Electrical Resistivity of Compacted Kaolin and its Relation with Suction

Transcription

1 Electrical Resistivity of Compacted Kaolin and its Relation with Suction Dias, Ana Sofia Summary The electrical characteristics of compacted kaolin were studied and related with their water content in order to propose relationships between suction and electrical resistivity. Knowledge in such relationships is important for the interpretation of electrical resistivity measurements considering the degree of saturation of the soils in geophysical prospection tests, or to develop resistive sensors for soil suction measurement. Samples studied were prepared with different void ratios. The presence of salt with known concentration was also investigated. Water retention curves were measured using vapour equilibrium technique and equipment WP4, in parallel to measurements of electrical resistivity for each case. Experimental data was interpreted considering the continuity of the liquid phase. Introduction The electrical resistivity of soils is a property which can be used in geophysical prospection tests as depends on the type of soil. However it is affected by their degree of saturation, because the electrical conductivity of water is much larger than that of the solids. The electrical properties of a compacted kaolin were studied in parallel with suction measurement for a better understanding of the coupling between electrical current flow and the degree of saturation, and also between suction and electrical resistivity. Besides the improvement on the interpretation of ins situ tests, the interest on knowing these relationships may also contribute to developing resistive sensors, which measure the electrical resistivity in soil and convert the value into total suction after calibration. Samples of compacted kaolin were prepared with different void ratios for the same water content. Suction was applied using vapour equilibrium and electrical resistivity was measured for each case. 2 Background fundaments 2. Water retention curve The water retention curve (WRC) (Figure ) relates water content, or degree of saturation, with total suction (matric and osmotic). This curve can be given by Equation (van Genuchten 980): ω = e G! + s P!!!!!! () where w is water content, e is voids ratio, Gs is the density of the solid particles, s is suction and P and λ are constants. Figure Typical water retention curve (adapted from Vanapalli et al. 999).

2 WRC present particular features that reflects the partial fill of the soil pores with water, as illustrated in Figure (Vanapalli et al. 999). 2.2 Soil electrical resistivity Flow of electrical current in soils occurs along soil's three phases (solid, liquid and gaseous). However the contribution of the gaseous phase is neglected due to the high resistivity of air. In case of granular materials, the conductivity of solid phase can also be neglected due to the same reason. In this context, Archie (942) proposed Equations 2 and 3 to explain the dependency of electrical resistivity on porosity, electrolyte resistivity and pores tortuosity. This would consider current path through the liquid phase in the porous material. F = ρ!"# ρ!" (2) F = a n!! (3) Parameter F is named formation factor, defined considering the electrical conductivity of the saturated porous medium, ρ!"#, and that of the electrolyte, ρ!". Parameter n is porosity and a and m are constants. Abu-Hassanein et al. (996) introduced Equation 4 to explain the dependency of the soil electrical resistivity ρ on the degree of saturation, Sr. In this equation, B is a constant. ρ = ρ!"# S!!! (4) Therefore, soil s electrical resistivity is mainly influenced by the degree of saturation, resistivity of the liquid phase and pores size and tortuosity, as documented by Archie (942), Abu-Hassanein et al. (996) and Gunn et al. (204). The previous relations can be joined into Equation 5. ρ = a ρ!" n!! S!!! (5) It is important to note that the continuity of the liquid phase in soil pores strongly affects 2 resistivity. Indeed, for natural and remoulded clays Fukue et al. (999) observed an abrupt increase in the resistivity once the liquid phase become discontinuous. This occurs when water contents equals the critical water content identified in Figure 2. Figure 2 Relationship between electrical resistivity and water content of a clay (Fukue et al. 999). In the case of clays, the surface conductivity may also decrease soil s electrical resistivity for lower porosities ( Santamarina et al. 200). This is because clay minerals allow the formation of a double layer of charges favourable to the current flow. The contribution of this term was not considered in the calculations performed in this work due to the lack of information necessary for its quantification. However this contribution is considered in the interpretation of the experimental results presented. 3 Material and experimental setup suction and electrical resistivity were measured in compacted samples of commercial white kaolin classified as MH accordingly to USCS. The main physical properties of this material are presented in Table (Gingine & Cardoso, 205), where w L and w p are the liquid and plastic limits, respectively, IP is the plasticity index, Gs is the

