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ONKALO in Situ Concrete Spalling Experiment- Fracture Mechanics Prediction
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. )
October 2015
Working Report 2013-48
Topias Siren
October 2015
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.
Topias Siren
Posiva Oy
Working Report 2013-48
ONKALO in Situ Concrete Spalling Experiment- Fracture Mechanics Prediction
ONKALO IN SITU CONCRETE SPALLING EXPERIMENT - FRACTURE MECHANICS PREDICTION ABSTRACT During operation of the nuclear waste disposal facility, some sprayed concrete reinforced underground spaces will be in use for approximately 100 years. During this time of use, the local stress regime will be altered by the radioactive decay heat. The change in the stress state will impose high demands on sprayed concrete, as it may suffer stress damage, or lose its adhesion to the rock surface. It is also unclear what kind of support pressure the sprayed concrete layer will apply to the rock. To investigate this, an in situ concrete spalling (ICSE) experiment is planned in the ONKALO. In the experiment a vertical experiment hole ONK-EH3 will be concreted, and the surrounding rock mass will be instrumented with heat sources, in order to simulate increase in the surrounding stress field. The experiment is instrumented with an acoustic emission system for the observation of rock failure, temperature and strain gauges to observe the thermo-mechanical interactive behaviour of the concrete and rock at several levels, in both rock and concrete. This prediction is done by using the fracture mechanics code Fracod2D, which is based on the Displacement Discontinuity Method (DDM). The thermal coupling is implemented using an indirect method, which uses fictitious heat sources. The indirect method suits well the DDM used within Fracod 2D. 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 determine the initiation of a new fracture. The fracture propagation is, however, determined by using fracture toughness parameters with the F-criterion.
The correlation between the real rock behaviour and the results of the prediction is important 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 approach is not the most commonly used method in ONKALO, and therefore it gives a fresh baseline to the more common modelling approaches in ONKALO. A thermomechanical fracture mechanics study is necessary for the prediction of the damage before the experiment, in order to plan the experiment and instrumentation, and for generating a proper prediction/outcome-study due to the special nature of the in situ experiment. The prediction of acoustic emission pattern is created by Fracod, and the model later compared to the actual observed acoustic emissions. Keywords: Sprayed concrete, Shotcrete, Spalling, In situ experiment, Numerical modelling, Fracture mechanics, Rock Anisotropy, Thermal Spalling, ICSE, POSE.
ONKALO IN SITU BETONIN HILSEILYKOE - RAKOMEKAANINEN ENNUSTE TIIVISTELMÄ Ydinjätteen loppusijoituslaitoksen käytön aikana, osa ruiskubetonilla lujitetuista maanalaisista tiloista on käytössä noin 100 vuotta. Tänä aikana paikallinen jännityskenttä muuttuu radioaktiivisten aineiden hajoamista syntyvän lämmön seurauksena. Jännityskentän muutos asettaa suuret vaatimukset ruiskubetonille, johon voi aiheuta jännitysvaurioita, tai joka voi menettää adheesion kallion pintaan. On myös epäselvää kuinka suuren tukipaineen ruiskubetoni aiheuttaa kallion pintaan. Asian tutkimiseksi on suunniteltu in situ betonin hilseilykoetta (ICSE-koe) ONKALOssa. Kokeessa pystysuuntainen tutkimusreikä ONK-EH3 betonoidaan ja ympäröivään kallioon asennetaan lämmönlähteitä, joilla simuloidaan kasvavaa jännityskenttää. Koe instrumentoidaan akustisella emissiolaitteistolla kallion vaurioiden havaitsemiseksi, lämpöantureilla ja venymäliuskoilla ruiskubetonin ja kallion lämpömekaanisen vuorovaikutuksen seuraamiseksi useilla eri tasoilla. Tässä työssä esitetyn ennusteen ja kokeessa havaittavan kiven todellisen käyttäytymisen välinen korrelaatio antaa tärkeää tietoa siitä, miten hyvin kallion käyttäytyminen ja kalliomekaaniset 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). Lämpökytkentä on toteutettu epäsuoralla menetelmällä, joka käyttää fiktiivisiä lämpölähteitä. DDM:n etuja verrattuna muihin reunaelementtimenetelmiin on sen tapa esittää raot rakoelementteinä erillisten rakopintojen sijaan.
