Dip dir
(°)3431282432383718
25170
24668
25468
295293116284325313149310114318328294358158343355349347358345346339337345333323310333332317312272
7680887181
252
Dip
(°)76716770706888388187788784897877895667858388788080518289847990753326258789778257321061281486898989651162
Coordinatesx(m)3000274829163000289219593000256422172119244522242209265816721956180020111437100016362642277230003000253530003000100030001632300030003000242530003000300030003000300030003000300030001978104024232475201019312450
in they(m)6557650065006673650065006871650065006500650065006500650065006500650065006500683874688500850083597723722573747680739973198013742973788002767576827270744576567244719073287117713684816500650065006703650065006500
Aspo systemz(m)
00000000000000000000000000000000000000000000
-10000000000
Width(m)<51-51-5<10<10>10<10>101-21-2
>10?1-21-2
calO?1-51-5
5-101-2
5-10ca 101-51-51-2
5-10?5
1-21-51-2<11-2>251-51-5?1-5?1-51-21-55
1-210-20
1-21-2
50-75?10-15
50-75?5-10>5
5-105-101-2<51-2
11
2.2 Material models and properties
2.2.1 Material models
The dominant rock types at Aspo are Aspo diorite and Smaland granite. Theirmechanical properties are similar and they were assumed to have the same mechanicalproperties. An elastic and isotropic material behaviour was used for the intact rock.
For the fracture zones the deformability was assumed to be elastic/plastic with a Mohr-Coulomb failure criterion. The fracture zones were characterised by the friction angle,cohesion, normal stiffness and shear stiffness, see Chapter 2.2.3
2.2.2 Properties of rock mass, ice and water
Laboratory tests of rock samples have been conducted for samples from boreholeKAS 02 (Wikberg et al, 1991). The mean uniaxial compression strength for the diorite is183.5 MPa and for the Smaland granite it is 188.7 MPa. For both the Aspo diorite andthe Smaland granite the Young's modulus is close to 60 GPa and Poisson's ratio is 0.23and 0.24, respectively. Poisson's ratio was 0.32 in the modelling, according to this thedeviatoric stresses are reduced. A more appropriate value should have been closer to thelaboratory data for the specific rock. The thermal expansion coefficient was assumed tobe linear and the thermal conductivity and specific heat of the rock was assumed to beconstant for the considered temperature interval. Table 2.2 gives the value of thematerial properties used in the numerical models.
Table 2.2. Material properties used in modelling. The thermal properties are fromShen (1990). Mechanical properties were based on test from the Aspo area(Wikberg etal, 1991).
PropertyYoung's modulus,E (GPa)Poisson's ratio,V
Shear modulus,G (GPa)Density,p (kg/m3)Thermal conductivity,K (W/m30C)Specific heat,Cp (MJ/m30C)Thermal expansioncoefficient (1/°C)
Intact rock65
0.32
24.5
2700
3.0
2.0
8.5-10"6
Ice—
—
—-
920
—
—
Water
1000
--
12
2.2.3 Properties of fracture zones
This section is based on a method developed by Alrik Lundin at the Division ofEngineering Geology, Royal Institute of Technology. The determination of fracturezone properties at Aspo using this method was also made by Lundin.
The mechanical properties of fractures used in 3 DEC modelling are: (i) normal stiffness(Kn), (ii) shear stiffness (Ks), (iii) friction angle (<f>), and (iv) cohesion (c). Normal andshear stiffness' of fractures are the parameters that define the deformability of thestructure, while the values of friction angle and cohesion are those determining thestrength. Friction angle and shear stiffness are the most important parameters thatcontrol the strength and deformability of fractures. Normal stiffness and shear stiffnessof small single fractures can be estimated based on small scale laboratory tests andexperience based on the fracture characteristics, such as the filling and undulation.
Unlike a single fracture, a fracture zone usually does not have a distinct aperture.Instead, it is a zone that contains several fractures and intercalations of crushed rocks.The deformability of the fracture zone depends on the deformability of the fracturedrocks inside the zone. There is no test data available today for the mechanical propertiesof fracture zones. The mechanical behaviour of a fracture zone is also little understood.To perform the analysis an assumption was made that fracture zones behave like singlefractures with different material properties. Within the range of elastic deformation, thefracture zone is simplified as a zone of elastic material between hard rocks. The normaland shear stiffness of fracture zones depends on the width of the zone and the equivalentYoung's modulus (E) and Poisson's ratio (u) of the crushed rocks in the zone. In thisstudy the following equivalent elastic properties of a fracture zones were assumed:
Young's modulus: E=10 GPaPoisson's ratio: u=0
Non-weathered and hard, intact granite usually has the elastic properties E=40-80 GPa.Therefore, E=10 GPa was assumed to represent a reduced Young's modulus for thefractured and altered rocks in a fracture zone. Normally, no lateral dilation is consideredfor a fracture zone and therefore Poisson's ratio was set to be zero.
When a fracture zone is subjected to normal stress it will be compressed. The ratio ofchange of the width to the original width is called the strain of the fracture zone, seefigure 2.6. According to Hook's law the relation between stress and strain is constantand governed by the relationships:
o n = E - e = E - — (2.1)
an = Kn-Aw (2.2)
where w is the width of the fracture zone and Aw is the change of width under loading.The normal stiffness is then defined as
13
w
Figure 2.6. An elastic plate simulating a fracture zone before and during loading byan uniform normal stress.
frCTs
rFigure 2.7. An elastic plate before and during loading from shear stress.
(2.3)
Similarly the shear stiffness of a fracture zone was calculated with the assumption thatthe relation between shear stress and shear displacement is linear (see figure 2.7):
a = G - a t a n — « G - —S w W
(2.4)
(2.5)
Where Ax is shear displacement, and Ks is the shear stiffness of the fracture zone.The shear modulus (G) is calculated as:
G =2(1 +v)
(2.6)
14
From the equations above we have:
Ks = (2.7)' 2(l + v)w
The method described above defines the elastic properties of the fracture zones.
According to the Mohr-Coulomb failure criterion, T = c + a „ tan(<|>), where the frictionangle (<|>) and cohesion (c) are the two properties that determine the strength of adiscontinuity. From a large number of laboratory experiments and results fromnumerical modelling it is likely the friction angle (<|>) and cohesion (c) of faults andfracture zones are in the range: 15° < <|> < 35° and 0 < c < 20MPa, respectively. Minorfaults and fracture zones were assigned the same <f> and c values. When the strengthparameters in a sensitivity analysis are reduced until a failure occur, it is assumed thatthe minimum value for a combination of <(> and c for which the rock mass at Aspo site isstable can be determined. This combination of § and c is believed to be close to truevalues for the present stable condition.
Considering the fact that no evident sliding along the faults and fracture zones iscurrently observed at Aspo, it was assumed that the present rock mass at Aspo is stable.
Any random combination of the <j> and c values that causes the failure of major faultsand fracture zones is unrealistic. The combination of <]) and c that is found to result in astable rock mass and is close to the state of an unstable rock mass, is likely to reflect themost realistic <j) and c values. These values have been used throughout this study.
Three far-field testing models were established to determine the possible ranges ofcohesion and friction angle values. These models had sizes with a side length of one toone and a half kilometre. The models are generated from the structural data of the Aspoarea as reported by SKB, SKN and SKI. These three models were used to estimate thestrength of major faults and fracture zones in the Aspo area. The models were loadedwith boundary stresses according to the measured stress state in borehole KAS 02, seeequation. 5.1. It was found that the friction angle and cohesion of the faults and fracturezones were most likely to be <|>=20o and c=5 MPa, respectively, see figure 2.8 and Table2.3. It should be mentioned that the suggested values <j>=20° and c=5 MPa are onlydetermined for the most critical fractures that control the stability of the rock mass. Fornon dominating fracture zones the <|> and c values are difficult to estimate in this way.However, since they are considered to have less influence on the rock mass stability, theminor fracture zones were assigned with the same fracture strength as the dominatingfracture zones. In this study the values <|>=20o and c=5 MPa were used for the major partof the modelling of the rock mass response to thermal and glacial load.
The stiffness of fracture zones were determined by their widths, see equation. 2.3 and2.7. For two models The strength properties of fractures were reduced for two of themodels. The fracture properties for the models are listed in table 2.4. The reason for thiswas to study if the stress level in the repository change when the properties of thefracture zones were changed.
15
(a) Ground surface (b) Section A-A'
Figure 2.8. Block movement of the SKI 3DEC model for <t>=15° and c=5MPa.Size and direction of the displacement are indicated by arrows;a) horizontal plane, b) section A-A'.
Table 2.3. Stable and unstable state of the rock mass at Aspo site for differentcombinations of ty and c of the fracture zones.
Friction angle, §
Low (15°)Medium (20°)
High(35°)
Cohesion, c
Zero0
Unstable*#
Unstable#
Stable
Minimum5MPaStableStableStable
MeanlOMPaStableStableStable
Maximum20MPaStableStableStable
* Determined with the SKI 3DEC model. # Determined with the SKB 3DEC model.
Table 2.4. Used properties for fracture zones of the models.Model
E (MPa)Cohesion (MPa)Friction angle (°)Normal stiffness
Shear stiffness
SKI23:4000SKI15:0:aSKI15:400SKI15:4000:a,b
105
20
w
r E
" ' 2(1-v)w
SKI15:0:b
100
20
K - E
W
r - E
"* 2(1-v)w
SKI15:0:c
100
20
w
r E
"* 10(1-v)w
16
3 LOADING SCENARIOS
The far-field study considered thermal load from waste canisters and mechanical loadfrom a glaciation cycle. The hypothetical SITE-94 repository contained about 400 wastecanisters. For comparison a repository with heat load equal to about 4,000 canisters wasalso analysed. The thermal response and the response from a glaciation cycle of the rockmass were modelled in one sequence.
Thermal analyses were made for repositories containing 400 and 4,000 canisters,respectively. The lower number of canisters is approximately the same as for the otherparts of the SITE-94 project. A repository with 4,000 canisters is approximately what isneeded to dispose the total amount of Swedish nuclear waste, if all reactors are phasedout in the year 2010.
The predicted climate change during the next 130,000 years includes three glaciationcycles. The maximum glaciation with different extension and intensity are predicted tooccur after 20,000, 60,000 and 100,000 years. The glaciation with the thickest ice sheetat Aspo is estimated to appear after 60,000 years. This glacial loading sequence was inaccordance with the Central scenario for SITE-94, (King-Clayton et al, 1995).
3.1 Thermal loading
Three different thermal intensities were used for the calculations. They are; no thermalload, 400 canisters and 4,000 canisters, respectively. The heat release parameters from acanister were chosen according to Thunvik and Braester (1991). The initial heat effect,Qo, from a canister at the time of emplacement was 1,066 W. For the first 1,000 yearsafter deposition the following heat source function was used
(3.1)
where Qt is the time dependent heat generation per canister and t is time in years.The constants have the following values:
a , = 7.531212-10-!
a 2= 2.176060 10"2
a 3= 1.277985-10'3
After 1000 years the heat generation was approximated with the following expression
Q,/Qim=o.le-a"+(l-a])e-a"
17
where the constants have the following values:
a ,= 6.0-10-'
a2=1.30-10"3
a 3= 6.00 10 -5
Qmo is the heat generation per canister after 1,000 years and was calculated to be73.3 W (Thunvik and Braester, 1991). This expression was based on data obtained fromHakansson(1990).
The repository was located at the depth of 500 m, see figures 3.1 and 3.2. In therepository the waste canisters were not allowed to be located near a fracture zone. Thedistance from a fracture zone to the closest canister is called respect distance. When themapped fracture width and a respect distance of 10 m are considered, the repository areacan only contain 162 canisters. When the respect distance was neglected the repositorycan contain c. 400 canisters. For 3DEC calculations repositories with both 400 and4,000 canisters were used.
The temperature calculations do not take into account the influence of buffer materialsand because of the large size of the finite elements, the steep temperature gradient nearthe canisters was not considered. The waste canisters and the buffer material are thuslikely to have higher temperatures than those calculated for the surrounding rock mass.
