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

IIT Bombay 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

IIT Bombay 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 (Fine content) Sr : Degree of saturation

Laboratory Investigations IIT Bombay • Two-electrode or four-electrode methods • Application of : Surface Network Analyzer (SNA) Impedance analyzer LCR meter Methods based on high frequencies (f>10 7 Hz) are based on the • wave propagation concept. Methods based on low frequencies (f<10 6 Hz) are based on • equivalent elements (as the wavelength is much larger than the size of the measurement device).

Field Investigations IIT Bombay 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/

IIT Bombay State-of-the-art Researcher Contribution Developed Coulomb’s law Coulomb (1736-1806) Maxwell (1881) Electrical conductivity of a heterogeneous media Extended Maxwell’s equations for ellipsoidal particles Fricke (1924) Formation Factor=  -m Archie (1942) (FF: electrical resistivity of saturated soil divided by the electrical resistivity of its pore fluid) Researcher AC Soil Property Determination of Water content Smith and Rose 100 kHz - 10 MHz (1933) Soil structure/Particle Arulanandan and 1 - 100 MHz orientation, electrolyte effect Smith (1973) Determination of water content Topp et al. (1980) 20 MHz - 1 GHz soil liquefaction, relative density Arulmoli et al. (1985) DC

IIT Bombay State-of-the-art Researcher AC Soil Property 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

IIT Bombay 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

IIT Bombay 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. For the parallel plate capacitor  C d  A k   0

IIT Bombay Dielectric Constant k k=ε/ε o where, ε = material permittivity ε o = 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)

IIT Bombay 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 IIT Bombay • 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

IIT Bombay 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

IIT Bombay 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

IIT Bombay Impedance cells

IIT Bombay Details of a typical Impedance Cell Analysis of experimentally Plate electrode Perspex box obtained impedance data can be done by: Cole-Cole plot Nyquist plot----widely employed Specimen 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 '

IIT Bombay 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   polarization 60 - Z   40 20 R 0 0 20 40 60 80 100 120   Z 

IIT Bombay Development of Equivalent Circuits Fitting Circuits to Impedance Data Using Z-view software (Johnson, 2003) 5 EXP CKT1 4 3 -Z'' (  10 4  ) 2 1 0 Z' (  10 4  )

IIT Bombay 20 R gb 18 R g 16 14 The soil can be characterized as a granular material, if R gb is negligible or 12 3  very low. R (  10 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  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.

IIT Bombay 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  ) 1 0 0 1 2 3 4 5 0 1 2 3 4 5 Z' (  10 4  )

IIT Bombay 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

IIT Bombay 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

IIT Bombay 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