Page 1 NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1 Module 2 Lecture 10 Permeability and Seepage -6 Topics 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams 1.2.12 Entrance, Discharge, and Transfer Conditions of Line of Seepage through Earth Dams 1.2.13 Flow net Construction for Earth Dams 1.2.14 Filter Design 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams For construction of flow nets for seepage through earth dams, the phreatic line needs to be established first. This is usually done by the method proposed by Casagrande (1937) and is shown in Figure 2.60a. Note that in Figure 2.60a is the actual phreatic line. The curve is a parabola with its focus at ; the phreatic line coincides with this parabola, but with some deviations at the upstream and the downstream force. At a point , the phreatic line starts at an angle of to the upstream face of the dam and . Figure 2.60 Determination of phreatic line for seepage through an earth dam Page 2 NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1 Module 2 Lecture 10 Permeability and Seepage -6 Topics 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams 1.2.12 Entrance, Discharge, and Transfer Conditions of Line of Seepage through Earth Dams 1.2.13 Flow net Construction for Earth Dams 1.2.14 Filter Design 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams For construction of flow nets for seepage through earth dams, the phreatic line needs to be established first. This is usually done by the method proposed by Casagrande (1937) and is shown in Figure 2.60a. Note that in Figure 2.60a is the actual phreatic line. The curve is a parabola with its focus at ; the phreatic line coincides with this parabola, but with some deviations at the upstream and the downstream force. At a point , the phreatic line starts at an angle of to the upstream face of the dam and . Figure 2.60 Determination of phreatic line for seepage through an earth dam NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 2 The parabola can be constructed as follows: 1. Let the distance be equal to . Now referring to Figure 2.60b, based on the properties of a parabola), , thus (2.196) At substituting these conditions into equation (2.196) and rearranging, we obtain (2.197) Since are known, the value of can be calculated. 2. From equation (2.196), (2.198) With known, the values of for various values of can be calculated from equation (2.198) and the parabola can be constructed. To complete the phreatic line, the portion has to be approximated and drawn by hand. When , the value of can be calculated from equation (2.183) as Note that in Figure 2.60a. Once point has been located, the curve can be approximately drawn by hand. Figure 2.61 Plot of against downstream slope angle. (After A. Casagrande, Seepage through Dams. Contribution to Soil Mechanics, 1925-1940, Boston Society of Civil Enginering, Boston, 1937.) Page 3 NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1 Module 2 Lecture 10 Permeability and Seepage -6 Topics 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams 1.2.12 Entrance, Discharge, and Transfer Conditions of Line of Seepage through Earth Dams 1.2.13 Flow net Construction for Earth Dams 1.2.14 Filter Design 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams For construction of flow nets for seepage through earth dams, the phreatic line needs to be established first. This is usually done by the method proposed by Casagrande (1937) and is shown in Figure 2.60a. Note that in Figure 2.60a is the actual phreatic line. The curve is a parabola with its focus at ; the phreatic line coincides with this parabola, but with some deviations at the upstream and the downstream force. At a point , the phreatic line starts at an angle of to the upstream face of the dam and . Figure 2.60 Determination of phreatic line for seepage through an earth dam NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 2 The parabola can be constructed as follows: 1. Let the distance be equal to . Now referring to Figure 2.60b, based on the properties of a parabola), , thus (2.196) At substituting these conditions into equation (2.196) and rearranging, we obtain (2.197) Since are known, the value of can be calculated. 2. From equation (2.196), (2.198) With known, the values of for various values of can be calculated from equation (2.198) and the parabola can be constructed. To complete the phreatic line, the portion has to be approximated and drawn by hand. When , the value of can be calculated from equation (2.183) as Note that in Figure 2.60a. Once point has been located, the curve can be approximately drawn by hand. Figure 2.61 Plot of against downstream slope angle. (After A. Casagrande, Seepage through Dams. Contribution to Soil Mechanics, 1925-1940, Boston Society of Civil Enginering, Boston, 1937.) NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 3 If , Casagrande proposed that the value of can be determined by using the graph given in Figure 2.61. In Figure 2.60a, . After locating the point on the downstream face, the curve can be approximately drawn by hand. Example 1.10. An earth dam section is shown in Figure 2.62. Plot the phreatic line for seepage. For the earth dam section, . Solution And From equation (2.197), 1 Using equation (2.198), we can now determine the coordinates of several points of the parabola 70 166 65 142.1 60 120.04 55 99.73 50 81.2 45 64.42 Using the values of and corresponding calculated in the above table, the basic parabola has been plotted in Figure 2.62. Page 4 NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1 Module 2 Lecture 10 Permeability and Seepage -6 Topics 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams 1.2.12 Entrance, Discharge, and Transfer Conditions of Line of Seepage through Earth Dams 1.2.13 Flow net Construction for Earth Dams 1.2.14 Filter Design 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams For construction of flow nets for seepage through earth dams, the phreatic line needs to be established first. This is usually done by the method proposed by Casagrande (1937) and is shown in Figure 2.60a. Note that in Figure 2.60a is the actual phreatic line. The curve is a parabola with its focus at ; the phreatic line coincides with this parabola, but with some deviations at the upstream and the downstream force. At a point , the phreatic line starts at an angle of to the upstream face of the dam and . Figure 2.60 Determination of phreatic line for seepage through an earth dam NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 2 The parabola can be constructed as follows: 1. Let the distance be equal to . Now referring to Figure 2.60b, based on the properties of a parabola), , thus (2.196) At substituting these conditions into equation (2.196) and rearranging, we obtain (2.197) Since are known, the value of can be calculated. 