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A 3 m high vertical earth retaining wall retains a dry granular backfill with angle of internal friction of 30o and unit weight of 20 kN/m3. If the wall is prevented from yielding (no movement), the total horizontal thrust (in kN per unit length) on the wall is
- a)0
- b)30
- c)45
- d)270
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A 3 m high vertical earth retaining wall retains a dry granular backfi...
Soil is dry sand
K0 = 1 − sinØ = 1 - sin 30° = 0.5
Total horizontal thrust
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A 3 m high vertical earth retaining wall retains a dry granular backfi...
Given:
Height of retaining wall (H) = 3 m
Angle of internal friction (ϕ) = 30°
Unit weight of backfill (γ) = 20 kN/m³
To find: Total horizontal thrust on the wall
Solution:
The total horizontal thrust on the wall can be calculated using Coulomb's earth pressure theory.
1. Active earth pressure:
The granular backfill exerts a horizontal pressure on the retaining wall. This pressure is called active earth pressure. Coulomb's theory states that the active earth pressure (Pa) is given by:
Pa = Ka * γ * H²/2
where,
Ka = Active earth pressure coefficient
γ = Unit weight of backfill
H = Height of retaining wall
The value of Ka depends on the angle of internal friction (ϕ) of the backfill. For ϕ = 30°, Ka can be calculated using the following formula:
Ka = (1 - sin ϕ) / (1 + sin ϕ)
Plugging in the values, we get:
Ka = (1 - sin 30°) / (1 + sin 30°) = 0.33
Pa = 0.33 * 20 * 3²/2 = 27.9 kN/m
2. Passive earth pressure:
Since the retaining wall is prevented from yielding (no movement), the backfill exerts a horizontal pressure in the opposite direction to the active earth pressure. This pressure is called passive earth pressure. Coulomb's theory states that the passive earth pressure (Pp) is given by:
Pp = Kp * γ * H²/2
where,
Kp = Passive earth pressure coefficient
The value of Kp depends on the angle of internal friction (ϕ) of the backfill. For ϕ = 30°, Kp can be calculated using the following formula:
Kp = (1 + sin ϕ) / (1 - sin ϕ)
Plugging in the values, we get:
Kp = (1 + sin 30°) / (1 - sin 30°) = 1.43
Pp = 1.43 * 20 * 3²/2 = 42.9 kN/m
3. Total horizontal thrust:
The total horizontal thrust (P) on the retaining wall is given by:
P = Pa + Pp
Plugging in the values, we get:
P = 27.9 + 42.9 = 70.8 kN/m
Therefore, the total horizontal thrust on the wall is 70.8 kN/m.
Answer: Option C (45 kN/m) is incorrect.
Height of retaining wall (H) = 3 m
Angle of internal friction (ϕ) = 30°
Unit weight of backfill (γ) = 20 kN/m³
To find: Total horizontal thrust on the wall
Solution:
The total horizontal thrust on the wall can be calculated using Coulomb's earth pressure theory.
1. Active earth pressure:
The granular backfill exerts a horizontal pressure on the retaining wall. This pressure is called active earth pressure. Coulomb's theory states that the active earth pressure (Pa) is given by:
Pa = Ka * γ * H²/2
where,
Ka = Active earth pressure coefficient
γ = Unit weight of backfill
H = Height of retaining wall
The value of Ka depends on the angle of internal friction (ϕ) of the backfill. For ϕ = 30°, Ka can be calculated using the following formula:
Ka = (1 - sin ϕ) / (1 + sin ϕ)
Plugging in the values, we get:
Ka = (1 - sin 30°) / (1 + sin 30°) = 0.33
Pa = 0.33 * 20 * 3²/2 = 27.9 kN/m
2. Passive earth pressure:
Since the retaining wall is prevented from yielding (no movement), the backfill exerts a horizontal pressure in the opposite direction to the active earth pressure. This pressure is called passive earth pressure. Coulomb's theory states that the passive earth pressure (Pp) is given by:
Pp = Kp * γ * H²/2
where,
Kp = Passive earth pressure coefficient
The value of Kp depends on the angle of internal friction (ϕ) of the backfill. For ϕ = 30°, Kp can be calculated using the following formula:
Kp = (1 + sin ϕ) / (1 - sin ϕ)
Plugging in the values, we get:
Kp = (1 + sin 30°) / (1 - sin 30°) = 1.43
Pp = 1.43 * 20 * 3²/2 = 42.9 kN/m
3. Total horizontal thrust:
The total horizontal thrust (P) on the retaining wall is given by:
P = Pa + Pp
Plugging in the values, we get:
P = 27.9 + 42.9 = 70.8 kN/m
Therefore, the total horizontal thrust on the wall is 70.8 kN/m.
Answer: Option C (45 kN/m) is incorrect.
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A 3 m high vertical earth retaining wall retains a dry granular backfill with angle of internal friction of 30o and unit weight of 20 kN/m3. If the wall is prevented from yielding (no movement), the total horizontal thrust (in kN per unit length) on the wall isa)0b)30c)45d)270Correct answer is option 'C'. Can you explain this answer?
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