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ELECTROMAGNETIC WAVES and particulate materials
J. Carlos Santamarina Georgia Institute of Technology
Aussois 2012
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"
Fluids - Water
Mass
Bulk stiffness
Capillary forces
Seepage rate
Dipole
Hydration and double layers
O2-
H+ H+ 109o
0
30
60 90
120
150
180
210
240 270
300
330
L=1.25r
0
30
60 90
120
150
180
210
240 270
300
330
L=10r
Cl-
Cl-
Cl-
Cl-
C4+
Maxwell’s Equations
free
v
surf vol
d dvE s freev
1E
surf
H d 0s 0H
loop surf
dd H d
dtE l s
dt
dHE
loop surf surf
dd d d
dtH l J s E s
dt
dEEH
Gauss' Law of Electricity
Gauss' Law of Magnetism
Faraday's Law of Induction
Ampere-Maxwell's Law
Conductivity 0
Permittivity εo ε* = ε’ - j ε”
Permeability o = ’ - j ”
Electromagnetic Parameters
Free
space Materials
Wave Equation
22
2t t
E EE
x (j t x)
y oE E e e
Consider solution of the form (fluctuates in y - propagates in x)
Then 2j j
in real
materials
ph2
VIm( j ) Im j
Phase Velocity
In free space
o o 0
8
ph o
o o
1 mV c 3 10s
In non-ferromagnetic dielectric
o ' 0
oph
o
cV
'
Attenuation
In free space
o o 00
In non-ferromagnetic material
o ' j "
2Re j Re j
o 2
o
'
11 tan 1
c 2
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
Ohmic conduction losses
Polarization losses ε”ω
Magnetization losses ”ω
Note: Losses
"tan
'Non-Ferromagnetic
Electrical Conductivity of the Pore Fluid
0
10
20
30
40
0 2 4 6 8 10 12
concentration [mol/L]
conductivity [S
/m]
NaOH
NaCl
CaCl2
At low concentration (P. Annan): ]L/mg[TDS15.0]m/mS[fl
0.001
0.01
0.1
1
0.4 0.5 0.6 0.7 0.8 0.9 1
porosity, n
mix
ture
con
du
ctiv
ity
, m
ix [
S/m
]
c = 0.1 mol/L
c = 10-5 mol/L
Electrical Conductivity of Soils
Archie
sflsoil Sn1n
flsoil n
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
Summary: Electrical Conductivity
10-6 10-3 100
10-3
100
Controlled by n el
clays
sands
so
il
[S
/m]
el [S/m]
el= soil
de-ionized
water
fresh
water
sea
water
Controlled by (1-n) 2 g λSs
Ss
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
Polarization spectrum
1 10 100 1 103
1 104
1 105
1 106
1 107
1 108
1 109
1 1010
1 1011
1 1012
1 1013
1 1014
1 1015
1 1016
1 1017
1 1018
50
0
50
100
150
200
frequency [Hz]
"
'
spatial
orientational
ionic electronic
polarization
losses
conduction
losses
1 102 10
4 10
6 10
8 10
10 10
12 10
14 10
16 10
18
200
150
100
50
0
Water-Ion Interaction
20
30
40
50
60
70
80
90
0 1 2 3 4 5 6
'
ionic concentration [mol/L]
CaCl2
NaCl
KCl
LiCl FeCl3
f = 1.3 GHz
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
Two-phase media - Spatial polarization
(no relaxation) Maxwell relaxation
Wagner relaxation
Direction of Applied Field
Semi-permeable membrane
Polarizations
single phase material mixture
log(frequency/Hz)
-3 0 3 6 9 12 15
0
-3
-6
-9
-12
-15
visible
range
electronic
resonance
ionic
reson.
molecular
orient.
relax
scatter
grain
bound.
micro-space
polarization
double layer
macrospace
polarization
(interfacial polarization - relaxation)
log(size/m)
Summary: Relative Permittivity
water 78
ice ~3
most organic fluids 2-6
air, gasses ~1
minerals 5-10
2' ' '1 1soil m wn n S nS
' 2 33.03 9.3 146.0 76.7soil v v v Topp et al. 1980
CRIM
' ' '
m1 1soil wn n S nS Linear mixture
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
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
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
0.48 0.51 0.54 0.57 0.6 0.63
local volumetric water content
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
stre
ss [k
Pa]
'
"eff
(b)
(a)
stress
(Table 11.9)
Volumetric Water Content
Perm
itti
vit
y
'
Summary: Soils
2vv 7.186.8740.1'
3v
2vv 7.760.1463.903.3'
2vv 0.164.413.3'
2vv 0.168.2314.3'
2vvv 16003928.449.340'
2
v9.7n6.16.2'
VOLUMETRIC WATER CONTENT
Summary
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100volumetric water content [%]
real
rel
ativ
e per
mitt
ivity
[ ]
Kaolinite
Bentonite
Mixed clays
Sands and silts
Topp et al. (1980)
Selig and Mansukhani (1975)
Wang (1980)
Wensink (1993)
Based on CRI - S=100%
XRD: Mill Creek Hopper
Magnetically separated fraction:
hematite Fe2O3 (weakly magnetic), magnetite Fe3O4 and maghemite Fe2O3 (both strongly magnetic).
Magnetization
Electron orbits orbit alignment Diamagnetism
Electron spin unpaired Paramagnetism
Alignment within domains move domain walls Ferromagnetism
domain 1 domain 2 wall
Permeability iron fillings in kaolinite – f = 10 kHz
' rel
volume fraction of iron filings
0 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
Permeability iron in kaolinite – f = 10 kHz
0
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
Summary
Fe1 3v
2
Fe Fe1 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
o'/
VR
i
Vj L
i
V 1j
i C
Resistor (R) Inductor (L) Capacitor (C)
CjR
1
1
i
V*Z
C
1LjR
i
V*Z
Circuit Elements - Impedance
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
2 4 6 8
Resistance [k ]
Dep
th [
cm
]
X-Ray
Varved Clay
Laboratory: Electrical Needle
Rfix
VN
VS
SG
Photograph X-Ray
Lab-scale
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
2 4 6 8
Resistance [k ]
Dep
th [
cm
]
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
2 4 6 8
Resistance [k ]
Dep
th [
cm
]
Needle probe measurements GC. Cho
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.
TDR Probe – Honeycombs
Coarse
aggregate (honeycomb)
Fresh
concrete
Fresh
concrete
Time (10-9 sec) -2 0 2 4 6 8 10 12 14 16 18 20 22 24
Reflection at the probe tip
Pen
etr
ati
on
dep
th [
cm
]
5
20
25
30
10
15
Cone in TDR-mode MS Cha
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)
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)
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)
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
Recommended