IIT Bombay ENVIRONMENTAL GEOMECHANICS CE-641 Department of Civil Engineering DR. D. N. SINGH dns@civil.iitb.ac.in www.civil.iitb.ac.in/~dns
IIT Bombay Slide 1 24.10.2009 Lecture No. 21 Lecture Name: Geomaterial Characterization Sub-topics • Electrical Characterization • Basic Experimental Investigations • Determination of Electrical Conductivity & Dielectric constant • Generalized Archie’s law • Electrical Properties of Pore-Solution • Hygroscopic moisture content • Determination of Soil Suction from Conductivity measurements • Some important relationships for Dielectric constant • Mixing Model for Dielectric Constant • Soil characterization using Impedance Spectroscopy Environmental Geomechanics Lecture No. 21 D N Singh
Basic Experimental Investigations IIT Bombay Slide 2 Determination of Electrical Properties of Dry Soils Wet Soils Pore Solution ( σ w ) Determination of hygroscopic moisture content Determination of soil suction Shah, P.H. and Singh, D N., " A Simple Methodology For Determining Electrical Conductivity of Soils ", Journal of ASTM International. 1(5). Published Online:10 May 2004. 11 Pages. Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 3 28 2 =0.99185 24 R 20 σ (x10 -4 S/m) 16 σ = σ DC + S . ω 12 σ -4 S/m DC =10.7 x 10 8 4 0 1 2 3 4 5 6 7 ω ( × 10 6 rad/sec ) Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 4 Electrical Conductivity of Soils w.r.t. Volumetric water content 8 7 6 -2 S/m) 5 4 σ (x10 3 2 1 0 -1 0 10 20 30 40 50 θ (% ) Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 5 Generalized Archie’s law For unsaturated porous medium: σ = c ⋅ σ w ⋅ η B ⋅ S m σ = c ⋅ σ w ⋅ η B-m ⋅θ m or, However, B ≈m σ = c ⋅ σ w ⋅ θ m σ / σ w =1/ FF = c ⋅ θ m or, FF : Formation factor σ : Bulk conductivity of soils σ w : Pore solution conductivity η : Porosity S: Saturation C, B and m are empirical constants Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 6 Generalization of parameters c and m 10 c= 0.6 CL 0.55 m =0.92 CL 0.2 10 m = 1.25 c = 1.45 1 m c 1 0.1 1 10 100 1 10 100 CL (%) Shah, P. and Singh, D. N., " Generalized Archie's Law for Estimation of Soil Electrical Conductivity ", Journal of ASTM International. 2(5), Published Online: 2 May 2005. 20 Pages. Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 7 Electrical Properties of Pore-solution Safety Valve Pressure Pressure Gauge Pressure Pressure regulating Membrane Gauge valve Extractor Retention Unit Sampling Bottle Air Filter & Compressor Valve Membrane & Release Valve Filter Cloth Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 8 Pore-solution Conductivity 2.5 200 Distilled water Soil 2.0 150 3 Ω ) Z'' ( Ω ) 1.5 Z '' (x10 100 1.0 50 0.5 0.0 0 0.0 0.5 1.0 1.5 2.0 2.5 100 150 200 250 300 Z' ( Ω ) 3 Ω ) Z' (x10 Nyquist plots Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 9 500 5 Distilled water Distilled water 400 4 -4 S/m) 300 3 k σ (x10 200 2 ( σ -4 S/m dc = 1.68 x 10 ) k =76.58 100 1 0 0 200 400 600 800 1000 0 200 400 600 800 1000 f (kHz) f(kHz) Standard value of k = 78 (at the same temp.) Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 10 Variation of Dielectric constant with Frequency 8 10 7 10 6 10 5 10 k 4 10 3 10 2 10 1 10 0 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 f (Hz) Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 11 Hygroscopic moisture content, w h Moisture adsorbed by the soil from the environment due to electro- molecular forces Normally w h measured for air-dried soils, which is not correct. w h = f ( SSA , CEC , LL , SP , σ , k ) =f( σ h / σ dry ) = f( k diff ) = k h - k dry k diff Shah, Paresh H. and Singh, D. N., "Methodology for Determination of Hygroscopic Moisture Content of Soils”, Journal of ASTM International. 3(2), (2006), 14 Pages. Environmental Geomechanics Lecture No. 21 D N Singh
