Design Principles for Sarda Type Fall:
This type of falls are constructed on Sarda canal in Uttar Pradesh. It is a fall with raised crest and with vertical impact. The soils in Sarda command comprised sandy stratum overlain by sandy-clay on which depth of cutting was to be kept minimum. This made it obligatory to provide number of falls with small drops. In Sarda type falls (q) discharge intensity varied from 1.6 to 3.5 cumec/m and drop varied from 0.6 to 2.5 m.
Crest Dimensions:
This type of fall is not flumed.
For canal discharge 15 cumec and more
ADVERTISEMENTS:
Crest length of fall = Bed width of the canal.
For distributaries and minors
Crest length of fall = Bed width + Depth of flow.
Body wall: When the discharge of a canal is less than 14 m^/sec the section of body wall is kept rectangular (Fig. 19.22 (a)).
ADVERTISEMENTS:
When the discharge of a canal is more than 14 m3/sec the section of the body wall is kept trapezoidal with upstream batter 1: 3 and downstream batter 1: 8.
For rectangular body wall:
Top width ‘b’ = 0.552 √d
ADVERTISEMENTS:
Base width ‘B’ = H + d/√p
For trapezoidal body wall Top width b = 0.522 √(H + d)
The edges are rounded with a radius of 0.3 m.
Base width B is determined by the batter given to u/s and d/s sides.
ADVERTISEMENTS:
Here H is depth of water above the crest of the fall in metres. (It includes velocity of approach also).
d is the height of the crest above the downstream bed level in metres.
Discharge Over Crest:
The discharge formula used in this type of fall under free fall condition is:
Q = CLH {H/b}1/6
where L is length .of crest in m and Q is discharge in cumec.
Value of C for trapezoidal crest is 2 and for rectangular crest 1.85.
For submerged flow conditions (above 33% submergence) neglecting velocity of approach the discharge is given by the following formula
where Cd = 0.65
HL = drop in water surface
and h2 = depth of d/s water level over top of crest.
Crest Level:
The height of crest above the upstream bed level is fixed in such a way that the depth of flow u/s of the fall is not affected. From the discharge formula mentioned above since Q is known value of H can be calculated.
R . L of crest = F . S . L on the u/s – H.
The stability of body wall should be tested by usual procedure when the drops exceeding 1.5 m are to be designed. In the body wall drain holes may be provided at the u/s bed level to dry out the canal during closures for maintenance, etc.
Cistern dimensions: Dimensions of the cistern may be fixed from the Bahadurabad Research Institute formula given in article 19.17, i.e.,
LC = 5√E.HL and
X = ¼ (E.HL)2/3
Total Length of Impervious Floor:
As for any hydraulic structure total length of the impervious floor should be designed on the basis of Bligh’s theory for small structures and Khosla’s theory for other works. Maximum seepage head is experienced when on the u/s water is upto the crest level of the fall and there is no flow on the d/s side. Referring Fig. 19.22 maximum seepage head is given by ‘d’.
Length of d/s impervious floor:
The maximum length of the d/s impervious floor is given by the following relation.
Ld = 2D + 2.4 + HL in metres.
The balance of impervious floor may be provided under the body wall and on the u/s.
Thickness of the Floor:
The d/s floor should be made thick enough to resist uplift pressures. However, minimum thickness of 0.3 to 0.6 m (depending upon the size of the drop) of concrete under 35 cm of brick masonry may be provided on the d/s. On the u/s brick masonry is not necessary. The brick on the edge laid on the d/s impervious concrete floor provide additional strength and affords easy repairs to the floor.
Cut-off:
A sufficient depth of cut-off below the floor should be provided at the d/s end of the floor for providing safety against steep exit gradient. The depth of cut-off may range from 1 to 1.5 m. Sometimes deeper cut-offs may be necessary to reduce horizontal floor length to satisfy Khosla’s principle of exit gradient. For falls having 1 m and above head on the crest should be provided more cut-offs. Cut-off at u/s end of floor is also provided which may be smaller in depth.
Other Protective Works:
Provision of other accessories like upstream wings, staggered blocks on the cistern floor, downstream wings, bed and side pitching is generally done on the basis of thumb rules. For big structures, however, actual design calculations may be done. For general arrangement see Fig. 19.13.
Upstream wing walls:
For small falls upto 14 cumec the upstream wings may be splayed at 1: 1. For higher discharges u/s wing walls are kept segmental with a radius equal to 6 H and continued thereafter tangentially merging into the banks. The wings may be embedded into the bank for about 1 m.
Downstream wing walls:
For the length of the cistern the d/s wing walls are kept vertical from the crest. Thereafter they are wasped or flared to a slope of 1: 1. An average splay of 1 in 3 for attaining the required slope is given to the top of the wings. The wings may be taken deep into the banks.
Staggered blocks:
Staggered block of height dc should be provided at a distance of 1.0 dc to 1.5 dc from the d/s toe of the crest for clear falls. In case of submerged falls the blocks may be provided at the end of the cistern. A row of staggered cubical blocks of height equal to 0.1 to 0.13 of depth of water should invariably be provided at the end of the d/s impervious floor.
Bed and side pitching:
The d/s bed pitching with bricks 20 cm thick over 10 cm ballast is provided horizontally for a length of 6 m. Thereafter for lengths up to 5 to 15 m for falls varying from 0.75 to 1.5 m may be provided with down slope of 1 in 10. The side pitching with bricks on edge with 1: 1 slope is provided after the return-wing on the downstream. A toe wall should be provided between the bed pitching and the side pitching to provide a firm support to the latter.
Design Principles for Straight Glacis Fall:
Crest Dimensions:
Clear width of crest.
