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Work ing Repor t 2011 -23

Fracture Mechanics Prediction for Posiva’sOlkiluoto Spalling Experiment (POSE)

March 2011

Working Reports contain information on work in progress

or pending completion.

The conclusions and viewpoints presented in the report

are those of author(s) and do not necessarily

coincide with those of Posiva.

Top ias S i ren

Ka l l i osuunn i t t e lu Oy Rockp lan L td .

Work ing Report 2011 -23

Fracture Mechanics Prediction for Posiva’sOlkiluoto Spalling Experiment (POSE)

ABSTRACT In Olkiluoto, Posiva’s Olkiluoto Spalling Experiment (POSE), is currently being carried out. The objective of POSE is to establish the in situ spalling strength of the rock in Olkiluoto and also to establish the state of in situ stress at the -345-metre depth level. The experiment is based on boring three large holes at the bottom of a tunnel, of which two are modelled in this work. The pillar of rock between the two holes is expected to have crack growth due to the high stresses induced by the two holes drilled.

The aim of this work is to predict the fracture mechanical behaviour of the rock between the two holes. The prediction is done by using the parameters reported in Site Descrip-tion 2008 and with the help of laboratory results of the anisotropic behaviour of the rock. Primary objective is to analyse whether spalling occurs and to what extent. The correlation between the real rock behaviour and the results of the prediction is im-portant information that describes how well rock mechanical parameters are known and how well the behaviour of the rock can be modelled. Also, the fracture mechanics ap-proach is not the most commonly used method in ONKALO, and therefore it gives a fresh baseline to the more common modelling approaches in ONKALO. This prediction is done by using the fracture mechanics code Fracod2D, which is based on the Displacement Discontinuity Method (DDM). The advantage of the DDM in simulating the fracture propagation, compared with other boundary element techniques, is its direct presentation of a fracture as fracture elements instead of as separate fracture surfaces. In Fracod2D, the fracture initiation occurs when two principal stresses reach a critical value. More closely, the tensile and shear stresses and strengths are used to de-termine the initiation of a new fracture. The fracture propagation is, however, deter-mined by using fracture toughness parameters with the F-criterion. Mainly anisotropic models simulating the behaviour of migmatitic gneiss are analysed, but also isotropic models simulating the pegmatitic granite are analysed. The anisot-ropic models have lower strength parameters in the anisotropy direction. The parameters are determined from laboratory results of the anisotropic rock samples. The results show that with the parameters used, spalling occurs in almost every model. In the models with the anisotropy direction across the pillar, only crevices are formed. With the current stress state and parameters, the fracture growth starts when the rock strength is 63 MPa in the anisotropy direction and 73 MPa in the perpendicular direc-tion. The preliminary results show that the fracture propagation is very sensitive to changes in the anisotropy direction. Friction angle and cohesion are important parameters in fracture initiation, and they affect the results to a great extent. However, the fracture toughness is not a very sensitive parameter, although it controls the fracture growth af-ter it has been initiated. Keywords: Olkiluoto, ONKALO, POSE, fracture mechanics, spalling, DDM, anisot-ropy, fracture toughness

Rakomekaaninen ennuste Posivan Olkiluodon hilseilykokeesta (POSE) TIIVISTELMÄ Olkiluodossa toteutetaan -345 metrin syvyydessä POSE-koetta (Posiva’s Olkiluoto Spalling Experiment), jonka tarkoituksena on määrittää kallion in situ hilseilylujuus ja -jännitystila. Koe perustuu kolmen ison tutkimusreiän poraamiseen tutkimuskuprikan pohjaan. Kahden tutkimusreiän, jotka on mallinnettu tässä työssä, välisessä kalliopila-rissa valitsee suuri jännitys, jonka odotetaan aiheuttavan kiven rikkoutumista. Tämän työn tarkoituksena on ollut ennustaa kallion rakomekaaninen käyttäytyminen tutkimusreikien ympärillä. Lähtötietoina on käytetty Paikkaraportissa 2008:ssa esitettyjä arvoja ja laboratoriokokeiden tuloksia näytteiden anisotrooppisesta käyttäytymisestä. Pääasiallisena tavoitteena on tutkia, tapahtuuko tutkimusrei’issä hilseilyä ja missä laa-juudessa. Tässä työssä esitetyn ennusteen ja kokeessa havaittavan kiven todellisen käyttäytymisen välinen korrelaatio antaa tärkeää tietoa siitä, miten hyvin kallion käyttäytyminen ja kal-liomekaaniset parametrit tunnetaan. Rakomekaanista mallinnusta ei käytetä juurikaan ONKALOn mallintamisessa, ja siten se antaa hyvän vertailukohdan ONKALOssa enemmän käytettyihin mallinnustekniikoille. Ennuste on tehty käyttäen rakomekaanista Fracod2D-ohjelmaa, joka perustuu DDM-menetelmään (Displacement Discontinuity Method). DDM:n etuja verrattuna muihin reunaelementtimenetelmiin on sen tapa esittää raot rakoelementteinä erillisten rakopin-tojen sijaan. Fracod2D:ssa uusi rako syntyy, kun pääjännitykset saavuttavat kriittisen pisteen. Veto- ja leikkauslujuuksia käytetään raon syntymisen kriteerinä. Syntyneiden rakojen etene-misen määräävät rakojäykkyysparametrit muokatun G-kriteerin eli F-kriteerin avulla. Pääasiassa mallinnuksessa on käytetty migmatiittisen gneissin kuvaamiseksi aniso-trooppisia malleja, mutta myös isotrooppisia, pegmatiittista graniittia kuvaavia malleja käytetään. Anisotrooppisissa malleissa anisotropian suunnalla on heikompi lujuus, joka on määritetty laboratoriokokeiden tuloksista. Tulosten mukaan käytetyillä parametreilla aiheutuu hilseilyä lähes jokaisessa mallissa. Malleissa, joissa anisotropian suunta on pilarin poikki, syntyy vain syviä rakoja. Käyte-tyllä jännitystilalla ja parametreilla raon kasvu alkaa, kun kalliomassan lujuus on 63 MPa anisotropian suunnalle ja 73 MPa kohtisuoraan anisotropian suuntaa vastaan. Alustavat tulokset osoittavat, että rakojen synty mallissa on erittäin herkkä anisotropian suunnan muutoksille. Kitkakulma ja koheesio ovat erittäin tärkeitä parametreja rakojen syntymiselle, ja ne vaikuttavat merkittävästi tuloksiin. Raon jäykkyys ei kuitenkaan ole erityisen herkkä parametri, vaikka se kontrolloikin syntyneiden rakojen kasvua. Avainsanat: Olkiluoto, ONKALO, POSE, rakomekaniikka, hilseily, DDM, anisotropia, raon jäykkyys.

