1. The coefficient of earth pressure at rest is given by _________
a) \(K_0=\frac{μ}{1-μ}\)
b) \(K_0=\frac{μ}{1+μ}\)
c) \(K_0=\frac{2μ}{1-μ}\)
d) \(K_0=\frac{1}{1-μ}\)
Explanation: The coefficient of earth pressure at rest is the ratio of the horizontal stress to the vertical stress.
since, σh=μ(σh+σv),
\(\frac{σ_h}{σ_v} = \frac{μ}{1-μ}.\)
\(K_0 = \frac{μ}{1-μ}.\)
2. If γ is the unit weight of soil, then the lateral earth pressure at depth z of soil mass is ______
a) \(σ_h=\frac{3}{2} K_0 z\)
b) σh=γz
c) σh=-K0 γz
d) σh=K0 γz
Explanation: Since the lateral earth pressure is given by,
σh=μ(σh+σv )=K0 σv,
substituting σv=γz,
σh=K0 γz.
3. The pressure distribution diagram for earth pressure at rest is _______
a) circular
b) triangular
c) rectangular
d) square
Explanation: The pressure distribution diagram for earth pressure at rest is triangular. If the retaining wall has a height of H, then the pressure at the base of wall is K0γH. At the top of wall, the pressure is zero.
4. The total earth pressure P0 at rest per unit length for vertical height H is _______
a) \(P_0=\frac{1}{2}K_0γH^2\)
b) P0=γH2
c) P0=K0 γH2
d) \(P_0=\frac{1}{2}K_0H^2\)
Explanation: The pressure intensity P0 is given by,
P0=K0 γz,
The total earth pressure P0 at rest per unit length is,
\(P_0=\int_0^H K_0 γz.dz \)
∴ \(P_0=\frac{1}{2}K_0γH^2.\)
5. The coefficient of earth pressure at rest is represented as _________ expression given by Jaky.
a) K0=1-sinφ
b) K0=sinφ
c) K0=1-cosφ
d) K0=cosφ
Explanation: The coefficient of earth pressure at rest is also computed from the expression given by Jaky in 1944 as,
K0=1-sinφ,
where, φ=angle of internal friction of the soil specimen.
6. For cohesion-less soil, the angle of internal friction is 45°, find the K0.
a) 0.429
b) 0.784
c) 0.293
d) 0.334
Explanation: Given,
φ=450
K0=1-sinφ=1-sin45=0.293.
7. A backfill of a retaining wall consists of γ=19 kN/m3 which is 6 m high. Find the total earth pressure per meter length. Given coefficient of earth pressure at rest is 0.5.
a) 165 kN/m
b) 178 kN/m
c) 171 kN/m
d) 345 kN/m
Explanation: Given,
γ=19 kN/m3
H=6 m
\(P_0=\frac{1}{2}K_0γH^2\)
\(P_0=\frac{1}{2}(0.5)(19)6^2 = 171 kN/m.\)
8. If K0=0.4, then find the value of µ.
a) 0.438
b) 0.286
c) 0.472
d) 0.592
Explanation: Given,
K0=0.4
\(K_0=\frac{μ}{1-μ}\)
\(μ=\frac{K_0}{1-K_0}\)
\(μ=\frac{0.4}{1-0.4}\)
μ=0.286.
9. For μ=0.3, find K0.
a) 0.429
b) 0.289
c) 0.536
d) 0.375
Explanation: Given,
μ=0.3
\(K_0=\frac{μ}{1-μ}=\frac{0.3}{1-0.3} \)
K0=0.429.
10. A backfill of a retaining wall consists of γ=19 kN/m3 which is 6 m high. Find the lateral earth pressure per meter length. Given coefficient of earth pressure at rest is 0.5.
a) 43 kN/m2
b) 57 kN/m2
c) 48 kN/m2
d) 76 kN/m2
Explanation:
Given,
γ = 19 kN/m2
z = 6 m
K0 = 0.5
P0 = K0 γz = 0.5×19×6
P0 = 57 kN/m2.