A nonlinear Unified Hardening model for breakable siliceous mudstone coarse-grained soil under low confining pressure considering penetrating erosion

The stress–strain behavior of brittle siliceous mudstone coarse-grained soils (SMCGSs) under penetrating erosion critically affects the stability of SMCGS-filled embankments in erosion-prone areas, yet remains insufficiently understood, particularly regarding particle crushing and critical state behavior under low confining pressures. This study proposes a modified constitutive model to characterize erosion-induced mechanical degradation and nonlinear critical state evolution. A normalized parameter ϑ , derived from the principle of crushing equivalence, is introduced to capture the coupled effects of particle breakage and critical state shifts under varying erosion intensities. Along with a nonlinear tuning index δ , this parameter is integrated into the Unified Hardening model for low confining pressure (UH-L), resulting in the N-UH-LE model. Consolidated drained (CD) triaxial tests under confining pressures of 100-400 kPa are conducted for model calibration and validation. The model predictions exhibit strong agreement with experimental results, with a maximum relative error of 7.76%. The N-UH-LE model successfully reproduces key mechanical responses, including hardening, softening, shear dilation, and volumetric changes across different erosion levels. Furthermore, erosion-induced degradation decreases with lower confining pressures and higher initial void ratios ( e 0 = 0.3, 0.5, and 0.7), while variations in interlocking strength ( τ 0 cot φ = 40 kPa, 80 kPa, and 120 kPa) show limited influence. • Define a normalized ϑ linking coarse-grain crushing and critical-state behavior across penetrating-erosion intensities. • Embed ϑ and tuning index δ into UH-L to form N-UH-LE for brittle SMCGS, capturing erosion-driven nonlinear critical behavior. • Calibrate N-UH-LE with CD triaxial tests on SMCGS with/without penetrating erosion; verify validity and predictive power.