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Modelling of the bedrock response to glacial loading at the Olkiluoto site, Finland
Engineering Geology 67 (2002) 39 – 49 www.elsevier.com/locate/enggeo
Modelling of the bedrock response to glacial loading at the Olkiluoto site, Finland Kaisa-Leena Hutri a,*, Juha Antikainen b,1 a Radiation and Nuclear Safety Authority (STUK), P.O. Box 14, FIN-00881 Helsinki, Finland Helsinki University of Technology, Rock Engineering, P.O. Box 6200, FIN-02015 HUT, Finland
b
Received 15 May 2001; accepted 25 March 2002
Abstract The Olkiluoto Island is situated in Baltic Sea, near the southwestern coast of Finland. The most abundant rock type is migmatic mica gneiss, intruded by tonalites, granodiorites and granites. Response of bedrock at Olkiluoto site was modelled with 3DEC program considering four future ice age scenarios. Each scenario produces shear displacements of fractures with different time of occurrence and varying recovery rate. Generally, the larger the maximum ice load, the larger the permanent shear displacements will be. For basic case, the maximum shear displacements were few centimeters at suggested nuclear waste repository level. The sensitivity study performed showed that shear stiffness and joint friction angle of bedrock structures are the most critical parameters for bedrock displacements. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Climate change; Glaciation; Nuclear waste repository; Faults; Shearing; 3D modelling
1. Introduction The Northern Hemisphere has gone through several ice age cycles, which have occurred periodically for at least 2 million years. According to climate predictions, we will encounter a new glacial phase during the next 100 000 years (Kukla et al., 1981; Imbrie and Imbrie, 1980; Matthews, 1984; Berger and Loutre, 1997; Loutre and Berger, 2000). During the glaciation, the bedrock will undergo massive loading and depression followed by strong isostatic rebound. The stresses in rock masses will change greatly and as rock fractures and faults are already weak constitu*
Corresponding author. Fax: +358-9-7598-8670. E-mail addresses: [email protected] (K.-L. Hutri), [email protected] (J. Antikainen). 1 Fax: + 358-9-451-2812.
ents, these could be sites of displacements. In the past, displacements, especially in the retreating stages of the ice sheet, have been interpreted (Lundqvist and Lagerba¨ck, 1976; Kuivama¨ki et al., 1998). The bedrock of Olkiluoto Island, situated in the municipality of Eurajoki at the southwestern coast of Finland, is being investigated as a selected site for a repository of spent nuclear fuel in Finland. The area is a part of the nowadays seismically calm Fennoscandian Shield. According to GPS measurements carried out, only some rather small (less than 0.5 mm/year) bedrock movements correlated to a regional fracture zone have been found (Chen and Kakkuri, 1998). Long-term stability of the bedrock plays an essential role when evaluating the safety of the repository and a rock displacement of sufficient magnitude might damage nuclear waste canisters and the buffer around them (La Pointe et al., 1997; Bo¨rgesson, 1986).
0013-7952/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 3 - 7 9 5 2 ( 0 2 ) 0 0 1 0 8 - 4
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Fig. 1. (a) The geological map on the surface at Olkiluoto site (modified from Fig. 5.2 – 3 in Anttila et al., 1999). (b) A north – south vertical cross-section of the Olkiluoto bedrock model including boreholes KR2, KR4, KR6 and KR10 (modified from Fig. 5.2 – 5 in Anttila et al., 1999). (c) The fracture zones in 3DEC model of Olkiluoto site. The width of the entire model is 12 km, the width of the inner part is 7 km.
Stability changes and displacements of the bedrock can be modelled with different tools used in mining and civil engineering, such as UDEC and 3DEC. Previous modelling studies have been done on Swedish nuclear waste projects in the late 1980s and 1990s ¨ spo¨ sites (Stephansson, 1987; Shen at Finnsjo¨ and A and Stephansson, 1996; Rosengren and Stephansson, 1990; Hansson et al., 1995). In this work, the magnitudes of displacements along rock structures at the investigation site were evaluated according to four different glaciation scenarios. All the field data for model input are based on investigations produced by Posiva Oy (the Finnish Nuclear Waste Management). The significance of different rock properties on displacements was also estimated. To simplify the study, thermal, hydrological and chemical effects are omitted.
