Research and Application of a Polycrystalline Ice Softening Constitutive Model Based on Triple-shear Unified Strength Theory

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As global warming intensifies, mountain and polar glaciers are retreating at an accelerated pace. The frequency of large-scale glacier collapse and sliding is gradually increasing. Polycrystalline ice constitutes the primary form of glacial ice. The constitutive model of polycrystalline ice holds significant importance for glacier stability analysis, mass balance, and multi-field coupling simulation. Drawing from the Triple-shear unified strength theory, we propose yield and plastic potential functions that can effectively account for the influence of principal stress. Considering the variation of cohesion throughout the loading process, we construct a hardening function based on equivalent plastic strain. An elastoplastic constitutive model with non-associated flow is established to capture the softening characteristics of polycrystalline ice. The validity of this model is confirmed through conventional triaxial compression tests of polycrystalline ice, demonstrating its ability to accurately describe axial strain-deviator stress and axial strain-volumetric strain behaviors. Subsequently, we predict the true triaxial axial strain-deviator stress and axial strain-volumetric strain behaviors of polycrystalline ice under different medium principal stress coefficients. Our predictions reveal significant softening in the deviator stress-axial strain curves of polycrystalline ice, with both residual strength and peak strength increasing with the influence coefficient of the medium principal stress. Volumetric strain exhibits an initial shrinkage followed by expansion with axial strain, with the maximum shrinkage and expansion increasing alongside the influence coefficient of the medium principal stress. Furthermore, we derive and incorporate the finite difference scheme of the elastic-plastic constitutive model into Flac3d numerical software, verifying its effectiveness through a single element simulation. In the context of global warming, these research findings are poised to offer a theoretical and numerical foundation for predicting glacier stability.

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