Modeling of the thermohydromechanical–chemical response of Ontario sedimentary rocks to future...
48
MODELING OF THE THERMO-HYDRO-MECHANICAL-CHEMICAL RESPONSE OF 1 ONTARIO SEDIMENTARY ROCKS TO FUTURE GLACIATIONS 2 3 Othman Nasir 1 , Mamadou Fall 1* , T. Son Nguyen 2,1 , Erman Evgin 1 4 1 Civil Engineering Department, University of Ottawa, Ottawa, Ontario, Canada 5 2 Canadian Nuclear Safety Commission (CNSC), Ottawa, Ontario, Canada 6 7 8 9 *Corresponding author: 10 Dr. Mamadou Fall 11 Professor, 12 Director of OCIENE 13 Department of Civil Engineering, 14 University of Ottawa, Canada; 15 161 Colonel by, Ottawa (Ontario), K1N 6N5; 16 [email protected] 17 Phone: +1-613-562 5800 # 6558 18 Fax: +1-613-562 5173 19 20 21 22 Page 1 of 48 Can. Geotech. J. Downloaded from www.nrcresearchpress.com by CLEMSON UNIVERSITY on 11/13/14 For personal use only. This Just-IN manuscript is the accepted manuscript prior to copy editing and page composition. It may differ from the final official version of record.
Transcript of Modeling of the thermohydromechanical–chemical response of Ontario sedimentary rocks to future...
MODELING OF THE THERMO-HYDRO-MECHANICAL-CHEMICAL RESPONSE OF 1
ONTARIO SEDIMENTARY ROCKS TO FUTURE GLACIATIONS 2
3
Othman Nasir1, Mamadou Fall
1*, T. Son Nguyen
2,1, Erman Evgin
1 4
1Civil Engineering Department, University of Ottawa, Ottawa, Ontario, Canada 5
2Canadian Nuclear Safety Commission (CNSC), Ottawa, Ontario, Canada 6
7
8
9
*Corresponding author: 10
Dr. Mamadou Fall 11
Professor, 12
Director of OCIENE 13
Department of Civil Engineering, 14
University of Ottawa, Canada; 15
161 Colonel by, Ottawa (Ontario), K1N 6N5; 16
Phone: +1-613-562 5800 # 6558 18
Fax: +1-613-562 5173 19
20
21
22
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ABSTRACT 23
24
In this work, the response of a proposed deep geological repository (DGR), located in 25
sedimentary rock formations of southern Ontario, to potential future glaciation cycles is 26
numerically investigated. A coupled thermo-hydro-mechanical-chemical model is 27
developed and numerically solved by using the finite element method. The general 28
circulation model (GCM) from the University of Toronto is used to generate future glacial 29
cycles and related surface boundary conditions based on the past 120,000 years of glacial 30
history. The geometry of the hypothetical DGR is adopted from the proposed design. Two 31
types of vertical shaft conditions, effective and failed, are included and investigated in this 32
study. For the case with effective vertical shafts, the results show that the potential 33
radioactive solute transport is diffusion dominated and the transport distance is contained 34
within natural barriers. However, the results for the case of a shaft seal failure show that 35
future glaciations could potentially lead to significant advection transport of radionuclides 36
from the level of the DGR to the shallow ground water horizons. From a safety 37
perspective, the shaft structure is concluded to be a critical part of the DGR system and 38
needs to be considered as an important factor in safety assessments and future research. 39
40
Keywords: 41
Glaciation, deep geological repositories, coupled processes, THMC, nuclear waste, 42
coupling, COMSOL. 43
44
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1 Introduction 45
46
The problem of radioactive waste management started to attract a considerable amount of 47
attention in the 1940s (Hatch, 1953). Different techniques were proposed to deal with 48
radioactive waste disposal (Scott, 1950; Hatch, 1953), with the first formal long term 49
solution being proposed by the US National Academy of Sciences (NAS/NRC, 1957). This 50
involved the disposal of radioactive waste in porous media located at great depth. From a 51
scientific perspective, there is an international consensus that deep geological disposal is 52
the best option for the long term management of radioactive wastes (Radioactive Waste 53
Management Committee of the Organisation for Economic Co-operation and Development 54
(OECD), 1999). The time frame considered for the safety assessment of deep geological 55
repositories (DGR) is dependent on the half-lives of the radionuclides associated with the 56
wastes, and could span periods of 10,000 to 1,000,000 years (Fall and Nasir 2011a). 57
58
Due to those very long time frames, the numerous levels of redundancy for the protection 59
of human health and the environment need to be considered in the site selection and 60
design of a DGR system. One of the main concepts in DGR design is the multiple barrier 61
system, which includes both engineered and natural barriers for the containment and 62
isolation of the wastes (Nasir et al. 2011; Fall et al. 2014). There is also the concept of 63
robustness of the individual barrier and of the overall DGR system. The former is the ability 64
of the individual barrier to sustain possible extreme boundary conditions (BCs) during the 65
assessment time frame, including major natural climate changes and phenomena, such as 66
earthquakes and glaciations. The latter is associated with the fact that the failure of one 67
barrier does not compromise the safety of the overall DGR system. The safety assessment 68
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of DGR requires the investigation of extreme bounding scenarios. A shaft seal failure 69
represents an extreme bounding case. This is a conservative assumption. 70
71
During the last two decades, modeling studies (e.g., Nguyen et al., 1993; SKB, 1997; 72