Fracod2D:ssa uusi rako syntyy, kun pääjännitykset saavuttavat kriittisen pisteen. Veto- ja leikkauslujuuksia käytetään raon syntymisen kriteerinä. Syntyneiden rakojen etenemisen määräävät rakojäykkyysparametrit muokatun G-kriteerin eli F-kriteerin avulla. Lämpömekaaninen rakomekaaninen ennuste on välttämätön vaurion ennustamiseksi ennen kokeen suorittamista, jotta koe pystytään suunnittelemaan ja instrumentoimaan, sekä riittävän ennuste/lopputulos-tutkimuksen suorittamiseksi in situ-koetta varten. Akustisesta emissiojakaumasta on luotu Fracodilla ennuste, johon voidaan myöhemmin verrata toteutunutta akustista emissiojakaumaa. Avainsanat: Ruiskutettu betoni, ruiskubetoni, hilseily, In situ-koe, numeerinen mallinnus, rakomekaniikka, kiven anisotropia, terminen hilseily, POSE.
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TABLE OF CONTENTS
ABSTRACT TIIVISTELMÄ
1 INTRODUCTION .................................................................................................... 2
1.1 Background ................................................................................................... 2
1.2 The ONK-EH3 experiment hole .................................................................... 2
1.3 The shotcrete spalling experiment ................................................................ 3
2 THEORY ................................................................................................................. 6
2.1 Fracture initiation........................................................................................... 6
2.2 Fracture propagation ..................................................................................... 6
2.3 Fracture toughness values for concrete ........................................................ 7
2.4 Thermo mechanical coupling ........................................................................ 7
3 MATERIAL PROPERTIES AND HEATING SCHEME ............................................ 8
3.1 Material properties ........................................................................................ 8
3.2 The rock stress .............................................................................................. 9
3.3 Heating scheme .......................................................................................... 10
4 GEOMETRIC VARIABLES ................................................................................... 11
4.1 Simultaneous fracture propagation parameter ............................................ 11
4.2 Parameter for fracture merging tolerance ................................................... 12
4.3 Parameter for elastic fracture growth .......................................................... 12
4.4 Sensitivity of the parameters ....................................................................... 13
4.5 Comparison of the geometric variables ....................................................... 16
5 RESULTS ............................................................................................................. 18
5.1 Temperature evolution ................................................................................ 18
5.2 Fracture initiation and propagation .............................................................. 19
5.3 Acoustic emission pattern ........................................................................... 21
6 DISCUSSION........................................................................................................ 22
7 REFERENCES ..................................................................................................... 23
2
1 INTRODUCTION
This working report describes the fracture mechanics prediction for the planned shotcrete spalling experiment, which is planned to be conducted in experiment hole ONK-EH3 in POSE niche at depth -345 meters depth in the ONKALO underground rock characterisation facility.
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). 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. POSE pillar stability experiment (Phases 1 and 2) was conducted between years 2010 and 2011 and are documented in the Posiva Working Report 2012-60 (Johansson et al. 2014).
Figure 1. Experimental area in the ONKALO underground facility. The third phase of POSE experiment is conducted in single hole (ONK-EH3) in the beginning of year 2013 (reported in Valli et al. 2014). The single hole is not sensitive to the rock stress direction as the POSE pillar stability experiment was. The instrumentation plan and thermomechanical prediction for the third phase of POSE experiment is described in detail by Hakala & Valli (2013).
1.2 The ONK-EH3 experiment hole
In the phases 1 and 2 of POSE experiment it was noted that the geology in experiment holes ONK-EH1 and ONK-EH2 had significant role in the breaking of rock. The geology in the holes was migmatitic gneiss. The experiments ended up mainly with geology influenced extension fractures and only minor spalling. The third experiment hole is however mostly more homogeneous pegmatitic granite with some minor exposures of veined gneiss and should therefore be more applicable for spalling experiment Figure 2.
