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2.5D resistivity modeling of embankment dams to assess influence from geometry and
material properties
Sjödahl, Pontus; Dahlin, Torleif; Zhou, Bing
Published in:
Geophysics
DOI:
10.1190/1.2198217
2006
Link to publication
Citation for published version (APA):
Sjödahl, P., Dahlin, T., & Zhou, B. (2006). 2.5D resistivity modeling of embankment dams to assess influence
from geometry and material properties.
Geophysics
,
71
(3), G107-G114. https://doi.org/10.1190/1.2198217
Total number of authors:
3
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2.5D resistivity modeling of embankment dams to assess
influence from geometry and material properties
Pontus Sjödahl
1
, Torleif Dahlin
1
, and Bing Zhou
2
ABSTRACT
Repeated resistivity measurement is a potentially powerful
method for monitoring development of internal erosion and
anomalous seepage in earth embankment dams. This study is
part of a project to improve current longterm monitoring rou-
tines and data interpretation and increasing the understanding
when interpreting existing data. This is accomplished by mod-
eling various occurrences typical of embankment structures us-
ing properties from two rockfill embankment dams with central
till cores in the north of Sweden. The study evaluates the influ-
ence from 3D effects created by specific dam geometry and ef-
fects of water level fluctuations in the reservoir. Moreover, a
comparison between different layout locations is carried out,
and detectability of internal erosion scenarios is estimated
through modeling of simulated damage situations. Software
was especially developed to model apparent resistivity for ge-
ometries and material distributions for embankment dams. The
model shows that the 3D effect from the embankment geometry
is clearly significant when measuring along dam crests. For
dams constructed with a conductive core of fine-grained soil
and high-resistive rockfill, the effect becomes greatly enhanced.
Also, water level fluctuations have a clear effect on apparent re-
sistivities. Only small differences were found between the in-
vestigated arrays. A layout along the top of the crest is optimal
for monitoring on existing dams, where intrusive investigations
are normally avoided, because it is important to pass the current
through the conductive core, which is often the main target of
investigation. The investigation technique has proven beneficial
for improving monitoring routines and increasing the under-
standing of results from the ongoing monitoring programs. Al-
though the technique and software are developed for dam mod-
eling, it could be used for estimation of 3D influence on any
elongated structure with a 2D cross section.
INTRODUCTION
Internal erosion is one of the major causes of embankment dam
failures. Monitoring systems can significantly improve the safety
of such dams. However, to detect erosion early, monitoring sys-
tems must be highly sensitive and, at the same time, sufficiently
cover the embankment area. In addition, it should be possible to in-
stall such monitoring systems in existing dams, and these systems
should be capable of identifying small seepage changes, as well as
leakage. Experience from research and field installations carried
out in Sweden since 1993 indicates that monitoring systems based
on resistivity measurements may be able to meet this need 共Johans-
son and Dahlin, 1996; Johansson and Dahlin, 1998; Johansson et
al. 2000兲. In addition, using a resistivity monitoring technique is
essentially nondestructive. This is particularly important when
working with embankment dams, where drilling and other pen-
etrating investigations are normally avoided.
An electrode layout along the top of the dam core is the most
practical and favorable method of installing resistivity monitoring
systems on existing dams. This will be shown later in the paper.
This method has been shown to be effective in revealing informa-
tion about conditions in the core itself. In addition, good electrode
grounding conditions can be provided in the fine-grained environ-
ment commonly found in the dam core 共Dahlin et al., 2001兲. Stan-
dard 2D-inversion schemes are a common technique for processing
data from resistivity profiling 共Smith and Vozoff, 1984; Tripp et al.,
1984; Li and Oldenburg, 1992; Loke and Barker, 1995; LaBrecque
et al., 1996兲.
When doing 2D inversion, it is assumed that the properties of
the ground are constant in the third dimension, i.e., the direc-
tion perpendicular to the electrode layout. Deviations from this are
commonly referred to as 3D effects. This means that application of
standard 2D techniques on embankment dams with measurement
layouts along the crest of the dam cannot be used without cau-
Manuscript received by the Editor March 25, 2004; revised manuscript received August 13, 2005; published online May 24, 2006.
1
Lund University, Engineering Geology, Box 118, 221 00 Lund, Sweden. E-mail: pontus.sjodahl@tg.lth.se; torleif.dahlin@tg.lth.se.
