Modeling the Influence of Non-Constant Poisson’s Ratio on Crack Formation Under Uniaxial Compression of Rocks and Concrete

This article considers the effect of constant and variable Poisson’s ratio on cracking in concrete and rock specimens under uniaxial compression using mechanical systems modeling methods. The article presents an analysis of the data confirming the increase in Poisson’s ratio under specimen loading. A system of equations for modeling the effect of Poisson’s ratio on cracking under uniaxial compression is proposed. The comparison showed that the model with a constant Poisson’s ratio predicts a thickness of the surface layer with cracks that is underestimated by approximately 10%. In practice, this means that the model with a constant Poisson’s ratio underestimates the risk of failure. A technique for analyzing random deviations of Poisson’s ratio from the variable mathematical expectation is proposed. The comparison showed that the model with a variable Poisson’s ratio leads to results that are more cautious, i.e., it does not potentially overestimate the safety factor. The model predicts an increase in uniaxial compression strength when using external reinforcement. An equation is proposed for determining the required wall thickness of a conditional reinforcement shell depending on the axial compressive stress. The study contributes to understanding the potential vulnerability of load-bearing structures and makes a certain contribution to increasing their reliability.