# Seepage velocity and Seepage pressure

**Seepage velocity:**

The velocity of water obtained using the total cross-sectional area of the soil is known as discharge velocity or superficial velocity.

Since water flows only through voids and not through the total cross-sectional area, the actual velocity of water is much higher than the discharge velocity, that is known as **seepage velocity** (v_{s}).

By continuity equation used in fluid mechanics:-

q = vA = v_{s }× A_{v} •••••••••••• (1)

where v_{s} is the seepage velocity and A_{v} is the area of voids in the cross-section.

From Equation (1),

We have v_{s} = v A/A_{v}.

We know that:

(A_{v}/A) = [(A_{v} x L)/(A x L)] = (V_{v}/V) = n

where V_{v} is the volume of voids

V is the total volume of the soil, and n is the porosity of the soil. Hence:

v_{s }= v/n

Seepage velocity is always more than discharge velocity. The coefficient of percolation is always more than the coefficient of permeability.

**Seepage Pressure:**

The pressure exerted by the flowing water on the soil due to viscous friction between the water and soil particles is known as **seepage pressure.** Mathematically, it is given by –

Seepage pressure, σ_{s} = γ_{w}h •••••••••••(2)

where h is the hydraulic head lost due to the viscous friction and

γ_{w} is the density of water.

Seepage pressure always acts in the direction of flow. When the flow takes place in the vertical direction –

σ_{s }= γ_{w}h = γ_{w }(h/z). z = γ_{w}.i.z ••••••••••••(3)

where i is the hydraulic gradient. The vertical effective pressure may be increased or decreased due to the seepage, depending upon whether the flow takes place in the downward or the upward direction, respectively.

Effective pressure, σ’ = γ’z ± γ_{w} iz••••••••••••(4)

When the flow takes place in the upward direction, the seepage pressure therefore acts in the upward direction and the effective pressure is reduced. If the flow takes place at high hydraulic gradient, the net effective pressure, defined by Eq. (4)), is reduced to zero.

In such a case, a cohesionless soil mass becomes weightless and cannot support any load, because its shear strength is reduced to zero. This phenomenon of loss of shear strength of soil in the upward flow condition in cohesionless soils is known as the quick condition, boiling condition, or quicksand.

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