ENVIRONMENTAL GEOMECHANICS CE-641 Lecture No. 16 Prof. D N Singh - - PowerPoint PPT Presentation

ENVIRONMENTAL GEOMECHANICS

CE-641 Lecture No. 16

• Prof. D N Singh

Department of Civil Engineering

09.10.2019 Lecture No. 16 Lecture Name: Geomaterial Characterization

Sub-topics

• Chemical characterization

Sorption-Desorption (Contaminant Transport in Porous Media)

• Thermal Characterization
• Electrical Characterization
• Magnetic Characterization

Flow of water through porous media is extensively studied (seepage, consolidation and stability) The concept of hydraulic conductivity are well established.

Contaminant Transport in Porous Media

Chemical flows in soils are of great importance. Some important examples are: waste storage, remediation of contaminated sites leaching phenomena, etc. Contaminants are basically dissolved inorganic or organic substances in the solvent (water or fluids). Various concentration units are used to define the relative amounts of contaminants in the solvent: Mass concentration: milligrams of contam. in 1 litre of water (mg/L) Parts per million (ppm): grams of solution/ million grams of solution

Types of Flow through Porous Media

Electricity

I = V/L

Ohm’s law

L I V1 V2 T

Heat

Fourier’s law

L

1

T2 q

T1 >T2

q = KT/L

Chemicals

Fick’s law

L

C1

JD

JD = DC/L

C2

Fluid

q

= kH/L

Darcy’s law

q L H

H1 H2

If flow does not change the fabric and stress state of the porous media, then flow rate J relates linearly to its corresponding driving force, X: J = . X  : conductivity coefficient for flow

Advection (or Convection)

Solute (contaminant) gets transported (seepage velocity) along with the flowing fluid (water) in response to a gradient (hydraulic).

t0 t1 t2 Vs = k.i/

If a mass of solute (non reactive)

• f a concentration C is placed at
• ne end of a pipe, then in a

given time it will travel a certain distance as a Plug due to advection. The transit time required for a non-reactive solute to migrate through a saturated soil of thickness L would be:

t = L/Vs = .L/(k.i)

The advective mass flux, J, (or the mass flowing through a unit cross sectional area in a unit of time) is:

J =v.C=k.i.C

C = concentration of the solute (i.e., the mass of solute per unit volume

• f the mixture).

• Solutes (contaminants) migrate due to

their chemical activity in the absence of bulk fluid flow.

• From higher concentration to lower

concentration area.

• Difference in contaminant concentration

is the concentration gradient.

• Diffusion ceases when concentration

gradient becomes negligible.

Contaminant at concentration C0 at t0 Contaminant concentration = 0 at t0

Sample

• Time after introduction of contaminant

= t

• Relative contaminant concentration

=Ct/C0

Diffusion

1.0 0.5

to t Ct/C0 < 1.0 Ct / C0

Diffusion

• Add small amount of dye in a fluid
• Pulse gets spread out

Add continuous dye-- a sharp front

Types of Diffusion

• Steady State Diffusion
• Diffusion flux constant with time
• Fick’s First law applicable
• Non Steady-state Diffusion
• Concentration gradient non-uniform
• Follows Fick’s second law

   

            x t x C D x t t x C , ,

JD =-D..(C/x)

D = diffusion coefficient [L2/T] = porosity C/x = concentration gradient (i.e., change in concentration with distance)

Chemical Energy Field

• To study the mechanism(s) of contaminant transport –
• the intact and fractured rock samples (Gurumoorthy 2002)
• diffusion characteristics of the saturated and unsaturated

soils (Rakesh 2005)

• Investigations using the Cl-, I+2, Cs+1 and Sr+2 in their active

as well as inactive forms

• Development of Diffusion Cell

CONTAMINANT TRANSPORT MODELING THROUGH THE ROCK MASS

Fractured Rock mass (FRM) Co Ct Intact Rock mass (IRM) C0 Ct Ct

Diffusion cells

7 min. 50 days 6 m thick FRM 75 min. 520 days 0.3 m thick IRM (Di)m=(Di)p

2000 4000 6000 8000 10000 10 20 30 40 Intact rock mass 2000 4000 6000 8000 10000

C

t/C 0 (x10

• 4)

Fractured rock mass

N 33 50 75 100

Time (s)

1 10 100 10

1

10

2

10

3

10

4

10

5

10

6

y=1.8

Intact rock mass Fractured rock mass

y=1.97

Diffusion time (s)