2. Materials 2.1. The study area The Olkiluoto island rose from the Bothnian Sea about 3000 years ago (Eronen et al., 1995). The topography is subdued in relief, being usually less than 5
m above sea level. The bedrock consists of Precambrian Svecofennian rocks, 1850 –1900 Ma of age. Migmatic gneisses are the most abundant supracrustal rocks in the study area in which the palaeosome is mica gneiss and the neosome granite. It is intruded by intermediate and felsic plutonic rocks, tonalites, granodiorites, granites and pegmatites (Fig. 1a). Since there are only few outcrops, 14 boreholes, two investigation trenches and interpretation of geophysics have augmented knowledge of the bedrock. In the northern parts, the rocks are weakly migmatized. Towards the southern and southeastern parts of the site migmatizations comes gradually strongerforming vein gneisses. In the northern and the middle parts, the gneisses are intruded by foliated tonalites and granites. In the south and southeastern parts, where the migmatization is strong, the tonalites are gneissic in texture. Coarse-grain granites and pegmatites occur in other rocks migmatizing them or crosscutting the foliation (Fig. 1b). The youngest rocks are diabase dikes (1650 Ma), crossing the other rock types. All rock types, except diabase, have gone through five plastic deformational phases. The main fracture directions from surface mapping are firstly, ENE – WSW, which is parallel to the foliation and migmatic banding, secondly, a direction
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perpendicular to the previous one and thirdly, one which intersects these at an oblique angle (Anttila et al., 1999). The size of the studied area is about 12 9 3 km and its shape is rhomboid. The inner part of the area, 7 3.2 2.5 km, was modelled in more detail (Fig. 1c). The boundaries of the study area follow some major regional fracture zones in the regional fracture zone model. The bedrock model employed in this study is based on a conceptual bedrock model created and updated by Saksa et al. (1998). The geometry includes 32 fracture zones of which 27 are located in the inner study area. Parallel, closely spaced fracture zones were modelled as a single fracture zone. In the text, a capital R and a running number refer to the fractures. The dimensions of fracture planes vary from 100 m to 1.5 km. At least two fracture zones, named R11 and R24, are reported to be faulted (Paulama¨ki, 1995, 1996; Anttila et al., 1999).
Table 2 The in situ rock stresses in modelling, z is depth from surface (m) Parameter
Depth 0 – 300 m (MPa)
Depth 300 – 3000 m (MPa)
Maximum horizontal stress Minimum horizontal stress Vertical stress
0.041z + 2.67
0.060z + 2.67
0.030z + 2.00
0.030z + 2.00
0.0273z
0.0273z
2.3. Rock stress In the modelling, the rock stress was applied as in situ stresses using the mean values measured at Olkiluoto. The maximum horizontal stress is in east – west direction (Ljunggren and Klasson, 1996; ¨ ika¨s et al., 1999). The stresses are assumed to vary A stepwise linearly with depth (Table 2).
2.2. Material properties
3. Scenarios
Due to the scale of the model and the heterogeneous structure of the rock at the site, rock type variations were not taken into account in the model. Hence, the properties of the most common rock type, the migmatized mica gneiss, were used (Table 1) as ¨ ika¨s et al., the properties of all rock types in the area (A 1999; Johansson and Hakala, 1992).
According to presented climate scenarios, the climate in the future will gradually become colder, permitting the growth of small mountain glaciers in Caledonia after 5000 – 20 000 years. Forecasts on future climate changes and further development of the Fennoscandian glaciation have recently been presented by the Finnish and Swedish nuclear waste management companies. A total of three different scenarios have been published (Forsstro¨m, 1999; SKB, 1999). New results suggest that there was a larger ice-free area in Fennoscandia during the Middle Weichselian than previously assumed (Ukkonen et al., 1999), and that the ice sheet had not reached areas in eastern Finland prior to 22 500 B.P. There is also evidence from at least one Weichselian glaciation stage in southern Finland (Donner, 1999). Therefore, in collating these results, a rough draft has been made imitating the ice sheet development from Eemian interglacial to today as a fourth possible scenario. The ice age scenarios are presented in Figs. 2– 5 and labelled Forms A to D. The ice thicknesses are converted to ice load using 900 kg/m3 for the ice density. A common feature in the scenarios is that the biggest changes of the ice loads are the fastest.
Table 1 Material properties for 3DEC modelling Property
Value
Source
61.5 GPa
¨ ika¨s et al., 1999 A
49.2 GPa
estimated with iteration, see text ¨ ika¨s et al., 1999 A ¨ ika¨s et al., 1999 A
Intact rock: Young’s modulus (inner part of model) Young’s modulus (outer part of model) Poisson’s ratio Density
0.23 2730 kg/m3
Discontinuities: Cohesion
0
Friction angle Normal stiffness Shear stiffness
15j 2 GPa/m 0.2 GPa/m
Johansson and Hakala, 1992 Hoek et al., 1995 Martin et al., 1990 Bandis, 1990
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Fig. 2. Ice load on the ground surface, scenario A (according to Forsstro¨m, 1999). The ice edge on the dry land is predicted to be oblique (gradient 10 m/km) in 20 – 25 ka A.P. Around 50 ka A.P., a new glacial phase is expected to begin. Around 115 – 125 ka A.P., the ice will melt away rather fast discharging into a sea (with about 100 m of water) and finally, there will be 100 m of water before the land emerges.
In the retreating phase of an ice sheet, a 100-mthick end moraine, like that of Salpausselka¨, might be formed in front of the ice margin thus burdening the bedrock. Some parts of the Salpausselka¨ landforms are today still below sea level (Atlas of Finland, 1990), although the biggest are located on dry land. However, the loading effect of an end moraine is much less than that of a several kilometers thick ice
Fig. 3. Ice load on the ground surface, scenario B (according to Forsstro¨m, 1999). The phases are expected to show the same pattern as in scenario A.
