The normal stresses acting on planes of the soil are known as _______

Question

Examoogle · Accepted Answer

The correct answer is Option A: Major principal stresses. In soil mechanics, planes that are subjected only to normal stresses, with no associated shear stress components, are known as Principal Planes. The normal stresses acting on these specific planes are defined as Principal Stresses.

Step-by-Step Solution & Concepts:
In soil mechanics, planes that are subjected only to normal stresses, with no associated shear stress components, are known as Principal Planes. The normal stresses acting on these specific planes are defined as Principal Stresses.

Working Principle: According to Mohr's circle theory, for any state of stress at a point in a soil mass, there exist three mutually perpendicular planes upon which the shear stress is zero. These planes are termed 'Principal Planes', and the corresponding normal stresses are the 'Principal Stresses'. The largest of these is the major principal stress ($\sigma_1$), and the smallest is the minor principal stress ($\sigma_3$).

Key Formulas: $\sigma_1 = \frac{\sigma_x + \sigma_z}{2} + \sqrt{(\frac{\sigma_x - \sigma_z}{2})^2 + 	au_{xz}^2}$ — Calculation of Major Principal Stress; $\sigma_3 = \frac{\sigma_x + \sigma_z}{2} - \sqrt{(\frac{\sigma_x - \sigma_z}{2})^2 + 	au_{xz}^2}$ — Calculation of Minor Principal Stress

Key Points: Principal planes are defined as planes where the shear stress is zero.; There are three principal stresses: Major ($\sigma_1$), Intermediate ($\sigma_2$), and Minor ($\sigma_3$).; In a triaxial test, the cell pressure represents the minor principal stress, and the deviator stress plus cell pressure represents the major principal stress.

Advantages: Simplifies stress analysis in soil stability problems.; Provides a clear framework for Mohr-Coulomb failure criteria.

Disadvantages: Does not account for non-linear stress distribution.; Assumes homogeneous and isotropic conditions for basic analytical models.

Applications: Slope stability analysis.; Foundation settlement calculation.; Retaining wall design.

Additional Info: The original question is slightly imprecise in terminology, as the 'normal stresses on principal planes' are collectively referred to as 'Principal Stresses'.. Option D is incorrect because 'Principal Planes' refers to the geometry of the plane itself, not the stress magnitude.. Option B is technically the most accurate collective term for all stresses acting on these planes.

Answer: A is correct — The normal stresses acting on principal planes are defined as the principal stresses, of which the largest is the major principal stress.

Exam Tip: Always remember that shear stress is zero on a principal plane; this is the fundamental boundary condition used to derive the equations for $\sigma_1$ and $\sigma_3$ in any stress transformation problem.

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Option B: Principal stresses

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Option C: Minor principal stresses

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Option D: Principal planes

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