2 8 Drawing a Flow Net for a System with Anisotropic Hydraulic Conductivity Graphical Construction of Groundwater Flow Nets

Equipotential lines represent locations of equal hydraulic head, while flow lines indicate the path of water flow. The intersection of equipotential lines and flow lines creates a network that depicts the flow pattern within the soil mass. Flow nets are a crucial tool in geotechnical engineering, particularly in the analysis of groundwater flow and seepage through soils. A flow net is a graphical representation of the flow of water through a porous medium, such as soil or rock.

Graphical Construction of Groundwater Flow Nets

• The rate of inflow can be determined if the value of hydraulic conductivity is known.
• The flow net diagram is particularly useful for visualizing complex flow patterns and determining the direction and magnitude of flow.
• The flow lines should be drawn perpendicular to the constant-head boundaries.
• In computational fluid dynamics, flow nets can visually validate the results from simulations.

Using knowledge of Darcy’s Law and the fact that flow is parallel to no-flow boundaries, one flow path can be drawn along the concrete dam from the upgradient to the downgradient reservoir (Figure 6). Once the elevation grid is drawn, proceed to sketch the equipotential lines at right angles to no-flow boundaries and flow lines. Make sure that equipotential lines meet the water table and the seepage face at an elevation that is the same as the hydraulic head of the equipotential line. The equipotential lines and flow lines should intersect to form curvilinear squares. As before, one way to decide if you are creating curvilinear squares is to draw a circle between the intersecting lines. If the circle fits roughly within the shapes, then they are approximately curvilinear squares (Figure Box 4-4).

The diagram’s accuracy depends on carefully considering factors such as hydraulic conductivity, soil permeability, boundary conditions, and the presence of seepage lines. By following established techniques and guidelines, you can create reliable flow nets that accurately represent the subsurface water flow and support your geotechnical analyses. A key difference between graphical versus numerical construction of a flow net is that the graphical method requires creating both equipotential lines and flow lines, whereas the numerical method does not. Groundwater professionals commonly use a groundwater model to compute hydraulic head, then later use a flow path tracking model (also known as a particle tracking model) to compute flow lines. A project might require computing only hydraulic head, in which case flow paths are not computed.

Calculation of Seepage Quantity and Pore Water Pressure

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Foundation Design

Once the flow net has an acceptable form, the next step is to calculate the values of the equipotential lines and label them. The equipotential lines represent hydraulic heads within the system between the boundary heads. The difference between the value of head on adjacent equipotential lines is called the contour interval. To determine the magnitude of the contour interval, first determine the total head drop across the flow net, H, and divide that by the number of head drops, nd, in the flow net as shown in Equation 1. Gage pressure is typically used for quantifying pressure, with atmospheric pressure being equivalent to zero gage pressure. At the water table and along the seepage face, the gage pressure is zero so the hydraulic head is equal to the elevation.

What are the Common Problems Associated with Flow Net Diagrams in Soil Mechanics?

The only realistic way for the human eye to achieve constant aspect ratios, is to draw “curvilinear squares”, quadrilaterals with curved sides with an aspect ratio close to 1 (Figure 3). An exception to these requirements may occur near the edge of the domain where a partial (or fractional) flow tube may be drawn. A flow net diagram is a graphical representation used in soil mechanics to visualize the movement of water through a porous medium, such as a soil layer. It is a powerful tool for understanding the flow of water in a porous medium, particularly in the context of seepage and groundwater flow. The flow net diagram is constructed by combining a potential line network with a stream function, which helps to illustrate the direction and magnitude of the flow. A flow net is drawn in the transformed section (Figure Box 5-6) according to the steps of flow net construction under isotropic conditions as described in section 2.2 of this book.

You’ll discover the fundamental principles behind this graphical representation, learn the step-by-step process of construction, and gain a deeper understanding of how water movement influences soil mechanics. Yes, flow net diagrams can be used in soil mechanics for other applications, such as the design of drainage systems, water supply systems, and waste management systems. Additionally, flow net diagrams can be used to predict the behavior of water in the soil under various conditions, such as changes in rainfall or groundwater levels. However, the use of flow net diagrams for these applications may require additional expertise and specialized software, and the results may need to be interpreted in the context of the specific application.

