A comparative study of granular solid-like and fluid-like constitutive laws

Engineering Technology, University of Twente, 7522 NB Enschede, Netherlands

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Published online: 1 December 2025

Abstract

Continuum models are efficient tools for simulating granular materials at the macroscopic scale. These models rely on constitutive laws that typically capture only solid-like behavior or fluid-like behavior, rarely both. Critical State Soil Mechanics models such as Modified Cam Clay excel at capturing the quasistatic, history-dependent behavior of densely packed granular materials like soils, while rheological models such as the μ(I) rheology capture dense granular flows. This study compares these two constitutive models via two numerical tests of increasing complexity: (1) homogeneous constant-pressure shear flow with varying inertial numbers and (2) a column collapse where spatial gradients evolve during time. We demonstrate that the μ(I)-rheology with corrections describes the steady state and exhibits a large viscosity at low I. For such a model, the column collapse profile is smooth with diffuse shear bands. In contrast, Modified Cam Clay captures the consolidation history of the material. The collapse profile for the normally consolidated state shows layering and results in a bell-shaped pile, while the profile for the overconsolidated state shows chunk-like structures in the pile.