Boulton et al., 2004; Vidstrand et al., 2008) have investigated the coupled response of 73
DGR systems to potential future glaciations. These studies show that glaciations could 74
significantly impact the mechanical and hydraulic regime of DGRs. Person et al. (2012) 75
provided a review and summary of several studies related to the modeling of ice-sediment 76
hydrologic interactions in Europe and North America. They presented a detailed analysis 77
of these studies including description of the model, study areas, domain scales and 78
whether hydromechanical coupling was included or not. Person et al. (2012) highlighted 79
the uncertainties in boundary and initial conditions included in the studies reviewed and 80
the range of assumptions made to cover these uncertainties. In addition to that, they listed 81
the most important processes covered by the studies (e.g., hydro-mechanical effects, 82
hydrogeological processes, permafrost formation, brine transport processes). However, it 83
is worth noting that none of the studies reviewed by Person et al. (2012) involve modeling 84
that includes all of the processes listed as strong processes. 85
The aforementioned mentioned studies were limited in the following aspects. First, they did 86
not couple all relevant processes, such as mechanical, hydro-geological, thermal and 87
chemical processes, and there are limited parameter changes and evolution in the derived 88
governing equations (e.g., porosity and permeability changes). Secondly, these studies 89
either dealt with hypothetical rock formations or with granitic formations. Thirdly, there is a 90
lack of large scale field data to validate the predicted results. Thus, no modeling studies 91
have been done to investigate the thermo-hydro-mechanical-chemical (THMC) response 92
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of sedimentary rocks in Ontario to future climate changes. To the best of the authors’ 93
knowledge, this work is the first modeling study of glaciation impact on such formations, 94
using a comprehensive mathematical THMC model. 95
96
The paper is organized as follows. The first section describes the geological setting and 97
the geometry of the proposed DGR system and the model geometry. In the second 98
section, the development of the THMC model is presented. In the third section, the 99
conceptual modeling approach for the impacts of future glaciations is explained. In the 100
fourth section, the main modeling results are presented and discussed. Finally, the 101
conclusions are presented. 102
103
104
2 Site Geological Setting and DGR Engineering Geometry 105
106
2.1 Geological Setting 107
108
Figure 1 shows the location of the DGR at the Bruce nuclear site in Ontario being 109
proposed by Ontario Power Generation (OPG). The main objective of the proposed DGR 110
is to achieve long term containment and isolation of disposed nuclear waste. It is currently 111
proposed that this site will accept the disposal of low and intermediate level radioactive 112
wastes (LILWs) within the limestone host rock at a depth of 680 m. The limestone host 113
rock is one of the sedimentary rock formations of the Michigan basin shown in Figure 1. 114
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The limestone formation was formed in the Middle Ordovician period, approximately 550 to 115
390 million years ago and is located in the Bruce Megablock (Sanford et al., 1985). As part 116
of the environmental assessment process, OPG performed extensive investigations at the 117
proposed site by drilling boreholes with maximum depths to the Precambrian formation as 118
shown in Figure 2 (NWMO, 2011C). 119
120
2.2 DGR Geometry 121
122
The proposed DGR is located in the upper part of the Middle Ordovician limestone 123
formation, which is approximately 200 m in thickness, and overlain by approximately 200 124
m of upper Ordovician shale formation as shown in Figure 2. In the proposed OPG’S DGR, 125
there are two main barrier components; (i) the natural barrier system represented by the 126
natural rock formations; (ii) and the engineered barrier system represented by man-made 127
structures which are designed to provide additional barriers such as shaft filling materials, 128
including bentonite- sand mixture, asphalt, concrete and backfill, and the monolith 129
concrete. On the other hand, and in terms of DGR components, the DGR has three main 130
components, which include shafts (main and ventilation shaft), tunnels, storage rooms 131
(Figure 3). As only the shaft and the monolith are filled with engineered materials, 132
consequently only the shaft and monolith are designed to provide an engineered barrier. 133
The shaft will be mainly filled with bentonite – sand mixture with specific engineering 134
properties. The properties are expected to change with time due to degradation processes 135
(NWMO 2011A-D); this is considered as worst case scenario and termed as “shaft seal 136
failure scenario”. 137
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138
139
From a numerical analysis perspective, the proposed geometry requires a large number of 140
mesh elements which could exceed available resources. To overcome this difficulty, a 141
simplified equivalent geometry is generated based on the proposed DGR dimensions 142
(Quintessa Ltd. and Geofirma Engineering Ltd., 2011), as shown in Figure 4. In the 143
simplified geometry, the services area, access tunnels and storage rooms are merged into 144
