The prediction of the behaviour of cementitious materials and concrete structures under severe conditions and/or for long time spans is of paramount importance in civil, environmental and nuclear engineering. Often, commercial tools do not provide a sufficiently accurate response, so it is needed to use more sophisticated approaches. In this work, a general framework for the simulation of the non-linear behaviour of concrete is shown and described. It is based on the multiphase porous media mechanics (MPMM). The mathematical model is developed by writing the relevant balance equations for the constituents at the pore scale, i.e. the local form of governing equations formulated at micro-scale, and by upscaling these equations to the macroscopic scale, taking into account thermodynamic constraints according to the so-called TCAT (Thermodynamics Constrained Averaging Theory) which assures that the whole Thermodynamics is properly upscaled from micro to macro-level. Thanks to this approach, all the relevant quantities involved are thermodynamically correct, no unwanted dissipations are generated, and both the bulk phases and interfaces are considered. This procedure does not exclude however the use of a numerical multiscale approach in the formulation of the material properties. The numerical solution is obtained directly at macro-level by discretizing the governing equations in their final form. The resulting model can be usefully applied to several practical cases: evaluation of concrete's performance at early stages of maturing massive structures, structural repair works, concrete exposed to high temperature, e.g. during fire, cementitious materials subject to freezing/thawing cycles, etc. In this work, the general model is particularized to the specific situations described above and several examples are shown.