ADVERTISEMENTS:
In this article we will discuss about:- 1. Design of Earthen Dam 2. Downstream Drainage Systems in Earthen Dam 3. Computation of Seepage Flow 4. Slope Protection.
Design of Earthen Dam:
The preliminary design of an earthen dam is done on the basis of past experiences on similar types of dam regarding their performance and life. The empirical formulae are also used for the purpose.
An earthen dam consists of the following parameters for design:
ADVERTISEMENTS:
1. Top Width:
The top width of earthen dam to be used is decided on the following points:
i. Nature of the fill materials used for construction, and minimum allowable percolation limit through the embankment at normal reservoir level.
ii. Height and importance of the dam.
iii. Practicability of the dam.
ADVERTISEMENTS:
iv. Protection against earthquake shocks and wave action.
A minimum top width should be such that, it can provide a safe percolation gradient at the condition of full reservoir. The following formula can be used for calculating the width of dam as per height –
In which, H is the height of dam. According to the Indian Standard recommendation the top width of dam should be at least 6 m.
ADVERTISEMENTS:
2. Free Board:
It is the vertical distance between the top of the dam and the design water level in the reservoir.
The free board can be classified as:
(i) Normal free board, and
(ii) Minimum free board.
(i) Normal Free Board:
It is a specific term, refers to the difference in elevation between the top of the dam and the normal reservoir level.
(ii) Minimum Free Board:
ADVERTISEMENTS:
The minimum free board is the difference in elevation between the top of the dam and the maximum water level in the reservoir. The difference between normal and minimum free boards is known as surcharge head.
Sufficient free board must be given to the height of dam to avoid the chances of overtopping. Table 18.1, shows the recommended values of free board, depending on the nature of spillway and height of the dam.
3. Casing or Outer Shell:
The main function of casing or outer shell in the earthen dam is to provide stability and creating protection for the core. It is constructed with the previous materials, which are not cracked due to direct exposure of the sunlight. The recommended suitable soils for earth fill dams are given in Table 18.2.
Regarding upstream and downstream side slopes of the dam, these are fixed based on the characteristics of the available materials, foundation condition, dam height and types of the dam, also. The recommended u/s and d/s side slopes, given by Terzaghi are shown in Table 18.3.
4. Central Impervious Core:
The design of central impervious core of earthen dam, mainly done on the basis of following points:
1. Tolerable limit of seepage loss.
2. Maximum width of dam section that will permit proper construction of central impervious core.
3. Types of material available for core construction.
4. Design criteria of purposed filter etc.
In design of central impervious core, it should always be kept in mind that the shear strength of the core material should be less than the dam materials. A thinner shell provides comparatively more stability than a thick shell, because a thick shell causes more resistance to piping action and also develops the crack.
At the top of the dam, a core of 3 meter width is generally used. The height of the core should be at least up to 1 m above the maximum water level in the reservoir, to prevent the seepage due to capillary action. Fig. 18.4. Shows the size range of impervious core, used in the zoned type earthen dams.
A soil, which has less compressibility and liquid limit, is considered as the best material for core construction. On the other hand, the soils which have high compressibility and greater liquid limit, are not suitable for core construction, as they are affected by swelling and formation of cracks. Table 18.4 presents the list of suitable materials recommended by Indian Standard (IS-8826-1978) for core construction in zoned type earthen dam.
5. Cutoff Trench:
The main function of cutoff trench in earth fill dam is to reduce the loss of stored water in the reservoir, from the seepage flow through the foundation and its abutment. Furthermore it also prevents the sub-surface erosion caused by piping action.
The following recommendations have been made on cutoff trench:
1. The alignment of cutoff trench should be such that, its central line should fall within the u/s face of the impervious core; and it should also be fixed into the rock or continuous impervious soil strata.