In the repository the spacing between canisters was six meters in the deposition tunnelsand with 25 m spacing between the tunnels. For the model with 400 canisters therepository location without any respect distance can be seen in figure 3.1 and 3.2 (Tirenet al, 1995b). The repository area was 77,000 m2 and according to this the thermal heatrelease was equal to 5.6 MW/km2 at the time of emplacement. For the modelssimulating 4,000 canisters the canisters were evenly distributed over an area of 825meters square (figure 3.2). The repository contains 31 tunnels with 129 canisters in eachtunnel. Respect distance was not considered in the models and only the widths of 15fractures were considered when the distributions of canisters were determined. The heatrelease at the time of emplacement was 6.1 MW/km2 for the repository with c. 4,000canisters. If a greater number of fracture zones or the respect distances had beenconsidered when the area for the repository was determined, the repository will increasein size. This would decrease the thermal effect per square kilometre. The rock in theAspo region has a large number of fracture zones and was considered to be of poorquality. Therefor, an exact prediction of the area that is needed for a repository isdifficult to present.
18
NW SE
Figure 3.1. Location of repository at 500 m depth, vertical section NW-SE. Thehorizontal extension of a small repository with 400 canisters and a largewith c. 4,000 canisters, respectively are indicated. The figure is1.5x1.5 km
Repository defined for400 canisters.
Repository defined for4000 canisters.
Figure 3.2. Location of repository, horizontal section at 500 m depth. The respectdistance was not considered in the layout of the repository. The figure is1.5x1.5 km
19
3.2 Glaciation
The central scenario (King-Clayton et al, 1995) describes the future climatic changes inSouthern Sweden within the next 130,000 years. The maximal ice thickness wasestimated to be c. 2,200 m after 60,000 years. The same thickness of ice in the Aspoarea was also assumed for the maximal glaciation that occurred c. 10,000 years ago.
Permafrost
The permafrost causes expansion of fractures due to the freezing of the water down to340 m depth after in 50,000 years (King-Clayton et al, 1995). Whether permafrost hasany significant influence on the stability and deformabilty on the rock mass is difficultto predict. However, the rock will contract due to the cooling effect and this may reducethe horizontal stresses in the upper part of the bedrock. Because of the uncertaintieslisted above and the difficulties to simulate the permafrost, it was neglected in thisstudy. However, depth of permafrost distribution is discussed in more detail in King-Clayton et al (1995).
Forebulge
In front of the advancing ice a forebulge is likely to develop. However the feasibility ofoccurrence of this is still under discussion. According to King-Clayton (personalcommunication, 1994) the ground surface is likely to be subsided with approximately30 m at the ice front and be uplifted approximately 70 m about 130 km away from theice. These values are very approximate. There is a risk that the bending of the uppercrust can expand fracture widths. However, the development of a forebulge wasconsidered to give small stress changes and displacements and therefor have negligibleeffect on the stability of the rock mass at repository depth. Therefore, this effect was notconsidered in this far-field study.
Advancing ice front
The direction of the ice movement in the Aspo area is from North-West towards South-East, see figure 3.3. The weight of the ice will cause a vertical load on the bedrock,which was considered in the simulation. The ice was considered to be cold based untilthe thickness is approximately 500 m. This means that the ice sheet is in contact withthe ground. The shear stress created from friction at the ice-bedrock interface wasassumed to affect only a thin layer of the rock mass near the ground surface. Thiserosion effects of the ice was assumed to have no effect on the stability of the rock massat repository depth.
20
NW
Figure 3.3. Ice shape of advancing ice sheet.
Glaciation and deglaciation
The ice thickness was considered to gradually increase to 2,200 m after 60,000 yearsand thereafter the ice sheet retreats, see figure 3.4. Where the ice thickness exceeds500 m the ice sheet is likely to be warm-based. Under the ice there will be a film ofwater and the water pressure on the ground and in fracture zones near the surface will beequal to the weight of the ice. The water pressure will reduce the effective stresses in thefractures and thereby cause a reduction of effective stress across the fracture zones. Theinfluence of the water pressure is at maximum when the ice reaches its maximumthickness. An important factor is if hydraulic connections to the ground surface exists, ifthis is the case the water pressure can be applied in the fracture zones. This was notconsidered in the calculations, because the fracture properties were not determined forthis type of loading.
The glacial cycle with its maximum thickness 60,000 years after the emplacement of thewaste was estimated to end c. 75,000 years after the deposition of waste. During theretreat of the ice sheet the Baltic sea is likely to be dammed and the sea level wasassumed to be c. 100 m higher than the present sea level. When the ice front retreats, a200 m high ice cliff was assumed to appear, see figure 3.5 and 3.6. This gives a smallbut sharp discontinuity in the applied loading. However, the difference in ice loadingand water pressure is small and should not have any severe effect on the stability nearthe repository, although there can be local effects near the surface. The loadingconditions after the glaciation were assumed to be equal to the conditions today.
NW SE
Figure 3.4. Maximal glaciation with 2,200 m thick ice c. 60,000 after emplacement ofwaste. The high pressure at ground level causes the ice to melt and the icewill float on a water film.
21
NW
300m ice
SEr > 200 m ice cliff
+100 m sea level
Figure 3.5. Retreating ice sheet with 200 m high ice cliff above repository.
NW SE
Figure 3.6. Retreating ice sheet with 100 m water above repository.
22
4 COMPUTATIONAL METHOD
The calculations were made with a three-dimensional Distinct Element Code, 3DECversion 1.5. The determinations of fracture properties were made with the earlier version1.34. The computational models consisted of an assemblage of deformable blocks whichwere further discretized into finite difference elements. The blocks were defined by theintersecting fracture zones. The fracture zones in the computational models wereconsidered to be nominally planar and their locations were defined by coordinates ofany point of the fracture, dip directions and dip angles. The coordinate system used in3DEC is left hand oriented with y-axis upward, x and z-axes in the horizontal plane. Theprogram solves the equations of motion of deformable blocks and elements directly withsmall time steps. The algorithm can handle large displacements and deformations of therock mass.. For the static load the solution was obtained when the velocities in themodel approach zero. All stresses that are presented are total stresses and tensile stressesare by definition positive.
For the thermal calculation, the rock mass was assumed to be an infinite, thermallyisotropic medium. The temperature distribution of a point source was given by thefollowing equation:
T = %-, exp|—I (4.1)
where Q = quantity of heatp = density of rockCp = specific heat of rockK = thermal conductivity of rockt = time after source releaser = distance between heat source and observation point.
Based on this expression the temperature distribution for an exponential decay sourcefunction is obtained by integration over the considered time period. For a linear sourceor planar source the results are given by an area integration. In 3 DEC this integration issolved numerically for the specified time period. The present version of 3 DEC has onlyadiabatic and isothermal boundaries available for the thermal calculation.
All calculations were performed on personal computers, mainly a 90 MHz Pentium with32MB memory.
23
5 COMPUTATIONAL MODELS
In order to simulate the behaviour of the rock mass the geological data has to beinterpreted and a model for numerical calculation has to be established. One of theproblem in simulation is to describe the properties of the fractures length persistence,frequency and undulation. The undulation and surface characteristics of the zones affectthe strength of the fractures. In the modelling the fractures were assumed to be planarand the strength properties were governed by the friction angle and cohesion.
5.1 Criteria for reducing the number of fracture zones
Due to limitations of computer capacity, it was impossible to include all the fracturezones suggested in the different geological structural models in the computationalmodels. In order to simplify the structural model and thereby reduce the time needed forthe calculations, the number of fracture zones in the structural models was reduced.Fracture zones that were considered to have small influences on the stability of the rockmass close to the repository were eliminated. The following criteria were used to reducethe number of fracture zones at AspO. The options are presented in the same order asthey were applied:
1. Non-persistent fracture zones have a limited length and do not connect orintersect with other faults or fracture zones were omitted. These fracture zonesmay cause stress concentrations at their ends but do not cause largedisplacements. The displacements of these fracture zones are restrained by theintact rock at both ends. This option was not applicable to the SKI structuralmodel where almost all identified structures were considered to intersect thegeological model.
2. Uncertain fracture zones were omitted. In the geological models the fracturezones were divided into different groups based on the certainty of their existence.The uncertain fracture zones were excluded in the computational models.
3. Fracture zones that only cut an edge or a corner of the inner region of the modelswere excluded. This was justified because they have very little impact on the rockmass response at the centre of the models. The same applies to very shallowfractures. These were not considered to influence the rock mass behaviour andthe stability near the repository. Examples of this type of fractures are given infigure 5.1. The mechanical stability of the repository area was not considered tobe effected by these small zones far away from the repository.
4. Fracture zones close to each other were shown as one fracture zone and theirwidths were added together. If there exist a dominating zone, the location of thedominating zone was used, otherwise an average location of the fracture zoneswas used for the combined zone. This is only valid if the fracture properties havea linear relationship versus the fracture width, otherwise the properties have to be
24
adjusted for this relationship. Examples of this are fracture zones 1 to 3 and 5,which were merged into one zone in the model with 23 fracture zones, see figure5.2.a. Zone 5 was considered to be most important for rock stability, because thiszone was considered to be wider than the adjacent fracture zones. Therefore themajor parts of the displacements were considered to occur along this fracturezone. For the same reason zone number 9,10,12 and 13 were also merged intoone zone for this model, see figure 5.2.b
Figure 5.1. Zones 22, 24, 34,42 and 51 in the SKI model were consider to be of lessimportance and were omitted because they were shallow or were smallzones at a large distance from the repository.
(a) (b)
Figure 5.2. a) Orientation of fracture zones 1 to 3 and 5. b) Orientation of fracturezones 9, 10, 12 and 13.
5. Vertical or sub-vertical fracture zones with strikes close to the orientation of thehorizontal principal stresses were omitted in the model. These fracture zones willprobably not cause failure in shear because none, or only minor, shear stress is
25
likely to exists along the plane of these fractures. Examples of this category arepresented in figure 5.3.
Zone no. 21
,Zone no. 25
Figure 5.3. Zone 21 and 25 are steep fractures oriented parallel with the minorprincipal stress.
6. Fracture zones with the smallest widths were excluded as a last option.
The criteria presented above were used in several models, with different chosen options.Fractures which fall in the above options were excluded in sequential order until thetotal number of remaining fractures was equal to the accepted number. The approachwas the same for all models. The differences between the computational models werethe number of fracture zones that were eliminated. Fracture elimination was carefullydone to keep the balance between accuracy and complexity of the models. Section 5.3describes the computational models.
5.2 Model orientation and boundary conditions
The models were oriented so that the vertical boundaries coincide with the averagedirection of the maximum horizontal stress, i.e. in the direction N40°W (z-axis) and theaverage direction of the least horizontal stress N50°E (x-axis) at Aspo, see figure 5.4.The largest horizontal stresses were measured in borehole KAS 02 in the directionbetween N12°W and N68°W and in borehole KAS 03 the directions vary betweenN16°W and N65°W (Wikberg et al, 1991). For convenience the ice movement wasconsidered to be in the same direction as the major principal stress (N40°E). This valuewas well within the limit of uncertainty for the direction of the ice movements in theAspo area.
26
N
Figure 5.4. Model orientation and direction of principal horizontal stresses. Theorientation of the z-axis was N40°W.
The mean values from a regression analysis of the stress data from the boreholesKAS 02 and KAS 03 are presented below.
KAS02:All depths
cH=7.44+0.068 yah=3.74+0.037 y<jz=0.027 y
(5.1)
<515 m depthCJH=0.02 1+0.042 yGh=-0.10+0.023 yaz=0.027 y
(5.2)
KAS 03:All depths
CTH=6.43+0.051 y
ah=2.76+0.027 yaz=0.027 y
(5.3)
<739 m deptha^-4.49+0.026 yah=-3.49+0.012 yaz=0.027 y
(5.4)
where aH, ah, are the two horizontal stresses and CTZ the vertical stress, respectively, y isthe depth in meters with negative values downwards from the surface (Tiren et al,1996a). Tensile stresses are taken as positive. These expressions are based on(Bjarnasson et al, 1989).
27
Stress data from borehole KAS 02 give the maximum horizontal stresses and stressgradients. The borehole was also located close to the centre of the hypotheticalrepository. Therefore, stress data from KAS 02 was used as boundary stresses in the far-field modelling of the repository.
The base of the models were fixed in all three directions. Vertical boundaries hadstresses equal to measured stresses from KAS 02 applied during consolidation from theintrinsic weight of the rock mass. For the calculations following this stage the verticalboundaries did not allow normal displacement to occur, this was done to allow increaseof horizontal stresses during loading. The ice load was applied as stress at the groundsurface and all stresses that were applied and calculated were total stresses. Variation inwater pressure caused by glaciation was not considered. The two types of boundaryconditions are shown in figure 5.5.
