Linearised Identification of Mechanical and Structural Anisotropy of Granular Materials from Hollow-Cylinder Experiments

Abstract

Anisotropy in granular materials arises from both the internal fabric and the directionality of the stress state, yet separating these effects experimentally remains challenging. This study develops a first-order linearisation of the incremental stress-strain response that isolates mechanical anisotropy from structural anisotropy using two independent orientation measures. The formulation enables both contributions to be quantified directly from macroscopic laboratory data. The method is applied to hollow-cylinder tests with systematically varied loading directions. Results show that both anisotropy components intensify as the stress state becomes more deviatoric; mechanical anisotropy is consistently stronger; and its relative dominance decreases with increasing deviatoric stress. Comparison with an isotropic hypoplastic model confirms that mechanically induced directional effects are captured even without fabric anisotropy. The framework offers a practical and physically transparent means for quantifying and comparing anisotropy mechanisms in granular materials.

Figures (6)

• Figure 1: Schematics of consolidation stress and loading conditions for non--coaxial test series (left), and stress--coaxial test series (right).
• Figure 2: Effective stress paths (top row) for tests with various $\alpha_{\dot{\varepsilon}}$, and variation of $\frac{\dot{q}}{\dot{p}}$ with $\Omega_\sigma$ (bottom row) for non--coaxial loading experiments with (a, d) $K_c = 1.5$, (b, e) $K_c = 2.0$, and (c, f) $K_c=2.5$.
• Figure 3: Effective stress paths (top row) for tests with various $\alpha_{\dot{\varepsilon}}$, and variation of $\frac{\dot{q}}{\dot{p}}$ with $\Omega_\sigma$ (bottom row) for stress--coaxial loading experiments with (a, d) $K_c = 1.5$, (b, e) $K_c = 2.0$, and (c, f) $K_c=2.5$.
• Figure 4: Variation with $K_c$ of; (a) $A_\sigma$ and $A_F$ parameters from Eq. \ref{['eq:linPhi']}, and (b) the ratio of $\frac{A_\sigma}{A_F}$.
• Figure 5: Predictions of an isotropic hypoplasticity for the cases with $K_c=1.5$ and for two test series; (a) non--coaxial, and (b) stress--coaxial. The model predicts directional dependency for the non-coaxial cases, but not for the stress--coaxial series. In the simulations the mean initial void ratios of the experiments are used: (a) $e_\text{ini} = 0.74$, (b) $e_\text{ini} = 0.72$.