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ONKALO POSE Experiment - Phase 3:FRACOD2D Prediction
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POSIVA OY
Olki luoto
FI-27160 EURAJOKI, F INLAND
Phone (02) 8372 31 (nat. ) , (+358-2-) 8372 31 ( int. )
Fax (02) 8372 3809 (nat. ) , (+358-2-) 8372 3809 ( int. )
May 2015
Working Report 2012-59
Topias Siren
May 2015
Working Reports contain information on work in progress
or pending completion.
Topias Siren
Posiva Oy
Working Report 2012-59
ONKALO POSE Experiment - Phase 3:FRACOD2D Prediction
ABSTRACT The main objectives of the POSE experiment (Posiva’s Olkiluoto Spalling Experiment) are to determine the Olkiluoto rock mass spalling strength and to confirm the in situ stress state. The third phase of the POSE experiment is a test where a single experimental hole (ONK-EH3) is heated from inside. The heating is executed using eight heating elements and aluminium oxide is used as filling material to conduct the heat into the rock. The rock type in the experiment is mainly pegmatitic granite which is quite homogeneous compared to the migmatitic gneiss that was the rock material in earlier stages of the POSE experiment. Symmetrical heating, a homogeneous rock mass and symmetrical experiment geometry allows more reliable determination of the in situ stress direction. The experiment acts also as a prediction-outcome (P-O) exercise and therefore predictions were created before the execution of the experiment. The fracture mechanics prediction was created using a 2-dimensional fracture mechanics code FRACOD2D version 4.11 with thermo-mechanical coupling. The simulations used an isotropic constitutive model for the rock mass with fracture initiation and propagation simulated using the F-criterion. The temperature boundary conditions at the hole surface were acquired from the thermomechanical 3D predictions of the same experiment by Hakala & Valli (2013). The heating cycle used was three weeks of heating with individual power outputs of 400 W and the following nine weeks with 800 W power outputs. The results indicated that fractures start to grow in the direction of the minor principal stress 1.5 weeks after the start of heating. Depending on the stress interpretation, the fractures will increase in width as heating progresses and will surround the experimental hole by the end of heating. A common aspect in both modelled stress interpretations is that the majority of the damage is subsurface and the maximum depth is 130–140 mm. The acoustic emissions follow the development of fractures and indicate no clear concentration of AE events around the experiment hole. Keywords: in situ stress, fracture mechanics, thermomechanical, prediction, spalling, POSE.
ONKALO POSE-koe - Vaihe 3: FRACOD2D-ennuste TIIVISTELMÄ POSE-kokeen (Posiva’s Olkiluoto Spalling Experiment) päätavoitteet ovat määrittää Olkiluodon kalliomassan hilseilylujuus ja vahvistaa in situ jännityskenttä. POSE-kokeen kolmas vaihe on koe, jossa yksittäistä tutkimusreikää (ONK-EH3) lämmitetään sisältä. Lämmitys toteutetaan käyttämällä kahdeksaa lämmityselementtiä ja alumiinioksidia täyttömateriaalina lämmön johtamiseksi kallioon. Kivilaji kokeessa on pääasiassa pegmatiittinen graniitti, joka on melko homogeeninen verrattuna migmatiittiseen gneissiin, jossa suoritettiin POSE-kokeen aiemmat vaiheet. Symmetrinen lämmitys, homogeeninen kalliomassa ja symmetrinen koegeometria mahdollistavat aiempiin vaiheisiin verrattuna luotettavamman in situ jännityksen suunnan määrityksen. Koe toimii myös prediction-outcome (PO) harjoituksena ja siksi kokeesta laadittiin ennusteet ennen kokeen toteuttamista. Rakomekaaninen ennuste luotiin käyttämällä 2-dimensionaalista rakomekaanisen FRACOD2D -koodin 4.11 versiota lämpömekaani-sella kytkennällä. Simulaatioissa käytettiin isotrooppista konstitutiivista mallia kallio-massalle sekä rakojen syntymistä ja etenemistä käyttämällä F-kriteeriä. Lämpöreuna-ehtoina reiän pinnalla käytettiin arvoja Hakalan ja Vallin (2013) lämpömekaanisista 3D ennustelaskennoista. Lämmitys toteutettiin sykleissä, jossa 3 viikkoa lämmitettiin 400 W lämmitintä kohden, jonka jälkeen 9 viikkoa 800 W lämmitintä kohden. Tulosten mukaan raonkasvu alkaa pienemmän pääjännityksen suuntaan 1,5 viikkoa lämmityksen aloituksen jälkeen. Riippuen jännitystulkinnasta raot laajenevat lämmi-tyksen edetessä ja ympäröivät tutkimusreiän lämmityksen loppuun mennessä. Yhteinen tekijä molemmissa mallinnetuissa jännitystulkinnoissa on, että pääosa vaurioista syntyy pinnan taakse, maksimivauriosyvyyden ollessa 130-140 mm. Akustiset emissiot synty-vät yhdenmukaisesti rakojen kanssa ja eivät indikoit selvää akustisten emissioiden konsentraatiota reiän ympärillä. Avainsanat: in situ jännitystila, rakomekaniikka, termomekaaninen, ennuste, hilseily, POSE.