2. Bottom width of cutoff trench should be such that, it can provide a sufficient working space for compaction equipments, and can also be able to make the dam safe against piping. Generally, a minimum width of 4 m is recommended for cut-off trench. However, an adequate width of cutoff trench for small dams can also be determined, using the following formula –
W = h – d … (18.4)
Where,
W = bottom width of cutoff trench
h = reservoir head above the ground surface
d = depth of cutoff trench below the ground surface
3. The cutoff trench should also be extended to the depth at least 1 m into continuous impervious substratum below the foundation.
4. The cutoff trench on either sides should be extended up to crest of the impervious core in the flank, especially in case of steep abutment of earth dam.
Downstream Drainage Systems in Earthen Dam:
The down-stream drainage is performed by providing the filter materials in the earthen dam. The nature of filter materials should always be more pervious than the general fill materials. The filter in the dam reduces the pore water pressure at the down-stream face of the dam, thereby the stability of the dam gets increase. Filter also controls the piping action to a great extent by checking the migration of soil particles.
The down-stream drainage systems used in the earth fill dam are of following three types:
1. Toe Drains:
These drains are provided in the homogeneous type earthen dams to prevent sloughing action at the down-stream toe of the dam.
2. Horizontal Blanket:
The horizontal blanket as a drain, is widely used in the earthen dams of moderate height for downstream drainage work. This types of drains have disadvantages of greater stratification of dam materials by developing a high permeability zone in the horizontal direction, as compared to the vertical direction. This phenomena creates the horizontal flow of seepage water, which meets to the down-stream face of the dam; and thus causing surface sloughing.
3. Chimney Drain:
It is a most suitable drain, used to prevent the problems of stratification and horizontal flow of seepage water, as normally observed in case of horizontal blanket. Chimney drains are mainly used in higher homogeneous dams.
Filter:
Filters are also provided for solving the problem of down-stream drainage in the earthen dam. The size of filter material should be such that, neither foundation nor embankment materials can penetrate into the filter material, otherwise, there would be clogging of the filter. The minimum thickness of filter is kept as 1 m. As far as possible, the multilayer filters should always be avoided, because they involve additional investment of money.
Design Criteria of Filter Material:
Terzaghi has given the following criterion for design of the filter materials:
1. The D15 size of the filter material should not be more than 4 to 5 times D85 size of the base material to check the movement of foundation materials through the pores of filter materials.
2. The D15 size of filter material should be at least 4 to 5 times the D15 size of the base material.
The above two criterion can also be written as:
Computation of Seepage Flow through Dam:
The computation of amount of seepage flow through the dam and water pressure distribution in the dam section, is based on the theory of fluid flow through porous media. The flow of seepage water through the mass of porous soil is described by the Laplace equation (in two dimensional form), as –
Where,
ɸ = k.h. = velocity potential
k = permeability of soil
h = head causing flow
This equation is valid for an isotropic soil, which has the same permeability in all the directions. The equation states that the velocity potential is a scalar function of space and time, such that its deviation in a particular direction provides the fluid velocity in that direction.
The above equation is based on the following assumptions:
1. The water is in incompressible nature.
2. The soil is also incompressible and porous. The size of pore space does not change with the time regardless of water pressure.
3. The flow of seepage water is due to influence of hydraulic gradient, which is caused by gravity head loss. In other words, the Darcy’s law is valid for flow through soil media.
4. The quantity of seepage water entering into and outgoing through the soil at any given time is the same.
5. The boundary conditions regarding seepage flow at the entry and exit points of the soil mass are known.
The solution of above equation (i.e. eq. 18.5) can be obtained by the following methods:
(a) Analytical method
(b) Graphical method; and
(c) Experimental method.
The flow of seepage water through porous media (i.e. soil), using different assumptions, listed above can be represented by the flow net; which involves two sets of curves, i.e. the equipotential line and the flow line or stream line. These two lines are mutually perpendicular to each other, as shown in Fig. 18.7.
The equipotential line represents the contour of equal head or energy or potential. The direction of seepage flow is always perpendicular to the equipotential line.
Similarly, the stream line is defined as the path along which individual particle of water seeps through the soil.
