Design Of Weirs And Barrages 1ve6k

DESIGN OF WEIRS AND BARRAGES

CAUSES OF FAILURE OF WEIR OR BARRAGE ON PERMEABLE FOUNDATION •Failure by Subsurface Flow • Failure by Piping or undermining • Failure by Direct uplift •Failure by Surface Flow • By hydraulic jump • By scouring Bligh’s Creep Theory for Seepage Flow Total length of pucca floor (including twice the length othe cut-off), L  CH L h  Thickness of the floor, t  1.33   G 1 

LANE’S WEIGHTED CREEP •THEORY In Bligh’s theory, no distinction between horizontal creep length and vertical creep length •According to Lane, the horizontal creep is less effective in reducing the uplift or loss of head than the vertical creep. •Assigned weightage factor of 1/3 for horizontal creep and 1.0 for vertical creep. L = (d1 + d1) + (1/3) L1 + (d2 + d2) + (1/3) L2 + (d3 + d3) = (1/3) (L1 + L2) + 2(d1 + d2 + d3) = (1/3) b + 2(d1 + d2 + d3) Safety against piping:

L  C1 H L

C1 is the Lane’s Creep Length and H L is the Head causing flow

EXAMPLES Find the hydraulic gradient and uplift pressure at a point 15 m from the upstream end of the floor in the figure below.

According to Bligh’s theory, check the value of coefficient of creep, for hydraulic gradient H/L < 1/C

Structure would be safe on sand mixed with boulders

LIMITATIONS OF BLIGH’S THEORY The actual uplift pressures are found to be quite different from those computed on the basis of Bligh's theory Outer faces of the end sheet piles are much more effective than the inner faces and the horizontal length of floor Intermediate piles of smaller in length than the outer piles are investigated as ineffective except for some local redistribution of pressure. Piping of the floors starts from the tail end when the hydraulic gradient at the exit is greater than the critical gradient for that particular soil. The soil particles move with the flow of water and leads to progressive degradation of the subsoil and resulting in cavities below the floor and ultimate failure. A reasonably deep cutoff or pile at the d/s end of the floor is essential to prevent piping failure

KHOSLA’S THEORY The streamlines represent the paths along which the water flows through the sub-soil. There will be points on different streamlines having the same value of residual head h. If such points are ed together, the curve obtained is called an equipotential line. AB and CD are equipotential lines The seepage water does not creep along the bottom contour of pucca floor as stated by Bligh, but on the other hand, this water moves along a set of stream-lines. This steady seepage in a vertical plane for a homogeneous soil can be expressed by Laplacian equation: d 2 d 2

d 2 x2



d 2z2

Where  = Flow potential = kh; k = Co-efficient of permeability of soil defined by Darcy’s law; h = residual head at any point within the soil The resultant flow diagram showing both of the curves is called a Flow Net.

CRITICAL EXIT GRADIENT The seepage water exerts a force at each point in the direction of flow and tangential to the streamlines. This force (F) has an upward component from the point where the streamlines turns upward. For soil grains to remain stable, the upward component of this force should be counterbalanced by the submerged weight of the soil grain. This exit gradient is said to be critical, when the upward disturbing force on the grain is just equal to the submerged weight of the grain at the exit. An exit gradient equal to ¼ to 1/5 of the critical exit gradient is ensured, so as to keep the structure safe against piping.

At critical exit gradient F = Pressure gradient at that point =

=

F  Ws

dp The submerged weight (Ws) of a unit volume of soil is given as: dl = Unit weight of water = Specific gravity of soil particles

Ws   w (1  n)( S s  1)

= porosity of soil material

w

Ss

n

w 

dh dl

KHOSLA’S METHOD OF INDEPENDENT VARIABLES To study the seepage below the foundation of a hydraulic structure

 Study the flow net or solve Laplacian equations  Graphical sketching by adjusting the streamlines and equipotential lines with respect to the boundary conditions  A simple, quick and an accurate approach for design of weir and barrage on pervious foundations.  The complex profile of a weir is broken into simple profiles and mathematical solutions of flow nets for these simple standard profiles are studied.