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TABLE OF CONTENTS ABSTRACT
TIIVISTELMÄ
PREFACE ....................................................................................................................... 2
1 INTRODUCTION ................................................................................................... 3 1.1 Background .................................................................................................. 3 1.2 The third phase of the POSE experiment .................................................... 5 1.3 Fracture mechanics ...................................................................................... 8
2 THEORY ............................................................................................................... 9 2.1 Fracture initiation .......................................................................................... 9 2.2 Fracture propagation .................................................................................. 10 2.3 Thermo mechanical coupling ..................................................................... 10
3 MATERIAL PROPERTIES AND HEATING SCHEME ........................................ 11 3.1 Constitutive model and material properties ................................................ 11 3.2 The rock stress ........................................................................................... 12 3.3 Heating scheme ......................................................................................... 13
4 GEOMETRIC VARIABLES .................................................................................. 15 4.1 Simultaneous fracture propagation parameter ........................................... 16 4.2 Parameter for fracture merging tolerance .................................................. 16 4.3 Parameter for elastic fracture growth ......................................................... 16 4.4 Sensitivity of the parameters ...................................................................... 16 4.5 Comparison of the geometric variables ...................................................... 16
5 RESULTS ............................................................................................................ 18 5.1 Fracture propagation in EDZ & VT1 stress state ....................................... 19 5.2 Fracture propagation in ONK-EH3 stress state .......................................... 23 5.3 Acoustic emission prediction ...................................................................... 25
6 CONCLUSIONS AND DISCUSSION .................................................................. 28
REFERENCES ............................................................................................................. 29
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PREFACE
The predictions were calculated after the execution of the first and second phase of the POSE experiment and before the actual execution of the third phase of POSE experiment. Unfortunately, the reporting of the predictions wasn't possible before the execution of the experiment. In the reporting phase a minor geometrical difference in gridpoint spacing between the models with the two stress interpretations was found and corrected. The difference affected to the fracture pattern, since the fracture propagation process is recursive. The difference didn't have significant impact to the end results. The author wishes to thank Dr. Baotang Shen for valuable help in fracture mechanics modelling, for the commenting and proofreading of the report John Hudson, Johannes Suikkanen and Matti Hakala, and everyone involved in the process of making the POSE experiment possible.
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1 INTRODUCTION
This working report describes the fracture mechanics prediction for the third phase of Posiva's Olkiluoto Spalling Experiment (POSE). The third phase is called the single hole heating test and was executed in the ONK-EH3 experiment hole. All of the three phases of the POSE experiment were executed in the third investigation niche of ONKALO (Underground Rock Characterization Facility, see Figure 1-1) located at a depth of -345 metres.
Figure 1-1. Layout of ONKALO with the experiment area in the POSE-niche.
1.1 Background
Currently in Olkiluoto, the construction of the underground rock characterisation facility for the final disposal of spent nuclear fuel named ONKALO is on the way (see Figure 1-1). 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 questions, an in situ experiment called Posiva’s Olkiluoto Spalling Experiment (POSE) was started in 2009 (Aalto et al. 2009). The POSE pillar stability experiment (Phases 1 and 2) was conducted between the years 2010 and 2011 and is documented in Johansson et al. 2014. In Phases 1 and 2 of the POSE experiment (Figure 1-2), it was noted that the geology in experiment holes ONK-EH1 and ONK-EH2 had a significant role in the fracturing of surrounding rock. The geology in the holes is migmatitic gneiss. The experiments concluded mainly with geology influenced extension fractures along the hole wall and only minor spalling was observed. The third phase of the POSE experiment was conducted in a single hole (ONK-EH3 in Figure 1-3) at the beginning of year 2013.
