2 K C C C C = d D v . . s. i. - - PowerPoint PPT Presentation

t C . η K . ρ z C v z C D t C

d dry s. 2 2 i.

∂ ∂ − ∂ ∂ − ∂ ∂ = ∂ ∂

C = f (t,z) Advection-Diffusion equation

• Combined advection-diffusion equation

Di: Diffusion coefficient Kd : Distribution coefficient

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 5

Factors deciding type of Contaminant transport mechanism

• Grain size
• Density
• Seepage velocity
• Concentration
• Viscosity
• Hydraulic conductivity

Factors affecting the behavior of contaminant

• Contaminant
• Soil condition
• Mechanism

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 6

IIT Bombay

Concentration, C, of a contaminant in the porous media

( )

properties soil t, , l l, g, , ρ , T , V S, D, μ, f C

μ f f s

=

C : the concentration of contaminant in the pore water (ML-3) µ : the dynamic viscosity of the fluid (ML-1T-1) D: the diffusion coefficient (L2T-1) S : the mass of the adsorbed contaminant/unit volume (ML-3) Vs: corresponds to the interstitial flow velocity (LT-1) Tf : the surface tension of the fluid particle interface (MT-2) ρf : the fluid density (ML-3) g : the acceleration due to gravity [LT-2] l : the characteristic macroscopic length [L] lµ : the characteristic microscopic length (particle size) [L] t: the time [T].

Environmental Geomechanics Lecture No. 24 D N Singh Slide 7

IIT Bombay

Dimensionless Number Dimension Evaluation Concentration Number Ensures similarity of concentrations at homologous points in the model and prototype Advection Number Ensures kinematic similarity of motion in the model and prototype Diffusion Number Ensures similarity of diffusion process in the model and prototype Capillary Effects Number Ensures similarity of capillary effects in the model and prototype Adsorption Number Ensures similarity of adsorption process in the model and prototype Dynamic Effects Number Scaling is not done for contaminant flows. Significant in the case of dynamic events only.

f

C ρ

l t Vs.

2

l Dt

f f

T l l g

u

. . . ρ

f

ρ S

l gt 2

Coefficients of Contaminant Transport Mechanisms

Environmental Geomechanics Lecture No. 24 D N Singh Slide 8

IIT Bombay

Reynolds Number (Re) It is N times higher in the model. Scaling is not required if Re<1 (i.e. for laminar flow) Peclet Number (Pe) It is N times higher in the model. For low velocities dispersion is dependent of velocity and can be modelled accurately (i.e. Pe<1)

µ ρ

u f

l Vs.

D l V

u

s.

Discrepancies Pe= µ/(ρfD) Re µ : the viscosity of the contaminant (solution) ρf : the density of the contaminant solution D : the coefficient of diffusion for the contaminant ρf : the fluid density Vs : the seepage velocity lu : the characteristic microscopic length (such as particle size) and is equal to either d10 (or d50) or the mean particle size of the soil.

The relation between Pe and Re numbers depends only on the contaminant.

Environmental Geomechanics Lecture No. 24 D N Singh Slide 9

IIT Bombay

0.01 0.1 1 10 0.1 1 10 100

advection advection-diffusion dispersion diffusion

Peclet number Reynolds number

Sreedeep S., Berton, C., Moronnoz, T. and Singh, D. N., "Centrifuge and Numerical Modeling of Contaminant Transport Through the Unsaturated Silty Soil", ISSMGE International Conference on From Experimental Evidence towards Numerical Modelling of Unsaturated Soils, September 18/19, 2003, Bauhaus-Universität

• Weimar. 2003.

Environmental Geomechanics Lecture No. 24 D N Singh Slide 10

Sorption Absorption Adsorption atoms or molecules move into the bulk of a porous material, e.g. the absorption of water by a sponge atoms or molecules move from the bulk phase (that is, solid, liquid, or gas) onto a solid or liquid surface. e.g. purification by adsorption where impurities are filtered from liquids or gases by their adsorption onto the surface of a high-surface-area solid such as activated charcoal

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 11

Terms related to Sorption

• Adsorbates - molecules that have been adsorbed onto solid surfaces
• Substrate or Adsorbent - the surface to which adsorbates are adsorbed
• e.g. in case of adsorbed cations tightly held on surfaces of negatively

charged dry clay particles, clay particle is substrate and cations are adorbates. Clay particle

cations

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 12

Simple representation of these processes

The cations get fully hydrated, which results in their desorption from clay surface Dry condition (cations strongly sorbed on clay particles)

Clay layers Adsorbed cation

The water molecules wedge into the inter-layer after adding water

Water molecule

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 14

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

7.11.2015 Lecture No. 24 Lecture Name: Geomaterial Characterization

Sub-topics

Thermal Characterization Importance Methodologies Thermal properties Influence of Various soil specific Parameters Centrifuge Modelling

