Geotechnical Engineering

DHARM

SHEARING STRENGTH OF SOILS 255

force. Angles α and φ are equal; slip or sliding to the right is incipient or imminent. If the
applied shearing force is reversed in direction, the direction of imminent slip also gets re-
versed. The frictional force, as is easily understood, tends to oppose motion.
The friction angle is the limiting value of obliquity; the criterion of slip is therefore an
angle of obliquity equal to the friction angle. The condition of incipient slip for solid bodies in
contact may be expressed as follows :
F/P = tan φ = μ ...(Eq. 8.2)
For solid bodies which are in contact but which have no adhesion between them, the
term ‘friction’ is synonymous with the terms ‘shearing strength’ and ‘maximum shearing re-
sistance’. In most natural soils friction represents only a part of the shearing strength, al-
though an important part, but other phenomena contribute to the shearing strength, particu-
larly in fine-grained soils.

8.2.2 Internal Friction within Granular Soil Masses

In granular or cohesionless soil masses, the resistance to sliding on any plane through the

point within the mass is similar to that discussed in the previous sub-section; the friction

angle in this case is called the ‘angle of internal friction’. However, the frictional resistance in

granular soil masses is rather more complex than that between solid bodies, since the nature

of the resistance is partly sliding friction and partly rolling friction. Further, a phenomenon

known as ‘interlocking’ is also supposed to contribute to the shearing resistance of such soil

masses, as part of the frictional resistance.

The angle of internal friction, which is a limiting angle of obliquity and hence the pri-

mary criterion for slip or failure to occur on a certain plane, varies appreciably for a given sand

with the density index, since the degree of interlocking is known to be directly dependent upon

the density. This angle also varies somewhat with the normal stress. However, the angle of

internal friction is mostly considered constant, since it is almost so for a given sand at a given

density.

Since failure or slip within a soil mass cannot be restricted to any specific plane, it is

necessary to understand the relationships that exist between the stresses on different planes

passing through a point, as a prerequisite for further consideration of shearing strength of

soils.

8.3 PRINCIPAL PLANES AND PRINCIPAL STRESSES—MOHR’S CIRCLE

At a point in a stressed material, every plane will be subjected, in general, to a normal or

direct stress and a shearing stress. In the field of geotechnical engineering, compressive direct

stresses are usually considered positive, while tensile stresses are considered negative.

A ‘Principal plane’ is defined as a plane on which the stress is wholly normal, or one

which does not carry shearing stress. From mechanics, it is known that there exists three

principal planes at any point in a stressed material. The normal stresses acting on these prin-

cipal planes are known as the ‘principal stresses’. The three principal planes are to be mutu-

ally perpendicular. In the order of decreasing magnitude the principal stresses are designated

the ‘major principal stress’, the ‘intermediate principal stress’ and the ‘minor principal stress’,

the corresponding principal planes being designated exactly in the same manner. It can be