Shear Strength of Soils - Elements of Soil Mechanics - page 111

Fig. 4.23 Example 4.6 .

Example 4.7: Effective and total stress tests on same soil

A series of undisturbed samples from a normally consolidated clay was subjected to
consolidated undrained tests.
The results were:

Deviator stress
at failure (kPa)

Pore water pressure
at failure (kPa) Cell pressure (kPa)

200 118 110

400 240 220

600 352 320

Plot the strength envelope of the soil (a) with respect to total stresses and (b) with
respect to effective stresses.

Solution:

(a) Effective stress:
(1)

′ = ′ =

σ 200 110 − = 90 kPa ; σ 118 + = 90 208 kPa 3 1

′ = ′ =

(2) σ 400 220 − = 180 kPa ; σ 240 180 + = 420 kPa

3 1

′ = ′ =

(3) σ 600 320 − = 280 kPa ; σ 352 + 280 = 632 kPa 3 1

(b) Total stress:
(1) σ 3 = 200 kPa; σ 1 = 200 + 118 = 318 kPa
(2) σ 3 = 400 kPa; σ 1 = 400 + 240 = 640 kPa
(3) σ 3 = 600 kPa; σ 1 = 600 + 352 = 952 kPa

The two Mohr circle diagrams are shown in Fig. 4.24. The total stress circles are shown
in lighter colour.
The value of φ ′ can be obtained from Fig. 4.24 by direct measurement.
Alternatively, knowing that the effectice stress strength envelope goes through the
origin, the value can be obtained from the Mohr-Coulomb equation. Consider the
Mohr stress circle created when the cell pressure,

σ 3 ′ = 200 kPa :

′ − ′
′ + ′ =

σ σ 118

90

1 3

sin φ ′ = = 0 396 . , i e . . φ ′ = 23 3 . °

σ σ + 208

1 3