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TABLE OF CONTENTS ABSTRACT TIIVISTELMÄ ACKNOWLEDGEMENTS ............................................................................................... 2 1 INTRODUCTION ......................................................................................................... 3

1.1 Background ........................................................................................................... 3 1.2 Aim of this work .................................................................................................... 4 1.3 Method used ......................................................................................................... 5

2 INPUT DATA AND THEORY ....................................................................................... 7

2.1 Theory ................................................................................................................... 7 2.1.1 Fracture initiation ........................................................................................... 7 2.1.2 Fracture propagation...................................................................................... 8

2.2 The anisotropy direction ....................................................................................... 9 2.3 Input parameters ................................................................................................... 9

2.3.1 Tensile strength ........................................................................................... 10 2.3.2 Intact rock strength parameters ................................................................... 12 2.3.3 Rock mass strength ..................................................................................... 13 2.3.4 Fracture toughness properties ..................................................................... 13 2.3.5 Other fracture properties .............................................................................. 14

2.4 Sensitivity studies ............................................................................................... 15 2.4.1 Anisotropy direction ..................................................................................... 15 2.4.2 Tensile strength ........................................................................................... 15 2.4.3 Fracture toughness ...................................................................................... 15 2.4.4 Rock mass strength ..................................................................................... 16 2.4.5 Friction angle and cohesion ......................................................................... 16

3 MODELLING OF THE POSE TUNNEL ..................................................................... 17

3.1 Models of the POSE tunnel ................................................................................ 17 3.2 Models of the POSE holes .................................................................................. 18

4 RESULTS .................................................................................................................. 19

4.1 Tunnel model ...................................................................................................... 19 4.2 Isotropic model of the POSE holes ..................................................................... 20 4.3 Anisotropic model of the POSE holes ................................................................. 21 4.4 The effect of the anisotropy direction to the POSE holes ................................... 24 4.5 The sensitivity studies ......................................................................................... 25

4.5.1 Tensile strength ........................................................................................... 25 4.5.2 Fracture toughness parameters ................................................................... 26 4.5.3 Rock mass strength parameters .................................................................. 26 4.5.4 Friction angle and cohesion ......................................................................... 27

5 CONCLUSIONS ........................................................................................................ 28

5.1 Spalling ............................................................................................................... 28 5.2 Sensitivity studies ............................................................................................... 29 5.3 Final conclusions ................................................................................................ 29

REFERENCES ............................................................................................................. 30

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ACKNOWLEDGEMENTS

This analysis and working report has been written by Topias Siren. In addition to the author, several people have participated in the work:

- Supervising and commenting the work report: o Guido Nuijten (Rockplan Ltd.)

- Support and commenting the work: o Lauri Uotinen (Rockplan Ltd.) o Antti Matikainen (Rockplan Ltd.) o Dr. Baotang Shen (Framod Ltd.) o Dr. Tobias Backers (GeoFrames GmbH) o Prof. Mikael Rinne (Aalto University) o Matti Hakala (KMS Hakala Oy)

- Reviewing of the work report: o Prof. John Hudson (Rock Engineering Consultants) o Erik Johansson (Saanio & Riekkola Oy) o Kimmo Kemppainen (Posiva Oy)

- Proofreading: o Paula Saarelainen

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1 INTRODUCTION

In this chapter, the motivation for the fracture mechanical spalling prediction work and the spalling phenomenon are explained.

1.1 Background

Currently in Olkiluoto, the construction of the underground rock characterisation facil-ity for the final disposal of spent nuclear fuel named ONKALO is on the way. The site has been under thorough research many years, but there are still uncertainties, related especially to the in situ stress and to the rock spalling strength. To answer these ques-tions, an in situ experiment called Posiva’s Olkiluoto Spalling Experiment (POSE) was started (Aalto et al. 2009). The POSE niche is located in the middle of tunnel contract 4 (TU4), as presented in Figure 1-1.

Figure 1-1. The layout of ONKALO. The objective of the in situ experiment is to establish the in situ spalling strength of the Olkiluoto migmatitic gneiss and also to confirm the state of in situ stress at the -345-metre depth level. The experiment is based on boring three large holes at the bottom of a niche, called the POSE niche. Two of the holes are adjacent and the line joining their centres is oriented perpendicular to the major principal stress direction. The neck of rock between the two holes is expected to have rock spalling or damage due to the high stresses induced by the holes. The layout of the POSE niche is presented in Figure 1-2.

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Figure 1-2. The layout of the POSE niche, three round experiment holes and the major and intermediate principal stress direction.

1.2 Aim of this work

The aim of this work is to predict the fracture mechanical behaviour of the rock between the two holes. This prediction is done by using the parameters reported in Site Descrip-tion 2008 (Posiva 2009) and by using laboratory results of the anisotropic behaviour of the rock (GeoFrames 2009). This prediction is done by using the fracture mechanics code Fracod2D, and, parallel to this work, separate predictions were done with contin-uum mechanics (MIDAS/GTS, Examine3D, and Phase2) and discontinuum mechanics (3DEC). This analysis requires two types of models to be calculated. First of all, a 2-D cross-section of the tunnel geometry is used to calculate the stress components in the area of interest. The results of the tunnel model are then used as input for the models with the two holes. Each model with the two holes is calculated at the depths of one and three metres. Also within each model the two holes are excavated sequences. The third hole is not modelled, while it is a single hole and the first excavation sequence in the models presents a single hole. There are several different versions of the models with the two holes: for isotropic and anisotropic mediums with different sensitivity studies. The direction of the anisotropy is varied ±15 degrees. Also a sensitivity study of the tensile strength is done for anisot-ropic models. The modelling plan is presented in Figure 1-3.