3 density of solid particles, and Silt and Clay are the percentages of silt-size and clay-size particles, respectively. Table Kaolin properties. w L w P IP G s Silt Clay 52% 30% 22% % 40% Suction was applied by vapour equilibrium technique (Romero, 999), using NaCl solutions prepared with different concentrations. Five different solutions were prepared, applying MPa, 5MPa, 5MPa and 39MPa. Figure 4 shows a photograph of the one sample during equilibrium time. The samples were prepared with the same water content of 25% and different voids ratio (0.6, 0.9 and.2, named 6W, 9W and 2W, respectively) aiming to provide information on the effect of soil structure on electrical resistivity. For this reason, a reconstituted sample prepared with water content w=.5w L following the procedure suggested by Burland (990). Another kind of sample with voids ratio of 0.9 and same water content was prepared, however using a 0.5M NaCl solution in order to provide information on the nature of the electrolyte. The WRC of each kind of sample wwere measured using the water potentiometer equipment, WP4, defining the reference curve. small pieces were used for this measurement. All samples were compacted in moulds with the geometry presented in Figure 3, in which nails were inserted to work as electrodes. These electrodes were equally spaced and were used to measure the electrical resistivity using Wenner method (BS 377-3, 990). Figure 4 Vapour equilibrium setup. Both wetting and drying paths were applied, as illustrated in Figure 5: for the wetting path al the samples were previously dried in laboratory environment (s=07mpa) and then partially wetted, while for drying they all were first full saturated and then dried. The extreme cases of dried in the laboratory and full saturation provides extra points for the definition of the WRC. Figure 3 Scheme of the soil sample geometry. Figure 5 Paths followed by the samples in vapour equilibrium technique. 3

4 Electrical resistivity was measured once vapour equilibrium was reached.. Total suction was measured in pieces of samples using WP4, as well as water content. Suction applied using the solutions partially saturated with NaCl was corrected after measuring their electrical conductivity using a Crison probe and suction using WP4. The comparison between the reference curve measured with WP4 and the curves found by vapour equilibrium after each correction allowed to validate the methodology adopted when using vapour equilibrium technique for WRC measurement. Further details about the experimental work can be found at Dias (205). 4 Results and discussion 4. Reference water retention curves Equation was used to fit the different WRC. The calibration parameters are presented in Table 2. This table also presents the values of the residual state of saturation (Rss) previously identified in Figure. specimens with the largest voids ratio at compaction). a. Drying branches Suction (MPa) W 6W 2W 0.0 Macropore Water content (%) b. Wetting branches 000 Suction (MPa) 9W 6W 2W 0.0 Macropore Water content (%) Figure 6 Drying and wetting branches of the reference curves. Table 2 WRC parameters for the reference curve and residual state of saturation (Rss). Voids ratio Wetting Drying P Λ Rss P λ Rss (S) (R) As observed in Figure 6, for both branches the curves diverge only for the higher values of water content. This can be explained by the different structures of the compacted samples, differing mainly in the sizes of macropores (largest macropores are observed for the 4 The comparison between the WRC found for the samples compacted with e=0.9 using distilled water or the 0.5M NaCl solution is presented in Figure 7. It can be seen that the curve for the sample prepared using the salt solution is affected by the contribution of osmotic suction that depends on the concentration of NaCl in the pore fluid. When drying occurs and the fluid is saturated by salt, maximum osmotic suction is 39 MPa, while this concentration is minimum when the soil is full saturated. For the void ratio adopted, and assuming no volume changes, suction reaches MPa. This value corresponds to the horizontal branch in Figure 7.

5 000 9S wetting 250 Suction (MPa) 00 9W wetting Water content (%) Figure 7 WRC of 0.9 void ratio samples prepared with NaCl solution and distilled water. 4.2 Vapour equilibrium technique The electrical conductivity and suction of the NaCl solutions prepared for suction application using vapour equilibrium were measured after reaching equilibrium to check if these values are affected by water exchanges between the soil and the solution. Equations 6 and 7 were used to convert electrical conductivity χ into suction s, following the work of Romero (200), where m is the concentration of the solution. χ = 6,9858m! + 78,645m + 8,0453 (6) s = 4,784m!,!"#$ (7) As observed in Figure 8, suction presented only a very small variation. Therefore, the technique is reliable in terms of maintaining suction constant apart from the water exchanges during the process. 4.3 Electrical resistivity The calculation of the formation factor was done using Equation 2 considering the electrical resistivity of the different electrolyes shown Table 3. Table 3 Electrical resistivity of the electrolytes. Fluid ρ el (kωm) NaCl 0.5M 2.9 x 0-4 Distilled water.53 x 0-3 Electrical conductivity (ms/cm) Figure 8 Suction and electrical conductivity of NaCl solutions for vapour equilibrium. The formation factor defined by Archie's law (Equation 3) is presented in Figure 9 for the compacted samples prepared with water. High values were obtained for F. It can be seen in this figure that the signal of parameter m changes for the drying and wetting branches. The differences can be explained by changes in voids ratio during full saturation. Nevertheless, the swelling potential of the clays used was considered to be low (Dias, 205), and for this reason such volume changes were not expected to affect much the results. Formation factor Suction (MPa) Figure 9 Variation of the formation factor with porosity for the compacted samples prepared with water. calibration measured initial Porosity F = 62.4e.3625 R² = F = e R² = wetting drying 5

