Numerical identification of the thermal properties of early age concrete using inverse heat transfer problem

Abstract

The procedure of numerical identification of thermophysical properties of concrete during its hardening is presented. Heat of cement hydration, thermal conductivity and specific heat are determined for purpose of modelling temperature evolution in massive concrete elements. The developed method is based on point temperature measurements in a cylindrical mould and the numerical solution of the inverse heat transfer problem by means of direct search optimization algorithm. The determined thermal characteristics of concrete are not constant and depend on the maturity of concrete. The procedure was verified on set of concrete mixes designed with Portland cement CEM I 42.5R and Portland-slag cement CEM II/B-S 32.5 N. Calcareous fly ash was also used for partial replacement of cement in the mixtures. The obtained results have been compared with experimentally measured temperature in concrete and a fair agreement has been found.

Evaluation of Thermal Properties of Early-Age Concrete Containing Fly Ash

“…that where the partial knowledge of values ϑ from temperature sensors compensates the lack of knowledge of material characteristics λ and κ. Such problems may be ill-posed; [4] highlights namely the possible violation of the first one from the classical triple of requirements of Hadamard, as formulated in [3], p. 20. Nevertheless, we shall see that serious difficulties are inherited even from the direct problem with (in general) non-constant values λ and κ.…”

“…Following [9], making use of the arguments on weakly continuous mappings by [6], pp. 58, 63, 240 and 252, we are able to guarantee the existence of a unique solution of ( 7) under the assumptions f ∈ L 2 (I, L 6/5 (Ω)), g ∈ L 2 (I, L 4/3 (Γ)) and under the growth condition 0 < δ ≤ β′(r) ≤ C(1 + |r| 10/3-ω ) for any real r with some positive constants ω ≤ 10/3, δ and C. Especially in [4] (in our notation) β′(r) is allowed (ad hoc) to be a linear function of r.…”

“…the "double integration method" by [1], p. 63, applied to the 1-dimensional simplification of Ω in practice), usually β′ (for relatively slow processes) are considered as constant in particular time steps. In all cases some norm of u -ũ should be minimized: [4] presents a simple least squares approach, supplied by certain special regularizing term; more advanced regularization tricks, conjugate gradient techniques, etc., follow from [3], pp. 25 and 39, whereas the proper analysis of uncertainty forces the exploitation of probability measures and spaces.…”

“…Consequently, these characteristics, required in constitutive relations hidden in all formulations of thermodynamic principles, have to be evaluated from experimental work, although their time-dependence, due to the evolution of the hydration process, brings some difficulties both to the preparation of relevant experiments and to the design of identification procedures. Identification of standard mechanical properties, namely of compressive and split tensile strength, due to percentage of recycled aggregate, has been recently discussed in [5] and [7], whereas the evolution of characteristics of thermal transfer in such fresh mixture has been studied in [4]. The aim of this paper is to contribute to the improvement of the analysis sketched in [4] and to illustrate the identification procedure on the practical experiment, based on the special hot-plate measurement, performed at the Faculty of Civil Engineering of Brno University of Technology.…”

“…Identification of standard mechanical properties, namely of compressive and split tensile strength, due to percentage of recycled aggregate, has been recently discussed in [5] and [7], whereas the evolution of characteristics of thermal transfer in such fresh mixture has been studied in [4]. The aim of this paper is to contribute to the improvement of the analysis sketched in [4] and to illustrate the identification procedure on the practical experiment, based on the special hot-plate measurement, performed at the Faculty of Civil Engineering of Brno University of Technology.…”