Flow Net Properties and Applications

(Coefficient of permeability is constant everywhere in the soil
medium)
 The soil is isotropic. (Coefficient of permeability is same in all directions)
 During flow, the volume of soil & water remains constant. (No expansion or contraction
occurs)
 The soil and water are incompressible. Using the above mentioned geometry, the experimental earth dam model Cross Section view
was accurately drawn in CAD, as shown in figures 4 and 5. This accurate drawing was used for the
construction of the Flow Net consisting of Flow Lines and Equipotential Lines, as presented in
following sections.jordan shoes online buy sex toys online adidas promo code custom baseball jerseys sex toys for couples custom baseball jerseys adult sex toys for sale kansas city chiefs super bowl wins custom jerseys best sex toys for women adidas promo code dallas cowboys jersey nfl jersey sales braided headband wigs nfl fantasy football

Laplace’s equation governs the flow of an incompressible fluid, through an incompressible
homogeneous soil medium. Continuity equation for
steady state and Darcy’s equations and for the case of isotropic soil, the permeability coefficient is
independent of direction (Craig, 2004). The method is typically applied to these types of groundwater flow problems, but it can be applied to any problem described by the Laplace equation, such as the flow of electric current through the earth. Irregular points (also called singularities) in the flow field occur when streamlines have kinks in them (the derivative doesn’t exist at a point).

Graphical Method:

Historically, Stelzer et al, 1987, presented an introductory scheme for plotting contours that
are traced along paths of constant function values. Desai et al, 1988, presented a detailed
theoretical development of Residual Flow Procedure (R.F.) for three dimensional seepage,
and a scheme for locating of the three dimensional free surface. Fan et al, 1992, presented a
simple and unique method for generating flow nets based on nodal potentials and bilinear shape
functions. The method reduces the work of performing a second FEM to compute the stream
potentials at the nodes.

• Geotechnical problems usually have complex boundary conditions for which it is difficult to
  obtain a closed form solution.
• For simple embankment dams such as a homogeneous earthfill dam with simple
  configurations, the configuration of a flow net is relatively straightforward in the determination
  of seepage quantity.
• However, especially for zoned earthfill dams or embankment dams with
  different coefficients of permeability for each zone, the complexity of seepage behaviour
  increases dramatically.
• Calculation of the pore pressure ratio for an embankment is highly important, as this value is
  extremely useful in embankment stability analysis problems (Smith, 2006).

Since the boundary conditions of the majority of “real” structures are complex, an analytical or closed-form solution cannot be obtained for these structures. Using numerical techniques such as finite difference, finite element, and boundary element, it is possible to obtain approximate solutions. Values of ru vary between zero for groundwater at a considerable depth below the toe of slope
and about 0 (Smith, 2006). A value of about 0 for ru indicates that ground water conditions are
close to the surface. Therefore, that was proved true in our case study of the embankment of the
earth dam model, where the value for ru is equal to 0, which indicates that ground water
conditions are close to the surface, which indeed is.

Flow Rate

It has been noticed from experiments on homogeneous earth dam models that the line of
seepage assumes more or less the shape of a parabola. Also, assuming that hydraulic gradient i is
equal to the slope of the free surface and is constant with depth (Dupit’s theory), the resulting
solution of the phreatic surface is parabola. In some sections a little divergence from a regular
parabola is required particularly at the surfaces of entry and discharge of the line of seepage. The
properties of the regular parabola which are essential to obtain phreatic line are depicted in Figure
6.

• An equivalent amount of flow is passing through each streamtube (defined by two adjacent blue lines in diagram), therefore narrow streamtubes are located where there is more flow.
• Mathematically, the process of making out a flownet consists of contouring the two
  harmonic or analytic functions of potential and flow line function.
• All important geometric data for the construction of an accurate drawing of the experimental
  earth dam model are summarised as follows.
• In
  case that there is a substantial amount of water flow under the body of a dam, it can create a lot of
  pressure on the alluvium / sediments.
• The
  concept of ru is relevant to both granular and cohesive soils.

Construction of a flow net is often used for solving groundwater flow problems where the geometry makes analytical solutions impractical. The method is often used in civil engineering, hydrogeology or soil mechanics as a first check for problems of flow under hydraulic structures like dams or sheet pile walls. As such, a grid obtained by drawing a series of equipotential lines is called a flow net. The flow net is an important tool in analysing two-dimensional irrotational flow problems.

