In this article we will discuss about:- 1. Design of Lined Channels 2. Typical Sections of Lined Channels 3. Subsurface Drainage of Lined Canals 4. Design of Unlined Canals.
Design of Lined Channels:
The Bureau of Indian Standards code IS: 10430-1982 “Criteria for design of lined canals and guidelines for selection of type of lining” recommend trapezoidal sections with rounded corners for all channels-small or large. However, in India, the earlier practice had been to provide triangular channel sections with rounded bottom for smaller discharges.
The geometric elements of these two types of channels are given below:
A. Triangular Section:
For triangular section, the following expressions may be derived:
A = D2 (θ + cot θ)
P = 2D (θ + cot θ)
R = D/2
B. Trapezoidal Section:
For the Trapezoidal channel section, the corresponding expressions are:
A = BD + D2 (θ + cot θ)
P = B + 2D (θ + cot θ)
R = A/P
In all the above expressions, the value of is in radians.
The steps to be followed for selecting appropriate design parameters of a lined irrigation channel, according to IS: 10430 may be summarized as follows:
1. Select a suitable slope for the channel banks. These should be nearly equal to the angle of repose of the natural soil in the sub-grade so that no earth pressure is exerted from behind on the lining. For example, for canals passing through sandy soil, the slope may be kept as 2 H: 1V whereas canals in firm clay may have bank slopes as 1.5 H: 1V canals cut in rock may have almost vertical slopes, but slopes like 0.25 to 0.75 H: 1V is preferred from practical considerations.
2. Decide on the freeboard, which is the depth allowance by which the banks are raised above the full supply level (FSL) of a canal.
For channels of different discharge carrying capacities, the values recommended for freeboard are given in the following table:
3. Berms or horizontal strips of land provided at canal banks in deep cutting, have to be incorporated in the section, as shown in Fig. 3.12.
The berms serve as a road for inspection vehicles and also help to absorb any soil or rock that may drop from the cut-face of soil or rock of the excavations. Berm width may be kept at least 2 m. If vehicles are required to move, then a width of at least 5 m may be provided.
4. For canal sections in filling, banks on either side have to be provided with sufficient top width for movement of men or vehicles, as shown in Fig. 3.13.
The general recommendation for bank top width are as follows:
Next, the cross-section is to be determined for the channel section.
5. Assume a safe limiting velocity of flow, depending on the type of lining, as given below:
i. Cement concrete lining: 2.7 m/s
ii. Brick tile lining or burnt tile lining 1.8 m/s
iii. Boulder lining: 1.5 m/s
6. Assume the appropriate values of flow friction coefficients. Since Manning’s equation would usually be used for calculating the discharge in canals, values of Manning’s roughness coefficient, n, from the following table may be considered for the corresponding type of canal lining.
7. The longitudinal slope (S) of the canal may vary from reach to reach, depending upon the alignment. The slope of each reach has to be evaluated from the alignment of the canal drawn on the map of the region.
8. For the given discharge Q, permissible velocity V, longitudinal slope S, given side slope I, and Manning’ roughness coefficient, n, for the given canal section, find out the cross-section parameters of the canal, that is, bed width (B) and depth of flow (D).
Since two unknowns are to be found, two equations may be used, which are:
i. Continuity equation: Q = A * V
ii. Dynamic equation: V = 1/n (AR2/3 S1/2)
In the above equation, all variables stand for their usual notation, A and R is cross sectional area and hydraulic radius, respectively.
Typical Sections of Lined Channels:
Though there may be a large number of combinations of the factors on which the cross-section of a lined canal depends, some typical examples are given in the following figures 3.14 (a) to 3.14 (f). Which may be given an idea of laying and a practical channel cross section.
The Bureau of Indian Standard cod IS: 10430 -1982 “Criteria for design of lined canals and guidelines for selection of type of lining” may generally be used, in addition to special codes like IS: 9451-1985 “Guidelines for lining of canals in expansive soils (first revision)”, which may be used under particular circumstances.
Subsurface Drainage of Lined Canals:
Lined canals passing through excavations may face a situation when the canal is dry and the surrounding soil is saturated, like when the ground table is very near the surface. Similar situation may occur for lined canals in filling when the confining banks become saturated, as during rains and the canal is empty under the circumstances of repair of lining or general closure of canal.
The hydrostatic pressure built up behind the linings, unless released, causes heaving of the lining material, unless it is porous enough to release the pressure on its own. Hence, for most of the linings (except for the porous types like the boulder or various types of earth linings which develop inherent cracks), there is a need to provide a mechanism to release the back pressure or the water in the subgrade. This may be done by providing pressure relief valves, as shown in Fig. 3.15 (a).
