# Geophysical Characterization

Mechanics

Jul 18, 2012 (5 years and 10 months ago)

754 views

1
Geophysical
14
th
Pan-American Conference
Toronto – October 2011
Characterization
J. Carlos Santamarina
Georgia Institute of Technology
Energy Geo-Technology: Gas Fields
5km
500ms
J. Cartwright - www.3DLab.org.uk
New Phenomena: Polygonal Faults
500m
100m
J. Cartwright - www.3DLab.org.uk
New Phenomena: Polygonal Faults
200m
J. Cartwright - www.3DLab.org.uk
Massive Landslide - Storegga
J. Cartwright - www.3DLab.org.uk
Norwegian Sea
~6100 BC
3500 km
3
Bridge in Biloxi – Post Katrina
Before Katrina After Katrina
2
Biloxi
D’Iverville
I-110 Bridge
Cap 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Bridge in Biloxi – Post Katrina Scouring
Bathymetry: 200 kHz
Sub bottom profiling: 20 kHz
D. Fratta
GPR - 2D & 3D
www.sensoft.ca
Hearing
Sight
Thermoception
Mechanical
Waves
Electromagnetic
Waves
description
estimation
lab & field
examples
Thermal
Phenomena
Concepts & Caveats
! ! !
examples

(process monitoring)
Mechanical Waves
Electromagnetic Waves
D
V
P
V
s
Thermal Phenomena
Concepts & Caveats
! ! !
Newtonian Mechanics: F=ma
( )

+

+

+

∂∂

+
∂∂

+

−=

ρ
2
x
2
2
x
2
2
x
2
z
2
y
2
2
x
2
2
x
2
z
u
y
u
x
u
G
zx
u
yx
u
x
u
GM
t
u
G
x
u
x
xu
y
Longitudinal
Transverse
+
= =
ρ ρ
P
4
B G
M
3
V
=
ρ
S
G
V
3
Mechanical Waves
attenuation
S-waves
P-waves
1: Effective Stress
σ’ increases
σ’=1.4
σ’=10.1
σ’=27.4
σ’=62.1
σ’=131.5
σ’=270.3
σ’=409.1
σ’ decreases
σ
’=603.9
σ’=798.8
σ’=1062.5
σ’=798.8
σ’=603.9
σ’=409.1
σ’=270.3
σ’=131.5
σ’=62.1
σ’=27.4
σ’=10.1
σ’=1.4
[sec]
β

σ + σ
α
a
yx
S
P2
''
= V
Very soft clays

σ
kPa
'
log

sm
V
log
1: Effective Stress
β= 0.36 - α/700
0.10
0.20
0.30
0.
100
200
α-factor [m/s]
βexponent
Very

soft

clays
Sands
OC clays
Cemented soils
800
1000
1200
c
ity [m/s]
2: Suction - Unsaturated Soils
β

⋅+σ
α≈
a
rm
S
P
suctionS
V
0
200
400
600
800
0.0 0.2 0.4 0.6 0.8 1.0
Degree of saturation S
Shear wave velo
c
3: Cementation
σ’ increases
sand 4% cement
σ’=18.7
σ’=36.0
σ’=70.7
σ’=140.1
σ’=278.9
σ’=417.7
σ’=612.5
Cementation
Stress
σ’ decreases
[sec]
σ’=807.4
σ’=1071.1
σ’=807.4
σ’=612.5
σ’=417.7
σ’=278.9
σ’=140.1
σ’=70.7
σ’=36.0
σ’=18.7

σ
kPa
'
log

sm
V
log
Cementation

controlled
Stress

controlled
σ’ increases
σ’=18.7
σ’=36.0
σ’=70.7
σ’=140.1
σ’=278.9
σ’=417.7
σ

㘱6 5
loose sand – 2% cement

sm
V
log
σ’ decreases
[sec]
σ
612
.
5
σ’=807.4
σ’=1071.1
σ’=807.4
σ’=612.5
σ’=417.7
σ’=278.9
σ’=140.1
σ’=70.7
σ’=36.0
σ’=18.7

σ
kPa
'
log
T.Y. Yun
4
550
600
650
700
s
]
m/s]

sm
V
log
Uncemented
Vs
[m/
s
100
150
200
250
Vs
[
0 100 200 300 400 500
Confining Pressure [kPa]

