Analytical model for concrete crack width of steel lined reinforced concrete penstock

Abstract

Cracking in steel lined reinforced concrete penstock (SLRCP) poses substantial challenges to both serviceability and safety, particularly when crack width exceeds specified limits. Despite its critical implications, accurately calculating crack width remains a persistent challenge. To address this issue, a multi-layer steel-concrete ring analytical model is derived through the concept of orthotropic and thick-walled cylinder theories. In this model, the cracked concrete is assumed to be an orthotropic material incorporating both elastic modulus reduction and tensile softening behavior based on its cracking characteristic of radial penetrating cracks uniformly distributed on the circumference. The steel liner and reinforcing steel bar are modeled as continuous steel rings using equivalent stress theory, while thick-walled cylinder theory is applied due to geometric features and bearing characteristics. Crack width is determined through equilibrium of force and compatibility of deformations at steel-concrete interfaces, utilizing these assumptions and the developed calculation model. To validate the proposed model, data from prototype observations and large-scale model tests of SLRCPs were systematically collected. The crack width results obtained from the proposed model exhibit strong agreement with the collected data, confirming its accuracy and reliability. In conclusion, the proposed analytical model provides an effective solution for calculating the crack width of SLRCP and offers valuable insights for durability evaluation.