Stability of Retained Soils Behind Underground Walls with an Opening Using Lower Bound Limit Analysis and Second-Order Cone Programming

Lower bound finite element limit analysis in conjunction with second-order cone programming is developed and employed to investigate the stability of retained soils behind underground walls with an opening in cohesive-frictional soils. In this study, two-dimensional plane strain condition is setup for modelling the problem while the lower bound solution of the problem is obtained by employing the finite element approach of lower bound limit analysis. The lower bound optimization problem is cast as the second-order cone programming, and is solved by a conic programming algorithm. For practical use, the results of lower bound solution are summarized in the form of dimensionless stability charts of the load factor that is a function of the cover depth ratio of opening, overburden stress factor and soil friction angles. Plastic yielding zones predicted from the lower bound analysis are discussed and examined for these dimensionless parameters while the computed lower bound solutions are validated with an existing solution. Finally, a closed-form approximate expression is developed for predicting the lower bound solution of the load factor for the problem with practical ranges of cover depth ratios of opening, overburden stress factors, and soil friction angles. New opening stability factors with respect to soil cohesion and unit weight as a function of cover depth ratios of opening and soil friction angles are presented.