Soil Mechanics & Foundation Engineering: Seepage Analysis

By Sajal Gupta|Updated : February 18th, 2022

Seepage Analysis

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) image122 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

image130 and


Laplace Equation of Two Dimensional Flow and Flow Net: Graphical Solution of Laplace Equation

(i) image132

where, ∅ = Potential function = kH

H = Total head and k = Coefficient of permeability

(ii) image133 

… 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 = image135
  • image136

where, Nf = Total number of flow channels

image137 = Total number of flow lines.

  • image138

where, Nd = Total number equipotential drops.

image139 = Total number equipotential lines.

  • Hydrostatic pressure = U = image140

where, U = Pore pressure hw = Pressure head

hw = Hydrostatic head – Potential head

  • Seepage Pressure

Ps = h'γw where, image142


  • Exit gradient,


where, size of exit flow field is b x b.

and image145 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 = image148

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) image149

(iii) image150

(b) Phreatic Line without Filter


(i) For ∝ < 30°

q = k a sin2 ∝ 


(ii) For ∝ > 30°

q = k a sin ∝ tan ∝ and 


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