Estimation of Soil Permeability Using an Acoustic Technique Jin Won - - PowerPoint PPT Presentation

Estimation of Soil Permeability Using an Acoustic Technique

Jin Won Kim and Chung R. Song

Department of Civil Engineering The University of Mississippi University, MS 38677

Concepts

The propagation of elastic waves in saturated soils causes the l d ti b t lid ti l d t coupled motion between solid particles and pore water. Characteristic Frequency The coupled behavior involves the permeability of soils. By measuring the characteristic frequency of elastic waves in saturated soils, the permeability of soils is estimated.

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Theory: Characteristic Frequency and permeability

Characteristic Frequency and permeability (Biot, 1956) (Biot, 1956)

tion Attenuat

c

f

: Characteristic Frequency

= frequency at Maximum

Specific

f

q y (specific) Attenuation

Frequency (Hz)

• Characteristic frequency is related to the viscosity of the fluid and pore size (and

eventually to the permeability of soils).

c

f

Frequency (Hz)

• When the frictional loss is maximum, the attenuation is maximum.

y p y )

g ⋅ φ

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c

f g k ⋅ = π φ 2

Specific Attenuation Specific Attenuation

( )

Amp.:A1 A A2

2 1

( ) 2 1 r r

A A e α

− −

=

Amp.: A2

α

Underwater actuator = attenuation coefficient 1

r

2

r

• Specific attenuation

Specific attenuation

1

c Q α

− =

Q f π

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Experimental Set Up Experimental Set Up ( To capture )

( To capture )

c

f

Wave generator Digital oscilloscope Amplifier Receiver 2 Underground Actuator Receiver 1

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Measured Signal Measured Signal

x1 Frequency : 400 Hz

Receiver 1

x1

Receiver 2

x2

Receiver 2 Amplitude : X1 ≈ X2

Very little attenuation:

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not the characteristic frequency

Measured Signal Measured Signal

Frequency : 3000 Hz

Receiver 1 X1 X2 Receiver 2 Amplitude : X1 < X2

V hi h tt ti

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Very high attenuation: Characteristic frequency

Comparison of Dry and Saturated Conditions

Saturated Condition : w = 23.14 (%) Dry Condition : w = 0.098 (%) y ( )

1 Dry Soil 0.5 Saturated Soil 500 1000 1500 2000 2500 3000 3500 4000 4500

Q-1

Frequency (Hz)

• 0.5

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Field Testing Field Testing

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General General P Properties of roperties of S Soils for Field Tests

• ils for Field Tests

(%)

W Gs n

3

( / ) t m d

γ

Sardis Lake 2.65 24.15 1.616 0.390 Tillatoba River 2.67 25.90 1.364 0.489

1 3 2

C

1 3 2

T

1 2 2

S

1 4 2

B

Baton Rouge 2.68 45.56 1.210 0.550

. 4 1 . 4 3 1 . 2 . 6

C l e a

. 4 1 . 3 3 5 . 2 . 6

T i l l

. 3 1 . 6 2 4 . 2 . 6

S a r d

( t / ( % )

. 5

1 . 2 4 5 . 2 . 6

B a t

• 20

40 60 80 100 rcent Finer

6 5 6 5 8

a r C

8 9 6 4 9 7

l a t

• 9

1 6 1 5 5

d i s

/ m

2

) )

5

1 5 6 8

• n

R

20 0.000 0.001 0.010 0.100 1.000 10.000 Grain Size, D(mm) Per

C r e

• b

a L a k R

• u

Tillatoba River Baton Rouge Sardis Lake

e k R i k e g e

Field Test at the Sardis Lake (Sandy Soil) Field Test at the Sardis Lake (Sandy Soil)

0.4 0.6 0 4

• 0.2

0.2 1000 2000 3000 4000 5000 6000 7000

Q-1

• 0.6
• 0.4

Frequency (Hz) Frequency (Hz)

Acoustic Tech.: 2.02×10-4 m/sec Field Perm. Test: 3.65×10-4 m/sec

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Tillatoba River (Sandy Silt) Tillatoba River (Sandy Silt)

0.6 0.2 0.4

Q-1

• 0.4
• 0.2 0

2000 4000 6000 8000 10000 12000

Frequency (Hz) Frequency (Hz)

Acoustic Tech.: 1.73×10-4 m/sec Field Perm. Test: 3.70×10-5 m/sec

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LSU Lake, Baton Rouge, Louisiana (Silty Clay) LSU Lake, Baton Rouge, Louisiana (Silty Clay)

0.2 0.4 0.6

• 0.6
• 0.4
• 0.2

2000 4000 6000 8000 10000 12000

Q-1

• 1.2
• 1
• 0.8

Frequency (Hz)

Acoustic Tech.: N/A Field Perm. Test: 8.82×10-6 m/sec Expected fc=900 kHz

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Conclusions Conclusions

• Laboratory tests showed the existence of Biot’s

characteristic frequency characteristic frequency.

• Field tests for sandy soils and silty soils showed clear

h t i ti f i hi h b d t t th characteristic frequencies which can be used to compute the permeability of soils according to Biot (1956) theory.

• Field tests for silty soils did not show the good agreement

with the field permeability test data.

• Field tests for clayey soils did not provide the characteristic

frequency because of the limitation of the equipment.

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Thank you for your attention. Any Questions ?

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• Checking system compliancy

Checking system compliancy

• Lab. test with water only

3 4 5

0.92 m

1 2 3 2000 4000 6000 8000 10000 12000 14000 frequency (Hz)

0.47 m

Errors from incorrect alignment

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4 5 1 2 3

Ratio A2/A1

2000 4000 6000 8000 10000 12000 14000

Frequency (Hz)

4 5 1 2 3

Attenuation coefficient

• 1

2000 4000 6000 8000 10000 12000 14000

Frequency (Hz) System characteristic frequency is approximately 10000 Hz Frequency (Hz)

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System characteristic frequency is approximately 10000 Hz

• Checking Near Field Effect

Checking Near Field Effect

Near field ( Fresnel zone) : the amplitude with distance does not follow the geometric attenuation

2

R x π ≈

Hunter and Bolt (1955) ; Kinsler et al. (1982) : radius of the source : wavelength

x π λ ≈

R

λ

200 Hz

2000 4000 6000 plitude (mV)

7 kHz

2000 4000 6000 mplitdue (mV) 2 4 6 8 10 12 distance (cm) amp 2 4 6 8 10 12 distance (cm) am

near far near far

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• Hvorslev Equation (1951)

Hvorslev Equation (1951)

D L h π ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠

1 2 1 2

11 ln h k t t h ⎜ ⎟ ⎝ ⎠ = −

D : the diameter of a stand pipe L : the length of a sample h h

L

1

h

2

h

L

D

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