Spectral analysis of random shrinkage stresses in concrete

Random variation of environmental humidity is characterized by its power spectrum, and random variation of pore humidity and stresses in a halfspace is analyzed under the assumption that the problem is linear (or linearized). The diffusion equation and the superposition integral for stress relaxation are used. The dependence of both the creep properties and the drying diffusivity on age is taken into account. Complex variable expressions for the frequency response functions of humidity and stress are obtained and are evaluated numerically. In contrast to nonaging structures, these functions depend on both the current age of concrete and the age when drying starts. The standard deviations of pore humidity and of stress exhibit oscillations about a drifting mean. For typical diffusivities of concrete, the solution is nonstationary for at least 50 yr, and for environmental fluctuations whose period does not exceed one year, the fluctuations are not felt at depths over 20 cm below the surface. Since, even for aging structures, the spectral densities of input and response are related algebraically, the spectral method is computationally more efficient than the impulse response function method, in which the autocorrelation functions of the input and the response are related by integrals.