Estimating residual stress in the restrained ring test under circumferential drying

The restrained ring test is becoming widely used as a standard test method to assess the potential for early-age cracking in concrete mixtures. Previous research focused on the development of analytical solutions for quantifying residual stress development in restrained ring specimens that either assumed that the ring was thin (i.e., a thin wall approximation) or that the shrinkage was uniform along the radial direction for a thick-walled ring. This paper presents an analytical solution to consider the influence of moisture gradients that occur when a thick-walled ring specimen dries from the outer circumference. Toward this end, the ring that dries from the outer circumference is treated as the superposition of a stress field that is caused by external restraint and a stress field that arises due to differential shrinkage. An analytical expression is presented to estimate the stress components. To assess the suitability of the analytical solution, it was compared with results from a finite element analysis and a reasonably good agreement was observed.