A Microstructural Model for Soils and Granular Materials - Multiscale Geomechanics: From Soil to Engineering Projects - page 190

rate requires the φ 0 parameter to be determined. A value of φ 0 = φ μ was retained in
accordance with the fact that, for contractive samples, the critical state was reached
for the maximum value of the deviatoric stress, i.e. the sample was contractant all
the way up to the critical state.

The peak friction angle is not an intrinsic parameter, but varies with the void
ratio according to equation [7.9]. A value of m = 0.6 was determined from the test
results. The values of k p0 are directly connected to the elastic properties by
considering the relation: k p0 = a k n . Here we simply considered that k p0 = k n .

The set of parameters for Hostun sand is presented in Table 7.1.

e ref p ref (Mpa) λ φ μ (°) φ 0 (°) m

0.81 0.1 0.16 33 33 0.6

Table 7.1. Model parameters for Hostun sand

The numerical simulations are presented in Figure 7.5. A reasonable simulation
of the behavior of Hostun sand at various mean effective stresses and various initial
void ratios can be obtained with a single set of model parameters, capturing both the
contractive and dilative behavior of the sand, as well as the influence of this
contractive or dilative behavior on the stress−strain curves and on the maximum
strength. For large deformations, the curves corresponding to the same confining
stress and different initial void ratios converge towards an identical stress state and
void ratio, in accordance with the definition of critical state.

3 0.8

Loose
Dense

Loose

Dense

0.8MPa

0.1MPa
0.3MPa

0.7

A
B

2

0.8MPa

0.6

0.3MPa

0.1MPa

0.3MPa

1

0.8MPa

0.5

0.1MPa

0.4

0

C

0 5 10 15 20 0 5 10 15 20

ε 1 (%) ε 1 (%)

Figure 7.5. Numerical simulations of drained triaxial tests on Hostun sand