Experiment area
3
Figure 2. In order the north, south, east and west faces of the ONK-EH3 hole, viewpoint outside the hole, depth levels from the top of the hole in meters with black lines. (after Hakala & Valli 2013)
1.3 The shotcrete spalling experiment
The shotcrete spalling experiment is planned to be conducted in experiment hole ONK-EH3 where there is vast monitoring already installed in the earlier third phase of POSE experiment. The experiment hole ONK-EH3 is at the end of the POSE niche at the depth -345 meters. The experiment hole was bored through a 7 x 7 meter concrete slap (Figure 3). The existing monitoring instrumentation is shown in Figure 4 and described in detail by Hakala & Valli (2013). Purpose of the shotcrete spalling experiment is to study the behaviour of shotcreted surface and shotcretes adhesion to the rock during the disposal period when the far field stress state is affected by the heat generated by the disposed nuclear waste. This will
4
increase the stress state and put high demands to the tunnel support structures in long time periods. Shotcrete spalling experiment situation is similar to the vertical personal access shaft which is also mechanically bored as is the experiment hole, will be probably reinforced with shotcrete and will be in use during the whole disposal time for 100 years. The thickness of shotcrete layer used in the model is 40 mm. In the experiment the increase of thermal stresses is increased using 8 heaters installed in the rock mass around the experiment hole (see Figure 5). The distance of the heating holes from the experiment hole is 1 meter and 6 m long heaters are used in the experiment. The planned heating scheme is to increase the heating in steps: 8 x 1000 W for the first 3 weeks, 8 x 1500 W for 2 weeks, 8 x 2000 W for the last 4 weeks and 8 x 0 W for 7 weeks for the cooling period. The total duration of the experiment is 16 weeks.
Figure 3. The experiment area with 7 x 7 m concrete slap and the experiment hole ONK-EH3 in the middle of the concrete slap. (after Hakala & Valli 2013)
5
Figure 4. The existing monitoring locations from third phase of POSE experiment. The view is elevated from southeast with 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. (after Hakala & Valli 2013)
Figure 5. The drillholes surrounding the EH3 hole. The eight existing instrumentation holes are presented as black circles and the planned new heater holes for the shotcrete spalling experiment are presented as eight red triangles. (modified after Uotinen et al. 2013)
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2 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.
2.1 Fracture initiation
The intact rock failure can be caused by tension or shear. Fracture mechanics code considers fracture initiation in macro-scale by assessing initiation of new fractures in both modes in boundary and in intact rock. For the shear failure, the critical strength is presented with the friction angle (ϕ) and cohesion (c) of the intact rock and with tensile strength (σt) of the intact rock. The fracture initiation criterion for tensile stress (σtensile) and direction of failure (θit) is calculated by
1
/2 2
where σtensile is the critical tensile stress, Stensile is the tensile strength, θit is the direction of failure. The shear strength is calculated by
tan 3
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
tan 4
/2 /4 5
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 exceeds the shear strength, a shear failure will occur.
2.2 Fracture propagation
Fracod2D uses modified G-criterion, namely 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. After Shen & Stephansson (1993) the fracture propagates when F-criterion reaches
1.0 6
7
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 fracture will propagate to the direction where F-criterion reaches its maximum. The equation can also be written in terms of fracture intensity and anisotropy as
1.0 7
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 Fracture toughness values for concrete
Reinhart et al. (1997) conducted number of laboratory tests for high strength concrete where he concluded that the KIC is about one fifth of the KIIC. This conclusion is in line with Davies (1988) numerical and experimental studies where he reported the KIIC values to be between 1.8 to 2.0 MPa m and that KIIC values were around seven times higher than the KIC values 0.27 to 1.30 MPa m reported by Swamy (1979). To combine these two observations we derive the following equation for the relationship between KIC and KIIC in concrete
KIC = KIIC / 6 8
where KIC and KIIC are the mode I and II fracture toughness values correspondingly. Reinhart et al. (1997) also reported relation between the average uniaxial compressive strength and KIIC to be approximately according to the following equation
KIIC = fck / 19 9
where fck is the characteristic compressive strength of shotcrete.
