Hydration products of tricalcium silicate (C3S) are the calcium silicate hydrates (C-S-H) and Portlandite. Silica fume, added to anhydrous cement in industrial formulations reacts with Portlandite and leads to C-S-H different from the previous one. C3S hydration with and without silica fume has been studied under high pressure (1000 bar) and high temperature (160degreesC) by numerous techniques (Si-29 and H-1 NMR, XRD, Thermal analysis, SEM) for different hydration times. In these conditions, high temperature more stable crystalline phases are formed and their kinetics of formation is dependent on pressure. Besides, electrical conductivity measurement on hydrating cement under pressure have been carried out in order to evidence the great dependence of hydration kinetics with pressure. This study proposes a practical phase diagram which allows on a thermodynamical base to understand the change of equilibrium temperature with pressure. The kinetics of reaction has been studied and mechanisms of reaction proposed to explain the results.