Question

A 6 m high retaining wall with a surcharge of $5kN/m^2$ at the ground surface shown in the figure



The Rankine active pressure (in kN/m) on the wall before the formation of cracks is ?

• A. 81.12
• B. 78.84
• C. 76.56
• D. 74.28

Answer 1

The correct option is C 76.56

Active earth pressure coeficient

$k_a=\frac{1-sin\varphi }{1+sin\varphi }=\frac{1-sin{30}^0}{1+sin{30}^0}=\frac{1}{3}$

Earth pressure,

$p_a=k_a(q+\gamma z)-2C\sqrt{k_a}$

at z = 0

$p_a=\frac{1}{3}(5+18\times 0)-2\times 6\sqrt{0.33}$

$=-5.26kN/m^2$

For $p_a=0$

$0=\frac{1}{3}(5+18z)-2\times 6\sqrt{0.33}$

z = 0.87 m



at z = 6 m

$p_a=\frac{1}{3}(5+18\times 6)-12\sqrt{0.33}$

$=30.74kN/m^2$

Before the formation of crack,

Negative pressure,

$p_1=\frac{1}{2}\times 5.26\times 0.87=2.28kN/m$

Positive pressure,

$p_2=\frac{1}{2}\times 30.74\times 5.13=78.84kN/m$

$Net{p}_a=78.84-2.28$
$=76.56kN/m$