KHOSLA’S METHOD OF INDEPENDENT VARIABLES Khosla’s theory is used to find uplift pressure at the key points in a barrage or a weir. In this

method a composite barrage or weir section is split up into a number of simple standard forms of known analytical solution Case 1: Pile at D/s End The uplift pressure heads at key points E, D and C are E 

1   2 cos 1      

D 

1   1  cos 1      

1 1  2  2

b  d

Case 2: Pile at Upstream End

C1  100  E D1  100  D

Case 3: Intermediate Pile 1 1  1  1  E  cos      

D 

1    cos 1  1    

1 1  1  1  C  cos       1  12  1   22  2 b 1  1 d

1  12  1   22 1  2

2 

b2 d

Case 4: Depressed Floor

2 3   E  D   2 3  / D

D/ 1  100  D/

CORRECTIONS In actual weir structure the floor has some thickness (the uplift pressures are calculated with negligible thickness) and it may not be horizontal and also there may be more than one line of piles, so the following corrections have to be applied to the superposed values of the uplift pressures 1. correction for thickness of floor 2. correction for mutual interference of piles 3. correction for slope of the floor

CORRECTION FOR THICKNESS OF FLOOR The percentage pressures calculated by Khosla’s equations or graphs shall pertain to the top levels of the floor. While the actual junction points E and C are at the bottom of the floor. Hence, the pressures at the actual points are calculated by assuming a straight line pressure variation. Since the corrected pressure at E1 should be less than the calculated pressure at E1′, the correction to be applied for the t E1 shall be negative. Similarly, the pressure calculated C1′ is less than the corrected pressure at C1, and hence, the correction to be applied at point C1 is positive.

'

E1  E1 Correction is negative '

C1  C1

Correction is positive

Pile at U/S Correction for C1

D  C   t1 d1

Pressure at C1

D  C C 1  C   t1 d1

Intermediate Pile Correction for E1

E  D   t2 d2

Correction for C1

   D C  t2 d2

Pressure at E1

E  D E1  E   t2 d2

Pressure at C1

D  C C1  C   t2 d2

Pile at D/S Correction for E1

E  D   t3 d3

Pressure at E1 E 1  E 

E  D  t3 d3

CORRECTION FOR MUTUAL INTERFERENCE OF PILES

The correction C to be applied as percentage head due to this effect D d D C  19 /   b  b  b′ = The distance between two pile lines.

D = The depth of the pile line, the influence of which has to be determined on the neighboring pile of depth d. D is to be measured below the level at which interference is desired. d = The depth of the pile on which the effect is considered b = Total floor length

CORRECTION FOR MUTUAL OF INTERFERENCE Pile no. 2 will interfere only with the D/S face of PILES pile no. 1 and U/S face of pile no. 3  Pile no. 2 causes a blocking effect on the subsoil flow which results in increase in pressure at all points on its U/S side.  The correction is positive for the points in the rear of back water, and subtractive for the points forward in the direction of flow. If we are considering the influence of the pile no (2) on pile no (1) for correcting the pressure at C 1. Since the point C1 is in the rear, this correction shall be positive. While the correction to be applied to E 2 due to pile no (1) shall be negative, since the point E2 is in the forward direction of flow. Similarly, the correction at C 2 due to pile no (3) is positive and the correction at E2 due to pile no (2) is negative.

CORRECTION FOR THE SLOPE OF THE FLOOR

CORRECTION FOR THE SLOPE OF THE FLOOR Correction for slope is to be applied only to point E of pile no. 2.

Correction of slope bs  correction factor for a given slope  b Correction is additive for a downward sloping floor and subtractive for an upward sloping floor in the direction of floor From the estimation of uplift pressure at key points, the uplift pressure distribution along the floor may be obtained by assuming a linear variation of pressure between key points. Floor thickness may then be calculated.

