Khosla: two piles, floor at A, B, C, exit 0.2

Data and assumptions

Reading of the figure (two pile lines, as the question states): water level 105 m; with no flow the d/s water level is the d/s floor level 95 m, so $H = 10$ m. A = u/s pile junction at $x = 0$: floor top 100 m, floor bottom 99 m (1 m thick), pile bottom 94 m ($d = 6$ m). B = point on the floor at $x = 20$ m: floor top 99.5 m, thickness taken as 1.0 m. C = d/s pile junction at $x = 50$ m ($20 + 10 + 20$): floor top 95 m, bottom 93.5 m (1.5 m thick), pile bottom 90 m ($d = 5$ m). $G = 2.4$, safe exit gradient 0.2.

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 $b = 50$ 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 $H = 10.00$ m (no flow).

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 $b' = 50$ m (at $C_1$: $D = 100-90 = 10$ m, $d = 6$ m; at $E_2$: $D = 95-94 = 1$ m, $d = 5$ m), positive at $C_1$ and negative at $E_2$. The D points are not corrected.

Floor thickness

Unbalanced head $h$ = hydraulic-gradient level at the floor $-$ floor top level; required thickness $t = \dfrac{h}{G-1}$ with $G = 2.40$ (the HGL is taken as a straight line from $C_1$ to $E_2$ along the floor).

Exit gradient

$$G_E = \frac{H}{d}\cdot\frac{1}{\pi\sqrt{\lambda}} = \frac{10.00}{5.00}\times\frac{1}{\pi\sqrt{5.525}} = 0.2708\ (\approx 1/3.7)$$

Permissible $= 0.2000$. Not safe; deepen the d/s pile or lengthen the floor.

Answer: The floor is not safe at A (1.70 m needed, 1.0 m provided) or at C (1.79 m needed, 1.5 m provided), and is safe at B (0.66 m needed). The exit gradient of 0.271 exceeds 0.2, so the structure is not safe against piping.