σ
kPa
'
log
A. Fernandez
3: Sampling effects
0.0
0.5
1.0
1.5
Measurement
error
Sandy Soils
(a)
V
field
V. Rinaldi
0.0
0.5
1.0
1.5
0 200 400 600 800 1000
V
f
[m/s]
Measurement
error
Clayey Soils
(b)
Vlab
/
V
V
field
Laboratory Testing
f
Quasi static Wave propagationStanding wave
f
res
λ >> cell λ ~ cell λ << cell
E or G
E or G
V
P
or V
S
hyteresis
D
α
LDT
Laboratory: Bender Elements
A/D
signal
generator
(λ < cell)
Amp
A/D
DSO
computer
soil
deploy in all soil cells: GREAT additional information
Field: Surface Waves
(non-invasive)
x
x
Active
Sensor Arrays
G. Rix
Pasive
0
5
10
m)
Penetration-based
Field: Penetration-based (invasive)
S-CPTU

g
nals

S-fork
0
5
10
m
)
0
0.1
0.2
0.3
15
20
25
30
Time (sec)
Depth (
P. Mayne
Measured Si
g
JS Lee
0
15
20
25
30
Depth (
m
0 0.2 0.4
Time (msec)
5
Mechanical Waves
attenuation
S-waves
P-waves
Bulk Stiffness
1
r r
fl
w a
S 1 S
B
B B

⎛ ⎞

= +
⎜ ⎟
⎝ ⎠
(
)
fl r a r w
1 S Sρ = − ρ + ρ
Fluid Mixture
P
4
B G
M
3
V
+
= =
ρ ρ
1
sus
g fl
1 n n
B
B B

⎛ ⎞

= +
⎜ ⎟
⎜ ⎟
⎝ ⎠
(
)
sus g fl
1 n nρ = − ρ + ρ
(
)
soil sus g fl
1 n nρ = ρ = − ρ + ρ
Suspension
Soil
(fluid + skeleton)
soil sus sk
B B B
=
+
from G= V
s
2
ρ
Saturation
( )

⎡ ⎤
⎛ ⎞
− −
⎛ ⎞
+ + + +
⎢ ⎥
⎜ ⎟
⎜ ⎟
⎝ ⎠
⎢ ⎥
⎝ ⎠
⎣ ⎦
=
− ρ + ρ
1
sk sk
w a g
P
g w
4 S 1 S 1 n
B G n
3 B B B
V
1 n n S
K. Ishihara
Mechanical Waves
Examples
Monitoring
Porosity
(S=100%)
( )
2
4
g fl fl
Bρ −ρ
ρ ρ
V
P
and V
S
1
V
V
1
V
V
2
1
2
S
P
2
S
P

Poisson's ratio
(~dry)
( )
2 2
1
2
1 2
2
g g
sk
P S
sk
g fl
V V
n
ρ

ρ

⎛ ⎞
− ν

⎜ ⎟
− ν
⎝ ⎠
=
ρ −ρ
see Foti & Lancelotta
Venice (M. Jamiolkowski)
S-monitoring: Liquefaction
P
o
o
st Event Time [s]
Post Event Time [s]
Shea Wave
Velocity [m/s]
6
S-monitoring: Excavation & Retaining Walls
Force [kN]
10
20
30
40
Wall displacement / H
Velocity [m/s]
80
140
200
0%
1%
10
Wall displacement / H
0%
1%
Boulanger
S-monitoring: Tunnels
V
s
(m/s)
A. Fernandez
35
50
65
80
95
110
>125
Paracoccus denitrificans
Nitrate broth
F110 + 3%Kaolin
0 0.1 0.2 0.3 0.
4
Time (ms)
P-monitoring: Bio-gas
1 day
V. Rebata
Summary: P- and S-waves
Waves Small-strain phenomena
May be used to monitor large-strain processes
V
s
Skeletal stiffness: G Geo-mechanical design
Effective stress, suction, cementation
Sampling: pronounced effect measure in situ !
Simple lab & field devices and methods
V
P
Fluid & skeletal stiffness: B & G
Proximity to full saturation
V
P
&Vs: Dry skeletal Poisson's ratio
Saturated porosity
Spatial variability
Mechanical Waves
Electromagnetic Waves
μ
ε
σ
el
Thermal Phenomena
Concepts & Caveats
! ! !
Maxwell’s Equations – Wave Propagation
2
2
2
E E
E
t t

∇ = μσ +με

Conductivity σ
el
Permittivity κ = ε/ε
o
Permeability μ
non-ferromagnetic μ=1
all forms of losses
7
Velocity
non-ferromagnetic

