Soil Mechanics & Foundation Engineering: Seepage Analysis

 The seepage pressure is given by

P_S = hγ_ω where, P_s = Seepage pressure

γ_ω = 9.81 kN/m³

Here, h = head loss and z = length

(ii) F_S = hAγ_ω where, F_s = Seepage force

(iii)  where, f_s = 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, i_c = 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, ∅ = k_X H and ∅ = k_y H for Isotropic soil, k_x= k_y

Seepage discharge (q)

where, h = hydraulic head or head difference between upstream and downstream level or head loss through the soil.

• Shape factor = 
• 

where, N_f = Total number of flow channels

 = Total number of flow lines.

where, N_d = Total number equipotential drops.

 = Total number equipotential lines.

• Hydrostatic pressure = U = 

where, U = Pore pressure h_w = Pressure head

h_w = Hydrostatic head – Potential head

• Seepage Pressure

P_s = h'γ_w where, 

• Exit gradient,

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 

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