2
University of Adelaide, Department of Physics, School of Chemistry & Physics, South Australia 5005, Australis. E-mail: bing.zhou@adelaide.edu.au.
© 2006 Society of Exploration Geophysicists. All rights reserved.
GEOPHYSICS, VOL. 71, NO. 3 共MAY-JUNE 2006兲; P. G107–G114, 9 FIGS., 3 TABLES.
10.1190/1.2198217
G107
tion because of the obvious 3D effects from the dam geometry. It is
possible to use 3D inversion techniques 共Park and Van, 1991;
Sasaki, 1994; Zhang et al., 1995; Loke and Barker, 1996兲. How-
ever, they still may not be convenient for repeated measurements,
mainly because of limitations in computational resources and be-
cause data sets are 2D if only measured along the crest. Therefore,
a reasonable approach is to use common 2D techniques and then
estimate the distortions and errors that are induced in the process.
Heretofore, the terms 3D effect refer to the errors received when
measuring along an embankment, assuming standard 2D condi-
tions. The most obvious effect is the embankment topography;
however, the most significant effect might come from the variation
in electrical properties of the construction materials in the zoned
embankment dam.
The aim of this study was to improve current, longterm monitor-
ing routines on two embankment dams in the north of Sweden. The
study covered several situations and scenarios essential for inter-
preting and evaluating data from resistivity measurements on em-
bankment dams. Investigations of these different situations were
carried out through numerical calculations. The influence of the
specific dam geometry and zoned construction materials was in-
vestigated via dedicated, 2.5D software. Effects of reservoir water
level and natural, seasonal resistivity variation in the water were
examined as well. Moreover, a comparison was carried out to de-
termine the differences in the efficiency in detecting seepage zones
for four different electrode arrays.
Much work has been done on resistivity forward modeling in 2D
and 3D using the finite-difference method 共Mufti, 1976; Dey and
Morrison, 1979a, b; Fox et al., 1980兲 and the finite-element method
共Pridmore et al., 1981; Queralt et al., 1991; Sasaki, 1994; Zhou and
Greenhalgh, 2001兲. Investigative resistivity surveys on embank-
ments to detect structural defects or anomalous seepage are fairly
widespread 共Abuzeid, 1994; Engelbert et al., 1997; Titov et al.,
2000; Van Tuyen et al., 2000; Buselli and Lu, 2001; Panthulu et al.,
2001; Voronkov et al., 2004兲. However, modeling studies to find
out more about typical effects from dam geometries is less com-
mon.
If 3D modeling were to be used for our study, large and compu-
tationally heavy models would have been needed to assess the 3D
effects without influence from the finite length of the model.
Therefore, software capable of handling typical dam geometries
was developed for the numerical calculations. This software is a
useful tool for optimizing the monitoring program design and to
improve the interpretation of collected data. It uses forward model-
ing to find the apparent resistivity distribution in earth embank-
ment dams for a given geometry and measurement layout. Addi-
tionally, it is general and may be utilized for many types of
elongated structures, as long as they can be described with an arbi-
trary 共although constant兲 geometry in the plane perpendicular to
the electrode layout direction.
NUMERICAL MODELING
Software description
Software written for 2D resistivity/IP modeling was modified to
simulate a dam-monitoring survey by allowing dam geometries in
the 2D-model parameterization and a 3D measurement, which
means that the current injection and potential pickup may be at any
point in the dam. The original 2D software was written for 2D-
resistivity tomography and used the common practical situation,
where resistivity tomographic-imaging surveying is conducted in
the plane perpendicular to the strike direction, allowing arbitrary
variation of resistivity in that plane.
More precisely, the modification of the software was done in two
parts. The first considered adjustments of the elements to fit best
the outline and the inner structure of the dam 共Figure 1兲, which was
done by applying the finite-element method 共Zhou, 1998; Zhou
and Greenhalgh, 1999兲. The second part regarded the calculation
of the potentials parallel to the strike direction. This was accom-
plished by performing the inverse, Fourier-cosine transform with
nonzero y-coordinate of the potential position, according to the
method described by Queralt et al. 共1991兲.
