# 2.5D resistivity modeling of embankment dams to assess influence from geometry and material properties

## Summary (3 min read)

### INTRODUCTION

- Internal erosion is one of the major causes of embankment dam failures.
- This method has been shown to be effective in revealing information about conditions in the core itself.
- 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-tion because of the obvious 3D effects from the dam geometry.
- The study covered several situations and scenarios essential for interpreting and evaluating data from resistivity measurements on embankment dams.

### 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.
- 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 accomplished by involving the inverse Fourier transform for an electrode array parallel to the strike direction ͑Dey and Morrison, 1979a, b; Queralt et al., 1991͒.
- 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.
- The authors compared the results with different element sizes and wavenumber sampling schemes.

### 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 ͑Figure 1͒.
- Because of difficulties in estimating electrical properties of involved materials and lack of appropriate data in literature, some uncertainties are connected to these parameters.
- For this study, the core resistivity was estimated from existing monitoring data from two Swedish dams ͑Johansson et al., 2000͒ together with laboratory resistivity measurements of similar till samples ͑Bergström, 1998͒ -even though an unsatisfying variation was found in this data.
- Damaged zones often have this kind of extended shape because the dam is constructed in layers.
- A resistivity increase of five times in the core was assumed because of internal erosion.

### Modeling strategies

- To evaluate responses from different electrode arrays, four arrays were selected for all modeling situations.
- An electrode spacing of 5 m was selected for the dam model because that gives a reasonable relation between electrode spacing and dam height similar to what could be expected in an actual in situ situation.
- All combinations, including a-spacings from one to seven ͑multiples of five͒ and n-factors ͑one to six͒, were used for the calculations.
- Of the four examined arrays, dipole-dipole is by its nature most different from the others, and in some situations, it gave responses that were different than the others.
- Only when examining special cases, such as cylindrical damages or elongated damage zones with lim-.

### 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 properties of the model midsection, i.e., the section with the electrode layout extended to horizontal layers.
- Sample results for the dipole-dipole and the Schlumberger arrays are shown in Figure 2 .
- Next, the dependency of input-material parameters was similarly evaluated using a model with constant resistivity for the whole dam cross section, including the reservoir water.
- 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 section.

### Reservoir-level fluctuations

- The effect of lowering the reservoir was examined, using the dam model in Figure 1 .
- 3D effects estimated as relation between 1D and 2.5D models with assumed material properties for the modeled cross section and reservoir.
- For both arrays, a-spacing is the spacing between potential electrodes, and n-factor is the shortest distance between potential and current electrode divided by the a-spacing.
- The calculations were made once for each depth.
- For the large lowering of the reservoir, the same effect was estimated to be moving toward approximately 40% ͑1.40 times͒ for the largest electrode distances.

### Detectability of internal erosion zones

- When internal erosion occurs, the material properties of the eroded zone will change as porosity increases and fines are washed away.
- A permanent or possibly semipermanent change ͑because it may heal by itself͒ in the resistivity characteristics of the dam core will occur.
- To estimate the imaging potential of the damages, standard 1D, multilayer, smooth inversion ͑Auken et al., 2004͒ was carried out on the forward model responses.
- The anomaly effect is enhanced through inversion, but effects from the dam geometry cause the damage to localize at a shallower level than the real case ͑Figure 9͒.
- It is not likely that the damages would be detected by a single survey, but with repeated measurements the possibilities would be fair.

### Comparison of different layout locations

- Modeling of different layout placements is helpful for interpreting data from Swedish dam monitoring, especially at the Hällby Dam, where layouts are not only placed along the crest but also on a line along the upstream and the downstream side ͑Johansson et al., 2000͒.
- All of them are placed directly beneath the surface of the dam.
- For the layouts along the upstream toe and the mid-upstream slope, the upstream electrodes are placed below the water table.
- The calculated-anomaly effects are less than 1% ͑Ͻ1.01 times͒ for all different placements of the layouts, re- gardless of the damage location.
- Obviously, the channeling effect that concentrates current flow within the conductive dam core is an important factor.

### DISCUSSION AND CONCLUSIONS

- Resistivity measurements on embankment dam geometries are influenced by many factors, such as effects caused by the geometry and variation in material properties across the dam cross section, impact of water-level changes, and electrode-layout location.
- The influence is similar for all of the examined arrays, ranging from three to seven times the value of the standard 1D model for the geometry and material properties assumed.
- Resistivities measured along the dam crest were shown to be significantly influenced by fluctuations in the reservoir level.
- It is unlikely that such damages could be detected by a single resistivity survey using surface electrodes.
- Also note that all damage types were shaped as extended layers and that the results may not be fully applicable, for instance, to a cylindrically shaped damage and other damage zones with limited extent along the dam.

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##### Citations

145 citations

126 citations

### Cites background from "2.5D resistivity modeling of embank..."

...…studies of resistivity distribution on embankment geometries have shown that 3D effects are significant and that, for typical Swedish designs, the actual measurements with layouts along the dam crest may give readings several times higher than the resistivity of the core (Sjödahl et al., 2006)....

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...The explanation of this depth distortion is likely to originate from geometrical effects when inverting two-dimensional resistivity data over an embankment geometry (Sjödahl et al., 2006)....

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...Less consideration is given to absolute values as modelling studies of resistivity distribution on embankment geometries have shown that 3D effects are significant and that, for typical Swedish designs, the actual measurements with layouts along the dam crest may give readings several times higher than the resistivity of the core (Sjödahl et al., 2006)....

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87 citations

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### Cites background from "2.5D resistivity modeling of embank..."

...However, for heterogeneous subsurface conditions, the two-dimensional (2D) assumption is violated because of the influence of 3D features in close proximity to the survey lines, which can cause significant inaccuracies in the resulting 2D resistivity models (Chambers et al., 2002; Sjodahl et al., 2006)....

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...…for heterogeneous subsurface conditions, the two-dimensional (2D) assumption is violated because of the influence of 3D features in close proximity to the survey lines, which can cause significant inaccuracies in the resulting 2D resistivity models (Chambers et al., 2002; Sjodahl et al., 2006)....

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### "2.5D resistivity modeling of embank..." refers methods in this paper

...Such 2.5D modeling is simply accomlished by involving the inverse Fourier transform for an electrode rray parallel to the strike direction Dey and Morrison, 1979a, b; ueralt et al., 1991 ....

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