In buried water mains design, the surface traffic load transmitted to a pipe at depth is typically evaluated using which foundation stress solution?

Introduction / Context:
Design of buried pipelines must account for superimposed loads from surface traffic. Estimating how a surface wheel load distributes as vertical stress at pipe crown depth is a classical soil mechanics problem of stress distribution in a semi-infinite medium.

Given Data / Assumptions:

• Elastic, homogeneous, isotropic half-space assumption for soil (idealized).
• Concentrated or distributed load applied at the ground surface.
• Need vertical stress at pipe crown depth.

Concept / Approach:
Boussinesq developed closed-form solutions for stresses at any point in an elastic half-space due to surface point loads, line loads, or uniformly distributed loads. These are the standard basis for estimating vertical stress increase at a given depth above a pipe crown.

Step-by-Step Solution:

Verification / Alternative check:
For layered soils, methods such as Newmark charts or numerical analyses (elastic layer theory) can be used, but Boussinesq remains the classical starting point for preliminary design.

Why Other Options Are Wrong:

• Rankine: for lateral earth pressure on retaining walls, not vertical stress distribution to a buried pipe.
• Darcy–Weisbach: headloss in pipe flow, unrelated to soil stress.
• Lacey: canal design, regime theory for alluvial channels, not buried pipes.
• Westergaard: commonly for slabs on elastic foundations; not standard for deep half-space vertical stress.

Common Pitfalls:
Ignoring depth and load spread, misusing highway contact areas, or mixing elastic-half-space assumptions with plastic soil behavior without safety factors.

Final Answer:
Boussinesq’s formula for vertical stress in an elastic half-space