Fixed in normaldirection.
77//////////////Fixed in all directions.
(a)
Figure 5.5.
(b)77//////////////
Boundary conditions of 3 DEC models when different events weresimulated. Boundary conditions in x and z directions are the same,a) Applied boundary stresses during consolidation by the weight of therock mass, b) Vertical boundaries have no normal displacements for allloading events following the consolidation from the weight of the rockmass.
According to King-Clayton et al (1995) the surface temperature at Aspo was determinedto be approximately 7°C and decreases during the next 20,000 years to -4°C. Thetemperature during the first 1,000 years of the repository life time was considered to beof greatest interest, therefore the thermal boundary condition at the ground surface wasassumed to have a constant temperature of 6°C and all other boundaries have naturalboundary conditions at infinity. The thermal gradient used for the modelling was 16°Cper kilometre of depth. This value was probably too high for the Aspo area.King-Clayton et al (1995) have suggested a thermal gradient of 9°C per kilometre at thepresent conditions in the Aspo area.
28
5.3 Geometry of the models
The structural model of SKI (Tiren et al, 1996b) was simplified into three differentcomputational models; two of the models contain 15 fracture zones and the third modelcontains 23 fracture zones.
The models were cubic with four kilometres side lengths and the central region is a cubewith one and a half kilometre side length. In a horizontal plane the inner region waslocated in the centre of the model and downwards from the surface. The inner regionwas defined by fictitious fractures with high stiffness and strength. This was to restrictdisplacements along the interface, see figure 5.6. The mean values of the widths offracture zones were according to Tiren et al (1995b), see section 5.1. When severalfractures were merged as one fracture zone, the sum of the widths was used as width forthe new fracture. The major fracture zones intersect the whole model, while the minorfracture zones are restricted to the central region.
Figure 5.6. SKI model with 4 km side length and an inner region with 1.5 km sidelength.
5.3.1 Model geometry for SKI model with 23 fracture zones
When the model was defined the relative small blocks that occur in the outer part of thecentral region have not been intersected by any other fracture zone. This was done toavoid very small blocks in contact with the outer region. This operation was assumed tohave minor effect on the response in the central part of the model. The high accuracythat was used for the fracture zones leads to some very small blocks, even less than tencubic meters. To avoid problems during generation of finite difference zones in blockswith small volumes, the blocks with a volume smaller than 110 cubic meters wereremoved from the model. This was considered to have small influence on the rock massresponse. To be consequent with our classification of fracture zones the zone 44 shouldhave been intersecting the whole model. However, if zone 44 was considered as a majorzone, the finite difference elements in the outer region of the model have to be smaller.This was not considered to be practical because of the available computer capacity.
29
Different stiffness values were used for the central part of the model for the majorfracture zones. The selections of fracture stiffness were based on the width of thefracture zones, see table 5.1. The fracture zones in the outer part of the computationalmodel were considered to represent a larger number of fractures due to the lowerfracture frequency in the outer region of the computational model. Because of thelimited numbers of fracture widths that can be used in 3DEC, the fracture zones weredivided in groups. This leads to small discrepancies in the widths between thegeological interpretation and the numerical model. The smallest fracture width in thecomputational model was five meters. Fracture zones with a width equal to or smallerthan 5 m were given the width 5 m in the computational model. Fracture zones with awidth less than three meters were omitted in the model. This means that total 42 of the52 fracture zones were incorporated in the computational model, either separately ormerged with adjacent fractures. The ten fracture zones that were not incorporated in themodel were the fracture zones with smallest widths or fractures close to edges of themodel.
Figure 5.7 shows a perspective view of the fracture zones after the elimination process.This model contains 23 fracture zones, see table 5.2. The computational 3DEC modelsare presented in figure 5.8.
Figure 5.7. Perspective view of the structural model after reduction of fracture zones(Tirenetal, 1996).
30
Table 5.1. Comments to selection of fracture zones for the model with 23 fracturezones.
Comments for fracture selection Remainingzone
Zone 4 is kept 4Zones 1-3 and 5 are merged. 5Zones 6 and 8 are quite wide and are not close to any other zones. 6, 8Zone 7 is deleted. According to Tiren (personal comment) the existenceof this zone is uncertain.The group of zones from 9 to 13 merged into one zone, except for zone 911.Zone 11. 11Zones 14,48 and 49 are merged into two fracture zones. 14, 49In the group 15 to 17 zones 15 and 16 are merged to zone 17. The two 17firsts mentioned zones are small compared with zone 17.Zones 18 and 26 are merged. 18Zone 23 is neglected because of small fracture width.Zone 20 is considered to be important for modelling reasons. 20Zone 21 is close to the repository. 21Zones 22 and 24 are close to a corner respective an edge of the definedinner region. They are considered to have little effect on the stability ofthe rock mass and are therefore neglected.Zone 25 is near the centre of the repository and is quite wide. This one is 25included in spite of its favourable orientation compared with theorientation of the principal stresses.Zones 27 and 30 are merged. 27Zones 32 and 38 are merged. 38Zones 28, 29, 36 and 39 are merged. 36Zone 31 is one of the largest structures in the area and is kept. 31Zone 34 is close to a corner of the inner region. This zone is consideredto have little effect on the repository area.Zones 33 and 35 are merged. The most important one from rock stability 33is considered to be zone 33.Zone 37 is kept in this model. 37Zones 19,40 and 43 are merged. 43Zones 41 and 44 are merged. The largest zone is 44. 44Zone 42 is very shallow and is therefore neglected from the model.Zone 45 is the Avro fault zone. This is one of the largest structures in the 45area.Zone 46 is kept. 46Zone 47 is outside the inner region and it is narrow and is thereforeomitted.Zones 50 to 52 are neglected in the model, the zones are narrow and 50, 52zone 51 is also very shallow.
31
Table 5.2. Orientations and widths of the remaining 23 fracture zones after thereduction process. The minor fracture zones only intersect the innerregion. Remaining fracture zones after simplification of the geologicalmodel.
Zone
45*
689*
11
14*
17*
18*20212527*3133*36*3738*43*
44*454649*
Merged zones
41-3,5
9-10, 12-13
14 and half thewidth of 48
15-17
18,26
27,30
33,3528,29,36, 39
32,3819,40,43
41,44
49 and half thewidth of 48
Width
(m)
512.5
10105
15
15
12.5
310355
255537.5
65
1565
7.510
Type of zone
MinorMajor
MinorMinorMinorMajor
Major
Major
MinorMinorMinorMinorMinorMajorMinorMinorMinorMinorMajor
MinorMajorMinorMinor
Containszones no. asmajor zone.
Zones 1-5
Zones 9-12
Zones 14,48and 49
Zones 15to 17
31
Zones 19,40and 43
Zone 45
Width asmajor zones
(m)
17.5
25
25
12.5
25
65
65
* Merged with other zones.
The SKI model with 23 fracture zones consisted of 1,024 blocks and 84,574 finitedifference elements. The model requires 26Mb memory. In the centre of the inner regionthe edge length of discretized elements was 30 m and it was increased to 100 m near theouter region. In the outer region the zone size varied from 125 m close to the innerregion to 500 m near the outer boundaries.
32
(a)
(b)
Figure 5.8. Geometry of the far-field computational model with 23 fracture zonesafter the reduction process, a) Global view of the model, 4x4x4 km.b) A detailed view of the inner region, 1.5x1.5x1.5 km.
33
5.3.2 Model geometry for SKI models with 15 fracture zones
A computational model containing only 15 fracture zones was also set up by using the3DEC code. The sizes and orientations of both the inner region and the model wereidentical to the model with 23 fracture zones. An exception was a model without theinner region defined. For this model, called SKI15:4000:b, all of the fracturesintersected the whole model. Tables 5.3 and 5.4 lists the selected fracture zones.
Figure 5.9 show the global geometry of the models and the geometry of the inner regionof the model. The purpose of this model was to study the influence when differentfracture zone density was considered, the fracture properties were changed and influencefrom the inner region. The model with an inner region consists of 337 blocks whichwere discretized into 38,696 finite difference elements and requires 12 MB RAM. In themodel without an inner region (SKI15:4000:b) there were 405 blocks and 42,192 finitedifference elements.
34
Table 5.3. Comments to selection of fracture zones for the model with 15 fracturezones.
Comments for fracture selection. Remainingzone.
Zone 1 to 5 are merged. 5Zones 6 and 8 are quite wide and are not close to any other zones. 6, 8Zone 7 is deleted. According to Tiren (personal communication, 1994)the existence of this zone is uncertain.Of zones 9 to 13 the dominating zone is 11. All the others in this group 11are merged to this one.Zones 14,48 and 49 are merged to one fracture zone. 48In the group 15 to 17, zones 15 and 16 are merged to zone 17. The two 17firsts mentioned have small widths when compared with zone 17.Zones 18,23 and 26 are neglected because of their small width.Zone 20 is considered to be important for modelling reasons. 20Zone 21 is near the centre of the repository, but has a favourableorientation compared with the orientation of the principal stresses. Thiszone is neglectedZones 22 and 24 are close to a corner respective an edge of the definedinner region. They are considered to have little effect on the stability ofthe rock mass and are therefor neglected.Zone 25 is passing through the repository and is quite wide. This one is 25included in spite of its favourable orientation compared with theorientations of the principal stresses.Zones 27, 30, 32 and 38 are merged. 38Zones 28, 29, 36 and 39 are neglected. These are located quite close tozones 32 and 38.Zone 31 is one of the largest structures in the area. 31Zone 34 is close to a corner of the inner region. This one has little effecton the repository area.Zone 33 and 35 are merged. The most important one from rock stability 33is considered to be zone 33.Zone 37 is narrow and is deleted.Zones 19, 40 and 43 are merged. 43Zones 41 and 44 are merged. The largest zone is zone 44. 44Zone 42 is very shallow and is therefore neglected from the model.Zone 45 is the Avro fault zone. This is one of the largest structures in the 45area.Zone 46 is kept. 46Zone 47 is outside the central region and it is narrow, therefor it isomitted.Zones 50 to52 are neglected in the model. The zones are narrow andzone 51 is also very shallow.
35
Table 5.4. Orientations and widths of the remaining 15 fracture zones after thereduction process. The minor fracture zones only intersect the innerregion.
Zone
5*68
1117*20253133*38*43*44*454648*
Merged zones
1-5
9-1315-17
33,3527, 30, 32, 38
19,40,4341,44
14,48,49
Width (m)
17,510102512105
255
126514657,5
25
Type ofzonesMajorMinorMinorMajorMinorMinorMinorMajorMinorMinorMajorMinorMajorMinorMajor
* • : Merged with other zones.
36
(b)Figure 5.9. Geometry of the far-field computational model with 15 fracture zones
after the reduction process, a) Global view of the model, 4x4x4 km. b) Adetailed view of the inner region, 1.5x1.5x1.5 km.
37
6 MODELLING RESULTS FOR THE SKI MODELS
6.1 Introduction
The structural model supplied by SKI (Tiren et al, 1996b) was simplified into threedifferent computational models, two of the models contain 15 fracture zones and thethird model contains 23 fracture zones. For description of the models see chapter 5. Themodels were named SKIn:m:o, where n is the number of fracture zones, m is the numberof canisters and the option o stands for different fracture parameters or differentgeometry. The size of all the models was 4x4x4 km. Consolidation of the models wasdone for a loading that simulates the previous glaciation with an ice thickness of 2,200meters. This consolidation was done for all the loading sequences with or withoutthermal loading. After consolidation the ice loading was removed to reach a stagecorresponding to the present conditions. The displacements that occurred duringconsolidation were omitted in the presentation of the results.
A comparison between the calculated and measured stresses in KAS 02 and KAS 03were done for the model with 23 fracture zones. This model was the main computationalmodel.
The calculated temperatures for the rock mass are presented in section 6.2. Thetemperatures were obtained regardless of fracture geometry. The reason for this was thatthe thermal properties were for a homogen and isotropic rock mass.
In the following sections the calculated temperatures, stresses and displacements arepresented. The stresses versus depth near the centre of the repository are presented firstand then followed by the variation of stresses in the repository plane. The monitoringpoint for the time dependent variation of stresses in the centre of the repository waschosen in an area with high stress concentrations during glaciation. The samemonitoring point was used for all models. A profile A-A' across the centre of the modelis used to present the results, see figure 6.1. The maximum displacements in therepository area for fracture zone 43 are presented for all models.
