MATHEMATICAL MODELING OF THERMAL PROCESSES IN THE «CONCRETE-SOIL» SYSTEM

Abstract

The calculation of concrete curing modes and the development of mathematical models are greatly influenced by the temperature field in the concrete of channel linings. The problem is reduced to solving a nonlinear heat equation that takes into account the exothermic heat release of concrete and the phase transformation of moisture, and time-varying boundary conditions that allow taking into account the impact on concrete of the external environment during laying and maintenance. Variable thermophysical coefficients make it possible to take into account the inhomogeneity of the medium (in the case of laying concrete on the ground) and the change in the aggregate state of the substance when the phase transformation temperature is reached. Since it is impossible to obtain an analytical solution in a general form, a numerical solution method is used, based on a combination of a finite-difference solution with a method for calculating heat release and concrete strength from the corresponding fields of isothermal curves obtained experimentally. When constructing a difference scheme, an integro-interpolation method (balance method) is used, based on the law of conservation of heat. For an extended body of sufficiently large dimensions, the process of heat transfer in it is assumed to be linear, and the coordinate system with the center is taken to be on the axis of the body. The presented mathematical model of thermal processes in the “concrete-soil” system makes it possible to predict the modes of holding monolithic concrete to achieve the necessary technological requirements, as well as to apply the most economical modes.