Shear strength criterion – who proposed τ = c + σ tan φ? Identify the originator associated with the linear shear strength envelope τ = C + σ tan φ used in geotechnical engineering.

Introduction / Context:The linear shear strength relationship τ = c + σ tan φ underpins many earth pressure and slope stability analyses. It is popularly termed the Mohr–Coulomb criterion, reflecting contributions from both scientists in understanding shear failure of materials.

Given Data / Assumptions:

• c is cohesion intercept; φ is angle of internal friction.
• σ denotes normal stress on the potential failure plane.

Concept / Approach:Coulomb (1776) proposed the linear relationship between shear and normal stress, introducing c and φ concepts through frictional sliding and apparent cohesion. Mohr later (late 19th century) introduced stress circles and the concept of a failure envelope in principal stress space; the combination yields the Mohr–Coulomb criterion widely used today.

Step-by-Step Solution:

Verification / Alternative check:Standard soil mechanics texts title the combined theory “Mohr–Coulomb” while crediting Coulomb for the linear τ–σ law.

Why Other Options Are Wrong:

• Rankine proposed earth pressure theory assuming c = 0 soils.
• Culmann contributed to graphical earth pressure methods but not this basic law.
• Mohr did not originally propose the linear τ–σ equation alone.

Common Pitfalls:Confusing the combined name with the originator; assuming Rankine’s theory implies this relation.

Final Answer:Coulomb