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6

Figure 1-4. Fracture growth presented in the F-criterion (Shen & Stephansson 1993, Figure 1). The Fracod2D and F-criterion doesn’t consider microcrack formation, but the macro- fracture growth only. In macro-scale, the fracture growth can be a combination of mi-crocracking in mode I and mode II. In the F-criterion the resultant strain energy release rate (G) is divided to tension (GI) and shear (GII) components. The normalized sum of the mode I and mode II strain energy release rates is used to determine the failure and its direction.

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2 INPUT DATA AND THEORY

In this chapter, the input data and the theory are explained.

2.1 Theory

In Fracod2D, the fracture initiation occurs when the combination of two principal stresses reaches a critical value. More closely, the tensile and shear stresses and strengths are used to determine the initiation of a new fracture. The fracture propagation is, however, determined by using fracture toughness parameters. To take anisotropy of the rock into account, the parameters (�t, c, �, KIC, KIIC) have an elliptical variation from � to �+90�. For each point, calculations are done in all anisot-ropy directions, and the fracture will proceed or initiate in the direction where the maximum F value is reached. The “single plane of weakness theory” states that rock sample with a discontinuity should have its weakest direction should be associated with direction 45°+(�/2) where � is the friction angle (Hudson & Harrison 1997, p. 144). This is presented in Figure 2-1.

Figure 2-1. Observed effect of an isotropy to crack initation strength, crack damage strength, and peak strength (modified after Hakala et al. 2005 and Hudson et al. 1997). Assuming that the “single plane of weakness theory” is applicable with foliated rock, it can be observed in Figure 2-1 that the foliation has an effect on the crack damage and peak strength values. However, the crack initiation strength is dominated by the fa-vourably oriented weakest mineral contacts and is not affected by the foliation. (Hakala et al. 2005.)

2.1.1 Fracture initiation

For the shear failure, the critical strength is presented with the friction angle (�) and cohesion (c) of the intact rock and with tensile strength (�t) of the intact rock. The criti-

8

cal normal and shear stresses in anisotropic medium in an arbitrary plane after Shen et al. (2010, p. 50) are calculated by

��

� �� 1

�� 2

where �n is the normal stress, �s is the shear stress, � is the angle to the minor principal stress direction, and �1 and �3 are the major and minor concentrated principal stresses. After Shen et al. (2010, p. 50), in an anisotropic case the shear strength is calculated by �� 3 where S is the shear strength. When the shear stress exceeds the shear strength, a shear failure will occur. However, in an anisotropic case, the entire angle range from 0° to 360° must always be considered. The failure will initiate only in the direction in which the ratio of shear stress and strength is the highest. After Shen et al. (2010, p. 50), the ratio can be determined with a ratio calculated by

��

�� 4

After Shen et al. (2010, p. 52), the initiation of a tensile failure can be determined simi-larly with a ratio calculated by

��

�� 5

where �t is the tensile strength to the direction �.

2.1.2 Fracture propagation

Fracod2D uses the F-criterion to determine the fracture propagation. Mode I and II crack propagations are normalized and summed to produce a factor which expresses whether the crack is propagating and in which direction. The F-criterion is calculated after Shen (1993) by � � �

� ! �

� !� "#$ 6

where the GI and GII are strain energy release rates in modes I and II, and GIC and GIC are the critical strain energy release rate. GIC and GIIC are material constant values that express a stress state where the crack starts to propagate. After Shen et al. (2010, p. 52), the equation can also be written in terms of fracture intensity and anisotropy as

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��%� � & ' ' !�(�)

* & '

' !�(�)*� "#$ 7

where � is the arbitrary direction, KI and KII are stress intensity factors in modes I and II, and KIC and KIC are the corresponding fracture toughness values. The direction in which the fracture starts to propagate is where F(�) reaches its maximum.

2.2 The anisotropy direction

The parameters for the anisotropy direction for migmatitic gneiss are determined by using Posiva’s geological mapping of the POSE tunnel and projected to plane surfaces of the models. Posiva’s geological mapping of the foliation direction is shown in figure 2-2, dipping 52 degrees to direction of 175 degrees. A variation of 30° in all directions with steps of 15° is used in the models to investigate the effect of a change in the anisot-ropy direction.

Figure 2-2. Stereoplot of the variation of anisotropy direction.

2.3 Input parameters

The input parameters are determined by using existing test results for pegmatitic rock (PGR), which is assumed to be isotropic, and for migmatitic gneiss (MIGN.GN), which is assumed to be anisotropic. Both types are assumed to be homogeneous and linearly elastic. For migmatitic gneiss, individual rock strength and fracture strength parameters are determined for two perpendicular foliation directions. The input parameters, as listed in Table 2-1, are used.

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Table 2-1. Values of the mechanical parameters of the intact rock and fractures used as input in Fracod2D.

Parameter Value Unit Reference Intact rock Rock type PGR MIGM.GN Young’s modulus E 55 GPa *Biaxial tests Poisson’s ratio � 0.20 - *Biaxial tests Anisotropy dip - 52° deg Geological mapping Anisotropy direction - 175° deg Geological mapping Anisotropy direction isotr. parallel perpend. UCS �UCS 115 105 123 MPa **See chapter 0 Rock mass strength �cm 65.6 60 70 MPa **See chapter 0 Cohesion c 12.9 12.4 13.8 MPa Estimated after �cm Friction angle � 47° 45° 47° deg Estimated after �cm Tensile strength �T,I 12 10 14 MPa **See chapter 2.3.1 In situ stress Value Direction Major principal stress �1 25.1 MPa 166 (hor.) ° In situ tests Intermediate principal stress �2 17.1 MPa 256 (hor.) ° In situ tests Minor principal stress �3 12.3 MPa up ° In situ tests Fractures isotr. parallel perpend. Fracture toughness I KIC 1.96 1.87 3.05 MPa+, ***See chapter 2.3.4 Fracture toughness II KIIC 3.30 3.00 3.86 MPa+, ***See chapter 2.3.4 Cohesion – tensile c 10 MPa Estimated Cohesion – shear c 10 MPa Estimated Friction angle – tensile �t 35° deg Posiva 2009, table 5-6 Friction angle – shear �s 35° deg Posiva 2009, table 5-6 Dilatation angle – tensile �t 2.5° deg Posiva 2009, table 5-6 Dilatation angle – shear �s 2.5° deg Posiva 2009, table 5-6 Normal stiffness – tensile kn 20,000 GPa/m ****See chapter 2.3.5 Normal stiffness – shear kn 20,000 GPa/m ****See chapter 2.3.5 Shear stiffness – shear ks 2000 GPa/m ****See chapter 2.3.5 Shear stiffness – tensile ks 2000 GPa/m ****See chapter 2.3.5 Initial aperture 10x10-6 m Rutqvist et al. 2007 Residual aperture 1x10-6 m Rutqvist et al. 2007 Fracod models Initial crack element size 60 mm Estimated Model element size 37 - 75 mm Estimated

