Comparison of the reliability of strength limit calculation methods for prismatic samples with different spreading of normal contact stresses in their wedge failure shape

Abstract

This article explores methods for calculating the strength limits of solid objects subjected to compression. Traditionally, two stress distribution patterns are used: the exponential pattern by E.P. Unksov and the linear pattern by L. Prandtl. The authors introduce an enhanced stress distribution method. They compare the accuracy of these methods in calculating strength limits and constructing “normal stress - longitudinal strain” diagrams for wedge-shaped failures in rock samples. Four properties are considered: shear strength, coefficients of internal and external friction, and elasticity modulus. The results show that, with an external friction coefficient up to 0.3, all methods yield similar accuracy in strength limit calculations and ultimate stress-strain curves. Some curves exhibit stress drops, explained by a transition from convex to concave slip lines during failure. Additionally, there are hardening curves in the ultimate curves without theoretical justification. The comparison of calculated strength limits with experimental data confirms the method’s accuracy: 13.7% error for the exponential method, 11.4% for the linear method, and 8.1% for the enhanced distribution, especially for low contact friction values (up to f c=0.3).