38
A'
750m
0 Z
Repository for400 canisters.
Repository for4000 canisters.
-750m
Figure 6.1. Profile, A to A, where temperatures are calculated and presented in figure6.2 and 6.3. Horizontal section, 1.5x1.5 km, at the depth 500 m.
6.2 Temperature distributions
The peak temperature for the repository was reached about 200 years after theemplacement of the waste. The temperatures for the repositories with 400 and 4,000canisters were 35°C and 47.5°C, respectively. For the large repository with 4,000canisters, the maximum temperature in the model remains nearly constant from 200 to400 years after emplacement. After 400 years, the temperature distribution was morehomogeneous and a larger volume of the rock mass had increased temperature, thanafter 200 years, see figures 6.2 and.6.3 for the temperature distribution along profile A-A' for the repository with 400 and 4,000 canisters, respectively. Figure 6.4 shows thetemperature distribution at the depth of the repository 200 years after the emplacementof the waste.
E0>
50 -j-
45 -
40
35 -•
30 •
25 ••
20 -
15 -
10--
5 --
0
39
200 years •400 years 1,000 years
-700 -500 -300 -100 100
^coordinate (m)
300 500 700
Figure 6.2. Temperature distribution along profile A-A' in the repository from thermalheating by 400 canisters.
10
5 - •
-100 years
-1,000 years
60,000 years
200 years
2,500 years
•400 years
-10,000 years
0
-700 -500 -300 -100 100
Z-coordinate (m)
300 500 700
Figure 6.3. Temperature distribution along profile A-A' in the repository from thermalheating by 4,000 canisters.
40
geometric scale
i •
2E+02
Temperatureinterval =
min4.500E+013.750E+013.000E+012.250E+011.500E+OI
contours2.500E+00
max4.750E+014.250E+013.500E+012.750E+012.000E+01
Figure 6.4. Temperature distribution in a repository with 4,000 canisters 200 yearsafter emplacement.
41
6.3 SKI model with 23 fracture zones
6.3.1 Loading sequence
One combined thermal and ice loading sequence was calculated for the SKI23:4000model. Glaciation with a maximal load from a 2,200 m thick ice sheet was used forconsolidation of the model. The thermal response from a repository with 4,000 canisterswas calculated 200, 400, 1,000 and 60,000 years after emplacement of waste. Thethermal response from the glaciation was neglected. The glaciation sequence wasdivided into five loading steps. These were 1,000 m ice, 2,200 m ice, 1,000 m ice, 200m ice cliff and 100 m water level, see table 6.1. The last loading step was with a freeground surface.
6.3.2 Calculated stresses and comparison with measured values
The measured stresses in borehole KAS 02 and KAS 03 were used for comparison withthe initial stress field in the numerical model, see figure 6.6 and 6.7. Thereafter, the timedependent variations and the variations inside the repository are presented. The differentstress components are presented during the most severe loading sequences for theprofile A-A'(see figure 6.1) that intersects the repository. The reason is to indicate thelocal influence from the fracture zones on the stress distribution and the magnitude ofthe stress components. The locations of the boreholes are presented in figure 6.5 andcalculated stresses and measured stresses (Bjarnasson et al, 1989) are presented in figure6.6 to 6.8. Although there are discrepancies between the calculated and measuredstresses between 500-800 m, especially for borehole KAS 02, conformity generally isfairly good, see figure 6.7.
NW SE
B , KAS03 KAS02 Depth
B
-500 m
- 1000 m
Figure 6.5.(a) (b)
Location of boreholes KAS 02 (924 m deep) and KAS 03 (1024 m deep)a) Horizontal section at 500 m depth, 1.5><1.5 km. b) Vertical section(B'-B).
42
Table 6.1. Loading sequence for the model with 23 fracture zones, SKI23:4000.Type of glacial loading. Description of
loading stage.Consolidation fromrock weight.
~Consolidation from2,200 m icethickness.
V \Unloading with1,000 micethickness.
, Repository location
Present conditions
Thermal response200,400,1,000 and60,000 years afteremplacement.
Loading with 1,000m ice thickness.
U \ V V \ Loading with 2,200m ice thickness.
Loading with 1,000m ice thickness.
Loading with 200 mice thickness.
Loading with 100 mwater above therepository.After glaciation, freeground surface
43
The discrepancy between the calculated stresses and measured stresses are caused by thelocal geometry of the fracture zones and insufficient knowledge of the mechanicalbehaviour of the fracture zones.
Stress (MPa)
10 0 -10 -20 -30 -40 -50
-100
-200
-300
-400 .
-500
-600.
-700
-800.
-900
-1000 .
1
•
V
KAS 02
Maximumhorizontal
*V"^^stress, Szz
' Minimumhorizonta
- stress, Sxx
A 1
V ^ L . stress, Syy\ \
\
\1
\ \
•
\
Stress (MPa)
10 0 -10 -20 -30 -40 -50
0
-100
-200
-300
-400
-500
-600
-700.
KAS 03
^ Vertical stress, Syy
Maximum. horizontal.stress, Szz
Depth (m)
-1000Depth (m)
(a) (b)
Figure 6.6. Calculated stresses at locations of borehole KAS 02 and KAS 03.a) KAS 02. b) KAS 03. Calculated stresses are presented in the directionof the x-axis and z-axis of the model, these stresses are approximatelyequal to the principal stresses.
Stress (MPa)
10 0 -10 -20 -30 -40 -50
Stress (MPa)
10 0 -10 -20 -30 -40 -50
Stress (MPa)
10 0 -10 -20 -30 -40 -50
Stress (MPa)
10 0 -10 -20 -30 -40 -500
-100
-200
-300
-400
-500
-600
-700
-800
-900
-1000
Depth (m)
11(1A-V-> x
Calculated(Szz)
KAS 02
.__ Measured(SH)
v.X
(a)
-1000
Depth (m)
Calculated(Szz)
(a)
o
-100
-200
-300
-400
-500
-600
-700
-800
-900
-1000
Depth (m)
(b)
> Mea.sured
\\ (Sh)
. Calculatedg . ^ (Sxx)
VKAS 03 \
Figure 6.7. Measured and calculated stresses for boreholeKAS 02. a) Maximum horizontal stress, b) Minimumhorizontal stress.
Figure 6.8. Measured and calculated stresses for boreholeKAS 03.a) Maximum horizontal stress, b) Minimumhorizontal stress.
45
Repository defined for400 canisters.
I j
Repository defined for4000 canisters.
Figure 6.9. Position of monitoring point for rock stresses inside the repository ofmodel SKI23:4000. The x-axis is parallel to the direction of the averageminimum principal stress. Horizontal section, 1.5x1.5 km, at 500 m depth.
The calculated peak stresses during thermal loading appear after approximately 200years and can be seen in figure 6.10 and table 6.2. The stresses were more homogeneousand evenly distributed for the glacial loading than during the thermal loading. For bothloading conditions the stresses reached almost the same magnitudes, but the maximumprincipal stress has different orientation, see figure 6.10. The limiting criteria forfracture propagation was taken to be a stress ratio of minimum versus maximumprincipal stress less than 0.25 (Shen and Stephansson, 1996). This condition is exceededin some areas near fracture zones approximately 200 years after emplacement, but theoccurrence of such conditions during glaciation are few. The stress state after 60,000years of thermal loading and after a glacial cycle is close to the present state.
Regions with low ratio between vertical stress and maximum principal stress werelocated near fracture zones, see figures 6.19 and 6.20. The maximum compressive stressat these locations were mostly less than 20 MPa and at some locations there were tensilestresses, see figure 6.20. The tensile stress was approximately 5 MPa, but there existextreme values that exceed 20 MPa close to some contacts in the rock mass. These areaswere assumed to have minor effect of the stability of the rock mass. At the 500 m depththe distance from the fracture zones to areas with low stress ratio or tensile stress wasless than 100 m.
The stress states after 60,000 years of thermal loading and after the glacial cycle wereclose to the stresses at present conditions. Figures 6.14 to 6.18 present the variation ofstress components along the profile A-A' for different loading. Syy is the vertical stress.Sxx and Szz are the two horizontal stresses in the direction of the average in-situprincipal stresses. Below the diagram is a cut out of figure 6.13 showing the fracture
46
zones. The calculated stresses along profile A-A' vary by the same magnitude as thediscrepancies between calculated and measured stresses. Hence, a stress variation of theorder of ±10 MPa is likely to occur at 500 m depth due to the existence of fracturezones. During the thermal loading the horizontal stresses are strongly increased, whilethe vertical stresses are only slightly increased.
^.OOE+07
£ -1.00E+07to
_»_Sxxj
-«-Sxy|
—*—Sxz !
- X - S y y !
-X-Syz
m Szz
5 6 7
Loading step
10 11
Figure 6.10. Stress response during eleven loading steps for model SKI23:4000.Loading step; 1 :Present conditions. 2: Thermal response after 200 years.3: Thermal response after 400 years. 4: Thermal response after 1,000years. 5: Thermal response after 60,000 years. 6: 1,000m ice thickness.7: 2,200m ice thickness. 8: 1,000m ice thickness. 9: 200m ice cliff.10: 100m water. 11: After glaciation.
Table 6.2. Calculated stresses in a repository with 4,000 canisters.Present conditions
Average5% percentile*95% percentile*
Sxx(MPa)-10.0
-5.8-15.8
Syy(MPa)-10.1
-2.8-18.1
Szz(MPa)-16.2-10.7-22.0
Sxx/Szz
0.620.420.86
200 years after emplacement
Average5% percentile*95% percentile*
Sxx(MPa)-20.8-16.2-25.9
Syy(MPa)-12.8
-5.4-21.3
Szz(MPa)-25.7-20.0-31.6
Syy/Szz
0.490.240.76
M
Average5% percentile*95% percentile*
Sxx(MPa)-18.4-15.1-21.9
Syy(MPa)-30.3-24.9-37.2
Szz(MPa)-21.7-17.0-26.8
Sxx/Syy
0.610.510.71
*: Refers to the number of finite discrete elements in the repository area.
47
geometric scale
2E+02
zz-stressinterval
max-2.300E+-2.000E+-1.700E+-1.400E+-1.100E+-9.000E+
contours= 1.000E+06
min07 -2.500E+0707 -2.200E+0707 -1.900E+0707 -1.600E+0707 -1.300E+0706 -1.000E+07
Figure 6.11. Stress Szz for model with 23 fracture zones (SKI23:4000) at presentcondition and at the depth of 500 m.
48
geometric scale
2E+02
zz-stress contoursinterval = 2.000E+06
max min-3.000E+07 -3.200E+07-2.600E+07 -2.800E+07-2.200E+07 -2.400E+07-1.800E+07 -2.000E+07-1.400E+07 -1.600E+07
Figure 6.12. Stress Szz at 500 m depth for the model SKI23:4000 200 years afteremplacement of canisters.
49
A'750m
-750m
Figure 6.13. Profile, A-A', where stresses in figure 6.14 to 6.18 are presented.Horizontal section at the depth of 500 m.
-4,50E+07
5.OOE+O6 -1-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
Figure 6.14. Calculated stresses at present condition. Profile A-A' show the location ofthe fracture zones.
50
-t , JUDTU / -
-4,00E+07 -
-3.50E+07 -
-3.00E+07 -
,-. -2.50E+07-
~g -2.00E+07-
55 -1.50E+07-
-1.00E+07 -
-5.O0E+O6
0,O0E+0O
5.00E+06
11
, ; 1 1 \
r
11•ail*!
I
1
' V . Sxx
M
4ll
-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
Figure 6.15. Calculated stresses 200 years after emplacement of canisters.Profile A-A' show the location of the fracture zones.
-4.50E+07
-4,00E+07
-3,50E+O7
-3.OOE+O7
- . -2,50E+07
5.00E+06
-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
Figure 6.16. Calculated stresses after 60,000 years of thermal heating.Profile A-A' show the location of the fracture zones.
51
-4,50E+07
-4,0OE+O7 •
-3,50E+07--
-2.50E+07 - -
« -2.00E+07--i
55 -l,50E+07 - . - ••-- '
-1.00E+07--
-5,00E+06 • -
O.OOE+00 • -
5.00E+06
-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
~~ ^ | A'
Figure 6.17. Calculated stresses during maximum ice load from glaciation.Profile A-A' show the location of the fracture zones.