Seepage Rate through Isotropic Soil:
The seepage rate through isotropic soil can be determined from the flow-net theory. Flow-net is the network of equipotential lines and flow lines. In Fig. 18.7 the segment ABCD is indicated as the field, is the portion enclosed between two successive equipotential lines and two stream lines.
Let, b and I are the width and length of the field, respectively. And,
(i) h is the head drop between two equipotential lines.
(ii) q is the discharge passing through the flow channel of flow-net; and
(iii) Δh is the total head, causing flow.
The seepage rate (q) through the dam can be computed from the flow-net, using Darcy’s law. Applying principle of continuity between a pair of flow line, it is evident that the flow velocity varies inversely with the spacing of flow lines. According to the Darcy’s law, the flow of seepage water through a single flow channel is equal to –
If the field thickness is taken as unit and total number of potential drops in the entire flow-net is Nd, then Δh = h/Nd; and thus the equation 18.6 is written as –
Seepage Flow through Non-Isotropic Soils:
If permeability of the soil varies, both in the horizontal and vertical directions (i.e. Kx ≠ Ky) then soil is defined as the non-isotropic soil. In other words a soil is said to be non-isotropic when its permeability does not remain constant in all the directions. In this case, for computing seepage rate, the flow-net is drawn in case of isotropic soils, but difference is that, in this case all vertical scales are transformed into horizontal scales by multiplying a factor given by √Kx/Ky.
The flow-net for this transformed section is constructed in the same way as for the isotropic soils. Lastly, the actual flow-net for non-isotropic soil is derived by re-transforming the cross-section of the flow-net. This is shown in Fig. 18.8, in which it is observed that the transformed field is in square shape, while actual section (re-transformed) is in rectangular shape, having the length in X-direction equal to √Kx/Ky times the width of field in y-direction.
Let, if
Kx = coefficient of permeability in X-direction of the actual field of anistropic soil
K’ = equivalent permeability of transformed field.
Then, the rate of seepage flow through transformed section will be equal to –
Slope Protection of Earth Dam:
The slope protection of earth dam is divided into following two parts, given as:
The upstream slope of earth dam is mainly protected against wave action caused by the water in the reservoir. However, sometimes a provision is also made against burrowing animals for preventing the failure due to damage caused by their burrowing action.
The followings are the various methods used for u/s slope protection:
(i) Rock rip-rap
(ii) Concrete slab
(iii) Steel fencing
(iv) Bituminous pavement
(v) Precast concrete block.
The rock rip-rap is done in small thickness. It proves more economical, when suitable rocks are available in nearby area in large quantity. At smaller thickness (i.e. in single layer) of rip-rap there is more chance to get disturbed by the erosion, caused by wave action. The thickness of rock rip-rap should be kept about 0.3 m, and it should be extended up to 1 m above the gravel filter.
The filter controls the washing of finer soil particles from the spaces left between the rip-rap. The provision of rock rip-rap on slope is most effective, especially when nature of water current is very strong. From several observations, it has been found that about 95% cases are success by rock rip-rap accomplished with filter material, while only about 30% cases of hand placed rock rip-raps of single layer are found success.
The use of concrete slab for slope protection is done simply by placing the slabs over the filter and weep holes to prevent the passing of water, when water level of reservoir is suddenly dropped.
If the filter is not provided with the concrete slab, then finer particles from the embankment are washed out through the joint places, and thus causing to create a hollow just below the slab. The development of hole results the cracking of the slab due to own weight of slab.
From observations it has been found that the protection of u/s slope, using concrete slab, are failed by about 36% cases, mainly because of not providing of the filter below them.
2. Downstream Slope Protection:
The downstream slope of earthen dam is protected against erosive action of water’s wave from tail water depth. The protection method to be used, is the same to the upstream slope protection work.
Moreover, the downstream slope should also be protected against the rainfall and run-off by providing suitable berms at suitable intervals (say for 15 m or so), to intercept the rainwaters over the-slope and discharge them safely.
In addition, an attempt should also be made for establishment of grasses and plants towards the downstream face, soon after construction of the dam, as they fully cover the sloppy area by their rapid vegetative growth; and thus to control the slope against various causes.