2.2. Stresses as a result of the soil self-weight

Geostatic stresses

When the soil has a horizontal surface and there is no horizontal variability in its properties, the stresses that are developed within the soil mass which are due to its weight are called geostatic stresses. In this case on a horizontal and on a vertical plane, only normal stresses are acting.

The vertical normal stress, σv, is given by the equation:

If γₜ is constant, and from the equation:

if the γₜ is a function of the depth.

The horizontal normal stress, σₕ, is given by the equation:

where the factor Kₒ is the lateral earth pressure coefficient at rest, and this value varies from values less than 1 (0.4 - 0.5), for normally consolidated soils, to values >1, for overconsolidated soils. 

In case of saturated soil, the normal stress, σ, which acts on a random plane, consists of two components: the effective stress and the pore water pressure, u:

The sum of the effective stress and the pore water pressure is called total stress.

In saturated soil, the lateral earth pressure coefficient at rest, Kₒ, is defined based on the effective stresses,

The vertical effective stress, σᵥ, at a certain depth beneath the water table can be calculated in two ways: (a) by finding the total stress at the depth that we are interested in (by using saturated unit weights under the water table) and deduct the pore water pressure, (b) by using the effective unit weights, γₐᵥ, for the soil layers under the water table.

Effective stress principle (Terzaghi, 1925, 1936)

  

 

The mechanical behavior of soil (compressibility, strength, lateral earth pressure,  bearing capacity) depends on the value of effective stresses.

Capillary water

The phenomenon of water buoyancy within capillary piping is observed in soils and the role of the capillary piping is played by the voids in between the soil particles. Naturally, in soils, the phenomenon becomes complicated by the fact that the voids have an irregular and variable shape, dimensions and communication paths. Approximately, the height of the capillary buoyancy above the level of the ground water table can be estimated by the equation:

Where, r is the radius of the capillary piping, which usually is considered smaller than the radius of the soil particles.

The pore water pressure in the zone of capillary pipping is negative (less than the atmospheric) and at a high h₁ above the water table, is given by the equation:

The height of the capillary buoyancy hc in soils is given also by the empirical equation (Hazen, 1930): 

Where: