Energy dissipation models of soil nails for 3D upper bound analyses of steep reinforced slopes

Abstract

Analytical energy dissipation models of nail-soil systems under the ultimate limit state are rare. In this study, a rigorous plastic energy dissipation model (RPEDM) is employed and a pseudo-plastic energy dissipation model (PPEDM) of nails is proposed to analyze the stability of nailed slopes. In the RPEDM, the energy dissipation rate of nails was assumed to be independent of nail-grout interaction. However, in the PPEDM, the nail-soil interaction was analytically accounted for. Based on the upper bound of the plastic theorem, the RPEDM and PPEDM are then incorporated into a three-dimensional discretized failure mechanism to analyze the stability of steep nailed slopes. External work rates and energy dissipation rates are computed to formulate the work rare balance equation, followed by a global search of the critical factors of safety (FS). A comparison with numerical simulations and existing solutions demonstrated that: (1) the RPEDM obeyed the basic principle of the plastic theorem but the estimated FSs had a significant discrepancy with numerical simulations; (2) the PPEDM could predict more accurate FSs and variation of axial forces mobilized within nails compared with the RPEDM but the FSs obtained by PPEDM did not provide rigorous upper bound solutions since “elastic energy dissipation” was factored in the analysis; (3) the PPEDM can degrade into RPEDM if the width of the nail-soil interaction zone is equal to zero. In the end, the RPEDM and PPEDM were used to explore the effects of the layout and the size of nails on the FSs of steep nailed slopes.