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Field observations of hydrogeological scale effects in crystalline rocks
PATRIK VIDSTRAND
M.Sc., Civ. Eng.
Department of Geology
Chalmers University of
Technology
s-412 96 Göteborg, Sweden
phone + 46 31 772 2046
fax + 46 31 772 2070
Patrik.Vidstrand@geo.chalmers.se
Abstract
In order to test and establish how the effective
hydraulic conductivity varies with increasing scale at a crystalline rock site
in south-east Sweden a test programme named La Scale was performed during the
spring of 1998. The field test was performed with systematically scaled
sections from the 2-metre scale up to the entire borehole scale, of
approximately 300 metres. From this field data set it was possible to test an
earlier proposed scale trend and also to test the ability of different
upscaling methods to predict the larger scale conductivity. This paper presents
some of the results of the field test La Scala and also the results from some
previous conducted investigations at the same site. All presented data clearly
indicate a scale effect in the effective hydraulic conductivity when calculated
as the geometric mean of each scale.
Keywords:
crystalline rocks, field tests, hydraulic conductivity, scale effects
Introduction
In hydrogeological measurements it is frequently observed
that effective hydraulic conductivity values varies with the scale of
measurement. This effect is most common in fractured, fissured and karstic
media and hence an important problem in the field of modelling groundwater
fluxes around and towards underground facilities, such as nuclear waste
repositories.
In the south-east part of Sweden a hard rock
laboratory, Äspö HRL (Figure 1), has been constructed by Swedish Nuclear Fuel
and Waste Management Company (SKB) in order to investigate the ability to predict,
construct and maintain the safety and performance of a nuclear waste
repository. The Äspö HRL project began in the mid-eighties and at present the
whole underground construction is finished. Many repository-associated
investigations have been and are presently conducted, among others hydraulic
tests in order to establish scale relations of the effective hydraulic
conductivity at the Äspö HRL. During the spring of 1998 a test programme named
La Scala was performed in order to test and establish the scale relation of
effective conductivity values, which had previously been proposed based on
sub-vertical surface borehole data (e.g. Rhén et al., 1997).

Figure 1. Location of the
Äspö HRL (from Rhén et al., 1997) The thick block line illustrate the location
of the tunnel chainage.
The
La Scala test programme
The hydraulic tests were performed in a sub-horizontal
borehole at a depth of approximately 340 metres below sea. The length of the
borehole is approximately 300 metres and it is dominated by one single rock
type, i.e. granite (e.g. Rhén et al., 1997). The ambient formation pressure is
approximately 250 metres of groundwater giving that the borehole is highly
pressurised and traditionally tests are difficult to conduct. In order to be able to perform underground
hydraulic tests without loosing too much of the ambient formation pressure
before the actual test, SKB has developed an equipment, named UHT1, which is
thoroughly described by Hansson (1997, in Swedish). With this equipment it is
possible to perform tests and also to move the packer-ensemble without any
significant losses of formation pressure.
The borehole was divided into sub-sections, which
could be added up to the larger scales, where scale just relates to the
interesting rock volume. The scales were 2, 10, 30, 90 metres and the entire
borehole. It is herein assumed that the distance between the packers can be
used as an indicator of the tested rock volume (scale). By the use of these
sub-sections it was possible to test the borehole systematically and hence
compare the results directly.
The
observations
Hydraulic conductivity is in many cases found to be
log-normally distributed (e.g. Jetel,1964; Carlsson & Carlstedt, 1976; Rhén
et al, 1997). The geometric mean is used as a characteristic value for the
hydraulic conductivity at each scale. Matheron (1967) showed mathematically
that for a statistically homogeneous medium, the effective hydraulic
conductivity equals the geometric mean of the individual block values in a 2D
environment, e.g. cylindrical flow towards a borehole. However, if hydraulic
measurements are averaged by the geometric mean at each scale it has frequently
been observed that the effective conductivity increases with increasing scale
of observation (e.g. Beauheim, 1988; Guimerà et al., 1995).
