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A Retaining wall 6m high supports a backfill with a surcharge angle of 10 deg.The back of the wall is inclined to the vertical at a positive batter angle of 5 deg.If the angle of wall friction is 7 deg,then the resultant active earth pressure will act a distance of 2m above the base and inclined to the horizontal at an angle of A) 7 deg B) 10 deg C) 12 deg D)17 deg?
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A Retaining wall 6m high supports a backfill with a surcharge angle of...
Given parameters:
- Height of retaining wall (h) = 6m
- Surcharge angle (δ) = 10 deg
- Back slope angle (β) = 5 deg
- Angle of wall friction (φ) = 7 deg
- Resultant active earth pressure acts at a distance (d) = 2m above the base
To find: Angle (α) at which the resultant active earth pressure is inclined to the horizontal
Solution:
1. Calculate the active earth pressure coefficient (Ka) using Rankine's theory:
Ka = (1 - sinφ) / (1 + sinφ) * (1 - sinδ) / (1 + sinδ)
Ka = (1 - sin7) / (1 + sin7) * (1 - sin10) / (1 + sin10)
Ka = 0.261
2. Calculate the horizontal and vertical components of active earth pressure:
P_h = Ka * γ * h^2 * (1 - sinβ) * cosβ
P_h = 0.261 * 20 * 6^2 * (1 - sin5) * cos5
P_h = 30.28 kN/m
P_v = Ka * γ * h * (1 + sinβ)
P_v = 0.261 * 20 * 6 * (1 + sin5)
P_v = 10.47 kN/m
3. Calculate the moment of active earth pressure about the base of the retaining wall:
M = P_h * d + P_v * (h/2 - d/3)
M = 30.28 * 2 + 10.47 * (6/2 - 2/3)
M = 87.48 kN-m
4. Calculate the angle (α) at which the resultant active earth pressure is inclined to the horizontal:
tanα = M / (P_v * d)
tanα = 87.48 / (10.47 * 2)
tanα = 4.17
α = tan^-1(4.17)
α = 77.38 deg
Therefore, the angle (α) at which the resultant active earth pressure is inclined to the horizontal is 77.38 deg, which is not one of the given options.
- Height of retaining wall (h) = 6m
- Surcharge angle (δ) = 10 deg
- Back slope angle (β) = 5 deg
- Angle of wall friction (φ) = 7 deg
- Resultant active earth pressure acts at a distance (d) = 2m above the base
To find: Angle (α) at which the resultant active earth pressure is inclined to the horizontal
Solution:
1. Calculate the active earth pressure coefficient (Ka) using Rankine's theory:
Ka = (1 - sinφ) / (1 + sinφ) * (1 - sinδ) / (1 + sinδ)
Ka = (1 - sin7) / (1 + sin7) * (1 - sin10) / (1 + sin10)
Ka = 0.261
2. Calculate the horizontal and vertical components of active earth pressure:
P_h = Ka * γ * h^2 * (1 - sinβ) * cosβ
P_h = 0.261 * 20 * 6^2 * (1 - sin5) * cos5
P_h = 30.28 kN/m
P_v = Ka * γ * h * (1 + sinβ)
P_v = 0.261 * 20 * 6 * (1 + sin5)
P_v = 10.47 kN/m
3. Calculate the moment of active earth pressure about the base of the retaining wall:
M = P_h * d + P_v * (h/2 - d/3)
M = 30.28 * 2 + 10.47 * (6/2 - 2/3)
M = 87.48 kN-m
4. Calculate the angle (α) at which the resultant active earth pressure is inclined to the horizontal:
tanα = M / (P_v * d)
tanα = 87.48 / (10.47 * 2)
tanα = 4.17
α = tan^-1(4.17)
α = 77.38 deg
Therefore, the angle (α) at which the resultant active earth pressure is inclined to the horizontal is 77.38 deg, which is not one of the given options.
Community Answer
A Retaining wall 6m high supports a backfill with a surcharge angle of...
12 degree
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A Retaining wall 6m high supports a backfill with a surcharge angle of 10 deg.The back of the wall is inclined to the vertical at a positive batter angle of 5 deg.If the angle of wall friction is 7 deg,then the resultant active earth pressure will act a distance of 2m above the base and inclined to the horizontal at an angle of A) 7 deg B) 10 deg C) 12 deg D)17 deg?
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A Retaining wall 6m high supports a backfill with a surcharge angle of 10 deg.The back of the wall is inclined to the vertical at a positive batter angle of 5 deg.If the angle of wall friction is 7 deg,then the resultant active earth pressure will act a distance of 2m above the base and inclined to the horizontal at an angle of A) 7 deg B) 10 deg C) 12 deg D)17 deg? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A Retaining wall 6m high supports a backfill with a surcharge angle of 10 deg.The back of the wall is inclined to the vertical at a positive batter angle of 5 deg.If the angle of wall friction is 7 deg,then the resultant active earth pressure will act a distance of 2m above the base and inclined to the horizontal at an angle of A) 7 deg B) 10 deg C) 12 deg D)17 deg? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Retaining wall 6m high supports a backfill with a surcharge angle of 10 deg.The back of the wall is inclined to the vertical at a positive batter angle of 5 deg.If the angle of wall friction is 7 deg,then the resultant active earth pressure will act a distance of 2m above the base and inclined to the horizontal at an angle of A) 7 deg B) 10 deg C) 12 deg D)17 deg?.
A Retaining wall 6m high supports a backfill with a surcharge angle of 10 deg.The back of the wall is inclined to the vertical at a positive batter angle of 5 deg.If the angle of wall friction is 7 deg,then the resultant active earth pressure will act a distance of 2m above the base and inclined to the horizontal at an angle of A) 7 deg B) 10 deg C) 12 deg D)17 deg? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A Retaining wall 6m high supports a backfill with a surcharge angle of 10 deg.The back of the wall is inclined to the vertical at a positive batter angle of 5 deg.If the angle of wall friction is 7 deg,then the resultant active earth pressure will act a distance of 2m above the base and inclined to the horizontal at an angle of A) 7 deg B) 10 deg C) 12 deg D)17 deg? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Retaining wall 6m high supports a backfill with a surcharge angle of 10 deg.The back of the wall is inclined to the vertical at a positive batter angle of 5 deg.If the angle of wall friction is 7 deg,then the resultant active earth pressure will act a distance of 2m above the base and inclined to the horizontal at an angle of A) 7 deg B) 10 deg C) 12 deg D)17 deg?.
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