For a soil element located at a depth, z = 5 m underneath the ground surface, determine the vertical effective stress if:

the soil saturated unit weight, gsat = 20 kN/m3
the water table is located at the ground surface
Ko = 0.5

Hint: take unit weight of water gw = 10 kN/m3

Question

For a soil element located at a depth, z = 5 m underneath the ground surface, determine the vertical effective stress if:

the soil saturated unit weight, gsat = 20 kN/m3
the water table is located at the ground surface
Ko = 0.5

Hint: take unit weight of water gw  = 10 kN/m3

BlackTom AI · Accepted Answer

Let me restate the problem to ensure clarity: a soil element is at depth z = 5 m below ground surface with saturated unit weight gsat = 20 kN/m3, a water table at the ground surface, Ko = 0.5, and the water unit weight gw = 10 kN/m3. We are to determine the vertical effective stress at that depth.

First, compute the total vertical stress at depth z. Since the soil is saturated up to depth and the vertical stress is carried by the saturated soil, the total vertical stress is proportional to the saturated unit weight: sigma_v = gamma_sat * z = 20 kN/m3 * 5 m = 100 kPa.

Next, determine the pore water pressure at that depth. With the water table at the ground surface (z = 0 at surface) and gw = 10 kN/m3, the pore water pressure increases linearly with depth: u = gamma_w * z = 10 kN/m3 * 5 m = 50 kPa.

Now, obtain the vertical effective stress using the effective stress principle: sigma_v' = sigma_v - u. Substituting the values gives sigma_v' = 100 kPa - 50 kPa = 50 kPa.

A few notes on potential confusion:
- Ko (the coefficient of earth pressure at rest) affects lateral stresses, not directly the vertical effective stress in this straightforward vertical loading scenario. Since the problem asks for vertical effective stress at depth, Ko is not required for this calculation.
- If one mistakenly used gamma = gsat as the driving weight for effective stress without accounting for pore pressure, they would get an incorrect result; the pore water pressure must be subtracted to obtain the effective stress.
- If the water table were deeper, or if the soil were unsaturated, the pore water pressure and thus the calculation would differ. Here, with the water table at the surface and full saturation, the pore pressure equals gw * z as used.

Therefore, the vertical effective stress at z = 5 m is 50 kPa.

ENEN20002_2025_SM1 Quiz on Lecture 32 material

For a soil element located at a depth, z = 5 m underneath the ground surface, determine the vertical effective stress if: the soil saturated unit weight, gsat = 20 kN/m3 the water table is located at the ground surface Ko = 0.5 Hint: take unit weight of water gw = 10 kN/m3

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