The Principle of Effective Stress
The deformations of soils are similar to the deformations of structural framework such as a truss. The truss deforms from changes in loads carried by each member. If the truss is loaded in air or submerged in water, the deformations under a given load will remain unchanged. Deformations of the truss are independent of hydrostatic pressure. The same is true for soils.
Let us consider an element of a saturated soil subjected to a normal stress, s, applied on the horizontal boundary, as shown in Figure The stress s is called the total stress, and for equilibrium (Newton’s third law) the stresses in the soil must be equal and opposite to s. The resistance or reaction to s is provided by a combination of the stresses from the solids, called effective stress (s9), and from water in the pores, called porewater pressure (u). We will denote effective stresses by a prime (9) following the symbol for normal stress, usually s. The equilibrium equation is
Equation (7.39) is called the principle of effective stress and was fi rst recognized by Terzaghi (1883–1963) in the mid-1920s during his research into soil consolidation (Chapter 9). The principle of effective stress is the most important principle in soil mechanics. Deformations of soils are a function of effective stresses, not total stresses. The principle of effective stresses applies only to normal stresses and not to shear stresses. The porewater cannot sustain shear stresses, and therefore the soil solids must resist the shear forces. Thus t 5 t9, where t is the total shear stress and t9 is the effective shear stress. The
effective stress is not the contact stress between the soil solids. Rather, it is the average stress on a plane through the soil mass.
Soils cannot sustain tension. Consequently, the effective stress cannot be less than zero. Porewater pressures can be positive or negative. The latter are sometimes called suction or suction pressure. For unsaturated soils, the effective stress (Bishop et al., 1960) is
where ua is the pore air pressure, u is the porewater pressure, and x is a factor depending on the degree of saturation. For dry soil, x 5 0; for saturated soil, x 5 1. Values of x for a silt are shown in fig.