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Fig. 4. Ice load on the ground surface, scenario C (according to SKB, 1999). The ice load is assumed to depress the land surface below sea level so that it is covered by about 50 m of water. By 70 ka A.P., all the ice will have melted away and the land will be covered by a 100-m-thick water layer until a maximum glaciation phase begins around 88 ka A.P. Finally, there will be 100 m of water before the land emerges.
sheet. Thus, end moraines are omitted from this study, although there is no doubt that they have a great effect on local stress and hydrogeology.
Fig. 5. Ice load on the ground surface, scenario D. The ice thickness in 5 – 20 ka A.P. will be about 500 m, corresponding to the Early Weichselian stage at the Olkiluoto site. This will be followed by a retreating phase when the ice melts away entirely. Around 50 and 100 ka A.P., two new glacial phases are expected to begin, corresponding in extent to the Middle and Late Weichselian stages. In both cases, the ice will melt away gradually, going through the same phases as in scenario A.
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4. Modelling approach and boundary conditions The modelling was made using the 3DEC program. The rock mass is modelled as a 3D assemblage of deformable blocks. Discontinuities are regarded as distinct boundary interactions between these blocks. Joint behavior is determined for these interactions (Itasca, 1994). The rock mass was modelled as an assembly of discrete rock blocks, which are separated by planar discontinuities. A horizontal discontinuity at 2500 m was added here just to facilitate the model generation. The outer part of the model was constructed just for providing realistic boundary conditions for the more detailed inner part of the model (Fig. 1b). The boundary conditions at the bottom and sides of the model were set to prevent displacement in normal direction to the boundary. The displacement along the boundary was set free. In the initial state, the top of the model (ground surface) was free, and the glaciation load was applied as vertical boundary stress. The model consists of 194 distinct element blocks that are internally divided into 112 735 deformable zones. The Young’s modulus is smaller for the entire rock mass than for an intact rock due to the rock jointing. Equal properties of rock mass were assumed for inner and outer modelling area. Because the rock
Fig. 7. Scenario A, shear displacement in selected fracture zones.
jointing was not modelled for the outer part, the modulus of elasticity for that part had to be reduced to produce uniform surface subsidence under glacial load. It was found with few iterations that 80% of intact rock modulus of elasticity applied in the outer part of the model produced rather uniform surface subsidence across the entire model. A linearly elastic material model was used for the blocks and the Mohr –Coulomb strength criterion was applied for discontinuities so that yielding is possible along the discontinuities but not inside the distinct blocks. The Mohr– Coulomb criterion explains the shear strength of the discontinuities (Eq. (1)). s ¼ c þ rn tan/
Fig. 6. Ground surface subsidence according to scenario D at selected surface points for the inner modelling area compared to the reference level 3000 m below.
ð1Þ
where s is the shear strength, c is the cohesion, rn is the normal stress and / is the friction angle. Normal and shear stiffness of rock joints are very scale-dependent, and they were evaluated using typical values of large-scale structures in hard rock (Bandis, 1990; Martin et al., 1990). The material properties are summarized in Table 1. The properties of rock mass in the study area are evaluated mostly from drill core tests. Thus, the properties of large-scale discontinuities are not well understood yet. A sensitivity study was carried out to find out which rock properties affect most the results. The ice age scenario D was selected as a basis for the
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Fig. 8. Scenario B, shear displacement in selected fracture zones.
sensitivity study partly because it represents the latest knowledge from the Weichselian glaciation in eastern Fennoscandia and partly because it has three clearly separated loading phases. The effect of changes in cohesion, friction angle, shear stiffness of discontinuities (shear stress/shear displacement ratio), horizontal
Fig. 9. Scenario C, shear displacement in selected fracture zones.
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Fig. 10. Scenario D, shear displacement in selected fracture zones.
rock stress and rock mass modulus of elasticity (stress/strain ratio in uniaxial loading) was studied.
5. Results In the 3DEC modelling results, the surface subsidence was proportional to the glacial load and the subsidence was almost completely recovered after the ice load was removed. The maximum surface subsidence according to scenario D was more than 1 m when the reference level was set at 3-km depth (Fig. 6). The maximum shear displacements of some of the essential fracture zones at 500-m depth are presented in Figs. 7 – 10. The shear displacements along fracture
Fig. 11. Shear displacements under the maximum ice load on surface according to scenarios A – D presented in Figs. 2 – 5.
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Fig. 12. Effect of friction angle of fracture zones on the maximum shear displacement along nine major fracture zones, scenario D.
