Khosla's simple profiles and corrections

Four simple Khosla profiles

Khosla's equations exist for simple forms into which a complex weir profile is broken down:

(a) Pile at the upstream end    (b) Pile at the downstream end
 ~~~|                            ~~~~~~~~~~~~~~|
 ___|_______________              _____________|__
    |                                          |
    d  (E1,D1,C1)                              d (E2,D2,C2)

(c) Depressed floor             (d) Intermediate pile
 ~~~ __     ___________          ~~~  ______|_______
 ___/  \___/                     ___/       |
        |                                    d

(a) a horizontal floor with a pile at its upstream end; (b) a horizontal floor with a pile at its downstream end; (c) a depressed floor (a horizontal floor lowered below the river bed, the depression acting like a short pile); (d) a floor with an intermediate pile. Their pressures at the key points (E, D, C) are given by Khosla's formulas in terms of $\alpha = b/d$ and $\lambda$.

Corrections suggested by Khosla

1. Correction for mutual interference of piles – when a pile of depth $d$ is influenced by another pile of depth $D$ at a distance $b'$ (total floor length $b$):

$$C = 19\sqrt{\frac{D}{b'}}\left(\frac{d+D}{b}\right)\ \%$$

It is positive for points upstream of the interfering pile and negative for points downstream of it.

2. Correction for thickness of the floor – the key points are taken at the floor top, while the uplift acts on the underside; the pressure is interpolated linearly between the point at floor level and the pile tip:

$$\text{Correction} = \frac{\phi_D - \phi_E}{d}\,t$$

(positive at the u/s pile's $C_1$, negative at the d/s pile's $E_2$).

3. Correction for the slope of the floor – a sloping floor (glacis) differs from the horizontal floor of the simple profile. A correction factor from a table (e.g. 11.2% for 1:1, 6.5% for 2:1, 4.5% for 3:1, 3.3% for 4:1) is multiplied by the ratio of the horizontal length of the slope to the distance between the two pile lines between which the slope lies. It is positive for a down slope and negative for an up slope in the direction of flow.