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Techniques for Large-Scale Site Characterization and Fracture Domain Modeling At The Forsmark Site, Uppland, Sweden
Aaron Fox1, Paul La Pointe
1, and Jan Hermanson
2
1Golder Associates, Inc., Redmond, WA, USA; 2Golder Associates AB, Stockholm, Sweden
Introduction to the Forsmark Site
Modeling Spatial Variation of Fracture Orientations
Fracture Domains as Control Volumes
Intensity Controls Through Multivariate Statistics
How Fracture (and Fault) Sizes are Treated
Acknowledgements and References
OSM Scale: 0.5m - ~ 564 m radius (~1m –
1000 m trace length) – Predominantly Joints
TFM Scale: 28m - 564m radius (50m – 1000m
trace length) – Predominantly Faults
OSM Scale: 0.5m - ~ 564 m radius (~1m –
1000 m trace length) – Predominantly Joints
TFM Scale: 28m - 564m radius (50m – 1000m
trace length) – Predominantly Faults
OSM Scale: 0.5m - ~ 564 m radius (~1m –
1000 m trace length) – Predominantly Joints
TFM Scale: 28m - 564m radius (50m – 1000m
trace length) – Predominantly Faults
NE Global Set (Euclidean scaling), Domain FFM03
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
1.00E+01
0.1 1 10 100 1000 10000 100000
Tracelength (m)
Are
a-N
orm
ali
ze
d C
um
ula
tiv
e N
um
be
r
PFM 2.2 DZ Model, Clipped
PFM 2.2 DZ Model, Regional
Ground Magnetic Lineaments
AFM000053 (Linked)
AFM001243 (Linked)
AFM001244 (Linked)
TCM
~0.28
Range of TCM / TCMF models (0.5m to 564m radius, ~ 0.89m – 1000m trace length )
NE Global Set (Euclidean scaling), Domain FFM03
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
1.00E+01
0.1 1 10 100 1000 10000 100000
Tracelength (m)
Are
a-N
orm
ali
ze
d C
um
ula
tiv
e N
um
be
r
PFM 2.2 DZ Model, Clipped
PFM 2.2 DZ Model, Regional
Ground Magnetic Lineaments
AFM000053 (Linked)
AFM001243 (Linked)
AFM001244 (Linked)
TCM
~0.28
Range of TCM / TCMF models (0.5m to 564m radius, ~ 0.89m – 1000m trace length )
Model Summaryb
.499a .249 .201 .53992 .249 5.202 3 47 .003
Model
1
R R Square
Adjusted
R Square
Std. Error of
the Estimate
R Square
Change F Change df1 df2 Sig. F Change
Change Statistics
Predictors: (Constant), BRNPegmatite_pegmatiticgranite, BRNBreccia, BRNGranite_finetomediumgraineda.
Dependent Variable: NEP10b.
Coefficientsa
.820 .122 6.734 .000 .575 1.064
83.819 30.888 .344 2.714 .009 21.681 145.957 .364 .368 .343 .995 1.005
-2.926 1.817 -.205 -1.610 .114 -6.581 .730 -.198 -.229 -.203 .987 1.013
-1.526 .658 -.295 -2.320 .025 -2.849 -.202 -.284 -.320 -.293 .990 1.010
(Constant)
BRNBreccia
BRNGranite_
finetomediumgrained
BRNPegmatite_
pegmatiticgranite
Model
1
B Std. Error
Unstandardized
Coefficients
Beta
Standardized
Coefficients
t Sig. Lower Bound Upper Bound
95% Confidence Interval for B
Zero-order Partial Part
Correlations
Tolerance VIF
Collinearity Statistics
Dependent Variable: NEP10a.
Collinearity Diagnosticsa
1.955 1.000 .09 .02 .06 .09
1.000 1.398 .00 .79 .16 .00
.816 1.547 .01 .18 .69 .09
.229 2.923 .90 .02 .09 .82
Dimension
1
2
3
4
Model
1
Eigenvalue
Condition
Index (Constant) BRNBreccia
BRNGranite
_finetomediu
mgrained
BRNPeg
matite_
pegmatiti
cgranite
Variance Proportions
Dependent Variable: NEP10a.
Residuals Statisticsa
-.0657 2.1027 .6053 .30165 51
-.75004 1.75567 .00000 .52347 51
-2.224 4.964 .000 1.000 51
-1.389 3.252 .000 .970 51
Predicted Value
Residual
Std. Predicted Value
Std. Residual
Minimum Maximum Mean Std. Deviation N
Dependent Variable: NEP10a.