N

tm=tp.N-2

Diffusion characteristics

Fractured Rock mass (FRM) Co Ct Intact Rock mass (IRM) C0 Ct Ct

Diffusion cells

CONTAMINANT TRANSPORT MODELING THROUGH THE ROCK MASS

70 30 U C 60 A A B B 60 Modeling Diffusion in soils using impedance spectroscopy (IS)

Diffusion cell Impedance value of the soil is measured by using LCR meter Diffusion of contaminant can be monitored by determining the change in the impedance of the soil

• Break-through curve

100 200 300 400 500 10 20 30 40

(a)

453

Ct/C0 (x10

• 4)

t (h)

• The slope of the break-through curve diffusion coefficient, D
• Archie’s law (D=.m) porosity of the geomaterials

Details of the diffusion studies Overall four cells were employed for each sample Z' measurement corresponding to 3rd, 6th, 9th and 20th day 1 M NaCl and 0.01 M SrCl2 used as model contaminants Na+ and Sr+2 analysis using AAS along the length of the cell

Soil Sample d (kN/m3) Sr (%) w (%) Θ (%) WC WC 100 13.8 100 80 60 33 45.54 WC 80 14.0 27 37.8 WC 60 13.8 22 30.36 CS CS 100 14.7 29 42.63 CS 80 14.9 23 34.27 CS 60 14.4 18 25.92

With time Ct increases on U due to diffusion Implies Z ′ decreases on U with time

Z′

t

C 1

Ct Contamination

1 2 3 4 5 6 7 8 9 10 11 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 C WC 60-N

Time (Days) 3 6 9

Z' (W) Length (cm) U

General observations

Influence of Saturation

For a time t, Diffusion decreases with decreasing saturation

1 2 3 4 5 6 7 8 9 10 11 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

C

9

th day

WC 60-N WC 80-N WC 100-N

Z' (W) Length (cm) U

(Normalized concentration) Ct/C0 vs Length

                      



  c c 1 m 2 c d 2 2 e c t

L mx sin L mx cos . m ) L R / t m D exp( 2 L x C C

(Diffusion coefficient) De vs volumetric water content

The solute (contaminant) spreads

• ut from the flow path.

Mixing or spreading of the solute. Solute will not move as a “plug” Negligible at low flow rates & short distances of transport

x 2 4 6 8 10 12 0.0 0.5 1.0 x 2 4 6 8 10 12 0.0 0.5 1.0 x 2 4 6 8 10 12 0.0 0.5 1.0

Dispersion (thinning out/scattering/spreading)

Ct / C0

Pore size Path length Friction in pore

Slow Fast Long path Short path Slow Slow Fast Slow Slow Fast

Variation in velocity due to tortuous nature of flow path On larger scale, dispersion is caused by different flow rates resulting from heterogeneities encountered. This process is repeated millions

• f times by millions of water

particles.

Dispersion

Water with dissolved contaminants Solid particle Tortuous flow paths General direction

• f flow

Porous media

MD = aL.Vs

aL = dynamic dispersivity [L] Vs = Seepage velocity [LT-1] aL = 0.0175 L1.46 for L < 3500 m

Hydrodynamic Dispersion

Processes of molecular diffusion and mechanical dispersivity cannot be separated in flowing groundwater Introduction of a factor which takes into account mixing and diffusion DL = aL.Vs+Di DL = Coefficient of hydrodynamic dispersion [L2T-1] Concentration at distance, L, from the source at time, t, is given by: C = 0.5.Co [erfc{(L-Vs.t)/2(DL.t)0.5}+ exp(Vs.L/DL) x erfc {(L+Vs.t)/2(DL.t)0.5 }]

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

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

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)  : 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) f : the fluid density (ML-3) g : the acceleration due to gravity [LT-2] l : the characteristic macroscopic length [L] l : the characteristic microscopic length (particle size) [L] t: the time [T].

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 

l t Vs.

2

l Dt

f f

T l l g

u

. . . 

f

 S

l gt 2

Coefficients of Contaminant Transport Mechanisms

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)

 

u f

l Vs.

D l V

u

s.

Discrepancies Pe= /(fD) Re  : the viscosity of the contaminant (solution) f : the density of the contaminant solution D : the coefficient of diffusion for the contaminant f : 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.

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

• f 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.