GRADIENT-BASED POROPLASTIC THEORY: PHD THESIS

J.L. MROGINSKI

AutoresEditores.com

Año: 2013 p. 160

9-8733-3708-3

In this work, a thermodynamically consistent gradient-based formulation for partially saturated cohesive-frictional porous media is proposed. The constitutive model includes a classical or local hardening law and a softening formulation with state parameters of nonlocal character based on gradient theory. Internal characteristic length in softening regime accounts for the strong shear band width sensitivity of partially saturated porous media regarding both governing stress state and hydraulic conditions. In this way the variation of the transition point of brittle-ductile failure mode can be realistically described depending on current confinement condition and saturation level. On the other hand, the strain localization problem is studied by the spectral analysis of discontinuous bifurcation condition in gradient-based poroplastic media. To evaluate the dependence of the transition point between ductile and brittle failure in terms of the hydraulic and stress conditions, the localization acoustic tensor for discontinuous bifurcation is formulated for both drained and undrained conditions, based on wave propagation criterion. On the other hand, the analytical expression for the critical hardening/softening module is obtained by exploring the spectral properties of the acoustic tensor for drained and undrained conditions. In this work, two materials models are used in order to describe the inelastic mechanical behavior of both clay and young concrete, within the framework of the theory of porous media. First of all, the material model employed to describe the plastic evolution of porous media is the Modified Cam Clay, which is widely used for saturated and partially saturated soils. Then, the gradient-dependent Parabolic Drucker-Prager material model originally proposed by Vrech and Etse (2005) [126] for concrete is extended by means of the constitutive theory in this thesis to account for gradient poroplastic behaviour. This enriched material model is considered to simulate the behaviour of young concrete whereby the hydraulic condition plays a very important role. Then, localization analysis of both gradient poroplastic material proposed in this thesis is performed, showing the influence of the pore pressure and of the non-associativity degree on the location of the transition point between ductile and brittle failure regime and on the critical bifurcation directions. A relevant novel aspect in this thesis is the consideration of the porous phase influence on the non-locality degree of the material model. This is done by the definition of an additional characteristic length for the porous phase to take into account its microstruture. To solve the boundary value problems in this thesis, a new finite element formulation for non-local and inelastic saturated and partially saturated gradient poroplastic materials is proposed. The novel finite element includes interpolation functions of first order (C1) for the internal variables field, while classical C0 interpolation functions for the kinematic and pore pressure fields. The proposed finite element formulation is compatible with the thermodynamically consistent gradient poroplastic theory developed in the framework of this thesis see, Mroginski, et al. (2011) [76]. To verify the numerical efficiency of the proposed finite element formulation, the nonlocal gradient poroplastic constitutive theory is combined with the Modified Cam Clay model for partially saturated continua. Thereby, the volumetric strain of the solid skeleton and the plastic porosity are the internal variables of the constitutive theory. The numerical results in this work demonstrate the capabilities of the proposed finite element formulation to capture diffuse and localized failure modes of boundary value problems of porous media, depending on the acting confining pressure and on the material saturation degree.