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Effective Stress

Effective Stress. Soil is a multi phase system To perform any kind of analysis - we must understand stress distribution The concept of effective stress: The soil is “loaded” (footing for example) The resulting stress is transmitted to the soil mass

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Effective Stress

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  1. Effective Stress • Soil is a multi phase system • To perform any kind of analysis - we must understand stress distribution • The concept of effective stress: • The soil is “loaded” (footing for example) • The resulting stress is transmitted to the soil mass • The soil mass supports those stresses at the point to point contacts of the individual soil grains

  2. Effective Stress

  3. Effective Stress The total stress at A is calculated from: The weight of the soil above A The weight of the water above A F = H*w + (HA - H) *sat F = Total Stress at A *w = Unit Weight of Water (62.4 pcf) *sat = Saturated Unit Weight HA = Height of A to Top of water H = Height of water

  4. Effective Stress • F is the stress applied to the soil by its own weight • As you go deeper in the soil mass, the stress increases • Like in a swimming pool, as you go deeper, the stress of the weight of the water increases • The soil carries the stress in 2 ways: • A portion is carried by the water (acts equally in all directions) • A portion is carried by the soil solids at their point of contact.

  5. Effective Stress • The sum of the vert. components of the forces at their points of contact per unit of X- sectional area is the effective stress. an = Area of points of contact A = Cross Sectional area of soil mass Pn = Forces acting at points of contact

  6. Effective Stress • The sum of vertical components of forces over the area is the effective stressF’ • F’= (P1v+P2v+P3v .....+Pnv) / A • If as = a1 + a2 + a3 +...an • Then the space occupied by water = A - as • Assume u = HA * *w Ht of water * *w= stress due to water (ft*pcf = psf = stress) • F = F’ + u(A - as) / A Since as is very small, assume 0 • F = F’ + u

  7. Effective Stress Recall the following equation: F = H*w + (HA - H) *sat Now, F’ = F - u Substituting: F’ = [H*w + (HA - H) *sat] - HA * *w Rearranging: F’ = (HA - H)(*sat - *w) Height of Soil Column * *’ Where *’ = *sat - *w *’ = EFFECTIVE UNIT WEIGHT Effective Stress is independent of height of water In the equation: F = F’ + u F’ is the soil skeleton stress u is the stress in the water, or pore water pressure

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