one equivalent component, and the main and ventilation shafts are merged into one 145
equivalent shaft. Initial scoping simulations indicated that merging the two shafts into one 146
shaft has no effect on the model response and near-field fluid flow. In addition to that, the 147
shafts and the access tunnel sizes are adjusted to take into consideration the effect of the 148
excavation damage zone (EDZ) with a ratio of 1R (R is the radius of the excavation) 149
(ANDRA, 2005). 150
3 Governing Equations of the Mathematical Model 151
152
The conceptual and mathematical models used to simulate the THMC processes 153
associated with the impact of future glaciations is described in more details by Fall and 154
Nasir (2011a) and Nasir et al. (2011). The governing equations of the mathematical model 155
represent the flow, heat transfer, solute transport and mechanical processes, respectively, 156
as follows: 157
( )
( ) ( )( )dt
dTnn
dt
dp
K
n
K
n
Kdt
de
t
Cn
Dgp
fSSf
fSS
f
ff
f
ff
ββββαβρα
ραργ
ρηκ
ρ
−−+−+
+−++
∂∂
=
∇+∇⋅∇
''
'
MM.M.... (1) 158
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( ) TCTKt
TC Leqeq ∇−=∇−∇+
∂∂
u. MMMMMMMMMMMMMMMMMMMMMMMM..(2) 159
[ ] CL SccnDt
cn =+∇−∇+∂∂ uuuu. MMMMMMMMMMMMMMMMMMMMMMMMMMM..(3) 160
( ) 0
22
=+∂∂
−∂∂
−∂∂
∂++
∂∂
∂i
i
D
iji
j
jj
i Fx
TK
x
p
yx
uG
yx
uG βαλ MMMMMMMMMMMMMMMMM..(4) 161
where: 162
T Average temperature of the porous medium
Ceq Effective volumetric heat capacity
Keq Effective thermal conductivity
CL Volumetric heat capacity of the moving fluid
u Fluid velocity vector
fρ Fluid density
t Time
n Porosity
s Solid
f Fluid
κ Permeability
η Dynamic viscosity
p Pressure
D
Direction of gravitational acceleration (g)
eff Volumetric deformation
DK ,SK and
fK Bulk moduli of solid matrix, solid grains and water fluid, respectively
β ,sβ and
fβ Thermal expansion coefficients for the solid matrix, solid grains and water
fluid, respectively,
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α Biot coefficient
S
D
K
K−= 1α
'α ( )( )n
n
−−
1
α
C
Concentration of total dissolved solids (TDS)
ji uu , x and y direction displacements
DL
Hydrodynamic dispersion tensor
Sc Solute source or sink
G Shear modulus
λ Lamé constant
g Gravity acceleration
Fi Body force
γ Rate of change in fluid density to change in total dissolved solid
concentration C
163
As discussed in Fall and Nasir (2011a) and Nasir et al. (2011), the model has been used 164
to simulate the effects of past glaciation cycles on the THMC regimes in the rock 165
formations. The model results were compared with field data obtained from the 166
geoscientific site investigations performed by OPG. The main results of the comparison 167
can be summarized as follows: 168
- The comparison of the predicted pore water pressures with the specific pore water 169
pressures (including anomalous under and over-pressure) observed at sites shows 170
that past glaciations had a contribution to the observed anomalous under and over-171
pressure; 172
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- Total dissolved solid profile predicted by the model shows a very good agreement 173
with the site specific observations; 174
- Predicted depth of glacial melted water are in good agreement with the oxygen 175
isotope tracers observed at the specific site 176
- Predicted depths of permafrost are consistent with that predicted by other models 177
(e.g., Peltier, 2008). 178
This type of validation provides additional confidence in the use of the developed 179
model to simulate the effects of future glaciation cycles, which are presented in the 180
present paper. It should be emphasized that, in this work four coupled processes are 181
implemented in the modeling, including, hydraulic, mechanical, thermal, and chemical 182
processes. Only strong coupled processes (poroelastic, hydro-mechanical, thermo-183
mechanical, thermo-hydraulic, hydro-chemical, chemico-mechanical) are included in 184
the modeling. The weak coupling processes (e.g. change in temperature due to 185
chemical reaction) are not included in the model. 186
187
4 Model Geometry and Material Properties 188
189
The governing equations with assumed boundary and initial conditions are numerically 190
solved using the finite element method implemented in the commercial COMSOL code 191
(COMSOL 2009). The simplified geometry shown in Figure 5 shows the axisymmetric 192
geometry and the BCs used in the modeling process, and is discretized into a mesh of 193
21946 triangular elements as shown in Figure 6. Finer mesh discretization is adopted at 194
the DGR repository to reduce the impact of element size on the results. Sensitivity analysis 195
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was performed to investigate the impact of mesh refinement on the results, and only the 196
location of the GDR was sensitive and hence a finer mesh is adopted at that location. 197
Tables 1 and 2 show the material properties used as input to the model. Hydraulic, 198
diffusion and mechanical data of the rock formations are presented in Table 1 based from 199
an OPG report, “Descriptive Geosphere Site Model” (NWMO, 2011C). The material 200
properties of a failed shaft seal presented in Table 2 are adopted from the NWMO (2011E) 201
and Alonso and Olivella (2008). After the closure of the DGR, the excavated spaces at the 202
repository level, including repository rooms and access tunnels, are assumed to be filled 203
with a mixture of LILW waste, some concrete, and rockfill (rockfalls from the EDZ). The 204
OPG’s DGR is designed in this way to minimise the gas pressure resulting from the 205