Model Summaryb
.499a .249 .201 .53992 .249 5.202 3 47 .003
Model
1
R R Square
Adjusted
R Square
Std. Error of
the Estimate
R Square
Change F Change df1 df2 Sig. F Change
Change Statistics
Predictors: (Constant), BRNPegmatite_pegmatiticgranite, BRNBreccia, BRNGranite_finetomediumgraineda.
Dependent Variable: NEP10b.
Coefficientsa
.820 .122 6.734 .000 .575 1.064
83.819 30.888 .344 2.714 .009 21.681 145.957 .364 .368 .343 .995 1.005
-2.926 1.817 -.205 -1.610 .114 -6.581 .730 -.198 -.229 -.203 .987 1.013
-1.526 .658 -.295 -2.320 .025 -2.849 -.202 -.284 -.320 -.293 .990 1.010
(Constant)
BRNBreccia
BRNGranite_
finetomediumgrained
BRNPegmatite_
pegmatiticgranite
Model
1
B Std. Error
Unstandardized
Coefficients
Beta
Standardized
Coefficients
t Sig. Lower Bound Upper Bound
95% Confidence Interval for B
Zero-order Partial Part
Correlations
Tolerance VIF
Collinearity Statistics
Dependent Variable: NEP10a.
Collinearity Diagnosticsa
1.955 1.000 .09 .02 .06 .09
1.000 1.398 .00 .79 .16 .00
.816 1.547 .01 .18 .69 .09
.229 2.923 .90 .02 .09 .82
Dimension
1
2
3
4
Model
1
Eigenvalue
Condition
Index (Constant) BRNBreccia
BRNGranite
_finetomediu
mgrained
BRNPeg
matite_
pegmatiti
cgranite
Variance Proportions
Dependent Variable: NEP10a.
Residuals Statisticsa
-.0657 2.1027 .6053 .30165 51
-.75004 1.75567 .00000 .52347 51
-2.224 4.964 .000 1.000 51
-1.389 3.252 .000 .970 51
Predicted Value
Residual
Std. Predicted Value
Std. Residual
Minimum Maximum Mean Std. Deviation N
Dependent Variable: NEP10a.
1625000
16
25
00
0
1626000
16
26
00
0
1627000
16
27
00
0
1628000
16
28
00
0
1629000
16
29
00
0
1630000
16
30
00
0
1631000
16
31
00
0
1632000
16
32
00
0
1633000
16
33
00
0
1634000
1634000
1635000
1635000
1636000
1636000 1637000
16
37
00
0
1638000
16
38
00
0
1639000
16
39
00
0
1640000
16
40
00
0
1641000
16
41
00
0
1642000
16
42
00
0
1643000
16
43
00
0
1644000
16
44
00
0
6702000
0 1,500 3,000 4,500 6,000750Meters ±
Legend
Local Model Area
Candidate area
Repository Draft Layout, 11/08/2005
Regional Model Area
Aerial photo of the Forsmark site, with modeling domains and
draft repository layout overlain.
250 0 250 500 750 1,000125
Meters
F
Legend
NS Set Ground Magnetic Lineaments
NW Set Ground Magnetic Lineaments
NE Set Ground Magnetic Lineaments
ENE Set Ground Magnetic Lineaments
EW Set Ground Magnetic Lineaments
Candidate Area (limits of GeoDFN)
Lineament (DZ and MDZ) map created from high-resolution
ground magnetic survey data /Isaksson and others, 2006/
Work is currently underway at two
candidate sites in Sweden to license and
construct a long-term geologic repository
for spent nuclear fuel. The Forsmark site,
located in the municipality of Östhammar,
in northern Uppland, is one of these
candidate sites. The site sits on
Sweden’s eastern coast, and is adjacent
to the Forsmark Nuclear Power Plant and
the CLAB interim waste storage facility.
The site is located in Precambrian rocks
of the Fennoscandian Shield, in a
complex structural domain consisting
primarily of high-grade metamorphic
rocks of cut by slightly younger dikes and
igneous intrusions.
The proposed repository volume lies within a
volume of relatively low-strain rock (the ‘tectonic
lens’) surrounded by zones of high ductile strain
and past brittle deformation.
Substantial geological modeling is being
completed in support of repository design and site
licensure efforts. These models include the
classification of bedrock lithology (Rock Domain),
faults and ductile strain zones (DZ), and surficial
geology.