Experiment area
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Figure 1-2. The third investigation niche during the execution of the second phase of the POSE experiment. (Photo courtesy of Posiva).
Figure 1-3. Layout of the POSE experiment niche with two stress interpretations visualized and experiment hole ONK-EH3 marked. (modified after Hakala & Valli 2013)
Experiment hole ONK-EH3
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1.2 The third phase of the POSE experiment
The purpose of the third phase of the POSE experiment is to study the rock mass spalling strength and to determine the prevailing in situ rock stress interpretation. The experiment hole ONK-EH3 is located at the end of the POSE niche, and the hole is mostly in homogeneous pegmatitic granite with some minor exposures of veined gneiss and should therefore be more applicable for a spalling experiment (Figure 1-4). In the experiment, the increase of thermal stresses is produced using eight heaters installed inside the experiment hole (see Figure 1-5). The experiment hole is filled with aluminium oxide to conduct the heat from the heaters into the rock. The single hole is not sensitive to the rock stress direction as opposed to, unlike the POSE pillar stability experiment. Symmetrical heating, a homogeneous rock mass and symmetrical experiment geometry allows a more reliable determination of in situ stress direction. The experiment hole was bored through a 7 x 7 metre concrete slab (Figure 1-6). The monitoring instrumentation is shown in Figure 1-5, and the instrumentation is described in more detail by Hakala & Valli (2013), together with the thermomechanical prediction. The experiment acts also as an prediction-outcome (P-O) exercise and therefore predictions were created before the execution of the experiment.
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Figure 1-4. A stitched panorama of the ONK-EH3 wall before the experiment, up to a depth of 2 m. Note the four fractures in red. (Hakala & Valli 2013)
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Figure 1-5. The existing monitoring locations from the third phase of the POSE experiment. The view is elevated from the southeast with the Y-axis pointing towards north. In the Figure the temperature sensors are marked red and green, strain gauge rosettes green and single strain gauges yellow. (Hakala & Valli 2013)
Figure 1-6. The experiment area with 7 x 7 m concrete slab. The experiment hole ONK-EH3 is located at the middle of the concrete slab. (Hakala & Valli 2013)
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1.3 Fracture mechanics
2-D fracture mechanics predictions were performed with version 4.11 of the FRACOD2D code, which is based on the Displacement Discontinuity Method (DDM). The DDM utilises the principles of the Boundary Element Method (BEM) but, since the BEM does not cope with problems with a fracture—that is, two surfaces coinciding with each other—therefore the DDM method was developed by Crouch (1976) to deal with the BEM's problems with fractures. The advantage of the DDM in simulating the fracture propagation, compared with other boundary element techniques, is the direct presentation of a fracture as fracture elements —instead of separate fracture surfaces. In FRACOD2D, fracture initiation occurs when stresses reach a critical value; the tensile and shear stresses and strengths are used to determine the initiation of a new fracture (Shen & Stephansson 1993). Fracture propagation is, however, determined by using fracture toughness parameters with the modified G-criterion, namely the F-criterion, which compares the strain energy released with the surface energy gained when a fracture propagates.
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2 THEORY
In FRACOD2D, the fracture initiation occurs when the combination of two principal stresses reaches a critical value, i.e., the tensile and shear stresses, and the corresponding material strengths are used to determine the initiation of a new fracture. The fracture propagation is, however, determined by using fracture toughness parameters. 2.1 Fracture initiation
The intact rock failure can be caused by tension or shear. The fracture mechanics code considers fracture initiation on the macro-scale by assessing the initiation of new fractures in both modes of failure, at the excavation boundary and in the intact rock. For the shear failure, the critical strength is presented via the friction angle (ϕ) and cohesion (c) of the intact rock. For the tensile failure, the corresponding material parameter is the tensile strength (σt) of the intact rock. The fracture initiation criterion for tensile stress (σtensile) and direction of failure (θit) is calculated by
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where σtensile is the critical tensile stress, Stensile is the tensile strength, θit is the direction of failure. The shear strength is calculated by
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where σn is the normal stress, ϕ is the friction angle and c is the cohesion. For an isotropic case the critical shear stress and direction of failure is calculated by
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where , σshear is the critical shear stress, ϕ is the friction angle, c is the cohesion and θis is the direction of failure. When the shear stress reaches the shear strength, a shear failure will occur.