-4,50E+07
-4.00E+07 -
-3.50E+O7 - •
-3.00E+O7 • •
^ -2.50E+07 - -esa."s" -2.00E+07 • •t
53 -1.50E+07--
-1.00E+07 ••
-5.00E+O6 - -
0.00E+O0 - •
5,0OE+O6
-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
Figure 6.18. Calculated stresses after the glaciation cycle.Profile A-A' show the location of the fracture zones.
52
Figure 6.19 Regions with stress ratio Syy/Szz<0.225 in the intact rock at presentconditions. Horizontal section at 500 m depth.
Figure 6.20 Regions with tensile stress in the intact rock at present conditions.Horizontal section at 500 m depth.
53
6.3.3 Deformations
Deformations of fracture zones are assessed for the thermal and glaciation loadingsequence. There were small changes in displacement after 1,000 years, in comparisonwith the displacements after 200 years. The magnitude of maximum shear displacementwas approximately 25 mm for this time period. This displacement occurred in fracturezone 43. Fracture zone 4, 5 and 8 also gave relatively large displacements. All zonesmentioned above have dip angles between 38° and 71°, see table 6.3. After 1,000 yearsof heating there was a larger volume of rock that display shear displacement, but themagnitude was almost the same or lower than that after 200 years of heating. Thedeformation had a maximum for fracture zone 43 although the relative deformationaccording to fracture width was largest for fracture zone 5. Deformations reach the peakvalue during maximum glaciation. The calculated deformations for fracture zone 43 arepresented in figures 6.21 and 6.22. During the glaciation the large displacements wereconcentrated to a few hundred meters near the surface. The fractures zones that weresensitive for glaciation have dip angles between 38° and 70°. The more steep orsubhorizontal fracture zones have small displacements, see Table 6.3. The major part ofthe shear displacements during the glaciation was elastic, this can be affected by thematerial model that have been used to simulate the fracture behaviour. With othermaterial and fracture models the results may change.
In general the fracture zone deformations are greater during glacial loading than duringthermal loading, especially for shear displacements. Deformation reaches its maximumat the peak ice loading and there are permanent shear displacements after heating andglaciation. There are only minor changes in the widths of fracture zones before and afterglaciation.
54
Table 6.3. Shear displacement of fracture zones at repository level. The presentedwidths of the fracture zones are valid for the inner region of the model.
Zone
45*689*
1114*17*18*20212527*3133*36*3738*43*44*454649*
Width(m)
512.510105
151512.53
10355
255537.5
651565
7.510
Type ofzone
MinorMajorMinorMinorMinorMajorMajorMajorMinorMinorMinorMinorMinorMajorMinorMinorMinorMinorMajorMinorMajorMinorMinor
Dipdirection
24°32°38°18°
251°246°
68°116°284°313°149°328°358°349°358°339°337°345°332°317°312°272°
88°
Dipangle70°70°68°38°81°78°89°89°56°85°83°80°81°90°33°87°89°77°61°28°14°86°89°
Shear displacementafter 200 years.
9.9 mm24.3 mm
2.8 mm12.2 mm5.5 mm5.8 mm2.9 mm6.3 mm
16.0 mm3.5 mm0.6 mm
10.3 mm3.8 mm1.0 mm
* •
5.4 mm8.0 mm
18.1mm25.0 mm
6.5 mm**
9.4 mm5.7 mm
Shear displacement formaximum ice load.
28.3 mm60.7 mm
6.9 mm38.5 mm
8.0 mm34.1 mm
9.1 mm26.3 mm33.0 mm
7.4 mm2.8 mm
20.1 mm22.5 mm0.8 mm
**17.6 mm28.2 mm28.5 mm81.9 mm19.2 mm
**33.4 mm27.9 mm
*: Merged with other zones. **: No data available near repository at repository level.
s£
10 11
Loading step
Figure 6.21. Maximum shear displacement inside the repository for fracture zone 43.Loading step: 1 :Present conditions. 2: Thermal response after 200 years.3: Thermal response after 400 years. 4: Thermal response after 1,000years. 5: Thermal response after 60,000 years. 6: 1,000m ice thickness.7: 2,200m ice thickness. 8: 1,000m ice thickness. 9: 200m ice cliff.10: 100m water. 11: After glaciation.
55
10 11
Loading step
Figure 6.22. Maximum and minimum normal displacement for fracture zone 43.Opening of the fracture zone is positive. Loading step: 1 :Presentconditions. 2: Thermal response after 200 years. 3: Thermal response after400 years. 4: Thermal response after 1,000 years. 5: Thermal responseafter 60,000 years. 6: 1,000m ice thickness. 7: 2,200m ice thickness.8: 1,000m ice thickness. 9: 200m ice cliff. 10: 100m water. 11: Afterglaciation.
56
6.4 SKI models with 15 fracture zones
Models with 15 fracture zones were analysed to study the influence of number offracture zones on stresses and displacements. The modelling with 15 fracture zones wasdone with several different loading sequences for comparison. Results from this seriesof models were used to determine the required loading sequence for the more advancedmodel with 23 fracture zones, see Chapter 6.3.
6.4.1 Loading sequences
Four different ice loading sequences where applied to these models and they arepresented in table 6.4.
One loading sequence was conducted without thermal load and this was the referencecase for a rock mass without a repository (model SKI15:0:a). There were two moresequences developed with different fracture properties, designated as SKI15:0:b andSKI15:0:c, see table 6.4.
A loading sequence with low thermal loading of 400 canisters in the repository wasnamed SKI 15:400. The applied thermal load was about 10% of the capacity for a fullscale repository. The thermal loading after 200, 400, 1,000 and 60,000 years, and aglaciation cycle were simulated in the loading sequence for the model with 400canisters, see table 6.4. The small thermal effect during the glaciation was neglected.Therefore, the temperature distribution during the glaciation period was equal to thetemperature after 60,000 years of heating. The first glacial load was calculated for 1,000m ice thickness. The following two loading steps had an evenly distributed ice load of2,200 m and 1,000 m ice thickness, respectively. The next two loading steps simulatethe ice cliff (200 m) over the repository and the last loading was with a free groundsurface.
For the sequence with high thermal load, designated SKI 15:4000, the thermal load was4,000 canisters and the thermal response was calculated after 100, 200, 400, 1,000,2,500, 10,000 and 60,000 years. The first glacial load had 1,000 m ice thickness. Thesuccessive loading sequences had an evenly distributed ice load with 2,200 m and 1,000m ice thickness, respectively. The next two loading steps were with a 200 m ice cliffabove the repository and 100 m water table over the repository, respectively. The lastloading step was with a free ground surface. The thermal response after 200 years andthe response to maximum glaciation for a model without an inner region were alsocalculated (model SKI15:4000:b).
For two of the models the cohesion and shear stiffness of the fractures were reduced,model SKI15:0:b and SKI15:0:c. The reason for this approach was to study theinfluence of these parameters on the stress and deformations, see section 5.3.2.
57
Table 6.4. Loading sequence for models with 15 fracture zones. Simulated loadingsteps are marked with X.
Type of glacial loading Description ofloading stage
SKI15:0:a-c
SKI15:400
SKI15:4000:a
SKI15:4000:b
Present conditions
X X
NW SE
, Repository location
Thermal responseafter 100 years.
Thermal responseafter 200 years. X
Thermal responseafter 400 years. XThermal responseafter 1,000 years.
Thermal responseafter 2,500 years.
Thermal responseafter 10,000 years.
Thermal responseafter 60,000 years.
X
X
X
X
X
X
X
X
X
s V \Loading with1,000 micethickness.
X
VTT Loading with2,200 m icethickness.
X X X
\
Loading with1,000 m icethickness.
X
Loading with200 m icethicknessabove therepository.Loading with100 m water abovethe repository.
X
After glaciation,free groundsurface.
X X X
58
6.4.2 Stresses
Consolidation of the models with an ice load caused permanent deformations in thefracture zones and redistribution of stresses. The measured stresses were applied prior toconsolidation. Figure 6.23 shows the location of the repository area and the stressmonitoring point in the models. The stresses prior to consolidation were not equal to thestresses calculated for the present conditions. This was due to the plastic deformationsof the fractures and the stress changes caused by these deformations, see figure 6.24 and6.25. During the glacial cycles the calculated stresses showed only small variations, seefigure 6.24 loading step 4 and 7. Small shear stresses developed in the rock mass duringconsolidation with ice load and were maintained in the model for the remaining loadingsteps. This caused small changes in the direction of the principal stresses in the models.The rotations of principal stresses were caused by the existence of fracture zones. Shearstresses in the intact rock remained constant in the centre of the repository during theloading and unloading. Figure 6.25 to 6.27 present the variation in stress versus loadingfor model SKI15:4000:a, SKI15:4000:b and SKI 15:400. Syy is the vertical stress. Sxxand Szz are the two horizontal stresses in the direction of the average in-situ principalstresses.
N
rV6
\r
A 520 \
1/ j
^ " /i *Moflf\ point
^ 311
mtoring~V"
1
—.
\
\
46
1
1
i
4 S N
I?5 17
"^-38
^ 4 3 .
X
Repository for400 canisters.
aRepository for4000 canisters.
Figure 6.23. Location of monitoring point for rock stresses in repository area of modelSKI 15 at 500 m depth. The repository areas for 400 and 4,000 canisters areindicated. Horizontal section 1.5x1.5 km.
The stresses were higher for the larger repository in spite of the almost identical heatgeneration per square kilometre for the repositories. The most important result was thedevelopment of high horizontal stresses in combination with a low vertical stress, whichwas very different from the stress field before thermal loading.
59
-4.00E+07-3,50E+07 .-3.00E+07-2,50E+07 ..-2,00E+07 ..-1,5OE+O7-l,00E+07'!-5,00E+06! f i : J
0,00E+005,00E+06''. _
1.00E+071
Loading step
-Sxx-Sxy-Sxz-Syy-Syz-Szz
Figure 6.24. Stresses versus loading steps for model SKI15:0:a. Consolidation by iceloading is included. Loading sequence: 1: Consolidation from rock massweight. 2: 2,200 m ice thickness. 3: 1,000 m ice thickness. 4: No load,present conditions. 5: 2,200 m ice thickness. 6: 1,000 m ice thickness.7: After glaciation.
The cohesion and shear stiffness were lower for models SKI15:0:b-c than for the othermodels, all other parameters were the same, see table 2.4. Reduction of cohesion andshear stiffness for the fracture zones resulted in a redistribution of stresses in the model,but changes in stress magnitudes were small. The calculated stress difference was inapproximately 10%, although there were local regions with greater changes. Neglectingthe cohesion seemed to have minor effect on the stresses in the model at 500 m depth.At these depths the normal stress across the fractures was high and the governing part ofthe fracture strength was from friction. In the centre of the repository area there was nosignificant change in stresses between the models. The magnitudes of stresses are givenin Table 6.5 to 6.7.
Both the stress field and the displacements were affected by the fractures that definedthe inner region. These fractures can be considered as internal boundaries and theyreduce the deformabilty of the rock mass, although the differences for the calculatedstresses were assumed to be small. Compare figure 6.25 with figure 6.27 and Table 6.8with Table 6.9.
The stresses along profile A-A', see figure 6.28, are presented for the modelSKI15:4000:a in figure 6.29 to 6.33. The areas in the repository with a low ratiobetween the stress in vertical direction and the stress in the direction of the z-axis for themodel SKI15:4000:a during present conditions are marked in figure 6.34. These stressconditions did not exist in the model SKI15:4000:b during present conditions and werevery limited during the other of the loading sequence. The stresses along line A-A' formodel SKI15:4000:b 200 years after emplacement and during maximal glaciation arepresented in figure 6.35 and 6.36. Syy is the vertical stress. Sxx and Szz are the twohorizontal stresses in the direction of the average in-situ principal stresses. Below thediagram is a cut out of figure 6.28 showing the fracture zones.
60
-Sxx
-Sxy
-Sxz
-Syy
-Syz
-Szz
1.00E+071 2 3 4 5 6 7 8 9 10
Loading step
Figure 6.25. Stresses versus loading step for model SKI15:4000:b. Consolidation fromice load is included. Loading sequence: 1: Consolidation from rock massweight. 2: 2,200 m ice thickness. 3: 1,000 m ice thickness. 4: No load,present conditions. 5: Thermal response after 200 years. 6: Thermalresponse after 60,000 years. 7: 1,000 m ice thickness. 8: 2,200 m icethickness. 9: 1,000 m ice thickness. 10: After glaciation.
