关键词: mathematical model, qualitative theory, equilibrium points, Hopf bifurcation

Abstract: This paper treats the soil and rock or concrete as a two-phase medium composed of a solid skeleton and an interstitial fluid. Under the unsaturated condition of interstitial fluid, the third phase is taken into consideration. In this paper, we consider the constitutive relation, dynamic and kinematic relations, and also various approximations with their limits of validity, including those of most practical engineering situations such as the consolidation problem and the undrained behaviour. The finite element discretization and the time dependent solution of various classes of soil problem are also discussed.

Key words: mathematical model, qualitative theory, equilibrium points, Hopf bifurcation