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, 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"
Soils: An Electrical View
Fluids - Water Mass Bulk stiffness Capillary forces Seepage rate Dipole Hydration and double layers Cl - H + 109 o H+ 150 120 90 60 30 150 120 90 60 30 Cl - C 4+ Cl - 180 0 180 0 Cl - O 2-210 330 240 300 270 210 240 270 330 300 L=1.25r L=10r
Electrical View of Soils dry soil water wet soil pore fluid Precipitated salt mineral double layer
Wet clay Laponite 1200 H 2 O 24 Na + N. Skipper (UCL)
Electromagnetic Waves
Maxwell s Equations Gauss' Law of Electricity surf E ds dv free vol free v E 1 v Gauss' Law of Magnetism surf H ds 0 H 0 Faraday's Law of Induction loop d E dl H ds dt surf E dh dt Ampere-Maxwell's Law d H dl J ds E ds dt loop surf surf H E de dt
Electromagnetic Parameters Free space Materials Conductivity 0 Permittivity ε o ε* = ε - j ε Permeability o = - j
Wave Equation 2 E E t 2 t E 2 in real materials Consider solution of the form (fluctuates in y - propagates in x) E E e e y o x (j t x ) Then j j 2
if E E e e y o x (j t x ) Faraday E dh dt * * H j E e j E then j t * x z o y y x z
Phase Velocity V ph Im( j ) Im j 2 In free space o o 0 ph o 1 8 m V c 3 10 o o s In non-ferromagnetic dielectric o ' 0 V ph c o ' o
Attenuation Re j Re j 2 In free space o o 0 0 In non-ferromagnetic material o ' j " o ' 1 c 2 1 tan 1 o 2
Electromagnetic Spectrum Frequency [Hz] Wave Wave length [m] 10 22 10-14 10 21 Gamma rays 10-13 10 20 10-12 10 19 10-11 10 18 X rays 10-10 10 17 10-9 10 16 Ultraviolet 10-8 10 15 10-7 10 14 Visible * 10-6 10 13 Infrared 10-5 10 12 10-4 10 11 Microwaves 10-3 10 10 10-2 GHz 10 9 10-1 10 8 1 10 7 10 1 MHz 10 6 10 2 10 5 Radio waves 10 3 10 4 10 4 KHz 10 3 10 5 10 2 10 6 10 1 10 7
and God said: E H E H 1 0 free v dh dt de E dt and there was light!
Light-surface interaction (Atlanta Airport) and blue butterflies?
Reflection Fresnel s Ellipse van Gogh - La Nuit Etoilee
Scatter St. Peter - Rome
Electromagnetic Material Properties
Electromagnetic Parameters Conductivity Permittivity ε* = ε - j ε Permeability = - j
Note: Losses Ohmic conduction losses Polarization losses ε ω Magnetization losses ω Non-Ferromagnetic tan " '
Conductivity charges & mobility
conductivity [S/m] Electrical Conductivity of the Pore Fluid 40 30 20 10 CaCl 2 NaCl NaOH 0 0 2 4 6 8 10 12 concentration [mol/l] At low concentration (P. Annan): [ms /m] 0.15 TDS[mg /L] fl
Archie s Law? soil n el
Electrical Conductivity Pore fluid Surface conduction Wet Soil soil n el 1 n g S s
mixture conductivity, mix [S/m] Electrical Conductivity of Soils 1 c = 0.1 mol/l soil n fl Archie 0.1 0.01 c = 10-5 mol/l soil n fl 1 n S s 0.001 0.4 0.5 0.6 0.7 0.8 0.9 1 porosity, n
Summary 10 0 Controlled by (1-n) gs s el= soil soil [S/m] clays Controlled by eln 10-3 S s sands 10-6 10-3 10 0 de-ionized water fresh water sea water el [S/m]
soil [S/m] Summary: Electrical Conductivity Controlled by (1-n) 2 g λs s el= soil 10 0 Controlled by n el clays 10-3 S s sands 10-6 10-3 10 0 de-ionized water fresh water sea water el [S/m]
Permittivity Polarizability
Single phase Direction of Applied Field Electronic (resonance) Ionic (resonance) Orientational (relaxation) t =10-16 s (Ultraviolet) t =10-13 s (Infrared) - 12 t = 9 10 s (Microwave water)
Polarization spectrum 200 200 150 150 spatial 100 100 ' orientational ionic electronic 50 50 0 0 conduction losses polarization losses " 50 1 10 100 1 10 3 1 10 4 1 10 5 1 10 6 1 10 7 1 10 8 1 10 9 1 10 10 1 10 11 1 10 12 1 10 13 1 10 14 1 10 15 1 10 16 1 10 17 1 10 18 1 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 frequency [Hz]
Water-Ion Interaction 90 80 f = 1.3 GHz 70 KCl ' 60 50 FeCl 3 LiCl 40 30 20 NaCl CaCl 2 0 1 2 3 4 5 6 ionic concentration [mol/l]
Double layer effects Direction of Applied Field Stern layer Bound water (relaxation) (Infrared) Double layer (deionized) (Radio frequency) Double layer (electrolyte) Double layer - Normal particle interactions (surface conduction)
Two-phase media - Spatial polarization Direction of Applied Field (no relaxation) Maxwell relaxation Wagner relaxation Semi-permeable membrane
Polarizations log(size/m) 0 mixture (interfacial polarization - relaxation) macrospace polarization single phase material -3-6 micro-space polarization double layer scatter grain bound. visible range -9-12 molecular orient. relax ionic reson. electronic resonance -15-3 0 3 6 9 12 15 log(frequency/hz)
Summary: Relative Permittivity ice ~3 most organic fluids 2-6 water 78 air, gasses ~1 minerals 5-10 1 n n 1 S ns Linear mixture ' ' ' soil m w 1 n n 1 S ns ' ' ' soil m w 2 CRIM ' 2 3 soil 3.03 9.3 v 146.0 v 76.7 v Topp et al. 1980
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
Permittivity Free Water - Consolidation Orientational Pol. 40 35 1.3 GHz 0.20 GHz DeLoor (Table 11.9) ' 30 ' 25 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62 2.6 2.4 Volumetric local volumetric Water water Content content (a) 1.E+07 1.E+06
Summary: Soils VOLUMETRIC WATER CONTENT ' 2.6 1.6n 7.9 v 2 ' 40 v 3.9 44.8 392 v 1600 2 v ' 1.40 87.6 v 18. 7 2 v ' 3.03 9.3 2 v 146.0 v 76. 7 3 v ' 3.14 23.8 v 16. 0 2 v ' 3.3 41.4 v 16. 0 2 v
real relative permittivity [ ] Summary 90 80 70 60 50 40 30 20 10 Kaolinite Bentonite Mixed clays Sands and silts Topp et al. (1980) Based on CRI - S=100% Selig and Mansukhani (1975) Wang (1980) Wensink (1993) 0 0 20 40 60 80 100 volumetric water content [%]
Permeability Magnetizability
Kingston Fossil Plant (12/22/2008) [Photo: U.S. Environmental Protection Agency]
XRD: Mill Creek Hopper Magnetically separated fraction: hematite Fe 2 O 3 (weakly magnetic), magnetite Fe 3 O 4 and maghemite Fe 2 O 3 (both strongly magnetic).