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2.2 Fracture propagation
FRACOD2D uses a modified G-criterion, namely 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 fracture propagation occurs. After Shen & Stephansson (1993), the fracture propagates when the F-criterion reaches
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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. The equation can also be written in terms of fracture intensity as
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where 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. 2.3 Thermo mechanical coupling
The FRACOD2D code is based on constitutive thermo-elastic equations that can be found for example in Timoshenko & Goodier (1970). The thermo-elasticity is divided in to constitutive equations of deviatoric and volumetric responses of which the latter contains the thermal coupling terms. The thermal coupling is implemented using an indirect method which uses fictitious heat sources. The indirect method is suited well for the Displacement Discontinuity (DD) method used in FRACOD2D. The coupling is implemented so that the thermal solution is calculated before the mechanical equations. The thermal stresses are calculated for each boundary element and added into the boundary stresses. Finally, the stresses and displacements are calculated for the internal points with added thermal stresses and displacements.
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3 MATERIAL PROPERTIES AND HEATING SCHEME
3.1 Constitutive model and material properties
The predictions use the isotropic constitutive model with quarter symmetry for the rock mass with fracture propagation and initiation simulated using the F-criterion. The parameters used for the rock mass (Table 3-1) were the same, as the parameters used in the thermomechanics prediction for the third phase POSE-experiment by Hakala & Valli (2013). The rock mass was assumed to be homogeneous, isotropic and linearly elastic pegmatitic granite. The initial temperature of the rock is expected to be 13°C. The fracture mechanics parameters are mostly after Siren (2011 and 2012) presented in Table 3-2 complemented with data from various other sources. Mostly mean values are used as representative value.
Table 3-1. Rock mass properties after Hakala & Valli (2013).
Property rock mass unit Elastic modulus 53(1) GPa Poisson’s ratio 0.25(2) - Density 2635(3) kg/m3 Thermal capacity 716(1) J/kgK Thermal conductivity 3.33(1) W/mK Lin. thermal expansion 9.7e-6(2) K-1 (1) Hakala & Valli 2013 (2) Posiva 2011 (3) Kukkonen et al. 2011 Table 3-2. Fracture mechanics modelling parameters. Property symbol pegmatitic
granite unit
Cohesion c 12.9(1) MPa
Friction angle φ 47(1) °
Tensile strength σT, 12(1) MPa
Major principal stress σ1 23 (305) (2) MPa (°)
Intermediate principal stress σ2 15 (215) (2) MPa (°)
Minor principal stress σ3 3 (vert.) (2) MPa (°)
Mode I fracture toughness KIC 1.96(3) MPa m
Mode II fracture toughness KIIC 3.30(3) MPa m
Cohesion – tensile & shear c 10(1) MPa
Friction angle – tensile & shear φt, φs 35(4), 35(4) °, °
Dilatation angle – tensile & shear ψt, ψs 2.5(4), 2.5(4) °, °
Normal stiffness – tensile & shear kn 20,000(1) GPa/m
Shear stiffness – tensile & shear ks 2,000(1) GPa/m (1) Siren 2011 (2) Situation below the tunnel floor including in-situ and tunnel effect at depth of -3 m after Hakala & Valli 2013 (3) Modified after Siren 2012 (4) Posiva 2009
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3.2 The rock stress
There are two different in situ stress state interpretations available nearby the POSE niche. The earlier interpretation is based on LVDT cell stress measurements from the access tunnel (VT1) at chainage 3620 m and from the experiment niche (Figure 3-1) before the excavation to the full width of the niche (at the time the niche was named EDZ niche). This interpretation is referred as the EDZ & VT1 interpretation and it resulted in the direction of 166° for the maximum principal stress direction. The latest prediction is based on LVDT cell stress measurements conducted in the same experiment hole (ONK-EH3) where the third phase of POSE experiment is planned to be executed. This interpretation is referred to as ONK-EH3 interpretation and it resulted in the direction of 120° for the maximum principal stress direction. These two stress interpretations are reported and explained in detail in Hakala & Valli 2013. In the 2D fracture mechanics prediction the stress state below the tunnel floor must be calculated as an input parameter because the 2D model in the horizontal plane cannot take into account the tunnel geometry above the plane of analysis. The tunnel geometry has an effect on the secondary stress field around the experiment hole ONK-EH3. For the two stress states used in this study, the secondary stress field below the tunnel floor includes the in situ and tunnel effect at a depth of -3 m calculated by Siren (2011) for the VT1 & EDZ interpretation and Uotinen et al. (2013) for the ONK-EH3 interpretation. The secondary stress parameters are presented in Table 3-3.
