A model of chemo-mechanical evolution of new cementitious materials such as low-heat or low-pH cements is described. The proposed phenomenological model, usable at structure scale, is based at early age on a multiphasic hydration developed for blended cements. At higher ages, the evolution of mechanical properties of such binder with high silica content cannot be explained by pozzolanic reaction (because portlandite is entirely consumed at early ages). At these ages, mineralogy analyses showed that the hydration of remaining anhydrous silica oxide is still developing by consumption of calcium from hydrates with high C/S ratios (for instance C-S-H produced by clinker hydration at early age). These chemical evolutions are modeled taking into account chemical equilibrium of solution and solid phases in terms of calcium concentration. The impact on mechanical properties is then also predicted. Finally the chemo-mechanical model is applied on the prediction of mechanical behavior of nuclear waste storage structures casted with low pH based concrete.