Fig. 14. Effect of shear stiffness of fracture zones on the maximum shear displacement, scenario D.
zones were not completely elastic and some permanent shear displacement remained when the glacial load was removed. The maximum shear displacement was about 3 cm and the maximum permanent shear displacement was about 3 mm. There was not a significant difference in magnitudes of shear displacement between the different ice age scenarios. Generally, the larger the maximum ice load, the larger the maximum and permanent shear displacements (Fig. 11). According to every scenario, the greatest shear displacements are related to the maximum glacial stage; hence, for scenario C, shear displacements will take place in two main periods, and in scenario D, in three main periods. The effects of friction angle, shear stiffness and cohesion of fractures, in situ rock stress and rock deformability were studied for scenario D and the results are presented in Figs. 12 –16. In general, the largest shear displacement developed along long fracture zones with more than 30j dip. The sensitivity analysis indicated that variation of the friction angle
and shear stiffness resulted in the greatest changes of shear displacement, while effects of cohesion, in situ rock stress and rock mass deformability were less. The effect of the friction angle varies from one fracture zone to another. Shear displacement of a fracture zone with a very small friction angle might be several centimeters or even up to several decimeters (Fig. 12). A very small friction angle is typical for a fracture zone filled with clay minerals (Hoek et al., 1995), but such kind of fracture zones has not been found at the study site. It is also worth noticing that a shear displacement along one fracture zone affects the rock stresses and thus the displacements in other fracture zones. For example, it can be seen in Fig. 12 that the shear displacement of some fracture zones increases with bigger values of friction angle. The effects of cohesion on the magnitude of shear displacements seem to be quite small (Fig. 13). The normal stress across the fracture zones caused by in situ rock stresses and the ice loading is so great that
Fig. 13. Effect of cohesion of fracture zones on the maximum shear displacement, scenario D.
Fig. 15. Effect of maximum horizontal stress gradient by depth on the maximum shear displacement, scenario D.
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Fig. 16. Effect of rock deformability in inner and outer part of the model on the maximum shear displacement, scenario D. A value of 100% denotes the modulus of elasticity for rock mass in inner part of the model in basic case.
the shear strength governed by the joint friction angle dominates. The shear stiffness of the fracture zones has strong effect on rock deformation, producing large shear displacements when the joint shear stiffness values are small (Fig. 14). The effect of in situ horizontal stress on rock mass deformation was investigated in addition to the basic case in two other cases. In the first case, it was assumed that the rock stress changes as it changes when going from the surface to 300 m down with a stress gradient of 0.041 MPa/m. In the second case, the maximum and minimum horizontal stresses were assumed to grow 30% faster than in the basic case. In general, the effect was on exiguous shear displacement (Fig. 15). The variation of rock mass deformability did not show any major effect on the size of the shear displacements (Fig. 16). For situations where the rock mass consists of blocks of different deformability, it could have an effect on the magnitude of the shear displacements.
6. Discussion The produced displacement differences between the ice age scenarios were due mainly to the differences in ice loading, i.e. the bigger the loading, the greater the displacement. The displacements along the fractures are not completely recovered when the ice load is removed because the shear deformation is generally not reversible.
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Subsidence depends on the selected reference level; if the whole crustal thickness had been modelled, the subsidence would have been about 1 km. If the selected reference level had been deeper, the overall dimensions of the model would also have been larger, thus demanding additional calculations. In modelling, simplifications had to be made to reduce the number of details to a manageable level. Simple material model was used both due to the limitations of modelling program and due to difficulties to obtain parameters for more advanced models. In this work, the simplifications, which obviously have largest effect on results, are the assumption of continuous, planar fracture zones and the use of constant values for normal and shear stiffness of fracture zones. The normal and shear stiffnesses are strongly dependent on normal stress. In this work, the values were selected according to the stress level in the suggested repository depth, 500 m. The shear displacements above this level are likely underestimated and overestimated below 500 m. This may have also some effect on the results on the repository level. The modelling program, 3DEC, employs distinct, convex shape blocks which are separated with planar discontinuities. Complex shapes can be formed by manually joining blocks, but for large models, this is impractical and creates frequently numerical instability. In reality, many fracture zones are neither planar nor continuous. This has effect on both the deformability and shear strength of fracture zones. In modelling of large-scale problems, the fracture zones are often modelled as continuous structures with low or zero cohesion values (Johansson and Hakala, 1992). When the modelling scale is more detailed, also smaller, less continuous rock structures are included in models. Even a small portion of intact rock across a fracture zone can increase the apparent cohesion significantly. In addition, the nonplanar shape can increase the shear strength and stiffness of a fracture zone, especially when the fracture zone is thin compared to the amplitude of waviness of the zone. Because the largest part of the model is below the repository level, the use of a constant value for fracture zone stiffnesses and the assumption of continuous, planar fracture zones result in rather overestimating than underestimating the shear displacements. The shear displacements for the basic case are in the same
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order of magnitude, few centimeters in maximum, than in a study performed by Hansson et al. (1995) for a case resembling this study.
7. Conclusions Different ice age scenarios produce shear displacements with different time of occurrence and varying recovery rate. The sizes of the enduring shear displacements are less than 1 cm. The most critical parameters for shear displacements of the model are the shear stiffness and the friction angle of the fracture zones. A better knowledge of mechanical properties and geometry of the fracture zones could enable a more accurate modelling and a better prediction of the bedrock behavior under glacial circumstances. The magnitude of the shear displacements is in agreement with results modelled with generic conceptual bedrock models.
Acknowledgements The authors are very grateful to Dr. Esko Eloranta for many fruitful discussions and his interest in this study. We also like to thank Prof. Joakim Donner who made valuable suggestions and improved the manuscript and Mr. Juha Ha¨ikio¨ who helped us with graphics.
