Seepage takes place through and under all dam, both earth and concrete. The problem is to minimize and control seepage so that it will have no harmful effects. Control of the total quantity of seepage and seepage pressure is an essential part of earth dam design.
When water seeps through the dam it fails depending upon the resistance offered by the material to flow. The seepage line in the body of the dam is such a line below which there is positive hydrostatic pressure. On the line itself, the hydrostatic pressure is zero. Above the line, there is a zone of capillary saturation. The effect of capillary is neglected in dams.
The earth dam fails in most of the cases due to seepage. Hence it is utmost important of know the characteristics of seepage flow as well as distribution of water pressures.
While analysing the seepage flow, the following assumptions must be kept in mind:
1. Water is incompressible.
2. Earth dam and natural Inundation soils are incompressible porous media.
3. Pore spaces do not change with time regardless of water pressure.
4. Flow of water through porous medium follows Darcy’s law. In other words the seeping water flows under the hydraulic gradient due to gravity head loss only.
5. The hydraulic boundary conditions at entry and exit are known.
6. The quantity of water entering and leaving the soil element is same.
Computation of Rate of Seepage from Flow Net:
A network of flow lines and equipotential lines is known as a flow net. Figure 12.19 (b) shows a portion of such a flow net. The space between any two successive flow lines is known as flow channel. The area enclosed between two successive flow lines and successive equipotential lines is known as ‘field’.
Let B and L be the width and length of a field:
Δh = head drop through the field,
Δq = Discharge passing through the flow channel
h = Total head causing flow.
According to Darch’s law of flow through soils
If Nd = total number of potential dress in the complete flow net.
Total discharge through the complete flow net is given by
Nf = number of flow channels in the net.
When field is square then B=L
Equation (7) is the required expression for discharge passing through a flow net. This equation is valid for isotropic soils in which Kx = Ky = K.
Seepage Discharge for Anisotropic Soil:
In such soils K is not equal to Ky. The equation becomes –
This equation is not a Laplacian equation and as such flow net cannot be directly drawn from it.
Rewrite this equation as follows:
Where xn is the new co-ordinate variable in the x-direction.
The equation becomes as follows:
This is again a Laplacian equation.
In order to plot the flow net in such a case the cross-section through anisotropic soils is plotted in y-axis direction on natural scale. Bill, in x-axis direction the cross-section is plotted on a transformed scale. All the dimensions parallel to x-axis are reduced by multiplying by a factor
.
The flow net obtained for this transformed section will now be constructed in the normal manner as if the soil were isotropic. The actual flow net is thus obtained by re-writing the cross-section including the flow net, back to the natural scale by multiplying the x-axis coordinates by a factor
. The actual flow net will thus not have orthogonal set of curves.
Actual field and transformed fields are shown in Fig. 12.20 (c) and (d). Field of transformed section is square, while field of the actual section (re-transformed) will be rectangular having its length in x-axis direction equal to
times the width in y-axis direction.
Let Kx = permeability coefficient in x-direction of the actual anisotropic soil field.
K’ = equivalent permeability of the transformed field.
Then for actual field
For transformed field
Since quantity of flow net is the same
Hence the distance is given by Eq. (12) as follows-
Seepage from Phreatic Line in an Earth Dam:
Seepage from Phreatic Line in an Earth Dam having a Horizontal Filter:
Before a flow net is drawn, it is essential to find the location and shape of the phreatic line separating saturated and unsaturated zones. This can be done by graphical, analytic or experimental methods.
Only Graphical method is explained below:
Graphical Method:
This method was suggested by Casagrande. He assumed Phreatic line as the base parabola with its local point at the starting point (A) of the filter.
See Fig. 12.21 AB is the horizontal filter with A as the focal point of base parabola. EF is the U/S face of the dam. Let horizontal projection of EF is say L. From F measure a length FC equal to 0.3 L at the level of water as shown in figure. Point C thus obtained is considered as the starting point of the base parabola.
With C as the centre and CA as radius draw an arc cutting the horizontal line through CF in point D. Draw a vertical line DH tangential to the curve AD at point D. Evidently CD will be equal to CA and thus vertical line DH would be directrix of the parabola. Bisect AH by point G. G is the last point of the parabola.
In order to locate intermediate points on the parabola, the fact that distance of any point on parabola are equal both from focus A and directrix point H, is used.
For example – to locate nay point P on parabola draw vertical line at any distance say x from A. Measure the distance QH. Taking A as centre and radius QH draw an arc cutting the vertical line through Q in point P. Several point like P can be located and base parabola drawn by joining all these points.
However some correction has to be made at the point of entry. The phreatic line must start from point F and not from C. Also phreatic line must start in direction perpendicular to the U/S face, EF which is also a 100% equipotential line. Hence part of parabola from F is drawn free hand, keeping in view that it must start from F at right angle to face EF and meet the rest parabola tangentially. Hence starting point of parabola is F and end point is at G. The parabola meets horizontal filter vertically at point G.
In order to develop an expression for base parabola consider any point P having xy as its co-ordinates, with respect to the focus point A as the origin.
This is the equation of base parabola.
