Internal variable gradient model for active earth pressure of rigid retaining wall moving with translation

The instability of retaining wall is a key factor for many geo-hazards, such as landslides. To estimate the stability of retaining wall, the distribution of earth pressure is necessary. The results of in-situ observations and indoor experiments demonstrate that the distribution of earth pressure behind the retaining wall exhibits remarkable nonlinearity. When the results are analyzed in details, the oscillation and quasi-periodicity of the distribution of earth pressure are observed, which has not been given widely concerns and cannot be described by the existing analytical models. Based on the internal variable gradient theory and operator averaging method, a gradient-enhanced softening constitutive model is proposed in this paper to describe the oscillation and quasi-periodicity of the distribution of earth pressure acting on the retaining wall, by introducing the high-order gradient terms of the hydrostatic pressure into Mohr-Coulomb yield condition. In order to check the applicability of the proposed formulation, the predictions from the formulations are compared with the full-scale and laboratory-scale test results as well as the existing formulations. It is noted from the comparisons between predicted and measured values that the results of gradient-dependent softening constitutive model provides the comparable approximations for active earth pressure and describes the oscillation and quasi-periodicity very well. This model may enhance the comprehension of soil mechanics and provide a novel view for the design of the retaining wall.