degradation of the LILW waste by not filling the rooms and tunnels, with the exception of 206
filling the monolith and the closure walls. The storage rooms are not meant to provide any 207
engineered barriers. In order to take into account the properties of the new mixture, a 208
single equivalent material is considered for the excavated parts (access tunnels and 209
rooms) with a porosity of 0.5 and a permeability of 1.16E-13 m2 as used in NWMO 210
(2011E). In the present work, the shaft and repository post-closure properties are assumed 211
to be similar to those of the failed shaft seal (shaft seal failure case); the permeability of 212
the failed shaft is assumed to increase by four orders of magnitude (10-14 m2) as compared 213
to the effective design conditions 10-18 m2). 214
215
5 Initial and Boundary Conditions 216
217
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In order to solve the four PDEs, appropriate initial and boundary conditions are used as 218
presented in the following sections. 219
5.1 Initial Conditions 220
221
The initial conditions (ICs) assumed in this study represent the conditions at the beginning 222
of the post-closure period, when all waste emplacement activities have ceased, and the 223
shafts have been sealed. 224
5.1.1 Hydraulic and Mechanical Initial Conditions 225
226
The rock formations are assumed to be saturated and at hydrostatic pressure. The field 227
investigation results (NWMO, 20011A and 20011C) show that currently there are 228
anomalous pressure zones, with underpressure in the rock formations of the repository 229
and overpressure in the Cambrian and some of the overlying formations. These 230
anomalous pressures could subsist for very long periods of time (Fall and Nasir 2011a, 231
Nasir et al. 2011). Furthermore, gas generated by the corrosion of metals and the 232
degradation of organics in the wastes can desaturate some of the rock walls (Fall and 233
Nasir 2011b). However, the assumption of initial hydrostatic pressure and saturated rock 234
conditions, prevailing before the onset of future glaciations is conservative for the 235
simulation of contaminant transport. The initial vertical stress is assumed to be lithostatic, 236
while the maximum horizontal stress is assumed to be 1.5 times the vertical one, as is 237
commonly found in southern Ontario. This initial hydraulic/mechanical regime will be 238
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disturbed by future glaciation cycles, with the first glacial period predicted to occur in 239
approximately 60,000 years (Peltier, 2008). 240
241
5.1.2 Thermal Initial Conditions 242
243
In this work, the linear geothermal gradient is assumed by using the equation suggested 244
by Vugrinovich (1989), which can be written as follows: 245
246
Temperature (°C) = 14.5 (°C) + 0.0192(°C/m) x depth (m). 247
248
According to this equation, the initial temperature profile is approximated by 14.5 (°C) near 249
the surface and linearly increased to a constant temperature of 27.5°C at a depth of 680m 250
at level of the DGR. 251
5.1.3 Chemical Initial Conditions 252
253
In this work, the chemical process is focused on the effect of ice loading cycles on the 254
transport of solute generated within the DGR. It should be emphasized that the aim of the 255
current paper is not to perform a complete numerical modeling of the radionuclide 256
transport (this is beyond the scope of the present project), but to provide an indication of 257
the potential impact of ice loading cycles on the solute transport in the study area. In this 258
work, solute transport is represented by relative concentrations (%) which are normalized 259
to the initial concentrations ( 1000
xC
C ), where Co is the initial solute concentration at the DGR, 260
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and C is the solute concentration at time t. Figure 7 shows the initial relative 261
concentrations, and it is assumed that the solute in the host rock that surrounds the DGR 262
and shaft is zero, whereas the initial solute concentration in the source (DGR level) is 263
considered to be equal to 100%. The OPG’S DGR is designed for LILW to be stored in the 264
DGR rooms with high volume without the usage of special canister as it is the case for the 265
high level waste. Consequently, it is reasonable to assume an initial solute concentration 266
of 100% for the whole volume of the repository. 267
268
5.2 Boundary Conditions (BCs) 269
270
The BCs at the surface are considered as a function of the potential climate changes on 271
earth in the future. The prediction of past climate changes during the Quaternary period 272
(University of Toronto Glacial Systems Model (GSM), Peltier, 2008) are used to estimate 273
future ice loading due to glaciations as shown in Figure 8. It should be emphasized that 274
there are uncertainties regarding the suitable ice sheet – surface boundary conditions. For 275
example, ice sheet – surface hydraulic pressure can range from 0 up to 90% of the ice 276
load. However, from a safety perspective, it was found that the 0% hydraulic pressure 277
boundary condition represents a worst case scenario as it results in both higher effective 278
stresses and hydraulic gradients (Fall and Nasir 2011a; Nasir et al., 2011). Accordingly, 279
this boundary condition was assumed for this work. 280
Glaciations cause changes in the ground surface BCs with respect to mechanical stresses, 281
surface temperature, surface water chemistry and surface water pressure. Four sets of 282