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Modelling of the bedrock response to glacial loading at the Olkiluoto site, Finland Kaisa-Leena Hutri a,*, Juha Antikainen b,1 a Radiation and Nuclear Safety Authority (STUK), P.O. Box 14, FIN-00881 Helsinki, Finland Helsinki University of Technology, Rock Engineering, P.O. Box 6200, FIN-02015 HUT, Finland
b
Received 15 May 2001; accepted 25 March 2002
Abstract The Olkiluoto Island is situated in Baltic Sea, near the southwestern coast of Finland. The most abundant rock type is migmatic mica gneiss, intruded by tonalites, granodiorites and granites. Response of bedrock at Olkiluoto site was modelled with 3DEC program considering four future ice age scenarios. Each scenario produces shear displacements of fractures with different time of occurrence and varying recovery rate. Generally, the larger the maximum ice load, the larger the permanent shear displacements will be. For basic case, the maximum shear displacements were few centimeters at suggested nuclear waste repository level. The sensitivity study performed showed that shear stiffness and joint friction angle of bedrock structures are the most critical parameters for bedrock displacements. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Climate change; Glaciation; Nuclear waste repository; Faults; Shearing; 3D modelling
1. Introduction The Northern Hemisphere has gone through several ice age cycles, which have occurred periodically for at least 2 million years. According to climate predictions, we will encounter a new glacial phase during the next 100 000 years (Kukla et al., 1981; Imbrie and Imbrie, 1980; Matthews, 1984; Berger and Loutre, 1997; Loutre and Berger, 2000). During the glaciation, the bedrock will undergo massive loading and depression followed by strong isostatic rebound. The stresses in rock masses will change greatly and as rock fractures and faults are already weak constitu*
Corresponding author. Fax: +358-9-7598-8670. E-mail addresses: [email protected] (K.-L. Hutri), [email protected] (J. Antikainen). 1 Fax: + 358-9-451-2812.
ents, these could be sites of displacements. In the past, displacements, especially in the retreating stages of the ice sheet, have been interpreted (Lundqvist and Lagerba¨ck, 1976; Kuivama¨ki et al., 1998). The bedrock of Olkiluoto Island, situated in the municipality of Eurajoki at the southwestern coast of Finland, is being investigated as a selected site for a repository of spent nuclear fuel in Finland. The area is a part of the nowadays seismically calm Fennoscandian Shield. According to GPS measurements carried out, only some rather small (less than 0.5 mm/year) bedrock movements correlated to a regional fracture zone have been found (Chen and Kakkuri, 1998). Long-term stability of the bedrock plays an essential role when evaluating the safety of the repository and a rock displacement of sufficient magnitude might damage nuclear waste canisters and the buffer around them (La Pointe et al., 1997; Bo¨rgesson, 1986).
0013-7952/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 3 - 7 9 5 2 ( 0 2 ) 0 0 1 0 8 - 4
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Fig. 1. (a) The geological map on the surface at Olkiluoto site (modified from Fig. 5.2 – 3 in Anttila et al., 1999). (b) A north – south vertical cross-section of the Olkiluoto bedrock model including boreholes KR2, KR4, KR6 and KR10 (modified from Fig. 5.2 – 5 in Anttila et al., 1999). (c) The fracture zones in 3DEC model of Olkiluoto site. The width of the entire model is 12 km, the width of the inner part is 7 km.
Stability changes and displacements of the bedrock can be modelled with different tools used in mining and civil engineering, such as UDEC and 3DEC. Previous modelling studies have been done on Swedish nuclear waste projects in the late 1980s and 1990s ¨ spo¨ sites (Stephansson, 1987; Shen at Finnsjo¨ and A and Stephansson, 1996; Rosengren and Stephansson, 1990; Hansson et al., 1995). In this work, the magnitudes of displacements along rock structures at the investigation site were evaluated according to four different glaciation scenarios. All the field data for model input are based on investigations produced by Posiva Oy (the Finnish Nuclear Waste Management). The significance of different rock properties on displacements was also estimated. To simplify the study, thermal, hydrological and chemical effects are omitted.
