Contents preface (VII) introduction 1—37

15.4.2. Shear Strength of Soils
Soils derive their strength from contact between particles capable of transmitting normal as well as shear forces. The contact between soil particles is mainly due to friction and the corresponding stress between the soil grains is called the effective (or intergranular) stress σ′. Thus, the shear strength of a soil is mainly governed by the effective stress. Besides the effective stress between soil grains, the pore water contained in the void spaces of the soil also exerts pressure which is known as pore pressure, u. The sum of the effective stress and pore pressure acting an any given surface within a compacted earth embankment is called the total stress σ. As the pore water cannot resist shear, all shear stresses are resisted by the soil grains only. The effective stress is approximately equal to the average intergranular force per unit area and cannot be measured directly (14). The total stress is equal to the total force per unit area acting normal to the plane. The pore water affects the physical interaction of soil particles. Soils with inactive surfaces do not absorb water. But, clay particles, formed of silicates which are, frequently, charged electrically, absorb water readily and exhibit plastic, shrinkage, and swelling characteristics. Besides, a change in pore pressure can directly affect the effective stress. The pore water thus influences the shear strength parameters of a soil to a considerable extent.

The shear strength of a soil is fully mobilised when a soil element can only just support the stresses exerted on it. For most soils, the shear strength of any surface, at failure, is approximated by the following Mohr-Coulomb’s linear relationship [Fig. 15.27]:

s = c′ + σ′ tan φ′

(15.31)

524 IRRIGATION AND WATER RESOURCES ENGINEERING
where, s = shear strength of soil (or shear stress at failure) on the surface under consideration, c′ = cohesion,
φ′ = angle of internal friction (or angle of shearing resistance), and σ′ = effective normal stress acting on the failure surface = σ – u. Here, c′ and φ′ are determined using effective stresses.

Shear stress	Failure envelope
τ
^σ1f	X
^σ3f	^σ1f	Normal stress
^σ3f		σ

1. 
   (b)
   

(a) Element of soil at failure (b) Mohr’s circles

Shearstrengths

c′

φ′
Stress range

of interest
Results of
measurements
s = c′ + σ′ tan φ′
Normal stress ^σ′

3. 
   Straight line approximation of curved failure envelope