Question

Water flows in the upward direction in a tank through 2.5 m thick sand layer as shown in the figure. The void ratio and specific gravity of sand are 0.58 and 2.7, respectively. The sand is fully saturated. Unit weight of water is$10kN/m^3$.
The effective stress ( in kPa, round off to two decimal places) at point A, located 1 m above the base of tank, is .

• A. 8.93

Answer 1

The correct option is A 8.93
Effective stress at point A,

$={\gamma }_{sub}\cdot h-ih{\gamma }_w$

${\gamma }_{sat}=\left(\frac{G+e}{1+e}\right){\gamma }_w$

e = $\frac{2.7+0.58}{1+0.58}\times 10$

= 20.75 kN/$m^2$

${\gamma }_{sub}={\gamma }_{sat}-{\gamma }_w$

= 20.759 - 10

= 10.759 kN/$m^2$

Total stress at A,

= 1 $\times$ ${\gamma }_w+1.5{\gamma }_{sat,sand}$

= 1 $\times$ 10 + 1.5 $\times$ 20.75

= 41.125 kN/$m^2$

Total $h_L$ in sand = 1.2 m


Head loss upto A =

$\frac{1.2}{2.5}\times 1m$

$\Rightarrow$ Pore water pressure at A,

$=\left(\frac{P_A}{{\gamma }_w}\right){\gamma }_w$

$=[3.7-\frac{1.2}{2.5}]{\gamma }_w$

= 32.2 kN/$m^2$

$\Rightarrow$ Effective stress at A

= 41.125 - 32.2

= 8.925 kN/$m^2$