The flow lines represent the path of water flow through the soil, while the equipotential lines represent the hydraulic head, or pressure, of the water at different points in the soil. Flow nets are graphical representations used in hydrogeology and soil mechanics to analyze two-dimensional flow fields of fluids through porous media. They consist of a network of streamlines and equipotential lines that intersect at right angles, helping visualize the paths and rates of fluid flow.

Small details can be adjusted after the entire flow net has been roughly drawn. Let b and L be the dimensions of the field and Δh be the head drop through this field. To accomplish this, we use the formula presented here as Equation Box 5-3. Either transform results in an acceptable isotropic geometry for the system as shown in Figure Box 5-2. Alternatively, we could multiply the x-coordinates of the ellipse by the ratio .

Applications of Flow Nets in Foundation Engineering

• A flow net diagram is a graphical representation of the flow of water through a soil mass, and it is essential to understand the fundamentals of flow net diagrams to accurately draw and interpret them.
• It is used to visualize and quantify the movement of water, which is essential for designing safe and stable foundations, dams, and other hydraulic structures.
• The size of the square in a flow channel should change gradually from the upstream to the downstream.
• Flow net analysis can be further enriched by integrating numerical simulations.
• For this reason, it is useful to add lines of equal elevation before sketching the equipotential lines (Figure Box 4-3) as a guide for drawing the flow net.

In the field, the porous geologic material below the dam extends a long distance in the upgradient and downgradient directions, but only a portion of it is illustrated here. The water level in the reservoir contained by the dam is 10 meters above the surface of the low hydraulic conductivity material below the aquifer which is used as a datum. The water level in the reservoir below the dam is 4 meters lower than the water behind the dam and the water below the dam runs off downstream. This is especially the case in groundwater basins comprised of layered sedimentary rocks of differing hydraulic conductivity.

The horizontal and vertical component of the hydraulic gradient are, respectively. The uplift pressure at any point within the soil mass can be found using the undermentioned formula. Figure 13 – Click here to go to Box 4 draw flow nets which describes the procedure for drawing a flow net with a water table boundary. Begin the steps for drawing a flow net as described in section 2.3 and shown in Figure Box 4-1.

For an anisotropic system in a plan view, it is necessary to know the principal directions and align the x–y coordinate system to these directions. The geometric transformation can then be carried out for flow net construction. Figure Box 4-4 – The shapes are curvilinear squares if circles fit approximately within them, but some flow nets may include partial flow tubes as shown here by the narrow flow tube at the bottom of the flow net.

Begin by drawing a line representing the water table, if applicable, and then add additional lines, ensuring they are spaced evenly. From understanding equipotential lines to interpreting flow lines, we’ll demystify the intricacies of flow net diagrams and empower you to apply this essential tool in your own projects and analyses. In today’s world, where infrastructure projects and environmental concerns intertwine, the ability to predict and manage water flow in soil is more critical than ever. Whether it’s designing a dam, analyzing a landfill, or mitigating erosion, a well-constructed flow net diagram provides invaluable insights into the complex dynamics of groundwater. By following these steps and tips, engineers can draw accurate and informative flow net diagrams that are essential in a wide range of applications in soil mechanics.

The equipotential lines are further extended downward, and one more flow line GHJ is drawn, representing the step (4). When Equation Box 5-3 is applied to an anisotropic system, an equivalent hydraulic conductivity is used to account for the differing values in the horizontal and vertical direction. Equivalent hydraulic conductivity for an anisotropic system is calculated as shown in Equation Box 5-4. Figure Box 5-4 Only a small portion of the field with parallel drains needs to be drawn to develop a flow net. A groundwater divide (no-flow boundary) occurs halfway between two adjacent drains. In addition, flow to the drain from the left is a mirror image of flow from the right.

This is especially crucial for maintaining water quality and preventing seawater intrusion. Recuperative heat exchangers play a crucial role in thermal systems design, enabling efficient heat… The increasing complexity of modern embedded systems demands high reliability from their processors…. Phreatic line is a seepage line as the line within a dam section below which there are positive hydrostatic pressures in the dam. Starting from the upstream end, divide the first flow channel into approximate squares. The appearance of the entire flow net should be watched and not that of a part of it.