Continuous Geometry, Continuous Flow, Continuous Compression: A Numerical Component-Interaction Assessment for Fractional Clay Plasticity

Constitutive models for clays have historically treated yield geometry, plastic-flow direction, and compression as separate problems, with little regard for their interaction. This paper presents a controlled numerical assessment of how three components—Chatwong et al.’s verified teardrop yield surface, a stress-fractional flow rule, and an AJOP-derived hardening modulus— interact when coupled in a 2 × 2 × 2 factorial design. The components are integrated incrementally along one idealized shear-strain-controlled constant-p′ path with an approximate undrained variant for two independently calibrated clays (Boston Blue Clay and London Clay) under a specified state-dependent fractional order. Within this scope, the main flow effect is consistently the largest single quantity for both soils, and the flow × compression interaction is comparably large wherever defined. Compression’s role grows substantially with the overconsolidation ratio, and the main geometry effect is markedly soil-dependent, scaling with the surface-shape parameter. Two structural singularities are identified: a phase-transformation point in the teardrop surface’s non-associated flow rule, absent from the fractional rule, and a hardening singularity in the AJOP-based modulus, whose tangent falls to the swelling index at a finite, soil-dependent preconsolidation stress, bounding the evaluable overconsolidation range of the compression-related interactions; a proportional-κ variant removes this singularity by construction while preserving the factorial ranking, identifying it as a property of the constant-κ embedding, not of AJOP itself. Under an approximate undrained path, the geometry × flow interaction carries over unchanged, while compression’s role is suppressed several-fold. The borrowed yield surface and flow rule are validated independently against 379 points from real undrained triaxial tests across four calibrated soils using this paper’s own re-calibrated predictions; the fractional–AJOP framework itself is assessed for internal consistency only, and its laboratory validation, together with K0, cyclic and multi-axial paths, remains for future work.