Near Surface Geoscience 2013 – 19th European Meeting of Environmental and Engineering Geophysics Bochum, Germany, 9-11 September 2013

We S2a 03Estimation of van Genuchten-Mualem Parametersfrom Spectral Induced PolarizationMeasurementsS. Nordsiek* (TU Braunschweig), A. Hördt (TU Braunschweig), E.Diamantopoulos (TU Braunschweig) & W. Durner (TU Braunschweig)

SUMMARYThe application of spectral induced polarization (SIP) surveys to estimate hydrological properties of thesubsurface is promising. For the interpretation of the SIP data, the knowledge of the relationships betweensoil hydraulic properties and parameters obtained from SIP measurements is essential. Therefore, weperformed hydrological and SIP measurements in the laboratory on seven natural soils and a medium sandsample with a narrow grain size distribution. The SIP spectra were interpreted with the Debyedecomposition, which yields integrating parameters for the resulting relaxation time distribution. To derivesoil hydraulic parameters from the hydrological experiments, we fitted the van Genuchten-Mualem model,which is widespread in soil physics, to the measured hydrological data. In this study, we concentrate on therelationship between two parameters: the normalized chargeability from the Debye decomposition of SIPspectra and the parameter alpha from the van Genuchten-Mualem model. We present an approach toestimate the parameter alpha from the normalized chargeability.

Near Surface Geoscience 2013 – 19th European Meeting of Environmental and Engineering Geophysics Bochum, Germany, 9-11 September 2013

Introduction

Spectral induced polarization (SIP) measurements can be a useful tool to estimate the hydraulic conductivity of the subsurface (e. g., Hördt et al., 2009; Breede et al., 2011). To identify relationships between complex geoelectrical parameters and soil hydraulic properties, studies often focus on sand or sand-clay mixtures (e. g., Breede et al., 2012). We performed SIP and hydrological laboratory measurements on soil samples from different locations in the vicinity of Braunschweig, Germany. The SIP spectra are interpreted with the Debye decomposition, which yields integrating parameters to summarize the resulting relaxation time distribution. From the hydrological experiments characteristic parameters are derived by fitting the van Genuchten-Mualem model, which is widespread in soil physics. For this study we limit to the correlation between two parameters, the normalized chargeability resulting from the Debye decomposition of SIP spectra and the parameter from the van Genuchten-Mualem model.

Methods

SIP is a geoelectrical method, where the complex resistivity is measured at several frequencies, usually between 1 mHz and 1 kHz. For our study, we confine the frequency range between 10 mHz and 100 Hz, because measuring at frequencies lower than 10 mHz is very time consuming and the investigation of frequencies higher than 100 Hz is interfered by electromagnetic coupling effects. The resulting amplitude and phase angle spectra of the complex resistivity are interpreted with the Debye decomposition presented by Nordsiek and Weller (2008), where the measured complex resistivity

is interpreted as the result of a superposition of Debye relaxation processes with relaxation times and chargeability values :

∙ 1 ∑ ∙ 1 , (1)

with the DC resistivity , the angular frequency ω and the imaginary unit √ 1. The resulting relaxation time distribution ( , ) is summarized by integrating parameters. One of these parameters is the total chargeability

∑ . (2) Weller et al. (2010) suggested to use the normalized chargeability , which is the ratio of the total chargeability to the DC resistivity . We conducted the SIP measurements on samples saturated with calcium chloride solutions of different ionic strengths, varying from 0.001 to 0.02 mol/l. After finishing all SIP measurements, the Multi-Step Outflow (MSO) experiments were performed to determine the soil hydraulic properties. For the MSO experiments, a negative pressure head was applied to the bottom of the initially saturated soil column and was decreased step-wise. The volume of water flowing out of the sample was measured. The water retention curve and the hydraulic conductivity curve, were obtained as function of the pressure head. As an alternative to the MSO experiments, in some cases an evaporation experiment with the commercial HYPROP device by UMS GmbH (Munich) was used to determine the soil hydraulic properties. Instead of applying a decreasing pressure head to the samples, this method utilizes the evaporation of the water from the pore space of an initially saturated sample. A detailed description can be found in Peters and Durner (2008). The van Genuchten-Mualem relation (Mualem, 1976; van Genuchten, 1980) describes the hydraulic conductivity

∙ ∙ 1 1 / with the effective saturation 1 | | , (3)

which depends on the pressure head . is the saturated hydraulic conductivity and , , , and are empirical parameters. Fitting this relation to the results of the MSO and HYPROP measurements,

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Near Surface Geoscience 2013 – 19th European Meeting of Environmental and Engineering Geophysics Bochum, Germany, 9-11 September 2013

Conclusions

We investigated eight samples of unconsolidated sediments with SIP and the MSO/HYPROP method. The resulting complex resistivity spectra and the hydraulic conductivity curves were parameterized by the Debye decomposition approach and the van Genuchten-Mualem model, respectively. The parameter was estimated with the normalized chargeability resulting from the Debye decomposition of the SIP spectra. The estimation of can be improved when the electrical conductivity of the pore fluid is considered.

Acknowledgements

We are grateful to A. Kemna (University of Bonn), E. Zimmermann, J. A. Huisman, and K. Breede (all Forschungszentrum Jülich) for helpful comments concerning the construction of the sample holder. We thank I. Andrä, S. Mathesius, K. Bairlein, and T. Zimny (all TU Braunschweig) for providing and preparing the soil samples. The grain size analysis was performed by I. Andrä. This work was part of project HO 1506/17-1 supported by the German Research Foundation (DFG).

References

Bairlein, K., Hördt, A. and Nordsiek, S. 2013. The influence of the sample preparation on induced polarization spectra of unconsolidated sediments. Near Surface Geophysics, submitted. Breede, K., Kemna, A., Esser, O., Zimmermann, E., Vereecken, H. and Huisman, J. A. 2011. Joint measurement setup for determining spectral induced polarization and soil hydraulic properties. Vadose Zone Journal 10, 716-726. Breede, K., Kemna, A., Esser, O., Zimmermann, E., Vereecken, H. and Huisman, J. A. 2012. Spectral induced polarization measurements on variably saturated sand-clay mixtures. Near Surface Geophysics 10, 479-489. Hördt, A., Blaschek, R., Binot, F., Druiventak, A., Kemna, A., Kreye, P. and Zisser, N. 2009. Case histories of hydraulic conductivity estimation with induced polarization at the field scale. Near Surface Geophysics 7, 529-545. Mualem, Y. 1976. A new model of predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12, 513-522. Nordsiek, S. and Weller, A. 2008. A new approach to fitting induced-polarization spectra. Geophysics 73(6), F235-F245. Peters, A. and Durner, W. 2008. Simplified evaporation method for determining soil hydraulic properties. Journal of Hydrology 356, 147-162. van Genuchten, M. T. 1980. A closed-form equation for predicting the hydraulic conductivity of saturated soils. Soil Science Society of America Journal 44, 892-898. Weller, A., Slater, L., Nordsiek, S. and Ntarlagiannis, D. 2010. On the estimation of specific surface per unit pore volume from induced polarization: A robust empirical relation fits multiple data sets. Geophysics 75(4), WA105-WA112. Weller, A., Breede, K., Slater, L. and Nordsiek, S. 2011. Effect of changing water salinity on complex conductivity spectra of sandstones. Geophysics 76(5), F315-F327. Zisser, N. 2010. Relationship between hydraulic permeability and spectral electrical response of sandstones. Ph.D. thesis. Rheinische Friedrich-Wilhelms-Universität Bonn.