Argentinean loess is a typical collapsible soil which strength and stiffness are mainly governed by water content and unit weight. Electrical resistivity of soils depends fundamentally from water content, porosity, and salt concentration in the pore fluid. The interest of this work is to discuss the applicability of electrical resistivity survey to predict variations in density and water content in loess. Samples of loess were prepared in laboratory at varied densities and water contents. The results show that loess resistivity depends mainly on water content and that soil density has little influence. Mapping water content distribution by means
of resistivity measurements is possible if salt concentration in pore fluid is known in advance and assumed uniformly distributed in the whole soil mass. A real scale work is described here for which resistivity mapping was used successfully to evaluate distribution of water content in loess formation.Fil: Rinaldi, V.  Universidad Nacional de Córdoba;  Argentina.Ingeniería de la Construcció

Rinaldi, V.

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Fil: Rinaldi, V.  Universidad Nacional de Córdoba;  Argentina.Argentinean loess is a typical collapsible soil which strength and stiffness are mainly governed by water content and unit weight. Electrical resistivity of soils depends fundamentally from water content, porosity, and salt concentration in the pore fluid. The interest of this work is to discuss the applicability of electrical resistivity survey to predict variations in density and water content in loess. Samples of loess were prepared in laboratory at varied densities and water contents. The results show that loess resistivity depends mainly on water content and that soil density has little influence. Mapping water content distribution by means
of resistivity measurements is possible if salt concentration in pore fluid is known in advance and assumed uniformly distributed in the whole soil mass. A real scale work is described here for which resistivity mapping was used successfully to evaluate distribution of water content in loess formation.Fil: Rinaldi, V.  Universidad Nacional de Córdoba;  Argentina.Ingeniería de la Construcció

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1 INTRODUCTION The Argentinean loess is of eolian origin and can be classified in the unstable group of soils as collapsible (Aitchinson, 1973).The most relevant properties Ar-gentinean deposit has been extensively described by Moll & Rocca (1991), and Rinaldi et al. (2007). Most loess deposits were naturally deposited by wind (primary loess) while others were removed and re-deposited by water (secondary loess). Additional-ly, is of common practice to improve the behavior of loess by means of static and dynamic compaction.  In any case, natural water content and final density mainly governs shear strength, permeability and compressibility of the soil.  McCarter (1984), Kalinski & Kelly (1994), Knight, (1991), Abu-Hassanein et al. (1996) Zhou et al. (1997), and Rinaldi & Cuestas (2001) discussed the potential application of electrical conductivity (or its inverse value, the resistivity) to evaluate soil com-paction. In general, electrical conduction in soils de-pends mainly on temperature and frequency of mea-surement, electrolyte type and concentration in the porous, water content and density. Minor influence can be attributed to soil structure and saturation his-tory of the soil. The possibility of monitoring soil density by means of an electrical methods is advantageous since the control in the field can be performed from the sur-face to any depth just working with different separa-tion of electrodes when any of the four-electrode configuration is adopted (see for example ASTM G57). On the other hand, to the experience of the au-thors, measurement of conductivity is fast and little data processing is required in order to obtain accu-rate and repeatable results.  The purpose of this work is to present a fundamental study to discuss the applicability of electrical resis-tivity to predict water content and density of loess soil. Thus, various samples were prepared in the la-boratory at different densities and water contents.  Electrical conductivity was measured for each sam-ple by using a two electrode device. The relationship between the electrical conductivity, soil density and water content is described in terms of the well known Archie´s law. An example of in-situ control by mean of conductivity measurement is presented. 2 BACKGROUND The influence of the different parameters in the elec-trical conductivity of compacted specimens of loess was discussed elsewhere (Rinaldi & Cuestas, 2001). The most relevant are: frequency of measurement, electrolyte type and concentration (c), initial salt concentration in the soil, dry unit weight (d), degree of saturation (S), and temperature (T).  