Lateral earth pressure due to uniform surcharge: A backfill carries a uniform surcharge of intensity q (force per unit area). The additional lateral pressure on a vertical retaining wall is equivalent to which of the following?

Introduction / Context:
Uniform surcharge on the backfill surface adds a depth-independent vertical stress q. In lateral earth pressure theory (e.g., Rankine), this surcharge produces an additional lateral pressure equal to K times q at all depths, which is equivalent to the pressure from an imaginary extra soil cover of height z = q/γ.

Given Data / Assumptions:

• Uniform surface surcharge intensity = q (stress units).
• Backfill unit weight = γ.
• Classical active/passive/at-rest relationships apply.

Concept / Approach:

The surcharge contributes a constant vertical stress q. The corresponding lateral pressure increment is Δσ_h = K * q (independent of depth). This is exactly what would occur if the soil surface were raised by an additional height z such that γ * z = q, i.e., z = q/γ. Hence we model the surcharge as an equivalent height of soil to compute lateral pressures conveniently.

Step-by-Step Solution:

Verification / Alternative check:

Check dimensions: q and γz are both stresses; at any depth, adding z to the backfill height increases lateral pressure by Kγz = Kq, identical to surcharge effect.

Why Other Options Are Wrong:

(a) and (b) are dimensionally and conceptually incorrect; (d) is false since (c) is correct; (e) is incorrect because the surcharge-induced increment is uniform with depth, not triangular.

Common Pitfalls:

Drawing surcharge effect as a triangular distribution; forgetting to multiply by K when adding to total lateral pressure.

Final Answer:

Equal to the pressure from an added fill of height z = q / γ, where γ is the unit weight of the backfill