6 The values found for the electrical resistivity of the unsaturated specimens were used to calibrate Equation 4. As expected, electrical resistivity decreases with increasing degree of saturation, tending to a fixed value. This shows that the pore fluid is a preferential medium for current flow. For the same degree of saturation the compacted samples present increasing resistivity with decreasing voids ratio. This may be explained by the fact that samples with higher voids ratio have larger pores, which for a fixed water content may be filled with mass of water larger then when the pores are small. Figure 0 also shows the results found for the samples 9S prepared with the salt solution. They show lower resistivity when compared with the others because of the higher conductivity of the electrolyte. Yet, for low degrees of saturation this curve tends to the electrical resistivity of the samples prepared with distilled water, which can be explained by the appearance of repulsive forces decreasing ions mobility. The destructured samples present behaviours distinct from the others, which may prove that soil structure has a strong influence on electrical resistivity, even for the unsaturated cases. The separation between the continuity and discontinuity of the liquid phase (residual state of saturation) occurs for values of degree of saturation ranging between 7.8% and 2.3%. Resistivity presents a significant increase for water contents larger than this value, as observed by Fukue et al. (999). An interpolation to obtain the evolution of the parameter B with void ratio was done and is presented in Figure Figure. These equations, with those presented in Figures 9 and, were used to define electrical 6 resistivity as function of the degree of saturation and void ratios. (a) (b) Figure 0 - Electrical resistivity variation with degree of saturation of (a) drying and (b) wetting paths. These curves are in Figure 2. For constant voids ratio the highest resistivity occurs for low degrees of saturation, as expected. The graphs are divided in two zones (A and B) to consider different trends of behaviour. They may be explained considering some hypothesis about the contribution of the clay minerals surface for electrical conductivity.

7 B B = e e R² = B = e e R² = Void ratio e wetting drying Salt Figure Variation of B with void ratio Void ratio Degree of saturation 0, 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Zone A Zone A Zone B Zone B Figure 2 Electrical resistivity variation with degree of saturation and void ratio. a. Drying b. Wetting Void ratio Degree of saturation 0, 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 In Zone A, for the lowest voids ratio, electrical resistivity decreases with increasing voids ratio. It appears that in Zone A the surface electrical conductivity may be favourable enough to allow the increase of current flow, in opposition to the expected increase of resistivity caused by the reduction of the pores size reducing the amount of water through which water can flow. in Zone B, for the largest voids ratio, electrical resistivity decreases with decreasing voids ratio for the same degree of saturation. Such behaviour was predicted by Equations 3 and 4. In this case surface conductivity would decrease soil resistivity because the number of contacts between the particles would increase This may also explain the decreasing formation factor (F), proportional to the electrical resistivity, with porosity in the case of the drying branch (Figure 6). 4.4 Electrical resistivity and suction A final expression that relates total suction and electrical resistivity was deduced from joining Equations and 4, resulting into Equation 8. The calibration parameters are in Table 2 and Figure Figure. ρ = ρ!"# + s P!!!!!" (8) The comparison between the experimental data and the curves defined by this equation, presented in Figure 3, appears to provide a good adjustment, except for higher values of electrical resistivity. The hysteresis of the WRC and changes in structure caused by the drying or saturation process are well visible when comparing Figures 3Figure.a and 3.b. Though, the curves for the destructured samples appear to be the least dependent from the branch (Figure 3.d). 7

8 The electrical resistivity of the samples for e=0-9 (9s) prepared with NaCl is lower than the values found fo the samples prepared with water (9W) in all the suction range (Figure 4Figure.c). This may be consequence of the presence of ions in the solution responsible for increasing osmotic suction and for decreasing the electrical resistivity. For the same suction, the highest void ratio sample presents low resistivity because it has the bigger voids with more water. The sample with voids ratio of 0.6 has the smallest voids and the least content of water, therefore higher resistivity. However, the relative position of the curves in Figure 3.b. is not clear considering the voids ratio at preparation, because the sample with a void ratio of 0.9 appears to have the highest resistivity followed by the samples prepared with the voids ratio of 0.6 and the.2. This may be explained by the contribution of the surface electrical conductivity. 00 a. Wetting 000 b. Drying W 6W 9W 9W 2W 6W 2W 6W 9W 9W 2W 6W 000 c. 9S - 9W 0 d. R W wetting 9W drying 9S wetting 9S drying 9W wetting 9S wetting 9W drying 9S drying R wetting R drying R drying R wetting Figure 3 Comparison of experimental data with Equation 8 deduced curves. The experimental data was adjusted to Equation 9 in order to obtain an alternative way of relate electrical resistivity and suction: Data is presented in Figure 4Figure 8 ρ = α e!! (9) In this case, the relative position of the drying branch curves is according with the expected, i.e. for the same suction, the highest void ratio

