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## Thin expansive shell around the aggregate

One proposal for the mechanism for damage during so-called delayed ettringite formation is the formation of expansive ettringite right at the cement paste-aggregate interface [8,9]. The expansion of this thin shell then produces tensile radial stresses at the interface, which causes the aggregates to de-bond with the matrix, so that a rim of free space will be observed around the aggregate. By letting h/a be much less than 1, so as to simulate a thin shell, and ε1o = ε3o = 0, ε2o = ε, we can investigate the kinds of stresses and displacements that are produced in this scenario. Solving eqs. (3)-(7) for this choice of parameters, we find that, to first order in h/a,

The radial stress is tensile, with again a maximum at the aggregate-cement paste matrix interface. Cracking, if any, will again be circumferential. Separating the aggregate from the matrix by taking σrr = 0 at r = a, we can find the displacement of the cement paste edge at r = a by re-solving the equations under this assumption. We find that the thickness of the ensuing gap at the aggregate edge will be, to leading order in h/a, u(r = a) = 3h ε c/(1-c), which is proportional to the thickness of the expansive region, not the aggregate radius. The assumption of h/a being much less than 1 simplified the mathematics, but approximately the same result will be found for larger values of h.

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Expansive aggregate Up: Results for various Previous: Uniform matrix expansion