For discharge (q) seeping through the body of the dam when horizontal filter is installed we consider the section PQ.
Equation (15) is very simple expression for discharge (q) in terms of focal distance f.
The value of f can be determined either graphically or analytically by considering co-ordinates of point C as follows:
Seepage from Phreatic Line for a Dam with No Horizontal Filter:
General Solution by Casagrande:
In this case there is no horizontal filter and as such D/S end point (A) of the embankment is considered as the focal point for base parabola BJG. The base parabola would evidently cut the D/S slope at point / and extend beyond the limits of the dam as shown in Fig. 12.22 (dotted lines).
However, as per exit conditions shown in Fig. 12.24, the phreatic line must come out of the dam at some point M meeting the D/S face tangentially. The D/S MA part of the slope is known as discharge face and always remains wet. The correction Δa by which the parabola should be shifted downwards is found by the values of 
given by Casagrande for various values of slope x of the discharge face or D/S face of the dam. The slope x can be even more than the value of 90ᴼ and it happens where dam, is provided with a rock fill toe as shown in Fig. 12.24 (c).
For Slope Angles of D/S Slope less than 30ᴼ
Mr. Schaffernak and Van lterson gave the following equation to get value a analytically –
Where α is angle in degrees that D/S slope makes with the horizontal.
Casagrande gave following equation for finding value α for D/S slopes lying between 30ᴼ and 60ᴼ –
If S is taken approximately equal to 
, we get this equation in following form –
Where a = as shown in Fig. 12.24 (a)
α = angle in degrees made by D/S slope of the dam with horizontal
H = depth of water at entry point
d = Total horizontal length from D/S end point of the dam to starting point C of parabola.
Seepage Control Measures for Earth Dam:
The safety of earth dam depends almost entirely on seepage control through dam and its foundation. Hence measures of seepage control are very important for the success of an earthen dam.
Seepage control measures can be divided under two heads, namely:
1. Seepage control through the dam.
2. Seepage control through the foundation.
Various measures of seepage control under each category have been discussed in brief:
1. Seepage Control through the Dam:
i. Rock Toe:
Rock toe keeps seepage line well within the dam section. It also helps a great deal for the drainage purposes. The height of the rock toe is kept about one fourth of the height of the dam. Rock toe should be designed like filter.
ii. Horizontal Drainage Filter:
It is provided at the base of the dam, starting from downstream end of the dam and extending backwards into the dam. Backward extension of the filter depends upon so many factors. But this extension may at the most be up to centre line of the dam. This filter controls seepage line and does not allow it to get exposed on D/S face of the dam. It also accelerates the process of consolidation. It also causes drainage of foundation.
If seepage pressure at the D/S end of the dam is still excessive, the horizontal filter drain may be continued even beyond the D/S toe of the dam. Sometimes rock toe and horizontal filter drains are dispensed with and entire D/S portion of the dam may be made from coarse grained soil.
iii. Chimney Drains:
Under conditions of large stratification, the permeability in horizontal direction is more than in vertical direction. This causes greater speed of horizontal seepage than vertical seepage. Chimney drain or filter, if correctly built, intercepts all the seepage from the dam regardless of the stratification in the dam. Chimney drains also render earth dam earthquake resistant.
2. Seepage Control through the Foundation:
i. Impervious Cut-Off:
Cut-off is a wall of relatively impervious material. It is used to prevent seepage through the foundation. It is always led down into the foundation from the ground surface. If possible, cut-off should extend upto the impervious strata lying below the ground level. Partial cut-offs do not prove much effective in preventing seepage. A 90% depth of cut-off reduces about 25% seepage.
ii. D/S Seepage Berms:
Additional berms may be built on the D/S side of the dam in continuation of the D/S end. Such a bean is useful in controlling seepage where D/S top strata is relatively thin and uniform or even top strata is absent. Such berms help in checking uplift of soil and also check sloughing of D/S slope of the dam.
iii. Drainage Trenches:
This measure is adopted when top stratum is pervious and thin. They are provided along the axis of the dam. They may be more than one depending upon the spread of the dam. They have a porous drain having longitudinal slope. Porous drains remain enclosed in gravel filters.
iv. Relief Well:
It is such a well which if not constructed would cause formation of sand boils and possibly sub-surface piping. They reduce the sub surface uplift pressure D/S of the dam. They intercept the seepage through the foundation and control the outlet for seepage. Relief wells become necessary when impervious layer overlies a pervious layer and the thickness of overlying impervious layer is less than the depth of water impounded. Relief wells consist of 10 cm to 15 cm diameter holes filled with filter material.
v. Upstream Impervious Blanket:
Such a blanket when constructed over a pervious foundation reduces the quantity of seepage on D/S side. It also causes reduction in uplift pressure throughout the D/S side.
The provision of U/S blanket is found economical and more effective, when the depth of pervious over burden is large and provision of cut-off wall is uneconomical. Blankets are particularly effective when there are cracks and fissures in the foundation beneath the dam structure. In such cases they seal such openings and reduce the seepage considerably. The blanket should be composed of such material which is at least 100 times less pervious than the foundation material. Thickness of the blanket varies usually between 1 ½ m and 3 m.