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STADIUM® Overview

STADIUM® is a numerical model dedicated to the prediction of chloride and other contaminant ingress in cementitious materials. STADIUM® allows owners, managers, engineers and contractors to reduce initial construction costs, avoid unnecessary inspection and maintenance costs, as well as prioritize capital expenditures. It also offers assistance for optimal material selection and identification of cost-effective rehabilitation strategies for a maximum service-life extension.

Contrary, to the first generation of chloride penetration models, such as Life-365™ and Duramodel™, STADIUM® is based on the most recent developments in ionic transport modeling and numerical solutions. Its finite-element calculation core can model the ingress of chloride and other species under different types of environmental conditions. The model also considers the complex interactions between contaminants penetrating the porous network of concrete and the hydrated phases of the cement paste. STADIUM® offers the possibility to take into account the chemical composition of local cements and supplementing admixtures such as silica fume, fly ash and slag.

The model also considers the impact of temperature and moisture content variations in materials on the rate of chloride ingress. It is thus possible to provide STADIUM® with time-dependent environmental conditions in order to simulate the effect of wetting and drying cycles on the chloride penetration rate, which allows engineers to simulate complex, but realistic exposure cases. The simulation of more accurate environmental conditions provides a better evaluation of the extent of chloride ingress and other contaminants in a structure during its service life.

STADIUM® requires adequate material parameters, therefore, a series of experimental methods were developed based on already existing standard procedures. These methods allow for the evaluation of the quality of concrete in order to assess the influence of various types of cements and admixtures as well as to consider material mixture proportions

STADIUM® vs. Fick’s Law Comparison

The following table highlights the differences between STADIUM® and simplified modeling approaches based on Fick’s second law.

Transport EquationBased on the Extended Nernst-Planck model, accounts for:

  • Diffusion
  • Electrochemical coupling
  • Nonlinear activity effects
  • Water saturation level in pores
  • Temperature
  • Effect of chemical species like alkalis, sulfate, calcium, magnesium
Fick’s second law of diffusion, valid under the following assumptions:

  • Diffusion is the only driving mechanism
  • Linear chloride binding isotherm
  • Saturated material only
  • Isothermal material
  • Free and bound chloride diffuse at the same rate
Chemical ReactionsHandled by a separate module with the following characteristics:

  • Pitzer model for calculation of chemical activity at high pH/high alkali concentrations
  • Dissolution/precipitation handled by law of mass action
  • Solid solution mechanism for Friedel salt formation from AFm phases
  • Equilibrium constants from CEMDATA07 v1c (2013) database
  • Physical binding to C-S-H handled separately using Freundlich isotherm
  • No specific term to account for chemical reactions
  • Chemical reactions embedded in the apparent diffusion coefficient, under the assumption of linear chloride binding (not supported by experimental observations)
Material Properties
  • Porosity
  • Intrinsic diffusion coefficient
  • Water permeability
  • Moisture retention function
  • Initial pore solution composition
  • Initial mineral phase content of hydrated cement paste
  • All properties hidden under the apparent diffusion coefficient
  • The apparent diffusion coefficient is not a material property but depends on the specific conditions under which it was measured
Boundary Conditions
  • Concentration of species in the environment (chloride, sulfate, magnesium,etc.)
  • Temperature (may be time-dependent)
  • Relative humidity (may be time-dependent)
  • Boundary conditions all embedded in the Co surface concentration term
  • Co incorporate chloride species in the environment and chloride bound to the material near the boundary
  • Co is not an actual representation of the environment

Comparison of predictive capabilities

A direct comparison can be made between both approaches. The following case presents both models that were used to predict chloride ingress in a 20-year old parking structure where de-icing salts are applied during winter.

  • Cores from the actual structure were extracted. A petrographic analysis was performed and revealed that the in-place concrete was an OPC mix with a water-to-cement ratio of approximately 0.45.
  • A 0.45 w/c OPC mix was prepared in laboratory and cast in cylinders. The cylinders were cured 28 days in moist conditions.
  • After 28 days of curing, one set of cylinders was tested using SIMCO’s test methods:
    • Porosity: ASTM C642
    • Diffusion coefficients: migration test (modified ASTM C642)
    • Permeability: ASTM C1792 drying test
    • Water retention function modified ASTM C1792
  • Another set of samples was immersed in a 0.5M NaCl ponding solution. After 80 days, chloride profiles were measured at different depth increments using an acid-dissolution technique (ASTM C1152). This chloride profile was used to estimate the apparent diffusion coefficient Dapp on the basis of Fick’s second law.
  • For boundary conditions, solution samples collected directly from the concrete surface during one winter were analyzed for chloride content. The data was used in STADIUM. Temperature and relative humidity data collected from a local weather station was also used.
  • To measure Co for Fick’s law analysis, chloride profiles from field cores were measured using the same depth increment technique as for the lab samples.

The data was then used as input for each model in order to predict chloride ingress after 20 years. The results are presented in figure 1. In the present case, the simplified Fick’s law approach vastly overestimates the chloride ingress rate.


Figure 1 – Chloride ingress in a parking slab after 20 years of exposure to deicing salts

STADIUM Validation

Over the years, STADIUM® has been extensively validated on the basis of laboratory and field data. This section shows examples of validation test cases performed by SIMCO that were either published in scientific papers/conferences or generated through different engineering projects. In all cases, the same procedure was used:

  • Concrete samples (lab cured or cored from concrete elements) were tested using SIMCO’s test methods to independently measure transport properties:
    • Porosity: ASTM C642
    • Diffusion coefficients: migration test (modified ASTM C642)
    • Permeability: ASTM C1792
    • Water retention function modified ASTM C1792
  • Chloride profiles from lab and field samples were measured at different depth increments using an acid-dissolution technique (ASTM C1152).
  • The parameters measured in the first step are entered in STADIUM as input data to verify that the model can replicate the measured chloride profiles.



Figure 2 – 0.45 w/c OPC mix exposed to 0.5M NaCl (published: Samson E., Marchand J. (2006) Multiionic Approaches to Model Chloride Binding in Cementitious Materials, in Proceedings of the 2nd International Symposium on Advances in Concrete Through Science and Engineering (Quebec, Canada), Marchand et al. Eds, RILEM Proceedings 51, p. 101-122.)



Figure 3 – 0.65 w/c OPC mortar exposed 2 years to 0.5M NaCl in saturated and wetting/drying cycles (presented at the American Ceramic Society/Advanced Cement-Based Materials meeting, Nashville (USA), 2011.



Figure 4 – Chloride profile from 100-year old concrete (Pacific Walls of Panama Canal) exposed to seawater

Technical Information