BCs, including hydraulic, mechanical (transient loading is derived from Peltier’s climate 283
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change model), thermal and chemical conditions, were used to simulate the effect of past 284
glaciations. Table 3 shows the BCs used in this study with reference to Figure 5. 285
286
6 Modeling Results and Discussions 287
288
6.1 Hydrogeological Response 289
290
The results show that the hydraulic response of a DGR system to future glaciation-291
deglaciation cycles follows the same sequence of advance/growth and retreat/decrease of 292
the ice sheet. Figure 9 shows the change in the water pressure induced by one glacial 293
cycle at a point within the repository (point A) and at a point within the limestone formation 294
at the same elevation (point B). The water pressure at those points shows a characteristic 295
poroleastic response as follows. The two water pressure peaks (approximately, 60 and 99 296
kaBP) occurred as a direct response to the peak surface loads imposed by the ice sheets 297
at the two peaks during the glacial cycle. Additionally, the hydraulic response of the rock 298
formations at the level of the repository have some memory of the previous peak surface 299
load, with water pressure returning (relatively) slowly to non-glacial conditions shortly after 300
each peak load (Figure 9). The rate of dissipation of the pressure depends mainly on the 301
permeability of the medium. Point A shows lower excess pore water pressure and faster 302
dissipation to hydrostatic conditions due to higher permeability, while point B shows higher 303
excess pressure due to lower permeability of the limestone formation as compared to the 304
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repository rooms. Furthermore, after removal of the surface load, point B even shows an 305
underpressure compared to hydrostatic conditions. 306
Figure 10 shows the vertical profile of the pore water pressure with respect to seven 307
different time periods within the glacial cycles in comparison with the hydrostatic water 308
pressure profile. The profile line is located 1000 m away from the DGR location. The 309
results show an increase in the pore water pressure under loading (over-pressure with 310
respect to hydrostatic pressure) and decrease in pore water pressure under unloading 311
conditions (under-pressure with respect to hydrostatic pressure). This type of behaviour is 312
similar to the effects of past glaciations modelled by (Fall and Nasir 2011a) and Nasir et al. 313
(2011). 314
Figure 11, which represents the case of an effective shaft, shows the vertical profile of 315
pore water pressure along the axis of the DGR shaft with respect to the same time periods 316
as presented in Figure 10. For the effective shaft scenario, the glaciations lead to a 317
significant increase in the pore pressure within the shaft at depth of 200-700 m (zone of 318
interest for the DGR). 319
Figure 12 shows, for the case of a failed shaft seal, the pore water pressure distribution 320
and the Darcy flow direction within the DGR and the surrounding natural and engineered 321
barriers for four time periods. The periods of time presented are: initial conditions at time of 322
0 years, first peak at 60,000 years, second peak at 99,000 years and 106,000 years in the 323
future. By analysing Figure 10, it can be observed that during the glaciation events, the 324
study area shows an overpressure from a depth of 200 to 1000 m. This overpressure is 325
attributed to the load applied by the ice sheet and will affect the hydraulic gradient in the 326
study area, and thus the groundwater flow direction as shown in Figure 12. 327
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Figure 13, which represents the case of a severe shaft seal failure, shows the vertical 328
profile of pore water pressure along the axis of the DGR shaft with respect to the same 329
time periods as presented in Figure 10. It can be noticed that the glaciations do not lead to 330
a significant increase in the pore pressure within the shaft up to a depth of 700 m with a 331
water pressure close to the hydrostatic pressure. This behaviour can be attributed to the 332
quick release of both over and under pressures due to the high permeability (10-14 m2) of 333
the failed shaft seal. 334
335
6.2 Mechanical Response 336
337
The impact of ice mechanical loading and the hydraulic response of the host rock caused 338
significant changes in the effective stress. Figure 14 depicts the distribution of vertical 339
effective stress in the host rock, shaft and the proposed DGR. Again, it can be noted that 340
ice loading has a significant effect on the effective stress and its distribution. The ice load 341
induced changes in effective stresses that are not uniform. The magnitude of the change 342
depends on the depth and formations. The rock formations, the shaft and the repository 343
rooms have different response from one another due to different poroelastic responses 344
which are governed by their respective values of hydraulic conductivity and modulus of 345
elasticity. 346
The high effective stress around the edge of the DGR room can be attributed to the high 347
compressibility of the filling materials of the room. However, the extension of the high 348
effective stress is limited to 10 m and its impact is not significant to natural barrier 349
formations that are 200 m in thickness. 350
