# Foundation Engineering Questions and Answers – Earth Pressure at Rest

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This set of Foundation Engineering Questions and Answers for Entrance exams focuses on “Earth Pressure at Rest”.

1. The coefficient of active earth pressure is_______ than the coefficient of passive pressure.
a) less than
b) greater than
c) equal to
d) insufficient data

Explanation: The coefficient of active earth pressure is less than that of the coefficient of passive earth pressure. The coefficient of active earth pressure is also less than that of the coefficient of earth pressure at rest.

2. The coefficient earth pressure at rest is _______________
a) less than coefficient of active pressure
b) greater than coefficient of active pressure
c) equal to coefficient of active pressure
d) one

Explanation: The coefficient earth pressure at rest is greater than that of the coefficient of active earth pressure. But, he coefficient earth pressure at rest is less than the coefficient of passive earth pressure.

3. For earth pressure at rest, there will be no ______
a) vertical stress
b) shear stress
c) horizontal stress
d) both vertical and horizontal stress

Explanation: For earth pressure at rest, there is horizontal stress as well as the vertical stress. For earth pressure at rest, there will be no shear stresses.
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4. The lateral strain in the horizontal direction is _______
a) $$∈_h=\frac{1}{E} [σ_h-μ(σ_v)]$$
b) $$∈_h=\frac{1}{E} [σ_h-μ(σ_h-σ_v)]$$
c) $$∈_h=\frac{1}{E} [σ_h-μ(σ_h+σ_v)]$$
d) $$∈_h=\frac{1}{E} [σ_h-(σ_h-σ_v)]$$

Explanation: The lateral strain ∈h in the horizontal direction is given by,
$$∈_h=\frac{1}{E} [σ_h-μ(σ_h-σ_v )],$$
where, σh =horizontal stress
σv =vertical stress
E=elastic modulus
μ= Poisson’s ratio.

5. The lateral earth pressure at rest with respect to Poisson’s ratio is _______
a) σh=μ(σhv)
b) σh=μ(σhv)
c) σh=μ(σhv)
d) σh=-μ(σhv)

Explanation: The earth pressure at rest has the condition corresponding to ∈h=0.
Since, $$∈_h=\frac{1}{E} [σ_h-μ(σ_h-σ_v)],$$
∴ σh=μ(σhv).

6. 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(σhv),
∴ $$\frac{σ_h}{σ_v} = \frac{μ}{1-μ}.$$
∴ $$K_0 = \frac{μ}{1-μ}.$$

7. 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(σhv )=K0 σv,
substituting σv=γz,
∴ σh=K0 γz.

8. 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.

9. 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,
$$P_0=\int_0^H K_0 γz.dz$$
∴ $$P_0=\frac{1}{2}K_0γH^2.$$

10. 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.

11. 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.

12. 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
$$P_0=\frac{1}{2}K_0γH^2$$
$$P_0=\frac{1}{2}(0.5)(19)6^2 = 171 kN/m.$$

13. 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.

14. 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.

15. 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.

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