A versatile mathematical approach for environmental geomechanic modelling based on stress state decomposition

Abstract

a b s t r a c tThe main goal of the present paper is to present a mathematical framework for modelling multi-phase non-saturated soil consolidation with pollutant transport based on stress state configurations with special emphasis in its versatility. Non-linear saturation and permeability dependence on suction for both water and pollutant transport is regarded. Furthermore, through the introduction of a suction saturation surface instead of simple suction saturation curves, the implementation of the saturation-suction coupling effect is considerably simplified. The achieved differential equation system is discretized within a Galerkin approach along with the finite element method implementation. A widespread set of practical situations is encompassed by simply setting certain coefficients of the discrete system of equation according to concrete problem conditions. When the model is coped with certain selected fringe conditions, the approach adaptability feature came up showing a robust performance.

Preliminaries for a New Mathematical Framework for Modelling Tumour Growth Using Stress State Decomposition Technique

“…Thought either the TCAT-based or SSDT-based viewpoint rely on geotechnical concept grounds, the later tenet is to set up a suitable idealization of the RVE in which different stress states are selected ( Figure 1) in order to link all the internal variables arisen in the modelization process to those selected as primary. In brief, the SSDT is a technique that provides additional equations whenever are required (see [20] for a complete description of SSDT).…”

“…This choice is hinged on the fact that the liquid phase, a priori more suitable from tumour physical standpoint, will be set aside to be equated to interstitial fluid phase. Therefore, the gaseous phase equation is, [20]:…”

“…An alternative to mixture theory ([12] [17]) and volume fraction concept for modelling consolidation in nonsaturated porous media was presented in [20]. Here, a stress state decomposition technique (SSDT) brought forth the differential equations that efficiently solve the environmental issue using the stress analysis instead of the mixture theory.…”

“…In the present manuscript, an extension of the mathematical framework appeared in [20], is carried out. Hinged on the very same stress decomposition structure, the different constituents of the representative soil portion are paralleled with those standing for the cancer representative one however bewaring to preserve the substantial difference, i.e.…”

A selective genetic algorithm for multiobjective optimization of cross sections in 3D trussed structures based on a spatial sensitivity analysis

“…In this paper, a computational tool based on GA, applied to the 3D structural design is proposed. Though for the time being the analysis is bounded to 3D truss-based structures, it is perfectly possible to extend the general conclusions hereafter posed to cope with many other stress-involved problems, namely, geometrically induced non-linearities (Di Rado et al, 2008), geo-mechanical stress determination (Mroginski et al, 2010;Beneyto et al, 2015), non-linear finite element (FE) analysis (Mroginski and Etse, 2013), etc.…”