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Figure 15 shows the profile of the estimated factor of safety against mechanical failure by 351
using the Hoek-Brown failure criterion along a vertical line of 15 m on the left side of the 352
DGR room. The equation used for Hoek-Brown failure criterion is: 353
a
ci
ci smb
++=
σσ
σσσ 331
''' MMMMMMMMMMMMMMMMMMMMMMM..(5) 354
Where: σ’1 and σ’3 are the major and minor principle stresses; σci is the uniaxial 355
compressive strength (assumed here to be 20MPa for the Silurian formation); and mb, a 356
and s are empirical fitting constants. These constants were determined for the rock mass 357
using the Geological Strength Index (GSI) as per Hoek et al. (2002); GSI = 70 and mi = 7 358
were assumed for the Silurian formation (thus, mb∼2.41, a∼0.5 and s∼0.035). 359
360
The factor of safety is predicted by using the following equation: 361
F.of.S= σ1 of Hoek-Brown failure criterion / Predicted σ1. 362
363
Two profiles of factor of safety against mechanical failure are presented in Figure 15. For 364
one profile (red color), it is considered that the initial horizontal stress of σh = 1.5 σv is as 365
given by Lo (1978) and Zoback and Zoback (1980), whereas for the other profile (blue 366
color) a conservative initial value of σh ≈ σv was assumed. From Figure 15, it can be seen 367
that the primary natural barrier (450-650 m shale formation) has a factor of safety of more 368
than 1.5 and more against rock mass failure regardless of the selected σh/σv ratio. In 369
addition, the results show that the host rock formation at the level of the DGR has a factor 370
of safety higher than 3.0 regardless of the σh/σv ratio. 371
Figure 16 depicts the surface displacement under the impact of the two future glaciation 372
peaks. Two main episodes of loading-unloading, with peaks at approximately 60,000 and 373
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100,000 years, can be identified; each one is mainly characterized by the shape of the 374
surface loading with a maximum surface displacement of about 1.1 m. The downward 375
displacement primarily follows the time-varying loading of the ice sheet at the top 376
boundary. The displacement can be attributed to the mechanical deformation and 377
consolidation of the host rock and DGR system relative to the base of the model. 378
6.3 Solute Transport 379
380
In this work, the solute transport simulations are applied on a single chemical element 381
representing a hypothetical species released from the LILW waste with a concentration C 382
and four glaciation cycles are considered, i.e. simulations are performed for over 480,000 383
years. The modeling results are presented in terms of relative concentration (%) of the 384
element which is normalized by the initial concentration ( 1000
xC
C ; where Co is the initial 385
solute concentration at the DGR, C is the solute concentration at time (t). With respect to 386
the properties of the shaft, two cases are considered: (i) effective, and (ii) severe shaft seal 387
failure (worst case). The initial mechanical, hydraulic and thermal properties adopted for 388
the host rocks and the shaft (both cases) are already given in the previous sections and 389
the NWMO reports (NWMO, 2011A, 2011B, 2011C, and 2011D). 390
In this work, several numerical simulation results have been obtained. The results show 391
that the solute transport in natural limestone and shale barrier formations is dominated by 392
diffusion. The diffusion dominant solute transport in natural rock barriers (limestone and 393
shale formations) is determined to be not significantly sensitive to glaciation cycles. In 394
contrast, the results have shown that advective and diffusive transports both occur within 395
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the failed shaft seal and that the solute transport within the shaft is significantly influenced 396
by the ice loading cycles. 397
The primary simulation results are presented in Figures 17 and 18. These figures illustrate 398
the impact of the second peak of the four glaciation cycles for both effective and worst 399
cases, respectively. The time periods are: first glacial cycle at 100K years, second glacial 400
cycle at 220K years, third glacial cycle at 340K years and fourth glacial cycle at 460K 401
years. In each figure, the relative concentration (%) is presented for both the effective and 402
worst case scenarios. 403
It can be seen from Figure 17 that regardless of the number of glaciation cycles when the 404
shaft seal is intact (effective scenario), the migration of solute released from the horizon of 405
the proposed DGR will be limited and the solute will still remain in the natural shale barrier 406
layer. This is positive with regards to the safety of the DGR and may suggest that 407
limestone and shale formations act as very effective barriers with regards to radionuclide 408
transport. 409
In contrast, Figure 18 shows that if the shaft seal severely fails, contaminants could 410
potentially reach the shallow bedrock groundwater zone. These results suggest that the 411
long term effectiveness of the shaft seals has important implications to the safety of the 412
DGR. The longevity of shaft seals should be considered in future research programs. It is 413
worth to mention that in this work flow is density driven flow, in which, density is related to 414
the total dissolved solid concentration. However, the assumed hypothetical species 415
released from the LILW waste with a concentration at the level of the DGR is not 416
