Question

A retaining wall of height 8 m retains dry sand. In the initial state, the soil is loose and has a void ratio of 0.5, ${\gamma }_d=17.8kN/m^3$ and $\varphi ={30}^{\circ }$, Subsequently, the backfill is compacted to a state where void ratio is 0.4, ${\gamma }_d=18.8kN/m^3$ and $\varphi ={35}^{\circ }$, The ratio of initial passive thrust to the final passive thrust, according to Rankine's earth pressure theory, is

• A. 0.38
• B. 0.64
• C. 0.77
• D. 1.5

Answer 1

The correct option is C 0.77

Height of wall,

z = 8m

Void ratio, e = 0.5

c = 0

${\gamma }_d=17.8kN/m^3$

$\varphi ={30}^{\circ }$

Passive earth pressure coefficient,

$K_p=\frac{1+sin\varphi }{1-sin\varphi }$

Initial passive thrust,

$P_1=\frac{1}{2}{K}_p\gamma z^2$

$=\frac{1}{2}\times 3\times 17.8\times 8^2$

= 1708.8 kN per meter length of wall.

When backfill is compacted,

$\varphi ={35}^{\circ }$

${\gamma }_d=18.8kN/m^3$

$K_p=\frac{1+sin\varphi }{1-sin\varphi }$

$=\frac{1+sin{35}^{\circ }}{1-sin{35}^{\circ }}=3.69$

$Passivethrust,P_2=\frac{1}{2}{K}_p\gamma z^2$

$=\frac{1}{2}\times 3.69\times 18.8\times 8^2$

= 2220 kN/ length of wall

$\frac{P_1}{P_2}=\frac{1708.8}{2220}=0.77$