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Aussois 2012 ELECTROMAGNETIC WAVES and particulate materials J. Carlos Santamarina Georgia Institute of Technology References: Santamarina, J.C., in collaboration with Klein, K. and Fam, M. (2001). Soils and Waves, J. Wiley and Sons,

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SLIDE 1

ELECTROMAGNETIC WAVES

and particulate materials

  • J. Carlos Santamarina

Georgia Institute of Technology

Aussois 2012

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SLIDE 2

References: Santamarina, J.C., in collaboration with Klein, K. and Fam, M. (2001). Soils and Waves, J. Wiley and Sons, Chichester, UK, 488 pages. Klein, K. and Santamarina, J. C. (2003b). "Electrical Conductivity In Soils: Underlying Phenomena." Journal of Environmental & Engineering Geophysics, Vol. 8, No. 4, pp. 263-273. Klein, K. and Santamarina, J. C. (1997). "Methods for Broad-Band Dielectric Permittivity Measurements (Soil- Water Mixtures, 5 Hz to 1.3 GHz)." ASTM Geotechnical Testing Journal, Vol. 20, No. 2, pp. 168-178. Santamarina, J. C. and Fam, M. (1997b). "Dielectric Permittivity of Soils Mixed with Organic and Inorganic Fluids (0.02 GHz to 1.30 GHz)." Journal of Environmental & Engineering Geophysics, Vol. 2, No. 1, pp. 37-52. Santamarina, J. C. and Fam, M. (1995). "Changes in Dielectric Permittivity and Shear Wave Velocity During Concentration Diffusion." Canadian Geotechnical Journal, Vol. 32, No. 4, pp. 647-659. Some pdfs (these and related papers) available at http://pmrl.ce.gatech.edu under "Publications"

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SLIDE 3

Soils: An Electrical View

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SLIDE 4

Fluids - Water

Mass Bulk stiffness Capillary forces Seepage rate Dipole Hydration and double layers

O2- H+ H+ 109o

30 60 90 120 150 180 210 240 270 300 330

L=1.25r

30 60 90 120 150 180 210 240 270 300 330

L=10r Cl- Cl- Cl- Cl- C4+

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SLIDE 5

Electrical View of Soils

Precipitated salt mineral

dry soil water

pore fluid

wet soil

double layer

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SLIDE 6

Wet clay

Laponite 1200 H2O 24 Na+

  • N. Skipper (UCL)
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SLIDE 7

Electromagnetic Waves

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SLIDE 8

Maxwell’s Equations

free v surf vol

d dv E s E s

free v

1 E

surf

H d s

H

loop surf

d d H d dt E l s

dt dH E

loop surf surf

d d d d dt H l J s E s

dt dE E H

Gauss' Law of Electricity Gauss' Law of Magnetism Faraday's Law of Induction Ampere-Maxwell's Law

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SLIDE 9

Conductivity Permittivity εo ε* = ε’ - j ε” Permeability

  • = ’ - j ”

Electromagnetic Parameters

Free space Materials

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SLIDE 10

Wave Equation

2 2 2

t t E E E E E

x ( j t x ) y

  • E

E e e

Consider solution of the form (fluctuates in y - propagates in x) Then

2

j j

in real materials

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SLIDE 11

x ( j t x ) y

  • E

E e e

if

dH dt E

Faraday then

j t * x z

  • y

* * H j E e j E

x y z

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SLIDE 12

ph 2

V Im( j ) Im j Phase Velocity

In free space

  • 8

ph

  • 1

m V c 3 10 s

In non-ferromagnetic dielectric

  • '
  • ph
  • c

V '

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SLIDE 13

Attenuation

In free space

  • In non-ferromagnetic material
  • '

j "

2

Re j Re j

  • 2
  • '

1 1 tan 1 c 2

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SLIDE 14

Frequency [Hz] Wave Wave length [m] 1022 10-14 1021 Gamma rays 10-13 1020 10-12 1019 10-11 1018 X rays 10-10 1017 10-9 1016 Ultraviolet 10-8 1015 10-7 1014 Visible * 10-6 1013 Infrared 10-5 1012 10-4 1011 Microwaves 10-3 1010 10-2 GHz 109 10-1 108 1 107 101 MHz 106 102 105 Radio waves 103 104 104 KHz 103 105 102 106 101 107

Electromagnetic Spectrum

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SLIDE 15

free v

1 E

H dt dH E

dt dE E H

and God said: and there was light…!

