ENVIRONMENTAL GEOMECHANICS CE-641 Department of Civil Engineering - - PowerPoint PPT Presentation

ENVIRONMENTAL GEOMECHANICS CE-641 Department of Civil Engineering

• DR. D. N. SINGH

dns@civil.iitb.ac.in www.civil.iitb.ac.in/~dns

IIT Bombay

24.10.2009 Lecture No. 21 Lecture Name: Geomaterial Characterization

Sub-topics

• Electrical Characterization
• Basic Experimental Investigations
• Determination of Electrical Conductivity & Dielectric constant
• Generalized Archie’s law
• Electrical Properties of Pore-Solution
• Hygroscopic moisture content
• Determination of Soil Suction from Conductivity measurements
• Some important relationships for Dielectric constant
• Mixing Model for Dielectric Constant
• Soil characterization using Impedance Spectroscopy

IIT Bombay Slide 1 Environmental Geomechanics Lecture No. 21 D N Singh

Basic Experimental Investigations

Determination of Electrical Properties of Dry Soils Wet Soils Pore Solution (σw) Determination of hygroscopic moisture content Determination of soil suction

Shah, P.H. and Singh, D N., "A Simple Methodology For Determining Electrical Conductivity of Soils", Journal of ASTM International. 1(5). Published Online:10 May 2004. 11 Pages.

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 2

1 2 3 4 5 6 7 4 8 12 16 20 24 28

R

2=0.99185

σ

DC=10.7 x 10

• 4 S/m

σ (x10-4 S/m)

ω (× 106 rad/sec ) σ = σDC + S . ω

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 3

Electrical Conductivity of Soils w.r.t. Volumetric water content

10 20 30 40 50

• 1

1 2 3 4 5 6 7 8

σ (x10

• 2 S/m)

θ (% )

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 4

For unsaturated porous medium: σ = c ⋅σw⋅ηB⋅Sm

• r,

σ = c ⋅σw⋅ηB-m⋅θm However, B≈m σ = c ⋅σw⋅θm

• r,

σ /σw =1/FF =c⋅θm FF: Formation factor σ: Bulk conductivity of soils σw: Pore solution conductivity η: Porosity S: Saturation C, B and m are empirical constants Generalized Archie’s law

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 5

1 10 100 0.1 1 10 1 10 100 1 10 m = 1.25

m CL (%)

m=0.92 CL0.2 c=0.6 CL0.55 c = 1.45

c

Generalization of parameters c and m

Shah, P. and Singh, D. N., "Generalized Archie's Law for Estimation of Soil Electrical Conductivity", Journal of ASTM International. 2(5), Published Online: 2 May 2005. 20 Pages.

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 6

Pressure Gauge Pressure Membrane Extractor Air Filter & Valve Pressure regulating valve Pressure Gauge Safety Valve Compressor Release Valve Retention Unit Sampling Bottle Membrane & Filter Cloth

Electrical Properties of Pore-solution

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 7

100 150 200 250 300 50 100 150 200 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5

Z'' (Ω)

Z' (Ω)

Soil Distilled water

Z'' (x10

3 Ω)

Z'(x10

3 Ω)

Nyquist plots Pore-solution Conductivity

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 8

200 400 600 800 1000 100 200 300 400 500 200 400 600 800 1000 1 2 3 4 5 Distilled water k f(kHz) k=76.58 (σ

dc = 1.68 x 10

• 4 S/m

) Distilled water σ (x10

• 4S/m)

f (kHz)

Standard value of k = 78 (at the same temp.)

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 9

10

• 1 10

0 10 1 10 2 10 3 10 4 10 5 10 6 10 7

10 10

1

10

2

10

3

10

4

10

5

10

6

10

7

10

8

k f(Hz)

Variation of Dielectric constant with Frequency

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 10

Hygroscopic moisture content, wh

Moisture adsorbed by the soil from the environment due to electro- molecular forces Normally wh measured for air-dried soils, which is not correct. wh = f (SSA, CEC, LL, SP, σ, k) =f(σh/σdry ) = f(kdiff ) kdiff

= kh - kdry

Shah, Paresh H. and Singh, D. N., "Methodology for Determination of Hygroscopic Moisture Content of Soils”, Journal of ASTM International. 3(2), (2006), 14 Pages.