2. From equation (2.196), (2.198) With known, the values of for various values of can be calculated from equation (2.198) and the parabola can be constructed. To complete the phreatic line, the portion has to be approximated and drawn by hand. When , the value of can be calculated from equation (2.183) as Note that in Figure 2.60a. Once point has been located, the curve can be approximately drawn by hand. Figure 2.61 Plot of against downstream slope angle. (After A. Casagrande, Seepage through Dams. Contribution to Soil Mechanics, 1925-1940, Boston Society of Civil Enginering, Boston, 1937.) NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 3 If , Casagrande proposed that the value of can be determined by using the graph given in Figure 2.61. In Figure 2.60a, . After locating the point on the downstream face, the curve can be approximately drawn by hand. Example 1.10. An earth dam section is shown in Figure 2.62. Plot the phreatic line for seepage. For the earth dam section, . Solution And From equation (2.197), 1 Using equation (2.198), we can now determine the coordinates of several points of the parabola 70 166 65 142.1 60 120.04 55 99.73 50 81.2 45 64.42 Using the values of and corresponding calculated in the above table, the basic parabola has been plotted in Figure 2.62. NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 4 We calculate as follows. The equation of the line can be given by and the equation of the parabola [equation (2.198)] is . The coordinates of point can be determined by solving the above two equations: Or Hence The solution of the above equation gives so From Figure 2.61, for , So, . The curve portions can now be approximately drawn by hand which completes the phreatic line Figure 2.62. Figure 2.62 Page 5 NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1 Module 2 Lecture 10 Permeability and Seepage -6 Topics 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams 1.2.12 Entrance, Discharge, and Transfer Conditions of Line of Seepage through Earth Dams 1.2.13 Flow net Construction for Earth Dams 1.2.14 Filter Design 1.2.11 Plotting of Phreatic Line for Seepage through Earth Dams For construction of flow nets for seepage through earth dams, the phreatic line needs to be established first. This is usually done by the method proposed by Casagrande (1937) and is shown in Figure 2.60a. Note that in Figure 2.60a is the actual phreatic line. The curve is a parabola with its focus at ; the phreatic line coincides with this parabola, but with some deviations at the upstream and the downstream force. At a point , the phreatic line starts at an angle of to the upstream face of the dam and . Figure 2.60 Determination of phreatic line for seepage through an earth dam NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 2 The parabola can be constructed as follows: 1. Let the distance be equal to . Now referring to Figure 2.60b, based on the properties of a parabola), , thus (2.196) At substituting these conditions into equation (2.196) and rearranging, we obtain (2.197) Since are known, the value of can be calculated. 2. From equation (2.196), (2.198) With known, the values of for various values of can be calculated from equation (2.198) and the parabola can be constructed. To complete the phreatic line, the portion has to be approximated and drawn by hand. When , the value of can be calculated from equation (2.183) as Note that in Figure 2.60a. Once point has been located, the curve can be approximately drawn by hand. Figure 2.61 Plot of against downstream slope angle. (After A. Casagrande, Seepage through Dams. Contribution to Soil Mechanics, 1925-1940, Boston Society of Civil Enginering, Boston, 1937.) NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 3 If , Casagrande proposed that the value of can be determined by using the graph given in Figure 2.61. In Figure 2.60a, . After locating the point on the downstream face, the curve can be approximately drawn by hand. Example 1.10. An earth dam section is shown in Figure 2.62. Plot the phreatic line for seepage. For the earth dam section, . Solution And From equation (2.197), 1 Using equation (2.198), we can now determine the coordinates of several points of the parabola 70 166 65 142.1 60 120.04 55 99.73 50 81.2 45 64.42 Using the values of and corresponding calculated in the above table, the basic parabola has been plotted in Figure 2.62. NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 4 We calculate as follows. The equation of the line can be given by and the equation of the parabola [equation (2.198)] is . The coordinates of point can be determined by solving the above two equations: Or Hence The solution of the above equation gives so From Figure 2.61, for , So, . The curve portions can now be approximately drawn by hand which completes the phreatic line Figure 2.62. Figure 2.62 NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 5 1.2.12 Entrance, Discharge, and Transfer Conditions of Line of Seepage through Earth Dams A.Casagrande (1937) analyzed the entrance, discharge, and transfer conditions for the line of seepage through earth dams. When we consider the flow from a free draining material (coefficient of permeability very large; into a material of permeability it is called an entrance. Similarly, when the flow is from a material of permeability into a free draining material ( ) it is referred to as discharge. Figure 2.63 shows various entrances, discharge, and transfer conditions. The transfer conditions show the nature of deflection of the line of seepage when passing from a materials of permeability . Using the conditions given in Figure 2.63 we can determine the nature of the phreatic lines for various types of earth dam sections. 1.2.13 Flow net Construction for Earth Dams With knowledge of the nature of the phreatic line and the entrance, discharge, and transfer conditions, we can proceed to draw flow nets for earth dam sections. Figure 2.64 shows an earth Figure 2.63 Entrance, discharge, and transfer conditions.. (After A. Casagrande, Seepage through Dams, Contribution to Soil Mechanics, 1925-1940, Boston.Read More

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