Shear Strength of Soils - Elements of Soil Mechanics - page 127

Table 4.2 Results of triaxial compression tests on normally consolidated clay samples (after
Parry, 1960 ).

Undrained tests

p (kPa)
r σ r (kPa) σ af − σ r (kPa) u f (kPa) w f (%) v

103.4 68.3 50.3 25.1 75.9 1.67

206.9 119.3 113.8 23.0 132.9 1.61

310.3 172.4 171.7 21.5 196.1 1.57

413.7 224.8 227.5 20.3 261.1 1.54

827.4 468.9 458.5 18.5 525.2 1.49

Drained tests

σ r (kPa) ′ σ ′ − ′ σ

r (kPa)

w f (%) p (kPa)

f

v

af

103.4 114.5 23.0 141.6 1.61

206.9 244.8 20.4 288.5 1.54

310.3 348.2 19.3 426.4 1.51

413.7 481.3 18.5 574.1 1.49

827.4 930.8 16.1 1138.0 1.43

4.14.2 The critical state line

Parry ( 1960 ) published a comprehensive set of results obtained from drained and undrained triaxial tests
carried out on normally and overconsolidated samples of Weald clay. A few of his results of tests on
normally consolidated samples are reproduced in the first four columns of Table 4.2 (converted into SI
units). With this information and taking G s = 2.75, the tabulated values of q, p ′ and v were calculated.
The (p ′ , q) points obtained from each of the test results are plotted in Fig. 4.37a and the (p ′ , v) points are
plotted in Fig. 4.37b .
We can deduce from these diagrams that there must be a single line of failure points within the p ′ -q-v
space which projects as a straight line on to the q-p ′ plane and projects as a curved line, close to the
normal consolidation line, on to the v-p ′ plane. This line is known as the critical state line and its position
is illustrated in Fig. 4.38.

The equation of the critical state line
The line's projection on to the q-p ′ plane is a straight line with the equation q = Mp ′ , where M is the
slope of the line.
The projection of the critical state line on to the v-p ′ plane is unfortunately curved but if we consider
the projection on to the v : ln p ′ plane we obtain a straight line with a slope that can be assumed to be
equal to the slope of the normal consolidation line.
The values for

′ ′

p f are tabulated in Table 4.2 and it is a simple matter to obtain a set of ln p f

values so that a v-ln p f plot can be obtained. Figure 4.39 shows the v-ln ′ p f plot for Parry's results from ′

Table 4.2.
If we use the symbol Γ to represent the value of v which corresponds to a ln p ′ = 0 (i.e. a p ′ value of
unity, usually taken as 1.0 kPa) then the equation of the straight line projection is:

v

Γ λ ln

p ′

= −