INTERPRETATION OF FLOW NET - IN SOIL MECHANICS :

FLOW RATE:

Let the total head loss across the flow domain be ΔH, that is, the difference between upstream and downstream water level elevation. 

Then the head loss (Δh) between each consecutive pair of equipotential lines is 

• ∆h = ∆H/Nd 

where Nd is the number of equipotential drops, 

that is = the number of equipotential lines minus one. 

• Therefore, Δh = ΔH/Nd 

From Darcy’s law, the flow rate is 

• q= k.H.Nf /Nd 

where Nf is the number of flow channels (number of flow lines minus one).

The ratio N f /N d is called the shape factor. Finer discretization of the flow-net by drawing more flow lines and equipotential lines does not significantly change the shape factor. 

 

Hydraulic Gradient:

• You can find the hydraulic gradient over each curvilinear square by dividing the head loss by the length, L.that is,
• i= ∆h/L 
• You should notice that L is not constant. Therefore, the hydraulic gradient is not constant. 
• The maximum hydraulic gradient occurs where L is a minimum; that is, 
• Imax =∆h / Lmin 
• where L min is the minimum length of the cells within the flow domain. 
• Usually, L min occurs at exit points or around corners, and it is at these points that we usually get the maximum hydraulic gradient.  

Critical Hydraulic Gradient:

• We can determine the hydraulic gradient that brings a soil mass (essentially, coarse-grained soils) to static liquefaction. 
• Static liquefaction, called quicksand condition, occurs when the seepage stress balances the vertical stress from the soil. The critical hydraulic gradient, i cr , is
•  icr = (G-1) /1+e) 
• where G s is specific gravity of the soil particles, and e is the void ratio. 
• Since G s is constant, the critical hydraulic gradient is solely a function of the void ratio of the soil. 
• In designing structures that are subjected to steady-state seepage, it is absolutely essential to ensure that the critical hydraulic gradient cannot develop.  

Pore Water Pressure Distribution:

 

Uplift Forces:

Lateral and uplift forces due to groundwater flow can adversely affect the stability of struc- tures such as dams and weirs. The uplift force per unit length (length is normal to the xz plane) is found by calculating the porewater pressure at discrete points along the base (in the x direction,) and then finding the area under the porewater pressure distribu- tion diagram  

IMPORTENT Terms:

• 1. A flow-net is a graphical representation of a flow field that satisfies Laplace’s equation and comprises a family of flow lines and equipotential lines. 

• 2. From the flownet, we can calculate the flow rate, the distribution of heads, pore- water pressures, and the maximum hydraulic gradient. 

• 3. The critical hydraulic gradient should not be exceeded in design practice.

 

SUMMARY:

• The governing equation for flow of water through soils is Laplace’s equation. 
• A graphical technique, called flownet sketching, was used to solve Laplace’s equation.
• A flownet consists of a network of flow and equipotential lines. 
• From the flow-net, we can calculate the flow rate, the distribution of heads, pore-water pressures, and the maximum hydraulic gradient.