Figure 3-1. LVDT cell stress measurements being conducted in the third investigation niche before the expansion excavations. (Photo courtesy of Posiva).
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Table 3-3. The secondary stresses at 3 m under the floor of the POSE tunnel according to Siren 2011 and Uotinen et al. 2013 for the different stress interpretations.
Interpretation σxx (horizontal, perp. To POSE)
σv (vertical comp., ignored)
σyy (horizontal, parallel to POSE)
EDZ & VT1 21.5 MPa 4.0 MPa 25.1 MPa ONK-EH3 23.0 MPa 3.0 MPa 15.0 MPa
The maximum principal stress around the experiment hole for the VT1 & EDZ interpretation is between 53 – 39 MPa (Figure 3-2 on left). For the ONK-EH3 stress interpretation, the maximum principal stress around the experiment hole is between 59 – 21 MPa (Figure 3-2 on right). All models are rotated so that the maximum principal stress is in the σyy direction and vertical in the Figures.
Figure 3-2. Maximum principal stress distributions for two different stress interpretations EDZ & VT1 and ONK-EH3 (modified after Hakala & Valli 2013).
3.3 Heating scheme
The planned heating scheme is to impose heat power of 8 x 400 W for the first 3 weeks and 8 x 800 W for 9 weeks. The total planned duration of the experiment is 12 weeks. Heating was applied as a thermal boundary condition based on calculations by Hakala & Valli (2013) at the hole surface as presented in Figure 3-3. The temperature at the modelled hole wall at the depth of -3 m (SG level -3 in Figure 3-3 is used as reference temperature). In the fracture mechanics modelling, the input temperature at each time step (1.5 weeks) is calculated as an average from the temperature at the beginning and end of each timestep. The heating scheme is therefore evened out but retains the same total temperature as presented in Figure 3-4.
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Figure 3-3. The temperatures modelled by Hakala & Valli 2013.
Figure 3-4. Temperature evolution in the experiment and in the fracture mechanics prediction.
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4 GEOMETRIC VARIABLES
The parameters controlling the fracture propagation have a significant role in fracture mechanics modelling and need to be carefully addressed. With scoping studies, the realistic set of parameters can be obtained for certain rock types. Effects of the following parameters were studied:
- the cut-off level of simultaneous multiple fracture propagations (defined by SETF function)
- tolerance factor that defines the tolerance distance (defined by SETT function) - SETE: the check-up level for elastic fracture growth (defined by SETE function)
The mesh geometry, especially the different element spacing, has also significance. For the effect of mesh geometry, the following items were studied:
- the fracture initiation element size (defined by ISIZE function) - the grid point spacing (defined in SWINDOW function) - boundary element spacing (defined by various functions)
All parameters mentioned may have complex relations between each other and the fracture propagation may vary significantly depending on the parameters. Therefore, the overall picture of the parameters must be understood for different rock types and also for different experiment scales. The different geometrical parameters are visualised in Figure 4-1. In the visualization, the fracture growth is initiated from the excavation surface to the left. The fracture tip is merged to the existing element (grid point) which is within the tolerance distance set.
Figure 4-1. The different parameters visualized.
