Spectral finite element analysis of random shrinkage in concrete

The spectral method, previously generalized for aging linear systems, is applied in conjunction with the finite element method to analyze shrinkage stresses in aging viscoelastic structures exposed to random environmental humidity. The age-dependence of both drying diffusivity and creep properties are taken into account. The solution of pore humidity is obtained from a matrix differential equation in time, with complex-valued matrices. Elastic shrinkage stresses are then obtained from the matrix equations of the finite element method, in which the matrices are also complex-valued. The stresses in presence of aging creep are determined by a superposition integral in time based on the relaxation function. Numerical examples concerning a long cylindrical vessel exposed at the outer surface are given. The standard deviations of pore humidity and of stresses significantly vary with time, and their standard deviation exhibits fluctuations about a drifting mean. The solution is practically meaningful only if concrete does not crack, e.g., when a prestress sufficient to prevent cracking is introduced. For environmental fluctuations of long periods, such as one year, the computation is quite efficient; however, if shorttime fluctuations are considered, the computing time becomes very large.