Magnetization Electron orbits orbit alignment Diamagnetism Electron spin unpaired Paramagnetism Alignment within domains move domain walls Ferromagnetism domain 1 wall domain 2
Permeability iron fillings in kaolinite f = 10 khz 3 2.5 μ rel = 1 + 4 v Fe + 7 v Fe ' rel 2 Maxwell μ rel = 1 + 3 v Fe 1.5 Wagner 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 volume fraction of iron filings
Permeability iron in kaolinite f = 10 khz ' rel 2.2 2 1.8 1.6 1.4 1.2 1 (a) (b) (c) (d) (e) (f) (g) 0.5 10 2 10 3 10 4 10 5 10 6 10 7 frequency [Hz] " rel 0.4 0.3 0.2 Series1 (a) Series2 (b) Series3 (c) Series4 (d) Series5 (e) Series6 (f) Series7 (g) 0.1 0 10 2 10 3 10 4 10 5 10 6 10 7 frequency [Hz]
Summary Single materials water, quartz, kaolinite (diamagnetic) montmorillonite, illite, granite, hematite (paramagnetic) nickel, iron (ferromagnetic) '/ o ~0.9999 1.00002-1.0005 > 300 Predictive relations spherical ferromagnetic inclusions Kaolinite with iron filings (at 10 khz) 1 3v Fe 1 4v 7v Fe 2 Fe for v Fe <0.2 for v Fe <0.3
Measurement
Testing Quasi-DC Standing wave f res Wave propagation f R, C, L Complex Reflectivity V α
Quasi-static
Circuit Elements - Impedance Resistor (R) Capacitor (C) Inductor (L) V i R V 1 j i C V i j L Z* V i R j L 1 C Z* V i 1 R 1 j C
Laboratory measurements V 1 SG V 2
Depth [cm] Laboratory: Electrical Needle SG Varved Clay 0 V S R fix -1-2 -3 V N -4-5 -6-7 -8-9 X-Ray -10 2 4 6 8 Resistance [k ]
Depth [cm] Depth [cm] Lab-scale 0 0-1 -1-2 -2-3 -3-4 -4-5 -5-6 -6-7 -7-8 -8-9 -9-10 2 4 6 8 Resistance [k ] -10 2 4 6 8 Resistance [k ] X-Ray Photograph Needle probe measurements GC. Cho
Numerical and Experimental Study high conductivity anomaly 2 1 16 2 1 16 3 15 3 15 4 14 4 14 5 13 5 13 6 12 6 12 7 11 7 11 8 9 10 8 9 10 JY Lee see also Fotti et al.
WAVE PROPAGATION
Laboratory measurements
Penetration depth [cm] TDR Probe Honeycombs Reflection at the probe tip 5 10 Fresh concrete 15 20 Coarse aggregate (honeycomb) 25 Fresh concrete 30-2 0 2 4 6 8 10 12 14 16 18 20 22 24 Time (10-9 sec) Cone in TDR-mode MS Cha
Field Devices Typical Data
Resistivity measurement / imaging Syscal Kid Switch 24 Resistivity range: 0.001 to 10,000 Ohm meter Depth less than 70m Typical pulse duration: ~0.5s to 2s. (images from http://www.terraplus.com)
EM devices (conductivity) EM38 Ground Conductivity Instrument Very shallow (~<1m) Conductivity range: 100, 1000mS/m Frequency 14.6kHz 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 Geonics (Mississauga): http://web.idirect.com/~geonics/index.html Images from the Terraplus (Colorado) site: http://www.terraplus.com
Ground Penetrating Radar (permittivity conductivity and permeability) Pulse EKKO 1000 antenna frequencies; 110, 225, 450, 900, 1200 MHz Pulse EKKO 100 antenna frequencies; 12.5, 25, 50, 100, and 200 MHz (also borehole) Borehole Antennas (50, 100, 200 MHz) Sensors and Software (Mississauga)
GPR - 2D & 3D www.sensoft.ca
GPR on Ice www.sensoft.ca
GPR: Saltwater Intrusion www.sensoft.ca
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 S d S d when el Use volumetric water content consolidation advect./diffus. fluid fronts salt water intrusion freezing fronts hydrates spatial variability buried anomalies