Sub-topics Electrical Characterization Laboratory & Field - PowerPoint PPT Presentation

Sub-topics • Electrical Characterization • Laboratory & Field Investigations • State-of-the-art • Electrical Properties (Resistivity & Dielectric constant) • Ohmic Conduction in Geomaterials • Electrical Impedance • Basic Model • Determination of Electrical Properties • Flow of AC in Geomaterials: Basic Models • Equivalent electrical circuits: Basic concepts

Laboratory Investigations • Two-electrode or four-electrode methods • Application of : Surface Network Analyzer (SNA) Impedance analyzer LCR meter

Two-electrode method Power supply Voltage Measurement SAMPLE Electrode Electrode

Four-electrode method Power supply ~ V SAMPLE Electrode

Low Frequency Method 5 6 4 C V 7 3 V 2 8 C 1 5 6 C 4 V 7 3 V 2 C 8 1 Sequence of Circular Four-Probe Resistivity Cells Measurements

ELECTRICAL RESISTIVITY PROBE Top nut 1 2 23 4 3 55 mm Lock nut 32 Ebonite ring Copper electrode 25 25 95 mm 25 20 SS pointed tip 16

ELECTRICAL RESISTIVITY BOX (TWO-ELECTRODE METHOD) 12 cm Point Electrodes @ 12 cm 3 cm It is difficult to determine A A   R L 12 cm   R . a a: shape factor for the electrode

Electrical Resistivity Box (100 mm cube) Plate electrode  V A   I L A   R L Plate electrode  = resistivity R= resistance Electrode point A = Area of electrodes L = spacing between the electrodes

Calibration (using NaCl solutions) Resistivity Probe Resistivity Box 400 220 Electrode 200 350 1 2 3 4 5 6 180 7 8 9 300 160 Current(mA) 140 Current(mA) 250 120 200 100 150 80 60 100 40 50 20 0 0 0 50 100 150 200 250 300 350 400 450 500 0 5 10 15 20 25 30 35 40 Applied voltage (mV) Applied voltage (V)

100000 ERP ERB 80000 -cm) 60000 Comparison of W the (  ERB and ERP 40000 results (Silty soil) 20000 0 0 10 20 30 40 50 60 70 80 90 100 S (%) r

Generalized relationship for Determining Soil Electrical Resistivity  = A  e (-(Sr-5)/B) Relationship between Electrical Resistivity and Thermal Resistivity Log (  ) = C R  Log (R T ) C R = A+B.e (-Sr  C) A, B and C = f (Fines content) Sr : Degree of saturation

Field Investigations Ground Penetrating Radar (GPR) Time Domain Reflectometry (TDR) Capacitance sensor Portable dielectric probe (PDP) Electrical conductivity probe (ECP) Monitoring Slope deformation & Movement 2 nd International Symposium and Workshop on Time Domain Reflectometry for Innovative Geotechnical Applications (TDR 2001). www.iti.northwestern.edu/tdr/tdr2001/proceedings/

State-of-the-art Researcher AC Soil Property Smith and Rose (1933) 100 kHz - 10 MHz Determination of Water content Arulanandan and Smith 1 - 100 MHz Soil structure/Particle orientation, (1973) electrolyte effect Topp et al. (1980) 20 MHz - 1 GHz Determination of water content Arulmoli et al. (1985) DC soil liquefaction, relative density Lovell (1985) 4 Hz porosity, permeability Loon et al. (1990) 0.1-1 GHz Conductivity of soil Arulanandan (1991) 50 MHz Porosity Thevanayagam (1993) All ranges porosity, pore fluid Knoll and Knight (1994) 0.1-10 MHz clay %, porosity, Shang et al. (1995) 60 Hz conductivity of clay Thevanayagam (1995) 1 MHz - 1 GHz electrical dispersion in soils

Ohmic Conduction in Geomaterials: Basics • Conduction of current in due to ionic movement I =  .V  : Resistivity • • Factors affecting electrical conduction in case of coarse-grained soils:  void ratio  degree of saturation  Grain size & shape & orientation  Pore structure  the nature of the pore fluid and its conductivity Negligible surface charge of grains • Electrical conduction in fine-grained soils: Complex phenomenon, due to development of double layers around the grains

