Geotechnical Engineering

DHARM

254 GEOTECHNICAL ENGINEERING

8.2.1 Friction between Solid Bodies

When two solid bodies are in contact with each other, the frictional resistance available is

dependent upon the normal force between the two and an intrinsic property known as the

‘Coefficient of friction’. The coefficient of friction, in turn, depends upon the nature and the

condition of the surfaces in contact. This is so even when a solid body rests on a rigid surface,

as shown in Fig. 8.1.

Body

P

Surface

Available

frictional

force

ff

P

No friction comes into play

or is mobilised ( = 0) since

no shear force is applied

a

P

a

P

Partial friction

<

Applied shear force less

than maximum available

friction : frictional force

mobilised just equals

applied shear force.

No slip.

af

R¢

F¢

F¢

R¢ P

f f

P

Full friction

=

Applied shear force just

equals maximum available

friction : maximum frictional

force is mobilised. Slip

imminent to the right

(critical condition)

af

R

F

a

F

R

(a) (b) (c)

a

Fig. 8.1 Friction between a solid and a rigid surface
The available frictional resistance F when a normal force P is acting is related to P as
follows:
F = P. μ = P. tan φ ...(Eq. 8.1)
Here μ is called the ‘Coefficient of friction’ and φ is known as the ‘Angle of friction’.
The characteristics μ and φ are properties of the materials in contact and they are inde-
pendent of the applied forces and are fairly constant. The available frictional resistance F does
not come into play or get mobilised unless it is required to resist an applied shearing force.
In Fig. 8.1 (a), no frictional resistance is mobilised beasue there is no applied shearing
force. The normal force exerted by the solid body on the rigid surface is resisted by an equal
force by way of reaction from the rigid surface.
In Fig. 8.1 (b), a small magnitude of shearing force is applied. This causes a resultant
force R′ to be acting at an angle α with respect to the normal to the rigid surface. This angle is
called the ‘Angle of Obliquity’ and is dependent only upon the applied forces. To resist this
applied shearing force R′, an equal magnitude of the available frictional resistance is mobi-
lised. Since F′ is less than the maximum available frictional resistance F, the angle of obliquity
α is less than φ. In this case there is equilibrium and there is no slip between the body and the
surface.

In Fig. 8.1 (c) a shearing force equal to the maximum available frictional resistance is
applied. The entire frictional resistance available will get mobilised now to resist the applied