κ+

ωε
σ

=
2
o
2
0
2
1
1
cV
Electromagnetic Wave Propagation
Skin Depth

κ−

ωε
σ

ω
=
2
o
2
0
d
2
1
1
c
S
Electromagnetic Properties
permeability
conductivity
permittivity
Electrical Conductivity of the Pore Fluid
20
30
40
t
ivity [S/m]
NaOH
NaCl
0
10
20
0 2 4 6 8 10 12
concentration [mol/L]
conduc
t
CaCl
2
At low concentration
(P. Annan):
]L/mg[TDS15.0]m/mS[
fl
⋅=σ
Pore fluid (pores)
Electrical Conductivity of Soils

Surface conduction
Wet Soil
(
)
sflsoil
Sn1n
α

+σ=σ

0.1
1
u
ctivity, σmix
[S/m]
c = 0.1 mol/L
Electrical Conductivity of Soils
Archie
flsoil
n σ=σ
β
0.001
0.01
0.4 0.5 0.6 0.7 0.8 0.9 1
porosity, n
mixture cond
u
c = 10
-5
mol/L
( )
sflsoil
Sn1n
α
−+σ=σ
Summary: Electrical Conductivity
10
0
Controlled by nσ
el
[
S/m]
σ
el
=
σ
soil
Controlled by (1-n) 2
ρ
g
λ
S
s
10
-6
10
-3
10
0
10
-3
clays
sands
σsoil
[
σ
el
[S/m]
de-ionized
water
fresh
water
sea
water
S
s
8
-3
-2
-1
0
Varved Clay
Laboratory: Electrical Needle
R
fix
Δ
V
N
V
S
SG
-10
-9
-8
-7
-6
-5
-4
2 4 6 8
Resistance [k
Ω
]
Depth [cm]
X-Ray
N
Laboratory and Field ERT
1
2
3
16
15
14
13
12
11
7
6
5
4
V
2
3
4
5
6
7
8
V
V
V
V
V
V
V
1
16
9
15
14
13
12
11
10
JY Lee
Rao et al 2011
11
10
9
8
7
Electromagnetic Properties
permeability
conductivity
permittivity
Free Water - Consolidation
Orientational Pol.
35
40
1.3 GHz
0.20 GHz
DeLoor
(Table 11.9)
y
κ
25
30
35
0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62
local volumetric water content
κ
Δ
Volumetric Water Content
Permittivit
y
σ' ↑
Permittivity of Wet Soils
50
60
70
80
90
m
ittivity [ ]
Kaolinite
Bentonite
Mixed clays
Sands and silts
v
ity κ
0
10
20
30
40
50
0 20 40 60 80 10
0
volumetric water content [%]
real relative per
m
Volumetric Water Content
Permitti
v
Summary: Relative Permittivity
water 78
ice ~3
most organic fluids 2-6
air, gasses ~1
minerals 5-10
( )
( )
2
'''
1 1

= − + − +

κ κ κ
soil m w
n n S nS
'2 3
3.03 9.3 146.0 76.7= + + −
κ
θ θ θ
soil v v v
Topp et al. 1980
CRIM
(
)
(
)
'''
m
1 1< − + − +
s
oil w
n n S nS
κ
κ κ
Linear mixture
9
TDR Probe – Honeycombs
Coarse
Fresh
concrete
Reflection at the probe tip
p
th [cm]
5
10
Coarse

aggregate
(honeycomb)
Fresh
concrete
Time (10
-9
sec)
-2 0 2 4 6 8 10 12 14 16 18 20 22 24
Penetration de
p
20
25
30
15
Cone in TDR-mode
MS Cha
GPR on Ice
www.sensoft.ca
GPR: Saltwater Intrusion
www.sensoft.ca
Summary: EM-waves
μ typically non-ferromagnetic
caution otherwise (e.g., some mine waste)
σ ionic concentration … and mobility
fresh water: clay surface conduction
Simple measurement: ERT, Elect. Needle Probe (invasive)
κ
free water orientation (new microwave frequency)
κ
free

