SoilMech Ch10 Flow Nets Soil Mechanics Flow Nets page 1 Contents of this chapter : CHAPITRE 10 FLOW NETS .1 10.1 INTRODUCTION .1 10.2 REPRESENTATION

Draw the structure and soil mass to a suitable scale. The quantity of flow through each flow channel is constant. This assumption leads to the following two-dimensional relationship in velocity gradients. The angle of intersection between each flow line and an equipotential line must be 90o which means they should be orthogonal to each other.

• A groundwater flow model can be built with Visual MODFLOW or GMS, as a prerequisite for contaminant transport simulations with software such as MT3DMS.
• Successful seepage analysis is achieved on the proper and accurate construction of a flow net.
• This method requires a lot of erasing to get the proper shape of a flow net and also consume a lots of time.
• Sketching may start by constructing the first flow line as shown in the figure 7.3 .
• The flow line is divided into a number of squares and equipotential lines are projected outwards into second flow line.
• Before delving into these solution techniques, however, we will establish a few key conditions necessary to comprehend two-dimensional flow.

Water flow through dams is one of the basic problems for geotechnical engineers. Seepage analysis in an important factor to be considered in the proper design of many civil engineering structures. Seepage can occur in both through the structure itself as the case of earth dams and under foundations of an engineering structure. Successful seepage analysis is achieved on the proper and accurate construction of a flow net. Amongst the various existing methods of seepage analysis, the “Finite Element Method” and the method of “Experimental Flow Nets” are the most widely used ones. Construction of a flow net is mainly used for solving water flow problems through porous media where the geometry makes sometimes analytical solutions impractical.

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The uplift pressure at any point within the soil mass can be found using the undermentioned formula. Equal quantity of seepage occurs in each flow channel. The second flow net pictured here (modified from Ferris, et al., 1962) shows a flow net being used to analyze map-view flow , 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 , there must be a recharge boundary nearby to provide water and allow a steady-state flowfield to develop.

The flow lines must start and end at right angles to the ground surface upstream and downstream respectively. We can also attempt to replicate the flow through the actual structure using physical models. There are two major techniques for solving Laplace’s equation. The first is an approximation known as flownet sketching, and the second is the finite difference method.

The equation corresponding curve ǿ and Ѱ are first

The horizontal and vertical component of the hydraulic gradient are, respectively. Where H is the total head and kx and kz are the hydraulic conductivities in the X and Z directions. The condition that the changes in hydraulic gradient in one direction are balanced by changes in the other directions is expressed by Laplace’s equation. Two flow lines or two equipotential lines can never cross each other.

In drawing flow nets for the sand-tank model, potentiometric contours must meet impermeable boundaries at right angles, such as along the glass or the Styrofoam dam, because flow is parallel to an impermeable boundary. Similarly, the downstream interface of sand and open water is a constant-head boundary at 0.7 ft. A groundwater flow model can be built with Visual MODFLOW or GMS, as a prerequisite for contaminant transport simulations with software such as MT3DMS. Grids of 70 rows by 250 columns with cell sizes of 0.01 ft × 0.01 ft were used, although somewhat coarser grid spacings can be used. Students can visualize the dye’s migration in response to the hydraulic gradient, which leads to a greater understanding of advective-dispersion transport processes in the aquifer (see Fig.4). Also, the dye migration with time can be used to calibrate the groundwater model .

Electrical Analogy Method:

The hydraulic boundary conditions are examined and keeping in mind the properties of flow net initial sketching is done and by trial and error the flow net is improved to make it acceptable for practical application. The general solution of the Laplace equation yields two sets of curves orthogonal to each other. One set of curves is known as the flow lines and the other set as equipotential lines.

For these cases, the distribution of Ksat and alpha must be known as well as the angle of anisotropy. For problems in the horizontal plane, water table gradients, saturated flow rates, and land slope gradients can be calculated. For land slope analysis, input the land elevation in place of the pressure head and set Ksat values equal to 1.0. The flownet in confined areas between parallel boundaries typically consists of elliptical and symmetrical flow lines and equipotential lines . 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.

Soil Mechanics – Exams (2007-

Students learn from the sand tank through interaction and visualization, and by collecting and interpreting data. This integrates the theories from lectures into the sand-tank laboratories, enhancing students’ skills and understanding. This document describes the necessary input and interpretation of the output for the program FLOWNET. FLOWNET is a simple computer program developed to calculate hydraulic and topographic gradients for two-dimensional surfaces. Flow rates are calculated for saturated and unsaturated conditions based upon application of Darcy’s law and the exponential hydraulic conductivity equation.

These two systems are similar in the respect that electric potential is analogus to the velocity potential. The electric current is analogus to the velocity of flow and the homogeneous conductor is analogus to the homogeneous fluid. This method only for a practical method of drawing a flow net for a particular set of boundaries. They by drawing equipotential lines the flow net is completed. The procedure is continued until the last flow line is formed.

This method based on the fact that the flow of

The shape of the successive flow lines represents gradual transition from one to the other. If required more trials may be taken to draw the flownet finally. Flownet.zip, a zip archive of the FLOWNET program and sample data drawing flow nets files, is available for download. The size of the square in a flow channel should change gradually from the upstream to the downstream. The appearance of the entire flow net should be watched and not that of a part of it.

The uniform nature of the sand makes it suitable for the sand-tank model. Figure2 is a photomicrograph of sand grains from the St. Peter Sandstone . Part of the sand-tank laboratory can involve a binocular microscope that is set up for students to observe the sand grains and make inferences about the environment of deposition. In an earlier laboratory exercise, the same sand can be used in a permeameter for determination of hydraulic conductivity, which can be compared to the value determined in the sand-tank and flow-net laboratory exercise. The graphical method is most extensively used method among the methods stated above. The graphical method of flow net construction involves sketching by trial and error.