Geoscience Reference
In-Depth Information
268
Multiscale Geomechanics
- the compressibility of the fluid is adapted to reproduce the compressibility of the
mixture of water and air.
It should be noted that this approach can be used to model the construction phase. If
we are interested in the other phases of a dam's lifetime, the approach is not useful. If the
gasphaseiscontinuousandtheliquidphasediscontinuous,orratherunbalancedinthese
conditions, capillarity plays an important role in the hardening of soil, essential to keep
in mind during modeling. Other classes of models are the non-linear elasticity models
with state surfaces. In these models, which were applied for the first time to a dam by
Lloret and Alonso [LLO 85] in a partially coupled manner, the state surface defines the
evolution of the degree of saturation and void ratio on a humidification path in terms of
total stress and capillary pressure ( p a − p w ). The third category of models consists of
elastoplastic models written either in terms of total or effective stress. If no hardening
due to unsaturation is introduced, these models cannot be used if the gas phase is
discontinuous. When the latter is continuous and the capillary pressure influences the
mechanical behavior, it is necessary for the model to take it into account. The model
of Alonso and Gens written in terms of total stress is a pioneering elastoplastic model
obtained from the generalization of the Cam Clay model. The major drawback of
these traditional approaches is that they do not describe certain phenomena observed
in unsaturated soils. Based on work conducted by J. Biarez and J.M. Fleureau [BIA 93]
and the microstructural model composed of particles [TAI 94], we can introduce the
concept of generalized effective stress into unsaturated soils (see Chapter 6 of this
volume). A capillary stress can be defined, so that the effective stress becomes:
σ = σ + p a I − σ c
[9.62]
where σ c is a function of capillary pressure as well as the density and grain-size
of the material. The capillary stress, depending on the geometry of pores, is not
necessarily spherical. However, for the sake of simplicity and lack of an experimentally
validated model, only the spherical part of this tensor is considered and we assume that
σ c = π c I . However, the same terminology has been kept to avoid confusion with the
capillary pressure ( P c ). A given density and particle-size, this capillary stress must
comply with the conditions obtained from microstructural models and experimental
observations. The deduction made from the intrinsic curves obtained for unsaturated
samples [BIA 93] shows that, for a given density and particle-size, the variation of
capillary stress as a function of capillary pressure reaches a plateau for high values
of capillary pressure. This deduction was made by Taibi [TAI 94] in considering a
microstructural model. For an assembly of deformable particles in contact, he gives
the following relationship:
(1 + 3(3T − 8 · T · R · P c +9T 2 )
4R·P c
π c = π max
)
[9.63]
c
 
Search WWH ::




Custom Search