Geotechnical Engineering

DHARM

SHEARING STRENGTH OF SOILS 263

Coulomb’s envelope

s=c+

sftan

f

c

t

O s

t

O s

s=f( )s

ts=f( ) I

II

s
(a) Coulomb’s envelope for a c- soilf (b) Mohr’s generalized failure envelope
Fig. 8.6 Mohr-Coulomb Theory—failure envelopes
Coulomb’s law is also written as follows to indicate that the stress condition refers to
that on the plane of failure:

s = c + σf tan φ ...(Eq. 8.26)
In a different way, it can be said that the Mohr’s circle of stress relating to a given stress
condition would represent, incipient failure condition if it just touches or is tangent to the
strength or failure envelope (circle I); otherwise, it would wholly lie below the envelopes as
shown in circle II, Fig. 8.6 (b).

The Coulomb envelope in special cases may take the shapes given in Fig. 8.7 (a) and (b);
for a purely cohesionless or granular soil or a pure sand, it would be as shown in Fig. 8.7 (a)
and for a purely cohesive soil or a pure clay, it would be as shown in Fig. 8.7 (b).

f

t

O s

s =

sftan

c

t

O s

s=c

(a) Pure sand “c = 0” or “ -soilf” (b) Pure clay (“ = 0” or “c”-soil)f

Fig. 8.7 Coulomb envelopes for pure sand and for pure clay

8.5 SHEARING STRENGTH—A FUNCTION OF EFFECTIVE STRESS

Equation 8.26 apparently indicates that the shearing strength of a soil is governed by the total
normal stress on the failure plane. However, according to Terzaghi, it is the effective stress on
the failure plane that governs the shearing strength and not the total stress.

It may be expected intuitively that the denser a soil, the greater the shearing strength.
It has been learnt in chapter seven that a soil deposit becomes densest under any given pressure