DESIGN OF PERMANENT GULLY CONTROL STRUCTURES
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HYDROLOGIC DESIGN OF DROP SPILLWAY
Total Fall = 3m
So the discharge =6 cumec
HYDRAULIC DESIGN OF DROP SPILLWAY
Discharge to be handled by the Spillway = 6 Cumec
Total Fall = 3 m
Determination of Length of crest(L) and Spillway depth(h) is done by following formula:
L = Q(1.10 + 0.03*F)/ C*h^(3/2) = 1
Where,
Q = Discharge in cumec =0.68
C = Discharge coefficient = 1.77
L = length of crest in m =1
h = depth of weir in m=0.45
F = Total drop in m=3
So by entering the values of Q and F and following trial and Error method we gets several combinations of L and h
The final selected combination is as follows
Practical length of crest =2.45
m
Discharge carrying capacity of the structure =2.45
cumec
Free Board provided = 0.15
m
The Dimensions of different components of the structure is as follows
Critical depth (Dc) = (Q^2 / L^2 * 9.81)^3/2
=0
Height of transverse sill(S) = 0 m
Height of Head Wall(Hb) = F + S = 3
Height of Head Wall extension (He) = F + S + h = 3.45
Minimum length of head wall extension (E) = 1.95 OR 1.5*F, Which ever is greater
So He = 4.5 m
Minimum length of Apron(Lb) =2.586
Height of Side wall and Wing wall at the junction
J =0.9OR [2.107] Whichever is greater
Depth of cutoff wall(c) and Toe Wall(T) =0.804375
STRUCTURAL DESIGN OF DROP SPILLWAY
Input Data for the structural design of drop spillway are:
Total Fall (F) = 3m
Height of end sill(s) = 0m
Depth of flow above crest(H) = 0.45m
Tail water height(t) = 0.45m
Thickness of apron = 0.3m
Length of apron = 2.586m
Toe wall thickness = 0.804375m
Cuttoff wall thickness = 0.804375m
Depth of cutoff wall and Toe wall = 0.8m
Backfill Properties:
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Properties Earth Sand and Gravel
Dry weight, Kg/cu.m 1600 1900
Moist Weight, kg/cu.m 1750 2000
Submerged weight, kg/cu.m 1000 1900
Angle of internal friction 25 25
Thickness of head wall = 2m
Thickness of side wall = 1.65m
Unit weight of concrete (γ_material) = 2400kg/cu.m
Voids ratio of foundation materials = 0.65
Voids ratio of sand = 3
Bottom width of headwall (Headwall_BotW) = 0.45m
Top width of headwall (Headwall_TopW) = 0.9m
K_a = coefficient of active earth pressure
Y_w = Unit weight of water
Conditions for Designing are as follows:
(Case A) No back fill against head wall
Permeability of foundation material > Permeability of backfill
Type 'a' drainage condition
High Watertable
Full flow condition
*********** Calculation for structural design ************
Forces acting on a drop structure:
The horizontal forces acting on the headwall are:
(1) Hydrostatic force due to flowing water of depth H, F1 = Y_w * H * F = 1000*0.45*3 = 13.5
F1 acts at the height of (F/2) =1.5 m from the base
Lateral force due to water of depth F, F2 = 1/2 * Unit weight of water * F^2 = 0.5*10003^2 = 45
(2) F2 acts at the height of (F/3) =1 m from the base
Lateral force due to submerged weight of soil of depth F, F3 = 1/2 * K_a * Submerged weight * F^2 = 0.5*0.4058*1900*3^2 = 34.6959
(3) F3 acts at the height of (F/3) =1 m from the base
Components of uplift pressure:
(4) Uplift force due to the head equal to the depth of the Toewall, T, U1 = (T * (Lb + Headwall thickness))*Y_w =
(0.8*(2.586+2))*1000 = 24.288
U1 acts at a distance of ((Lb + Headwall thickness)/2) =1.518 m from the toe.
