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Modeling diffusion and reaction of sulfates with cement concrete using mixture theory

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Abstract

Here mixture theory is used to capture the changes in cement concrete exposed to sodium sulfate till cracks develop. Toward this, the mixture is assumed to be made of eleven constituents of which the sodium sulfate and water move relative to themselves and the remaining nine solid constituents. The nine solid constituents constrained to move together are the eight relevant chemical constituents in concrete that react with sodium sulfate and all the other remaining chemical constituents of concrete that do not react with sulfates. Constitutive assumptions needed to be made within this mixture theory framework are the same as those reported by Gouder and Saravanan (Acta Mech 227(11):3123–3146, 2016). Within this framework of mixture theory, the radial ingress and reaction of sodium sulfate solution with the concrete cylinder sealed at top and bottom, exposed to a constant concentration of sodium sulfate at its outer surface, are formulated. The resulting nonlinear governing differential equations are converted into a system of nonlinear algebraic equations using a forward finite difference scheme in space and a backward difference in time. The nonlinear algebraic equations are solved simultaneously using constrained minimization technique till the water reaches the center of the cylinder. The results obtained for ingress without chemical reactions agree with those predicted by Fick’s equation. The axial expansion of the cylinder and the increase in the value of Young’s modulus of the part of concrete which reacted with sulfates agree qualitatively with the experiments.

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

    Chethan Gouder & U. Saravanan

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  1. Chethan Gouder
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  2. U. Saravanan
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Correspondence to U. Saravanan.

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Gouder, C., Saravanan, U. Modeling diffusion and reaction of sulfates with cement concrete using mixture theory. Acta Mech 229, 1353–1385 (2018). https://doi.org/10.1007/s00707-017-2035-9

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  • DOI: https://doi.org/10.1007/s00707-017-2035-9

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