considered as a factor affecting the liquid density. We believe our assumption is 417
conservative, and this issue could be investigated in the future. 418
419
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7 Conclusions 420
Based on the results obtained from this work, the following conclusions can be drawn. 421
A numerical study for the THMC processes associated with future glaciation cycles in 422
sedimentary rocks in southern Ontario is conducted by taking into consideration the DGR 423
geometry. It is found that future glaciations will have a significant impact on the pore water 424
pressure gradient and effective stress distribution within both the sedimentary rocks and 425
the proposed DGR. It is also found that future ice loading will not lead to the failure or 426
fracturing of natural rock barrier (limestone, shale) formations. 427
The results obtained show that solute transport in natural limestone and shale barrier 428
formations is diffusion dominated transport; this conclusion is limited to the assumed 429
boundary conditions and could be affected by any potential permeable limestone 430
formations beyond the boundary of the investigated domain. Moreover, regardless of the 431
number of glaciations cycles, the migration of solute released from the horizon of the 432
proposed DGR will be limited and the solute will still remain in the natural shale barrier 433
layer. 434
In this work, it is found that in a shaft failure scenario, the solute transport within the failed 435
shaft will be controlled by diffusion and advection. The simulation results show that the 436
solute transported in the failed shaft can reach the shallow bedrock groundwater zone. It 437
should be noted, however, that the level of degradation of the shaft seals in that scenario 438
is rather extreme and thus could be considered as a bounding case (the scenario spans 439
220,000 years and requires a minimum of two glacial cycles). The main type of material for 440
shaft seals is a 30/70 bentonite/sand mixture and with proper quality control during 441
emplacement, its target permeability of 10-18 m2 should be achieved. An increase of the 442
permeability to 10-14 m2 would make this bentonite-sand mixture to be equivalent to a 443
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sandy silt material. Current research did not identify any plausible mechanical or chemical 444
processes that could trigger that type of degradation. Nevertheless, research programs on 445
longevity of shaft seals are currently very active, and include both laboratory and field tests 446
and mathematical modelling. The construction and operation of a repository would take 447
many decades and the shafts would only be sealed at the end of this period. It is 448
anticipated that the results of this research would provide sufficient information in order to 449
finalize the design of the shaft seals at the time of closure. 450
451
. 452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
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472
473
8 References 474
475
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(January 4): 157-176. 477
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Engineering Ltd and Quintessa Ltd, NWMO DGR-TR-2011-31. 521
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Vidstrand, P., Wallroth, T., & Ericsson, L.O., 2008. Coupled HM effects in a crystalline rock 542
mass due to glaciation: Indicative results from groundwater flow regimes and stresses 543
from an FEM study. Bulletin of Engineering Geology and the Environment, 67(2), 187-544
197. 545
Vugrinovich, R.,1989. Subsurface temperatures and surface heat flow in the Michigan 546
Basin and their relationships to regional subsurface fluid movement, Marine and 547
Petroleum Geology, Volume 6, Issue 1, Pages 60-70. 548
Zoback, M.L., Zoback, M., 1980. State of stress in the conterminuous United States. 549
Journal of Geophysical Research, 85 (B11), pp. 6113-6156. 550
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Figure 1. Location of the Bruce nuclear site in Ontario where Ontario Power Generation (OPG)
proposes to locate the DGR (this figure was originally published by NWMO (2011A) and
modified from Johnson et al. (1992)).
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Figure 2. Stratigraphy of sedimentary rock formation of the Michigan basin, showing the
locations of deep boreholes [NWMO, 2011C].
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Figure 3. Proposed DGR layout (figure from NWMO (2011B)).
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Figure 4. Simplified (equivalent volume) DGR geometry
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Figure 5. Simplified DGR geometry used for modeling.
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Figure 6. Finite element method (FEM) mesh discretization by using COMSOL mesh generation
(units in meters).
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Figure 7. Initial conditions of relative solute concentrations
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Figure 8. Ice sheet induced normal stresses with respect to run number nn9930 (data adopted
from Peltier (2008))
0
5
10
15
20
25
30
-120
-100
-80
-60
-40
-20
0 20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
Time (ka)
Norm
al str
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Pa)
Present
Past
(Peltier, 2008)Future
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Figure 9. Evolution of the pore water pressure at the DGR level.
