Soil Arching in Dry Sand: Numerical Simulations Using Double-Slip Plasticity Gradient Model

The arching phenomenon is intrinsic to granular materials and is a manifestation of the effects of their discrete microstructure. The fundamental mechanism of arching is the ability of discrete granular particles to transfer loads through force chains. Its effects are reflected through changes in the amount of stresses experienced by underground structures. Recent experiments and discrete element simulations have shown that stress distributions evolve, and different arching patterns form depending on the microstructure. While such studies can highlight the important effects of microstructures on soil arching, their use in developing solutions to arching in the field is limited. This study uses a double-slip gradient model implemented in the ABAQUS finite-element software to account for the microstructural effects and simulates the effects of arching in dry sand. The model assumes plastic deformation in granular materials to consist of dilatant shearing along two active planes. Furthermore, this model uses a gradient term of effective plastic strain that directly incorporates the effects of the material length scale. Numerical simulations were conducted to model the classic trap-door problem. It is found that strains begin to localize and form rupture bands during deformation. Furthermore, the pattern of localization of plastic strains is observed to be dependent on the orientation of the initial slip system. While arching effects were observed to initiate early with trap-door movement, its maximum effect is only realized after full localization. The variation of normalized vertical stress is found to be near linear and reaches a maximum value around a normalized height of 0.8 above the trap-door irrespective of the orientation of the initial slip system. On the other hand, the maximum value of the stress and the value of its reduction is dependent on both the displacement of the trap-door and the initial slip system orientation. It is shown that such a reduction in stresses cannot be predicted by the current analytical formulations, as they do not account for the effects of the microstructure or the amount of displacement.