-3.00E+07
£ -2.00E+07
I -1,OOE+07
O.OOE+00
l,O0E+07
»=3
., 1 i 1II 1* t '1 1
s A
i • 1
N
i Si 1
> o« 3 :> i >
1 II
1 5 6
Loading step
10
Figure 6.26. Stresses versus loading steps for model SKI 15:400. Loading sequence:1: Present conditions. 2: Thermal response after 200 years. 3: Thermalresponse after 400 years. 4: Thermal response after 1,000 years.5: Thermal response after 60,000 years. 6: 1,000m ice thickness.7: 2,200m ice thickness. 8: 1,000m ice thickness. 9: 200m ice cliff.10: After glaciation.
61
•4.00E+07 .
-3.00E+07 .
2 -2.00E+07*
i -1.00E+07
O.OOE+OOi
I1.OOE+O7 .
*—-i—>i
ii • y •
t ;
-i i i
I A
i-M_i-S-i
>—(i
*—y.
t—11
1
-Sxx
-Sxy
-Sxz
-Syy
-Syz
-Szz
6 7 8 9
Loading step
10 11 12 13 14
Figure 6.27. Stresses versus loading steps for model SKI15:4000:a. Loading sequence:1: Present conditions. 2: Thermal response after 100 years. 3: Thermalresponse after 200 years. 4: Thermal response after 400 years. 5: Thermalresponse after 1,000 years. 6: Thermal response after 2,500 years.7: Thermal response after 10 000 years. 8: Thermal response after 60,000years. 9: 1,000m ice thickness. 10: 2,200m ice thickness. 11: 1,000m icethickness. 12: 200m ice cliff. 13: 100 m water. 14: After glaciation.
Table 6.5. Calculated stresses in the repository for model SKI15:0:a.Present conditions
Average5% percentile*95% percentile*
Sxx(MPa)
-7.8-3.6
-12.9
Syy(MPa)-10.4-2.8
-17.4
Szz(MPa)-15.9-10.0-21.2
Sxx/Szz
0.480.280.66
Maximum glaciation
Average5% percentile*95% percentile*
Sxx(MPa)-14.7
-8.8-21.5
Syy(MPa)-27.0-16.1-37.9
SzzL(MPa)
-21.3-13.4-29.1
Sxx/Syy
0.550.390.73
*: The value refers to the number of finite difference elements in the repository area.
62
Table 6.6. Calculated stresses in the repository for model SKI 15:0:b.Present conditions
Average5% percentile*95% percentile*
Sxx(MPa)
-8.5-4.9
-12.5
Syy(MPa)-10.7-3.8
-16.4
Szz(MPa)-15.7-10.4-20.7
Sxx/Szz
0.540.400.68
Maximum glaciation
Average5% percentile*95% percentile*
Sxx(MPa)-15.2
-9,7-21.7
Syy(MPa)-26.6-17.237.1
Szz(MPa)-20.4-12.9-28.1
Sxx/Syy
0.580.420.74
*: The value refers to the number of finite difference elements in the repository area.
Table 6.7. Calculated stresses in the repository for model SKI 15:0: c.Present conditions
Average5% percentile*95% percentile*
Sxx(MPa)
-7.1-3.7
-10.9
Syy(MPa)-11.1
-4.2-16.9
Szz(MPa)-13.1
-8.1-17.9
Sxx/Szz
0.530.390.70
Maximum glaciation
Average5% percentile*95% percentile*
Sxx(MPa)-15.7
-9.9-21.4
Syy(MPa)-26.4-15.4-36.5
Szz(MPa)-21.0-12.8-29.0
Sxx/Syy
0.610.440.80
*: The value refers to the number of finite difference elements in the repository area.
63
Table 6.8. Calculated stresses in the repository for model SKI15:4000:a.Present conditions
Average5% percentile*95% percentile*
Sxx(MPa)
-7.8-3.6
-12.9
Syy(MPa)-10.3
-2.8-17.4
Szz(MPa)-15.9-10.1-21.4
Sxx/Szz
0.480.280.66
200 years after emplacement
Average5% percentile*95% percentile*
Sxx(MPa)-18.0-14.0-22.0
Syy(MPa)-13.4
-5.8-19.8
Szz(MPa)-25.2-19.4-30.5
Syy/Szz
0.520.290.75
Maximum glaciation
Average5% percentile*95% percentile*
Sxx(MPa)-15.4-11.5-19.5
Syy(MPa)-30.6-24.3-36.8
Szz(MPa)-22.3-16.3-27.0
Sxx/Syy
0.500.400.60
*: The value refers to the number of finite difference elements in the repository area.
Table 6.9. Calculated stresses in the repository for model SKI15:4000:b.Present conditions
Average5% percentile*95% percentile*
Sxx(MPa)
-7.1-4.8-9.5
Syy(MPa)-12.3-9.0
-15.7
Szz(MPa)-14.4-10.7-18.0
Sxx/Szz
0.500.360.65
200 years after emplacement
Average5% percentile*95% percentile*
Sxx(MPa)-17.3-13.6-20.3
Syy(MPa)-14.6-10.0-19.4
Szz(MPa)-22.6-17.4-27.3
Syy/Szz
0.660.480.87
Maximum glaciation
Average5% percentile*95% percentile*
Sxx(MPa)-17.3-14.0-20.6
Syy(MPa)-30.3-24.8-35.8
Szz(MPa)-19.6-14.6-24.6
Sxx/Syy
0.570.460.66
*: The value refers to the number of finite difference elements in the repository area.
64
A'750m
-750m
Figure 6.28. Profile, A-A', indicates where stresses in figure 6.29 to 6.33 and 6.35 arecalculated. Horizontal section, 1.5xkm at the depth of 500 m.
-4.50E+07
Sxx
-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
Figure 6.29. Calculated stresses at present condition for model SKI15:4000:a.Profile A-A' show the location of fracture zones.
65
-4.00E+07 .
-3.50E+O7
-3.00E+07
^ -2.50E+07 •03
g -2.00E+07 •
1 0 -1.50E+O7 -
-l.OOE+07 •
-5.00E+06
0.00E+00 -
5.00E+O6 •
• - ' " ' . /syy " " \
* V Sxx
-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
Figure 6.30. Calculated stresses 200 years after emplacement model SKI15:4000:a.Profile A-A' show the location of fracture zones.
-4.50E+O7
-4.00E+07
-3.5OE+O7
-3.00E+07
5.0OE+O6
Sxx
-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordioate (m)
Figure 6.31. Calculated stresses after 60,000 years of thermal heating for modelSKI15:4000:a. Profile A-A' show the location of fracture zones.
66
-4.50E+07
-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350
Z-coordinate (m)
450 550 650 750
Figure 6.32. Calculated stresses during maximal glaciation for model SKI15:4000:a.Profile A-A' show the location of fracture zones.
-4.50E+07
-4.00E+07
-3.50E+07 •
-3.00E+07
5.OOE+06
Sxx
-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
Figure 6.33. Calculated stresses after glaciation for model SKI15:4000:a.Profile A-A' show the location of fracture zones.
67
Figure 6.34. Regions with Syy/Szz<0.225 in the intact rock at present condition formodel SKI15:4000:a. Horizontal section at 500 m depth.
5.0OE+06-750 -650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
^ ^ A >
Figure 6.35. Calculated stresses 200 years after waste emplacement for modelSKI15:4000:b. Profile A-A' show the location of fracture zones.
68
-650 -550 -450 -350 -250 -150 -50 50 150 250 350 450 550 650 750
Z-coordinate (m)
Figure 6.36. Calculated stresses during maximal glaciation for modelSKI15:4000:b. Profile A-A' show the location of fracture zones.
6.4.3 Deformations
The loading sequences with only glaciation considered, models SKI15:0:a-c, were usedto study the rock mass response with different fracture properties. The cohesion of thefracture zones had a small effect on the shear displacements. However, the shearstiffness was very important to consider. A reduction of shear stiffness to 1/5 of theoriginal value gave 3 to 8 times increased magnitudes shear displacement. Also thenormal displacement showed changes in this case, approximately 10%. The magnitudevaries however with the density of fractures. The major increases in shear displacementswere concentrated to parts of the model with a larger number of intersections betweenfracture zones. With zero cohesion and with reduction of the shear stiffness down to 1/5of the original value, the maximal shear displacement during glaciation at the repositorylevel was increased from 9 to 29 cm, i.e. more than three times, see figures 6.37 to 6.39.
69
300
| 250
iT 200
I 150
| 100
-I" 50Q
0
/^ ^ i
—•—SKI15:0:a
-«-SKI15:0:b
-*-SKJ15:0:c
^
Loading step
Figure 6.37. Maximum shear displacement in the repository for fracture zone 43,models SKI15:0:a-c. Loading sequence: 1: No load, present conditions.2: 2,200 m ice thickness. 3: 1,000 m ice thickness. 4: After glaciation.
20
I °t -20| -40vS -60
2* -80Q
-100
^ ^ ^— ^ "
SKI15:0:a!SKI15:0:c
Loading step
Figure 6.38. Maximum and minimum normal displacement for fracture 43, modelsSKI15:0:a and SKI15:0:c. Opening of fracture zones are positive.Loading sequence: 1: No load, present conditions. 2: 2,200 m icethickness. 3: 1,000 m ice thickness. 4: After glaciation.
The increased stresses from ice loading caused closure of the fracture zones, althoughthere were local openings as well. The remaining opening or closure of fractures wasdue to the stress relief or stress concentration near the fracture zone. For modelSKI15:4000:a the heat load causes expansion of the rock mass and causes permanentdisplacements in the fracture zones after cooling. After 60,000 years thermal loadingand before the glacial load was applied, some fractures have expanded in the normaldirection. At a few local areas in the rock mass there were openings of fracture zonesduring cooling. These areas were local and were not likely to affect the stability of therock mass. The fracture zones that were expanding in or close to the repository area formodel SKI15:4000:a were zones 8, 11, 20, 25, 38, 43 and 44. Figure 6.40 presents thedeformation for fracture zone 43. The largest expansion was approximately 30 mm at500 m depth for fracture zone 43, model SKI15:4000:b. This zone was 65 meters wideand the large displacements were probably caused by the large width. During the glacialloading some fracture zones opened at local contacts, but after the glaciation themajority of these fracture zones were closed again.
70
E
(a)
ES
4)Eatues
(b)
Loading step
-70
10
Loading step
Figure 6.39. Displacement versus loading steps for model SKI15:400. a) Maximumshear displacement in repository for fracture zone 43. b) Maximum andminimum normal displacement for fracture zone 43. Loading sequence;1: Present condition. 2: Thermal response after 200 years. 3: Thermalresponse after 400 years. 4: Thermal response after 1,000 years.5: Thermal response after 60,000 years. 6: 1,000 m ice thickness.7: 2,200 m ice thickness. 8: 1,000 m ice thickness.9: 200 m ice cliff. 10: After glaciation.
71
SKI15:4000:a
- • H - SKI15:4000:b!
(a)
(b)
EE
s8
(c)
Loading step
S
Loading step
10 11 12 13 14
3020100
-10-20-30-40-50-60-70
1
V
1
! '
\
\
i
\ /V \ /
\ T /I
iI
10 11 12 13 14
Loading step
Figure 6.40. Fracture displacement of fracture 43 versus loading steps for modelSKI15:4000:a and b. a): Maximum shear displacement in repository forfracture zone 43. b): Maximum and minimum normal displacement forfracture zone 43, model SKI 15.-4000.-a. c): Maximum and minimumnormal displacement for fracture zone 43, model SKI15:4000:b.Loading sequence: 1: Present conditions. 2: Thermal response after100 years. 3: Thermal response after 200 years. 4: Thermal response after400 years. 5: Thermal response after 1,000 years. 6: Thermal responseafter 2,500 years. 7: Thermal response after 10,000 years. 8: Thermalresponse after 60,000 years. 9: 1,000 m ice thickness. 10: 2,200 m icethickness. 11: 1,000 m ice thickness. 12: 200 m ice cliff. 13: 100 m water.14: After glaciation.
72
7 DISCUSSION
Even though every effort has been made to simulate the fractured rock mass at AspQ forthis rock mechanics study, significant idealisations and simplifications have had to bemade, not only because of the uncertainty of the on-site rock structure but also owing tothe limitations of the numerical tools. The geological model, the computational model,material parameters, boundary conditions and effect of excavation are initiallydiscussed. Thereafter the results from analysis of thermal and glacial loading arepresented. Water pressure and seismic events are two parameters that have not beenused in the study, these are also discussed. The accuracy problem of the Intel Pentiumprocessors is briefly discussed at the end of this chapter.
