Modelling discrete soil reinforcement in numerical limit analysis

Soil reinforcement is widely used in geotechnical engineering. While there are various means of accounting for the presence of soil reinforcement in limit analysis and limit equilibrium type calculations, these are often highly problem-specific. In this paper, a general means of incorporating soil reinforcement within numerical limit analysis calculations is presented. A key feature of this implementation is that the reinforcement is modelled “in parallel” with the soil model, which allows the soil to flow past the reinforcement as might occur in soil nailing. To illustrate this, the “discontinuity layout optimization” (DLO) numerical limit analysis procedure is used, and the efficacy of the approach is evaluated via application to reinforced slope problems involving rigid soil nails under plane strain conditions. The analyses are calibrated against a two-part wedge analysis method, as presented in British Standard BS 8006:1995 or AASHTO’s LRFD bridge design specifications. It is shown that the DLO-based procedure produces identical results only when the two-part wedge collapse mechanism is prescribed in advance (achieved by artificially strengthening the soil except along pre-defined failure planes). A more critical mechanism is otherwise predicted, with the soil strength at collapse required to be approximately 10% higher than predicted by the two-part wedge method (or alternatively, soil nail lengths required to be approximately 20% greater).