# Soil Mechanics & Foundation Engg. : Sepage stress and permeabilty of soil

By Deepanshu Rastogi|Updated : March 17th, 2021

The article contains fundamental notes on "Seepage and Permeability of Soils"  topic of "Soil Mechanics & Foundation Engineering" subject. Also useful for the preparation of various upcoming exams like GATE Civil Engineering(CE)/ IES/ BARC/ ISRO/ SSC-JE /State Engineering Services exams and other important upcoming competitive exams.

### Seepage & Permeability of Soil

Seepage Pressure and Seepage Force

Seepage pressure is exerted by the water on the soil due to friction drag. This drag force/seepage force always acts in the direction of flow.

The seepage pressure is given by

PS = ω where, Ps = Seepage pressure

γω = 9.81 kN/m3

Here, h = head loss and z = length

(ii) FS = hAγω where, Fs = Seepage force

(iii) where, fs = Seepage force per unit volume.

i = h/z where, I = Hydraulic gradient.

Quick Sand Condition

It is condition but not the type of sand in which the net effective vertical stress becomes zero, when seepage occurs vertically up through the sands/cohesionless soils.

Net effective vertical stress = 0 where, ic = Critical hydraulic gradient.

2.65 ≤ G≤ 2.70 0.65 ≤ e ≤ 0.70

• To Avoid Floating Condition and Laplace Equation of Two Dimensional Flow and Flow Net: Graphical Solution of Laplace Equation

(i) where, ∅ = Potential function = kH

H = Total head and k = Coefficient of permeability

(ii) … 2D Laplace equation for Homogeneous soil.

where, ∅ = kX H and ∅ = ky H for Isotropic soil, kx= ky

Seepage discharge (q) where, h = hydraulic head or head difference between upstream and downstream level or head loss through the soil.

• Shape factor = • where, Nf = Total number of flow channels = Total number of flow lines.

• where, Nd = Total number equipotential drops. = Total number equipotential lines.

• Hydrostatic pressure = U = where, U = Pore pressure hw = Pressure head

• Seepage Pressure

Ps = h'γw where,   where, size of exit flow field is b x b.

and is equipotential drop.

Phreatic Line

It is top flow line which follows the path of base parabola. It is a stream line. The pressure on this line is atmospheric (zero) and below this line pressure is hydrostatic.

(a) Phreatic Line with Filter  Phreatic line (Top flow line).

↓

Follows the path of base parabola

CF = Radius of circular arc = C = Entry point of base parabola

F = Junction of permeable and impermeable surface

S = Distance between focus and directrix

= Focal length.

FH = S

(i) q = ks where, q = Discharge through unit length of dam.

(ii) (iii) (b) Phreatic Line without Filter (i) For ∝ < 30°

q = k a sin2 ∝ (ii) For ∝ > 30°

q = k a sin ∝ tan ∝ and ### Permeability

#### Permeability of Soil

The permeability of a soil is a property which describes quantitatively, the ease with which water flows through that soil.

Darcy's Law : Darcy established that the flow occurring per unit time is directly proportional to the head causing flow and the area of cross-section of the soil sample but is inversely proportional to the length of the sample.

(i) Rate of flow (q)  Where, q = rate of flow in m3/sec.

K = Coefficient of permeability in m/s

A = Area of cross-section of sample where, HL = Head loss = (H1 – H2) (ii) Seepage velocity where, Vs = Seepage velocity (m/sec)

n = Porosity & V = discharge velocity (m/s)

(iii) Coefficient of percolation where, KP = coefficient of percolation and n = Porosity. where, Q = Volume of water collected in time t in m3.

Constant Head Permeability test is useful for coarse grain soil and it is a laboratory method.  a = Area of tube in m2

A = Area of sample in m2

t = time in 'sec'

L = length in 'm'

h1 = level of upstream edge at t = 0

h2 = level of upstream edge after 't'. Konzey-Karman Equation Where, C = Shape coefficient, ∼5mm for spherical particle

S = Specific surface area = For spherical particle. R = Radius of spherical particle. When particles are not spherical and of variable size. If these particles passes through sieve of size 'a' and retain on sieve of size 'n'.

e = void ratio

μ = dynamic viscosity, in (N-s/m2) = unit weight of water in kN/m3 Allen Hazen Equation Where, D10 = Effective size in cm. k is in cm/s C = 100 to 150

Loudens Equation Where, S = Specific surface area

n = Porosity.

a and b are constant.

Consolidation equation Where, Cv = Coefficient of consolidation in cm2/sec

mv = Coefficient of volume Compressibility in cm2/N

Capillary Permeability Test  where, S = Degree of saturation

K = Coefficient of permeability of partially saturated soil. where hc = remains constant (but not known as depends upon soil) = head under first set of observation,

n = porosity, hc = capillary height

Another set of data gives,  = head under second set of observation

• For S = 100%, K = maximum. Also, ku ∝ S.

Permeability of a stratified soil

(i) Average permeability of the soil in which flow is parallel to bedding plane,   (ii) Average permeability of soil in which flow is perpendicular to bedding plane.   (iii) For 2-D flow in x and z direction (iv) For 3-D flow in x, y and z direction Coefficient of absolute permeability (k0)  GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 bepstudentsupport@byjus.com