The velocities of water flowing through the voids in a soil are very small, and the velocity head in the previous equation may be neglected. Therefore, for flow of water in soil the equation is:
Water is flowing in the direction indicated in the figure.
Only the portion of the soil cross-sectional area representing the void spaces has water flowing. The solid portion of the area will not allow flow. Flow rate calculations are done using the average velocity, v, and the total cross-sectional area, A. If we let seepage velocity represent the actual velocity of water flowing through the void spaces, then the following equation may be developed.
Link To Example Problem 1
The notation for coefficient of permeability is k. It is sometimes called hydraulic conductivity.
|Clean Gravel||1.0 to 100||2.0 to 200|
|Coarse Sand||0.01 to 1.0||0.02 to 2.0|
|Fine Sand||0.001 to 0.01||0.002 to 0.02|
|Silty Clay||0.00001 to 0.001||0.00002 to 0.002|
|Clay||Less Than 0.000001||Less Than 0.000002|
Several empirical equations have been proposed. Probably the most well known is Hazen's approximation.
In nature, soil is normally stratified or layered. The layers are usually horizontal as most soils are deposited in this manner.
The figure shows horizontal layers of soil with flow parallel to the layers. Following the figure, an equation is developed to calculate the equivalent permeability for flow parallel to the layers.
The figure shows horizontal layers of soil with flow perpendicular to the layers. Following the figure, an equation is developed to calculate the equivalent permeability for flow perpendicular to the layers.
Link To Example Problem 2
Link To Example Problem 3
This example for constructing a flow net is similar to Figure 5.21 in the textbook. In the example, water is flowing under a sheet pile wall that is driven partially through a permeable isotropic soil. The first step is to draw the situation to scale.
A flow net is a combination of flow lines and equipotential lines that satisfy Laplace's equation and the boundary conditions.
The flow net for this example follows. Equipotential lines are red and dashed, while flow lines are green and solid. The length and width of one of the fields is shown. The length in the direction of flow is L, while the width is b. To be "square" ( L= b ).
The flow net from the previous section will be used for the calculations. The coefficient of permeability for the soil is 0.04 ft/s
B. Flow Rate
We will calculate the water pressure at point A in the flow net.
Gradients are different for each field in a flow net. Head losses across each field will be the same, but the flow length depends on the size of the field. Small fields will have a small flow length and a large gradient. Conversely, large fields will have a large flow length and small gradients. Flow length may be measured directly from the flow net, since it is drawn to scale. Following is a gradient calculation for the field with " L = 11' " printed inside. The length, L, was determined by direct measurement and multiplication by the scale factor.