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CivilSoil Mechanics
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Mohr envelope can be considered to be straight if the angle of internal friction ╧Ж is assumed to be __________

A

90┬░

B

90┬░

C

<90┬░

D

None of the mentioned

Correct Answer

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

None of the mentioned

Quick Summary:

The Mohr envelope (or failure envelope) for soil shear strength is considered straight if the angle of internal friction ╧Х\phi╧Х is assumed to be constant (or independent of the normal stress). It does not depend on ╧Х\phi╧Х being specifically 90┬░90┬░90┬░, >90┬░>90┬░>90┬░, or <90┬░<90┬░<90┬░.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

The Mohr envelope (or failure envelope) for soil shear strength is considered straight if the angle of internal friction ╧Х\phi╧Х is assumed to be constant (or independent of the normal stress). It does not depend on ╧Х\phi╧Х being specifically 90┬░90┬░90┬░, >90┬░>90┬░>90┬░, or <90┬░<90┬░<90┬░.

ЁЯФв Key Formulas

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

тЪЩя╕П Working Principle

According to the Mohr-Coulomb failure criterion, shear strength is given by ╧Д=c+╧ГtanтБб╧Х\tau = c + \sigma \tan\phi╧Д=c+╧Гtan╧Х. In this equation, if cohesion ccc and friction angle ╧Х\phi╧Х are treated as constants, the envelope represents a straight line. In reality, the Mohr envelope is curved at high stress ranges, but it is approximated as a straight line by assuming a constant angle of internal friction ╧Х\phi╧Х.

ЁЯУМ Key Points
  • тЦ╕

    A constant value of ╧Х\phi╧Х results in a linear Mohr envelope.

  • тЦ╕

    For actual soils under a wide range of stresses, the Mohr envelope is curved rather than straight.

  • тЦ╕

    Assuming ╧Х\phi╧Х is constant is a common simplification used in conventional soil mechanics.

тЬЕ Advantages
  • тЦ╕

    Simplifies analytical calculations for slope stability and bearing capacity.

  • тЦ╕

    Provides a close approximation for standard structural load stress ranges.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Overestimates shear strength at very high normal stress levels.

  • тЦ╕

    Ignores stress-dependency of the internal friction angle.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Design of shallow and deep foundations.

  • тЦ╕

    Stability analysis of earth retaining structures and embankments.

ЁЯУД Additional Information
  • тЦ╕

    None of the numerical values or ranges given in Options A, B, or C (90┬░90┬░90┬░, >90┬░>90┬░>90┬░, or <90┬░<90┬░<90┬░) specifically define the condition for a straight line; the requirement is that ╧Х\phi╧Х is assumed to be constant.

  • тЦ╕

    Angle of internal friction ╧Х\phi╧Х typically ranges between 0┬░0┬░0┬░ and 45┬░45┬░45┬░ for real soils.

ЁЯУК Diagram / Illustration
Normal Stress(╧Г)Shear Stress (╧Д)╧Ж (Constant)cStraight Envelope: ╧Д = c + ╧Гtan ╧Ж
тЬЕ

D is correct тАФ Mohr envelope is assumed to be straight when the angle of internal friction ╧Х\phi╧Х is assumed to be constant, not because of a specific numerical value of ╧Х\phi╧Х.

Core Concepts Used
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Mohr-Coulomb Failure Criterion Angle of Internal Friction Shear Strength Parameters
ЁЯТб EXAM TIP

Remember that the linear Mohr-Coulomb criterion is a idealization; for high-pressure applications like deep rock mechanics or deep foundation analysis, non-linear failure envelopes are often required.

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