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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Mohr envelope can be considered to be straight if the angle of internal friction φ is assumed to be __________
A) 90°
B) >90°
C) <90°
D) None of the mentioned
None of the mentioned
The Mohr envelope (or failure envelope) for soil shear strength is considered straight if the angle of internal friction ϕ is assumed to be constant (or independent of the normal stress). It does not depend on ϕ being specifically 90°, >90°, or <90°.
The Mohr envelope (or failure envelope) for soil shear strength is considered straight if the angle of internal friction ϕ is assumed to be constant (or independent of the normal stress). It does not depend on ϕ being specifically 90°, >90°, or <90°.
τ=c+σtanϕ — Mohr-Coulomb shear strength equation
According to the Mohr-Coulomb failure criterion, shear strength is given by τ=c+σtanϕ. In this equation, if cohesion c and friction angle ϕ 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 ϕ.
A constant value of ϕ results in a linear Mohr envelope.
For actual soils under a wide range of stresses, the Mohr envelope is curved rather than straight.
Assuming ϕ is constant is a common simplification used in conventional soil mechanics.
Simplifies analytical calculations for slope stability and bearing capacity.
Provides a close approximation for standard structural load stress ranges.
Overestimates shear strength at very high normal stress levels.
Ignores stress-dependency of the internal friction angle.
Design of shallow and deep foundations.
Stability analysis of earth retaining structures and embankments.
None of the numerical values or ranges given in Options A, B, or C (90°, >90°, or <90°) specifically define the condition for a straight line; the requirement is that ϕ is assumed to be constant.
Angle of internal friction ϕ typically ranges between 0° and 45° for real soils.
D is correct — Mohr envelope is assumed to be straight when the angle of internal friction ϕ is assumed to be constant, not because of a specific numerical value of ϕ.
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.