Which statements about Rankine's failure plane are FALSE in GATE Civil 2026 Set-1 Q46?

A and D are FALSE. For active earth pressure, the failure plane makes (45+φ/2) with the minor principal plane (horizontal), which equals (45-φ/2) with the major principal plane (vertical). Statement A claiming (45+φ/2) with the major principal plane is false. For passive earth pressure, the failure plane makes (45+φ/2) with the major principal plane. Statement D claiming (45-φ/2) with the major principal plane is false.

What is the failure plane angle for active earth pressure in Rankine's theory?

In active earth pressure, the major principal stress is vertical. The failure plane makes (45+φ/2) with the minor principal plane (horizontal) or equivalently (45-φ/2) with the major principal plane (vertical). This is the angle at which shear failure occurs in Mohr's circle analysis when the stress state reaches the failure envelope.

What is the failure plane angle for passive earth pressure in Rankine's theory?

In passive earth pressure, the major principal stress is horizontal. The failure plane makes (45+φ/2) with the minor principal plane (vertical) or equivalently (45+φ/2) with the major principal plane (horizontal). This is steeper than the active case failure plane, consistent with passive conditions requiring more resistance.

Rankine Earth Pressure Failure Plane Inclination Active Passive | GATE Civil 2026 Set-1 Q46

Civil Engineering > GATE 2026 SET-1 > Earth Pressure

As per the Rankine’s earth pressure theory, which of the following statements is/are FALSE?

For the active earth pressure, the inclination of failure plane is (45 + φ/2) with respect to the major principal plane.

For the active earth pressure, the inclination of failure plane is (45 − φ/2) with respect to the major principal plane.

For the passive earth pressure, the inclination of failure plane is (45 + φ/2) with respect to the major principal plane.

For the passive earth pressure, the inclination of failure plane is (45 − φ/2) with respect to the major principal plane.

Correct : a,d

In Rankine''s earth pressure theory, the failure plane orientation is measured from the major principal plane.
Active earth pressure case:
The major principal stress is vertical (σ₁ = vertical) and minor is horizontal (σ₃ = horizontal). The failure plane makes an angle of (45 + φ/2) with the minor principal plane (horizontal). Since the major principal plane is vertical (90° to horizontal), the failure plane makes (45 − φ/2) with the major principal plane. Statement A claims (45 + φ/2) with major principal plane — this is FALSE. Statement B claims (45 − φ/2) with major principal plane — this is TRUE.
Passive earth pressure case:
The major principal stress is horizontal and minor is vertical. The failure plane makes (45 + φ/2) with the minor principal plane (vertical) = (45 + φ/2) with the major principal plane. Statement C claims (45 + φ/2) with major principal plane — this is TRUE. Statement D claims (45 − φ/2) with major principal plane — this is FALSE.
Correct answer: A and D are FALSE

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