*Based in unpublished biaxial tests from POSE niche, Posiva 2009 gives also similar values **Modified after Hakala et al. 2005 ***Modified after GeoFrames 2009 ****Modified after Rutqvist et al. 2007

2.3.1 Tensile strength

The tensile strength as a function of anisotropy is determined by using the test results reported in Hakala et al. 2005, Figure 5-17. The tests were done with the Brazilian test. The test results are presented in Figure 2-3.

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Figure 2-3. Tensile strength reported by Hakala et al. 2005, figure 5-17. The tensile strength values for different anisotropy directions are shown in red dashed line.

The mean value and the standard deviation of tensile strength by Hakala et al. 2005 are 14.5 MPa (n=18) and 2.8 MPa. This is different from values 12 MPa and 4 MPa re-ported by Posiva 2009. The number of samples is much higher in Posiva 2009 and therefore the results should be also more reliable. It should be noted that Hakala et al. 2005 test specimens were stored in a normal room temperature and were unsaturated, so the test results are higher than in other tests; also, the number of samples was low compared to the deviation and to the heterogeneity of Olkiluoto gneissic rocks. This means the values need to be corrected. The corrected values can be established, by selecting two regions (mean values 16.5 MPa and 12.5 MPa, see Figure 2-3) by Hakala et al. 2005, and by correcting them with the difference 2.5 MPa to the mean value reported by Posiva 2009. By shifting the re-sults down with 2.5 MPa the corrected mean values for the tensile strengths for different anisotropy directions can be determined. The correction is done by using equations 8 and 9. �t(0°) = 12.5 MPa – 2.5 MPa = 10 MPa

8

�t(90°) = 16.5 MPa – 2.5 MPa = 14 MPa

9

10 MPa

14 MPa

12

The corrected values for different anisotropy directions still stay within the standard deviation of the Posiva 2009 values.

2.3.2 Intact rock strength parameters

The uniaxial compressive strength mean value of 115 MPa reported in Posiva 2009 is used for the pegmatitic granite. For the migmatitic gneiss, the peak strength as a func-tion of the anisotropy direction is determined by using the results of (Figure 2-4) Hakala et al. 2005. The test specimens were stored in a normal room temperature and were un-saturated, so the test results are higher than in other tests.

Figure 2-4. Peak compressive strength versus anisotropy angle (Hakala et al. 2005, figure 5-17). The peak strength values for different anisotropy directions are shown in red dashed line. It can be observed in Figure 2-4 that the peak strength is the lowest at the angles near 45 degrees. This is explained by Hakala et al. (2005) by that the foliation directions in an-gle 45°+(�/2) should be associated with the lowest strength values, as presented in Fig-ure 2-1. The peak strength values for different anisotropy directions are determined by dividing the test results (see Figure 2-4) into two regions and by taking a lower quartile of the values in the regions. This results in low and conservative values (123 MPa and 105

123 MPa

105 MPa

13

MPa), however the results are still within the standard deviation reported by Posiva 2009, Table 5-3 (with the mean value of 115 MPa).

2.3.3 Rock mass strength

The rock mass strength (spalling strength) is estimated to be 57 % of the UCS, as re-ported in Posiva 2009, page 197. It should be noted that this is estimated after the re-sults in Underground research laboratory (URL) in Canada and Äspö Hard Rock Labo-ratory (HRL) in Sweden. The rock mass strength of the rocks in Olkiluoto is an object of research in the POSE in situ experiment. For pegmatitic granite the 65.6 MPa (57 % of UCS) is used. For the migmatitic gneiss, the values of 60 MPa and 70 MPa were estimated as the rock mass strength after results by Hakala et al. 2005. From these values, cohesion and friction angle were determined using the equation -./01 � 234��56789:�

* ;<69: 10

The friction angle is estimated to be 45° for the anisotropy direction and 47° for the perpendicular direction and for the isotropic rock mass. The cohesion calculated with equation 10 is correspondingly 12.9 MPa for pegmatitic granite, 12.4 MPa for the ani-sotropy direction and 13.8 MPa for the perpendicular direction to anisotropy.

2.3.4 Fracture toughness properties

The fracture toughness properties are determined by using the results of the Olkiluoto laboratory tests by GeoFrames (2009). Values are calculated by using for KIC the Chev-ron Bend test results and for KIIC the Punch-Through Shear with Confining Pressure (PTS/CP) test results. For pegmatitic granite, the values are calculated as mean of three test values. For different anisotropy directions, the KIC values are determined by using corrected CB results. The results are separated in two regions corresponding to anisotropy directions shown in figure 2-5. For the foliation direction, there are five samples within the range of 1.50…2.25 MPam1/2 with the average of 1.87 MPam1/2. For the direction perpendicu-lar to the foliation direction, there are five samples within the range of 2.50…3.75 MPam1/2 with the average of 3.05 MPam1/2.

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Figure 2-5. Chevron Bend test results separated in regions. The KIIc values are similarly determined by using PTS/CP test results shown in Figure 2-6. For the foliation direction, there are five samples within the range of 1.50…3.40 MPam1/2 with the average of 3.00 MPam1/2. For the direction perpendicular to the folia-tion direction, there are five samples within the range of 3.40…4.20 MPam1/2 with the average of 3.86 MPam1/2.