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

IMPORTANCE (in REAL LIFE SITUATIONS)

HIGH LEVEL RADIOACTIVE WASTE DISPOSAL HIGH VOLTAGE UNDERGROUND POWER CABLES ROADS, PIPELINES, STRUCTURES IN COLD REGIONS AGRI- & AQUA-CULTURE FIELDS/ SOLAR PONDS GROUND IMPROVEMENT TECHNIQUES (SOIL HEATING & FREEZING) ENERGY CONSERVATION SCHEMES TRANSMISSION OF HOT FLUIDS (CHEMICALS/GAS) HEAT LOSS FROM THE BASEMENTS OF BUILDINGS

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

THERMAL PROPERTIES

THERMAL RESISTIVITY (inverse is Conductivity, k) RT (inverse is Conductivity, k) THERMAL DIFFUSIVITY (α) SPECIFIC HEAT (Cp)

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

Cp=(RT.ρ.α)-1 ρ is the density of the media K CAN BE CORRELATED TO HYDRAULIC CONDUCTIVITY

Factors Influencing Thermal properties of Geomaterials

Type of Soil Moisture Content Distribution and Size of the Grains Density of the Soil Temperature and Pressure Presence of Contaminants Method of Measurements

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

Cp, RT, and α can be used for geomaterial characterization

The Transient Method

Grounded junction Insulated T-type Thermocouple Stainless steel tube of dia 1.2mm Thermocouple leads

6mm dia copper tube Power supply leads Thermocouple leads (T-type) Nichrome wire Thermocouple 95 mm

T-type thermocouple Thermal probe

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

Thermal probes and thermocouples

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

Temperature indicator

• 0000
• Set Off on

Switch

300 600 900 1200 1500

• big

S

000.0 000.0 000.0

Constant Power Supply Unit

• A.C. Power Supply

Field Thermal Probe

000.0

Timer

Temperatures Fine tuning

Coarse tuning

small

Current

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

Laboratory thermal probe

THERMODET DDTHERM (software)

Field thermal probe

Various Devices used for Thermal Property Determination

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

1

2 2

        + = r r r t ∂ ∂θ ∂ θ ∂ α ∂ ∂θ Transient Method Governing Equation for Line Heat Source in an Infinite Medium Initial and boundary conditions: θ = θ0 , for t = 0, r = ∞

Q r θ r k. . π 2 lim

r

− = ∂ ∂

→

Solution of the Differential Equation:

( ) ( )

      − − − − = −

∑

∞ =1 n n n

n.n! u 1 γ lnu k π 4 Q ) θ θ (

t α 4 r u

2

=

γ is the Euler’s constant and is equal to 0.5772.

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

r

1 2 1 2

t t ln k π 4 Q ) θ θ ( = −

1 T

4π Q s. R

−

      =

For r→0 and t→∞, the higher order terms of u can be neglected

5 10 15 20 25 30 35 40 20 40 60 80 100 (b)

t (min)

0.1 1 10 100 20 40 60 80 100

(a) s

θ (0C)

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

70 mm Thermocouple leads Power leads 25 mm thick Perspex disk 20 mm thick Styrofoam Thermal probe Top cap Bottom cap Thermocouple Rubber washer Compacted soil 140 mm Cap of the probe Rubber washer 220 mm long SS tube 25 mm thick Styrofoam 5 mm thick Perspex disk

Details of the thermal property detector (THERMODET)

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

0 10 20 30 40 50 60 70 80 90 100 20 30 40 50 60 70 (b)

θ (

0C)

t (min)

1 10 100 20 30 40 50 60 70

(a)

Variation of temperature with time for THERMODET

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

α =

50 2

t T D

where α is the thermal diffusivity D is the diameter of the soil sample T is the time factor corresponding to 50% change in temperature t50 is the time corresponding to 50% change in temperature

120 100 80 60 40 20 0.01 0.1 1

H=2D H=∞ T µ (%)

Percentage change in temperature versus time factor curves

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay

It is quite difficult to state the quantitative value of resistivity

• f any soil mainly due to the

fact that the type of the soil is not clearly defined in most of the practical situations. For instance, the word clay can cover a wide variety of soils.