At a constant temperature and frequencies of measurement, these authors showed that the influence of the different va-riables in the electrical conductivity of the soil can Application of electrical resistivity for the control of water content and density in loess V. Rinaldi National University of Córdoba, Argentina    ABSTRACT: Argentinean loess is a typical collapsible soil which strength and stiffness are mainly governed by water content and unit weight. Electrical resistivity of soils depends fundamentally from water content, po-rosity, and salt concentration in the pore fluid. The interest of this work is to discuss the applicability of elec-trical resistivity survey to predict variations in density and water content in loess. Samples of loess were pre-pared in laboratory at varied densities and water contents. The results show that loess resistivity depends mainly on water content and that soil density has little influence. Mapping water content distribution by means of resistivity measurements is possible if salt concentration in pore fluid is known in advance and assumed  uniformly distributed in the whole soil mass. A real scale work is described here for which resistivity mapping was used successfully to evaluate distribution of water content in loess formation. be take in consideration by using the well known Archie´s expression (Archie, 1942) which for satu-rated conditions can be expressed as: mnaF                  (1) Where F is the formation factor defined from the slope of the e vs. s curves as:  seF                   (2) Being e and s the electrical conductivity of the pore fluid and the saturated soil respectively, n is the porosity, a is the tortuosity factor, and m is the ce-mentation factor. The value 1/F is also known as the resistivity index (RI). For the unsaturated condition equation (1) can be ex-tended as follows: ps SFF                 (3)  Where S is the degree of saturation and p is the satu-ration exponent. Then, by replacing (1) in (3): pms SnaF                (4) The values of a, m and n are normally determined from experiments for a given soil. Notice that for sa-turated samples S=1, and n = v and equations (4) reduce to equation (1), which was empirically ob-tained by Archie for some saturated rocks and then extensively validated in practice for a variety of por-ous formations. Equations (1) and (4) assume that in the porous media the particles and the air are non conductive phases and conduction takes place only through the fluid (Glover, 2010). In terms of the volumetric water content (v), equa-tion (4) can be rewritten as: pvmps naF )(               (5) Thus, for soils in the saturated condition, the meas-ured conductivity of the soil mass becomes:  mes na                  (6) Equation (7) shows that electrical conductivity for saturated soils is mainly dependent on porosity or the volumetric water content (since n = v) and salt con-centration of the pore fluid which governs the value of e. The values of e and a are difficult to be ob-tained in practice specially in fine grained soils.  Therefore, for a given soil in saturated conditions for which salt concentration in the pore fluid is approx-imately the same along the whole soil mass (e=constant), there is always possible to find a cor-relation between the measured bulk conductivity and the porosity as follows:  )( soilsaturatednms             (7) or alternatively,  )( soilsaturatedmvs             (8) Where  is a curve fitting parameter. For unsaturated soils, the bulk electrical conductivity of the soil can be obtained from equation (5) as:  pvpmes na )(                (9) In a similar approach developed for the saturated conditions, it is always possible to find a more gen-eral expression for a given soils assuming that e is constant everywhere in the soil mass of the type:  pvpms n )(                 (10) Equation (10) is a more general expression for soils at any compaction density and water content condi-tion.  It can be seen that for saturated soils (n = v) and equation (10) reduces to equation (8).  Notice that in equations (6) to (10) soil dry density is included in n and also in v since:  wwdv                      (11) Where (d) is the dry unit weight of the soil, (w) is the unit weight of water and (w) is the gravimetric moisture content. Equations (10) and (11) are the basic relationship to determine water content and density from the meas-ured soil resistivity of the soil. From these equations it becomes clear that soil conductivity depends on soil density and water content (w). In saturated soils, conductivity is directly related to volumetric water content. The parameters a and m depend mainly on mineral composition, grain size distribution and fa-bric. The exponent p for a given soil is slightly de-pendent on soil density.   3 TESTING PROGRAM The soil tested here is the typical loess obtained from the campus of the Universidad Nacional de Córdoba which can be classified in USCS as ML. In natural state the dry density is d= 13.5 kN/m3, liquid limit LL=31, and plasticity index PI = 26.  