Computations indicate that a planned building loading will...

Computations indicate that a planned building loading will cause the principal stresses in the soil at a point beneath the building to increase to total values of $4,500 \mathrm{pst}$ and 1,500 pof (majer and minor principal stresses, respectively). If the soil is a dry sand with an angle of internal friction equal to $35^{\circ}$, will the indicatod stresses cause a shear failure at the point?

Key Concepts

Effective Stress Analysis

Effective stress analysis in soil mechanics accounts for the difference between the total stress and the pore water pressure within the soil. Even though the discussed problem involves dry soil conditions where pore pressures are negligible, understanding effective stress is critical in general soil stability analyses, as it governs the soil's response to loading and its failure behavior.

Angle of Internal Friction

The angle of internal friction is a measure of the resistance of soil particles to sliding over each other and is a key parameter in determining shear strength. In the Mohr-Coulomb framework, it defines the slope of the failure envelope in a stress plot, indicating how much additional normal stress is required to mobilize further shear strength.

Shear Failure Mechanism in Soils

Shear failure in soils occurs when the applied shear stresses exceed the soil's shear strength, which depends on the normal stress, cohesion, and the angle of internal friction. Evaluating whether a given state of stress can lead to failure involves comparing the induced stress conditions with the expected shear strength of the soil according to the relevant failure criterion.

Principal Stresses

Principal stresses are the maximum and minimum normal stresses that occur at a point in a material, acting on mutually perpendicular planes. These stresses represent the state of stress independent of the coordinate system and are fundamental in analyzing failure modes in soil and other materials.

Mohr-Coulomb Failure Criterion

The Mohr-Coulomb failure criterion is a model used in geotechnical engineering to predict the failure of materials under shear stress. It relates the shear strength of the material to the normal stress acting on a failure plane, incorporating both the cohesive strength (if any) and the frictional resistance, often quantified by the angle of internal friction.

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