Grid point
Boundary element spacing
Grid point spacing
Tolerance distance
Fracture growth (initiation element size)
Boundary Boundary element
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4.1 Simultaneous fracture propagation parameter
The SETF parameter controls whether there can be simultaneous fracture propagation in one iteration step or whether fractures propagated are one at the time (SETF is 1.0). The default value for this parameter is 0.9. When in-plane stresses are alike, this parameter can have significant effects on the results. In hydrostatic stress conditions, if the SETF parameter is set low (0...0.9), the fractures can propagate in all directions—this could be the case in dynamic loading conditions. In contrast, if the parameter is set reasonably (0.9...1.0), the most critical fracture will propagate first. The propagation of critical fractures may change the stress state, so that the stress regime may not be suitable anymore for fracture growth in all directions. Values near 1.0 should be used in static loading problems. 4.2 Parameter for fracture merging tolerance
The SETT parameter defines the fracture merging tolerance when new fractures are propagated. The tolerance distance is calculated by multiplying the SETT parameter with the average element size. If a new fracture tip is within this tolerance distance from an existing element, the fracture is merged to the existing element. The default value for this parameter is 1.0. 4.3 Parameter for elastic fracture growth
The SETE parameter defines how critical fracture tips are checked for elastic fracture growth. If the parameter is set to zero, all fracture tips will be checked. The default value for this parameter is 0.5. A larger value will basically reduce the calculation time by ignoring less critical fracture tips. When using the SETF parameter near a value of one (meaning that only one or few fractures propagate at each time step), only the most critical fractures during each iteration step are calculated. This means that only after a number of calculation rounds is the most critical fractures propagated enough to achieve equilibrium and there is potential for less critical fractures to propagate. In the sensitivity studies, no effect was observed when changing the SETE parameter. 4.4 Sensitivity of the parameters
The SETF and SETT parameters were varied to have an understanding of their inter-relationship with different geometrical constants (boundary element spacing, grid point spacing and the fracture initiation element size). Setting SETF to the 0.9995 value ensured compatibility with previous studies and versions, in which there was a problem with the SETF=1.0 value. The difference between the 0.9995 and 1.0 values is marginal. 4.5 Comparison of the geometric variables
From the sensitivity studies conducted, the parameters presented in Table 4-1 are selected to be used as final model parameters. In the DECOVALEX 2011 (Development of Coupled Model and Validation Against Experiments) project, the Team Posiva conducted a fracture mechanics prediction for the ASPE experiment case
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study. The results matched well with the experiment results and with other teams’ models. The model was similar compared to the third phase of the POSE experiment case and the parameters used then can be compared to the current case.
Table 4-1. Parameters used in Decovalex 2011 project with ÄSPÖ diorite, compared to default parameters and parameters determined for the third phase of the POSE spalling experiment.
Parameter Default D-2011 This study
Fracture initiation element size 1.5x 75 mm 45 mm Grid point spacing 1.0x 75 mm 57 mm Boundary element spacing 1.0x 61 mm 33 mm SETF 0.9 0.9995 1.0 SETT 1.0 0.25 1.0 SETE 0.5 1.0 0.5
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5 RESULTS
The results indicated that fractures start to grow in the direction of the minor principal stress in the vicinity of the hole boundary approximately 2 weeks after the start of heating. Depending on the stress interpretation, the fractures will increase in width as heating timestep progresses, and the will surround the experimental hole by the end of heating. The results for the two different stress interpretations are analysed together to point out the differences. The temperature evolution (Figure 5-1) in both stress interpretations is similar. The temperature reaches 95 degrees at the rock surface (0.00 m in Figure 5-2) which is in line with the thermomechanical 3D predictions by Hakala & Valli (2013). The thermomechanical predictions were used as input parameter for the fracture mechanics predictions.
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Figure 5-1. The temperature evolution as a function of distance from the rock surface to minimum principal stress direction for the ONK-EH3 stress interpretation. The 0.14 m line is the first point in the rock behind the rock surface.
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-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 1.8X Axis (m)
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Maximum Displacement (m): 8.27565E-4
Flow Time (s): 0E+0
Flow Time Step (s): 0E+0
Thermal Time (s): 8.1648E+6
Cycle: 118 of 118
Elastic fracture
Open fracture
Slipping fracture
Fracture with Water
Posiva Oy
Date: 08.04.2015 10:01:43
Figure 5-2. The temperature distribution in EDZ & VT1 stress state after 9 weeks of heating.
5.1 Fracture propagation in EDZ & VT1 stress state
In the EDZ & VT1 stress state, the fracture initiation is predicted to start 1.5 weeks after the start of experiment with 1 fracture (2 if also counting the symmetric one) in the location where the tangential stresses are highest (see upper leftmost image in Figure 5-3). The fractures form a small notch after 3 weeks after which fractures start to propagate all over the experiment hole surface. A set of notches is formed after 12 weeks in a shear fracture pattern. The situation after 12 weeks is shown in Figure 5-7. The maximum displacement after 12 weeks at the experiment hole surface is ca. 0.5 mm (Figure 5-4 and Figure 5-5).
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Weeks 1.5...3
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Figure 5-3. Predicted fracture propagation during 12 week heating period for EDZ & VT1 stress interpretation.