A discrete fracture network model (DFN) has also
been constructed as a component of the site
descriptive model (SDM) efforts. The GeoDFN
provides a statistical model of rock fracturing for
use in stochastic geomechanical and hydrologic
modeling, as a parameter in the estimation of
available repository volumes, and for the
evaluation of the seismic design safety case.
FFM02
FFM05
FFM04
FFM04
FFM03
FFM03
FFM02
FFM02
FFM04
FFM02
FFM03 AFM100201
AFM001265
AFM001264
AFM001244AFM001243
AFM001097
AFM000054
AFM000053
AFM001098
1630000
1630000
1631000
1631000
1632000
1632000
1633000
1633000
1634000
1634000
1635000
1635000
1636000
1636000
66
98
00
0
66
98
00
0
66
99
00
0
66
99
00
0
67
00
00
0
67
00
00
0
67
01
00
0
67
01
00
0
67
02
00
0
67
02
00
0
0 500 1,000 1,500 2,000250Meters
±Legend
DZ_PFM_v22_2Dmodel
Forsmark Mapped Outcrops
Preliminary Fracture Domain Model
Fracture Domain
FFM02
FFM03
FFM04
FFM05
Candidate area
Above: Fracture domains within the version 2.2 simulation volume.
Stippled grey lines represent the surface traces of the Deformation Zone
(DZ) model
Fundamental to the version 2.2
revision of the geological DFN is
the concept of ‘fracture
domains’. A fracture domain is a
volume of rock, existing outside
of deformation zones (faults),
where the rock units
encountered during drilling
exhibited similar fracture
intensity patterns. /Olofsson and
others, 2006/.
The goal of casting DFN models
in the context of fracture
domains is to constrain the
spatial variability of fracturing to
relatively homogenous volume
constructs. It also brings the
DFN models in line with other
site geological models, and
allows for the representation of
the DFN in the site 3D volume
models.
Below: 3D view of the modeled fracture domains at Forsmark. FFM02
represents a zone of higher near-surface fracture intensity. FFM03
represents more highly fractured rocks in the hanging wall above several
large, shallow-dipping brittle-ductile structures (deformation zone ZFMA1
and ZFMA2 in the figure below)
0 1 2 3 4 50.5Meters
EOutcrop AFM001098 Linked Fracture Sets
Legend
WNW Strike: (70-130 / 250-310)
NW Strike: (130-180 / 310-360)
NNE Strike: (0-30 / 180-210)
NE Strike: (30-70 / 210-250)
Subhorizontal Fractures (Dip <= 50)
Fractures classified into sets by orientation and termination relationships
Fracture orientation sets are the
fundamental component of the site
geological models. All other model
parameters, such as size or intensity,
are packaged within the context of the
orientation sets.
A key goal of the DFN modeling effort
was to allow for the stochastic spatial
variation of set orientations. It is well-
recognized that, though general
patterns are seen in the outcrop
fracture patterns, there is a level of
spatial variability in the mean
orientations. Fracture set orientations
are modeled as univariate Fisher
spherical probability distributions. Orientation set parameters were calculated
from borehole fracture data and detailed
outcrop fracture maps. Spatial variability in
orientation sets was simulated assuming:
1) The location of the mean pole vector on
the sphere for an orientation set is NOT a
constant. Instead, it was assumed to follow a
second Fisher distribution, with a
concentration parameter (κmp) defined by the
clustering of the mean poles fit to individual
fracture sets.
2) The concentration parameter for each set
(Fisher’s κ) in a stochastic model is taken as
a random draw from a normal distribution.
The Shapiro- Wilk W-test was used to test the
hypothesis of normality.
N
S
EW
FRACTURE SET NAME
ENE [6]
EW [8]
NE [19]
NNE [3]
NS [16]
NW [18]
SH [20]
SH2 [1]
SH3 [2]
Equal Area
Lower Hemisphere
93 Poles
93 Entries
N
S
EW
FRACTURE SET NAME
ENE [6]
EW [8]
NE [19]
NNE [3]
NS [16]
NW [18]
SH [20]
SH2 [1]
SH3 [2]
Equal Area
Lower Hemisphere
93 Poles
93 Entries
Stereonet plot of mean pole vectors for orientation sets fit to
borehole and outcrop data. For a given set, the cluster of mean
poles is then used to estimate a new mean pole and Fisher K
Fracture size is one of the more
difficult parameters of a geological
DFN to characterize. Modelers
have limited access to size data,
and the data sources available are
often limited in scale or are subject
to truncations or sampling artifacts.
