A Microstructural Model for Soils and Granular Materials - Multiscale Geomechanics: From Soil to Engineering Projects - page 195

loading stresses. This result confirmed that volume change during loading is mainly
due to the rearrangement of the clay clusters.

Therefore, we can extend the micro-structural model presented above by
considering the clayey material as a collection of clusters. The clusters interact with
each other mainly on mechanical bases and play the same role as the grains in a
granular material. In order to account for the compressible behavior between clay
clusters during consolidation, a second yield surface is added. The second yield
function is assumed to be [CHA 09]:

()

F σκ =− σ κ ε

p

for σ > p [7.16]

2 2 2 p

k 2 is another hardening parameter, which can be written as

p

ε / c

κ = p 10 [7.17]

p

2 p

where p c is the compression coefficient in the

p

− log ' σ plane. When the

compression σ is less than p , the plastic strain produced by the second yield
function is null. Thus, p p in equation [7.11] corresponds to the pre-consolidation
stress in soil mechanics.

7.4.1. Remolded clays

The black kaolinite clay is a remolded clay with plastic limit ( wp ) of 30%, and
liquid limit ( wl ) of 70%. The macro parameterλ was determined experimentally
from the measured slope of the critical state line in the e − log p' curve: λ = 0.53.

From the photograph in Figure 7.10, we assume that the mean particle size d is
0.001 mm. The influence of the aggregate deformability is particularly pronounced
on the elastic properties of clayey materials, since the elastic domain is restricted to
very small strains (< 10 -5 ), for which the relative displacements of the constituents
are negligible. Under these conditions, the elastic moduli measured in sands and
gravels are much higher than in clays. From test results at very small strains, we
estimated the value of the inter-aggregate stiffness to be k n0 = 35 N/mm, and the
value of k t0 /k n0 = 0.4.

The position of the critical state line is given by ref e = 1.39, corresponding to
reference pressure p ref = 0.01 MPa. The isotropic compression line gave a value of