Modeling of Capillary Shrinkage and Cracking in Early-Age Concrete
Authors: Leonovich S. N. 
Published: July 2018

. Scientific hypothesis on moistening shrinkage mechanism for cement stone and concrete has been assumed as a basis for the present paper. Physical ideas on a mechanism for cracks volume increment in a concrete model presented as two-level structure have been accepted as a theoretical basis for a calculation method of crack resistance during capillary shrinkage. These ideas are the following: a matrix of hardening cement stone with inclusions and emptiness of various forms (cracks) as result of influences that change an intense deformed state in a point and a volume. The following assumptions have been accepted while making a theoretical justification for a calculation method of shrinkable concrete crack resistance. Following this methodology approaches of fracture mechanics according to a generalized criterion have been applied in the paper. Concrete is considered as an elastic quasi-homogeneous two-component medium which consists of the following parts:

a) constructive part: a matrix – a cement stone with structural elements of crushed stone, sand; b) destructive part: emptiness – capillaries cracks and pores (cavities with initial cracks in walls). Emptiness in a matrix and contact zones are presented by a coordinated five-level system in the form and sizes which are multiple to a diameter due to impacts while reaching critical sizes. These critical sizes make it possible to pass from one level into another one according to the following scheme: size stabilization – accumulation delocalization – critical concentration in single volume – transition to the following level. Process of cracks formation and their growth are considered as a result of non-power influences on the basis of crack theory principles from a condition that fields of deformation and tension creating schemes of a normal separation and shift occur in the top part of each crack at its level in the initial concrete volume. Ксij(t) parameter as algebraic amount of critical values Kij in the whole system of all levels of cracks filling canonical volume up to critical concentration has been accepted as a generalized constant of property for concrete crack resistance in time, its resistance to formation, accumulation in volumes of micro-cracks and formation of trunk cracks with critical values. External temperature, moistening long influences create fields of tension in the top parts of cracks. Concrete destruction processes due to cracks are considered as generalized deformedintensed state in some initial volume having physical features which are inherent to a composite with strength and deformative properties. It is possible to realize analytical calculations for assessment of tension and crack resistance of concrete at early age on the basis of a generalized criterion in terms of stress intensity factor due to modern experimental data on capillary pressure value (70 kPa in 180 min after concrete placing). The developed algorithm of calculation allows to consider factors influencing on capillary pressure: type of cement, modifiers and mineral additives, concrete curing conditions.