4. (a) The critical state properties of a clay are M = 0.89, r = 3.05,

N= 3.1 and λ = 0.14. One sample of this clay is isotropically

normally compressed in a triaxial apparatus to p'=400 kN/m².

Maintaining this consolidation pressure (i.e. without letting the

sample swell) the sample is then subjected to a standard drained

compression test. Calculate the deviator stress at failure and also

the volumetric strain to failure.

(9

marks)

(b) A number of drained and undrained triaxial tests were carried

out on a clay soil. Table 3 below gives data for the stress

parameters q and p and the specific volume v when the

samples had reached failure at their critical states. Plot the

results in terms of vf versus p and qe versus pe respectively, and

determine the critical state parameters M, λ and of the clay.

(11 marks)

Test

number

1

2

3

4

q₁ (kPa)

198

297

411

598

Table 3

Pr (kPa)

202

300

420

610

Vf

2.03

1.95

1.87

1.80

Total 20 marks