Effective Stress Soil is a multi phase system

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Presentation transcript:

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

Effective Stress

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

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.

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

Effective Stress The sum of vertical components of forces over the area is the effective stress F’ 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

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