Design of the Main Diversion Structure of a Barrage (Part - 4) - Civil Engineering (CE) PDF Download

 Fixing dimensions of barrage components  

The hydraulic calculation for a barrage starts with determination of the waterway, the minimum stable width (P) can be calculated from Lacey’s modified formula

       P=4.83 Q^1/2          (27) 

Where, the discharge Q is in m³/s. For rivers with very wide sections, the width of the barrage is limited to Lacey’s width multiplied by looseness factor and the balance width is blocked by tie bunds with suitable training measures. Assuming the width of each bay to be between 18m to 20m and pier width to be around 1.5 the total number of bays is worked out. The total number of bays is distributed between spillway, under-sluice and river-sluice bays. The crest levels of the different bays may be fixed up on the basis of the formulations.

With these tentative values, the adequacy of the water way for passing the design flood within the permissible afflux needs to be checked up. Otherwise, the water way and crest levels will need to be readjusted in such a way that the permissible values of afflux are not exceeded.

The discharge through the bays of a barrage (spillway or under sluices) for an uncontrolled condition (as during a flood discharge) is given as: 

Q=CLH^3/2            (28) 

Where L is the clear water way (in meters) H is the total head (including velocity head) over crest (in meters) and C is the coefficient of discharge, which for free flow conditions [as shown in Figure 13 (b)] may be taken as 1.705 (for Broad-crested weirs/spillways) or 1.84 (for Sharp-crested weirs/ spillways). Roughly, a spillway or weir is considered to be Broad Crested if a critical depth occurs over its crest. However, with the general dimensions of a barrage spillway (with the crest width generally being kept at about 2m) and the corresponding flow depths usually prevailing, it would mostly act like a SharpCrested spillway. Under sluices and river sluices (without a crest) would behave as broad-crested weir. Another point that may be kept in mind is that the total head H also includes the velocity head V_a²/2g, where V_a is the velocity of approach and may be found by dividing the total discharge by the flow Q cross section area A. The quantity A, in turn, may be found out by multiplying the river width by the depth of flow, which has to be taken not as the difference of the affluxed water level and the normal river bed, but as the depth of scour measured from water surface.

FIGURE 13. Jump formation modes in a barrage due to same discharge ; (a) Submerged jump for high tail water level; (b) Free jump for low tail water level due to retrogression or steep river slope

It may be noticed from Figure 13 (a) that a barrage spillway/under sluice can also get submerged by the tail water. In such a case, one has to modify the discharge by multiplying with a coefficient, k, which is dependent on the degree of submergence, as shown in Fig .14.

FIGURE 14, Multiplying coefficient (k) for transition from free flow to submerged flow conditions,

Since the crest levels of spillway, under sluice and river-sluice bays would be different, the discharge passing through each will have to be estimated separately and then summed up. Wherever silt excluder tunnels are proposed to be provided in the undersluice bays, the discharge through these tunnels and over them need to be calculated separately and added up.

Having fixed the number of spillway, river-sluice and under sluice bays and their crest levels, it is necessary to work out the length and elevation of the corresponding downstream floors. The downstream sloping apron extending from the crest level to the horizontal floor is usually laid at an inclination of 3H:1V, and the structure is designed in such a way that any hydraulic jump formation (during free flow condition) may take place only on the sloping apron. Thus, the worst case of low tail water level, which governs the formation of a hydraulic jump at the lowest elevation decides the location of the bottom end elevation of the slope as well as that of the horizontal floor (Figure 15). The length of the horizontal floor (also called the cistern) is governed by the length of the jump, which is usually taken as 5(D₂-D₁) where D₁ is the depth of water just upstream of the jump and D₂ is the depth of water downstream of the jump (Figure 15). 

FIGURE 15. Jump formation at lowest orvd of Glads for (a) Spillway bays ; (b) Underslice bays.

It may be observed from the figure that though the upstream and downstream water levels of the spillway and under sluice bays are same for a particular flow condition, the difference in crest elevations (here the under sluice portion is shown without a crest) causes more flow per unit width to pass through the undersluice bays. This results in a depressed floor for the under sluices bays compared to the spillway bays. 

The cistern level and its length for the spillway, river-sluice or under sluice bays have to be determined for various sets of flow and downstream water level combinations that may be physically possible on the basis of the gate opening corresponding to the river inflow value, The most severe condition would give the lowest cistern level and the maximum length required, the hydraulic conditions that have to be checked are as follows: 

1. Flow at Pond level, with a few gates opened.
2. Case 1 with discharge concentration enhanced by 20% and a retrogressed downstream riverbed level.
3. Flow at High Flood Level, with all gates opened.
4. Case 3 with discharge concentration enhanced by 20% and a retrogressed downstream riverbed level.

The determination of cistern level, either through the use of the set of curves known as Blench Curves and Montague curves have to be used, or they may be solved analytically. Here, the latter has been demonstrated and readers interested to know 

about graphical method, may go through any standard textbook on hydraulic structures or irrigation engineering as the following: 

The various steps followed in the determination of the cistern level by analytical methods are as follows: 

1. For any given hydraulic condition, calculate the Total Energy T.E. (=H+ V²/2g, where H is the water head above a datum and V is the average velocity) on both upstream            and  down stream of the barrage corresponding discharge per unit width q.

2. Assume a cistern level. 

3. Then, the energy above crest level on the upstream, E_f1, is determined as : E_f1=upstream T.E.L - Assumed cistern level.

4. From the known values of E_f1 and q with 20% concentration, D₁ (the depth of water before jump) is calculated using the following relationship:

  E_fi = D₁+q₂/(2gD₁²)

 Here, it is assumed that there is negligible energy loss between the upstream point where Ef1 is calculated and up to beginning of the hydraulic jump. In the above equation,     g  is the acceleration due to gravity. 

5.  Calculate the pre-jump Froude number Fr1 using the equation : 

      Fr1² =q²/ (gD₁³) 

6. From the calculated values of D₁ and F_r1, the post jump depth (D₂) can be calculated from the following relationship:  

    D₂= D₁/2(-1+√1+8 F_r1²) 

7. The required cistern level for the considered case of hydraulic condition would be equal to the retrogressed down stream water level minus D₂. 

8. In the first trial, the initially assumed cistern level chosen in step 2 and the calculated cistern level in step 7 may not be the same which indicates that the cistern level                    assumed initially has to be revised. A few trials may be required to arrive at a final level of the cistern. The required length of the cistern is then found out as 5(D₂-D₁). 

The cistern is designed with the final dimension arrived at from the hydraulic calculations mentioned above. However, the length of the horizontal floor can be reduced with a corresponding saving in cost if the normal steady level of the downstream water is obtained in a distance less than 5 times the jump height by addition of some appurtenant structures. The most common is the addition of either one or a combination of the following to the horizontal downstream floor: 

1. A continuous end sill
2. Raised blocks  

According to Bureau of Indian Standards Code IS:4997-1968 “Criteria for design of hydraulic jump type stilling basins with horizontal and sloping apron”, there are many designs of the appurtenant structures recommended for different Froude numbers of  flow over the spillway and downstream tail water level. As such, the Type1 Indian standard stilling basin (Figure 16), which is recommended for inflow Froude number less than 4.5, is suitable for the design of cisterns of barrages. 

Figure 16. Stilling Basin Of Type I Recommended For Barrage Spillways

The length of the upstream floor of the barrage may be fixed after knowing the total floor length required from sub-surface flow conditions and subtracting the crest length, glacis length and down stream cistern length as calculated from the surface flow conditions.