Between the intermediate and d/s piles (40 m), the pressure falls from 65% at C2 to 55% at E3. How is phi at x from the intermediate pile found?

Linear interpolation: phi = 65 - 10 x/40

Why is the thickness at 30 m smaller than at 20 m?

Pressure falls along the floor (57.5% against 60%), so the uplift head is smaller

The net head changes with distance

2064 Kartik (old course) · 8 marks

Khosla: HGL and d/s floor thickness, three piles

Short answer

Between intermediate and d/s piles, pressure drops linearly from 65% to 55% of total head. With 10 m net head, required floor thickness at 20 m is 5.00 m and at 30 m is 4.79 m.

Following corrected φ values were computed from Khosla's curves in a barrage placed on permeable foundation. U/S sheet pile: φE1 = 100%, φD1 = 90%, φC1 = 85% Intermediate pile: φE2 = 80%, φD2 = 70%, φC2 = 65% D/S sheet pile: φE3 = 55%, φD3 = 45%, φC3 = 0% Distance between the U/S and intermediate piles is 20 m and that between the intermediate and D/S piles is 40 m. Assuming that the floor is horizontal throughout, draw the HGL for the subsoil flow. If the net head is 10 m, determine the thickness of D/S floor at a distance of 20 m and 30 m away from the intermediate sheet pile. Assume G for the floor material equal to 2.2. The symbols has usual meanings.

Given

Corrected pressures (percent of head): u/s pile $E_1 = 100$ , $D_1 = 90$ , $C_1 = 85$ ; intermediate pile $E_2 = 80$ , $D_2 = 70$ , $C_2 = 65$ ; d/s pile $E_3 = 55$ , $D_3 = 45$ , $C_3 = 0$ . Net head $H = 10$ m, $G = 2.2$ . Piles at 0, 20 m and 60 m (20 m and 40 m apart). The floor is horizontal, with its level taken as the datum (d/s water level).

Hydraulic gradient line

The HGL is a vertical drop across each pile and a straight line along the floor between piles:

Point	Pressure (%)	Head above floor (m)
$E_1$	100	10.0
$D_1$	90	9.0
$C_1$	85	8.5
$E_2$	80	8.0
$D_2$	70	7.0
$C_2$	65	6.5
$E_3$	55	5.5
$D_3$	45	4.5
$C_3$	0	0

 100 E1 |#############################
  90 D1 |##########################
  85 C1 |########################    (floor, 20 m)
  80 E2 |#######################
  70 D2 |####################
  65 C2 |##################          (floor, 40 m)
  55 E3 |################
  45 D3 |#############
   0 C3 |

Thickness of the d/s floor (between intermediate and d/s piles)

On the 40 m floor the pressure falls linearly from 65% at $C_2$ to 55% at $E_3$ :

\phi(x) = 65 - (65-55)\frac{x}{40}

Unbalanced head $h = \phi H/100$ and thickness $t = \dfrac{h}{G-1} = \dfrac{h}{1.2}$ :

Distance from intermediate pile	$\phi$ (%)	$h$ (m)	$t$ (m)
20 m	60.0	6.00	5.00
30 m	57.5	5.75	4.79

Answer: Required floor thickness $\approx 5.00$ m at 20 m and $\approx 4.79$ m at 30 m from the intermediate sheet pile.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Khosla: HGL and d/s floor thickness, three piles

Given

Hydraulic gradient line

Thickness of the d/s floor (between intermediate and d/s piles)

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