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dilatancy law [ROW 62] for granular media. An additional parameter, the friction
angle between grains Φ f , has been introduced:
εθθ θεθ
=+
p(
− −
)
exp(
θε
)
[5.19]
v
0
1
2 1
3
4 1
φ
σ
π
 
d
ε
2
1
=
tg
+
1
[5.20]
 
σ
4
2
d
3
1
Every path in both the (q - ε 1 ) and (ε v - ε 1 ) planes imposes two conditions (at the
origin and at the infinite). In this way, the set of experimental standards becomes
reduced to a parameter of nature and a parameter of arrangement, such as:
- Φ pp (or M ) as “nature of grains” parameter;
- ΦOCR (or e pp - e OC , or Ψ) as “grains arrangement” parameter.
Favre's model [FAV 80] gives Φ pp as a function of grain distribution for sands;
the Biarez and Hicher's model [BIA 94] gives Φ pp as a function of w L for clays.
Hachi and Favre [HAC 01] quantified the Rowe internal friction angle as a function
of the perfect plastic friction angle and of OCR [5.21], in agreement with the model
given by Bolton [BOL 86] for the peak friction angle [5.22]:
Φ f = Φ pp - 12.4 ( e pp - e OC )
[5.21]
Φ peak = Φpp + 0.6 Ψ
[5.22]
and the OCR, for which Φ peak = Φ pp (Ψ = 0) would finally be:
OCR = 2.6 (for clays with w L = 70%);
OCR = 5.8 (for clean sands).
5.6. The undrained triaxial path for sands
Biarez became attached to sand models because, unlike clays, sands produce a
complex path in the (q - ε 1 ) plane. We shall see later that clay paths are actually of
the same nature when plotted in the same plane.
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