Difference between effective stress, pore water pressure and total stress

The concepts of effective stress, pore water pressure, and total stress are fundamental in soil mechanics, a key area of geotechnical engineering. These terms describe different aspects of how forces are distributed in soil, and understanding their differences is essential for analyzing soil behavior and designing stable structures like foundations, slopes, and retaining walls. Below, I’ll explain each term, highlight their differences, and show how they relate to one another.

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Definitions

• Total Stress (σ)
  Total stress is the overall pressure acting on the soil at a given point. It includes the weight of the soil itself plus any external loads, such as the weight of a building or additional soil layers. Essentially, it’s the total force per unit area exerted on the soil from above.
  • Example: At a depth of 5 meters in soil with a unit weight of 20 kN/m³, the total stress would be 20 kN/m³ × 5 m = 100 kPa, assuming no additional surface load.
• Pore Water Pressure (u)
  Pore water pressure is the pressure exerted by water that fills the spaces (pores) between soil particles. In saturated soils—where all pores are filled with water—this pressure depends on the depth of the water and the unit weight of water (typically 10 kN/m³). It can increase due to factors like rainfall or decrease with drainage.
  • Example: If the groundwater table is at the surface, at 5 meters depth, the pore water pressure would be 10 kN/m³ × 5 m = 50 kPa.
• Effective Stress (σ’)
  Effective stress is the portion of the total stress that is carried by the soil skeleton—the network of soil particles in contact with each other. It’s the stress that actually controls the soil’s strength, compressibility, and deformation behavior. Effective stress is calculated by subtracting the pore water pressure from the total stress.
  • Formula:
    [ σ = σ’ + u ]
  • Example: Using the values above, effective stress at 5 meters would be 100 kPa – 50 kPa = 50 kPa.

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Relationship Between the Three

The connection between total stress, pore water pressure, and effective stress is given by this simple equation:

[ σ = σ’ + u ]

This means the total stress applied to the soil is split between:

• The soil skeleton (effective stress), which bears the load through particle-to-particle contact.
• The water in the pores (pore water pressure), which supports part of the load by pushing against the particles.

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Key Differences

Here’s a breakdown of how these terms differ:

• Total Stress (σ)
  • Represents the entire pressure acting on the soil.
  • Includes contributions from both the soil and the water.
  • Does not directly determine the soil’s strength or behavior.
• Pore Water Pressure (u)
  • The pressure from water in the soil’s pores.
  • Acts to oppose or reduce the stress carried by the soil particles.
  • Can fluctuate with changes in water levels (e.g., rain or drainage).
• Effective Stress (σ’)
  • The stress carried by the soil skeleton alone.
  • Directly controls the soil’s strength and deformation properties.
  • Increases when pore water pressure decreases, and vice versa.

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Why This Matters

The effective stress is the most critical of the three because it determines how the soil behaves under load. For instance:

• High pore water pressure reduces effective stress, weakening the soil and potentially leading to failures like landslides.
• Lowering pore water pressure (e.g., through drainage) increases effective stress, making the soil stronger and more stable.

Practical Example:
Imagine a saturated soil layer at 5 meters depth (unit weight 20 kN/m³, groundwater at the surface):

• Total stress = 100 kPa
• Pore water pressure = 50 kPa
• Effective stress = 100 kPa – 50 kPa = 50 kPa

If heavy rain raises the pore water pressure to 70 kPa (due to additional water), the effective stress drops to 100 kPa – 70 kPa = 30 kPa. This reduction could make the soil less stable, increasing the risk of failure.

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In conclusion, total stress is the combined pressure on the soil, pore water pressure is the water’s contribution, and effective stress is what the soil particles themselves carry—and it’s the effective stress that ultimately determines how the soil will hold up under load. These distinctions are vital for engineers to ensure the stability of structures built on or in soil.