Design of Unlined Canals:
The Bureau of Indian Standard code IS: 7112 – 1973 “Criterion for design of cross-section for unlined canals in alluvial soils” is an important document that may be consulted for choosing various parameters of an unlined channel, specifically in alluvial soils. There are unlined canals flowing through other types of natural material like silty clay, but formal guidelines are yet to be brought out on their design. Nevertheless, the general principles of design of unlined canals in alluvial soils are enumerated here, which may be suitably external for other types as well after analyzing prototype data from a few such canals.
The design of unlined alluvial canals as compared to lined canals is more complex since here the bed slope cannot be determined only on the basis of canal layout, since there would be a limiting slope, more than which the velocity of the flowing water would start eroding the particles of the canal bed as well as banks. The problem becomes further complicated if the water entering the canal from the head-works is itself carrying sediment particles.
In that case, there would be a limiting slope, less than which the sediment particles would start depositing on the bed and banks of the canal.
The design concept of unlined canals in alluvium for clear water as well as sediment-laden water is discussed as:
a. Unlined Alluvial Canals in Clear Water:
A method of design of stable channels in coarse non-cohesive material carrying clear water has been developed by the United States Bureau of Reclamation as reported by Lane (1955), which is commonly known as the Tractive Force Method. Fig. 3.16 shows schematically shows such a situation where the banks are inclined to the horizontal at a given angle θ.
It is also assumed that the particles A and B both have the same physical properties, like size, density, etc. and also possess the same internal friction angle θ. Naturally the bank inclination θ should be less than ф, for the particle B to remain stable, even under a dry canal condition. When there is a flow of water, there is a tendency for the particle A to be dragged along the direction of canal bed slope, whereas the particle B tries to get dislodged in an inclined direction due to the shear stress of the flowing water as shown in Figure 3.17.
The particle A would get dislodged when the shear stress, τ, is just able to overcome the frictional resistance. This critical value of shear stress is designated as τc may be related to the weight of the particle, W, as
τCs =W tan ф
For the particle B, a smaller shear stress is likely to get it dislodged, since it is an inclined plane. In fact, the resultant of its weight component down the plane, W Sin and the shear stress (designated as τCs) would together cause the particle to move.
Hence, in this case,
In the above expression it must be noted, that the normal reaction on the plane for the particle B is W cos θ.
Eliminating the weight of the particles, W, from above equation, one obtains;
This simplifies to:
As expected, τcs is less than τcb, since the right hand side expression of equation is less than 1.0. This means that the shear stress required moving a grain on the side slope is less than that required to move on the bed. It is now required to find out an expression for the shear stress due to flowing water in a trapezoidal channel.
It is known that in a wide rectangular channel, the shear stress at the bottom, τ0 is given by the following expression:
τ0 = ϒ R S
Where ϒ is the unit weight of water, R is the hydraulic radius of the channel section and S is the longitudinal bed slope. Actually, this is only an average value of the shear stress acting on the bed, but actually, the shear stress varies across the channel width. Studies conducted to find the variation of shear stress have revealed interesting results, like the variation of maximum shear stress at channel base (τb) and sides (τs) shown in Fig. 3.18 to 3.20.
As may be seen from the above figures, for any type of channel section, the maximum shear stress at the bed is somewhat more than for that at the sides for a given depth of water (compare τb and τs for same B/h value for any graph). Very roughly, for trapezoidal channels with a wide base compared to the depth as is practically provided, the bottom stress may be taken as ϒ RS and that at the sides as 0.75 ϒ RS.
Finally, it remains to find out the values of Band h for a given discharge Q that may be passed through an unlined trapezoidal channel of given side slope and soil, such that both the bed and banks particles are dislodged at about the same time. This would ensure an optimum channel section.
Researchers have investigated for long, the relation between shear stress and incipient motion of non-cohesive alluvial particles in the bed of a flowing stream. One of the most commonly used relation, as suggested by Shields (1936), is provided in Fig. 3.21.
Swamee and Mittal (1976) have proposed a general relation for the incipient motion which is accurate to within 5 percent. For ϒs = 2650 kg/m3 and ϒ = 1000kg/m3 the relation between the critical shear stress τc (in N/m2) diameter of particle ds (in mm) is given by the equation.
The application of the above formula for design of the section may be illustrated with an example.
Say, a small trapezoidal canal with side slope 2H: 1V is to be designed in a soil having an internal friction angle of 35° and grain size 2 mm. The canal has to be designed to cary 10m3/sec on a bed slope of 1 in 5000.
To start with, we find out the critical shear stress for the bed and banks. We may use the graph in Fig. 3.21 or; more conveniently, use equation mentioned above.
Thus, we have the critical shear stress for bed, τcb for bed particle size of 2 mm as:
The critical shear stress for the sloping banks of the canal can be found out with the help of expression mentioned above. Using the slope of the banks (2H: IV), which converts to θ = 26.6°.
The values for the critical stresses at bed and at sides are the limiting values. One does not wish to design the canal velocity and water depth in such a way that the actual shear stress reaches these values exactly since a slight variation may cause scouring of the bed and banks.