The electrical conductivity of the soil samples was measured in the two-electrode cell. Basically the cell consists on a cylindrical glass tube (33.4 mm internal diameter) and two circular electrodes of the same di-ameter located at both ends of the tube. Electrodes were made of cooper and coated with nickel. The measurements of conductivity were performed by means of a Stanford Research impedance analyzer SR715 at the frequency of 10 kHz. Specific details of the testing cell used here and its calibration pro-cedure are described in Rinaldi & Cuestas (2001). The natural samples of loess were air-dried, sieved through sieve No 40 and then oven dried at 105 ºC. The dried soil was then mixed with the different vo-lumes of NaCl electrolyte prepared at concentrations between 0,5 % and 2% by weight. The prepared soil specimens were then compacted to the desired densi-ty in the glass tube of the cell.  4 ARCHIE´S LAW FOR LOESS Figure 1 display the variation of the formation factor obtained for a sample of loess saturated with NaCl solutions and compacted at various densities. The exponent of the correlation was m = 2.6 and the fac-tor a= 0.5.   The range of porosities included in Fig-ure 1 range between 0.37 and 0.50 which are the maximum and minimum densities that may be ob-served in the field. The agreement of equation (1) is acceptable in the rage of densities tested. The values of the constants a and the exponent m may be differ-ent even for the same soil at other compaction densi-ties.   Fs= 0,5 n-2,60123456789100,30 0,35 0,40 0,45 0,50 0,55 0,60Formation Factor (Fs)Porosity (n) Figure 1. Formation factor of loess saturated with NaCl solu-tions at concentrations between 0.5% and 2% as a function of porosity (n).  0,000,050,100,150,200,250,0 0,1 0,2 0,3 0,4 0,5Resistivity Index (1 / Fs)Volumetric Water Content (v)Model: n = 0.3Model: n = 0.5 Figure 2. Formation factor of loess samples prepared with NaCl solutions at concentrations between 0.5% and 2% as a function of volumetric water content (v).  Figure 2 shows the variation of the formation factor for samples prepared at various water content and concentrations of NaCl. Equation (5) was evaluated for porosities n= 0.3 and n= 0.5 and plotted in the same figure. The constant parameters were fixed as a = 0.5, m = 2.6 and p = 2.4.  The variation of the ex-ponent p is presented on Figure 3 for samples pre-pared at different densities and mixed with different concentrations of NaCl. Therefore, equation (5) can be written for the present results as:  4.2)4.26.2(1ves na                (12)  0,00,51,01,52,02,53,00,0 0,5 1,0 1,5 2,0 2,5Exponent pConcentration of NaCl (%)n = 0.5n = 0.4n = 0.3 Figure 3. Variation of the exponent p for samples of loess of loess prepared at various porosities and mixed with NaCl solu-tions at concentrations between 0.5% and 2%.  From Figure 2 it can be observed that for the model porosity has negligible effect on the formation factor and that water content is the main parameter that go-verns conduction trough the soil. This result can be explained from the close values obtained for the ex-ponent p and m. The physical meaning of this result can be further clarified from the phase diagram for the soil displayed on Figure 4. Three conduction paths can be identified through the soil in the unsatu-rated condition: solid particles (p), fluid (e) and air (a). Thus, the total conduction can be expressed in a simplified approach as:  evavps nn   )()1(           (13)              Figure 4. Phase diagram of soil and simplified conduction paths assumed.  The second term of equation (12) vanishes since conductivity of the air is close to zero. Additionally, the first term also has a negligible influence for soils Solids Fluid Air e a p 1-n Vt = 1   n v n-v which particles can be considered as nonconductive. Then, the total conduction depends mainly from the volumetric water content of the soil.  Notice from Figure 4 that for any variation in the fraction volume of solids and air (which changes soil density), con-ductivity through the fluid will remain practically unchanged.   The volumetric water content depends also from the soil unit weight (d) according to equation (11) how-ever, this parameter has not significant variation from the loosest to densest condition for most soils. For example in loess density usually ranges from 13,5 kN/m3 to 16,5 kN/m3 when heavily compacted which represent an increment of 20 % . Conversely, water content (w) may vary from 2% in the air dry condition to almost 40 % in the saturated condition which represent an increment of 2000 %. Then for practical purposes and for loess, equation (12) can be simplified to: (5) as:  pves                    (13) That for the soil tested here yield:   6.214.2 ves                 (14) In order to obtain the soil conductivity from equation (14) it is required to know in advance the conduc-tivity of the pore fluid (e). This parameter is nor-mally unknown, however it is clear that for a given soil formation, the concentration of salt in the pore fluid can be assumed homogeneously distributed in the whole mass (due to ion diffusion) and thus the value of e can be considered the same everywhere.  5 FIELD EVALUATION Figure 5 displays the variation of electrical resistivity obtained in an area of 60 m x 150 m located at the south of the city of Córdoba. The thickness of loess formation at the site is larger than 60 m.  