Formula Sheets: Cross Drainage Structures

 Page 1


Design of W eirs and Cross Dr ainage
Structures F ormula Sheet for GA TE Civil
Engineering
Design of W eirs on Permeable F oundation; Cross Dr ainage
Structures
1. W eirs on Permeable F oundation: Bligh’ s Creep Theory
• Creep Length (L ) :
L =
?
( horizontal creep+2× vertical creep)
• Safe Creep Length :
L =C·H
whereC = Bligh’ s creep coefficient (depends on soil type, e.g., 12–18 for sand),
H = head difference across weir .
• Hydr aulic Gr adient :
i =
H
L
Safe h ydr aulic gr adient: i=
1
C
.
• Uplift Pressure at an y point :
p =?g(H-
h·x
L
)
whereh = head loss,x = creep distance from upstream.
2. Khosla’ s Theory
• Uplift Pressure : Determined using Khosla’ s curves for specific points (e.g.,
junction points, k ey points of sheet piles).
• Exit Gr adient :
G
E
=
H
d
·
1
p
v
?
whereH = head difference, d = depth of downstream cutoff, ? =
1+
v
1+a
2
2
,a =
b
d
,
b = floor length.
1
Page 2


Design of W eirs and Cross Dr ainage
Structures F ormula Sheet for GA TE Civil
Engineering
Design of W eirs on Permeable F oundation; Cross Dr ainage
Structures
1. W eirs on Permeable F oundation: Bligh’ s Creep Theory
• Creep Length (L ) :
L =
?
( horizontal creep+2× vertical creep)
• Safe Creep Length :
L =C·H
whereC = Bligh’ s creep coefficient (depends on soil type, e.g., 12–18 for sand),
H = head difference across weir .
• Hydr aulic Gr adient :
i =
H
L
Safe h ydr aulic gr adient: i=
1
C
.
• Uplift Pressure at an y point :
p =?g(H-
h·x
L
)
whereh = head loss,x = creep distance from upstream.
2. Khosla’ s Theory
• Uplift Pressure : Determined using Khosla’ s curves for specific points (e.g.,
junction points, k ey points of sheet piles).
• Exit Gr adient :
G
E
=
H
d
·
1
p
v
?
whereH = head difference, d = depth of downstream cutoff, ? =
1+
v
1+a
2
2
,a =
b
d
,
b = floor length.
1
• Safe Exit Gr adient : Depends on soil type (e.g., 0.14–0.25 for fine sand).
• Corrections for Khosla’ s Theory :
– Floor thickness correction.
– Mutual interference of piles.
– Slope correction for sloping floors.
3. Stability of W eirs
• F actor of Safety A gainst Uplift :
FOS
uplift
=
W
P
u
whereW = weight of structure,P
u
= uplift force.
• F actor of Safety A gainst Sliding :
FOS
sliding
=
µW
P
h
whereµ = friction coefficient, P
h
= horizontal force (e.g., water pressure).
• Base Pressure :
s =
W
A
(
1±
6e
B
)
wheres = base pressure,A = base area,e = eccentricity ,B = base width.
4. Seepage Control Measures
• Cutoffs and Sheet Piles : Increase creep length, reduce uplift pressure.
• Impervious Floor Length : Designed to ensure safe h ydr aulic gr adient.
• Apron : Protects against scouring.
5. Cross Dr ainage Structures
• Types :
– A queduct: Canal over dr ain.
– Superpassage: Dr ain over canal.
– S yphon A queduct: Canal over dr ain with syphon action.
– Canal S yphon: Dr ain over canal with syphon action.
– Level Crossing: Canal and dr ain at same level.
• Design Discharge for Canal :
Q =
1
n
AR
2/3
S
1/2
where n = Manning’ s roughness coefficient, A = cross-sectional area, R = h y-
dr aulic r adius,S = bed slope.
2
Page 3


Design of W eirs and Cross Dr ainage
Structures F ormula Sheet for GA TE Civil
Engineering
Design of W eirs on Permeable F oundation; Cross Dr ainage
Structures
1. W eirs on Permeable F oundation: Bligh’ s Creep Theory
• Creep Length (L ) :
L =
?
( horizontal creep+2× vertical creep)
• Safe Creep Length :
L =C·H
whereC = Bligh’ s creep coefficient (depends on soil type, e.g., 12–18 for sand),
H = head difference across weir .
• Hydr aulic Gr adient :
i =
H
L
Safe h ydr aulic gr adient: i=
1
C
.
• Uplift Pressure at an y point :
p =?g(H-
h·x
L
)
whereh = head loss,x = creep distance from upstream.
2. Khosla’ s Theory
• Uplift Pressure : Determined using Khosla’ s curves for specific points (e.g.,
junction points, k ey points of sheet piles).
• Exit Gr adient :
G
E
=
H
d
·
1
p
v
?
whereH = head difference, d = depth of downstream cutoff, ? =
1+
v
1+a
2
2
,a =
b
d
,
b = floor length.
1
• Safe Exit Gr adient : Depends on soil type (e.g., 0.14–0.25 for fine sand).
• Corrections for Khosla’ s Theory :
– Floor thickness correction.
– Mutual interference of piles.
– Slope correction for sloping floors.
3. Stability of W eirs
• F actor of Safety A gainst Uplift :
FOS
uplift
=
W
P
u
whereW = weight of structure,P
u
= uplift force.
• F actor of Safety A gainst Sliding :
FOS
sliding
=
µW
P
h
whereµ = friction coefficient, P
h
= horizontal force (e.g., water pressure).
• Base Pressure :
s =
W
A
(
1±
6e
B
)
wheres = base pressure,A = base area,e = eccentricity ,B = base width.
4. Seepage Control Measures
• Cutoffs and Sheet Piles : Increase creep length, reduce uplift pressure.
• Impervious Floor Length : Designed to ensure safe h ydr aulic gr adient.
• Apron : Protects against scouring.
5. Cross Dr ainage Structures
• Types :
– A queduct: Canal over dr ain.
– Superpassage: Dr ain over canal.
– S yphon A queduct: Canal over dr ain with syphon action.
– Canal S yphon: Dr ain over canal with syphon action.
– Level Crossing: Canal and dr ain at same level.
• Design Discharge for Canal :
Q =
1
n
AR
2/3
S
1/2
where n = Manning’ s roughness coefficient, A = cross-sectional area, R = h y-
dr aulic r adius,S = bed slope.
2
6. Design of Cross Dr ainage Structures
• Hydr aulic Design :
– Ensure sufficient headroom for dr ain flow .
– Maintain canal flow without excessive backwater effect.
• Fluming Ratio :
Fluming Ratio =
Width of flumed section
Width of normal canal
Typically 0.5–0.7 for econom y .
• Head Loss in S yphon :
h
f
=f
L
D
V
2
2g
where f = friction factor , L = length of syphon, D = diameter , V = velocity , g =
gr avitational acceler ation.
• V entwa y Discharge (Dr ain) :
Q
d
=C
d
A
v
2gH
whereC
d
= discharge coefficient, A = ventwa y area,H = hea d over ventwa y .
7. Scour Protection
• Lacey’ s Scour Depth :
R = 1.35
(
q
2
f
)
1/3
whereR = scour depth,q = discharge per unit width,f = silt factor .
• T otal Scour Depth : Typically 1.5–2 times normal scour depth for safety .
3