σ3
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-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 1.8X Axis (m)
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(m)
-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 1.8X Axis (m)
-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
Y A
xis
(m)
POSE 3rd phase - EDZ&VT1 stress state
Maximum Displacement (m): 8.27565E-4
Flow Time (s): 0E+0
Flow Time Step (s): 0E+0
Thermal Time (s): 8.1648E+6
Cycle: 118 of 118
Elastic fracture
Open fracture
Slipping fracture
Fracture with Water
Posiva Oy
Date: 08.04.2015 10:01:43
Figure 5-4. Displacement vectors after 12 weeks in EDZ & VT1 interpretation.
22
-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 1.8X Axis (m)
-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
Y A
xis
(m)
-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 1.8X Axis (m)
-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
Y A
xis
(m)
POSE 3rd phase - EDZ&VT1 stress state
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Tot
al D
ispl
acem
ent (
m)
xE-4
Maximum Displacement (m): 8.27565E-4
Flow Time (s): 0E+0
Flow Time Step (s): 0E+0
Thermal Time (s): 8.1648E+6
Cycle: 118 of 118
Elastic fracture
Open fracture
Slipping fracture
Fracture with Water
Posiva Oy
Date: 08.04.2015 10:01:43
Figure 5-5. Displacement pattern after 12 weeks in EDZ & VT1 interpretation.
23
5.2 Fracture propagation in ONK-EH3 stress state
In the ONK-EH3 stress state, the fracture initiation is predicted to start 1.5 weeks after the start of the experiment with 1 fracture (2 if counting the symmetric ones) in the location where the tangential stresses are highest (see upper leftmost image in Figure 5-6). Between 1.5 and 3 weeks, the fractures form 4 thin notches to the direction of minor principal stress, after which a complex fracture formation starts to grow behind the fracture surface. The formation can be described as partly layered. After 12 weeks of heating, the pattern is complex and extends in all directions, except there is a small intact part to the major principal stress direction. The situation after 12 weeks is shown in Figure 5-8.
Weeks 1.5...3
Weeks 1.5...3
Weeks 3...4.5
Weeks 3...4.5
Weeks 4.5...6
Weeks 6...7.5
Weeks 7.5...9 Week 12
Figure 5-6. Predicted fracture propagation during 12 week heating period for ONK-EH3 stress interpretation.
σ3
σ1
24
-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 1.8X Axis (m)
-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
Y A
xis
(m)
-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 1.8X Axis (m)
-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
Y A
xis
(m)
Pxx (Pa): -2.15E+7 Pyy (Pa): -2.51E+7
Pxy (Pa): 0E+0
Max. Compres. Stress (Pa): 5.13614E+8
Max. Tensile Stress (Pa): 2.92385E+7
Flow Time (s): 0E+0
Flow Time Step (s): 0E+0
Thermal Time (s): 8.1648E+6
Cycle: 117 of 118
Elastic fracture
Open fracture
Slipping fracture
Fracture with Water
Compressive stress
Tensile stress
Posiva Oy
Date: 27.11.2013 17:01:52
Figure 5-7. Predicted fracture propagation during 12 week heating period for EDZ & VT1 stress interpretation.
Pxx (Pa): -1.5E+7 Pyy (Pa): -2.3E+7
Pxy (Pa): 0E+0
Max. Compres. Stress (Pa): 1.14317E+9
Max. Tensile Stress (Pa): 1.44963E+9
Flow Time (s): 0E+0
Flow Time Step (s): 0E+0
Thermal Time (s): 8.1648E+6
Cycle: 100 of 100
Elastic fracture
Open fracture
Slipping fracture
Fracture with Water
Compressive stress
Tensile stress
Posiva Oy
Date: 27.11.2013 17:13:01
-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 1.8X Axis (m)
-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
1.8Y
Axi
s (m
)
-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 1.8X Axis (m)
-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
Figure 5-8. Predicted fracture propagation during 12 week heating period for ONK-EH3 stress interpretation.
25
5.3 Acoustic emission prediction
The predicted acoustic emission (AE) patterns for the two stress predictions are presented in Figure 5-9 and in Figure 5-11. The accumulated acoustic emission events with tangential stresses and temperatures at 0.11 m depth in EDZ & VT1 stress interpretation are presented in Figure 5-10. According to Rinne et al. (2003), it is not reasonable to compare the predicted AE magnitudes with the measured magnitudes since the element size used is significantly larger than the rock grain size; therefore, only the acoustic emission pattern is plotted. The AE pattern follows the predicted fracture propagation closely.
Figure 5-9. Predicted cumulative acoustic emission patterns after the experiment for the EDZ & VT1 stress interpretation.