Electrical Impedance • Resistivity term is applicable to DC • Impedance – Resistance offered by soil mass to AC • Impedance captures both frequency and amplitude information Z=V(t)/I(t) =V  cos  t/I  cos(  t-  ) =R-jX where, R is resistance, which is the real part of Z(=Z  ), X is the imaginary part of Z (=Z  ) Impedance is frequency (of AC) dependent

Basic Model R Element Impedance Admittance Resistor (R) Z = R+j0 Y = 1/R+j0 C Z = 0+jωL Y = 0- j(ωL) -1 Inductor (L) Y = 0+jωC Z = 0- j(ωC) -1 Capacitor (C)   Z Z Elements in series : equiv i i Elements in parallel :   Y Y equiv i i

Determination of Electrical properties of Soils Plate electrode Perspex box Impedance cells Specimen 30 mm Scale 30 mm SS electrode Sample 100 mm Base 10 mm plate Connector 140 mm Perspex sheet

Impedance cells

Details of a typical Impedance Cell Plate electrode Analysis of experimentally Perspex box obtained impedance data can be done by: Cole-Cole plot Specimen Nyquist plot----widely employed Bode plot Nyquist plot Equivalent circuit -Z '' C E C S C E R E R S R E 0 R s (2 R E + R S ) Z '

Nyquist Impedance plot SS1: Grade-1 sand (Coarse) - Z'' SS2: Grade-2 sand (Medium) SS3: Grade-3 sand (Fine) 120 SS1 SS2 0 100 SS3 ω=  Z ' 80 Electrode  W polarization 60 - Z   40 20 R 0 0 20 40 60 80 100 120  W Z 

Bode plot 0.7 0.6 0.5 0.4  0.3  =tan -1 (Z  /Z  ) 0.2 0.114 0.1 5 2.51x10 0.0 1 10 100 1000 10000 2 rad/s)  (x10

Basic Models to Depict Flow Paths of AC in Dry Geomaterials AC flow through a dry soil may occur due to: c b a (i) a-a (the surface of the soil grains, which is mainly due to the presence of surface charge carriers/ions) (ii) b-b (the soil cluster, wherein soil grains are in contact with each other and current may flow through the interconnected grains) (iii) c-c (partly through the soil grains and partly through the air present in the voids, which is a least likely path due to its very high resistance, unless the air is contaminated with fumes of water or chemicals c b a : Conduction path : Electrodes : Soil grains : Air

Basic Models to Depict Flow Paths of AC in Partially Saturated Geomaterials AC flow through a partially-saturated soil may occur d  c  b  a  through: a  -a  (interconnected pores filled with pore- (i) solution, which offers least resistance to the flow of current) b  -b  (interconnected soil grains) (ii) (iii) c  -c  (partly through the connected soil grains and partly through interconnected pores) (iv) d  -d  (partly through soil grains and partly through the voids, which contain air and pore- solution. d  c  b  a  : Air : Conduction path : Electrodes : Soil grains : Water filled voids

Basic Models to Depict Flow Paths of AC in Saturated Geomaterials c  b  a  As the air is not present in the voids, the AC can flow through; a  -a  (continuous pore-fluid) (i) b  -b  (interconnected soil grains) (ii) (iii) c  -c  (partly through interconnected soil grains and partly through the pore-fluid). c  b  a  : Conduction path : Electrodes : Soil grains : Water filled voids

Basic Experimental Investigations Determination of Electrical Properties of Dry Soils Wet Soils Pore Solution (  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.

28 2 =0.99185 24 R 20 -4 S/m) 16  =  DC + S . ω  (x10 12 -4 S/m  DC =10.7 x 10 8 4 0 1 2 3 4 5 6 7 ω (  10 6 rad/sec )

Electrical Conductivity of Soils w.r.t. Volumetric water content 8 7 6 -2 S/m) 5 4  (x10 3 2 1 0 -1 0 10 20 30 40 50  (%)

Generalized Archie’s law For unsaturated porous medium:  = c   w   B  S m  = c   w   B-m  m or, However, B≈m  = c   w   m  /  w =1/ FF = c   m or, FF : Formation factor  : Bulk conductivity of soils  w : Pore solution conductivity  : Porosity S: Saturation C, B and m are empirical constants

Generalization of parameters c and m 10 0.55 c= 0.6 CL 0.2 m =0.92 CL 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.

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)

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 ,  , k ) =f(  h /  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.