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

A

Linear curve

B

Parabolic curve

C

Straight line

D

None of the mentioned

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleCivilSoil Mechanics
Option B

Parabolic curve

Quick Summary:

Coulomb's Law of shear strength in soils states that the shear strength (╧Д\tau╧Д) of a soil is a linear function of the normal stress (╧Г\sigma╧Г) applied to the failure plane. Mathematically, this is expressed as ╧Д=c+╧ГtanтБб╧Х\tau = c + \sigma \tan \phi╧Д=c+╧Гtan╧Х, representing a straight-line relationship on a Mohr-Coulomb plot.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

Coulomb's Law of shear strength in soils states that the shear strength (╧Д\tau╧Д) of a soil is a linear function of the normal stress (╧Г\sigma╧Г) applied to the failure plane. Mathematically, this is expressed as ╧Д=c+╧ГtanтБб╧Х\tau = c + \sigma \tan \phi╧Д=c+╧Гtan╧Х, representing a straight-line relationship on a Mohr-Coulomb plot.

ЁЯФв Key Formulas

╧Д=c+╧ГtanтБб╧Х\tau = c + \sigma \tan \phi╧Д=c+╧Гtan╧Х тАФ Coulomb's shear strength equation

╧Д=c+╧ГntanтБб╧Х\tau = c + \sigma_n \tan \phi╧Д=c+╧ГnтАЛtan╧Х тАФ Where ╧Д\tau╧Д is shear strength, ccc is cohesion, ╧Гn\sigma_n╧ГnтАЛ is normal stress, and ╧Х\phi╧Х is the angle of internal friction

тЪЩя╕П Working Principle

The shear strength of soil is derived from two components: cohesion (ccc) and internal friction (tanтБб╧Х\tan \phitan╧Х). 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.

ЁЯУМ Key Points
  • тЦ╕

    Coulomb's theory is the basis for the Mohr-Coulomb failure criterion in geotechnical engineering.

  • тЦ╕

    The envelope is a straight line for most soil types under typical stress conditions.

  • тЦ╕

    The intercept on the Y-axis represents the cohesion (ccc) of the soil.

  • тЦ╕

    The slope of the line represents the angle of internal friction (╧Х\phi╧Х).

тЬЕ Advantages
  • тЦ╕

    Simple mathematical model for predicting soil failure.

  • тЦ╕

    Applicable to a wide range of soil types in practical engineering.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Does not account for non-linear behavior in heavily overconsolidated clays.

  • тЦ╕

    Assumes soil as a continuum, ignoring individual particle interactions.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Slope stability analysis.

  • тЦ╕

    Bearing capacity of foundations.

  • тЦ╕

    Lateral earth pressure calculations.

ЁЯУД Additional Information
  • тЦ╕

    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.

  • тЦ╕

    The Mohr-Coulomb failure criterion is essentially a straight-line simplification of the actual failure behavior of many geomaterials.

ЁЯУК Diagram / Illustration
Mohr-Coulomb Failure EnvelopeNormal Stress (╧Г)Shear Strength(╧Д)c╧Д = c + ╧Гtan ╧Ж
тЬЕ

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

Core Concepts Used
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Shear Strength of Soil Mohr-Coulomb Criterion Internal Friction Angle Cohesion
ЁЯТб 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.

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