Rheological Equations of State of Concrete

A quasilinear representation of a nonlinear rheological equation of concrete state has been established, derived on the basis of the concept of statistical strength distribution of individual fractions combined to form a structural element. In the nonlinear formulation for ageless concrete, L. Boltzmann’s well-known principle of superposition of creep deformations is realized by increments of structural stress of fractions capable of force resistance under non-decreasing loading. For aging concrete, in contrast to previous approaches, the superposition of partial increments of deformations generated by increments in stress levels is implemented. This leads to the correct consideration of concrete aging, clarifying the type of known rheological equations. Quasilinear forms of rheological equations that are convenient in applications are given. The concept of the strength structure of concrete and the identity of the aging functions of strength, modulus of elasticity and creep make it possible to reduce the creep equation to a linear differential equation with constant coefficients. This simplifies, in particular, the solution of stress relaxation problems, which are important in the calculations of structures for long-term safety.