Geotechnical Engineering

DHARM

SHEARING STRENGTH OF SOILS 283

the latter. An elementary way to monitor stress changes is by showing the Mohr’s stress cir-

cles at different stages of loading/unloading. But this may be cumbersome as well as confusing

when a number of circles are to be shown in the same diagram.

In order to overcome this, Lambe and Whitman (1969) have suggested the locus of points

representing the maximum shear stress acting on the soil at different stages be treated as a

‘stress path’, which can be drawn and studied in place of the corresponding Mohr’s circles. This

is shown in Fig. 8.23:

1

2

3

4

Stress

path

I II

III

IV

t

o s

1

2

3

4

Stress

path

t

o s

(a) Mohr’s circles (b) Stress path

Fig. 8.23 Stress path (Lambe and Whitman, 1969)

for the case of σ 1 increasing and σ 3 constant

The co-ordinates of the points on the stress path are σσ^13

2

F +

HG

I

KJ

and

σσ 13

2

F −

HG

I

KJ

. If σ 1 and

σ 3 are the vertical and horizontal principal stresses, these become Fσσvh+

HG

I

2 KJ

and Fσσvh−

HG

I

2 KJ

.

Either the effective stresses or the total stresses may be used for this purpose. The basic

types of stress path and the co-ordinates are:

(a) Effective Stress Path (ESP)

σσ σσ 13 13

22

F +

HG

I

KJ

F +

HG

I

KJ

L

N

M

O

Q

, P

(b) Total Stress Path (TSP)

σσ σσ 13 13

22

F +

HG

I

KJ

F −

HG

I

KJ

L

N

M

O

Q

, P

(c) Stress path of total stress less static pore water pressure (TSSP)

σσ 13 σσ

0

13

22

F + −

HG

I

KJ

F −

HG

I

KJ

L

N

M

O

Q

u , P

u 0 : Static pore water pressure
u 0 is zero in the conventional triaxial test, and (b) and (c) coincide in this case. But if
back pressure is used in the test, u 0 equals the back pressure. For an in-situ element, the static
pore water pressure depends upon the level of the ground water table.
Typical stress paths for triaxial compression and extension tests (loading as well as
unloading cases) are shown in Fig. 8.24.