A retaining wall 6m high supports a backfill with a surcharge angle of 10°. The back of the wall is inclined to the vertical at a positive batter angle of 5°. If the angle of wall friction is 7°, then the resultant active earth pressure will act at a distance of 2 m above the base and inclined to the horizontal at an angle of A. 7° B. 10° C. 12° D. 17°

The correct answer is C. 12°.

The resultant active earth pressure is the sum of the vertical and horizontal components of the active earth pressure. The vertical component of the active earth pressure is equal to the weight of the backfill, while the horizontal component is equal to the product of the lateral earth pressure coefficient and the active earth pressure.

The lateral earth pressure coefficient is a function of the angle of internal friction of the backfill and the angle of wall friction. The angle of internal friction of the backfill is equal to the angle of surcharge, while the angle of wall friction is equal to 7°.

The resultant active earth pressure will act at a distance of 2 m above the base of the wall, because the vertical component of the active earth pressure is equal to the weight of the backfill, which is acting at the base of the wall.

The resultant active earth pressure will be inclined to the horizontal at an angle of 12°, because the horizontal component of the active earth pressure is equal to the product of the lateral earth pressure coefficient and the active earth pressure, which is equal to the product of the angle of internal friction of the backfill and the angle of wall friction.

The following is a brief explanation of each option:

• Option A: 7°. This is the angle of wall friction. The resultant active earth pressure will not act at an angle of 7° to the horizontal, because the horizontal component of the active earth pressure is not equal to the product of the lateral earth pressure coefficient and the active earth pressure.
• Option B: 10°. This is the angle of surcharge. The resultant active earth pressure will not act at an angle of 10° to the horizontal, because the horizontal component of the active earth pressure is not equal to the product of the lateral earth pressure coefficient and the active earth pressure.
• Option C: 12°. This is the correct answer. The resultant active earth pressure will act at an angle of 12° to the horizontal, because the horizontal component of the active earth pressure is equal to the product of the lateral earth pressure coefficient and the active earth pressure.
• Option D: 17°. This is not the correct answer. The resultant active earth pressure will not act at an angle of 17° to the horizontal, because the horizontal component of the active earth pressure is not equal to the product of the lateral earth pressure coefficient and the active earth pressure.