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SLIDE 16
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SLIDE 17

Light-surface interaction (Atlanta Airport) and blue butterflies?

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SLIDE 18

van Gogh - La Nuit Etoilee

Fresnel’s Ellipse

Reflection

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SLIDE 19
  • St. Peter - Rome

Scatter

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SLIDE 20

Electromagnetic Material Properties

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SLIDE 21

Conductivity Permittivity ε* = ε’ - j ε” Permeability = ’ - j ”

Electromagnetic Parameters

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SLIDE 22

Ohmic conduction losses Polarization losses ε”ω Magnetization losses ”ω

Note: Losses

" tan '

Non-Ferromagnetic

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SLIDE 23

Conductivity  charges & mobility

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SLIDE 24

Electrical Conductivity of the Pore Fluid

10 20 30 40 2 4 6 8 10 12 concentration [mol/L] conductivity [S/m]

NaOH NaCl CaCl2

At low concentration (P. Annan):

] L / mg [ TDS 15 . ] m / mS [

fl

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SLIDE 25

Archie’s Law?

el soil

n

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SLIDE 26

Electrical Conductivity

Surface conduction Pore fluid Wet Soil

s g el soil

S n 1 n

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SLIDE 27

0.001 0.01 0.1 1 0.4 0.5 0.6 0.7 0.8 0.9 1 porosity, n mixture conductivity,

mix [S/m]

c = 0.1 mol/L c = 10-5 mol/L

Electrical Conductivity of Soils

Archie s fl soil

S n 1 n

fl soil

n

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SLIDE 28

Summary

10-6 10-3 100 10-3 100 Controlled by

eln

Ss clays sands

soil [S/m] el [S/m]

el= soil

de-ionized water fresh water sea water Controlled by (1-n)

gSs

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SLIDE 29

Summary: Electrical Conductivity

10-6 10-3 100 10-3 100

Controlled by n

el

clays

sands

soil [S/m] el [S/m]

el= soil

de-ionized water fresh water sea water

Controlled by (1-n) 2

g λSs

Ss

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SLIDE 30

Permittivity  Polarizability

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SLIDE 31

Single phase

Electronic (resonance) t =10

  • 16 s

(Ultraviolet) Ionic (resonance) t =10

  • 13

s

(Infrared) Orientational (relaxation) t = 9 × 10

  • 12

s

(Microwave – water) Direction of Applied Field

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SLIDE 32

Polarization spectrum

1 10 100 1 103 1 104 1 105 1 106 1 107 1 108 1 109 1 10101 1011 1 10121 10131 1014 1 10151 1016 1 10171 1018 50 50 100 150 200

frequency [Hz] " ' spatial

  • rientational

ionic electronic polarization losses conduction losses 1 102 104 106 108 1010 1012 1014 1016 1018

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SLIDE 33

Water-Ion Interaction

20 30 40 50 60 70 80 90 1 2 3 4 5 6

'

ionic concentration [mol/L]

CaCl2 NaCl KCl LiCl FeCl3

f = 1.3 GHz

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SLIDE 34

Double layer effects

Stern layer (Infrared) Bound water (relaxation) (Radio frequency) Double layer (deionized) Double layer (electrolyte) Double layer - Normal particle interactions (surface conduction) Direction of Applied Field

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SLIDE 35

Two-phase media - Spatial polarization

(no relaxation) Maxwell relaxation Wagner relaxation Direction of Applied Field Semi-permeable membrane

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SLIDE 36

Polarizations

single phase material mixture log(frequency/Hz)

