Khosla: inside corners and exit gradient (5 m head)

Data and assumptions

The figure details are only partly legible, so the following reading is adopted: head $H = 5$ m; total floor length $b = 35$ m between the end piles; u/s pile 3 m deep with floor thickness 1 m; d/s pile 6 m deep with floor thickness 2 m (floor top flush with the bed). The inside corners are $C_1$ (floor and u/s pile) and $E_2$ (floor and d/s pile). The safe exit gradient is not given, so 1/6 is assumed.

Khosla's constants

$\alpha = b/d$, $\lambda = \dfrac{1+\sqrt{1+\alpha^2}}{2}$, $\phi_E = \dfrac{1}{\pi}\cos^{-1}\dfrac{\lambda-2}{\lambda}$, $\phi_D = \dfrac{1}{\pi}\cos^{-1}\dfrac{\lambda-1}{\lambda}$ (in percent), total floor length $b = 35$ m. For the u/s pile, $\phi_{D1} = 100-\phi_D$ and $\phi_{C1} = 100-\phi_E$.

Pressures at the key points

Pressure is expressed as a percentage of the head $H = 5.00$ m.

Corrections: thk = floor thickness, $+\dfrac{\phi_D-\phi_C}{d}t$ at C and $-\dfrac{\phi_E-\phi_D}{d}t$ at E; int = mutual interference, $19\sqrt{D/b'}\,\dfrac{d+D}{b}$ with $b' = 35$ m (at $C_1$: $D = 6$, $d = 3$; at $E_2$: $D = 3$, $d = 6$), positive at $C_1$ and negative at $E_2$. The D points are not corrected.

Exit gradient

$$G_E = \frac{H}{d}\cdot\frac{1}{\pi\sqrt{\lambda}} = \frac{5.00}{6.00}\times\frac{1}{\pi\sqrt{3.459}} = 0.1426\ (\approx 1/7.0)$$

Permissible $= 1/6 = 0.1667$. Safe (less than the permissible value).

Answer: Uplift at the u/s inside corner $C_1 \approx 78.7\%$ of $H$ = 3.93 m; at the d/s inside corner $E_2 \approx 30.9\%$ of $H$ = 1.55 m; exit gradient $G_E = 0.143$ (about 1 in 7).