How is shear stress on a soil layer calculated?

Shear stress on a soil layer is indeed calculated using the appropriate formula that incorporates both the effective stress and the soil's strength parameters. The correct answer is derived from the Mohr-Coulomb failure criterion, which expresses the relationship between shear stress (τ), normal effective stress (σ'), cohesion (c), and the angle of internal friction (φ).

In this case, the formula τ = c + σ'tan(φ) indicates that the total shear strength of the soil is influenced by two key components: the cohesion of the soil, which provides resistance to sliding, and the contribution of effective normal stress from the overlying soil, modified by the angle of internal friction. As the effective stress (σ') increases, it enhances the shear strength of the soil, represented by the tangent of the angle of internal friction.

This equation is fundamental in geotechnical engineering for evaluating the stability of slopes, the bearing capacity of foundations, and other applications involving soil mechanics where shear failure might be a concern. Understanding how cohesion and effective stress interact to determine shear strength is crucial for ensuring safe and effective design in construction and civil engineering.