How to Determine Hydraulic Parameters from a Flow Net? | Soil Engineering

Flow net is used to determine various hydraulic parameters needed for the stability analysis of hydraulic struc­tures, as shown in the following subsections.

1. Determination of Discharge:

The space between the two successive flow lines is known as a flow channel. The discharge is given by –

q = KH N_f/N_d …(10.27)

where k is the coefficient of permeability, H is the head causing the flow, N_f is the number of flow channels, and N_d is the number of potential drops.

i. Total Head:

The head loss between successive equipotential lines is equal to H/N_d. The total head at any point (p) is given by –

h = H – n. Δh …(10.28)

where n is the number of equipotential drops from the upstream side up to point p –

Δh = H/N_d …(10.29)

ii. Seepage Pressure:

Seepage pressure can be obtained by –

P_s = γ_w h = γ_w(H-n × Δh) …(10.30)

iii. Hydraulic Gradient:

The average value of the hydraulic gradient for any flow field is given by –

i = Δh/l …(10.31)

where I is the length of the flow field in the direction of flow. Consider the flow net for the sheet pile structure shown in Fig. 10.12. There are five flow channels, with six flow lines. Similarly, there are 10 head drops with 11 equipoten­tial lines. Consider unit length of the sheet pile in the direction perpendicular to the plane of the paper. Consider the flow through the flow field shown hatched.

Let I be the length of the flow field along the flow channel and b the width of the flow field. As per Darcy’s law, the rate of flow through each flow channel will be –

where Δh is the potential drop between EPL 2 (Equipotential line-2) and EPL 3 –

Equation (10.32) represents discharge for an anisotropic soil, where k_x ≠ k_z and b ≠ l. For an isotropic soil, k_x = k_z and b = l. In this case, discharge is –

q = kH(N_f/N_d)

Total Head at Any Point:

The total head at any point p in the soil mass is given by –

h = H – n × Δh

where h is the total head at any point p, H is the total head causing the flow, N_d is the number of equipotential drops up to point p from the first equipotential line, and Δh is the head loss between successive equipotential lines.

2. Pressure Head:

The pressure head at any point is equal to the total head minus the elevation head. The elevation head is measured by taking the downstream water level as the datum. Thus, the pressure head at point p is given by –

h_p = h – (–h_e) = h + h_e

where h_e is negative because point p is below the datum.

3. Hydraulic Gradient:

The hydraulic gradient for any flow field is –

The hydraulic gradient for the flow field on the downstream end of the hydraulic structure is known as exit gradi­ent. To prevent piping failure, the exit gradient should be less than the critical hydraulic gradient.