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

SAMPLE Electrode Electrode Voltage Measurement

Four-electrode method

Power supply

SAMPLE

Electrode

~

V

1 2 3 4 5 6 7 8 C V V C 2 3 4 5 6 7 8 1 C V V C

Sequence of Circular Four-Probe Resistivity Cells Measurements

Low Frequency Method

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

ELECTRICAL RESISTIVITY PROBE

ELECTRICAL RESISTIVITY BOX (TWO-ELECTRODE METHOD)

12 cm @ 3 cm 12 cm

12 cm

Point Electrodes

It is difficult to determine A

L A R   a . R  

a: shape factor for the electrode

Electrical Resistivity Box (100 mm cube)

Plate electrode Plate electrode

Electrode point

L A I V    L A R  

A= Area of electrodes L= spacing between the electrodes = resistivity R= resistance

Calibration (using NaCl solutions)

5 10 15 20 25 30 35 40 50 100 150 200 250 300 350 400

Electrode 1 2 3 4 5 6 7 8 9

Current(mA) Applied voltage (V)

50 100 150 200 250 300 350 400 450 500 20 40 60 80 100 120 140 160 180 200 220

Current(mA) Applied voltage (mV)

Resistivity Probe Resistivity Box

10 20 30 40 50 60 70 80 90 100 20000 40000 60000 80000 100000

ERP ERB

S

r

(%)



(

W

• cm)

Comparison of the ERB and ERP results (Silty soil)

Generalized relationship for Determining Soil Electrical Resistivity  = Ae(-(Sr-5)/B) Relationship between Electrical Resistivity and Thermal Resistivity

Log () = CRLog (RT)

CR = 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

2nd 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) Arulanandan and Smith (1973) Topp et al. (1980) Arulmoli et al. (1985) 100 kHz - 10 MHz 1 - 100 MHz 20 MHz - 1 GHz DC Determination of Water content Soil structure/Particle orientation, electrolyte effect Determination of water content soil liquefaction, relative density Lovell (1985) Loon et al. (1990) Arulanandan (1991) Thevanayagam (1993) Knoll and Knight (1994) Shang et al. (1995) Thevanayagam (1995) 4 Hz 0.1-1 GHz 50 MHz All ranges 0.1-10 MHz 60 Hz 1 MHz - 1 GHz porosity, permeability Conductivity of soil Porosity porosity, pore fluid clay %, porosity, conductivity of clay 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
• Electrical conduction in fine-grained soils:

Complex phenomenon, due to development of double layers around the grains Negligible surface charge of grains

Electrical Impedance

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)

• Resistivity term is applicable to DC
• Impedance – Resistance offered by soil mass to AC
• Impedance captures both frequency and amplitude information

Impedance is frequency (of AC) dependent

Basic Model

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





i i equiv

Z Z





i i equiv

Y Y

R C

Determination of Electrical properties of Soils

140 mm Connector Perspex sheet 30 mm Scale Sample SS electrode 100 mm 30 mm 10 mm Base plate

Perspex box

Specimen

Plate electrode

Impedance cells

Impedance cells

Analysis of experimentally

• btained impedance data can be

done by: Cole-Cole plot Nyquist plot----widely employed Bode plot

Equivalent circuit

CE CS CE

RE

RS RE

• Z ''

Z ' (2RE+RS) Rs

Perspex box

Specimen

Plate electrode Details of a typical Impedance Cell Nyquist plot

20 40 60 80 100 120 20 40 60 80 100 120

• Z

W

Z

W

SS1 SS2 SS3

R

Electrode polarization

Nyquist Impedance plot

SS1: Grade-1 sand (Coarse) SS2: Grade-2 sand (Medium) SS3: Grade-3 sand (Fine)

• Z''

Z'

ω=

1 10 100 1000 10000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.114 2.51x10

5

 (x10

2 rad/s)

Bode plot  =tan-1(Z/Z)

c c a b b a

: Conduction path : Soil grains : Electrodes

: Air

Basic Models to Depict Flow Paths of AC in Dry Geomaterials

AC flow through a dry soil may occur due to: (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

d b d c c a a b

: Conduction path : Water filled voids : Soil grains : Electrodes

: Air

Basic Models to Depict Flow Paths of AC in Partially Saturated Geomaterials

AC flow through a partially-saturated soil may occur through: (i) a-a (interconnected pores filled with pore- solution, which offers least resistance to the flow

• f current)

(ii) b-b (interconnected soil grains) (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.

c b c b a a

: Conduction path : Water filled voids : Soil grains : Electrodes

Basic Models to Depict Flow Paths of AC in Saturated Geomaterials

As the air is not present in the voids, the AC can flow through; (i) a-a (continuous pore-fluid) (ii) b-b (interconnected soil grains) (iii) c-c (partly through interconnected soil grains and partly through the pore-fluid).

