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In this article we will discuss about:- 1. Meaning of Phreatic Line 2. Derivation of Phreatic Line with Filter 3. Phreatic Line in Earthen Dam without Filter 4. Properties.
Meaning of Phreatic Line:
Phreatic line is also known as the seepage line or saturation line. It is defined as an imaginary line within the dam section, below which there is positive hydrostatic pressure, and above there is negative hydrostatic pressure in the dam section. The hydrostatic pressure represents the atmospheric pressure, which is equal to zero at the face of phreatic line.
Above the phreatic line, there is capillary zone is also called as capillary fringe, in which hydrostatic pressure is in negative nature. The flow of seepage water, below the phreatic line reduces the effective weight of the soil, as result the shear strength of the soil is reduced due to development of greater pore pressure. But flow through capillary fringe (i.e. above the phreatic line) leads to a greater shear strength due to increased intergranular pressure in earth fill materials.
Derivation of Phreatic Line with Filter:
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In this case, before going directly on derivation technique, the important features of phreatic line must be known. From experimental evidence, it has been reported that the seepage line is pushed down by the filter; and is very close to parabolic shape, except at the junction point of the upstream face. The upstream face of the dam represents 100% equipotential line, when it is covered by the water, at this condition the seepage line should be drawn perpendicular to this face at the junction point.
The Casagrande method is used for deriving the phreatic line; the procedure is described as under:
(i) Let the phreatic line is assumed to be a base parabola with its focus at point F, i.e. at the starting point of the filter, FE. (Fig. 18.9)
(ii) AB is the upstream face of the earth dam, and L is the horizontal projection of face AB on the water surface. Measure the distance BC equal to 0.3 L. Take the point C as the starting point of the base parabola.
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(iii) For deciding the position of directrix of the parabola, the theory which states that every point of the parabola is at equidistance from the focus as well as directrix, is used. Hence, considering C as the centre and CF as radius, an arc is drawn which cut the horizontal line CB at point O. Since, CO = CF, therefore, vertical line OH will be the directrix of parabola.
(iv) The last point G of the parabola will fall at the middle of the points F and H.
(v) The intermediate points of parabola are located on the principle that their distance from the focus and directrix are the same. Here, to locate the point P as an intermediate point, a vertical line DP is drawn at any distance x from point F. Now considering the distance DH as radius with F as centre, an arc is drawn which cuts the vertical line DP at point P.
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(vi) Now, all these obtained points are joined by free hand to get the base parabola. However, this needs to be corrected at the entry point for the feature that the phreatic line must be stated from point B only, not from C. It should be sketched perpendicular to the upstream face AB, as it is 100 percent equipotential line.
Now phreatic line is sketched by free hand in such a way that, it should be perpendicular to face AB and meet to the rest of the points of the parabola tangentially. In addition, the base parabola should also be met perpendicular to the downstream face of the dam at point G. The view of phreatic line is shown in Fig. 18.9.
The equation of base parabola can be derived from its basic properties, i.e. the distance of any point P (x, y) on the parabola from its focus is the same to the distance of the point P (x, y) from the directrix.
This is the expression for computing the rate of seepage discharge through the body of earthen dam in terms of focal distance s. The distance s can be determined either graphically or analytically. Considering C as the co-ordinate, the value of s can be obtained as –
By using this equation, if the value of coefficient of permeability (k) and the focal distance (s) are known, then the discharge (q) can be calculated. This provides an accurate value of seepage rate and is applicable to that dam, which is provided with horizontal drainage (filter) system, but can also be used for other types of dam sections.
Phreatic Line in Earthen Dam without Filter:
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The position of phreatic line in an earth dam without filter can be determined using the same manner, as in previous case (i.e. with filter). In this case, the focus point (F) of the parabola will be the lowest point of the down-stream slope, as shown in Fig 18.10. The base parabola BJC cuts at point J on downstream slope; and is extended beyond the limit of the dam, as indicated by dotted line, but the seepage line should be emerged at point K, tangent to the down-stream face.
In this way, the phreatic line is shifted to the point K from J. The distance KF is known as discharge face, which always remains under saturation condition.
The correction JK (say Δa) by which the base parabola need to be shifted downward, can be determined by the following methods:
1. Graphical method; and
2. Analytical method.
1. Graphical Method:
Casagrande has given a general solution to determine the value of Δa for various degrees of inclination of the discharge face. The inclination angle may be more than the 90°, especially in case of rock fill dam.
Here, JF indicates the distance of the focus from the point, where base parabola cuts the downstream face.
The values of a and Δa can be determined by solving the above two equations (i.e. 18.22 and 18.23).
2. Analytical Method:
Under this method, the following cases are considered for determining the position of discharge face (a) at the down-stream face of the dam.
Case (1):
When slope angle α < 30°:
Schaffernak and Van Iterson have derived an equation for finding the value of a, to fix the position of K. The equation is given as under –
In which, d is the horizontal distance from the origin point of the phreatic line to the toe of the downstream face of the dam and H is the depth of water towards upstream face of the dam. (Fig. 18.11).
The above equation was derived based on the assumption that, the hydraulic gradient is equal to the slope of the phreatic line, which is valid for a relatively flat downstream slope.
Case (2):
When slope angle lies between 30° to 60°:
Casagrande has also derived the following equation for calculating the value of ‘a’, given as –
This equation provides satisfactory values of a ranging from 30 to 60°, but for steeper slopes than 60° yields quite high value. For such case Casagrande has suggested for modification in above equation i.e., to use sin α in place of tan α. In other words, it can be said that the hydraulic gradient (i) is equal to dy/ds but not as dy/dx as taken in the previous case.
Therefore, according to the Darcy’s law –
Properties of Phreatic Line:
A phreatic line has following properties:
1. The starting point of the phreatic line must be normal to the upstream face of the dam, because of the fact that the upstream face is a 100 percent equipotential line; and towards downstream side it should be tangent with the water surface.
2. The focus of the parabola is located at the break point of the bottom flow line. At this point the flow emerges from an impervious medium to a relatively highly pervious medium.
3. When dam is provided with the horizontal filter or drainage toe, then phreatic line should meet vertically at the filter point.
4. If dam is not provided with the filter, then phreatic line should cut the downstream face at some distance above the base.
5. If a pervious layer is present below the earth fill clam, then position of phreatic line is not affected.
6. In zoned type earth dam, the effect of outer zone on phreatic line is negligible. In such case the focus of base parabola is located at the downstream toe of the core, as shown in Fig. 18.12.