  • 3 0 3 6 9 12 15
  • 3
  • 6
  • 9
  • 12
  • 15

visible range electronic resonance ionic reson. molecular

  • rient.

relax scatter grain bound. micro-space polarization double layer macrospace polarization

(interfacial polarization - relaxation) log(size/m)

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SLIDE 37

Summary: Relative Permittivity

water 78 ice ~3 most organic fluids 2-6 air, gasses ~1 minerals 5-10

2 ' ' '

1 1

soil m w

n n S nS

' 2 3

3.03 9.3 146.0 76.7

soil v v v

Topp et al. 1980 CRIM

' ' ' m

1 1

soil w

n n S nS

Linear mixture

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SLIDE 38

Summary: Single materials

water 78.5 methanol 32.6 most organic fluids 2 - 6 quartz 4.2 - 5 calcite 7.7 - 8.5 most minerals 6 – 10

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SLIDE 39

Free Water - Consolidation

Orientational Pol.

25 30 35 40 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62 local volumetric water content 1.3 GHz 0.20 GHz DeLoor ' s (Table 11.9) Volumetric Water Content Permittivity

'

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SLIDE 40

Summary: Soils

2 v v

7 . 18 6 . 87 40 . 1 '

3 v 2 v v

7 . 76 . 146 3 . 9 03 . 3 '

2 v v

. 16 4 . 41 3 . 3 '

2 v v

. 16 8 . 23 14 . 3 '

2 v v v

1600 392 8 . 44 9 . 3 40 '

2 v

9 . 7 n 6 . 1 6 . 2 '

VOLUMETRIC WATER CONTENT

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SLIDE 41

Summary

10 20 30 40 50 60 70 80 90 20 40 60 80 100

volumetric water content [%] real relative permittivity [ ]

Kaolinite Bentonite Mixed clays Sands and silts Topp et al. (1980) Selig and Mansukhani (1975) Wang (1980) Wensink (1993) Based on CRI - S=100%

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SLIDE 42

Permeability  Magnetizability

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SLIDE 43

[Photo: U.S. Environmental Protection Agency]

Kingston Fossil Plant (12/22/2008)

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SLIDE 44
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SLIDE 45

XRD: Mill Creek Hopper

Magnetically separated fraction: hematite Fe2O3 (weakly magnetic), magnetite Fe3O4 and maghemite Fe2O3 (both strongly magnetic).

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SLIDE 46

Magnetization

Electron orbits

  • rbit alignment

Diamagnetism Electron spin unpaired Paramagnetism Alignment within domains move domain walls Ferromagnetism

domain 1 domain 2 wall

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SLIDE 47

Permeability

iron fillings in kaolinite – f = 10 kHz

'

rel

volume fraction of iron filings

0.05 0.1 0.15 0.2 0.25 0.3 0.35

1 1.5 2 2.5 3

μ’rel= 1 + 4 vFe+ 7 vFe μ’rel= 1 + 3 vFe Maxwell Wagner

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SLIDE 48

Permeability

iron in kaolinite – f = 10 kHz

0.1 0.2 0.3 0.4 0.5 102 103 104 105 106 107 Series1 Series2 Series3 Series4 Series5 Series6 Series7

1 1.2 1.4 1.6 1.8 2 2.2

(a) (b) (c) (d) (e) (f) (g) (a) (b) (c) (d) (e) (f) (g) frequency [Hz] frequency [Hz] "

rel

'

rel

102 103 104 105 106 107

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SLIDE 49

Summary

Fe

1 3v

2 Fe Fe

1 4v 7v

Single materials water, quartz, kaolinite

(diamagnetic)

~0.9999 montmorillonite, illite, granite, hematite

(paramagnetic)

1.00002-1.0005 nickel, iron

(ferromagnetic)

> 300 Predictive relations spherical ferromagnetic inclusions for vFe<0.2 Kaolinite with iron filings (at 10 kHz) for vFe<0.3

