Radial fictitious cracking of thick-walled cylinder due to bar pull-out

A new analytical model is suggested to describe the radial cracking around a ribbed reinforcement bar embedded in a quasibrittle material such as concrete. The model is based on the partly cracked solution of a thick-walled cylinder, exposed to radial internal pressure. For the partly cracked inner ring of the cylinder an exponential softening model is applied to model the hoop stresses across the fictitious crack. The main advantage of applying an exponential softening relationship instead of a linear or a power-law model, which have been applied in previous investigations, is that the asymptotic behaviour of the exponential softening turns out to be a useful analytical feature. Another difference between the present analytical model and the previous solutions is that the radial displacements in the inner ring are assumed to be equivalent with the linear-elastic displacement field. Furthermore, the solution employs the brittleness number to give a dimensionless description of the problem. Through this brittleness number the size effect of the problem is investigated and it is demonstrated that the maximum capacity of the cylinder has correct small-size and large-size strength behaviour. Finally, the solution is compared with a simplified model, with experimental results and with Tepfers' classic solutions.