Effect of the type of soil

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 200 400 600 800 1000 1200 1400

Black Cotton Soil Silty Sand Fine Sand Coarse Sand Fly Ash

Thermal Resistivity (deg C-cm/watt) Dry density (g/cc) Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay

Heat conduction through soil is largely electrolytic, the quantity of water present plays an important role. The amount of water present is dependent on a number of factors viz. weather, time of the year, nature of the sub-soil and the depth of permanent water table. Dry soils depict low conductivity. It is mainly due to the presence of air, a poor conductor (4000°C-cm/watt), separates the solid grains (4°C-cm/watt) of the soil. If the moisture content (Resistivity of water 165°C-cm/watt) of the soil increases, then conductivity also increases. Saturated soil has high conductivity as compared to the water. The moisture content, from where rate of decrease of resistivity is less, is known as critical moisture content for the soil.

Effect of moisture content

5 10 15 20 25 30 35 200 400 600 800 1000 1200 1400

Dry density 1.0g/cc 1.1g/cc 1.2g/cc 1.3g/cc 1.4g/cc Thermal Resistivity (deg C-cm/watt) Moisture Content ( % )

Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay

Determination of Thermal Properties in a Geotechnical Centrifuge

Environmental Geomechanics Lecture No. 24 D N Singh

Though, several analytical and numerical models are available to model heat migration in geomaterials they lack simulation of the prototype conditions in terms of in-situ stresses. To overcome this, field tests, which are relatively costly, time consuming and difficult to perform, are found to be of immense help. Under these circumstances, a geotechnical centrifuge should be used for studying heat migration in geomaterials.

Summary of scaling factors

PARAMETER SCALING FACTOR Length 1/N Void ratio 1 Acceleration N Force 1/N2 Stress 1 Strain 1 Velocity N Mass 1/N3 Mass density 1

Time (diffusion)

1/N2 Hydraulic Conductivity N Thermal conductivity

?

Thermal l diffusivity

?

Specific heat

?

Heat flux ?

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

Data logger Batteries Axis of rotation Rheostat Micro switch Switch-on Switch-off Test setup Thermocouple leads Power supply leads Geomaterial

Centrifuge Setup

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

Thermal properties at Different Centrifugation Efforts

1 10 100 10 100 1000 10000

SS-D1 SS-D2 SS-D3 SS-D4 SS-SUB

R

T ( 0C-cm/W)

1 10 100 10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

SS-D1 SS-D2 SS-D3 SS-D4 SS-SUB

α (m

2/s)

50 100 150 200 1 2 3 4 5 SS-D1 SS-D2 SS-D3 SS-D4 SS-SUB

C

p (J/g- 0C)

N

IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

Krishnaiah, S. and Singh, D. N., “A Methodology to Determine Soil Moisture Movement Due to Thermal Gradients”, Experimental Thermal and Fluid Science, 27, 2003, 715-721. Krishnaiah, S. and Singh, D. N., "Centrifuge modelling of heat migration in soils," International Journal of Physical Modeling in Geotechnics.4(3), (2004), 39-47

Some results

0 5 10 15 20 25 20 30 40 50 60 70 80

125 100 50 N =1

0 5 10 15 20 25 r(cm ) 0.3 1.5 2.0 3.0 4.0 0 5 10 15 20 25

θ (

0C)

t (m in)

0 5 10 15 20 25 1 2 3 4 5 20 30 40 50 60 70

θ (

0C)

r (cm )

t (m in) 5 10 15 20 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 IIT Bombay Environmental Geomechanics Lecture No. 24 D N Singh

r z

IIT Bombay

Becoming essential for predicting/determining: Water content & Saturation Degree of compaction Porosity Hydraulic conductivity Liquefaction potential of the soil mass Detecting and locating geomembrane failures To estimate corrosive effects of soil on buried steel/concrete To investigate effects of soil freezing on buried structures Estimating soil salinity for agricultural activities.

Importance of Electrical Properties of Geomaterials In Geotechnical Engineering

Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay 33

Change in water content leads to change in the dielectric permittivity of the water-geomaterial system or vice versa. This fact leads to determination of water content of the geomaterial if its dielectric constant is known. Many sensing techniques have been developed, over years and are still being developed for measuring soil moisture and some of these techniques are: Capacitance probe/FD Sensor Time domain reflectometry, TDR, probe Useful for rapid determination of in-situ moisture content that too under non-invasive and non-destructive manner. Measure volumetric moisture content. Water has a high dielectric permittivity (=81, which is more than an

• rder of magnitude greater than that of the soils and geomaterials,

dry soil= 3). For air, dielectric permittivity= 1.

Importance…..