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Figure 10. Temporal evolution of the water pressure profile in the host rock (free draining
surface hydraulic conditions)
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Figure 11. Temporal evolution of the water pressure profile along the shaft (hydraulic conditions
of free draining surface, effective shaft scenario)
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Figure 12. Temporal evolution of the pressure and flow direction in the study area (distance
given in meters and pressure in Pa); first peak at 60,000 years, 2nd peak at 99,000 years and
unloading at 106,000 years
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Figure 13. Temporal evolution of the water pressure profile along the shaft (hydraulic conditions
of free draining surface, failed shaft seal scenario)
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Figure 14. Predicted vertical effective stresses at different times during glaciation cycle.
Page 41 of 48C
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Figure 15. Predicted factor of safety by using Hoek-Brown failure criterion.
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Figure 16. Temporal evolution of mechanical surface displacement at the location of the study
area
-1.10
-1.00
-0.90
-0.80
-0.70
-0.60
-0.50
-0.40
-0.30
0 10 20 30 40 50 60 70 80 90 100 110 120
Time in the future (x1000 years)
Surf
ace d
ispla
cem
ent (m
)
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Figure 17. Computed relative solute concentrations at the second ice loading peak for four
glaciations cycles (app. 100, 220, 340 and 460K years) in consideration of diffusion and
advection transport in a scenario with an effective shaft
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Figure 18. Computed relative solute concentrations at the second ice loading peak for four
glaciations cycles (app. 100, 220, 340 and 460K years) in consideration of diffusion and
advection transport for the worst case scenario with a failed shaft
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Table 1. Material properties of rock formations used in the modeling.
Subdomain
number
Rock
form
ation
Depth (m
)
Poisson's
ratio
Young's
modulus
(GPa)
Horizontal
hydraulic
conductivity
Kh (m/s)
Kh/Kv*
Therm
al
conductivity
W/(m.K)
Specific heat
capacity
J/(kg.K)
Diffusion
m2/s
1 Overburden Aquifer
0-20 0.2 10 8.0E-10 2:1 2 700 6.0E-10
2 Dolostone Aquifer 20-169.3
0.2 40 1.0E-5 10:1
2 700 8.0E-12
3 Silurian Aquifer 169.3-178.6
0.2 18 5.0E-12 10:1
2 700 1.0E-12
4 178.6-325.5
0.2 6 5.0E-12 10:1
2 700 1.0E-12
5 Silurian Aquifer 325.5-328.5
0.2 38 2.0E-7 1:1 2 700 7.0E-12
6 328.5-374.5
0.2 38 5.0E-12 10:1
2 700 1.0E-12
7 Silurian Aquifer 374.5-378.6
0.2 38 3.0E-8 1:1 2 700 3.0E-11
8 378.6-411
0.2 38 5.0E-12 10:1
2 700 1.0E-12
9 411-447.7
0.2 16 5.0E-12 10:1
2 700 1.0E-12
10 Ordovician shale 447.7-659.5
0.2 16 2.0E-14 10:1
2 700 1.0E-13
11 Ordovician limestone
659.5-688.1
0.2 39 1.0E-15 10:1
2 700 3.0E-13
12 688.1-762.0
0.2 24 1.0E-15 10:1
2 700 3.0E-13
13 Ordovician limestone
762.0-838.6
0.2 24 6.0E-12 100:1
2 700 3.0E-13
14 Cambrian 838.6-860.7
0.2 24 1.0E-7 1:1 2 700 1.0E-11
15 Precambrian >860.7 0.2 60 1.0E-11 1:1 1.375
700 3.0E-13
*: Kh: horizontal hydraulic conductivity, Kv: vertical hydraulic conductivity
Page 46 of 48C
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Table 2. Main properties of the shaft (worst case conditions for a failed shaft)
Hydraulic conductivity (m/s)
10-7
Permeability (m2) 10
-14
Density (kg/m3) 2500
Poisson’s ratio (-) 0.33
Modulus of elasticity (MPa)*
55
Porosity 0.5
Biot coefficient 0.9
*Alonso and Olivella, 2008
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Table 3. THMC boundary conditions used for simulation.
BCs BC 1 symmetric axis
BC 2 (Bottom) BC 3 (Side) BC 4 (Top)
Mechanical symmetric axis Fixed Roller Free deformation transient loading
a
Hydraulic symmetric axis No flow No flow Free drainage transient pressure
b
Chemical Co
symmetric axis 0 No solute flux 0
Thermal symmetric axis 33.7 C° No heat flux Transient temperaturec
a: transient loading is derived from Peltier’s climate change model b: transient pressure is taken differently as a fraction of ice loading derived from the climate change model c: transient temperature derived from Peltier’s climate change model
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