CASH+ solid solution cement model


Cement is widely used as matrix and backfill for low and intermediate level waste. Calcium-Aluminum-Silicate Hydrates (C-A-S-H) are the most important binding phases in cement. They are also responsible for the initial entrapment of radionuclides via sorption or solid solution formation mechanisms. Therefore, the thermodynamic modelling of C-A-S-H stability, solubility and interaction with radionuclides in cement porewater is crucial for understanding hydration, blending, degradation of cement-based materials and for the performance assessment of cementitious repositories.             

 Thermodynamic description of CASH is intrinsically difficult due to “gel-like” nanoparticulate state of this phase. Spectroscopic studies and molecular simulations reveal that the short-range order in C-A-S-H can be described using a lattice defects model based the structure of crystalline mineral tobermorite. Cations in C-A-S-H occupy specific structural positions, which can be associated with analogous structural sites in tobermorite crystal lattice.

Schematic diagram for the CASH+ model representing the C-S-H (defect tobermorite) structure. The dimeric unit (DU), bridging tetrahedral (BT), and the interlayer cation (IC) are sites in the C-S-H model structure that can be occupied by different elements.

With this structural information and the experimental data from numerous solubility studies, an incrementally extendable solid solution model for C-A-S-H was developed using the so-called sub-lattice model with real and virtual end members. The use of structural constraints  enhances the thermodynamic consistency and ensures the theory-based accurate predictions of CASH solid solution properties in a multicomponent system. 

Relative to older models, the latest improvement consists in a more accurate description of C-A-S-H stability, solubility and cation uptake from aqueous solutions. The CASH+ is the first incrementally extendable model of calcium silicate hydrate, which means that endmembers for the new cation can be added and their thermodynamic properties fitted or predicted without any re-fitting of properties of the previously available endmembers.

The CASH+ solid solution model is actually a thermodynamic database for endmembers and site interaction parameters, which grows with each next cation endmembers set added.

The CASH+ model can predict the uptake of different cations (Fig.2) and can be use to model the evolution of cement upon hydration (Fig.3).

Fig.2: C-S-H solubility with increasing Ca/Si in the solid. Comparison of CASH+ model prediction against experimental data.
Fig.3: The CASH+ model predicted effect of temperature on the uptake of alkaline earth metals represented as distribution ratios Rd as a function of Ca/Si in solid.

Currently, the model includes Ca, Si, H2O, Al, Fe, Na, K, Li, Cs, Mg, Ba, Ra, Sr; work is on-going on adding actinides U, Np; as well as Zn and other hazardous metals.  This is currently the most advanced and accurate chemical thermodynamic model for C-A-S-H worldwide.

The model will be added to the basis for the safety assessment studies in the final stage of the general license application is Switzerland.



Mr. George Dan Miron
+41 56 310 24 32
Laboratory Waste Management, LES
Geosphere Transport

Original Publication

Kulik, D. A., Miron, G. D., & Lothenbach, B. (2022). A structurally-consistent CASH+ sublattice solid solution model for fully hydrated C-S-H phases: Thermodynamic basis, methods, and Ca-Si-H2O core sub-model. Cement and Concrete Research, 151, 106585.

Miron, G. D., Kulik, D. A., Yan, Y., Tits, J., & Lothenbach, B. (2022). Extensions of CASH+ thermodynamic solid solution model for the uptake of alkali metals and alkaline earth metals in C-S-H. Cement and Concrete Research, 152, 106667.

Miron, G. D., Kulik, D. A., & Lothenbach, B. (2022). Porewater compositions of Portland cement with and without silica fume calculated using the fine-tuned CASH+NK solid solution model. Materials and Structures 2022 55:8, 55(8), 1–13.