water

orientation

(new

microwave

frequency)
GPR TDR (invasive)
V V ↓ when σ
el
↑ and κ↑
S
d
S
d
↓ when σ
el

Use volumetric water content consolidation
advect./diffus. fluid fronts salt water intrusion
freezing fronts hydrates
spatial variability buried anomalies
Mechanical Waves
Electromagnetic Waves
Thermal Phenomena
Concepts & Caveats
! ! !
L
c
p
k
T
Thermal Conductivity: Dry vs. Wet Soils
10
v
ity [W/m.K]
saturated
ice 2.21
quartz 8.4
0.1
1
10 100 1000 10000
Effective vertical stress [kPa]
Thermal conducti
v
dry
water 0.72
k= f(w, σ’)
10
0.20
0.25
0.30
0.35
0.40
0.30 0.35 0.40 0.45 0.50 0.55
0.20
0.25
0.30
0.35
0.40
0.30 0.35 0.40 0.45 0.50 0.55
0.20
0.25
0.30
0.35
0.40
0.30 0.35 0.40 0.45 0.50 0.55
Thermal Conductivity: Dry Soils
k[W⋅m-1K-1]
Ottawa 20/30 sand
F110 sand Blasting sand
|Δk/Δn|=0.908
|Δk/Δn|=0.95
|Δk/Δn|=0.654
n
max
n
min
n
min
n
min
n
max
n
max
0.20
0.25
0.30
0.35
0.40
0.30 0.35 0.40 0.45 0.50 0.55
0.20
0.25
0.30
0.35
0.40
0.30 0.35 0.40 0.45 0.50 0.55
0.20
0.25
0.30
0.35
0.40
0.30 0.35 0.40 0.45 0.50 0.55
Porosity, n
Porosity, n
Porosity, n
Porosity, n
Porosity, n
Porosity, n
Crushed sand-I
Crushed sand-II Crushed sand-III
k[W⋅m-1K-1]
|Δk/Δn|=0.935
|Δk/Δn|=0.811
|Δk/Δn|=1.014
n
max
n
max
n
max
k= f(n)
Thermal Conductivity in Soils
particle conduction
contact conduction
mineral
c#, n, σ’
p
article-
p
pore fluid conduction
pore fluid convection
fluid, S%
D
10
p
p
particle-fluid conduction
particle-fluid-part. cond.
Material k
T
(W/mK)
Air 0.02
Water at 21°C 0.72
Ice at 0 °C 2.2
Sand, dry 1.1
Sand, ω= 18% (unfrozen) 3.1
Thermal Conductivity: Values
k
gas
< k
water
< k
ice
Sand, ω= 18% (frozen) 3.8
Clay, dry 0.9
Clay, ω= 25% (unfrozen) 1.2
Clay, ω= 25% (frozen) 1.5
Quartz 8.4
Stainless Steel ~20
Copper 400
k
dry
< k
wet
< k
frozen
k
gas
< k
dry
< k
wet
< k
frozen
< k
min
k
clay
< k
sand
general
trends
Lab & Field: Needle Probe
DC Power supply
Ammeter
Voltmeter
-2.5
-2
[
ºC]
-2.5
-2
[
ºC]
( ) ( )
12
12
TT
tlntln
4
P
k

π
=
Heating wire
thermocouple
-4.5
-4
-3.5
-3
0 10 20 30 40 50 60 70
Time [sec]
Temperature
[
K= 0.61 W/mK
-4.5
-4
-3.5
-3
0 10 20 30 40 50 60 70
Time [sec]
Temperature
[
K= 0.61 W/mK
Application: Climate Change
25 yr 50 yr 100 yr 250 yr 500 yr
0
Period
T
atm
=Sinusoidal (2°C)
200
400
600
Depth [m]
0 2-1
0 2-1 0 2-1 0 2-1 0 2-1
Sacramento, California
Application: Cities = Thermal Islands
science.nasa.gov
11
Conductivity k ↑ Porosity n↓
Effective stress ↑ (heat transfer at contacts ↑)
Quartz content ↑
Frozen
Coarser grains
Summary: Thermal Properties
Coarser

