Contents preface (VII) introduction 1—37

Fig. 9.17 Blench’s curves

H/L x 2d₁

Sub-soil hydraulic

grade line

H / L x 2d₂

H




H/L x 2d₃

d	1	^b1			^b2
					d	3
					d	2

Fig. 9.18 Subsoil hydraulic grade line

336 IRRIGATION AND WATER RESOURCES ENGINEERING
It should be noted that the seepage head H is the difference between water levels upstream and downstream of the weir. The worst condition will occur when water is held up to the highest possible level on the upstream side with no flow. The downstream level is then taken as the downstream bed level.
The elevation of the subsoil hydraulic gradient line above the bottom of the floor at any point measures the uplift pressure at that point. If h′ is the height of the subsoil hydraulic gradient line above the bottom of the floor, the uplift pressure of subsoil water exerted on the floor is ρ gh′. Assuming the mass density of the floor material as ρ_s and the floor thickness as t, the downward force per unit area due to the weight of the floor is tρ_s g. For equilibrium, these two should be equal.

∴	ρ gh′ = t ρs g	(9.40)
or	t =	h′
(ρ s /ρ)

The surface profile of the floor is determined from the surface flow considerations and is known. But h′, measured from the bottom of the floor, can be known only if the thickness of the floor t is known. Equation (9.40) is, therefore, rewritten as
h′ = t(ρ_s/ρ)
Subtracting t from both sides,
h′ – t = t(ρ_s/ρ) – t
= t[(ρ_s/ρ) – 1]

h′ − t

^{t =} (ρ _s /ρ) − 1 ^(9.41)

(h′ – t) is the height of subsoil hydraulic gradient line measured above the top surface of the floor and, hence, is known. The thickness of the floor t can, therefore, be directly obtained.

On the upstream side of the barrier, the weight of water causing the seepage is more than sufficient to counterbalance the uplift pressure. In the absence of water upstream, there will be no seepage and, hence, no uplift pressure. Therefore, the upstream floor thickness may be kept equal to minimum practical thickness to resist wear and development of cracks. The floor downstream of the barrier must be in accordance with Eq. (9.41). This also suggests that it would be economical to keep as much floor length upstream as possible. A minimum floor length downstream of the barrier is, however, always required to resist the action of fast-flowing water. Shifting of the floor upstream also reduces the uplift pressure on the floor downstream of the barrier (Fig. 9.19) because a larger portion of the total loss of head has occurred up to the barrier. Further, an upstream cutoff reduces uplift pressure (Fig. 9.20) while a downstream cutoff increases uplift pressure all along the floor.


A′ A Β′ Β

Fig. 9.19 Effect of shifting floor upstream on subsoil H.G.L.

SURFACE AND SUBSURFACE FLOW CONSIDERATIONS FOR DESIGN OF CANAL STRUCTURES

337

Fig. 9.20 Effect of U/S and D/S cutoffs on subsoil H.G.L
In 1932, Lane (14), after analysing 290 weirs and dams, evolved what is now known as weighted creep theory which, in effect, is Bligh’s creep theory corrected for vertical creep. When the coefficient of horizontal permeability is three times the coefficient of vertical permeability, Lane suggested a weight of three for the vertical creep and one for the horizontal creep. Thus, for the case of Fig. 9.18, according to Lane’s method, the creep length is [3(2d₁ + 2d₂ + 2d₃) + (b₁ + b₂)]. Inclined floors may be treated as vertical if its slope exceeds 45° and horizontal if the slope is less than 45°. Alternatively, for inclined floors, the weight may be taken as equal to 3[1 + (2θ/90)] where θ is the angle (in degrees) of inclination of the floor with the horizontal. Because of their simplicity, Bligh’s and Lane’s methods are still useful for preliminary dimensioning of the floor. Bligh’s method is, obviously, more conservative.
Following the appearance of cracks at the upstream and downstream ends due to the undermining of soil at the upper Chenab canal structures in 1926-27, Khosla, et al. (12) carried out some studies. These studies disclosed that the measured pressures were not equal to those calculated from Bligh’s theory. Other notable findings of these studies (12) were as follows :
(i) The outer faces of the end sheet piles were more effective than the inner ones and the horizontal length of floor.
(ii) The intermediate piles, if smaller in length than the outer ones, were ineffective except for local redistribution of pressures.
(iii) Erosion of foundation soil below the structure started from the tail end. If the hy-draulic gradient at the exit was more than the critical gradient for the soil below the structure, the soil particles would move with the flow of water thus causing progres-sive degradation of the soil and resulting in cavities and ultimate failure.
(iv) It was absolutely essential to have a reasonably deep vertical cutoff at the down-stream end to prevent undermining.
In 1929, Terzaghi (15), based on his laboratory studies stated that failure occurred due to undermining if the hydraulic gradient at the exit was more than the floatation gradient. The floatation gradient is similar to the term ‘critical gradient’ used by Khosla, et al. (12). The floatation gradient implied a state of floatation of the soil at the toe of the work if the exit gradient exceeded the limit of 1 : 1 at which condition the upward force due to the flow of water was almost exactly counterbalanced by the weight of the soil.
The above-mentioned methods of determining seepage effects do not have any theoretical justification. Now that considerable knowledge of the theory of seepage is available, the equation governing the seepage flow has been solved to obtain the uplift pressures and the exit gradient.