Hence, the modified software is applicable for modeling of the
resistivity structure with surface profile or crosshole survey. How-
ever, because the current electrodes and the potential measure-
ments must be modeled in 3D for the dam survey, we refer to it as
2.5D modeling. Assumed resistivities must be constant in the
electrode-layout direction, i.e., along the dam, and variable in the
dam cross section, whereas the electrodes can be placed anywhere
in all three dimensions. Such 2.5D modeling is simply accom-
plished by involving the inverse Fourier transform for an electrode
array parallel to the strike direction 共Dey and Morrison, 1979a, b;
Queralt et al., 1991兲. The approach is more efficient than a full 3D
model, and for an elongated embankment with constant cross sec-
tion, the drawbacks are moderate. Hence, it is an efficient tool for
assessing 3D effects on 1D and 2D resistivity surveying.
The software uses the finite-element method because this
method makes it easier to deal with the dam geometry, compared to
the finite-difference method. It is valid for calculating potential,
apparent resistivity, or IP responses for a model with arbitrary re-
sistivity distribution in the plane perpendicular to the electrode-
layout direction and for any electrode configurations, e.g., surface,
crosshole, or mise-a-la-masse, off-line and in-line measurements
with pole-pole, pole-dipole, dipole-dipole, Schlumberger, and
mixed arrays 共Zhou and Greenhalgh, 1999兲.
The accuracy of 2.5D modeling has been checked by comparing
it with some known analytic solutions 共Zhou, 1998兲. It has been
shown that the modeling accuracy mainly depends on the element
size, electrode spacings 共that give different ranges of the wave-
number兲, and the wavenumber sampling 共for accurate inverse-
Fourier transform兲. To obtain satisfactory results for the dam mod-
eling, we determined the accuracy-control parameters by applying
the dam geometry and the electrode layouts employed in the fol-
lowing simulations. We compared the results with different ele-
ment sizes and wavenumber sampling schemes. We found that the
results showed relative errors less than 1%, using element sizes of
about 1 m and 40 wavenumber sampling points.
Model geometry, material properties,
and damage types
The dam model is a zoned embankment dam with a central till
core, surrounding filter zones, and support rockfill 共Figure 1兲. This
is the most common design of large Swedish embankment dams.
Geometry and design values are given in Table 1. The electrode
layout is buried 1 m into the top of the core at the midpoint of the
cross section.
Because of difficulties in estimating electrical properties of in-
volved materials and lack of appropriate data in literature, some
uncertainties are connected to these parameters. Here, the rockfill
G108 Sjödahl et al.
was treated as an insulated matrix with all electrical conduction
concentrated to the pore spaces. Thus, Archie’s law was used using
porosity estimates. However, the porosity estimates are to some
extent uncertain in themselves. Regarding the core, the matrix can
no longer be considered an insulator, and other material models
must be used. For this study, the core resistivity was estimated
from existing monitoring data from two Swedish dams 共Johansson
et al., 2000兲 together with laboratory resistivity measurements of
similar till samples 共Bergström, 1998兲 — even though an unsatis-
fying variation was found in this data.
The resistivity of the filter zones has less influence on the mod-
eling results and was assumed to be somewhere between the resis-
tivity of the core and the rockfill. The resistivity of the reservoir
water was taken from monitoring data 共Johansson et al., 2000兲.
Electrical material properties are listed in Table 2. In an interna-
tional perspective, these values are quite high, mainly because of
the high resistivity of the water. Assuming a porosity of approxi-
mately 25% may lead to resistivities of several thousand ohmme-
ters in the saturated rockfill. Keep in mind that the main factor in-
fluencing the results is the relative differences in resistivities for
the involved materials.
The simulated damages were studied for two different depths
共Table 3兲. They could be physically interpreted as damaged layers,
possibly resulting from less compaction at initial construction and
possibly worsened as a consequence of regional piping causing a
transport of fines from the core to the filter and fill. The damages
were extended along the full length of the dam. Damaged zones of-
ten have this kind of extended shape because the dam is con-
structed in layers. Even though an extension along the full length
of the dam is not realistic, simulating these kinds of scenarios still
yields useful information. Furthermore, because of software re-
strictions, the modeled-dam cross section must be identical along
the whole length of the dam. Therefore, for example, it was impos-
sible to simulate a concentrated, cylindrical, damage zone through
the dam.
A resistivity increase of five times in the core was assumed be-
cause of internal erosion. Experiments on similar tills have shown
that resistivity can increase up to 10 times because of removal of
fines under water-saturated conditions 共Bergström, 1998兲. How-
ever, this should be handled with care because internal erosion in-
creases porosity, affecting the resistivity in the opposite direction.
