The appearance of the entire flow net should be watched and not that of a part of it. Small details can be adjusted after the entire flow net has been roughly drawn. Let us consider an element of soil of size dx, dz through which flow is taking place. Dams are constructed to impound water for irrigation, water supply, energy generation,
flood control, recreation as well as pollution control. Moreover, disastrous effects of water are
significant on them.
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. 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.
obtained and the same are plotted to give the flow net pattern for the flow of
Many researches indicated that
failure of embankment dams due to seepage alone stands for about 25% of the total failure
cases, apart from overtopping, piping, internal erosion, etc (Singh, 1995). Darcy’s law describes the flow of water through the flow net. Since the head drops are uniform by construction, the gradient is inversely proportional to the size of the blocks. Big blocks mean there is a low gradient, and therefore low discharge (hydraulic conductivity is assumed constant here).
For this reason, approximate methods such as graphical methods
and numerical methods are often employed. Flow net technique is a graphical method, which
satisfies Laplace equation. A flow net is a graphical representation of a flow field (Solution of
Laplace equation) and comprises a family of flow lines and equipotential lines, as presented in
previous section. For simple embankment dams such as a homogeneous earthfill dam with simple
configurations, the configuration of a flow net https://accounting-services.net/chapter-5-flow-nets/ 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.
FEIT 2016 Past Paper Ans.pdf
The equipotential lines are further extended downward, and one more flow line GHJ is drawn, representing the step (4). Extend the equipotential lines downward forming the sides of the squares. These extensions point out appropriate width of the squares, such as squares marked (1) and (2). The accuracy of the computation of hydraulic quantities, such as discharge and pore water pressure, does not depend much on the exactness of the flow net. Also, let Δq represent the discharge passing through the flow channel, per unit length of structure (perpendicular to paper).
- (Flow is laminar)
The soil is completely saturated. - 8.3, the upstream bed level GDA represents 100% potential line and the downstream bed level CFJ, 0% potential line.
- Mathematically, the process of making out a flownet consists of contouring the two
harmonic or analytic functions of potential and flow line function. - The
flow nets are usually built through a trial and error procedure with sketches.
Unconfined seepage problems are commonly encountered in geotechnical
engineering. In these problems, the determination of the free surface and the calculation of
seepage usually requires sophisticated numerical techniques, unfamiliar to most engineers. The second flow net pictured here (modified from Ferris, et al., 1962) shows a flow net being used to analyze map-view flow (invariant in the vertical direction), rather than a cross-section. 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. From the drawn flow net, Nf and Nd can be easily counted, and hence, the seepage discharge can be easily computed by using Eqn.
They by drawing equipotential lines the flow net is
The method consists of filling the flow area with stream and equipotential lines, which are everywhere perpendicular to each other, making a curvilinear grid. First identify the hydraulic boundary conditions. 8.3, the upstream bed level GDA represents 100% potential line and the downstream bed level CFJ, 0% potential line.
Two sets of lines constitute a flow net, which should be always orthogonal to each
other. 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. The
flow nets are usually built through a trial and error procedure with sketches. The solution of Laplace equation requires knowledge of complex boundary conditions. Geotechnical problems usually have complex boundary conditions for which it is difficult to
obtain a closed form solution.
How to Construct a Flow Net for Seepage Analysis: Laplace’s Equation and Methods
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. Finally, using the above mentioned procedure the average pore pressure ratio, ru, for the whole
embankment of the earth dam model was calculated equal to 0. Flow lines and equipotentials should always be perpendicular to each other, in a
homogeneous isotropic system, and form curvilinear “squares”.