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.

1 2 3 4 5 6 7 4 8 12 16 20 24 28

R

2=0.99185

 DC=10.7 x 10

• 4 S/m

 (x10

• 4 S/m)

ω ( 106 rad/sec )  = DC + S . ω

Electrical Conductivity of Soils w.r.t. Volumetric water content

10 20 30 40 50

• 1

1 2 3 4 5 6 7 8

 (x10

• 2 S/m)

 (%)

For unsaturated porous medium:  = c wBSm

• r,

 = c wB-mm However, B≈m  = c wm

• r,

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

1 10 100 0.1 1 10 1 10 100 1 10 m = 1.25

m CL (%)

m=0.92 CL

0.2

c=0.6 CL

0.55

c = 1.45

c

Generalization of parameters c and m

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.

10

• 1 10

0 10 1 10 2 10 3 10 4 10 5 10 6 10 7

10 10

1

10

2

10

3

10

4

10

5

10

6

10

7

10

8

k f(Hz)

Variation of Dielectric constant with Frequency

Hygroscopic moisture content, wh

Moisture adsorbed by the soil from the environment due to electro- molecular forces Normally wh measured for air-dried soils, which is not correct. wh = f (SSA, CEC, LL, SP, , k) =f(h/dry ) = f(kdiff ) kdiff

= kh - kdry

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.

Determination of Soil Suction from its Conductivity measurements

10

• 3 10
• 2 10
• 1 10

10

1

10

2

10

3

10

4

10

5

10

6

10

7

• 1

1 2 3 4 5 6 7 8  (x10

• 2 S/m)

m (kPa)

m = f() i.e., the SWCC  = f() i.e., the Generalized Archie’s law

10

• 2 10
• 1

10 10

1

10

2

10

3

10

4

10

5

10

6

10

7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 SWCC fit FX BC vG Mu Experimental results



(kPa)

 

2 / 1 3 2

7 . 76 146 3 . 9 03 . 3          k ) 2 ( 8       k

) 1841 . ( 4674 . 8     k

208 . 1 454 . 2 93 . 9     

d

k  

    57 . 10 35 . 1 k

Topp et al. (1980) Roth et al. (1992) Yu et al. (1997) Gardner et al. (1998) Rohini and Singh (2004)

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.

Some Important Relationships

)] ). (1 . ( . ) . . ).( [(1

2 1 2 1

PF PF M 2 M 1

k S k S k M k M k

r r

      η η

Mixing Model

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.

where M1 and M2 are percentages of the minerals kM1 and kM2 are dielectric constants of the minerals kPF1 and kPF2 are dielectric constants of pore fluids  is the porosity Sr is the saturation

Soil characterization using Impedance Spectroscopy

Frequency Response of the Soil Under an Alternating Current Excitation

Response

Spectra

f G, , , e, Sr

Re(Z) = Z= ZCos Im(Z) = Z = ZSin Z=[(Z)2 +(Z)2]1/2 =tan-1(Z/Z) Apply An Electrical Stimulus Impedance Plots Material/ Substrate

Development of Equivalent Circuits Fitting Circuits to Impedance Data Using Z-view software (Johnson, 2003)

1 2 3 4 5 EXP CKT1

• Z'' (104W)

Z' (104W)

Development of Equivalent Circuits

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 EXP CKT1 EXP CKT2 X EXP CKT4 EXP CKT3 EXP CKT5

• Z'' (104W)

EXP CKT6

Z' (104W)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 2 4 6 8 10 12 14 16 18 20

R (10

3W



Rgb Rg

Grain resistance Rg Grain boundary resistance Rgb

The soil can be characterized as a granular material, if Rgb is negligible or very low. For these soils, the order of magnitude

• f the Rg would be very high.

The soil can be characterized as a fine- grained soil if both Rgb and Rg are present in the equivalent circuit. However, values of these resistances should be quite low as compared to the granular soils/materials.