At Forsmark, two alternative size
models were carried through the
full parameterization:
1) The ‘tectonic continuum’ models
(TCM/TCMF): These models
assume coupled size-intensity
scaling, using power laws (Pareto
distribution) to simultaneously
describe fracture size at multiple
scales. The TCM/TCMF models
are parameterized using a mixture
of outcrop fractures, quasi-regional
magnetic lineaments (50 – 500 m
scale), and regional deformation
zones (> 1000 m scale).
2) The combined outcrop-scale
and ‘tectonic fault’ models
(OSM+TFM): These models treat
fractures in the DFN as belonging
to one of two populations; outcrop
fractures, which are hypothesized
to primarily be joints, and ‘tectonic
faults’, which are thought to be
shear features. The ‘tectonic fault’
model is cut off at a radius of 28 m;
the joint model has no formal
upper limit. In practice, however,
few joints larger than 100 m show
up in the stochastic models.
Plots representing the size range, in terms of measured trace length in
outcrop, of the OSM+TFM (left) and TCM/TCMF models (right). The
charts plot trace lengths in terms of a cumulative number, normalized
for sampling area. This allows for the direct comparison of data at
different scales
Analysis of data from cored boreholes at Forsmark
suggests that fracture intensity (P32, volumetric
fracture intensity, measured as the total fracture
area divided by the target volume) is a highly
variable parameter, even inside a single fracture
domain. As such, it was necessary to develop
predictive models for fracture intensity to present a
complete model of fracturing at Forsmark.
Statistical modeling, consisting primarily of
multivariate stepwise regression analysis, was used
to test the dependence of fracture intensity on
geological properties such as depth, lithology,
fracture morphology, and degree of host rock
alteration. Though several different factors, such as
measured depth and degree of alteration, showed
positive correlations with fracture intensity, host
lithology was the only truly useful parameter in
prediction. The modeling was performed based on
contiguous segments of nearly constant fracture
intensity (mechanical layers) identified using
cumulative fracture intensity plots.
The intensity model in the version 2.2 Forsmark
geological DFN consists of:
Example output from the multivariate
regressions, illustrating fracture intensity
as a function of lithology.
1) Correlation of fracture size to lithologies. The DFN model accounts for lithologic variation of
fracture intensity through a correction factor relative to the dominant rock type (granodiorite).
2) Fracture intensity (P32) specified as a gamma distribution in space at a specified scale for
individual fracture sets in each fracture domain. This allows modelers using geocellular or finite-
difference based models to more accurately simulate spatial variability
Cumulative Fracture Intensity (CFI) plot, summarizing mechanical layers exposed in cored boreholes. A break in
slope represents a change in the fracture frequency (P10); this generally correlates to a change in lithology or degree
of host rock alteration.
The authors would like to thank members of the Forsmark geological modeling team for their hard
work and support in building the underlying geologic framework that this geological DFN rests upon:
• Raymond Munier, Martin Stigsson, and Isabelle Olofsson - Svensk Kärnbränslehantering AB (SKB)
• Michael Stephens – Swedish Geological Survey (SGU)
http://www.fracman.com or http://www.skb.se
This poster concerns a study which was conducted for SKB. The conclusions and viewpoints presented in the report are
those of the authors and do not necessarily coincide with those of the client.
Isaksson, H., Pitkänen, T., and Thunehed, H., 2006a. Ground magnetic survey and lineament interpretation in an area northwest of
Bolundsfjärden. Forsmark site investigation, report P-06-85, Svensk Kärnbränslehantering AB (SKB), Stockholm, Sweden.
Olofsson, I., Simeonov, A., Stigsson, M., Stephens, M., Follin, S., Nilsson, A-C., Röshoff, K., Lindberg, U., Lanaro, F., Fredriksson, L.,
2007 (In press), A fracture domain concept as a basis for the statistical modeling of fractures and minor deformation zones, and
interdisciplinary coordination. Site descriptive modeling Forsmark, stage 2.2, report R-07-15, Svensk Kärnbränslehantering AB (SKB),
Stockholm, Sweden.
CFI Plot for All Sets
-1200
-1000
-800
-600
-400
-200
0
200
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cumulative Fracture Intensity (normalized)
Su
bsea E
levati
on
(m
)
KFM01A
KFM01B
KFM01C
KFM01D
KFM02A
KFM03A
KFM03B
KFM04A
KFM05A
KFM06A
KFM06B
KFM06C
KFM07A
KFM07B
KFM07C
KFM08A
KFM08B
KFM08C
KFM09A
KFM09B
KFM10A