Figure 2-6. The Punch-Through Shear with Confining Pressure test result.

2.3.5 Other fracture properties

The properties of pre-existing fractures are determined by using the values by Posiva 2009, Table 5-6 set 4. From the first 2400 chainage metres of the drive tunnel, four frac-ture sets have been found, from which set 4 is reported to be parallel to the foliation.

00,5

11,5

22,5

33,5

Fracture toughness in mode I (MPam1/2)

Number of samples

CB-test

CB-test (corrected)

00,5

11,5

22,5

33,5

44,5

<2,8 2,8...3 3...3,2 3,2...3,4 3,4...3,6 3,6...3,8 3,8...4 4...4,2 >4,2

Fracture toughness in mode II (MPam1/2)

Number of samples

All Kiic PTS/CP -test results

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However, these properties are not used in the models, while there are no pre-existing fractures used in the model. Other fracture properties are estimated by using related literature and previous Fracod models. The ratio of Kn/Ks is usually 10, for example Rutqvist et al. 2007. Different values for the parameters with the same ratio were studied to determine a functional value. The values of Kn and Ks, respectively 20,000 GPa/m and 2000 GPa/m, were es-timated to produce the most realistic results; this is also close to the values used by Rutqvist et al. (2007): 26,976 GPa/m and 2697.6 GPa/m. The values of initial and re-sidual aperture are the same as used by Rutqvist et al. (2007).

2.4 Sensitivity studies

Several different sensitivity studies are done to study the sensitivity of the parameters used.

2.4.1 Anisotropy direction

The foliation direction with lower strength parameters is expected to be the direction in which the failure progresses. However, as the foliation direction is determined from the tunnel and has some natural variation, it is subject to the most comprehensive sensitivity analysis of this work. The effect of the foliation direction is studied in the models by changing the foliation direction by ±15 degrees.


Also the tensile strength of the rock is subject to a sensitivity analysis to determine how small changes in the tensile strength affect the results. This analysis is done by decreas-ing the tensile strength in the model with the widest spalling observed and by increasing the tensile strength in the model with the least spalling. The tensile strength values used for the analysis are listed in Table 2-2. Table 2-2. The parameters of the sensitivity study of the tensile strength. Anisotropy direction

Tensile strength

Model 1 Model 2 Model 3

parallel 8 MPa 12 MPa� 8 MPa perpendicular 12 MPa 16 MPa 16 MPa

2.4.3 Fracture toughness

The fracture toughness parameters are doubled to study the sensitivity of the parame-ters. The study is only done for the anisotropic model.

16

The sensitivity of fracture toughness parameters in mode I is studied with the values of 3.74 MPam1/2 and 6.10 MPam1/2 for the corresponding anisotropy directions. These val-ues are above the variation, which is from 1.63 MPam1/2 to 3.52 MPam1/2. Therefore the values can be considered to be high enough for the sensitivity studies. The sensitivity of fracture toughness parameters in mode II is studied with the values of 6.00 MPam1/2 and 7.72 MPam1/2 for the corresponding anisotropy directions. These val-ues are also above the variation of test results.

2.4.4 Rock mass strength

The sensitivity of the rock mass strength parameters is studied by using the rock mass strength values of 70 MPa and 80 MPa instead of 60 MPa and 70 MPa. The values are above the assumed spalling strength. Converted to cohesion and friction angle, the pa-rameters are respectively 50° / 12.7 MPa and 52° / 13.8 MPa. To determine the threshold of the fracture growth, the values of 65 MPa and 75 MPa were also used. Converted to cohesion and friction angles, the parameters are respec-tively 48° / 12.5 MPa and 52° / 12.9 MPa.

2.4.5 Friction angle and cohesion

The sensitivity of the balance between friction and cohesion is studied by using the rock mass strength values of 60 MPa and 70 MPa. The effect of high friction angles, 50° and 60°, with the low cohesion values of 10.9 MPa and 9.4 MPa is studied. Also Cohesion softening method (CS) suggested by Edelbro (2010) is studied, using friction angles close to zero, 0.1° and 0.1°, with the high cohesions values of 29.9 MPa and 34.9 MPa.

17

3 MODELLING OF THE POSE TUNNEL

These models consist of two models, the first of which is a vertical cross-section of the POSE tunnel, and the second of which is a horizontal section of the experiment holes. The layout is illustrated in Figure 3-1 with indication of the cross-sections modelled in 2-D by means of Fracod2D.

Figure 3-1. The layout of the POSE tunnel with the cross-section planes.

3.1 Models of the POSE tunnel

The POSE tunnel is oriented in north, and its inclination is towards south with the rate of 1:50. In the 2-D cross-section of the POSE tunnel, the foliation direction is almost vertical, and in the POSE hole 2-D cross-section. The model of the POSE tunnel is pre-sented in Figure 3-2. The tunnel was excavated in 2 stages when built; however, the tunnel is modelled in one stage only.

Figure 3-2. The model of POSE tunnel where projection of anisotropy in 2D plane is presented with red line and two additionally tested anisotropy directions with blue line.

18

Three different anisotropy directions are tested according to variation of anisotropy di-rections as projection on the modelled plane (blue lines in Figure 3-3). Different crack initiation lengths and element sizes are tested.

3.2 Models of the POSE holes

For the modelling of the POSE holes, a horizontal 2-D cross-section is used. The boundary stresses are defined the following way: The stress component aligned along the POSE tunnel axis (�YY) is the principal stress direction (�1 in table 2-1). The stress component perpendicular to the POSE tunnel (�XX) is calculated by using the POSE tunnel model. The cross-section and stress components used are presented in Figure 3-3. .

Figure 3-3. Cross-section of the POSE holes with the grid points and stress components. The model element size and initial crack length are set as 60 mm with different values tested from 6 mm to 150 mm. The holes are excavated in two stages.

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0X Axis (m)

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(m)

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(m)

�YY

�XX

19

4 RESULTS

In this chapter, the results of the models are described with special attention to spalling.

