Abstract
Thermo-technical installations consuming significant amounts of thermal energy are used in order to intensify precast and reinforced concrete production processes under industrial conditions. Despite significant progress in the study of concrete hardening in accelerated hydration devices, a prominent lack of reliable and cost-effective research and optimization methods of their operation is observed. The methods used in real production processes are mainly based on empirical dependences obtained for specific technological conditions. These methods can not always be applied for other modes and technologies. The present paper develops calculation methods based on fundamental laws that make it possible to obtain functions for evolution of concrete product hydration process. Methods of mathematical modeling permit to develop new ways directed on improvement of modes for heat treatment of concrete products and accelerated hydration technologies. The paper describes a mathematical model for calculating a hardening process of a concrete product that includes a transient three-dimensional heat conductivity equation, a function of internal heat release due to behavior of exothermic reactions of cement hydration and also a system of initial and boundary conditions. A numerical simulation for temperature and hydration coefficient of a concrete product having shape of a 0.1´0.1´0.1 m cube has been performed in the paper. Verification of the non-stationary mathematical model for calculating temperature fields and hydration degree while using experimental data on concrete product strength obtained under industrial conditions. Investigations on hydration degree function of time have shown that experimentally obtained values of compressive strength correlate with hydration coefficient and hydration rate functions of heat treatment time which are calculated on the basis of the proposed non-stationary mathematical model of concrete product hardening. Satisfactory agreement of experimental and calculated data confirms adequacy of the proposed non-stationary mathematical model for calculating temperature fields and hydration degree with accelerated heat treatment of concrete products.
Highlights
Строительство hardening in accelerated hydration devices, a prominent lack of reliable and cost-effective research and optimization methods of their operation is observed
The present paper develops calculation methods based on fundamental laws that make it possible to obtain functions for evolution of concrete product hydration process
Methods of mathematical modeling permit to develop new ways directed on improvement of modes for heat treatment of concrete products and accelerated hydration technologies
Summary
В качестве основного уравнения для расчета изменения температуры и степени (коэффициента) гидратации использовалось уравнение теплопроводности, в котором учтено тепловыделение, возникающее при гидратации. Температура бетона в точке с координатами ( x, y, z) в момент времени τ, °С; ρб – плотность бетона, кг/м3; Wc – удельный расход цемента в бетоне, кг/м3; сб – удельная теплоемкость бетона, Дж/(кг∙°С); Q ( x, y, z,τ) – удельная теплота, выделившаяся при гидратации цемента в точке с координатами (x, y, z) к моменту времени τ, Дж/кг; H ( x, y, z,τ) – степень гидратации цемента в точке с координатами (x, y, z), достигнутая к моменту времени τ, вычисляемая как отношение количества выделившейся теплоты гидратации в указанной точке на данный момент времени к предельно возможному тепловыделению, свойственному данному цементу: H ( x,= y, z,τ) Q ( x, y, z,τ) /Qmax; λ(H, T) – теплопроводность бетона, зависящая от его состава, степени гидратации и температуры, Вт/м2; Pq(Q, T) – удельная мощность тепловыделения при гидратации цемента, Вт/кг. В расчетах использованы: экспериментальные данные [7] в виде функции теплоты гидратации Q(T, τ) (кДж/кг) для портландцемента марки М400, а также коэффициент теплопроводности бетона λ(H, T), зависящий от температуры, водоцементного отношения, влажности, плотности, взятые из [10, 11]
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