EXIT GRADIENT For a standard form consisting of a floor length (b) with a vertical cutoff of depth (d), the exit gradient at its downstream end is given by 2 b H 1 1  1     GE    d d   2 H = Maximum Seepage Head

KHOSLA’S PRESSURE CHART

Determine the percentage pressures at various key points in figure below. Also determine the exit gradient and plot the hydraulic gradient line for pond level on upstream and no flow on downstream

C1  100  E D1  100  D

(b) Correction at C1 due to thickness of floor: Pressure calculated from curve is at C1′, but we want the pressure at C1. Pressure at C1 shall be more than at C1′ as the direction of flow is from C1 to C1′ and hence, the correction will be + ve and

For Intermediate Pile Line No. 2 d = 154 – 148 = 6 m b = 57 m α = b/d = 57/6 = 9.5 b1 = 0.6 + 15.8 = 16.4

C1  100  E D1  100  D

b = 57 m b1/b = 16.4/57 = 0.298 (for φC2) 1 – b1/b = 1 – 0.298 = 0.702 φE2 = 100 – 30 = 70 % (Where 30 % is φC for a base ratio of 0.702 and α = 9.5) φC2 = 56 % (For a base ratio 0.298 and α = 9.5) φD2 = 100 – 37 = 63 % (Where 37 % is φD for a base ratio of 0.702 and α = 9.5)

Corrections for φE2 : (a) Correction at E2 for sheet pile lines. Pile No. (1) will affect the pressure at E2 and since E2 is in the forward direction of flow, this correction shall be – ve.

(b) Correction at E2 due to floor thickness

Correction at E2 due to floor thickness = 1.17 % (- ve)

(c) Correction at E2 due to slope is nil corrected percentage pressure at E2 = Corrected φE2 = (70 – 1.88 – 1.17) % = 66.95 %

Corrections for φC2: Mutual Interference Correction at C2 due to pile interference. Pressure at C2 is affected by pile No.(3) and since the point C2 is in the back water in the direction of flow, this correction is (+) ve.

(b) Correction at C2 due to floor thickness. Pressure at C2 shall be more than at C2′, and since the observed pressure is at C2′, this correction shall be + ve and its amount is the same as was calculated for the point E2 = 1.17 %. Hence, correction at C2 due to floor thickness = 1.17 % (+ ve) (c) Correction at C2 due to slope. Since the point C2 is situated at the start of a slope of 3:1, i.e. an up slope in the direction of flow; the correction is negative Correction factor for 3:1 slope from table = 4.5 Horizontal length of the slope = 3 m Distance between two pile lines between which the sloping floor is located = 40 m Actual correction = 4.5 × (3/40) = 0.34 % (- ve) Corrected φC2 = (56 + 2.89 + 1.17 – 0.34) % = 59.72 %

Downstream Pile Line No. 3: d = 152 – 141.7 = 10.3 m b = 57 m 1/α = 10.3/57 = 0.181 From curves, we get φD3 = 26 % , φE3 = 38 % Corrections for φE3: Correction due to piles. The point E3 is affected by pile No. 2, and since E3 is in the forward direction of flow from pile No. 3, this correction is negative.

Correction due to floor thickness

(c) Correction due to slope at E3 is nil, as the point E3 is neither situated at the start nor at the end of any slope Hence, corrected φE3 = (38 – 1.02 – 0.76) % = 36.22 %

The corrected pressures at various key points are tabulated below in Table below

EXIT GRADIENT Let the water be headed up to pond level, i.e. on RL 158 m on the U/S side with no flow D/S The maximum seepage head, H = 158 – 152 = 6 m The depth of d/s cur-off, d = 152 – 141.7 = 10.3 m Total floor length, b = 57 m α = b/d = 57/10.3 = 5.53

H 1 GE   d  

GE 

6  0.18  0.105 10.3

Hence, the exit gradient shall be equal to 0.105, i.e. 1 in 9.53, which is very much safe.

Determine the uplift pressure at the key points and the exit gradient and find whether the section provided is safe against piping if it is founded on fine sand with permissible exit gradient of 1/6. Also find uplift pressure at point ‘X’ and check whether it is safe against uplift.

Design of Sheet piles on U/S and D/S of Impervious Floor • Sheet pile must be taken up to the level of possible deepest scour below the bed of the river. • Lacey depth of scour in alluvial soils is given by

 q    1.35  f  2

R = Scour depth measured below HFL R q = Discharge per unit length

1/ 3

f = Lacey’s silt factor • The scour depth is generally considered as 1.25 R to 2R to ensure safety • For conservative design an intermediate pile line has to be provided for additional factor of safety • The depth of the intermediate pile line should not be less than that of the upstream pile line