Tutorial Sheet 2 Flow Nets

CN214

Tutorial sheet 2 – Flow nets

Q1:

The figure below shows the cross section of a concrete dam founded on permeable soil, below which there is an impermeable stratum. Make a flow net assuming the soil to be isotropic.

Calculate

a) the seepage rate under the dam if the permeability k = 12.5 x 10-3 mm/s, and

b) the uplift pressure on the base of the dam.

Solution:

Draw as accurately as possible the flow net for the problem.

Determine the following

Number of flow lines Nf = 12

Number of equipotential drops Ne = 27

Seepage rate is given by

q = 5.75 m3/day per metre run of dam

The pressure drop between adjacent equipotential lines is

m of water

Pressure head under base at upstream face = (13.5-1.5) - 4 x 0.444 = 10.22 m head

Pressure head under base at downstream face = (13.5-1.5) - 23 x 0.444 = 1.788 m head

From the shape of the flow net (uniform spacing of equipotentials) it can be seen that the drop in uplift pressure between the two faces is linear as shown on the sketch above (you can of course calculate a few intermediate points)

The total uplift force/m run of dam is thus the area of the uplift pressure diagram

Uplift force =

Q2:

The figure shows the cross section of a long cofferdam into which the flow can be considered as two dimensional. Sketch the flow net for this situation.

The base of the soil stratum is at a considerable depth.

Determine the seepage into the cofferdam (per metre rum), if the water level inside is maintained at excavation level. The permeability of the soil is 0.015m/s in every direction.

Using the flow net determine the distribution of water pressure both on the outside and inside of the sheet piling. Express this pressure in metre head of water and indicate it on an adjacent plot.

Comment on the stability of the proposed structure.

Solution: Example taken from Sutton H.C 'Solving problems in soil mechanics'

Q3:(Example taken from GE Barnes 'Soil Mechanics; Principles and Practice')

A concrete weir is to be placed on a sand deposit as shown below. The coefficients of permeability of the sand are

Horizontalkh = 9 x 10-5 m/s

Vertical kv = 1 x 10-5 m/s

Determine the quantity of flow in litres/minute emanating downstream and the uplift force (upthrust) acting on the underside of the structure.

The soil is anisotropic with respect to permeability so the cross-section must be drawn to a transformed scale by reducing the horizontal dimensions by the factor and maintaining the vertical dimensions. A 'square' flow net is then drawn to the transformed cross-section as below.