Models by Jean Biarez for the Behavior of Clean Sands and Remolded Clays at Large Strains - Multiscale Geomechanics: From Soil to Engineering Projects - page 117

The perfect plastic state with the critical void ratio is characterized, in the ( q - p' )
plane, by a straight line with the slope M = 6sinΦ/(3 - sinΦ) or sinΦ = 3 M /(6 + M ).

For remolded clays , the perfect plastic state can be reached easily, starting from
the isotropic normally consolidated state in the drained and undrained paths. In the
( e - log p ') plane, these paths reach a straight line. Several tests demonstrate that this
line passes in the vicinity of two reference points: p' = 3 kPa for w sat = w L and
p' = 0.5 MPa for w sat = w P . Besides, the same line is reached from overconsolidated
states, even if it is more difficult to determine, due to the development of
localizations in the large strains.

Given the same ratio σ' v ( w L ) and σ' v ( w P ) of the oedometric path, which ensures
the parallelism, Biarez took relation [5.9] with p' = 3.5 kPa (instead of 3 kPa) for w sat
= w L , and a slope C c , defined by equation [5.10], as the model for the critical straight
line (CSL), which represents the critical void ratio.

w sat = w L for p' = 3.5 kPa

w sat = w P for p' = 500 kPa [5.9]

C c = 0.009( w L - 13) [5.10]

Equations [5.9] and [5.10] lead to equation [5.11] expressed in the ( I c - log p' )
plane with the consistence index I c = 1 - I L , p' being in kPa:

I c (CSL) = 0.46(log p' - 0.54) [5.11]

For “glue-less” sands , we found very few normally consolidated tests and the
overconsolidated tests tend to present localizations before the perfect plastic state.
Biarez [SAI 97] selected three tests that reached the perfect plastic state (see Figures
5.5 and 5.6).

The model of the critical void ratio line, represented by CSL for the clean sands,
is defined by system [5.12] where the slope is given by [5.13].

e = e max for p' = 0.1 MPa

e = e min for p' = 8 MPa [5.12]

C c = ( e max - e min )/1.90 [5.13]