2.4 Thermo mechanical coupling
The constitutive thermo-elastic equations to which Fracod2D is based on 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 latter contains the thermal coupling terms. The thermal coupling is implemented using indirect method which uses fictitious heat sources. The indirect method suites well the Displacement Discontinuity (DDM) 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 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 Material properties
The parameters used for the rock mass (Table 1) were the same used in thermomechanics prediction for the third phase POSE-experiment by Hakala & Valli (2013) complemented with data from various sources for shotcrete.The rock mass was assumed to be homogeneous, isotropic and linearly elastic pegmatitic granite. The initial temperature of the rock is expected to be 18°C after the third phase of POSE experiment in which the rock mass is expected to be heavily disturbed by the heating during the experiment. The fracture mechanics parameters are mostly after Siren (2012 and 2013) in Table 2 complemented with data from various other sources. There was no laboratory testing available for the shotcrete fracture mechanics parameters, therefore literature references were used to determine the parameters. Table 1. Material properties.
Property symbol pegmatitic
granite shotcrete 40 mm
C35-3/45-1 unit
Elastic modulus E 53(1) 34(4) GPa
Poisson’s ratio ν 0.29(2) 0.20(4)
Density ρ 2635(1) 2200(5) kg/m3
Thermal capacity Cp 689(3) 840(7) J/kgK
Thermal conductivity k 3.20(3) 1.7(6) W/mK
Linear thermal expansion α 7.2e-6(1) 10e-6(4) 1/K (1)
Hakala & Valli 2013 (2)
Posiva 2012 (3)
Kukkonen et al. 2011 (4)
EN 1992-1-1:2004
(5)
based on quality assurance tests (6)
Neville 1995 (7)
SRMK C4: 2003
Table 2. Fracture mechanics modelling parameters.
Property symbol pegmatitic granite
shotcrete C35-3/45-1
unit
Cohesion c 12.9(1) 17.5(4) MPa
Friction angle φ 47(1) 1(4) °
Tensile strength σT, 12(1) 2.2(4) MPa
Mode I fracture toughness KIC 1.96(2) 0.31(5) MPa m
Mode II fracture toughness KIIC 3.30(2) 1.84(6) MPa m
Cohesion for new fractures c 10(1) 10(1) MPa
Friction angle for new fractures φt, φs 35(3), 35(3) 35(3), 35(3) °, °
Dilatation angle for new fractures ψt, ψs 2.5(3), 2.5(3) 2.5(3), 2.5(3) °, °
Normal stiffness for new fractures kn 20,000(1) 20,000(1) GPa/m
Shear stiffness for new fractures ks 2,000(1) 2,000(1) GPa/m (1)
Siren 2011 (2)
Modified after Siren 2012 (3)
Posiva 2009, table 5-6 (4)
EN 1992-1-1:2004 (5)
using equation
8 derived after Davies (1988) and Reinhart et al. (1997) (6)
calculated after relation by Reinhart et al. (1997)
9
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 and from the experiment niche before the excavation to the full width of the niche (at the time the niche was named EDZ niche). This interpretation is referred as 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 shotcrete spalling experiment is planned to be executed. This interpretation is referred 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 2D fracture mechanics prediction the stress state below the tunnel floor must be calculated as an input parameter as the 2D model in horizontal plane cannot take in account the tunnel geometry above affecting to the secondary stress field around the tunnel. For the two stress states used in this study, the situation below the tunnel floor including in situ and tunnel effect at depth of -3 m were calculated after a 3-dimensional model by Hakala & Valli (2013). The secondary stress parameters are presented in Table 3. All models are rotated so that the maximum principal stress is on σyy direction and vertical in Figures. Table 3. The secondary stresses at 3 m under the floor of the POSE tunnel calculated after Hakala & Valli (2013) for the different stress interpretations.