4.1 Tunnel model

The modelling of the vertical cross-section of the POSE tunnel results shows no fractur-ing at all. A plot of the horizontal (�xx) and vertical (�yy) stresses along a line between the experiments holes is shown in Figure 4-1.

Figure 4-1. Left: Plot of the horizontal (�xx) and vertical (�yy) stresses along a line be-tween the experiment holes heading downwards from the tunnel floor to 6 metres’ depth. The stresses at 1 m and 3 m under the floor are presented with blue boxes. Right: Major stress component plotted. Although three anisotropy directions were tested, the results remain constant, because there is no fracture growth or geometry changes in the model. The results of the tunnel model are used in the following models with the two holes. The results and the input parameters for the next models are presented in Table 4-1. Table 4-1. The stresses at 1 m and 3 m under the floor of the POSE tunnel, that are used as input values for POSE hole models. Stress component Depth below the POSE tunnel floor

�xx (horizontal, perpendicular to POSE)

�v (vertical, calcu-lated with POSE tunnel model)

�zz (horizontal, parallel to POSE) [MPa]

1 m 19.0 MPa 0.5 MPa� 25.1 MPa 3 m 21.5 MPa 4.0 MPa 25.1 MPa

-7400E4 -6400E4

-5400E4

-3400E4-3400E4

-3400E4

-2400E4

-2400E4-2400E4

0E4

-14

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14X Axis (m)

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

Y A

xis

(m)

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14X Axis (m)

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

Y A

xis

(m)

POSE tunnel

20

4.2 Isotropic model of the POSE holes

The model with the parameters of pegmatitic granite is homogeneous with no anisot-ropy directions. However, the results are asymmetric, because the elements at the hole boundary are not symmetrically aligned and the model does not use symmetry. In addi-tion, the excavation of the first hole causes deformations in the rock, which affects the results when the second hole is excavated. The results from the depths of 1 metre and 3 metres are shown in Figure 4-2.

Figure 4-2. Fracture propagation on pegmatitic granite at 1 metre’s depth (up) and 3 metres’ depth (down). Hole 1 is excavated first (left,) and hole 2 in the next stage (right). In both models (1 and 3 metres), spalling can be observed after the drilling of the sec-ond hole. The depth of spalling is 20 to 40 mm. However, the fracture growth and spalling is more pronounced at 3 metres’ depth that metre. In both models, a single frac-ture progresses (148 mm and 241 mm deep) into the pillar, forming a crevice.

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(m)

POSE holes 1m depth

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xis

(m)

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-3.0

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-0.5

0

0.5

1.0

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2.5

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Y A

xis

(m)

POSE holes 1m depth

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0X Axis (m)

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0

0.5

1.0

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xis

(m)

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-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

Y A

xis

(m)

POSE holes 3m depth

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0X Axis (m)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

Y A

xis

(m)

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0X Axis (m)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

Y A

xis

(m)

POSE holes 3m depth

148 mm

44 mm

241 mm

40 mm

�1=25.1 MPa

�xx=19.0 - 21.5 MPa

21

4.3 Anisotropic model of the POSE holes

Migmatitic gneissic rock with interpreted anisotropy in the direction of 99° results in some fracture propagation at both sides of both holes, as shown in figure 4-3, at the depth of both 1 metre and 3 metres. The results indicate only minor differences between the depths and that spalling will occur in both. Notches that form are deeper than in iso-tropic model.

Figure 4-3. Anisotropic model showing the spalling and crevice at the depth of 1 metre (up) and 3 metres (down). The direction of anisotropy is shown in the figure with red line and two additionally tested anisotropy directions with blue line.

The major and minor principal stresses are illustrated in Figure 4-4. In the major princi-pal stress figure (left), small disturbances in the surface of the whole hole can be no-ticed. The disturbances are due to the changing distances between the rectangular grid of the model and the round grid around the excavations. The maximum compressive stresses at the pillar between the holes are at the highest 73 MPa, which is over the assumed spalling limit of 65.6 MPa. This leads to crack growth that starts with a single crack growing in the anisotropy direction or perpendicular to it. The cracks form crevices, which join and form spalling when the crack growth turns its

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0X Axis (m)

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POSE holes 1m depth

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(m)

POSE holes 1m depth

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0

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Y A

xis

(m)

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-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

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xis

(m)

POSE holes 3m depth

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0X Axis (m)

-3.0

-2.5

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-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

Y A

xis

(m)

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0X Axis (m)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

Y A

xis

(m)

POSE holes 3m depth

109 mm

94 mm

85 mm

98 mm

Linkitettyä kuvaa ei voi näyttää. Tiedosto on ehkä siirretty, nimetty uudelleen tai poistettu. Tarkista, että linkki osoittaa oikaan tiedostoon tai sijaintiin.




22

direction parallel to the tangential stress direction. The forming of cracks stops when a balanced state is reached. At this state, the maximum tangential stress in the pillar sur-face is 64 MPa. The maximum tensile stress stays much below the tensile strength, at the maximum at 0.5 MPa. The maximum shear stress is 34 MPa.

Figure 4-4. The major (left) and minor (right) principal stresses with mean anisotropy direction of 99° at 3 metres depth. The tangential stress after the fracture growth in the pillar between the holes is pre-sented in table 4-2. It should be noted that, since this is stage-dependent, values differ from the one presented in Figure 4-4. However, as the pillar is fractured, the stresses are lower at the excavation surface; therefore the values are maximum values from the pil-lar. Table 4-2. The stresses in the pillar between the holes.