Hence, we adopt a slightly lower value for each, as:
Allowable critical shear stress for bed τCb = 0.9τCb = 1.266 N/m2
Allowable critical shear stress for banks τcs = 0.9τCs = 0.792 N/m2
The dimensions of the canal is now to be determined, which means finding out the water depth D and canal bottom B. for this, we have to assume a B/D ratio and a value of 10 may be chosen for convenience. We now read the shear stress values of the bed and banks in terms of flow variable ‘R’, the hydraulic radius, canal slope ‘S’ and unit weight of water ϒ from the figure corresponding to a channel having side slope 2H: IV. However, approximately we may consider the bed and bank shear stresses to be y RS and 0.75 ϒ RS, respectively.
Further, since we have assumed a rather large value of B/D, we may assume R to be nearly equal too -this gives the following expressions for shear stresses at bed and bank:
Unit shear stress at bed = τb = ϒDS = 9810 × D × 1/5000 = 1.962 d N/m2 per metre width.
Unit shear stress at bank τs = 0.75 ϒ DS = 0.75 × 9810 × D × 1/5000 = 1.471 d N/m2 per metre width.
For stability, the shear stresses do not exceed corresponding allowable critical stresses.
Therefore, the value of D satisfying both the expression is the minimum value of the two, which means D should be limited to 0.538 m, say 0.54 m. Since the B/D ratio was chosen to be 10, we may assume B to be 5.3 m, or say, 5.5 m for practical purposes. For a trapezoidal shaped channel with side slopes 2H: IV,
we have;
For the grain size 2 mm, we may find the corresponding Manning’s roughness coefficient ‘n’ using the Strieker’s formula given by the expression:
Since the value of Q does not match the desired discharge that is to be passed in the channel, given in the problem as 100 m3/s, we have to change the B/D ratio, which was assumed to be 10.
Suppose we assume a B/D ratio of, say, k we obtain the following expression for the flow:
Substituting the value D 0 as 0.53 m, as found earlier, it remains to find out the value of k from the, above expression. It may be verified that the value of k evaluates to around 55, from which the bed width of the canal, B, is found out to be 29.15 m, say, 30 m, for practical purposes.
It may be noted that IS: 7112 – 1973 gives a list of Manning’s n values for different materials. However, it recommends that for small canals (0 < 15 m3/s), n may be taken as 0.02. (In the above example, n was evaluated as 0.014 by Strickler’s formula).
b. Unlined Alluvial Channels in Sediment Laden Water:
It is natural for channel carrying sediment particles along with its flow to deposit them if the velocity is slower than a certain value. Velocity in excess of another limit may start scouring the bed and banks. Hence, for channels carrying a certain amount of sediment may neither deposit, nor scour for a particular velocity.
Observations by the irrigation engineers of pre-independence India of the characteristics of certain canals in north India that had shown any deposition or erosion for several years, led to the theory of regime channel szas. These channels generally carry a sediment load smaller than 500 ppm.
The first regime equation was proposed by Kennedy in the year 1895, who was an engineer in the Punjab PWD. Lindley, another engineer in the Punjab proposed certain regime relations in 1919. Later these equations were modified by Lacey, who was at one time the Chief Engineer of the UP Irrigation Department. In 1929 he published a paper describing his findings, which have been quite popularly used in India.
These have even been adopted by the Bureau of Indian Standards code IS: 7112-1973 Criteria for design of cross section for unlined canals in alluvial soils, which prescribes that the following equations have to be used:
Where the variables are as explained below:
S: Bed slope of the channel
Q: The discharge in m3/s
P: Wetted perimeter of the channel, in m
R: Hydraulic mean radius, in m
f: The silt factor for the bed particles, which may be found out by the following formula, in which d50 is the mean particle size in mm;
The Indian Standard code IS: 7112 – 1973 has also recommended simplified equations for canals in certain parts of India by fitting different equations to data obtained from different states and assuming similar average boundary conditions throughout the region.
It may be noted that the regime equations proposed by Lacey are actually meant for channels with sediment of approximately 500ppm. Hence, for canals with other sediment loads, the formula may not yield correct results, as has been pointed out by Lane (1937), Blench and King (1941), Simons and Alberts on (1963), etc. however, the regime equations proposed by Lacey are used widely in India, though it is advised that the validity of the equations for a particular region may be checked before applying the same.
For example, Lacey’s equations have been derived for non-cohesive alluvial channels and hence very satisfactory results may not be expected from lower reaches of river systems where silty or silty-clay type of bed materials are encountered, which are cohesive in nature.
Application of Lacey’s regime equations generally involves problems where the discharge (Q), silt factor (f) and canal side slopes (Z) are given and parameters like water depth (D), canal bed width (B) or canal longitudinal slope (S) have to be determined or Conversely, if S is known for a given f and Z, it may be required to find out B, D and Q.