Interpretation σxx (horizontal,
perp. To POSE) σv (vertical comp.,
ignored) σyy (horizontal,
parallel to POSE) EDZ & VT1 -3 m 25.1 MPa 21.5 MPa 4.0 MPa ONK-EH3 -3 m 23.0 MPa 15.0 MPa 3.0 MPa
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3.3 Heating scheme
In the experiment the increase of thermal stresses is produced using 8 heaters installed in the rock mass around the experiment hole. The distance of the heating holes from the experiment hole is 1 meter and the planned heating scheme is to increase the heating in steps: 8 x 1000 W for the first 3 weeks, 8 x 1500 W for 2 weeks, 8 x 2000 W for the last 4 weeks and 8 x 0 W for 7 weeks for the cooling period. The total duration of the experiment is 16 weeks. Fracture mechanics code Fracod2D uses fictitious heat source method to calculate thermal stresses. The thermal input is constructed so that the input power for each time step (3 weeks) is calculated as an average from the input power at the beginning and end of each timestep. Therefore the heating scheme smoothens but retains the same total power as presented in Figure 6. On the hole surface, a heat flux is set to zero corresponding to the fully insulated condition. The experience from previous experiments is that modelling with zero thermal flux corresponds well with observations. In the model the initial state is calculated during the first week from where the temperature is being increased according to the heating scheme.
Figure 6. 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 parameters can be validated 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 (see Figure 7). For the effect of mesh geometry following things was 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 highly 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 the Figure 9. In the visualization the fracture growth is initiated from the excavation surface to left. When initiating from the boundary, a fracture consists of two elements with a total length determined by the ISIZE function. In the following steps the propagating fracture length is half the length determined by the ISIZE function. If the new fracture point is within the tolerance distance of an existing element point, the new fracture tip is merged to it. The tolerance distance is determined by the function SETT*ISIZE/2. The existing element can be either a fracture or a boundary element, however not a grid point as they are ignored.
4.1 Simultaneous fracture propagation parameter
The SETF parameter controls whether there can be simultaneous fracture propagation on one iteration step or are fractures propagated 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 to 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 and 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.
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Figure 7. The different parameters visualized where fracture initiation element size is 60 mm, grid point spacing is 60 mm, boundary element spacing is 40 mm and SETT parameter is set to 1.0. The tolerance distance is therefore 1.0 * 30 mm.
4.2 Parameter for fracture merging tolerance
The SETT parameter defines the fracture merging tolerance when new fractures are propagated. Tolerance distance is calculated by multiplying the SETT parameter with the average element size. If new fracture tip is within this tolerance distance from 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. Larger value will basically reduce the calculation time by the ignoring less critical fracture tips. When using SETF parameter near 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 number of calculation rounds is 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.
Boundary element spacing 40 mm
Fracture is about to propage to dotted direction but is
merged to an existing element (black) within the tolerance distance (30 mm)
Fracture initiation (60 mm)
Existing element
Boundary element Boundary
13
4.4 Sensitivity of the parameters
The SETF and SETT parameters were varied to have understanding of their interrelationship with different geometrical constants (boundary element spacing, grid point spacing and the fracture initiation element size). The results are presented in Figures from Figure 8 to Figure 11. Set SETF=0.9995 value was used to ensure compatibility with previous studies and versions, in which there was a problem with SETF=1.0 value. The difference between 0.9995 and 1.0 value is marginal. The models were calculated using the EDZ & VT1 stress interpretation. In the parameter studies only the final situation is calculated, that is the situation after 9 weeks of heating according to the heating scheme with strong shotcreted to prevent breakouts that would dramatically increase the calculation speed. Although the final thermal stresses match the heating scheme, the fracture initiation and propagation process is not staged and therefore differ from the final results shown later.
SETF=0.5 SETF=0.9 SETF=0.9995
SE
TT
=0.
0
SE
TT
=0.
5 S
ET
T=
1.0
Figure 8. Sensitivity study of SETT and SETF parameters using boundary element spacing of 40 mm, grid point spacing of 60 mm and the fracture initiation element size of 40 mm.
