Quasi-Static Analysis of Reinforced Soil Slopes Stability in Plane Strain Mode by Upper Bound Limit Analysis Method

Reinforcement of soil structures such as slopes and walls has become an accepted engineering practice in the last three decades. This paper focuses on reinforced slopes; in particular, the required strength of reinforcement and its length necessary to avoid collapse during seismic events in special factor of safety (FS). The seismic influence is substituted with a quasi-static horizontal force. The reinforcement considered here is of a geosynthetics type (geogrids or geotextile), and it contributes to the stability of the structure only through its tensile strength (the reinforcement's resistance to shear, torsion and bending is negligible). Calculations were performed assuming uniform distribution of reinforcement strength through the slope height, and assuming the Mohr-Coulomb failure criterion holds for the soil. The technique of calculations is based on the kinematic theorem of limit analysis. This theorem states that the rate of work done by traction and body forces is less than or equal to the rate of energy dissipation in any kinematically admissible failure mechanism. Algorithms were written, based on two main mechanisms; (a) several horizontal hexagonal blocks and one pentagonal block at the bottom for overall failure mechanism, and (b) Two pentagonal blocks for direct sliding mechanism. Numerical optimization methods were used to determine FS and critical failure surface. Required reinforcement strength calculated with this assumption that the reinforcement fails by plastic flow referred here as tensile rupture. This happens only when the reinforcement is of sufficient length. The length of reinforcement was also calculated, based on collapse mechanisms that include rupture in some layers and pull-out in others, and the last set of calculations for required length was performed assuming a different mode of failure: direct sliding. For each mechanism, a non-linear equation and a numerical method of optimization was used for solving the equations. The results obtained in this study are presented as dimension less charts which can be used in design, and to evaluate the effect of different parameters such as geometrical parameters of the slope, soil strength, and seismic coefficient on the reinforced soil slopes stability. Obtained results may be applicable to walls, although design of walls requires consideration of additional failure modes not presented here. The results clearly indicate how the required strength increases with decrease in the internal friction angle, increase in the slope inclination angle and increase in the seismic coefficient. The required length is almost in dependent from slope inclination angle in direct sliding mechanism.