(5) Uplift force due to the head equal to (F – T), U2 = 1/2 * γ_w * (F - T)* (Lb + Headwall thickness) 0.5*1000*( = 3-0.804375)*(2.586+2) = 33.396
U2 acts at a distance of (2/3 * (Lb + Headwall thickness)) =2.024 m from the toe
Components of weight of the structure:
(6) Weight of the rectangular portion of the headwall, W1 = F * Headwall thickness × γ_material = 3*2*2400 = 64.8
W1 acts at a distance of (Lb + (Headwall_BotW + (Headwall_TopW/2)) =3.486 m from the toe
(7) Weight of the triangular portion of the headwall, W2 = 1/2 * F * (Headwall_BotW -Headwall_TopW ) * γ_material = 0.5*3*(0.45-0.9) = -16.2
W2 acts at a distance of (LB + 2/3 (Headwall_BotW - Headwall_TopW) =2.286 m from the toe
(8) Weight of the stilling basin, W3 = (Lb + Headwall_BotW) * T_Apron * γ_material = (2.586+0.45)*0.3*2400 = 21.8592
W3 acts at a distance of ((Lb + Headwall_BotW)/2) =1.518 m from the toe
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Force Magnitude, kg ARM, m Moment, Tm Nature
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F1 13.5 1.5 20.25 T
F2 45 1 45 T
F3 34.6959 1 34.6959 T
U1 24.288 1.518 36.869184 T
U2 33.396 2.024 67.593504 T
W1 64.8 3.486 225.8928 R
W2 -16.2 2.286 -37.0332 R
W3 21.8592 1.518 33.1822656 R
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Contact Pressures:
Pu = sum V/ A[1 + 6e/d] = 1.71370800959
Pd = sum V/ A[1 - 6e/d] = -0.0217517944786
Checking the stabilty of the stucture
Check safety against Overturning:
Sum of turning moments = 204.408588
Sum of retaning moments = 222.0418656
Fator of safty (FSo) = Sum of turning moments/Sum of resisting moments = 1.08626485693
For the structure to be safe against overturning FSo should be more than 1.5
Hence, the structure is [Not safe against turning]
Check safety against Sliding:
f = coefficient of friction = tan∅
C = cohesive resistance of the foundation material
A = area of the plane of sliding = F * (Lb + Headwall_TopW) = 10.458
Factor of safety against sliding (FSs) = (f * sumV + C * A) / sumH = 0.802138488925
For the structure to be safe against sliding, FSs should be more than 1.1
Hence, the structure is [Not Safe aginst sliding]
Check safety against piping:
Sum of all horizontal or flat contact lengths (sumHl) = Lb + thickness of the cutoff wall + thickness of the toewall = 4.19475
sum of all vertical or steep contact lengths (sumVl) = 2 * depth of the Toewall + 2 * (depth of the Toewall - apron thickness) = 2.6
Cw = (1/3 (sumHl + sumVl))/H = 1.33275
For a stable structure the computed Cw should be equal to or greater than Cw’s recommended value for a stable structure
Hence, the structure is [Not Safe aginst pipimg]
Check safety against tension:
Z = sum M/sum V = 1.38027409356
Sum of all vertical forces (V) = (W1 + W2 + W3) - (U1 + U2) = 12.7752
sum of all horizontal forces (H) = (F1 + F2 + F3) = 93.1959
sum M = sum of retaning moment (RM) - sum of turning moment (TM) = 17.6332776
eccentricity = Z - d/2 = 0.717100906444
For a stable of structure ecentricity <= d/6 = 0.699125
Hence, the structure is [Not safe aginst tention]
Check safety against compression or contact pressure:
P1 = sum V/ A[1 + 6e/d] = 1.71370800959
P2 = sum V/ A[1 - 6e/d] = -0.0217517944786
For a stable of structure both the pressure should be positive
Hence, the structure is [Not safe aginst compression]