ABSTRACT
The unsaturated breakage model adopted for this study follows the typical formalism of continuum thermodynamics. As a consequence, it enforces the first and second principles of thermodynamics:
W = ≥Ψ Φ+ Φwith 0 (1)
where W is the incremental energy input, Ψ the increment of the Helmholtz free energy and Φ the non-negative incremental energy dissipation. Following Buscarnera & Einav (2012), the three terms in (1) are defined as follows:
− Energy input:
( )Sr⎡⎣ ⎤⎦ − ( )u ua w− = ′′ σ δS u εδ
σ ij ij rnsS ε − (2)
1 INTRODUCTION
Mechanical properties of soils such as compressibility and yielding are often found to be a function of saturation conditions and matric suction (Fredlund & Rahardjo 1993, Gens 2010). In particular, as the degree of saturation decreases, soils are subjected to a hardening process, i.e. to an expansion of the yielding domain. Many attempts have been made to incorporate the interplay between mechanical response and hydraulic state variables into constitutive laws for soils (e.g. Alonso et al. 1990, Wheeler & Sivakumar 1995, Gallipoli et al. 2003). One of the most widely used concepts to capture such effects is the loading-collapse yield surface (Alonso et al., 1990), according to which the yielding stress depends on the matric suction via a phenomenological relation.