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 11

Determination of Soil Suction from its Conductivity measurements

10

• 3 10
• 2 10
• 1 10

0 10 1 10 2 10 3 10 4 10 5 10 6 10 7

• 1

1 2 3 4 5 6 7 8

σ (x10-2 S/m) ψ

m (kPa)

ψm = f(θ) i.e., the SWCC σ = f(θ) i.e., the Generalized Archie’s law

10

• 2 10
• 1 10

0 10 1 10 2 10 3 10 4 10 5 10 6 10 7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 SWCC fit FX BC vG Mu Experimental results

θ

ψ (kPa)

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 12

[ ]

2 / 1 3 2

7 . 76 146 3 . 9 03 . 3 θ θ θ − ⋅ + ⋅ + = k ) 2 ( 8 η θ − + ⋅ = k

) 1841 . ( 4674 . 8 + ⋅ = θ k

208 . 1 454 . 2 93 . 9 − ⋅ + ⋅ =

d

k ρ θ

θ ⋅ + = 57 . 10 35 . 1 k

Topp et al. (1980) Roth et al. (1992) Yu et al. (1997) Gardner et al. (1998) Rohini and Singh (2004)

Rohini, K. and Singh, D. N., "A Methodology for Determination of Electrical Properties of Soils", Journal of Testing and Evaluation, ASTM. 32(1), 2004, 64-70.

Some Important Relationships

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 13

)] ). (1 . ( . ) . . ).( [(1

2 1 2 1

PF PF M 2 M 1

k S k S k M k M k

r r

− + + + − = η η

Mixing Model

Bhat, A.M., Rao, B.H., and Singh, D.N., “A Generalized Relationship for Estimating Dielectric Constant of Soils”, Journal of ASTM International, 2007, Published Online: 15 August 2007, pages: 12, 2007, DOI: 10.1520/JAI100635.

where M1 and M2 are percentages of the minerals kM1 and kM2 are dielectric constants of the minerals kPF1 and kPF2 are dielectric constants of pore fluids η is the porosity Sr is the saturation

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 14

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 15

Soil characterization using Impedance Spectroscopy

Frequency Response of the Soil Under an Alternating Current Excitation

Response Spectra

f G, θ, γ, e, Sr

Re(Z) = Z′= Z⋅Cosφ Im(Z) = Z″ = Z⋅Sinφ Z=[(Z′)2 +(Z″)2]1/2 φ=tan-1(Z″/Z′) Apply An Electrical Stimulus Impedance Plots Material/ Substrate

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 16

IIT Bombay

1 10 100 1000 10000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.114 2.51x10

5

ω (x10

2 rad/s)

Bode plot φ φ=tan-1(Z″/Z′)

Environmental Geomechanics Lecture No. 21 D N Singh Slide 17

Development of Equivalent Circuits Fitting Circuits to Impedance Data Using Z-view software (Johnson, 2003)

1 2 3 4 5 EXP CKT1

• Z'' (×104Ω)

Z' (×104Ω)

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 18

Development of Equivalent Circuits

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 EXP CKT1 EXP CKT2 X EXP CKT4 EXP CKT3 EXP CKT5

• Z'' (×104Ω

)

EXP CKT6

Z' (×104Ω)

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 19

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 2 4 6 8 10 12 14 16 18 20

R (×103Ω) θ Rgb Rg

Grain resistance Rg Grain boundary resistance Rgb

The soil can be characterized as a granular material, if Rgb is negligible or very low. For these soils, the order of magnitude

• f the Rg would be very high.

The soil can be characterized as a fine- grained soil if both Rgb and Rg are present in the equivalent circuit. However, values of these resistances should be quite low as compared to the granular soils/materials.

Environmental Geomechanics Lecture No. 21 D N Singh IIT Bombay Slide 20