Hole 1 Hole 2 Excavation phase �1 (MPa) �3 (MPa) �1 (MPa) �3 (MPa) First hole 1 m deep <57 >0 ~30 ~17 Second hole 1 m deep <73 >0 <73 >0 First hole 3 m deep <55 >0 ~30 ~17 Second hole 3 m deep <72 >0 <72 >0

-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0X Axis (m)

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-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0X Axis (m)

-3.0

-2.8

-2.6

-2.4

-2.2

-2.0

-1.8

-1.6

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-0.8

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0

0.2

0.4

0.6

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1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Y A

xis

(m)

POSE holes 3m depth

-5.2

-5.0

-4.8

-4.6

-4.4

-4.2

-4.0

-3.8

-3.6

-3.4

-3.2

-3.0

-2.8

-2.6

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-1.8

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0

Prin

cipa

l Maj

or S

tres

s (

Pa)

xE

7

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-3.0

-2.8

-2.6

-2.4

-2.2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Y A

xis

(m)

-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0X Axis (m)

-3.0

-2.8

-2.6

-2.4

-2.2

-2.0

-1.8

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-1.4

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-1.0

-0.8

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-0.2

0

0.2

0.4

0.6

0.8

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1.2

1.4

1.6

1.8

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2.2

2.4

2.6

2.8

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xis

(m)

POSE holes 3m depth

-2.3

-2.2

-2.1

-2.0

-1.9

-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

Prin

cipa

l Min

or S

tres

s (P

a) x

E7

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-3.0

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0

0.5

1.0

1.5

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2.5

3.0

Y Ax

is (m

)

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-1.0

-0.5

0

0.5

1.0

1.5

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2.5

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Y Ax

is (m

)

POSE holes 3m depth

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

Prin

cipa

l Maj

or S

tress

(Pa

) xE7

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-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

Y Ax

is (m

)

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0X Axis (m)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

Y Ax

is (m

)

POSE holes 3m depth

-2.2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0

Prin

cipa

l Min

or S

tress

(Pa)

xE7

<72 MPa

<72 MPa

<55 MPa >0 MPa

>0 MPa

>0 MPa

~17 MPa ~30 MPa

23

The displacements are shown in Figure 4-5. The maximum total displacement is 0.6 millimetres to the principal stress direction. In the middle of the pillar there is no dis-placement.

Figure 4-5. Displacements with the mean anisotropy direction (99°). The fracture propagation in stages with the mean anisotropy direction (99°) is in Figure 4-6. The figures are close-ups of the pillar between the holes. From the figures it can be observed that small notches, which are about the size of the grid density, form at the right side at 2nd cycle and the large wedge on left forms last.

Figure 4-6. The fracture propagation in stages with the mean anisotropy direction (99°). Fractures marked with green are slipping and fractures marked with red are open.

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2.5

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is (m

)

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0X Axis (m)

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is (m

)

POSE holes 3m depth

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Tota

l Dis

plac

emen

t (m

) xE-

4

24

4.4 The effect of the anisotropy direction to the POSE holes

The anisotropy direction has some influence on the fracture propagation and on spalling. The results of the influence of the anisotropy direction are shown in Figure 4-7 and Figure 4-8.

Figure 4-7. Anisotropic model showing the spalling and crevice at the depth of 1 metre (up) and 3 metres (down). The direction of anisotropy is shown in the figure. The anisotropy direction in figure 4-7 is 84 degrees, thus almost in the minor principal stress direction. As can be noticed, the fracturing is vastly reduced due to the fact that the compression in the pillar is almost directly perpendicular to the anisotropy direction. The fracture growth is only initiated in the pillar edges, where the tangential stress is the largest and displacements are small.

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25

Figure 4-8. Anisotropic model showing the spalling and crevice at the depth of 1 metre (up) and 3 metres (down). The direction of anisotropy is shown in the figure.

The anisotropy direction in Figure 4-8 is 114 degrees. This leads to a slightly larger fracture growth than in the model with the anisotropy direction of 84 degrees; however, the fracture growth is smaller than in the model with mean values.

4.5 The sensitivity studies

The results of the sensitivity studies of POSE hole models are shown in the following chapters.


The sensitivity of the results to the tensile strength was studied by varying the parameter according to table 2-2. However, no change in the results was observed with a change of 2–4 MPa in the tensile strength. This is consistent with the observations from the mod-els that the maximum tensile stress of 0.5 MPa is significantly smaller than the used tensile strength.

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4.5.2 Fracture toughness parameters

The sensitivity of the fracture toughness parameters was studied by doubling the pa-rameters so that all values were above the variation of the test results. The results of the model from the depth of 3 metres below the tunnel are shown in figure 4-9 right; in the left, the original model for comparison.

Figure 4-9. The effect of the fracture toughness parameters studied with the original parameters (left) and the higher (doubled) parameters (right).

4.5.3 Rock mass strength parameters

Using the rock mass strengths of 70 MPa and 80 MPa totally eliminated all fracture growth from the model. Therefore, the rock mass strength values of 65 MPa and 75 MPa were studied. Again, neither fracture growth nor spalling was observed. Narrowing down the spalling strength, the rock mass strength values of 62.5 MPa and 72.5 MPa were used. Correspondingly, the cohesions and friction angles are 46° and 12.6 MPa and 48° and 13.9 MPa. Increasing the spalling strength a bit more, the rock mass strength values were raised to 63.75 MPa and 73.75 MPa. Correspondingly, the cohesions and friction angles are 46° and 12.9 MPa and 48° and 14.2 MPa. This time, no crack growth was observed. The results are presented in Figure 4-10.

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Linkitettyä kuvaa ei voi näyttää. Tiedosto on ehkä siirretty, nimetty uudelleen tai poistettu. Tarkista, että linkki osoittaa oikaan tiedostoon tai sijaintiin.Linkitettyä kuvaa ei voi näyttää. Tiedosto on ehkä siirretty, nimetty uudelleen tai poistettu. Tarkista, että linkki osoittaa oikaan tiedostoon tai sijaintiin.

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Figure 4-10. The sensitivity of rock mass strength parameters studied with rock mass strength of 62.5/72.5 MPa with fracture growth on left and 63.75/73.75 MPa on right.

4.5.4 Friction angle and cohesion

The effect of the balance between the friction angle and cohesion was studied by using approaches with a high friction angle with low cohesion and high cohesion with a low friction angle. The model mentioned first results in only one fracture growing on both sides of the pillar with no spalling. The model mentioned second results in multiple fractures, although shorter and with no observed spalling. The results are presented in Figure 4-11.

Figure 4-11. The sensitivity of friction angles and cohesion was studied; a model with a high friction angle with low cohesion on the left, and high cohesion with a low friction angle on the right.

