Theory: In Situ Stress
How geostatic stresses are worked out in layered ground, the part played by the water table and the effective stress principle, and where the horizontal stresses at rest come from.
Geostatic stresses
In ground with a level surface and horizontal layers, there are no shear stresses on vertical or horizontal planes. The total vertical stress at a depth is then the weight of everything above it, per unit area.
Above the water table the moist unit weight (γ) is used and below it the saturated one (γsat). Since the weights are constant in each stretch, the σv diagram is a polyline, changing slope at the layer boundaries and at the water table.
Pore pressure
With no flow, the pore water is in hydrostatic equilibrium: the pore pressure is zero at the water table and rises linearly below it.
Above the water table, this page takes u = 0. In the capillary fringe the pore pressure is negative (suction), which raises the effective stress; that isn't considered here.
Effective stress
By Terzaghi's principle (1936), it's the effective stress, the part of the total stress carried by the soil skeleton, that controls the strength and deformation of soil.
Below the water table, σ′v grows with the buoyant unit weight, γ′ = γsat − γw. That's why lowering the water table raises the effective stresses and can cause settlement, and raising it lowers them.
Horizontal stresses at rest
With no lateral strain, the effective horizontal stress is a fraction of the vertical one, given by the coefficient of earth pressure at rest. The relation holds for effective stresses; the total horizontal stress adds the pore pressure, which is the same in every direction.
Since K0 changes from one layer to the next, σ′h jumps at the boundaries. For normally consolidated soils, Jaky's expression gives a good estimate; overconsolidation raises K0, which can exceed 1.
| Soil | Typical K0 |
|---|---|
| Loose sand | 0.45 to 0.50 |
| Dense sand | 0.35 to 0.45 |
| Normally consolidated clay | 0.55 to 0.70 |
| Overconsolidated clay | 0.8 to 2.0 |
Limitations
- The ground is treated in one dimension: level surface and layers and an infinite surcharge. Loads of finite area, such as footings and embankments, spread with depth and call for solutions such as Boussinesq's.
- The pore pressure is hydrostatic: with vertical flow, artesian conditions or excess pore pressure from consolidation, it differs.
- Capillary suction above the water table is ignored, as is any change of γ with water content within a layer.
References
- Terzaghi, K. The shearing resistance of saturated soils and the angle between the planes of shear. Proceedings of the 1st International Conference on Soil Mechanics and Foundation Engineering, Cambridge, v. 1, p. 54–56, 1936.
- Jaky, J. The coefficient of earth pressure at rest. Journal of the Society of Hungarian Architects and Engineers, v. 78, n. 22, p. 355–358, 1944.
- Mayne, P. W.; Kulhawy, F. H. K0–OCR relationships in soil. Journal of the Geotechnical Engineering Division, ASCE, v. 108, n. GT6, p. 851–872, 1982.
- Das, B. M.; Sobhan, K. Principles of Geotechnical Engineering. 9th ed. Boston: Cengage, 2018.