Chapter 5: Effective Stress Principle

Geostatic Stresses

• Definition: Stresses due to the self-weight of soil, known as geostatic stresses.
• Importance: Essential for understanding the transmission and distribution of stresses in large soil masses.
  • Examples include:
    • Wheel loads transmitted through embankments or to culverts.
    • Foundation pressures transmitted to soil strata beneath footings.
    • Pressures from isolated footings transmitted to retaining walls.
    • Wheel loads transmitted through stabilized soil pavements to the subgrade below.
• Key Concept: Stresses are transmitted in downward and lateral directions, leading to a need for estimating vertical stresses for predicting settlement.

Vertical or Total Stress

• Definition: The total vertical stress at a point below the ground surface due to the weight of everything above, including soil, water, and surface loading.
• Calculation:
  • Total stress increases with depth and unit weight.
  • Formula:
    [ \sigma_v = \gamma \cdot z ]
    • Where ( \sigma_v ) is vertical stress, ( \gamma ) is the unit weight of the soil, and ( z ) is the depth.
• Water Influence:
  • Below a water body, total stress is the sum of soil weight and water weight above it.
  • Formula:
    [ \sigma = \gamma z + \gamma_w z_w ]
    • Where ( \gamma_w ) is the unit weight of water.

Variation of Stress with Depth

• Vertical stress increases from the top to the bottom of the soil mass due to overlying material.
• Stresses in Layer Deposits:
  • Total stress in deposits with layers of differing densities can be determined.
  • Formula:
    [ \sigma_z = \sum_{i=1}^{n} \gamma_i \cdot h_i ]
    • Where ( \sigma_z ) is the vertical stress at depth, ( \gamma_i ) is the unit weight of each layer, and ( h_i ) is the height of each layer._

Examples of Stress Calculation

• At depth ( z_1 ):
  [ \sigma_{z1} = \gamma_1 imes h_1 ]
• At depth ( z_2 ):
  [ \sigma_{z2} = \gamma_1 imes h_1 + \gamma_2 imes z_2 ]
• At depth ( z_3 ):
  [ \sigma_{z3} = \gamma_1 imes h_1 + \gamma_2 imes h_2 + \gamma_3 imes h_3 ]_

Summary: Understanding geostatic stresses and total vertical stress is crucial in foundation engineering to predict the behavior and settlement of structures.