2. Materials 2.1. The study area The Olkiluoto island rose from the Bothnian Sea about 3000 years ago (Eronen et al., 1995). The topography is subdued in relief, being usually less than 5
m above sea level. The bedrock consists of Precambrian Svecofennian rocks, 1850 –1900 Ma of age. Migmatic gneisses are the most abundant supracrustal rocks in the study area in which the palaeosome is mica gneiss and the neosome granite. It is intruded by intermediate and felsic plutonic rocks, tonalites, granodiorites, granites and pegmatites (Fig. 1a). Since there are only few outcrops, 14 boreholes, two investigation trenches and interpretation of geophysics have augmented knowledge of the bedrock. In the northern parts, the rocks are weakly migmatized. Towards the southern and southeastern parts of the site migmatizations comes gradually strongerforming vein gneisses. In the northern and the middle parts, the gneisses are intruded by foliated tonalites and granites. In the south and southeastern parts, where the migmatization is strong, the tonalites are gneissic in texture. Coarse-grain granites and pegmatites occur in other rocks migmatizing them or crosscutting the foliation (Fig. 1b). The youngest rocks are diabase dikes (1650 Ma), crossing the other rock types. All rock types, except diabase, have gone through five plastic deformational phases. The main fracture directions from surface mapping are firstly, ENE – WSW, which is parallel to the foliation and migmatic banding, secondly, a direction
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perpendicular to the previous one and thirdly, one which intersects these at an oblique angle (Anttila et al., 1999). The size of the studied area is about 12 9 3 km and its shape is rhomboid. The inner part of the area, 7 3.2 2.5 km, was modelled in more detail (Fig. 1c). The boundaries of the study area follow some major regional fracture zones in the regional fracture zone model. The bedrock model employed in this study is based on a conceptual bedrock model created and updated by Saksa et al. (1998). The geometry includes 32 fracture zones of which 27 are located in the inner study area. Parallel, closely spaced fracture zones were modelled as a single fracture zone. In the text, a capital R and a running number refer to the fractures. The dimensions of fracture planes vary from 100 m to 1.5 km. At least two fracture zones, named R11 and R24, are reported to be faulted (Paulama¨ki, 1995, 1996; Anttila et al., 1999).
Table 2 The in situ rock stresses in modelling, z is depth from surface (m) Parameter
Depth 0 – 300 m (MPa)
Depth 300 – 3000 m (MPa)
Maximum horizontal stress Minimum horizontal stress Vertical stress
0.041z + 2.67
0.060z + 2.67
0.030z + 2.00
0.030z + 2.00
0.0273z
0.0273z
2.3. Rock stress In the modelling, the rock stress was applied as in situ stresses using the mean values measured at Olkiluoto. The maximum horizontal stress is in east – west direction (Ljunggren and Klasson, 1996; ¨ ika¨s et al., 1999). The stresses are assumed to vary A stepwise linearly with depth (Table 2).
2.2. Material properties
3. Scenarios
Due to the scale of the model and the heterogeneous structure of the rock at the site, rock type variations were not taken into account in the model. Hence, the properties of the most common rock type, the migmatized mica gneiss, were used (Table 1) as ¨ ika¨s et al., the properties of all rock types in the area (A 1999; Johansson and Hakala, 1992).
According to presented climate scenarios, the climate in the future will gradually become colder, permitting the growth of small mountain glaciers in Caledonia after 5000 – 20 000 years. Forecasts on future climate changes and further development of the Fennoscandian glaciation have recently been presented by the Finnish and Swedish nuclear waste management companies. A total of three different scenarios have been published (Forsstro¨m, 1999; SKB, 1999). New results suggest that there was a larger ice-free area in Fennoscandia during the Middle Weichselian than previously assumed (Ukkonen et al., 1999), and that the ice sheet had not reached areas in eastern Finland prior to 22 500 B.P. There is also evidence from at least one Weichselian glaciation stage in southern Finland (Donner, 1999). Therefore, in collating these results, a rough draft has been made imitating the ice sheet development from Eemian interglacial to today as a fourth possible scenario. The ice age scenarios are presented in Figs. 2– 5 and labelled Forms A to D. The ice thicknesses are converted to ice load using 900 kg/m3 for the ice density. A common feature in the scenarios is that the biggest changes of the ice loads are the fastest.
Table 1 Material properties for 3DEC modelling Property
Value
Source
61.5 GPa
¨ ika¨s et al., 1999 A
49.2 GPa
estimated with iteration, see text ¨ ika¨s et al., 1999 A ¨ ika¨s et al., 1999 A
Intact rock: Young’s modulus (inner part of model) Young’s modulus (outer part of model) Poisson’s ratio Density
0.23 2730 kg/m3
Discontinuities: Cohesion
0
Friction angle Normal stiffness Shear stiffness
15j 2 GPa/m 0.2 GPa/m
Johansson and Hakala, 1992 Hoek et al., 1995 Martin et al., 1990 Bandis, 1990
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Fig. 2. Ice load on the ground surface, scenario A (according to Forsstro¨m, 1999). The ice edge on the dry land is predicted to be oblique (gradient 10 m/km) in 20 – 25 ka A.P. Around 50 ka A.P., a new glacial phase is expected to begin. Around 115 – 125 ka A.P., the ice will melt away rather fast discharging into a sea (with about 100 m of water) and finally, there will be 100 m of water before the land emerges.
In the retreating phase of an ice sheet, a 100-mthick end moraine, like that of Salpausselka¨, might be formed in front of the ice margin thus burdening the bedrock. Some parts of the Salpausselka¨ landforms are today still below sea level (Atlas of Finland, 1990), although the biggest are located on dry land. However, the loading effect of an end moraine is much less than that of a several kilometers thick ice
Fig. 3. Ice load on the ground surface, scenario B (according to Forsstro¨m, 1999). The phases are expected to show the same pattern as in scenario A.
