Geotechnical Engineering

DHARM

SHEARING STRENGTH OF SOILS 273

The cell pressure, σc which is also the minor principal stress is constant and σ 11 , σ 12 , σ 13 ,
.... σ 1 f are the major principal stresses at different stages of loading and at failure. The Mohr’s
circle at failure will be tangential to the Mohr-Coulomb strength envelope, while those at
intermediate stages will be lying wholly below it. The Mohr’s circle at failure for one particular
value of cell pressure will be as shown in Fig. 8.13.

t

c

f

F D

s=

sfntan +c

()tfs

H

G M A a E B

s 3

sn

(ss 13 – )/2

s 1

(ss 13 + )/2

s

2 a

C

f

(a) Mohr’s circle at failure for a general c- soilf

Op

O : Origin of planesp

t

()tfs

a= 45°

s 3

sn

(ss 13 – )/2

s 1

(ss 13 + )/2

2 = 90°a

c

s=c

s

t

s =

tan

sfn

()tfs

a

s 3

sn

(ss 13 – )/2

s 1

(ss 13 + )/2

f

2 a

f

s

(b) Mohr’s circle at failure for a pure

frictional or -soilf

(c) Mohr’s circle for a pure cohesive

soil or c-soil at failure

Op

Fig. 8.13 Mohr’s circle at failure for one particular cell pressure for triaxial test
The Mohr’s circles at failure for one particular cell pressure are shown for the three
typical cases of a general c–φ soil, a φ-soil and a c-soil in Figs. 8.13 (a), (b), and (c) respectively.

With reference to Fig. 8.13 (a), the relationship between the major and minor principal
stresses at failure may be established from the geometry of the Mohr’s circle, as follows:

From ∆DCG, 2 α = 90° + φ

∴ α = 45° + φ/2