Shear Strength of Soils

Why it matters

The shear strength of soils is a critical parameter in geotechnical engineering, influencing the stability of slopes, the bearing capacity of foundations, and the design of retaining structures. Understanding this property helps engineers ensure the safety and reliability of various civil engineering projects.

Key ideas

• Shear Strength: It is the resistance of soil to shear stress and is a function of the soil's cohesion and internal friction.
• Mohr-Coulomb Failure Criterion: This is a widely used model to describe the shear strength of soils, expressed as a linear relationship between shear stress and normal stress.
• Cohesion (c): The intercept of a fitted shear-strength envelope over the relevant stress range; it is not necessarily intrinsic bonding and should not be extrapolated freely.
• Angle of Internal Friction (φ): Represents the frictional resistance between soil particles.
• Effective Stress Principle: Shear strength is often analyzed in terms of effective stress, which considers the pore water pressure within the soil.

Formulas

All c and φ parameters below are effective-stress parameters c′ and φ′, and τ is shear strength at failure. Do not combine undrained total-stress parameters with effective normal stress.

• τ = c + σ'·tan(φ)
  • τ: Shear stress (Pa)
  • c: Cohesion (Pa)
  • σ': Effective normal stress (Pa)
  • φ: Angle of internal friction (degrees)

Worked example

Given:

• Cohesion, c = 25 kPa
• Angle of internal friction, φ = 30°
• Effective normal stress, σ' = 100 kPa

Steps:

1. Identify the formula: τ = c + σ'·tan(φ)
2. Substitute the values: τ = 25 kPa + 100 kPa·tan(30°)
3. Calculate tan(30°): tan(30°) ≈ 0.577
4. Calculate shear stress: τ = 25 kPa + 100 kPa·0.577 τ = 25 kPa + 57.7 kPa τ = 82.7 kPa

Final Answer: 82.7 kPa

Common mistakes

• Confusing total stress with effective stress.
• Incorrectly calculating the angle of internal friction in radians instead of degrees.
• Neglecting the effect of pore water pressure on effective stress.

For GATE CE

Questions often involve calculating shear strength using given values of cohesion, angle of internal friction, and normal stress. Practice problems that require understanding the Mohr-Coulomb failure criterion and effective stress principle.

Quick check

1. What is the formula for shear strength according to the Mohr-Coulomb criterion?
2. How does pore water pressure affect effective stress?
3. What are the units of cohesion in SI?

Answers: 1. τ = c + σ'·tan(φ) 2. Increasing pore pressure at fixed total normal stress reduces effective normal stress. 3. Pascal (Pa).