RATE OF SEEPAGE THROUGH THE EARTH DAM

The inference from Equations (4a) and (4b) is that the velocity of flow (v) is normal to lines of constant total head, as illustrated in Figure 1 The direction of v is in the direction of decreasing total head. The head difference between two equipotential lines is called a potential drop or head loss. The method consists of filling the flow area with stream and equipotential lines, which are everywhere perpendicular to each other, making a curvilinear grid. As mentioned earlier the main application of flow net is that it is employed in estimating
quantity of seepage. If H is the net hydraulic head of flow (i. the difference in total head between
the first and last equipotential), the quantity of seepage due to flow may be estimated by drawing
the flow net, which is shown in Figure 15.

Note that this problem has symmetry, and only the left or right portions of it needed to have been done. To create a flow net to a point sink (a singularity), there must be a recharge boundary nearby to provide water and allow a steady-state flowfield to develop. Dams are constructed to impound water for irrigation, water supply, energy generation,
flood control, recreation as well as pollution control.

t hrough t he eart h dam m odel

Mathematically, the process of constructing a flow net consists of contouring the two harmonic or analytic functions of potential and stream function. These functions both satisfy the Laplace equation and the contour lines represent lines of constant head (equipotentials) and lines tangent to flowpaths (streamlines). Together, the potential function and the stream function form the complex potential, where the potential is the real part, and the stream function is the imaginary part.  The pressure drop from one side of the embankment to the other,
 The seepage flow rate in each flow “channel”,
 The total seepage flow rate, and
 The pore pressure ratio, ru, for the embankment. A Flow net is a graphical representation of flow of water
through a soil mass.

The flownet in confined areas between parallel boundaries typically consists of elliptical and symmetrical flow lines and equipotential lines (Figure 2). Avoid abrupt changes between straight and curved flow and equipotential lines. For certain problems, portions of the flownet are enlarged, are not curvilinear squares, and do not satisfy Laplace’s equation. Since flow lines are normal to equipotential lines, there can be no flow across flow lines.

 Flow lines should always be perpendicular to a constant head boundary, and Equipotential
lines are always parallel to it. An infinite number of flow lines and equipotential lines can be drawn to satisfy Laplace’s equation. Finally, using the above mentioned procedure the average pore pressure ratio, ru, for the whole
embankment https://personal-accounting.org/github/ of the earth dam model was calculated equal to 0.  A photograph of the experiment set up of the earth dam model was taken as shown in
Figure 2, where the seepage flow lines through the earth dam model and the boundary
conditions are also shown. These seepage flow lines were used as a rough guide for the
flow net construction.

• For this reason, approximate methods such as graphical methods
  and numerical methods are often employed.
• The flow lines indicate the direction of groundwater flow and the equipotential lines or head
  lines (lines which represent the constant head), indicate the distribution of potential energy.
• Flow lines represent the path of flow along which the water will seep through the soil.
•  Flow lines should always be parallel to an impermeable boundary, and Equipotential lines
  are always perpendicular to it.
• Where H is the total head and kx and kz are the hydraulic conductivities in the X and Z directions.
• The inference from Equations (4a) and (4b) is that the velocity of flow (v) is normal to lines of constant total head, as illustrated in Figure 1 The direction of v is in the direction of decreasing total head.

It is a curvilinear net formed by the combination of flow
lines and equipotential lines. Properties and application of flow net are
explained in this article. Flow nets are a graphical way / technique for predicting the quantity of groundwater flow from
a given set of boundary conditions. Flow nets are not a rigorous determination of flow, but they
can give an idea of what head looks like underground.  Flow lines and equipotentials should always be perpendicular to each other, in a
homogeneous isotropic system, and form curvilinear “squares”.  Flow lines should always be parallel to an impermeable boundary, and Equipotential lines
are always perpendicular to it.

Foundation for Bridges Over Water

For simple embankment dams such as a homogeneous earthfill dam with simple
configurations, the configuration of a flow net is relatively straightforward in the determination
of seepage quantity. However, especially for zoned earthfill dams or embankment dams with
different coefficients of permeability for each zone, the complexity of seepage behaviour
increases dramatically. Therefore, seepage modelling using a drainage and seepage tank as well
as a finite element analysis technique can help to solve the problem promptly, thus saving funds
and time, but immolating a marginal reduction of accuracy. Several authors such as
Papagianakis, 1984, Lam et al, 1988, Potts et al, 1999, Rushton et al, 1979, Vandammea et al,
2013, had performed seepage analysis using either finite element or drainage and seepage tank
apparatus method.