Measure-ments were performed by using the four electrode configuration equally spaced 5m apart. Separations of electrodes were kept constant and measurements of resistivity were performed at different points in the surface of the soil following a square grid of 20m. The measured resistivity was estimated to cor-respond to an average thickness of 2.5 m. The range of resistivities values obtained in this test collapse in a narrow band between 22 Ohm-m and 43 Ohm-m, however, data are consistent. According to equation (14) the mapped resistivity is directly re-lated to soil water content. In order to determine the relationship between the resistivity values and water content, the following procedure was used here:    Figure 5. Resistivity variation obtained in an area of 60 m x 150 m of loess formation. Numbers on the figure display resis-tivity values in Ohm-m. White dots indicate the position of con-trol points.  a) Three field points of control were selected and from each point were determined mois-ture content (w%) and soil density (d). Figure 5 shows the location of each point. b) Volumetric water content (v) was determined for the three control points from equation (11). c) For convenience, equation (14) was rewritten in terms of resistivity as:    6.214.2 ves                 (15) d) From equation (15) the value of e was de-termined for the three control points since the values of v and e are known. e) Assuming constant density (d) and fluid re-sistivity (e) everywhere, equation (15) is then the field curve that can be used to determine water content for any other point where resis-tivity is known. Equation (15) is plotted on Figure 6 as a function of water content. The three control points are also shown on the same figure.  The study presented here assumes the validity of eq-uation (14) obtained for loess formation. For any other formation, it is recommended to obtain in the laboratory a calibration of the model, or to increase the number of control points and to determine a field curve from these points.    (m) (m) 0204060801001201401601800 10 20 30 40Resistivity (Ohm-m)Water Content (w%)Control PointsField Curve Figure 6. Variation of resistivity as a function of water content for the field test performed. 6 CONCLUSIONS The main conclusion of this work can be summa-rized as follows:  a) Resistivity or electrical conductivity of loess has a significant dependence on water con-tent and is little influenced by density. b) Archie´s equation can be used to model the dependence of electrical resistivty from wa-ter content for loess in saturated and unsatu-rated condition. c) The main dependence of soil resistivity from water content was explained here by means of a simple physical model. d) A field procedure was described here which allows mapping the distribution of water content from electrical resistivity measure-ments. The procedure assumes little varia-tion in the conductivity of the soil mass un-der test. e) Further studies are required to evaluate the influence of fine contents and to what ex-tends can be applied Archie´s model.  REFERENCES Abu-Hassanein Z., Benson C., and Blotz L., 1996, Electrical Resistivity of Compacted Clays, Journal of Geotechnical  and Geoenvironmental Engineering, ASCE, No 5, Vol. 122, pp. 397-406. Aitchinson, G.D. 1973, Structurally Unstable Soils; State of the Art. Proc. VIII ICSMFE, Moscu, pp.161-190. Archie, G. E., 1942, The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics, Transactions of the American Institute of Mechanical Engineers, 146, pp.54–67. Glover, P. W. J., 2010, A Generalized Archie’s Law For N Phases, Geophysics,Vol. 75, No. 6, pp. 247-265. Kalinski, R.J., & Kelly W.E., 1994, Electrical-Resistivity Mea-surement for Evaluating Compacted-Soil Liners, Journal of Geotechnical Engineering, Vol. 120, No. 2, pp. 451-457. Knight R., 1991, Hysteresis in the Electrical Resistivity of Par-tially Saturated Sandstones, Geophysics, Vol. 56, No. 12, pp. 2139-2147. McCarter W.J., 1984, The Electrical Resistivity Characteristics of Compacted Clay, Geotechnique, No 2, Vol. 34, pp 263-267. Moll L. & Rocca R. 1991, “Properties of Loess in the Center of Argentina”. IX Panamerican Conference on Soil Mechanics and Foundations Engineering. Chile, Vol. 1. Rinaldi V. & Cuestas G. 2001, The Ohmic Conductivity of a Compacted Silty Clay, ASCE Journal of Geotechnical and Geoenvironmenta Engineering. Vol 128, No. 10, pp. 824-835. Rinaldi V. A., Rocca R. J. & Zeballos, M. E. 2007. Geotech-nical Characterization and Behaviour of Argentinean Col-lapsible Loess. Characterisation and Engineering Proper-ties of Natural Soils. Tan, Phoon, Hight & Leroueil (eds). Balkema, London, Vol. 4, pp. 2259-2286. Zhou D., Arbabi S., & Stenby E., 1997, A Percolation Study of Wettability Effect on the Electrical Properties of Reservoir Rocks, Transport in Porous Media, No.29, pp. 85-98.   

Application of electrical resistivity for the control of water content and density in loess

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Application of electrical resistivity for the control of water content and density in loess

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