Environmental Geomechanics Lecture No. 24 D N Singh

METHODS FOR LABORATORY MEASUREMENT OF SOIL RESISTIVITY Two-electrode method

Power supply SAMPLE Electrode Electrode Voltage Measurement Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

Four-electrode method

Power supply

SAMPLE

Electrode

~

V Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

1 2 3 4 5 6 7 8 C V V C 2 3 4 5 6 7 8 1 C V V C

Sequence of Circular Four-Probe Resistivity Cells Measurements

Low Frequency Method

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

ELECTRICAL RESISTIVITY BOX (TWO-ELECTRODE METHOD)

12 cm @ 3 cm 12 cm 12 cm Point Electrodes

It is difficult to determine A

L A R = ρ a . R = ρ

a: shape factor for the electrode

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

1 2 3 4 16 Ebonite ring 55 mm 25 25 25 95 mm Lock nut Top nut SS pointed tip Copper electrode 32 23 20

ELECTRICAL RESISTIVITY PROBE

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

10 20 30 40 50 60 70 80 90 100 20000 40000 60000 80000 100000

ERP ERB

Sr (%)

ρ (Ω

• cm)

Comparison of the ERB and ERP results (Silty soil)

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

Field Investigations

Ground Penetrating Radar (GPR) Time Domain Reflectometry (TDR) Capacitance sensor Portable dielectric probe (PDP) Electrical conductivity probe (ECP) Monitoring Slope deformation & Movement

2nd International Symposium and Workshop on Time Domain Reflectometry for Innovative Geotechnical Applications (TDR 2001). www.iti.northwestern.edu/tdr/tdr2001/proceedings/

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

Electrical Properties of Geomaterials

Electrical properties (conductivity, σ, and dielectric constant, k) can be used for geomaterial characterization. Electrical conductivity is a measure of charge mobility in response to an electric field. Dielectric constant is a measure of the capacity of a material to reduce the strength of an electric energy field and to behave like an insulator. Variation in electrical properties with alternating current frequency

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

Electrical Properties of Geomaterials

• Electrical conduction in moist geomaterials occurs as a result of the

movement of ions

• These materials are dielectric material (characterized by polarization)
• However, they behave neither as a conducting material nor as a

perfectly dielectric material, and hence they can be modeled as a ‘lossy dielectric material’.

• A frequency-dependent complex permittivity, k, is used to capture both

amplitude and phase information.

ε ⋅ ⋅ = A d C k

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

For the parallel plate capacitor

Electrical Impedance

Z=V(t)/I(t) =V⋅cosωt/I⋅cos(ωt-δ) =R-jX where, R is resistance, which is the real part of Z (= Z′), X is the imaginary part of Z (=Z′′)

• Resistivity term is applicable to DC
• Impedance – Resistance offered by soil mass to AC
• Impedance captures both frequency and amplitude information

Impedance is frequency (of AC) dependent

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

Basic Model R C

Element Impedance Admittance Resistor (R) Inductor (L) Capacitor (C) Z = R+j0 Z = 0+jωL Z = 0-j(ωC)-1 Y = 1/R+j0 Y = 0-j(ωL)-1 Y = 0+jωC Elements in series : Elements in parallel :

∑

=

i i equiv

Z Z

∑

=

i i equiv

Y Y

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

Determination of Electrical properties of Soils

140 mm Connector Perspex sheet 30 mm Scale Sample SS electrode 100 mm 30 mm 10 mm Base plate

Perspex box

Specimen

Plate electrode

Impedance cells

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

Impedance cells

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

Analysis of experimentally

• btained impedance data can be

done by: Cole-Cole plot Nyquist plot----widely employed Bode plot

Equivalent circuit

CE CS CE RE RS RE

• Z ''

Z ' (2RE+RS) Rs

Perspex box

Specimen

Plate electrode

Details of a typical Impedance Cell Nyquist plot

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay

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. 24 D N Singh IIT Bombay

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. 20 D N Singh IIT Bombay

IIT Bombay

c c a b b a

: Conduction path : Soil grains : Electrodes

: Air

Basic Models to Depict Flow Paths of AC in Dry Geomaterials

AC flow through a dry soil may occur due to: (i) a-a (the surface of the soil grains, which is mainly due to the presence of surface charge carriers/ions) (ii) b-b (the soil cluster, wherein soil grains are in contact with each other and current may flow through the interconnected grains) (iii) c-c (partly through the soil grains and partly through the air present in the voids, which is a least likely path due to its very high resistance, unless the air is contaminated with fumes of water or chemicals

Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay

d′ b′ d′ c′ c′ a′ a′ b′

: Conduction path : Water filled voids : Soil grains : Electrodes

: Air

Basic Models to Depict Flow Paths of AC in Partially Saturated Geomaterials

AC flow through a partially-saturated soil may occur through: (i) a′-a′ (interconnected pores filled with pore- solution, which offers least resistance to the flow

• f current)

(ii) b′-b′ (interconnected soil grains) (iii) c′-c′ (partly through the connected soil grains and partly through interconnected pores) (iv) d′-d′ (partly through soil grains and partly through the voids, which contain air and pore- solution.

Environmental Geomechanics Lecture No. 24 D N Singh