A compressive rate-dependent hypoplastic constitutive model and numerical application in SPH for granular soil

Abstract

The mechanical behavior of granular soil is significantly influenced by the strain rate to which it is subjected. However, there is currently no widely applicable constitutive model that effectively captures the rate-dependent behavior of granular soil across the spectrum from quasi-static to extreme dynamic loading conditions. This paper presents the findings from both physical and numerical experiments, demonstrating that particle strength displays three distinct regimes over a strain rate range of 10⁻⁶ to 10⁵ s⁻¹ resulting from the competition between coexisting thermally activated and macro-viscous mechanisms. Given that particle strength is associated with the granular hardness (h_s), this study proposes a compressive rate-dependent hypoplastic constitutive (CRDHC) model by establishing a rate-dependent h_s. Furthermore, the significantly elevated initial stiffness resulting from high strain rates and the concave limit stress surface induced by denser states are addressed through small strain stiffness and stress transformation, respectively. The proposed CRDHC model is validated through a one-dimensional quasi-static test and a Split Hopkinson Pressure Bar (SHPB) test, and it is implemented numerically using the Smoothed Particle Hydrodynamics (SPH) meshfree method. The method incorporates the substepping scheme with error control and stability correction at minimal stress states to establish a comprehensive framework for granular soil under low to high strain rates. Both discharge of silo and high-velocity penetration are simulated to validate the efficiency and accuracy of the framework in capturing the rate-dependent response in large deformation problems.