During the pre-investigation phase at the Äspö HRL
project a number of sub-vertical surface boreholes were drilled and tested with
numerous hydraulic test methods (e.g. Rhén et al., 1997). Eight of these
boreholes were tested with packer tests at the three-metre scale. These
three-metre packer tests were more or less systematic (i.e. complete series
from top to bottom) and comprehensive through the whole borehole length. Three
of the surface boreholes were partly tested with thirty-metre packer tests.
However, the untested sections were few and compensations could be implied.
From four of the boreholes it was possible to produce transmissivity estimates
for the 100-metre scale. Finally, all eight boreholes were also tested with traditional
pumping tests, giving transmissivity values for the entire borehole scale.
The La Scala test programme was aimed at creating a
systematic test sequence. This can be achieved if the borehole is divided into
two sub-categories. The first sub-category is the first ninety metres of the
borehole. This part of the borehole is the most permeable section and was
tested with packer tests in 2 metres, through 10-metre, 30-metre as well as the
entire 90-metre section. The second sub-category was the entire borehole, which
could be systematically tested with the packer tests from 10 metres, through 30
and 90 up to the entire borehole. The reason for not testing the entire
borehole with the 2-metre packer tests was simply the available time.
The hydraulic tests described above gave rise to the
following scale to estimated hydraulic conductivity relationship (Figure 2).
Where the hydraulic conductivity is calculated as the ratio of the evaluated
transmissivity and the length of the tested section, the latter is also
representing the scale. Data are taken from Rhén et al. (1997) and Vidstrand
(1999).
In figure 2, it can clearly be observed that the rock
volume at Äspö HRL does show the same trend of scale versus hydraulic
conductivity relationship as many previous investigations at other crystalline
rock sites have shown (e.g. Clauser, 1992; Rhén et al., 1997).

Figure 2. The relationship between scale and the
geometric mean of the hydraulic conductivity. Data are taken from Rhén et al.
(1997) and Vidstrand (1999).
Discussion
The problems that the scale effects in effective
hydraulic conductivity create for numerical simulations have long been well
known. Models with a stochastic continuum approach require a hydraulic
conductivity distribution to assign to model cells. Since the cell size in
general deviates in scale from the scale of measurements the need for good and
of course plausible upscaling methods is obvious. Through the years many
theoretical and numerical methods have been developed (e.g. Renard & de
Marsily, 1997). Within the Äspö HRL project an alternative method have been
tested together with more "traditional" upscaling methods. This alternative
method is to use the result of a curve-regression performed on data presented
by Rhén et al. (1997). This regression was conducted with the values of both
the scale (length of test section) and the geometric mean of the hydraulic
conductivity plotted in logarithmic space. This kind of upscaling is believed
to be site correct and hence give good predictions. The new data from the La
Scala test programme do not change the important behaviour of the regression
line. However, it can be stated (Vidstrand, 1999) that some theoretical
upscaling methods (e.g. based on stochastic thoery by e.g. Gutjahr et al. 1978)
shows much better agreement with measured larger scale field values.
Conclusions
The crystalline rock mass at Äspö HRL does show an
increasing effective hydraulic conductivity if the geometric mean values are
used at each scale with increasing scale of observation. This is the
"classical" scale effect in effective hydraulic conductivity and it is
frequently reported from many different hard rock sites.
The need of good upscaling methodologies is crucial
for many numerical models. Results such as these gives good opportunities to
create site specific knowledge and/or to test established theoretical upscaling
methods.
Acknowledgement
Both SKB and the European Commision, DG XII are
acknowledged for economic support. Professor Gunnar Gustafson at Chalmers
University of Technology and Ingvar Rhén at Sweco AB are acknowledged for
discussions and valuable comments.
References
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Carlsson, L. & Carlstedt, A., 1976: Estimation of
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Clauser, C., 1992: Permeability of crystalline rocks.
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