Application of the improved twin-shear unified strength theory to the multiaxial strength of S2 columnar ice

An enhanced twin-shear unified strength theory is presented in this study, effectively decoupling the dual effects of intermediate principal stress on S2 columnar ice. By introducing two novel parameters, ${\lambda }_1$ and ${\lambda }_2$, the improved model separately quantifies the weakening and strengthening contributions of ${\sigma }_2$ to the multiaxial strength, thereby overcoming limitations in traditional formulations where these effects were coupled. The rate-dependent behavior and anisotropic responses under various loading directions are not only captured by the proposed model, but its descriptive scope of the intermediate principal stress inflection points is also extended from a linear to a surface-based representation. Biaxial and triaxial experimental data are systematically analyzed to validate the model, with results indicating a significant increase in both the strengthening and weakening effects as strain rates rise. Furthermore, the enhanced theory is integrated into a constitutive framework to compute the variable failure envelope of S2 columnar ice, which is subsequently implemented in Four-dimensional Lattice Spring Model (4D-LSM). Numerical simulations demonstrate that the modified envelope surface accurately reproduces experimental observations across diverse strain rate conditions and loading orientations. An orthotropic envelope surface design is also proposed to incorporate anisotropy induced by columnar jointing, thereby lending physical significance to the modification term. Moreover, the refined formulation bridges the gap between theoretical analysis and practical simulation, providing a robust framework for evaluating complex multiaxial stress states in anisotropic ice. Overall, comprehensive insights into the intermediate principal stress effects are provided in this study, and the characterization of S2 columnar ice is significantly improved.