Contents preface (VII) introduction 1—37

Solution: Upstream Pile :

Depth of pile

d = 256.00 – 250.00 = 6.0 m

Total floor length

b = 36.5 m

Using Eqs. (9.51) to (9.55),

b

36.5

α =

^= 6.0

= 6.083

d

λ =

1

[1 +

1 + α ^2 ] = 3.083

2

−1 F

2I

1

λ −

φE =

cos

G

J = 0.386

π

λ

H

K

∴

φC

= 1 – 0.386 = 0.614 = 61.4%

1

−1 F

I

λ −

1

1

φD =

cos

G

J = 0.264

π

λ

H

K

∴

φ D

= 1 – 0.264 = 0.736 = 73.6%

1

Using Fig. 9.23 with

1

=

d

=

6.0

= 0.164

36.5

α

b

φC

= 100 – φ

= 100 – 36 = 64%

1

E

and

φ D

= 100 – φ

= 100 – 25 = 75%

1

D

It may be noted that there is slight difference between the values calculated from mathematical expressions and those read from Fig. 9.23. Corrections have been calculated and applied to the values obtained from mathematical expressions.

Thickness correction for φC =	^73.6 ^− ^61.4 × 1.0 = 2.03% (+)
1	6.0
Correction for interference of intermediate pile on	φ C of upstream pile
		1
= 19	(255 − 248) [(255 − 248 ) + 5]	= 3.65% ( +)
	20.5	36.5

346 IRRIGATION AND WATER RESOURCES ENGINEERING

∴ φ_C1 (corrected) = 61.4 + 2.03 + 3.65 = 67.08%

Intermediate Pile:
Using Eqs. (9.56) to (9.60),
α₁ = ^b_d¹ = ²¹⁰_7.^.₀ = 3.0
α₂ = ^b_d² = ¹⁵₇^.5 = 2.2143

λ2 =

1

L

2

+

1

+ α

2

O

=

2.796

M

1 + α 1

2

P

2 N

Q

λ1 =

1

L

2

−

1

2

O

=

0.366

M

1 + α 1

+ α 2

P

2 N

− 1^F

1I

Q

1

λ 1 −

1

−1F

− 0.634I

φE =

cos

G

J =

cos

G

J =

0.5728 = 57.28%

π

λ 2

π

H

K

H

2.796 K

1

−1^F

λ 1 I

1

−1F

0.366I

φD =

cos

G

J ^=

cos

G

J = 0.4582 = 45.82%

π

H

λ

2 K

π

H

2.796 K

1

− 1^F

λ 1 +

1I

1

−1F

1.366 I

φC =

cos

G

J ^=

cos

G

J = 0.3375 =

33.75%

λ 2

π

H

K

π

H

2.796K

Using Fig. 9.23 with
b = 36.5 m, b₁ = 21.0 m, d = 255 – 248 = 7.0 m, and b₂ = 15.5 m

210.

^b1^{/b =} _36.5 ^{= 0.575}

∴1 – (b₁/b) = 0.425

	36.5
and	^α ^= 7.0	= 5.21
∴	φC = 34%
	φE = 100 – 42 = 58%
and	φD = 46%

The values of φ obtained from Eqs. (9.56) to (9.60) have been corrected as follows:

Thickness correction for φ =	57.28 − 45.82	× 2 = 3.28% (–)
E	7	F	10.5I
Slope correction for φE = Cs (bs/b′) = 4.5	× G			J
		H	20.5K
= 2.31% (+)
Correction for interference of the upstream pile (for φE)
= 19	(253 − 250)	× [( 253 − 250) + 5]
	20.5			36.5
= 1.59% (–)

φ_E(corrected) = 57.28 – 3.28 + 2.31 – 1.59 = 54.72%

SURFACE AND SUBSURFACE FLOW CONSIDERATIONS FOR DESIGN OF CANAL STRUCTURES

347

Thickness correction for φ

=

^45.82 ^− ^33.75 × 2 = 3.45% (+)

C

7

Correction for interference of the downstream pile (for φC)

= 19

(253 − 248) ×

(253 − 248 ) + 5 = 3.01% (+)

15

36.5

∴ φC (corrected) = 33.75 + 3.45 + 3.01 = 40.21%