7.1 Geological interpretations for the Aspo area
In the current geologic structural model provided by SKI (Tiren et al, 1996b) thefracture zones are infinite in size and planar in geometry. The finite dimension and largescale undulations of the fracture zones are ignored. Planar fracture surfaces areacceptable for the global interpretation of the regional geology, the infinite size andundulation of the fracture zones may have a serious influence on the computationalresults, since these change the overall geometry of the model and over-estimates thenumber of intersections of fractures. The undulation of the fracture zones is likely tocause stress concentrations and stress relief, especially at the corners of the blocks. Thefinite length of fracture zones is likely to restrict movements along the fractures andincrease the horizontal stresses.
The modelling results showed that the stress field changes drastically in the vicinity offracture intersections. These changes can be concentration (stress increase) or relief(stress decrease) across fracture zones and may have unpredictable influence on theperformance of the repository. Since the intersections are entirely determined by thedensity, orientation and fracture dimensions, it emphasis the need for accurategeological interpretation of fracture zones in the repository area. The introduction ofrespect distances between canisters and major fracture zones will solve some of theseproblems, once the location and orientation of the fracture zones are defined.
7.2 Computational models
Three different computational models were set up and analysed with the code 3DEC.According to the geological interpretations of Aspo provided by SKI (Tiren et al,1996b), two computational models with 15 fracture zones and one computational modelwith 23 fractures zones were analysed. An inner region surrounding the hypotheticalrepository area was defined inside the global models. Here a finer mesh is used for amore detailed examination. This inner region was defined by using artificial fractureswhose stiffness, friction angle and cohesion were deliberately chosen very high toensure that there was no relative movement along these artificial fractures. Introduction
73
of such artificial fracture was necessary for the computation and their effect on theresults of stresses and deformations were considered to be minor, except at the interfacebetween the outer and inner region where they caused local errors.
The calculated stresses produced by the computational model match the measuredstresses from borehole KAS 02 and KAS 03 fairly well. A major discrepancy occurs atabout 600 m level. The calculated stresses have a variation of ±10 MPa at the depth of500 m, where the stress magnitude is 20 to 40 MPa. This variation is of the samemagnitude as the difference between the measured and calculated stresses. The reasonfor this may be: i) effect of local rock structures, ii) change of rock type at the local areaof the measured site (which was not considered in the models), iii) an inaccuraterepresentation of local stress change by the global stress boundary condition, iv) thereduction in the number of major fracture zones in the computational models, whichuses far fewer than those shown in the structural model (Tiren et al, 1996b), v) theomission of joints in the computational models, vi) uncertainties in the estimation offracture zone properties. Despite all these uncertainties, the overall effect of the stressesdifference was, however, small and the calculated stress results can be taken asrepresentative for the global behaviour in general.
Tensile stresses are obtained in the computational model. Basically they are distributedalong major fracture zones. The reason for their appearance is possibly the selectedvalue of cohesion (5 MPa) for the fracture zones. This value was chosen from a limitedsensitivity analysis and the value gave, in combination with the applied boundarystresses and the used friction angle, a stable rock mass before loading. If a moreadvanced computational model with the same accuracy as the far-field model describedin this report and the calculated stresses are correlated against the measured stresses inthe rock mass, it might be possible to determine more accurate values for friction angleand cohesion of the fracture zones. The lack of data about fracture properties andbehaviour of large fracture zones is a problem in modelling studies of this kind.
One major concern of this study is the likelihood of a global fracture propagation, i.e.the connection of existing fractures to larger fracture zones. This mechanism cannot besimulated explicitly at present, but is estimated from the ratio of the maximum andminimum principal stress components. For convenience the stresses oriented parallel tothe model axis have been used. The likelihood of fracture propagation increases whenthis ratio decreases. The computational stress results show that the maximum stress ratiobefore waste emplacement is 0.62. It is reduced to 0.49 by heating and becomes 0.61 atthe peak of glaciation. Therefore the risk for fracture propagation is increased by theheating, specially for some local areas close to fracture zones. This problem has beenstudied by Shen and Stephansson (1995b) for near-field models.
Different layout of waste canister distribution in the repository area will affect thetemperature and stresses. Modelling such options is beyond the scope of this study.
74
The fracture zone geometry has a major influence on the stress state in the models. Thisinfluence shows itself in two ways. The first is the stress concentration or stress relief atthe intersections of fracture zones and the second is the stress change across fracturezone planes when a large slip occurs along the fracture zones. Due to the location offracture zones the calculated stresses have a variation of ±10 MPa at a depth of 500 m,where the stress magnitude is 20 to 40 MPa. This variation is of the same magnitude asthe discrepancy between the measured and calculated stresses and may also explain thevariation for the measured stresses. The stress concentration at the intersections can beexplained by the wedge shape of block corners at the intersections. According to thetheory of elasticity, the sharp comers are stress singularity points and the stressmagnitude at these corners is very high, theoretically infinite. However, the finitestrength of the rock material would most likely crush the corners. To simulate such acrushing effect is however very difficult and beyond the current capacity of the 3 DECcode. Stress relief may also appear in the vicinity of intersections. This is perhaps due torelative movements between the block wedges (corners). The dead-locked corners willhave high stresses (concentration) and the squeezed-out corners will have low stresses(relief). The mechanics at these intersections can only be understood through detailedstudy of the contact mechanics of wedges. Today the mechanics of wedge deformationare not fully understood. It has to be recognised that the complex three-dimensionalgeometry of fracture/rock systems create complex phenomena that require more detailedstudy in order to understand or explain them fully.
In studies carried out at URL in Canada, the failure process around undergroundexcavations begins when the loading path exceeds the in situ crack-initiation stress,which for the granite at URL is about 70 MPa at low confining stresses. Once thisthreshold is crossed, the path to failure will dictate the ultimate strength of the rock(Martin et al, 1995). The underground openings will undergo several loading pathsduring construction and subsequently following heat loading and loading fromglaciation. The near-face cracking around an excavation caused by the complex loadingpath reduces the in situ strength to about half the laboratory strength, Martin et al(op.cit.). Hence, the stress concentrations at corners and fracture intersections are areasfor local failure.
Stress concentration and relief appears at isolated areas at fracture intersections and isnot likely to effect the stress behaviour globally, because of this they are not likely tocause any serious stability problem at the global scale. However, stability of tunnels anddeposition holes close to fracture intersections may be seriously affected. Theseintersections are also major conduits of water flow. Therefore, a proper respect distanceshould be kept between the excavations and the intersections of major fault zones. As aconsequence, detailed knowledge about the local structure of the rock mass is of vitalimportance for the performance of the repository. A proper study of the effect offracture intersections on the repository performance can only be done by using smallercomputational models with detailed representation of fracture system and repositorylayout.
75
7.3 Material models and properties
The material models used for the rock matrix in this study are linear elastic togetherwith a Mohr-Coulomb friction model for fracture zones, with constant normal and shearstiffness, were assumed. These are reasonable assumptions for this study. Theexcavation is not likely to change the global stress state in the rock mass. A shortcomingof the analysis is that the time effect of the rock material and fracture behaviour, creep,was not included. This effect may be significant because of the very long time spanconsidered in this study. This phenomena has not been included in the study becauselimited knowledge of the creep of large rock masses and fractures that exist.
Failure of rock matrix and fractures is most likely to occur after excavating of repositoryor emplacement of waste canisters. Study of the failure mechanisms, especially relatedto the respect distance, can only be performed with a near-field model of much finermesh and with more comprehensive material models. These more complicated materialmodels, in turn, require the knowledge of material properties which has to be obtainedby laboratory or field tests. Major development of a computer code like 3DEC is alsoneeded to accommodate such developments and analyses, e.g. generation of timedependent material models.
A major difficulty of the present study is the uncertainty about the properties of fracturezones in the Aspo area. The fracture zone stiffness, specially the shear stiffness, affectsthe deformation of the rock mass. Since the laboratory data can only determine, at best,the properties of small fractures like joints, the normal and shear stiffness of fracturezones have to be estimated without any validation. This will introduce someuncertainties in the results. However, the overall stress state of the model may still bereasonable since the stress results are not particularly sensitive to shear and normalstiffness of fracture zones.
Uncertainty may also exist for intact rock properties, especially Young's modulus andPoisson's ratio, since only 23 major fracture zones are considered in the model, and agreat number of other major and minor fracture zones are ignored. The effects of theseexcluded fracture zones on the properties of rocks are not fully understood. Theavailable data are from small scale testing and the mechanical properties are likely todepend on the occurrence and locations of fractures in the rock mass.
In conclusion, a proper material model for the mechanics of fracture zones is notavailable at present. The available models are valid, at best, for small fractures, but notfor large scale fracture zones with multiple layers of rock and filling materials.Fundamental research is needed to study this problem so that a better physical basis isavailable for future analysis. In view of the lack of a proper constitutive model andparameters for the fracture zones, a possible solution is to perform sensitivity analysesfor certain ranges of stiffness, friction and cohesion to determine the influence of thesemechanical properties.
76
7.4 Boundary stress conditions
The boundary stresses used in the computational models were derived from themeasured stresses from two boreholes. Since the measured stresses are affected by thepresence of fractures near the measuring point, the results obtained at each measuringpoint represent a local stress state. However, the discrepancy between global stress stateand point stress state will diminish with the increase of number and spatial distributionof measurements. For computation, it is assumed that the boundary stresses arerepresentative of the regional stress state at Aspo. The variation of stress state caused bylocal fractures close to the boundary of the computational model should be small andhave been ignored.
A more serious problem concerning the stress boundary conditions is the change ofboundary stresses during future glaciation. This state of stress is unknown and difficultto predict at present. During the heating and glacial loading the vertical boundaries donot allow normal displacement in this study. This situation will result in higherhorizontal stress than for a model with stress boundary conditions. Therefore, theboundary stress obtained in the modelling may not be true or representative for heatingand glacial loading in the future.
A partial solution to this problem is a synchronised change of boundary stresses with thesequence of ice loading. This will result in a better estimation of the future stresschanges. This effect should be considered in future analysis.
7.5 Excavation of a repository
The loading mechanisms simulated in this study are thermal loading due toemplacement of waste canisters and ice loading due to glaciation and deglaciation. Theeffect of excavation of the repository is not considered in this far-field study. However,in jointed and faulted hard rocks such as that at Aspo, the interaction between theexcavation of the repository and fractures nearby may cause considerable changes instress distribution and mode of deformation (Martin et al, 1995). Such a detailedanalysis is beyond the scope of this study, but is recommended for consideration instudies to follow. Different designs of tunnel systems and canister holes should beconsidered in such an analysis. The design of tunnels and deposition holes will affectnot only the mechanical stability, but also the temperature in the repository area and itssurroundings. A greater heat-load per square kilometre increases both temperature andstress in the repository.
77
7.6 Effect of thermal loading
In this study thermal loading of heat intensities 5.6 MW/km2 and 6.1 MW/km2 are usedfor the repositories with 400 and 4,000 canisters, respectively. From the heat intensityand repository capacities of canisters, the maximum temperature reaches 35°C and47.5°C, respectively, about 200 years after deposition of the waste. For the largerepository the average value of the principal stresses increases from 10 MPa to 21 MPafor the horizontal stress in x-direction, from 16 MPa to 26 MPa for the horizontal stressin z-direction, and from 10 MPa to 13 MPa for the vertical stress, respectively. Thedifference in these two horizontal stress changes is due to different horizontal boundarystress conditions along these two directions and the fracture zone geometry. The majorthermal effect is the increase of horizontal stresses since the vertical boundaries arefixed and do not allow horizontal displacements.
Heat convection due to fluid flow was not considered in the simulation. The dominantmode of deformation of fractures due to thermal loading was closure, this is caused bythe increased stress level near the repository. The fracture openings were basically dueto the local geometry of fractures and local stress variations. Since only linear elasticbehaviour was assumed for the intact rock, no failure mechanism was considered.
It may be possible to increase the heat intensity of the repository so that the maximumtemperature can be raised further. Such an increase will naturally cause further increaseof stresses and may cause mechanical failure. Therefore, a more detailed sensitivitystudy of different heat intensities, coupled with excavation of the repository, isrecommended. Such an analysis can only be performed with a small, near-field model.
