Effective stress
Effective stress is the most important idea in soil mechanics. Terzaghi showed that the stress carried by the soil skeleton, the grain-to-grain contact stress, controls strength and settlement, not the total stress.
At a depth in saturated ground, the total vertical stress is the weight of everything above per unit area. Part of it is carried by pore water pressure, which pushes equally in all directions and cannot resist shear. The rest is the effective stress. Raising the water table, or building up excess pore pressure under rapid loading, reduces effective stress and therefore strength. That is why slopes fail after heavy rain and why loose saturated sand can liquefy in earthquakes.
Lowering the water table by pumping raises effective stress and can cause settlement of nearby buildings, a well-known effect around deep excavations in cities.
In steady upward seepage, effective stress falls; if the upward gradient reaches the critical value, effective stress becomes zero and sand boils, the quick condition.
Draw the water table on the sketch before calculating anything.
σ′ = σ − uu = γ_w × depth below water table (hydrostatic)Critical hydraulic gradient i_c = (G_s − 1) / (1 + e) ≈ γ′ / γ_w
Using the saturated unit weight above the water table.
Problem. Ground: 3 m of sand (γ = 18 kN/m³) above the water table, then saturated clay (γ_sat = 20 kN/m³). Find σ′ at 7 m depth. γ_w = 9.81.
- σ = 3 × 18 + 4 × 20 = 54 + 80 = 134 kPa.
- u = 4 × 9.81 = 39.2 kPa.
- σ′ = 134 − 39.2 = 94.8 kPa.
Answer. About 95 kPa
Quick quiz
1Can pore water resist shear?
No.
2What happens to effective stress if the water table rises?
It falls.
3What is the quick condition?
Zero effective stress under upward seepage, so sand loses strength.
- EN 1997 (Eurocode 7) (Europe): Geotechnical design.
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References and further reading
Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.
- Gopal Ranjan, A. S. R. Rao, Basic and Applied Soil Mechanics, New Age International, latest edition.
- B. M. Das, Principles of Geotechnical Engineering, Cengage, latest edition.
- K. Terzaghi, R. B. Peck, G. Mesri, Soil Mechanics in Engineering Practice, Wiley, 3rd edition.
- J. A. Knappett, R. F. Craig, Craig's Soil Mechanics, CRC Press, latest edition.
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