Bayesian calibration of thermodynamic parameters for geochemical speciation modeling of cementitious materials

https://doi.org/10.1016/j.cemconres.2012.02.004Get rights and content

Abstract

Chemical equilibrium modeling of cementitious materials requires aqueous–solid equilibrium constants of the controlling mineral phases (Ksp) and the available concentrations of primary components. Inherent randomness of the input and model parameters, experimental measurement error, the assumptions and approximations required for numerical simulation, and inadequate knowledge of the chemical process contribute to uncertainty in model prediction. A numerical simulation framework is developed in this paper to assess uncertainty in Ksp values used in geochemical speciation models. A Bayesian statistical method is used in combination with an efficient, adaptive Metropolis sampling technique to develop probability density functions for Ksp values. One set of leaching experimental observations is used for calibration and another set is used for comparison to evaluate the applicability of the approach. The estimated probability distributions of Ksp values can be used in Monte Carlo simulation to assess uncertainty in the behavior of aqueous–solid partitioning of constituents in cement-based materials.

Section snippets

Introduction and objectives

Cementitious materials exposed to aggressive environmental conditions (e.g., sulfate and chloride attack, carbonation, leaching, aging) degrade over time which eventually leads to performance degradation and potential failure of the structure or its intended characteristics (e.g., as a hydraulic or contaminant release barrier). One of the most important components in numerical modeling of the degradation of cementitious materials under chemical attack is accurate simulation of the chemical

Materials and aqueous–solid partitioning data

Two types of cementitious materials were selected for evaluation in this paper

  • (i)

    cements mixed with slag (samples A1 and A2), and

  • (ii)

    cements mixed with slag and fly ash (samples B1, B2 and B3).

Notably, samples A1, B1 and B2 were of U.S. origin and testing (Vanderbilt University, Nashville, TN) while samples A2 and B3 were of EU origin and testing (Energy Research Centre of The Netherlands, Petten, NL). Each of these materials was evaluated for equilibrium aqueous–solid partitioning of constituents

Geochemical speciation model for aqueous–solid equilibrium

The geochemical speciation code, ORCHESTRA [24], was used to numerically model the leaching behavior of the materials evaluated in this paper. The chemical reaction equations were written in terms of the selected primary species Al+ 3, Ca+ 2,Fe+ 3, Mg+ 2, H4SiO4,SO4 2, H2CO3 and H+. The simulations were performed by including all aqueous complexes available for these components in the MINTEQ database [25], as well as the mineral phases chosen from Cemdata2007 [5] and MINTEQ database [25] as listed in

Bayesian calibration framework

In Fig. 3, G(θ, s) represents a numerical model in general. The model can be a simple equation, a set of simultaneous equations (such as the chemical equilibrium model, ORCHESTRA, used here), or a multi-scale, multi-physics coupled model. In the figure, θ is an array of model parameters (having one or more values), s is an array of inputs (having one or more values), and y is a scalar array or a matrix of output variables (such as aqueous concentrations as a function of pH as in the problem

Results and discussions

One set of materials was used for calibration of the chemical equilibrium constants and then another set of materials, using the same model and probability distributions for Ksp values as determined from the calibration cases, was used as comparison cases to assess the robustness of the approach. The MATLAB implementation of the adaptive Metropolis and delayed rejection adaptive Metropolis schemes (DRAM) by Laine [49] was used in this paper in conjunction with the geochemical speciation code

Conclusions

A Bayesian calibration method was used in this paper to quantify uncertainty in the chemical equilibrium model used for cement-based materials. A set of 17 mineral phases was chosen to describe the chemical behavior of the materials studied after a preliminary investigation with several mineral sets. First, one set of experimental results on the leaching behavior of cement-based materials was used for calibration of the equilibrium constants, and then another set of experimental data was used

Disclaimer

This report is prepared as an account of work sponsored by an Agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific

Acknowledgments

This study was based on work supported by the U. S. Department of Energy, under Cooperative Agreement Number DE-FC01-06EW07053 entitled ‘The Consortium for Risk Evaluation with Stakeholder Participation III’ awarded to Vanderbilt University. This research was also carried out in part as part of the Cementitious Barriers Partnership supported by U.S. DOE Office of Environmental Management. The opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do

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