Question

29. Coloumb and Rankine theories for calculating simple earth pressures are based on which of the following assumptions:
(A). Soil is cohesionless
(B). Soil is isotropic
(C). Soil is homogeneous
(D). Soil is semi-infinite
Choose the correct answer from the options given below:

• A. (A) and (B) only
• B. (B) and (C) only
• C. (B), (C) and (D) only
• D. (A), (B), (C) and (D)

Hint:

Rankine's theory assumes a smooth vertical wall back, whereas Coulomb's wedge theory accounts for wall friction and inclined wall backs.
However, both share the fundamental simplifying assumptions of a homogeneous, isotropic, semi-infinite, and cohesionless backfill.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Lateral earth pressure theories developed by Rankine (1857) and Coulomb (1776) are the foundation of geotechnical design for retaining structures.
To simplify the complex mathematical formulation of stress distribution in soils, both investigators established several idealized assumptions regarding the properties and extent of the soil mass.

Step 2: Detailed Explanation:
Let us review the key assumptions shared by both classical lateral earth pressure theories:
(A) Soil is cohesionless: The original formulations of both Rankine and Coulomb theories assume that the backfill material is dry and completely cohesionless (\(c = 0\)), where the shear strength is derived solely from internal friction.
While modern extensions incorporate cohesion, the classical theories are fundamentally based on cohesionless soils.
(B) Soil is isotropic: The elastic and shear properties of the soil are assumed to be identical in all directions at any given point.
(C) Soil is homogeneous: The soil properties (such as unit weight \(\gamma\) and internal friction angle \(\phi\)) are assumed to be constant throughout the entire soil mass, which means the soil is uniform.
(D) Soil is semi-infinite: The soil mass is assumed to extend infinitely in the horizontal direction and downwards, bounded only by a flat or inclined ground surface at the top.
This boundary condition allows the stress calculations to remain independent of far-field lateral boundary constraints.
Since all four parameters (A), (B), (C), and (D) are core assumptions of both classical theories, option 4 is the correct choice.

Step 3: Final Answer:
The assumptions are (A), (B), (C), and (D).