Vertical falls should be full width falls, i.e., the width of the crest should be same as bed width of the canal because increased intensity of discharge due to fluming creates scour on the downstream.
Unlike vertical falls the glacis falls can be flumed when combined with bridge so as to economize in the cost. It k quite rational to select such (q) discharge per metre run of crest width which with the height of drop (HL) available gives value of total energy on the d/s (Ef2) equal to F.S. depth of the canal. (It can be read from Blench curves). It does not require deep cistern on d/s and avoids construction difficulty particularly when subsoil water level is high. The throat width may be rounded off to next half metre. The fluming thus calculated may not, however, exceed limits given below subject to the condition that overall width of fall crest is not more than bed width of the canal on the downstream.
Crest level = u/s TEL – E
In case of full width falls and sometimes in flumed falls if crest level works out unreasonably high fluming may be done or increased if already flumed so that crest is not higher than 0.4 –D1 above the u/s bed as otherwise it will increase afflux at low supplies and may cause alternate silting/scouring.
The value of E is given by discharge formula Q = 1.84 Bt X E3/2
where Bt is clear width of crest. Therefore if n piers are provided in between effective
Bt = (Bt – 0.2 n H)
and E is depth of crest below u/s TEL.
Length of crest (Lt) = 2/3 E.
The crest is joined to u/s and d/s canal bed with sloping glacis.
The u/s glacis (for non-meter falls) is given a slope of 1/2: 1. The u/s crest end is kept curved with a radius of E/2,
The d/s glacis is given 2: 1 slope and it joins the cistern d/s with curve having radius equal to E.
Cistern Dimensions:
- R.L. of cistern = d/s TEL -1.25 Ef2 = d/s FSL -1.25 D2
Length of cistern = 5 Ef2 for good earthen bed
or Ld = 6 Ef2 for erodible sandy soils.
The cistern should be joined to the designed d/s bed with a up slope of 1 in 5 (1: 5) This arrangement enables formation of hydraulic jump on the sloping glacis.
Provisions of Cut-Offs:
The cut-offs should be invariably provided at the upstream end of upstream glacis and at the downstream end of the downstream cistern. The width of each curtain wall may be kept 0.4 m.
The depth may be as follows:
Depth of u/s cut-off = D1/3
Depth of d/s cut-off = D2/2
The minimum depth should however be 0.5 m.
Total Length of Impervious Floor:
The total length of floor should be such that with the depth of curtain walls as fixed earlier give permissible exit gradient. Khosla’s curve for exit gradient may be used for this purpose.
The length of floor between u/s and d/s cut-offs so determined if appears excessive the downstream cut-off may be further deepened suitably to achieve adequate floor length.
It may be noted that the total impervious floor length comprises:
i. Length of cistern;
ii. Horizontal length of d/s glacis;
iii. Crest length along the axis of the canal; and
iv. Horizontal length of u/s glacis.
In case some little length is still remains to be provided as per earlier calculations it may be provided on the u/s side of u/s glacis.
Thickness of the Floor:
Minimum thickness on the u/s may be from 0.3 to 0.6 m. Floor thickness in the glacis and cistern should be sufficient to withstand uplift pressure safely.
U/s Approach and U/s Protection:
(i) If the fall combines with it functions of a discharge meter as well, the side and bed approaches to the crest have necessarily to be gradual and smooth so as to avoid eddies and impact losses and to reduce concentration of flow.
In non-meter falls, however, the side walls may be splayed at an angle of 45° from the upstream edge of the crest. The walls are carried straight into the canal berm for a length of at least 1 m.
(ii) The bed approach may be by means of u/s glacis having 1/2: 1 slope and joining tangentially the u/s end of crest with a radius equal to E/2.
(iii) Protection of bed and sides by stone or dry brick pitching may be done for a length of (D1 + 0.5) m. The bed pitching may be laid at a slope of 1 in 10.
D/s Expansion and D/s Protection:
(i) On the downstream parallel and vertical walls are provided upto the toe of the glacis.
(ii) The expansion afterwards should be gradual so that the expanding flow adheres to the sides and scour due to formation of back-rollers on sides is prevented. A rectangular hyperbolic expansion given by Mitra’s equation for hyperbolic expansion is generally adopted.
If this expansion works out too long, side splay of about 1 in 5 may be adopted. For small falls to effect economy expansion with side splay of 1 in 3 considered sufficient.
(iii) Side walls in expansion may be flared out from vertical to 1: 1 if the earth fill behind is not problematic like black cotton soil. In such cases the side walls may be designed as vertical gravity walls.
(iv) Side protection consisting of 20 cm thick dry brick pitching for a length of 3 D2 should be provided. It should rest on a toe wall 1½ brick thick and of depth equal to D2/2 subject to minimum of 0.5 m depth.
(v) A deflector wall of height D2/10 above d/s bed may be provided at the downstream end of the cistern. The minimum height should be 15 cm. Thickness of the deflector wall may be kept 0.4 m.
(vi) With provision of deflector wall at the end of the floor d/s bed pitching beyond the floor is not necessary.
Friction Blocks as Energy Dissipators:
Friction blocks are found to be most effective. In case of flumed straight glacis falls (without baffle) four rows of friction blocks may be provided. they are staggered in plan. The u/s edge of the first row of the friction block is located at a distance of 5 times the height of the blocks (5 . h) from the toe of the glacis. The dimensions of the blocks may be as follows:
Let, height of the blocks = h
h = D1/8
Length of the block = 3 h
Width of the block =2/3 h
Distance between rows = 2/3 h
When glacis is provided with baffle only two rows of friction blocks is sufficient upto 2 m fall. The u/s edge of the first row may be located at 1/3 length of d/s expansion from the end of the cristern floor.
CIVIL ENGINEERING 