  • '/
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SLIDE 50

Measurement

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SLIDE 51

Testing

f

Quasi-DC Wave propagation Standing wave

fres

R, C, L Complex Reflectivity V α

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SLIDE 52

Quasi-static

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SLIDE 53

V R i

V j L i V 1 j i C

Resistor (R) Inductor (L) Capacitor (C)

C j R 1 1 i V * Z C 1 L j R i V * Z

Circuit Elements - Impedance

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SLIDE 54

Laboratory measurements

SG V1 V2

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SLIDE 55
  • 10
  • 9
  • 8
  • 7
  • 6
  • 5
  • 4
  • 3
  • 2
  • 1

2 4 6 8 Resistance [k ] Depth [cm]

X-Ray

Varved Clay

Laboratory: Electrical Needle

Rfix VN VS SG

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SLIDE 56

Photograph X-Ray

Lab-scale

  • 10
  • 9
  • 8
  • 7
  • 6
  • 5
  • 4
  • 3
  • 2
  • 1

2 4 6 8 Resistance [k ] Depth [cm]

  • 10
  • 9
  • 8
  • 7
  • 6
  • 5
  • 4
  • 3
  • 2
  • 1

2 4 6 8 Resistance [k ] Depth [cm]

Needle probe measurements

  • GC. Cho
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SLIDE 57

1 2 3 16 15 14 13 12 11 10 9 8 7 6 5 4 1 2 3 16 15 14 13 12 11 10 9 8 7 6 5 4

Numerical and Experimental Study

high conductivity anomaly

JY Lee see also Fotti et al.

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SLIDE 58

WAVE PROPAGATION

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SLIDE 59

Laboratory measurements

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SLIDE 60

TDR Probe – Honeycombs

Coarse aggregate

(honeycomb)

Fresh concrete Fresh concrete Time (10-9 sec)

  • 2

2 4 6 8 10 12 14 16 18 20 22 24

Reflection at the probe tip

Penetration depth [cm]

5 20 25 30 10 15

Cone in TDR-mode

MS Cha

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SLIDE 61

Field Devices Typical Data

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SLIDE 62

Syscal Kid Switch 24 Resistivity range: 0.001 to 10,000 Ohm meter Depth less than 70m Typical pulse duration: ~0.5s to 2s.

Resistivity measurement / imaging

(images from http://www.terraplus.com)

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SLIDE 63

EM38 Ground Conductivity Instrument Very shallow (~<1m) Conductivity range: 100, 1000mS/m Frequency 14.6kHz Geonics (Mississauga): http://web.idirect.com/~geonics/index.html Images from the Terraplus (Colorado) site: http://www.terraplus.com EM 34 - Ground Conductivity Instrument Shallow (<60 m) Intercoil spacing and operating frequency: 10m at 6.4kHz, 20m at 1.6kHz, 40m at 0.4kHz Conductivity Ranges 10, 100, 1000 mS/m

EM devices (conductivity)

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SLIDE 64

Sensors and Software (Mississauga) Borehole Antennas (50, 100, 200 MHz) Pulse EKKO 100 antenna frequencies; 12.5, 25, 50, 100, and 200 MHz (also borehole) Pulse EKKO 1000 antenna frequencies; 110, 225, 450, 900, 1200 MHz

Ground Penetrating Radar

(permittivity … conductivity and permeability)

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SLIDE 65

GPR - 2D & 3D

www.sensoft.ca

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SLIDE 66

GPR on Ice

www.sensoft.ca

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SLIDE 67

www.sensoft.ca

GPR: Saltwater Intrusion

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SLIDE 68

Summary: EM-waves

typically non-ferromagnetic caution otherwise (e.g., some mine waste, fly ash) ionic concentration … and mobility fresh water: clay surface conduction Simple measurement: ERT, Needle Probe (invasive) free water orientation (microwave frequency) GPR TDR probe (invasive) V V when

el and

Sd Sd when

el

Use volumetric water content consolidation advect./diffus. fluid fronts salt water intrusion freezing fronts hydrates spatial variability buried anomalies