grains
Implications Energy: Geothermal, Nuclear (foundations & waste), …
Climate change
Urban settings
Mechanical Waves
Electromagnetic Waves
Thermal Phenomena
Concepts & Caveats
! ! !
Wave phenomena
Signal processing
Inverse Problems
Fresnel’s Ellipse
Reflection
van Gogh - La Nuit Etoilee
Interference
Audi
Diffraction Healing
defects in piles? honeycombs in concrete? tunnels (KMZ, US-Mx, Israel-Palestine)?
Vertical Heterogeneity
Vertically heterogeneous
Cross-anisotropic
Linear Elastic
Homogeneous
Isotropic
Linear Elastic
12
Signals →Information
Katrina (8/29)
-1
0
1
2
0 10 20 30 40 50 60 70 80 90 100
Days
Water Level [m
]
Pilots Station, Louisiana – NOAA
7/1/05
9/30/05
Signal Processing: FFT
x
i
0
200
400
0.1
1
10
100
X
u
u
i
Fourier Transform = curve-fitting the signal using the Fourier Series (avoid with BE !)
Signal Processing: Tracking Small Changes
e
p
0 kPa
(every 1.4 kPa)
0 1000 2000
Time [μs]
e
70 kPa
0psi
(every 1.4 kPa)
dry Ottawa sand
Signal at 67.57kPa
Signal at 68.95kPa
d
e
9.8psi
10psi
Coda Wave Analysis: Creep in Dry Sand
0 1000 2000 3000 4000
Wave Traveling Time [μs]
Signal Amplitu
d
0 400
1800 2200
3600 4000
direct travel
time
t
D
9-to-11 times of
t
D
18-to-20 times of
t
D
388
390
392
o
city [m/s]
Coda Wave Analysis: Creep in Dry Sand
V
p
= 2 m/s log(t/min) + 384.5 m/s
384
386
388
1 10 100 1000
P-wave vel
o
Time [min]
Inversion: Tomography
Unknown
internal
conditions
?
13
S
1
S
3
S
4

R
1
1
2

Mathematically…
S
2
R
3

R
4
R
2
4
3
11 1 2
1 1
2 3 2 4
2 2
31 3 3
3 3
4 2 4 4
4 4
0 0
1
0 0
1
0 0
1
0 0
1
,,
,,
,,
,,
t/V
t/V
t/V
t/V
⎡ ⎤
⎡ ⎤ ⎡ ⎤
⎢ ⎥
⎢ ⎥ ⎢ ⎥
⎢ ⎥
⎢ ⎥ ⎢ ⎥
= ⋅
⎢ ⎥
⎢ ⎥ ⎢ ⎥
⎢ ⎥
⎢ ⎥ ⎢ ⎥
⎣ ⎦ ⎣ ⎦
⎣ ⎦
l l
l l
l l
l l
Summary: Related Concepts and Caveats
Waves:Complex phenomena
yet… information-rich
Signal Processing:
Needed to extract information
Needed

to

extract

information
Inverse Problems:
CAUTION with ill-posed problems
How much information is in the data?
14
Mechanical Waves
El t ti W
Closing Thoughts
El
ec
t
romagne
ti
c
W
aves
Thermal Phenomena
Geophysical methods extend our senses…
Mechanical waves
V
s
: skeletal stiffness (σ’,cement, suction)
V
P
: saturation
Electromagnetic Waves
κ
㨠Ω→汵浥mr楣i∂a瑥爠捯湴敮琠

y
⁩映匽㄰π%
)
⡰ y )
σ: pore fluid conductivity
(and… specific surface)
Thermal:
Effective stress & water content (frozen?)
Mechanical waves, EM waves and thermal:
Complementary information
Physically sound concepts
Parameters critical to geotech design
Low perturbation process monitoring
Boundary measurements tomography
Spatial variability and anisotropy
Some complexity… but information rich
Process Monitoring:
Sedimentation Pressure diffusion
Ageing Thixotropy and Creep
Drying – Unsaturation Cementation / de-cementation
Ionic diffusion Chemo-osmosis
Dynamic energy coupling Seismic-electric coupling
Stochastic resonance Liquefaction
Ground modification
Mixed fluid
phase
Ground

modification

Mixed

fluid
-
phase
Freezing Hydrates
Failure Stress tomography
Fabric anisotropy Spatial variability
Acknowledgements
G.G.Cho KAIST J.Y.Lee KIGAM
A. Fernandez GMI-Tx D. Fratta UWM
H.K.Kim Kookmin U.M.S. Cha GaTech
K.A.Klein Guelph J.S.Lee Korea U.
G.A.Narsilio U. Melbourne V. Rebata Petro-Tx
V.A. Rinaldi U. Cordoba G.J.Rix GaTec
Y.H.Wan
g
HKUS
T
T.S.Yun Lehi
g
h U.
g
g
S. Dai GaTech F. Wuttke Bauhaus U.
Great colleagues at Georgia Tech
Organizers
Thank you !