Models by Jean Biarez for the Behavior of Clean Sands and Remolded Clays at Large Strains - Multiscale Geomechanics: From Soil to Engineering Projects - page 130

On the other hand, for the fourth test - with p' 0 = 0.3 MPa - the peak under the
straight M line disappears. Its theoretical overconsolidation stress is p' iC = 2 MPa,
obtained with the C s model (see Figure 5.13b). The fictive NC test with p' iC = 2 MPa
is represented in Figure 5.13d. The locus of the peak of overconsolidated paths with
a same p' iC = 2 MPa could be a straight line (dotted line) that meets up with the M
line at the same point as the test performed at 0.3 MPa (OCR = 6.7).

A fictive test can be drawn by considering a homothetic curve with the same
OCR = 6.7 for which p' iC = 3.5 MPa ( p' 0 = 0.5). We, therefore, normalized all the
tests in relation to their theoretical overconsolidation stress p' iC , as shown in
Figure 5.14.

The locus, in the ( q / p' iC - p' / p' iC ) plane of the intermediate maxima under the M
line is a line passing through the peak-point of the theoretical NC path, for which the
coordinates are given by the system of equation [5.24]. Figure 5.14 gives the
coordinates of the point on the straight M line: p' / p' iC = 0.1 and q / p' iC = 0.1 M.

5.7. Standard behavior for undrained sands

5.7.1. Normalization by the theoretical overconsolidation stress p' iC

To be able to compare tests of one material to another, Biarez divides the
deviator by M . In Figure 5.15c, the dotted theoretical NC curve is drawn, deduced
from equation [5.23] for a clayey material of which the liquidity limit is w L = 70%,
resulting in C c = 0.53. The parameter M would, therefore, be 1.09 and the stress ratio
on the peak would be η peak = 1.84 M = 2.

This theoretical curve shows a maximum, but placed beyond line M . From an
experimental point of view, this would not be possible, since the predictive path has
to stop on the perfect plastic line M .

Therefore, for clays with a C c value in the range 0.33> C c >2 C d , corresponding to
w L values between 50% and 80%, the maximum stress ratio is located above the M
line. For highly plastic clays ( w L >80%), the effective stress path is characterized by
a value of q going to the infinite when p' converges towards zero.

We can determine the theoretical consolidation stress p' iC by drawing the
intercepting point between the C s line passing on the initial point ( I d0 -p' i0 ) and the
ISL line (equation [5.18]) for the sands, which leads to the value (equation [5.25]) of
p' i0 in kPa.

1.290 +− Id 0.52log ' p

0 0

log ' p = [5.25]

0