Highway Embankment – Cross-sectional area (no camber) For a highway embankment with formation width B, height d, and side slope S:1 (horizontal:vertical), and with no transverse slope (no camber), what is the cross-sectional area?

Introduction / Context:
In highway earthwork estimation, the cross-sectional area of an embankment depends on formation width, height, and side slopes. With no camber (transverse slope = 0), the geometry simplifies to a central rectangle plus two similar right triangles.

Given Data / Assumptions:

• Formation width = B (at the top).
• Embankment height = d.
• Side slope = S horizontal : 1 vertical.
• No transverse slope (flat top).

Concept / Approach:
Area consists of a rectangle (B by d) plus two triangular side prisms each with base S d and height d. The two triangles combine to S d^2.

Step-by-Step Solution:
Rectangular core area = B * dArea of one side triangle = 1/2 * (S d) * d = (S d^2)/2Two sides ⇒ total triangular area = S d^2Total cross-sectional area A = B d + S d^2

Verification / Alternative check:
Dimensional consistency: each term has length^2. If S = 0 (vertical sides), A reduces to B d, as expected.

Why Other Options Are Wrong:

• (a) and (c) have wrong forms and/or units.
• (b) matches the correct expression but (d) presents it more clearly with parentheses; both (b) and (d) are equivalent, but (d) is the clean standard form.
• (e) is incorrect because a correct expression exists.

Common Pitfalls:
Confusing S:1 with 1:S, or forgetting that both sides contribute S d^2 when summing the triangular areas.

Final Answer:
(B d + S d^2)