Contents preface (VII) introduction 1—37

Correction for Floor Thickness
The key points E (or E₁) and C (or C₁) correspond to the level at the top of the floor. The values of pressure at points E′ (or E₁′) and C′ (or C₁′) (Fig. 9.24) are interpolated assuming linear variation of pressure between the key points. Thus,

φ_E′ = φ_E –

φ_C′ = φ_C +
Here, t is the thickness of the floor.
^φ E ^{− φ} D _t d + t




^φ D ^{− φ}C _t d + t

(9.63)
(9.64)

E C

t

E′ C′
d

D
Fig. 9.24 Sketch for correction for floor thickness
Correction for Mutual Interference of Sheet Piles
Referring to Fig. 9.25, the amount of correction C (in per cent) for interference of sheet pile B for the key point C_1a of pile A is given as

C = 19	d1/b′	d1 + d	(9.65)
i		b

where, b′ is the distance between the two pile lines, d₁ the depth of the interfering pile (i.e., the pile whose influence is to be determined on the neighbouring pile of depth d) measured below the level at which the interference is desired, and b is the total floor length.
The correction C_i is additive for upstream (in relation to the interfering pile) points and negative for points downstream of the interfering pile. Equation (9.65) is not applicable for determining the effect of an outer pile on an intermediate pile when the latter is equal to or smaller than the former and is at a distance less than or equal to twice the length of the outer pile. The correction for interference of a pile is calculated only for the key points of the adjacent pile towards the interfering pile. In Fig. 9.25, pile B interferes with the downstream face (i.e., C_1a) of pile A and the upstream face (i.e., E_c) of pile C.

344 IRRIGATION AND WATER RESOURCES ENGINEERING

A

^Ela

^Cla

B

C

E

C

Cc

d

d

1

E

c

bs

^Dla

D

Dc

b

b

Fig. 9.25 Sketch for mutual interference of sheet piles and for the slope of the floor
Correction for the Slope of the Floor
The correction for the slope of the floor is applied to the pressures of the key point (on the side of the sloping floor) of that pile line which is fixed at either the beginning or the end of the slope. The correction is additive for positive slope (i.e., level of the floor is decreasing in the direction of flow) and is negative for the negative slope. In Fig. 9.25, the correction for slope is applicable only to the pressure at E of pile B and is positive. If b_s is the horizontal length of the sloping floor and b′ is the distance between the two pile lines between which the sloping floor is located, then the amount of slope correction is equal to C_s(b_s/b′). The value of C_s depends on the slope of the sloping floor and is as given in Table 9.2.
Table 9.2 Values of C_s

	Slope (V : H)	1 : 1	1 : 2	1 : 3	1 : 4	1 : 5	1 : 6	1 : 7	1 : 8
	Correction Cs
	(% of pressure)	11.2	6.5	4.5	3.3	2.8	2.5	2.3	2.0

9.3.4. Method for Determination of Exit Gradient
For the simple profile of the downstream sheet pile, [Fig. 9.22 (ii)], the exit gradient G_E, as obtained by Khosla, et al. (12), is given as

G =	H	1	(9.66)
E	d	π	λ

Equation (9.66) gives G_E equal to infinity for no sheet pile at the downstream end of the floor (i.e., d = 0). It is, therefore, necessary that a vertical cutoff (i.e., sheet pile) is always provided at the downstream end of the floor. To prevent piping, the exit gradient must not be allowed to exceed the critical value of the exit gradient which depends on the type of soil. The value of the critical exit gradient for sand varies from 1/5 to 1/7. One can also obtain the values

of 1/F λ from Fig. 9.23 and thus obtain the exit gradient.

Example 9.2 Using Khosla’s method, obtain the residual seepage pressures at the ‘key’ points for the weir profile shown in Fig. 9.26. Also calculate the value of the exit gradient. Consider the case of no flow at pond level.

SURFACE AND SUBSURFACE FLOW CONSIDERATIONS FOR DESIGN OF CANAL STRUCTURES

345

Pond level 260.0 M

H

:

V

2

258.35

:

1

256.0 M

1.0 M

0.5 M

3.0 M

5.0 M

250.0 M

258.5 M

1.20 M

2.0 M

(Figure not to scale)

Sub-soil H.G.L.

1

V

257.74

: :H

257.01

3

256.61

255.0 M

2.0 M

10.5 M

1.2 M

15.0 M

0.5 M

248.0 M

248.0 M

				Fig. 9.26 Figure for Example 9.2