Geotechnical Engineering

DHARM

272 GEOTECHNICAL ENGINEERING

If A 0 , h 0 and V 0 are the initial area of cross-section, height and volume of the soil speci-
men respectively, and if A, h, and V are the corresponding values at any stage of the test, the
corresponding changes in the values being designated ∆A, ∆h, and ∆V, then

A(ho + ∆h) = V = V 0 + ∆V

∴ A =

VV

hh

0

0

+

+

∆

∆

But, for axial compression, ∆h is known to be negative.

∴ A = VV

hh

0

0

+

−

∆

∆

=

V V

V

h h

h

A V

V

a

0

0

0

0

0

0

1

1

1

1

+

F

HG

I

KJ

−

F

HG

I

KJ

=

+

F

HG

I

KJ

−

∆

∆

∆

()ε

,

since the axial strain, εa = ∆h/h 0.

For an undrained test, A =

A

a

0

() 1 −ε

,

since ∆V = 0. ...(Eq. 8.32)

This is called the ‘Area correction’ and^1

() 1 −εa

is the correction factor.

A more accurate expression for the corrected area is given by

A =

A

a

0

() 1 −ε

. 1
0

+

F

HG

I

KJ

∆V

V

= VV

hh

0

0

+

−

∆

()∆

...(Eq. 8.33)

Once the corrected area is determined, the additional axial stress or the deviator stress,
∆σ, is obtained as

∆σ = σ 1 – σ 3 =

Axial load (from proving ring reading)

Corrected area

The cell pressure or the confining pressure, σc, itself being the minor principal stress,

σ 3 , this is constant for one test; however, the major principal stress, σ 1 , goes on increasing

until failure.

σ 1 = σ 3 + ∆σ ...(Eq. 8.34)

Mohr’s Circle for Triaxial Test
The stress conditions in a triaxial test may be represented by a Mohr’s circle, at any stage of
the test, as well as at failure, as shown in Fig. 8.12:

Mohr-Coulomb strength envelope

ss3c(= ) s 11 s 12 s 13 s1f s

t

Fig. 8.12 Mohr’s circles during triaxial test