Raiter O. Mathematical models for assessing the durability of fiber-reinforced concrete structural components under creep conditions

Applying the first law of thermodynamics on the balance of energy components and the balance of the energy components change rates, a general mathematical model is created – differential equation with initial and final conditions for determining the durability of fiber-reinforced concrete structural elements with initial bulk damage due to static load causing local creep - delayed crack growth, deformation and drawing of fibers. At the same time, the below assumptions and provisions are introduced: matrix and fiber materials are linearly elastic, homogeneous and isotropic; cracking in concrete occurs after the stresses have reached the concrete strength (except for the initial microcracks); the opening of the obtained microcracks and the drawing of fibers from concrete is considered to be the main mechanism of its creep; the fiber concrete tensile diagram is piecewise linear; for simplicity of calculations, the tensile diagram section corresponds to the second stage of deformation, is approximately depicted as rectilinear, like in compression; the fibers (of the same circular section and length) in the element under consideration are evenly spread in all directions and work only for tensile; the fibers and concrete are fully bonded (therefore, the deformation of the fiber is equal to the deformation of the composite); a complete diagram of the creep to the fracture of fiber concrete is implemented. Based on the analysis and synthesis of experimental studies of the fiber-reinforced concrete creep and the least squares method, an analytical dependence of the creep change on time and the magnitude of stress is created. The model is used to predict the durability of a fiber-reinforced concrete slab with a circular hole during long-term bilateral tensile causing creep in the hole area. It was revealed that even with a slight increase in the load within the second stage of the stress-strain state, the durability of the plate decreases sharply. A computational model has been developed to determine the durability of fiber-reinforced concrete structural elements with spherical cavities during their long-term tensile. This is built on an energy approach and a simplified tensile diagram of fiber concrete. The application of this model is demonstrated on a task with specific operational parameters of fiber concrete and a diagram of its creep. Applying the above-mentioned energy approach, a computational model is created for determining the durability of a fiber-concrete beam under pure bending by moments causing a damaged zone of initial depth and bulk in which creep is realized in the upper tensioned fibers. At the same time, the true hypothesis of plane sections was accepted. In the absence of experimental data on the compression zone, in order to assess the durability of the beam in the first approximation, it is suggested to use the dimensions of rheological characteristics as well as for the tensile zone (symmetrical bending). The influence of the flexing moment on the durability of the fiber-concrete beam is estimated. Based on the analytical relations known in the literature, a computational model was developed and based on it, the residual durability of a fiber-concrete beam with prestressed reinforcement weakened by two segmental creep cracks during its prolonged static bending was calculated. It is demonstrated that the presence of even sufficiently small cracks in the reinforcement leads to a sharp decrease in the residual durability of the reinforcement, and consequently of the fiber-concrete beam as a whole.