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Fig. 4. Ice load on the ground surface, scenario C (according to SKB, 1999). The ice load is assumed to depress the land surface below sea level so that it is covered by about 50 m of water. By 70 ka A.P., all the ice will have melted away and the land will be covered by a 100-m-thick water layer until a maximum glaciation phase begins around 88 ka A.P. Finally, there will be 100 m of water before the land emerges.
sheet. Thus, end moraines are omitted from this study, although there is no doubt that they have a great effect on local stress and hydrogeology.
Fig. 5. Ice load on the ground surface, scenario D. The ice thickness in 5 – 20 ka A.P. will be about 500 m, corresponding to the Early Weichselian stage at the Olkiluoto site. This will be followed by a retreating phase when the ice melts away entirely. Around 50 and 100 ka A.P., two new glacial phases are expected to begin, corresponding in extent to the Middle and Late Weichselian stages. In both cases, the ice will melt away gradually, going through the same phases as in scenario A.
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4. Modelling approach and boundary conditions The modelling was made using the 3DEC program. The rock mass is modelled as a 3D assemblage of deformable blocks. Discontinuities are regarded as distinct boundary interactions between these blocks. Joint behavior is determined for these interactions (Itasca, 1994). The rock mass was modelled as an assembly of discrete rock blocks, which are separated by planar discontinuities. A horizontal discontinuity at 2500 m was added here just to facilitate the model generation. The outer part of the model was constructed just for providing realistic boundary conditions for the more detailed inner part of the model (Fig. 1b). The boundary conditions at the bottom and sides of the model were set to prevent displacement in normal direction to the boundary. The displacement along the boundary was set free. In the initial state, the top of the model (ground surface) was free, and the glaciation load was applied as vertical boundary stress. The model consists of 194 distinct element blocks that are internally divided into 112 735 deformable zones. The Young’s modulus is smaller for the entire rock mass than for an intact rock due to the rock jointing. Equal properties of rock mass were assumed for inner and outer modelling area. Because the rock
Fig. 7. Scenario A, shear displacement in selected fracture zones.
jointing was not modelled for the outer part, the modulus of elasticity for that part had to be reduced to produce uniform surface subsidence under glacial load. It was found with few iterations that 80% of intact rock modulus of elasticity applied in the outer part of the model produced rather uniform surface subsidence across the entire model. A linearly elastic material model was used for the blocks and the Mohr –Coulomb strength criterion was applied for discontinuities so that yielding is possible along the discontinuities but not inside the distinct blocks. The Mohr– Coulomb criterion explains the shear strength of the discontinuities (Eq. (1)). s ¼ c þ rn tan/
Fig. 6. Ground surface subsidence according to scenario D at selected surface points for the inner modelling area compared to the reference level 3000 m below.
ð1Þ
where s is the shear strength, c is the cohesion, rn is the normal stress and / is the friction angle. Normal and shear stiffness of rock joints are very scale-dependent, and they were evaluated using typical values of large-scale structures in hard rock (Bandis, 1990; Martin et al., 1990). The material properties are summarized in Table 1. The properties of rock mass in the study area are evaluated mostly from drill core tests. Thus, the properties of large-scale discontinuities are not well understood yet. A sensitivity study was carried out to find out which rock properties affect most the results. The ice age scenario D was selected as a basis for the
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Fig. 8. Scenario B, shear displacement in selected fracture zones.
sensitivity study partly because it represents the latest knowledge from the Weichselian glaciation in eastern Fennoscandia and partly because it has three clearly separated loading phases. The effect of changes in cohesion, friction angle, shear stiffness of discontinuities (shear stress/shear displacement ratio), horizontal
Fig. 9. Scenario C, shear displacement in selected fracture zones.
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Fig. 10. Scenario D, shear displacement in selected fracture zones.
rock stress and rock mass modulus of elasticity (stress/strain ratio in uniaxial loading) was studied.
5. Results In the 3DEC modelling results, the surface subsidence was proportional to the glacial load and the subsidence was almost completely recovered after the ice load was removed. The maximum surface subsidence according to scenario D was more than 1 m when the reference level was set at 3-km depth (Fig. 6). The maximum shear displacements of some of the essential fracture zones at 500-m depth are presented in Figs. 7 – 10. The shear displacements along fracture
Fig. 11. Shear displacements under the maximum ice load on surface according to scenarios A – D presented in Figs. 2 – 5.
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Fig. 12. Effect of friction angle of fracture zones on the maximum shear displacement along nine major fracture zones, scenario D.
