Since in our case and , point L has such Figure 1. coordinates . At the same time, x coordinate of point M equals , while its z coordinate equals . Since in our case , , , and , point M has such coordinates . Points L and M are shown on Figure 1. We look for equation of the dam slope adjacent to the water reservoir in the form where and are constants. Since points L and M lie on this line, and can be found from the solution of the following system of equations (1) Solving the first equation of this system for we obtain the following . (2) Substituting the right hand side of equation (2) for in the second equation of system (1) we obtain the following . Therefore, . From equation (2) it follows that . Hence, the equation of the slope adjacent to the water reservoir has the following form:. The water level is equal to . Since and , the z coordinate of point A equals 43. Moreover, point A lies on line LM. Therefore, its x coordinate satisfies the following equation . Solving it for x we obtain that point A has such coordinates . In its turn, the difference between x coordinates of points L and A is the following:. Point F on the water surface at distance from point A has the following coordinates –. The difference between x coordinates of points F and O is the following: . ...

Table 1. 0.2*H 0.4*H 0.6*H 0.8*H H x= -0,539 11,579 31,774 60,048 96,400 z= 8,600 17,200 25,800 34,400 43,000 Problem # 2 In the second problem we are supposed to correct the shape of the phreatic line in the vicinity of point A. Therefore, we draw a curve that intersects line LM at right angle and “meets the base parabola smoothly and tangentially at a convenient point say,” N (Vijayendra, 2010, p. 15). The final shape of the free surface is shown on Figure 2. Figure 2 Problem # 3 Curve KNA shown on Figure 3 is a free water surface. Hence, the pore water pressure along this line is constant and equal to the atmospheric pressure (Vijayendra, 2010, p. 11). We assume that the pore water is incompressible. The hydraulic head is given by such the expression where here and below is the water density, is the acceleration of free fall, is pressure of the pore water (Wikipedia, n. d.). Therefore, the head loss between any two points belonging to this curve is proportional to the difference in their vertical coordinates. Since curve KNA is a phreatic line, it is a flow line (Vijayendra, 2010, p. 11). Segment LO shown on Figure 3 is the interface between the soil and the impermeable boundary. Therefore, it is a flow line (Vijayendra, 2010, p. 4). We draw the equipotential lines that start at points , , , and N making smooth transitions between their “straight and curved sections” (Vijayendra, 2010, p. 5). These lines are perpendicular to flow lines LO and KNA, as it is shown on Figure 3. Segment LA shown on Figure 3 is the “soil and permeable boundary” interface. Therefore, it is an equipotential line (Vijayendra, 2010, p. 4). The toe drain is a pipe
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