Estimation of Soil Permeability Using an Acoustic Technique for Sandy Soils Kim, Jin Won Advised by Dr. Chung R. Song Department of University, MS 38677
Order of Presentation Introduction Literature t Review Concepts and Theory Experiments Results Conclusions
Order of Presentation Introduction Literature t Review Concepts and Theory Experiments Results Conclusions
Introduction The estimation of permeability of soils using an acoustic technique is proposed here. The propagation of elastic waves in saturated soils are the coupled action between solid particles and pore water. The coupled behavior involves the permeability of soils. By analyzing the propagation characteristics of elastic waves in saturated soils, the permeability of soils is estimated.
Order of Presentation Introduction Literature t Review Concepts and Theory Experiments Results Conclusions
Literature Review Biot s contribution (1956) : Before Biot s prediction about slow P-wave, just one compressional wave was believed among People. Fast P wave (in-phase motion) Slow P wave (out of phase motion) (Chotiros, 1995)
Biot Equation (1956) V V V V 1 c ( σ 11σ 22 σ 12 ) 2 ( γ + γ ) 2 2 f 1 = 2 ζ ζ ζ + ζ + ζ ζ 1 2 1 2 1 2 f c 2 12 22 2 11 22 12 2 c f c ( γ 12 + γ 22 ) 1 2 2 f σ σ σ = 2 (Yamamoto, 2002)
Biot Equation (1956) L x 1 σ σ σ f = + fc 2 c 11 22 12 ζζ 1 2 1 2 ( γ12 γ22) 1 2 2 c 1 f σ11σ22 σ 12 L x = 2 f ( γ + γ ) 2 c 12 22 2 (Yamamoto, 2002)
Characteristic Frequency Attenuatio on /S Specific at ttenuation n factor f c Frequency (Hz) f : Characteristic Frequency c = frequency at Maximum (specific) )Attenuation Characteristic frequency is related to the viscosity of the fluid and permeability of soils. When the frictional loss is maximum, the damping will be maximum. On the other hand, when the frictional loss is minimum the damping will be minimum.
Biot Equation (1956) K length 2 ( ) = In the equation, ηφ ω cis the characteristic frequency, is the fluid density, is the porosity, η ρ φ is the viscosity c and K is the intrinsic permeability. ω ρ k( length/ time) = φ g π 2 fc In the equation, g is the gravity, f is the frequency in hertz, and k is the permeability in length/time unit.
Order of Presentation Introduction Literature t Review Concepts and Theory Experiments Results Conclusions
Experimental Set Up ( To capture f c )
Lab. Testing & Calibration Wave Generator Digital Oscilloscope Amplifier
Sample Close Up 67cm Lumber Frame 60cm 4cm Receiver 1 Receiver 2 Underwater actuator Vinyl Lining Acoustic Absorberb
Laboratory Test Results (Mortar Sand) General Properties w Gs γ d e n 2.64 23.14 1.639 0.611 0.379
Checking Mis-alignment Lab. test with water only 5 4 3 2 1 0 0 2000 4000 6000 8000 10000 12000 14000 Frequency (Hz) β 0.92 m Errors from incorrect alignment α 5 4 0.47 3 m 2 Data rati io Data ratio 1 0 0 2000 4000 6000 8000 10000 12000 14000 Frequency (Hz) Correct alignment
Checking Mis-alignment Bubble Tube is used to check the alignment
Order of Presentation Introduction Literature t Review Concepts and Theory Experiments Results Conclusions
Measured Signals ( Technique A ) The continuous sinusoidal input signal is generated and measured the amplitudes of the two received signals. Amp.:A 1 Amp.: A 2 r1 r2 Underwater actuator Inverse Quality Factor : 1 1 2 ln A c Q = ( r1 r2) A1 π f
Measured Signals ( Technique B ) The continuous sinusoidal input signal is generated and stopped to measure the decay of the vibration amplitude from one receiver Inverse Quality Factor : Q 1 z = 2D = 2 ln n zn+ 1 Knopoff (1964)
Laboratory Test Results (Mortar Sand) 1/Q 0.8 0.6 0.4 0.2 0 Technique 'A' Technique 'B' Water 0 1000 2000 3000 4000 5000 6000 Frequency (Hz) The inverse quality factor could not be measured beyond the 3000 Hz using the Technique (B).
Comparison of Results with Conventional Permeability Equation Mortar Sand
Order of Presentation Introduction Literature t Review Concepts and Theory Experiments Results Conclusions
Conclusions The acoustic technique is an easy way to estimate the permeability of soils This technique can be a non-destructive method. Application of the proposed method may be feasible for other soils. Field tests for sandy soils presented clear characteristic frequencies which can be used to compute the permeability of soils according to Biot (1956 a, b) theory.
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