Determination of Soil Suction from its IIT Bombay Slide 12 Conductivity measurements ψ m = f( θ ) i.e., the SWCC σ = f( θ ) i.e., the Generalized Archie’s law 8 0.8 7 SWCC fit 0.7 FX BC 6 vG Mu 0.6 Experimental results 5 σ (x10 -2 S/m) 0.5 4 θ 0.4 3 0.3 2 0.2 1 0.1 0 0.0 -1 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 10 7 10 ψ (kPa) ψ m (kPa) Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 13 Some Important Relationships [ ] 1 / 2 Topp et al. (1980) = + ⋅ θ + ⋅ θ − θ 2 3 k 3 . 03 9 . 3 146 76 . 7 Roth et al. (1992) = ⋅ θ + − η k 8 ( 2 ) = ⋅ θ + Yu et al. (1997) k 8 . 4674 ( 0 . 1841 ) = ⋅ θ + ⋅ ρ − Gardner et al. (1998) k 9 . 93 2 . 454 1 . 208 d = + ⋅ θ Rohini and Singh (2004) k 1 . 35 10 . 57 Rohini, K. and Singh, D. N., " A Methodology for Determination of Electrical Properties of Soils ", Journal of Testing and Evaluation, ASTM. 32(1), 2004, 64-70. Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 14 Mixing Model = − + + + − η η k [(1 ).( M . k M . k ) . ( S . k (1 S ). k )] 1 M 2 M PF PF r r 1 2 1 2 where M 1 and M 2 are percentages of the minerals k M1 and k M2 are dielectric constants of the minerals k PF1 and k PF2 are dielectric constants of pore fluids η is the porosity S r is the saturation Bhat, A.M., Rao, B.H., and Singh, D.N., “A Generalized Relationship for Estimating Dielectric Constant of Soils”, Journal of ASTM International , 2007, Published Online: 15 August 2007, pages: 12, 2007, DOI: 10.1520/JAI100635. Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 15 Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 16 Soil characterization using Impedance Spectroscopy Frequency Response of the Soil Under an Alternating Current Excitation Apply Response An Material/ Spectra Electrical Substrate Stimulus G, θ , γ , e, S r Impedance Plots f Re(Z) = Z ′ = Z ⋅ Cos φ Im(Z) = Z ″ = Z ⋅ Sin φ Z =[(Z ′ ) 2 +(Z ″ ) 2 ] 1/2 φ =tan -1 (Z ″ /Z ′ ) Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 17 Bode plot 0.7 0.6 0.5 0.4 φ 0.3 φ =tan -1 (Z ″ /Z ′ ) 0.2 0.114 0.1 5 2.51x10 0.0 1 10 100 1000 10000 ω 2 rad/s) (x10 Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 18 Development of Equivalent Circuits Fitting Circuits to Impedance Data Using Z-view software (Johnson, 2003) 5 EXP CKT1 4 3 -Z'' ( × 10 4 Ω ) 2 1 0 Z' ( × 10 4 Ω ) Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 19 Development of Equivalent Circuits 5 EXP EXP CKT1 CKT2 4 3 2 X 1 0 5 EXP EXP CKT3 CKT4 4 3 2 1 0 5 EXP EXP CKT5 CKT6 4 3 2 ) -Z'' ( × 10 4 Ω 1 0 0 1 2 3 4 5 0 1 2 3 4 5 Z' ( × 10 4 Ω ) Environmental Geomechanics Lecture No. 21 D N Singh
IIT Bombay Slide 20 20 R gb 18 R g 16 14 The soil can be characterized as a granular material, if R gb is negligible or 12 R ( × 10 3 Ω) very low. 10 8 For these soils, the order of magnitude 6 of the R g would be very high. 4 The soil can be characterized as a fine- 2 grained soil if both R gb and R g are 0 present in the equivalent circuit. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 θ However, values of these resistances Grain resistance R g should be quite low as compared to the Grain boundary resistance R gb granular soils/materials. Environmental Geomechanics Lecture No. 21 D N Singh
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