Abstract
When concrete is exposed to salt water, chloride ions diffuse into the concrete and cause the reinforcing steel to rust. Industry standards set the effective lifetime of concrete as the time at which the chloride ion concentration at the steel surface exceeds some threshold (for example, 0.5\% of binder). The problem is to find a lower bound on the time, for every depth of concrete between the sea and the underlying steel, so that one can state with, say, 95\% confidence that the concrete lifetime exceeds that bound. Estimation is complicated by the fact that there is only five years of data and we predict fifty or more years into the future. The solution set forth has two steps. First, a parametric model is proposed for the concentration field, based on Fick's law for diffusion, but modified to allow for a non-constant diffusion coefficient. Within the concrete industry the usual modification is an approximate method, but an exact solution is derived in an appendix. Both the approximate and exact methods are tested on data. Second, given a depth of concrete, lower confidence bounds on lifetime are estimated by smoothing a parametric bootstrap of the concentration field over a grid in space-time using interpolation. Some consistent differences emerge between the exact and approximate results, which may have implications for the concrete industry. References T. Siemes, R. Polder, H. De Vries Design of concrete structures for durability. HERON, 43, 1998, 227--244. R. M. Ferreira Probability based durability analysis of concrete structures in marine environment. PhD thesis, University of Minho, 2004. http://repositorium.sdum.uminho.pt/bitstream/1822/2675/1/PhDThesis(MiguelFerreira).pdf P. B. Bamforth. The derivation of input data for modeling chloride ingress from eight-year UK coastal exposure trials. Magazine of Concrete Research, 51, 1999, 87--96. G. S. Williamson, R. E. Weyers, M. C. Brown, A. Raminceanu, M. M. Sprinkel. Validation of probability-based chloride-induced corrosion service-life model.ACI Materials Journal, 105 (4), 2008, 375--380. N. P. Lee and D. H. Chisholm. Durability of Reinforced Concrete Structures under Marine Exposure in New Zealand. BRANZ Study Report SR145, 2005. http://www.branz.co.nz/cms_show_download.php?id=123
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