Default values
14
In Figure 8 the fractures develop more or less all around the hole in all models. The small fracture initiation element size (40 mm) can be observed from the very detailed and small scale fracturing to the major principal stress direction in models where SETT=0.0 and 0.5 and SETF=0.9995. This can be observed also in the Figure 13 with similar parameters. Also it can be noticed that the fracturing process is not finished in the mentioned models, there are still active processes indicated by the slipping (green) and open (red) fractures. In Figure 9 the model with SETT=0.0 and SETF=0.5 failed to produce stable results. Fracture initiation element size exceeds the element spacing in boundaries and with no merging of new fracture tips (tolerance distance set to zero) and multiple fractures developing at one time (SETF=0.5) there are overlapping of fractures. The parameters nearly equivalent to parameters used in Decovalex 2011 project produced reasonable results which on the other hand are very similar with the results on the lower row.
SETF=0.5 SETF=0.9 SETF=0.9995
SE
TT
= 0
.0
SE
TT
= 0
.5
SE
TT
= 1
.0
Figure 9. Sensitivity study of SETT and SETF parameters using boundary element spacing of 40 mm, grid point spacing of 60 mm and the fracture initiation element size of 60 mm.
Unsteady calculation
due to overlapping
fractures
Default values
Equivalent to parameters used
in Decovalex project
15
SETF=0.5 SETF=0.9 SETF=0.9995 S
ET
T=
0.0
Did not calculate due to floating point overflow
SE
TT
= 0
.5
SE
TT
= 1
.0
Figure 10. Sensitivity study of SETT and SETF parameters using boundary element spacing of 40 mm, grid point spacing of 40 mm and the fracture initiation element size of 60 mm. In Figure 10 the model with SETT=0.0 and SETF=0.5 failed to calculate due to combination of tolerance factor set to zero and multiple fractures propagating at the same time causing stability issues. The model with default values resulted with beautiful spalling formation behind the shotcrete surface. The result resembles log spiral formations that form in hydrostatic stress conditions in deep boreholes, though the default parameters might be selected to match this kind of case example. In Figure 11 the overall view is messier than with other studied sets of parameters. In models where SETT=0.0 and 0.5 and SETF=0.9995 the fracture formation is small but localized. Where as in all other models the fractures from all around the hole surface.
Default values
16
4.5 Comparison of the geometric variables
From the sensitivity studies conducted in section 4.1 the default parameters from Figure 11 are selected to be used as final model parameters. The default parameters are SETT=1.0, SETF=0.9 and fracture initiation element size is 1.5 times the average element size. The SETE parameter is reasoned to be 0.0 with the expense of calculation speed. In DECOVALEX 2011 (Developing Codes and Validating Against Experiments) project Team Posiva conducted a fracture mechanics prediction for ASPE experiment case study. The results matched well with the experiment results. The model was similar compared to the shotcrete spalling experiment case and parameters used then can be compared to the current case. The parameters used are presented in Table 4.
SETF=0.5 SETF=0.9 SETF=0.9995
SE
TT
= 0
.0
SE
TT
= 0
.5
SE
TT
= 1
.0
Figure 11. Sensitivity study of SETT and SETF parameters using boundary element spacing of 40 mm, grid point spacing of 40 mm and the fracture initiation element size of 40 mm.
Default values
17
Table 4. Parameters used in Decovalex 2011 project with ÄSPÖ diorite, compared to default parameters and parameters determined for shotcrete spalling experiment.
Parameter Default D-2011 This study
Fracture initiation element size 1.5x 75 mm 50 mm Grid point spacing >1.5x 75 mm 62 mm Boundary element spacing 1.0x 61 mm 36 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 for the two different stress interpretations are analysed together to point out the differences.
5.1 Temperature evolution
The temperature distribution during the heating period in both models with only different stress interpretation is almost the same. The minor differences are probably explained by different displacements or fracture growth and only temperatures for stress interpretation ONK-EH3 are shown in Figures 12 and 13. After six weeks temperature roughly corresponds to the designed maximum temperature of 100 ºC for the bentonite buffer and peaks out after 9 weeks of heating up to 130° C. The temperatures at the monitoring lines in the major and minor principal stress directions are shown in Figure 14.