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5 CONCLUSIONS

The primary objective of this work is to predict the results of the POSE project, which aims to establish the in situ spalling strength of the Olkiluoto migmatitic gneiss and also secondarily to establish the state of in situ stress. The experiment is based on boring two large holes on the bottom of the POSE tunnel First, the model with the tunnel geometry was calculated in order to achieve the stress state below the tunnel. Although three anisotropy directions were tested in tunnel model, no change in the stress state was noticed. This is because Fracod2D only takes into account the strength anisotropy but not the deformation anisotropy. A change in the results would require fracture growth or geometry changes in the model. However, ani-sotropy direction had influence on models with holes and concentrated stresses below the tunnel.

5.1 Spalling

Fracture growth happens in all of the models with the POSE holes. In the models with the anisotropy of 84 degrees, the cracks form only crevices, but in the rest of the models the fractures form notches—or in other words, spalling. The results are assembled in Table 5-1. In the table the number of crevices and spalling is stated as observed from the results. The scale of the fracture growth is divided into four categories. Table 5-1. The results of the models. Spalling in the 1st hole pillar Spalling in the 2nd hole pillar Model Depth Width Type Depth Width Type NotesPeg - 1m 44 mm 409 mm 3xNm,Cs 148 mm 593 mm Ns,2xCm,Cx Peg - 3m 40 mm 295 mm 3xNm 241 mm 421 mm Nm+Cx 84° - 1m 71 mm 295 mm Cl,2xCm 48 mm 296 mm 3xCm 1

84° - 3m 55 mm 294 mm 3xCm 48 mm 295 mm 3xCm 1

99° - 1m 98 mm 468 mm 2xNm,2xCl 85 mm 468 mm Nm+Cl,2xCl 99° - 3m 94 mm 352 mm 2xNs,Cl 109 mm 352 mm Nm+Cl,Cl 114° - 1m 82 mm 409 mm Nm,2xCl,Cm 78 mm 410 mm Nm+Cl,2xCl 2

114° - 3m 97 mm 410 mm Ns,3xCl 75 mm 410 mm Nm, 2xCl Abbreviations: N=Notch, C=Crevice Scale of the notches: s=Small (depth<50 mm), m=Medium (50…100 mm), l=Large (> 100 mm), x=Extra (400...500 mm) Example: Ns = small notch Note 1: All fractures are slipping. Note 2: Medium sized crevice at the opposite side of the pillar in the 1st hole. The results show that with the used parameters, new fractures initiate and grow in all models. However, in conditions with the anisotropy direction across the pillar (84°), no spalling is formed. This is possibly due to the fact that, compared to the isotropic model, the rock mass parameters are higher perpendicular to the anisotropy direction, which in this case is the major principal stress direction. It can also be observed in the results that the most vulnerable modelled anisotropy di-rection with regards to spalling is 99 degrees. Noting the previous and the results of the

29

models, it can be stated that the direction of anisotropy is very sensitive for spalling. A 15-degree change can determine whether spalling or a crevice occurs.

5.2 Sensitivity studies

The sensitivity studies showed that a 2-MPa change in the tensile stress does not have any noted effects. This is due to the significantly lower maximum tensile stresses in the models. It was also noted that changes in the fracture toughness values do not have significant effects on the results. Higher fracture toughness values only changed the form of the cracks with minor direction changes. This is due to the fact that the fracture initiation is controlled by the rock mass strength and the fracture growth by the fracture toughness parameters. The rock mass spalling strength with the current parameters was narrowed down to be between 62.5 MPa and 63.75 MPa for the anisotropy direction. The balance between the friction angle and cohesion is studied and noted to have a significant effect on the amount of the fractures growing.

5.3 Final conclusions

With the used parameters it is predicted that in most of the cases the second hole will have spalling and there will be new crack propagation in both holes.

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REFERENCES

Aalto, P., Aaltonen, I., Ahokas, H., Andersson, J., Hakala, M., Hellä, P., Hudson, J., Johansson, E., Kemppainen, K., Koskinen, L., Laaksoharju, M., Lahti, M., Lindgren, S., Mustonen, A., Pedersen, K., Pitkänen, P., Poteri, A., Snellman, M. & Ylä-Mella, M. 2009. Programme for Repository Host Rock Characterisation in ONKALO (ReRoc). Posiva Oy, Working Report 2009-31 Andersson, C. J. 2007. Rock mass response to coupled mechanical thermal loading Äspö Pillar stability Experiment. Doctoral Thesis, KTH, Sweden.

Crouch S.L., 1976. Solution of plane elasticity problems by the displacement disconti-nuity method. Int. J. Num. Methods Engng. 10, 301-343.

Edelbro, C. 2010. Different Approaches for Simulating Brittle Failure in Two Hard Rock Mass Cases: A Parametric Study. Rock Mechanics and Rock Engineering. 43 (2): (2010) 151-165. GeoFrames 2009, Determination of Rock Mechanical Parameters. Potsdam: GeoFrames GmbH. Unpublished. Hakala, M., Kuula, H. & Hudson, J. Strength and Strain Anisotropy of Olkiluoto Mica Gneiss. Working report 2005-61, Olkiluoto, Finland, Posiva Oy, 2005 Hudson, J. A. & Harrison, J. P., 1997. Engineering Rock Mechanics – An Introductio to the Principles. Pergamon. Posiva 2009. Olkiluoto Site Description 2008. Report Posiva 2009-01. Rutqvist J, Bäckström A, Jing L, Hudson J A, 2007. A benchmark simulation study of coupled THMC processes in the excavation disturbed zone associated with geological nuclear waste repositories. DTHMC, DECOVALEX, Task B, Phase 3 Report. Contribu-tions from modelling teams. Rutqvist, Bäckström, Jing and Hudson eds. The Swedish Nuclear Power Inspectorate, SKI Report. Shen B, Rinne M, Stephansson O, 2010. FRACOD2D. User’s Manual ver 3.1H, 2010. Fracom Ltd. Shen B. and Stephansson O., 1993. Numerical analysis of Mode I and Mode II propaga-tion of rock fractures. Int. J. Rock Mech. Min. Sci. & Geomech. Abst. 30(7), 861-867.

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