7.7 Effect of glacial loading
The present study considers only stress changes and rock deformation caused byglaciation and deglaciation, without any synchronised change of the boundary stresses.Synchronisation of the boundary stress in respect of future glaciation is likely toincrease the movements along fracture zones and increase the stress variations in therock mass.
Glaciation affects the vertical stress most, which causes an increase of the averagevertical stress component up to 30 MPa, compared with the initial value of 10 MPa. Theaverage value of the maximum horizontal stress increases from 10 MPa to 18 MPa inthe x-direction and from 16 MPa to 22 MPa in the z-direction, respectively. Theincrease of vertical stress reduces the deviatoric stress but increases the total stress level.This may affect the overall stability of the repository.
Boundary stresses during the glaciation and deglaciation may be different from theconditions before the glaciation. Furthermore permafrost in the ground will change thethermo-mechanical properties of the rock mass in the zone of permafrost. Finallydeglaciation will introduce considerable amounts of water and water flow in the region
78
which may change the global hydro-mechanical behaviour of the rock mass. The causeand effect of these factors are beyond the scope of this study, but should be consideredin future studies.
7.8 Other factors
The influence of water flow, variations in ground water level and dynamic loading dueto seismic events are important factors affecting the performance of a repository. Theseaspects have not been studied.
Flow through fractures dominates the water flow in the Aspo area. It will affect thetemperature field by convection and fracture behaviour by water pressure in fractures.Therefore, the coupled thermo-hydro-mechanical behaviour of the rock mass needs to beconsidered. At present the 3DEC code cannot calculate water flow and there is no 3-DDEM code available today to model coupled hydro-mechanical behaviour of fracturedrock masses. The options are therefore: (i) modify current 3DEC code so that the waterflow in fractures can be calculated; (ii) use another code to produce water pressure andflow velocity through the fracture system, e.g. FRACMAN, and use these results asinput to the 3 DEC modelling and treat the problem as one way coupled, (iii) use anothercode which can handle the fully coupled T-H-M processes.
The dynamic effects of seismic activity can be handled by the 3 DEC code. It is thereforeof interest to study this effect on the repository performance especially, in respect ofneotectonics and seismicity at the late stage of deglaciation.
There is an error in the first Intel Pentium processors. One of these was used for thisanalysis. The problem occurs at the division with floating point numbers. Severalverification tests were performed and the errors for 3 DEC calculations were found to bevery small. However, the risk for local errors in the computational model can not befully excluded.
79
8 CONCLUSION
The three-dimensional distinct element code 3 DEC was used to simulate the rockmechanical effect of a hypothetical nuclear waste repository located at Aspo. The studyconsidered thermal load from canisters and loading from a glaciation cycle.Computational models for the Aspo area were set up with 23 and 15 fractures zones,respectively. Attention was focused on the influence of fracture geometry, heating,glaciation and deglaciation on the stress distribution, deformation and temperaturedistribution of the rock mass. The rock matrix was assumed to be a linear-elastic andfractures followed a Mohr-Coulomb friction law with constant stiffness in normal andshear direction. Water flow and pressures were not considered in the computation.
From the numerical results, the initial stress distribution for the far-field model, beforethe emplacement of waste and prior to the simulation of glaciation, matches themeasured stress data fairly well from two boreholes in the area.
The temperature distribution obtained from the modelling was calculated bysuperposition of lumped heat sources from waste canisters, with a heat intensity of6.1 MW/km2 for 4,000 canisters for this far-field study. The calculated maximumtemperature in the rock mass reaches 48°C in the central part of the repository afterapproximately 200 years.
From the numerical results, the effect of the thermal loading from waste canisters on thefar-field stress field is to increase horizontal stress. At 500 metres' depth and with heatfrom 4,000 canisters, the average stresses increase to about 18 MPa in x-direction and22 MPa in z-direction. The major mode of fracture zone deformation is closure.However, fracture zone opening occurs in some local areas. Heating also increases theprobability of fracture propagation in the rock mass by reducing the average ratio ofmaximum and minimal principal stress from 0.62 (initial value with boundary stressesonly) to 0.49 after 200 years of heating.
The numerical results indicate that glaciation has a major effect on the vertical stresscomponent (Syy), but less effect on the two horizontal stress components for the far-field model. At the peak of glaciation, from a 2,200 meter thick ice sheet, the averagevertical stress at 500 metres' depth increases to 30 MPa, from an initial value of10 MPa. Complex stress distribution occurs in the rock mass, especially at the fracturezone intersections. The risk of a global fracture propagation due to heavy verticalloading is however small. The average ratio of Sxx/Syy is increased to 0.61.
Thermal loading mainly affects the local area of the repository, while glaciation has asignificant effect on stresses and deformations of rock masses on a large scale. From thenumerical results of the far-field modelling, thermal loading does not have a significantimpact on rock mass stability in a global sense, i.e. a large scale failure of rock mass isnot likely to be caused by heat release. However, the stability of tunnels close to fault orfracture zone intersections may be affected to some extent by the increased stress
80
concentrations due to thermal loading, which can only be studied in a near-field model.In this context, near-field studies with 3DEC is a useful complement to far-field study.
The effect of glaciation/deglaciation cycles, on the other hand, is significant in respectof the stability of the rock mass in a global sense on the basis of the numerical resultsfrom the far-field modelling. Permanent damage will be done to the surfaces of faultsand fracture zones due to the much larger shear deformation caused by glaciation andunfavourable stress may affect the stability of tunnels due to the significant increase inthe vertical stress component. This stress redistribution and large scale fracturedeformation occur not only at local areas around the waste canisters, but also over themuch larger area where glaciation takes place. It is also possible that failure of intactrocks (for example plastic yielding) may also be induced because of this significantstress concentration, which can only be studied more properly with a near-field modeland better understanding of the failure mechanisms of the rock matrix.
Fracture orientation and relative movements of blocks are the dominating factorsaffecting the stress distribution at the fracture intersections. Both stress concentrationand stress relief can occur and are determined by the combined wedge/corner geometryand relative modes of block movements. The mechanical behaviour at the fractureintersections needs to be studied more in the future.
81
9 RECOMMENDATIONS
To better understand the rock mass behaviour and performance of a repository, analysesin near-field scale with the three-dimensional distinct element method is recommended.These models should be smaller than the models used in this study. The models shouldsimulate the excavation of the repository with different layouts of canister and a detailedrepresentation of fractures around the potential repository. The results produced in thisstudy can be used to extract the boundary stresses for the smaller model. The followingfactors should be considered in the local model.
1) Improved constitutive model for the fracture zones and single fractures. Althoughmore comprehensive models exist for single fractures, they cannot simulate behaviourof large fracture zones. Basic research is therefor needed to overcome this lack ofunderstanding of mechanical properties of large scale fractures zones.
2) Groundwater flow through fracture networks and increased water pressures should beincluded in the analysis. Although the present 3DEC code cannot handle water flow byitself, a combined analysis with another independent fracture flow code, likeFRACMAN, can be used to perform this task. It is possible to use identical fracturenetworks in both codes. A minor modification to 3DEC code and other codes may benecessary to accommodate such an analysis. However, if temperature also is included, amajor improvement of 3DEC is needed as the heat convection must be considered.
3) A series of sensitivity analyses should be performed in the next phase. Besidesdifferent options of canister layout, the following subjects are recommended to bestudied: i) different heat intensity, ii) different fracture property, iii) undulation offracture zones, iv) different design of tunnel system with respect to the local fracturegeometry and respect distance, v) different boundary stresses.
4) A study of dynamic effect from seismic events.
5) Modelling of large scale tunnel excavations.
The suggested analyses can be performed with some modification of the 3 DEC code andtogether with other existing codes.
82
10 ACKNOWLEDGEMENTS
Jan-Erik Israelsson at Itasca Geomekanik AB has contributed support regarding 3DEC.Sven Tiren and Per Askling at Geosigma AB have contributed with figures and data forthis report and Sven Tiren also participated in discussions regarding the set-up ofcomputational models.
The method for determination of fracture zone properties was developed by AlrikLundin at Engineering Geology, the Royal Institute of Technology, Stockholm, and thedetermination of fracture properties was also made by Lundin.
The authors wish to express their gratitude to Johan Andersson, Fritz Kautsky andOivind Toverud at the Radioactive Waste Division of The Swedish Nuclear PowerInspectorate (SKI) for their assistance during the project and to SKI for their financialsupport.
11 REFERENCES
Bjarnasson, B., Klason, H., Leijon, B., Trindell, L. and Ohman, T., Rock stressmeasurements in bore holes KAS 02, KAS 03 and KAS 05 on Aspo.SKB PR 25-89-17, Swedish Nuclear Fuel and Waste Management Co., Stockholm,1989.
Gustafson, G., Liedholm, M, Rhen, I., Stanfors, R. and Wikberg, P., Aspo Hard RockLaboratory. Predictions prior to excavation and the process of their validation. SKB TR91-23, Swedish Nuclear Fuel and Waste Management Co., Stockholm, 1991.
Hakansson, R., Calculations of radio nuclide content and decay heat in spent fuel. SKBworking report 90-17, Swedish Nuclear Fuel and Waste Management Co., Stockholm,1990.
ITASCA, 3-D Distinct Element Code, Version 1.50 User's Manual. ITASCA ConsultingGroup Inc., Minneapolis, 1994.
King-Clayton, L. M., Chapman, N. A., Kautsky, F., Svensson, N.-O., de Marsily, G. andLedoux, E., The central scenario for SITE-94, SKI 95:42, Swedish Nuclear PowerInspectorate, Stockholm, 1995.
Martin, D., Read, R.S. and Dzick, E.J., Near-face cracking and strength aroundunderground openings, Proceedings Mechanics of jointed and faulted rocks, Vienna, pp765-770. Balkema: Rotterdam, 1995.
Palmqvist, K., Hargelius, H. and Sundquist, U., SKNs Continued review of predictionsand validations in connection with the Aspo Hard Rock Laboratory (in Swedish). SKNReport 61, The National Board for Spent Nuclear Fuel, Stockholm, 1992.
83
Rosengren, L. and Stephansson, O., Distinct elements modelling of the rock massresponse to glaciation at Finnsjon, central Sweden. SKB TR 90-40, Swedish NuclearFuel and Waste Management Co., Stockholm, 1990.
Shen, B. and Stephansson, 0., Modelling of rock mass response to repositoryexcavations, thermal loading from radioactive waste and swelling pressure of buffermaterial, SKI TR 90:12, Swedish Nuclear Power Inspectorate, Stockholm, 1990.
Shen, B., and Stephansson, O., Near-field rock mechanics modelling for nuclear wastedisposal (SITE-94), SKI Report 96:17, Swedish Nuclear Power Inspectorate,Stockholm, 1996a.
Shen, B., and Stephansson, O., Modelling of rock fracture propagation for nuclear wastedisposal (SITE-94), SKI Report 96:18, Swedish Nuclear Power Inspectorate,Stockholm, 1996b.
Thunvik, R., and Braester, C , Heat propagation from a radioactive waste repository,SKB 91 Reference canisters, SKB TR 91-61, Swedish Nuclear Fuel and WasteManagement Co., Stockholm, 1991.
Tiren, S., Andersson, K,. Halenius, U., Johansson, R., Stephansson, O., and Ohlander,B., A comprehensive review of earth science methods in site characterisation of nuclearwaste storage: Bedrock geology, structural geology, geophysics, rock mechanics andhydrochemistry, SKI repori(to be published), Swedish Nuclear Power Inspectorate,Stockholm, 1995a.
Tiren, S.A., Beckholmen, M., Voss, C , and Askling, P., Development of a geologicaland structural model of Aspo, southeastern Sweden (SITE-94), SKI Report 96:16,Swedish Nuclear Power Inspectorate, Stockholm, 1996.
Wikberg, P. (ed.), Gustafson, G., Rhen, I , and Stanfors, R., Aspo Hard RockLaboratory, Evaluation and conceptual modelling based on the pre-investigations 1986-1990, SKB TR 91-22, Swedish Nuclear Fuel and Waste Management Co., Stockholm,1991.
Postadress/Postal address
SKIS-106 58 STOCKHOLM
STATENS KARNKRAFTINSPEKTIONSwedish Nuclear Power Inspectorate
Telefon/Telephone
Nat 08-698 84 00Int +46 8 698 84 00
Telefax
Nat 08-661Int +46 8 661
90 8690 86
Telex
11961 SWEATOMS