180
16014012010080 60 40 20
After 3 weeks After 6 weeks After 9 weeks ºC
Figure 12. Spatial temperature distribution for the ONK-EH3 stress interpretation. The monitoring lines to σ3 and σ1 directions are shown in the figure.
Figure 13. Temperature evolution during 9 week heating period as a function of distance from the concrete surface for the ONK-EH3 stress interpretation. The 0.11 m line is the first point in rock behind the shotcrete layer.
40
65 65
65 65
65 65
65 65
40 40
40
65
90
115115
115 115
115 115
115 115
65 65
65
90
115
140 140
140 140
140 140
140 140
165165
165 165
165165
165 165
0
50
100
150
200
250
300
350
0
15
30
45
60
75
90
105
120
135
150
0 3 6 9
Pow
er p
er h
eate
r (W
)
Tem
pera
ture
(°C
)
Week
0.00 m
0.11 m
0.21 m
0.52 m
0.88 m
Pwr (exp)
Pwr (mdl)
σ3
σ1
19
Figure 14. Temperatures measured from the centre of the shotcrete layer (weeks 0–9) to major and minor principal stress directions for the ONK-EH3 stress interpretation.
5.2 Fracture initiation and propagation
The two stress interpretations produce similarly shaped fracture patterns, with respect to the principal stress directions (Figures 15 and 16). The principal stresses grow significantly between 6–9 weeks of heating (Figure 17). Singularities in fracture tips causes extremely high stresses, therefore the stresses are plotted only between 100 and -10 MPa. During three weeks of heating, the tangential stresses near the rock surface are 31 MPa, compared to the tangential stress 68 MPa without fracture growth enabled (elastic model). During the following weeks of the experiment, the fracture growth causes anomalous stress distributions behind the rock surface, with locally high tangential (locally over 170 MPa) and tensile stresses. The fracture initiation starts at concrete at early stages of the experiment and the concrete layer suffers a minor shear failure (see Figures 17 and 18) in the first three weeks of heating. In the ONK-EH3 stress state, the failure progresses to rock surface already after three weeks of heating, and the failure zone is large after nine weeks of heating with local 5 mm displacements; this is in contrast to the EDZ & VT1 stress interpretation, in which only minor fracture propagation was predicted to occur just after nine weeks of heating. The concrete fails slightly, only to the minor principal stress direction with the EDZ & VT1 stress interpretation, and the concrete structure remains coherent, whereas the failure covers all directions in the ONK-EH3 stress interpretation with lost structural integrity.
0
20
40
60
80
100
120
140
0.0 0.5 1.0
Tem
pera
ture
(°C
)
Distance (m)
Monitoring line to σ1 direction
0
20
40
60
80
100
120
140
0.0 0.5 1.0
Tem
pera
ture
(°C
)
Distance (m)
Monitoring line to σ3 direction
Weeks 0…3Weeks 3…6Weeks 6…9
20
Figure 15. Fracture propagation for the EDZ & VT1 stress state at -3 m depth.
Figure 16. Fracture propagation for the ONK-EH3 stress state at -3 m depth.
Figure 17. The maximum and minor principal stress evolution from the shotcrete surface to maximum principal stress direction for the ONK-EH3 stress interpretation.
Weeks 0-3 After 3 weeks Weeks 3-6 After 6 weeks After 9 weeks
σ3
σ1
Weeks 0-3 After 3 weeks Weeks 3-6 After 6 weeks After 9 weeks
σ3
σ1
after 6 weeks after 9 weeks
σ 1
>100
90
80
70
60
50
40
30
20
10
0
<-10 MPa
σ 3
21
5.3 Acoustic emission pattern
The predicted AE patterns for different calculation cases are presented in Figure 18. The ONK-EH3 case at -3 m depth is selected for AE result interpretation. In total 15,288 and 5,569 local seismic magnitudes of -2.4 ML or larger acoustic emission events are predicted for the unsupported and supported cases. Lower than -2.4 ML, events are probably too low to be recorded during the in situ experiment, based on the experience of Reyes-Montes et al. (2014) in the ONKALO. During the following weeks of the experiment, the fracture growth causes anomalous stress distributions behind the rock surface, with locally high tangential (locally over 170 MPa) and tensile stresses (see Figure 19).