Fig. 14. Effect of shear stiffness of fracture zones on the maximum shear displacement, scenario D.
zones were not completely elastic and some permanent shear displacement remained when the glacial load was removed. The maximum shear displacement was about 3 cm and the maximum permanent shear displacement was about 3 mm. There was not a significant difference in magnitudes of shear displacement between the different ice age scenarios. Generally, the larger the maximum ice load, the larger the maximum and permanent shear displacements (Fig. 11). According to every scenario, the greatest shear displacements are related to the maximum glacial stage; hence, for scenario C, shear displacements will take place in two main periods, and in scenario D, in three main periods. The effects of friction angle, shear stiffness and cohesion of fractures, in situ rock stress and rock deformability were studied for scenario D and the results are presented in Figs. 12 –16. In general, the largest shear displacement developed along long fracture zones with more than 30j dip. The sensitivity analysis indicated that variation of the friction angle
and shear stiffness resulted in the greatest changes of shear displacement, while effects of cohesion, in situ rock stress and rock mass deformability were less. The effect of the friction angle varies from one fracture zone to another. Shear displacement of a fracture zone with a very small friction angle might be several centimeters or even up to several decimeters (Fig. 12). A very small friction angle is typical for a fracture zone filled with clay minerals (Hoek et al., 1995), but such kind of fracture zones has not been found at the study site. It is also worth noticing that a shear displacement along one fracture zone affects the rock stresses and thus the displacements in other fracture zones. For example, it can be seen in Fig. 12 that the shear displacement of some fracture zones increases with bigger values of friction angle. The effects of cohesion on the magnitude of shear displacements seem to be quite small (Fig. 13). The normal stress across the fracture zones caused by in situ rock stresses and the ice loading is so great that
Fig. 13. Effect of cohesion of fracture zones on the maximum shear displacement, scenario D.
Fig. 15. Effect of maximum horizontal stress gradient by depth on the maximum shear displacement, scenario D.
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Fig. 16. Effect of rock deformability in inner and outer part of the model on the maximum shear displacement, scenario D. A value of 100% denotes the modulus of elasticity for rock mass in inner part of the model in basic case.
the shear strength governed by the joint friction angle dominates. The shear stiffness of the fracture zones has strong effect on rock deformation, producing large shear displacements when the joint shear stiffness values are small (Fig. 14). The effect of in situ horizontal stress on rock mass deformation was investigated in addition to the basic case in two other cases. In the first case, it was assumed that the rock stress changes as it changes when going from the surface to 300 m down with a stress gradient of 0.041 MPa/m. In the second case, the maximum and minimum horizontal stresses were assumed to grow 30% faster than in the basic case. In general, the effect was on exiguous shear displacement (Fig. 15). The variation of rock mass deformability did not show any major effect on the size of the shear displacements (Fig. 16). For situations where the rock mass consists of blocks of different deformability, it could have an effect on the magnitude of the shear displacements.
6. Discussion The produced displacement differences between the ice age scenarios were due mainly to the differences in ice loading, i.e. the bigger the loading, the greater the displacement. The displacements along the fractures are not completely recovered when the ice load is removed because the shear deformation is generally not reversible.
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Subsidence depends on the selected reference level; if the whole crustal thickness had been modelled, the subsidence would have been about 1 km. If the selected reference level had been deeper, the overall dimensions of the model would also have been larger, thus demanding additional calculations. In modelling, simplifications had to be made to reduce the number of details to a manageable level. Simple material model was used both due to the limitations of modelling program and due to difficulties to obtain parameters for more advanced models. In this work, the simplifications, which obviously have largest effect on results, are the assumption of continuous, planar fracture zones and the use of constant values for normal and shear stiffness of fracture zones. The normal and shear stiffnesses are strongly dependent on normal stress. In this work, the values were selected according to the stress level in the suggested repository depth, 500 m. The shear displacements above this level are likely underestimated and overestimated below 500 m. This may have also some effect on the results on the repository level. The modelling program, 3DEC, employs distinct, convex shape blocks which are separated with planar discontinuities. Complex shapes can be formed by manually joining blocks, but for large models, this is impractical and creates frequently numerical instability. In reality, many fracture zones are neither planar nor continuous. This has effect on both the deformability and shear strength of fracture zones. In modelling of large-scale problems, the fracture zones are often modelled as continuous structures with low or zero cohesion values (Johansson and Hakala, 1992). When the modelling scale is more detailed, also smaller, less continuous rock structures are included in models. Even a small portion of intact rock across a fracture zone can increase the apparent cohesion significantly. In addition, the nonplanar shape can increase the shear strength and stiffness of a fracture zone, especially when the fracture zone is thin compared to the amplitude of waviness of the zone. Because the largest part of the model is below the repository level, the use of a constant value for fracture zone stiffnesses and the assumption of continuous, planar fracture zones result in rather overestimating than underestimating the shear displacements. The shear displacements for the basic case are in the same
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order of magnitude, few centimeters in maximum, than in a study performed by Hansson et al. (1995) for a case resembling this study.
7. Conclusions Different ice age scenarios produce shear displacements with different time of occurrence and varying recovery rate. The sizes of the enduring shear displacements are less than 1 cm. The most critical parameters for shear displacements of the model are the shear stiffness and the friction angle of the fracture zones. A better knowledge of mechanical properties and geometry of the fracture zones could enable a more accurate modelling and a better prediction of the bedrock behavior under glacial circumstances. The magnitude of the shear displacements is in agreement with results modelled with generic conceptual bedrock models.
Acknowledgements The authors are very grateful to Dr. Esko Eloranta for many fruitful discussions and his interest in this study. We also like to thank Prof. Joakim Donner who made valuable suggestions and improved the manuscript and Mr. Juha Ha¨ikio¨ who helped us with graphics.
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