9 sample presents low resistivity and the opposite happens with lowest void ratio. Parameter α is responsible for the vertical translation of the curve, as the 9S curves have the lowest value of α. This indicates that this parameter depends on the nature of pore fluid. Parameter β controls the slope of the curves and depends on the void ratio because the curves are parallel in Figure 4.c. Such is not verified in Figures 4Figure.a and 4.b. A Their detailed comparison can be found in Dias (205). The results provided by both methods are very similar. Therefore, Equation 9 can be considered an alternative to Equation 8, having the advantage requiring less calibration parameters and not requiring the definition of a WRC for the material that is being used y = 0.364e x R² = y = e x R² = a. Wetting y = 0.722e x R² = y = e 0.204x R² = y = e x R² = y = 0.927e 0.043x R² = b. Drying W 2W 6W 9W 2W 6W y = 0.927e 0.043x R² = c. 9S - 9W y = 0.048e 0.042x R² = y = 0.09e x R² = y = 0.364e x R² = d. R y = 0.04e x R² = y = 0.086e x R² = W wetting 9S wetting 9W drying 9S drying R drying R wetting Figure 4 Adjustment of the experimental data with Equation 9. 5 Conclusions The major conclusions from this work are presented in the following points:. The WRC of soil prepared with NaCl reflect the contribution of osmotic suction Suction applied using vapour equilibrium technique is almost constant, therefore this technique can be considered reliable. 3. The continuity of liquid phase affects electrical resistivity because significant increase in electrical resistivity were

10 observed after drying the soil above its residual state of saturation RSS. 4. Soils compacted with water and with the larger voids ratio are expected to have lower electrical resistivity than those compacted with smaller voids ratio as the amount of electrolyte increases. 5. For the soils compacted with the lower values of void ratio, electrical resistivity is more probable to be affected by the surface electrical because the number of particle contacts increases, Finally, the relationship between total suction with electrical resistivity was found, which can be used in the calibration of resistive sensors for soil suction measurements. Acknowledgements The author acknowledges Professor Rafaela Cardoso for supervising the research performed and to INESC-MN for lending the setup to measure electrical resistivity. References Abu-Hassanein, Z., Benson, C. and Boltz, L., (996). Electrical Resistivity of Compacted Clays. Journal of Geotechnical Engineering, Vol. 22, No. 5, pp Archie, G. E. (942). The electrical resistivity log as an aid in determining some reservoir characteristics. Petroleum Transactions of AIME, Vol. 46 (), pp BS (990). British Standard part 3: Chemical and Electro-chemical tests, BSI Burland, J.B. (990). On the compressibility and shear strength of natural clays. Géotechnique, 40(3), pp Dias, A. S. (205). Electrical Resistivity of Compacted Kaolin and its Relation, MSc Thesis, Instituto Superior Técnico, Universidade de Lisboa. Gingine, V., and Cardoso, R. (205). Soil Structure Influence on Electrokinetic Dewatering Process. Electrokinetics Across Disciplines and Continents, pp Gunn, D.A., Chambers, J.E., Uhlemann, S., Wilkinson, P.B., Meldrum, P.I., Dijkstra, T.A., Haslam, E., Kirkham, M., Wragg, J., Holyoake, S., Hughes, P.N., Hen-Jones and R., Glendinning, S. (204). Moisture monitoring in clay embankments using electrical resistivity tomography. Construction and Building Materials, Vol. 92, pp Fukue, M., Minato, T., Horibe, H. and Taya, N. (999). The micro-structures of clay given by resistivity measurements. Engineering Geology, 54, pp Romero, E. (200). Controlled suction techniques. 4º Simpósio Brasileiro de Solos Não Saturados, pp Santamarina, J., Klein, K. and Fam, M. (200). Soils and Waves. John Wiley & Sons, pp van Genuchten, M. (980). A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society of American Journal, Vol. 44, No. 5, pp Vanapalli, S. K., Fredlund, D. G. and Pufahl, D. E. (999). The influence of soil structure and stress history on the soil-water characteristics of a compacted till. Géotechique, 49, No. 2, pp