Question

a 10 pages report about (Effective stress in soil). introduction-body-conclusion

Answer 1

Effective stress

Ground movements and instabilities can be caused by changes in total stress (such as loading due to foundations or unloading due to excavations), but they can also be caused by changes in pore pressures (slopes can fail after rainfall increases the pore pressures).

In fact, it is the combined effect of total stress and pore pressure that controls soil behaviour such as shear strength, compression and distortion. The difference between the total stress and the pore pressure is called the effective stress:

effective stress = total stress - pore pressure

or σ ´ = σ  - u

Terzaghi's principle and equation:

Karl Terzaghi was born in Vienna and subsequently became a professor of soil mechanics in the USA. He was the first person to propose the relationship for effective stress (in 1936):

All measurable effects of a change of stress, such as compression, distortion and a change of shearing resistance are due exclusively to changes in effective stress. The effective stress s´ is related to total stress and pore pressure by σ ´ = σ - u

The adjective 'effective' is particularly apt, because it is effective stress that is effective in causing important changes: changes in strength, changes in volume, changes in shape. It does not represent the exact contact stress between particles but the distribution of load carried by the soil over the area considered.

Mohr circles for total and effective stress:

Mohr circles for can be drawn for both total and effective stress. The points E and T represent the total and effective stresses on the same plane. The two circles are displaced along the normal stress axis by the amount of pore pressure (σ _n = σ _n' + u), and their diameters are the same. The total and effective shear stresses are equal (t´ = t).

The importance of effective stress:

The principle of effective stress is fundamentally important in soil mechanics. It must be treated as the basic axiom, since soil behaviour is governed by it. Total and effective stresses must be distinguishable in all calculations: algebraically the prime should indicate effective stress, e.g. σ ´

Changes in water level below ground (water table changes) result in changes in effective stresses below the water table. Changes in water level above ground (e.g. in lakes, rivers, etc.) do not cause changes in effective stresses in the ground below.

Changes in effective stress:

In some analyses it is better to work in changes of quantity, rather than in absolute quantities; the effective stress expression then becomes:
Δ σ ´ =Δ σ - Δ u

If both total stress and pore pressure change by the same amount, the effective stress remains constant. A change in effective stress will cause: a change in strength and a change in volume.

Changes in shear strength:

The critical shear strength of soil is proportional to the effective normal stress; thus, a change in effective stress brings about a change in strength.

Therefore, if the pore pressure in a soil slope increases, effective stresses will be reduced by Ds' and the critical strength of the soil will be reduced by Dt - sometimes leading to failure.

A seaside sandcastle will remain intact while damp, because the pore pressure is negative; as it dries, this pore pressure suction is lost and it collapses. Note: Sometimes a sandcastle will remain intact even when nearly dry because salt deposited as seawater evaporates slightly and cements the grains together.

Changes in Volume:

Immediately after the construction of a foundation on a fine soil, the pore pressure increases, but immediately begins to drop as drainage occurs.

The rate of change of effective stress under a loaded foundation, once it is constructed, will be the same as the rate of change of pore pressure, and this is controlled by the permeability of the soil.

Settlement occurs as the volume (and therefore thickness) of the soil layers change. Thus, settlement occurs rapidly in coarse soils with high permeabilities and slowly in fine soils with low permeabilities.