3D concrete printing is a rising technology which could help mitigate the productivity and sustainability issues of the construction sector, thanks to robotization and optimization of the quantities of material used in structures. However, the process of printing concrete is yet to be sufficiently understood and controlled in order to guarantee the printability and hardened material properties of printed structures. The development of predictive modeling tools is therefore paramount to the technology's maturity, replacing trial-and-error strategies of the early stages and advancing towards producing norms for 3D printed concrete. Cement-based materials are complex, especially in the early stages of cement hydration, which is of prime importance for 3D printing. Herein, we present a modeling framework based on poromechanics, and taking into account couplings between chemical, fluid, thermal et mechanical processes. The model has been implemented in a finite element code which was especially adapted to simulate the deposition process in 3D printing, allowing to assess buildability of particular print-pieces through plasticity and buckling analysis. Our code also extends to the post-printing period until the fully hardened state, taking into account the effect of curing conditions on the print-piece and its consequences on hardened properties. It is encompassed in a wider framework which starts with geometry reconstruction from a print path until data visualization. The predictive capacity of the framework is confirmed by comparison with printing experiments. It is namely shown that our material model generalizes well to printing parameters such as accelerator dosage in the case of two-component printing. Drying kinetics and altered hardened properties due to air curing are also quantitatively predicted by the model. Finally, we give some indication at model calibration, introducing some tests which may be easily back-analyzed to determine model parameters.