σ3
σ1
26
Figure 5-10. Accumulated acoustic emission events per week with tangential stresses and temperatures at 0.11 m depth in EDZ & VT1 stress interpretation.
0
20
40
60
80
100
120
140
160
180
0
200
400
600
800
1000
1200
1400
1600
1800
Week 0
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Tan
gent
ial s
tres
s (M
Pa)
or
Tem
pera
ture
(°C
)
Acc
umul
ated
aco
usti
c ev
ents
(pe
r w
eeek
) Acoustic events (ML>-2)
Tangential stress (0.11 m)
Temperature (0.11 m)
27
Figure 5-11. Predicted cumulative acoustic emission patterns after the experiment for the ONK-EH3 stress interpretation.
σ3
σ1
28
6 CONCLUSIONS AND DISCUSSION
In the EDZ & VT1 interpretation, a typical borehole breakout shear fracture (Shen et al. 2002) forms after 12 weeks, observed, for example, also by Syarifuddin & Busono (1999). The damage is slightly concentrated in the minor principal stress direction. Given the fracture pattern observed in the nature, the results can be stated as realistic for given parameters. The prediction using the ONK-EH3 stress interpretation exhibits a shallower damage depth in the σ1 direction although damage exists in all directions. A slight decrease of damage can be seen in the major principal stress direction, as could be expected. The slightly uniform damage in all directions indicates uniform stress conditions, thus not predicting the formation of spalling—which usually requires high differential stresses. The acoustic emissions follow the development of fractures and indicate no clear concentration of AE events around the experiment hole. A common aspect to both stress interpretations is that the majority of the damage is subsurface and the maximum depth is 130–140 mm. The overall picture from the fracture mechanics prediction is that failure is observed all around the experiment hole without clear spalling notches. The rock mass is modelled isotropic since the governing rock type is pegmatitic granite. However the lower part of the experiment hole has a major anisotropic gneiss inclusion. The lower part with two materials was not modelled due to the lack of resources and complex calculation geometry possibly leading to instability and increased calculation times. The anisotropy would however lead to a situation where fractures would possibly propagate to the anisotropy direction and probably deeper whilst the damages can be expected to be less perpendicular to the anisotropy direction.
29
REFERENCES
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Crouch S.L., 1976. Solution of plane elasticity problems by the displacement discontinuity method. Int. J. Num. Methods Engng. 10, 301-343.
Hakala, M. & Valli, J. 2013. ONKALO POSE Experiment – Phase 3: 3DEC Prediction. Working Report 2012-58. Posiva Oy, Eurajoki.
Johansson, E., Siren, T. & Hakala, M. 2014. ONKALO POSE experiment - Phases 1 & 2: Execution and outcome. Working Report 2012-60. Posiva Oy, Eurajoki.
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Rinne M, Shen B, Lee H-S (2003) Äspö Hard Rock Laboratory. Äspö Pillar Stability Experiment. Modelling of fracture stability by Fracod. Preliminary results. Swedish Nuclear Fuel and Waste Management Co, International Progress Report IPR-03-05, Stockholm.
Shen B. and Stephansson O., 1993. Numerical analysis of Mode I and Mode II propagation of rock fractures. Int. J. Rock Mech. Min. Sci. & Geomech. Abst. 30(7), pp. 861-867.
Shen, B., Stephansson, O. and Rinne, M. 2002. Simulation of borehole breakouts using FRACOD2D. Oil and Gas Science and Technology 57 (5), pp. 579-590
Siren, T. 2011. Fracture Mechanics Prediction for Posiva’s Olkiluoto Spalling Experiment (POSE). Working report 2011-23. Posiva Oy, Eurajoki.
Siren, T. 2012. Fracture Toughness Properties of Rocks in Olkiluoto: Laboratory Measurements 2008-2009. Working report 2012-25. Posiva Oy, Eurajoki.
Syarifuddin, N and Busono, I. 1999. Regional stress alignments in the Kutai Basin, East Kalimantan, Indonesia: a contribution from a borehole breakout study. Journal of Asian Earth Sciences, Volume 17, Issue 1, p. 123-135.
Timoshenko S.P., and Goodier J.N. 1970. Theory of Elasticity. McGraw-Hill. New York.
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Uotinen, L.K.T., Siren, T., Martinelli, D., Hakala, M. 2013. In-situ experiment concerning thermally induced spalling of circular shotcreted shafts in deep crystalline rock. World Tunnel Congress 2013. Geneva.
