SOIL MECHANICS: Permeability, Determination of Coefficient of Permeability, Lab Method & Field Method, Confined & Unconfined Aquifer

Water has the most significant effect on the behavior of soil.

Gravitational water:

• Percolates through the soil under gravity
• Pore water pressure at GWT = 0
• Soil above GWT is saturated by capillary action (pore water pressure is tensile and negative = -ϒwh)
• Above GWT – impervious formation above- local saturation
• Water occurring at local saturation – perched water

Held water:

• Water held in soil pores other than gravity.

Types of Held Water:

Structural Water

• Remains in the crystal structure of soil minerals chemically, cannot removed by normal drying (105-110⁰C)

Hygroscopic Water

• Removed by normal drying, replaced back

• Capillary Water
• Due to surface tension

Height of Capillarity = 4T/ϒwd

Note:

Soil Suction: in case of capillary tube, water above WT has a ‘-‘ pressure, soil remains in a state of reduced pressure, known as soil suction (P_F = log₁₀(h_c))

Permeability:

• Flow of water through interconnected voids.

Darcy’s Law :

Laminar flow:

• Flow follows a well-defined path and doesn’t cross the path of other particles (Re ≤ 2000)

Turbulent flow:

• Fluctuates with the time both in magnitude and direction (Re ≥ 2000)

v ∝ i

v = ki

q = vA = Aki

therefore, q= Aki

Seepage Velocity:

Seepage Velocity > Avg. Velocity (v = q/A; v_s = q/A_s)

q = v*A = v_s*A_s

v_s =v* A/A_s

     = v V/v_s

     = v/n

     = ki/n

K = cd² * (e³/(1+e)) * (ϒ_w/μ)

K ∝ c

K ∝ (1/μ) 

{(K_T/K₂₀) = (μ₂₀/μ_T)}

K ∝ e

K ∝ T (temp^r)

Note:

• Impurities (salts, alkalis) increases, K decreases
• Entrapped air, k decreases

Determination of coefficient of Permeability:

(A) Laboratory Method:

Constant Head Method (k > 10^-4)

• Coarse grained soil
• Constant head of water at supply tank
• Vol. of water flowing out of permeameter per unit time = q

H= head water level – tail water level

k_stone > k_soil

From Darcy’s law

q = Aki

   = Ak h/L  

 Where L = soil specimen ht.

Therefore,

k = qL/Ah

= qL/(A*h*t)   

Where,

k = (k1+K2+ ………………Kn)/n

Falling head method (10^-7 <K< 10^-4)

• Undisturbed sample
• Fine-grained soils
• A standpipe of area ‘a’ above the cylinder
• Variable head (h1 to h2) at time t

 rate of change of head = -dh/dt

Acc. Darcy’s Law

q = A*k*i

a*v = A*k*i

-a* (dh/dt) = A*k* (h/L)

After Integrating from 0 to t and from h1 to h2;

K = 2.303*(q/A) *(L/t) *log₁₀(h1/h2)

Note:

• soil in the permeameter should be fully saturated.

Determination of Coeff. Of Permeability (Field):

(B) In-situ method:

• More reliable than the lab method

(a) Pumping test (pumping out)

• Continuous pumping from test well and observation in bore wells (observation well) till steady state.
• Min. two observation wells
• Well should penetrate full depth of water-bearing strata

Confined Aquifer – upper and lower surface impervious

Unconfined Aquifer- no overburden lying over them, top most water-bearing strata.

Unconfined Aquifer:

Observation wells – (r1 and r2 apart test well)

Ht. of observations wells – (z1 and z2)

i = dh/dr

z =ht. of water level at a distance, r

A= 2π*r*z

Darcy’s law;

q = kAi

   = 2π*r*z* dh/dr

On integrating;

K = {2.303*q*log10(r2/r1)}/ {π*(z_z² – z₁²)}

If only one observation well;

K= {2.303*q*log10(R/rw)}/ {π*(H² – hw²)}

R = Radius of influence

H = depth to the bottom of the aquifer from WT

Rw = radius of the test well

Hw = ht. of water in the test well

 Confined Aquifer:

r, r1, r2 – same as above

z.z1.z2 – ht. from the bottom impervious layer (same as above)

b= spacing between two layers

i= dz/dr

A = 2π * r* b

q= kAi

= k * dz/dr * 2π*r*b

On integrating,

K = {q*log10(R/rw)}/ {2.727*b*(h – hw)}

R = 3000*d*√k, R in m

d = draw down, m

k= Coeff. of permeability, m/sec

(b) Bore Hole Test

Constant head method:

• Water    is allowed to flow through the bottom of the bore
• Low end of the casing should not be less than 5d from the top and bottom of the stratum.
• Water level in borehole = constant

Therefore, k = q/(2.7*d*h)

Where d = dia. of well

H = head above GWT

Variable head method:

• Drop from h1 to h2
• For D ≤ 1.5 m

k = (πd/11t) * log(h1/h2)

• For D > 1.5 m

K= (πd²/81t) * log (2L/d) * log (h1/h2)

Insitu measurement of seepage velocity:

• Two trial pits A & B
• Dye inserted in A
• Observe in t time in B

h= level diff. between A and B

i = h/AB

v_s (seepage velocity) =AB/t

We know;

v_s =ki/n

Therefore,

AB/t =(k*h)/(n*AB)

k = (AB²*n)/(t*h)

Permeability on layered deposit:

h= h1+h2

q= q1+q2

q = kz * A * h/(h1+h2)

= k1*A*h1/h1

=k2*A*h2/h2

Therefore,

k =(h1+h2)/{(h1/k1)+(h2/k2)}

In direction of bedding;

i = i1 =i2

q = q1+q2

A*k_x*i = A*k1*i + A*k2*i

k = (k1*h1+k2*h2)/(h1+h2)