The resistivity of the filter and fill was assumed not to change be-
cause of the simulated damages.
Modeling strategies
To evaluate responses from different electrode arrays, four ar-
rays were selected for all modeling situations. The dipole-dipole,
pole-dipole, Wenner-Schlumberger, and gradient arrays were cho-
sen because they have shown robust imaging quality in prior mod-
eling studies 共Dahlin and Zhou, 2004兲. An electrode spacing of
5 m was selected for the dam model because that gives a reason-
able relation between electrode spacing and dam height similar to
what could be expected in an actual in situ situation. All combina-
tions, including a-spacings from one to seven 共multiples of five兲
and n-factors 共one to six兲, were used for the calculations. The total
was 42 individual measurements for each array. Generally, the four
different arrays demonstrated similar responses for the different
modeled situations. This was particularly true for the pole-dipole,
Wenner-Schlumberger, and gradient, which are all geometrically
associated. Of the four examined arrays, dipole-dipole is by its na-
ture most different from the others, and in some situations, it gave
responses that were different than the others. Thus, only results
from dipole-dipole and Wenner-Schlumberger arrays will be pre-
sented.
Certainly, when investigating constant cross sections, i.e., no lat-
eral changes, the differences in the design of the arrays will not
show up fully in the results. Only when examining special cases,
such as cylindrical damages or elongated damage zones with lim-
Figure 1. The modeled cross section geometry. A zoned, rockfill
embankment dam with a central till core and surrounding filter
zones. Electrode layouts and damage zones that are used in the
study are marked out.
Table 1. Dam geometry design parameters (see also
Figure 1).
Dam height 60 m
Crest width 8 m
Upstream and downstream slopes 0.55:1
Distance: Top of core — crest 3 m
Distance: Max reservoir level — crest 6 m
Core width at top/bottom 4 m/20 m
Filter thickness outside core/top core 4 m/1 m
Table 2. Electrical material properties.
Material Resistivity 共
⍀
m兲
Core 300
Filter 2000
Upstream fill 4000
Downstream fill 20 000
Reservoir water 550
Damaged core 1500
Table 3. Damage types.
Damage type
Thickness of
damaged layer
Depth from crest to
center of damaged layer
Type 1: Thin seepage
zone layer
2 m 20 m
Type 2: Thin seepage
zone layer
2 m 50 m
2.5D Resistivity modeling of embankment dams G109
ited length, can a full verification of the performance of the differ-
ent arrays be obtained.
RESULTS
3D effects
The 3D effects and their dependency on material parameters
were examined for a dam with the model cross section described in
Figure 1. The effects were estimated by comparing the responses
from two models: a 2.5D model and a 1D model with the proper-
ties of the model midsection, i.e., the section with the electrode
layout extended to horizontal layers. The 2.5D model generated
three to seven times higher responses than the 1D model. Sam-
ple results for the dipole-dipole and the Schlumberger arrays are
shown in Figure 2.
Next, the dependency of input-material parameters was simi-
larly evaluated using a model with constant resistivity for the
whole dam cross section, including the reservoir water. The result-
ing effect, caused by the topography for a homogeneous embank-
ment, gave an increase in resistivity of about 30% 共1.30 times兲 for
the 2.5D model 共Figure 3兲. It is obvious that most of the huge 3D
effect arises from the contrast between the relatively conductive
core and the high resistivity of the main part of the dam cross sec-
tion. Most of the current flow is concentrated in the core that geo-
metrically constitutes a rather thin sheet 共Figure 4兲.
Reservoir-level fluctuations
The effect of lowering the reservoir was examined, using the
dam model in Figure 1. This was done because the reservoir water
Figure 2. 3D effects estimated as relation between 1D and 2.5D models with assumed material properties for the modeled cross section and
reservoir. 共a兲 Dipole-dipole and 共b兲 Wenner-Schlumberger arrays with a-spacing of 5–35 m in steps of 5 m and n-factors 1-6. For both ar-
rays, a-spacing is the spacing between potential electrodes, and n-factor is the shortest distance between potential and current electrode di-
vided by the a-spacing.
Figure 3. Purely geometrical 3D effects estimated as relation between 1D and 2.5D models with equal material properties in the whole cross
section and reservoir. 共a兲 Dipole-dipole and 共b兲 Wenner-Schlumberger arrays with a-spacing of 5–35 m in steps of 5 m and n-factors 1-6.
G110 Sjödahl et al.