Figure 18. Predicted cumulative acoustic emissions after 10 week heating period.
Figure 19. The differential stress evolution from the shotcrete surface to minimum principal stress direction for the ONK-EH3 stress interpretation.
ONK-EH3 stress state EDZ & VT1 stress state
σ3
σ1 σ3
σ1
0
50
100
150
200
250
300
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
22000
Weeks 0…3 Weeks 3…6 Weeks 6…9
Tan
gent
ial s
tres
s (M
Pa)
Acc
umul
ated
aco
ustic
eve
nts
(per
3 w
eeks
)
AE - No shotcrete
AE - Shotcrete
σ - No shotcrete
σ - Shotcrete
σ - No fracture growth
θθ
θθ
θθ
22
6 DISCUSSION
Fracod 2D suggests that the concrete will fail before the rock, with the first failure occurring after three weeks of heating. The concrete layer provides significant support pressure up, which is predicted to suppress the rock failure significantly. However, it is unclear what effect the loss of adhesion at the concrete-rock interface will have. The concrete support pressure is discussed in more detail in Siren et al. 2015. During the experiment, it will be monitored if the support pressure is enough to retain the damaged rock. The concrete parameters will be tested during the execution of the ICSE experiment, which will give more confidence in terms of the modelling of thin concrete layers, as well as the results from the actual in situ experiment.
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7 REFERENCES
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Johansson, E., Siren, T. & Hakala, M. 2014. POSE Experiment: Outcome from the POSE Phase 1 and 2. Working Report 2012-60. Posiva.
NA SFS-EN1992-1-1-YM:2007, The Finnish National Annex to the standard SFS-EN 1992-1-1 Eurocode 2: Design of concrete structures - Part 1: General rules and rules for buildings, 14 pp.
Neville, A.M. 1995. Properties of Concrete, Longman Group Ltd: London.
Kukkonen I., Kivekäs, L., Vuoriainen, S., Kääriä, M. 2011. Thermal properties of Rocks in Olkiluoto: Results of Laboratory Measurements 1994-2010. Olkiluoto: Posiva Oy.
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Reinhardt, H.W., Ošbolt, J., Shilang, X., Dinku, A. 1997. Shear of structural concrete members and pure mode II testing. Advanced Cement Based Materials (5)3-4, pp. 75-85.
Reyes-Montes J., Flynn W., Huang J. 2014 ONKALO POSE Experiment – Phase 3: Acoustic and Ultrasonic Monitoring. Working report 2013-39. Posiva.
Swamy, R. N. 1979. Developments in concrete technology. pp. 221-81. Applied Science Publishers Ltd.
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. Siren, T. 2011. Fracture Mechanics Prediction for Posiva’s Olkiluoto Spalling Experiment (POSE). Working report 2011-23. Posiva.
Siren, T. 2012. Fracture Toughness Properties of Rocks in Olkiluoto: Laboratory Measurements 2008-2009. Working report 2012-25. Posiva.
Siren, T., Uotinen, L., Rinne, M., and Shen, B. 2015. Fracture mechanics modelling of an in situ concrete spalling experiment. Rock Mechanics and Rock Engineering 48, pp. 1423-1438.
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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. In: Proceedings of the World Tunnel Congress (WTC) 2013, Geneva, Switzerland, May/June 2013.
Hakala, M. & Valli, J. 2013. ONKALO POSE experiment – Phase 3: 3DEC prediction. Working Report 2012-58. Posiva.
Valli, J., Hakala, M., Wanne, T., Siren, T., Kantia, P. (2014) ONKALO POSE experiment – Phase 3: Execution and monitoring. Working Report 2013-41. Posiva.