State-bounded directional accumulation in post-liquefaction sand: A hypoplastic formulation for asymmetric cyclic deformation

Experiments on saturated sand show finite, bilateral post-liquefaction strain accumulation with a larger strain excursion on the triaxial-extension (TE) than on the triaxial-compression (TC) side, whereas existing constitutive treatments still struggle to reproduce this asymmetric response without persistent or unbounded directional accumulation. To address this gap, a state-bounded directional mechanism is introduced into the hypoplastic model by coupling a smooth three-dimensional loading-direction weighting with the evolving semifluidized state, requiring only one additional material parameter, k A . After calibration against one cyclic test, the same parameter set is applied unchanged to two additional density–loading conditions. Additional cross-path evaluations further cover monotonic and cyclic drained and oedometer tests, together with stress- and strain-controlled CU loading conditions. The model reproduces the measured TE-biased strain partition while largely preserving the effective-stress path and loop half-width. The mean absolute error of the final-cycle centre decreases from 1.34 % to 0.20 %, an improvement of approximately 85 %. Long-cycle analysis shows that a permanent directional bias produces persistent ratcheting, reaching a cycle centre of − 24.82 % at 200 cycles, whereas the proposed model retains a finite offset of − 3.05 % with a strongly decaying per-cycle drift. Activity ablations identify the state-exhaustion term as the key ingredient governing long-cycle boundedness, while pressure activation localises and scales the mechanism during semifluidized excursions. Parameter sensitivity further shows that k A primarily governs directional strain redistribution with little influence on overall loop widening. The proposed formulation therefore provides a compact constitutive route for representing finite, asymmetric, and long-cycle-bounded post-liquefaction deformation without sacrificing the established cyclic-mobility response.