Shear Strength of Soils - Elements of Soil Mechanics - page 97

Fig. 4.9 A cohesive soil, subjected to undrained conditions and zero total normal stress will still exhibit a
shear stress, c u .

τ = + tan σ φ

f

where

τ f = shear stress at failure, i.e. the shear strength
c = unit cohesion
σ = total normal stress on failure plane
φ = angle of shearing resistance.

The equation gave satisfactory predictions for sands and gravels, for which it was originally intended,
but it was not so successful when applied to silts and clays. The reasons for this are now well known and
are that the drainage conditions under which the soil is operating together with the rate of the applied
loading have a considerable effect on the amount of shearing resistance that the soil will exhibit. None
of this was appreciated in the 18th century, and this lack of understanding continued more or less until
1925 when Terzaghi published his theory of effective stress.

Note: It should be noted that there are other factors that affect the value of the angle of shearing resist-
ance of a particular soil. These include the amount of friction between the soil particles, the shape of the
particles and the degree of interlock between them, the density of the soil and its previous stress history.

Effective stress, σ′

If a soil mass is subjected to the action of compressive forces applied at its boundaries, then the stresses
induced within the soil at any point can be estimated by the theory of elasticity, described in Chapter 3.
For most soil problems, estimations of the values of the principal stresses σ 1 , σ 2 and σ 3 acting at a particular
point are required. Once these values have been obtained, the values of the normal and shear stresses
acting on any plane through the point can be computed.
At any point in a saturated soil each of the three principal stresses consists of two parts:

(1) u, the neutral pressure acting in both the water and in the solid skeleton in every direction with equal
intensity;
(2) the balancing pressures ( σ 1 − u), ( σ 2 − u) and ( σ 3 − u).

As explained in Section 3.4, Terzaghi's theory is that only the balancing pressures, i.e. the effective
principal stresses, influence volume and strength changes in saturated soils: