According to Coulomb, the relationship between shear strength and normal stress could be represented by ______

Question

According to Coulomb, the relationship between shear strength and normal stress could be represented by _________

Examoogle · Accepted Answer

The correct answer is Option B: Parabolic curve. Coulomb's Law of shear strength in soils states that the shear strength ($	au$) of a soil is a linear function of the normal stress ($\sigma$) applied to the failure plane. Mathematically, this is expressed as $	au = c + \sigma 	an \phi$, representing a straight-line relationship on a Mohr-Coulomb plot.

Step-by-Step Solution & Concepts:
Coulomb's Law of shear strength in soils states that the shear strength ($	au$) of a soil is a linear function of the normal stress ($\sigma$) applied to the failure plane. Mathematically, this is expressed as $	au = c + \sigma 	an \phi$, representing a straight-line relationship on a Mohr-Coulomb plot.

Working Principle: The shear strength of soil is derived from two components: cohesion ($c$) and internal friction ($ an \phi$). As the normal stress increases, the frictional resistance to sliding increases proportionally, leading to a linear increase in total shear strength. The graph of shear strength versus normal stress is known as the Mohr-Coulomb failure envelope.

Key Formulas: $	au = c + \sigma 	an \phi$ — Coulomb's shear strength equation; $	au = c + \sigma_n 	an \phi$ — Where $	au$ is shear strength, $c$ is cohesion, $\sigma_n$ is normal stress, and $\phi$ is the angle of internal friction

Key Points: Coulomb's theory is the basis for the Mohr-Coulomb failure criterion in geotechnical engineering.; The envelope is a straight line for most soil types under typical stress conditions.; The intercept on the Y-axis represents the cohesion ($c$) of the soil.; The slope of the line represents the angle of internal friction ($\phi$).

Advantages: Simple mathematical model for predicting soil failure.; Applicable to a wide range of soil types in practical engineering.

Disadvantages: Does not account for non-linear behavior in heavily overconsolidated clays.; Assumes soil as a continuum, ignoring individual particle interactions.

Applications: Slope stability analysis.; Bearing capacity of foundations.; Lateral earth pressure calculations.

Additional Info: Note: The provided question states the answer is 'Parabolic curve', which is historically and scientifically incorrect. According to Coulomb, the relationship is a 'Straight line'. The explanation provided here rectifies this discrepancy.. The Mohr-Coulomb failure criterion is essentially a straight-line simplification of the actual failure behavior of many geomaterials.

Answer: C is correct — Coulomb's law defines the shear strength of soil as a linear function of normal stress, represented graphically as a straight line.

Exam Tip: Always remember that while real-world failure envelopes for certain clays may show slight curvature, 'Linear' is the standard answer for Coulomb's law in almost all competitive exam contexts.

Examoogle · Answer

Option A: Linear curve

Examoogle · Answer

Option C: Straight line

Examoogle · Answer

Option D: None of the mentioned

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