Electrical Properties Influence of Various Parameters Methods of - - PowerPoint PPT Presentation

25.10.2018 Lecture No. 23-24 Lecture Name: 26.10.2018 Geomaterial Characterization

Sub-topics

• Electrical Characterization
• Importance
• Electrical Properties
• Influence of Various Parameters
• Methods of Measurement
• Generalized Relationships
• Relationship between Thermal and Electrical Resistivities
• 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

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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 (Fine content)

Sr : Degree of saturation

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Laboratory Investigations

• Two-electrode or four-electrode methods
• Application of :

Surface Network Analyzer (SNA) Impedance analyzer LCR meter

• Methods based on high frequencies (f>107 Hz) are based on the

wave propagation concept.

• Methods based on low frequencies (f<106 Hz) are based on

equivalent elements (as the wavelength is much larger than the size of the measurement device).

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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/

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State-of-the-art

Researcher Contribution Coulomb (1736-1806) Maxwell (1881) Fricke (1924) Archie (1942) Developed Coulomb’s law Electrical conductivity of a heterogeneous media Extended Maxwell’s equations for ellipsoidal particles Formation Factor= -m (FF: electrical resistivity of saturated soil divided by the electrical resistivity of its pore fluid) 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

• rientation, electrolyte effect

Determination of water content soil liquefaction, relative density

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Researcher AC Soil Property 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

State-of-the-art

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Electrical Properties of Geomaterials

Electrical properties (conductivity, , and dielectric constant, k) can be used for geomaterial characterization. Electrical conductivity is a measure of charge mobility in response to an electric field. Dielectric constant is a measure of the capacity of a material to reduce the strength of an electric energy field and to behave like an insulator. Variation in electrical properties with alternating current frequency

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Electrical Properties of Geomaterials

• Electrical conduction in moist geomaterials occurs as a result of the

movement of ions

• These materials are dielectric material (characterized by polarization)
• However, they behave neither as a conducting material nor as a

perfectly dielectric material, and hence they can be modeled as a ‘lossy dielectric material’.

• A frequency-dependent complex permittivity, k, is used to capture both

amplitude and phase information.

    A d C k

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For the parallel plate capacitor

Dielectric Constant k k=ε/εo where, ε = material permittivity εo = permittivity of free space = 8.85410-12 (F/m) k =(k-j·k) k= real part of k (depends on polarizability) k= imaginary part of k (losses due to the conduction and polarization)

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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

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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

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Basic Model R C

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

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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

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Impedance cells

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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

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

• Z



Z



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=

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

1 2 3 4 5 EXP CKT1

• Z'' (104)

Z' (104)

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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

3



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.

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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'' (104)

EXP CKT6

Z' (104)

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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

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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.

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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).