LOWER BOUND LIMIT ANALYSIS ON BEARING CAPACITY OF SLOPE AND ITS RELIABILITY
边坡极限承载力的下限分析法及其可靠度理论

The lower bound limit analysis is applied to evaluate the undrained bearing capacity of a slope. In order to invoke the lower bound theorem of classical plasticity theory, a perfectly plastic soil model with an associated flow rule is assumed. The stress field is modeled using linear 3-noded triangles and statically admissible stress discontinuities may occur at the edges of each triangle. To ensure the solution obtained is a strict lower bound on the exact collapse load, the linetrized yield surface must lie inside the Tresca yield surface. Imposition of the stress boundary, equilibrium and yield conditions lead to an expression for the collapse load, which is maximized subject to a set of linear constraints on the nodal stresses. The lower bound solution so obtained can be applied directly in practice because it is inherently conservative. The comparisons between the bearing capacities of strip footing from classical plasticity theory and lower bound limit analysis illustrate the effectiveness and correctness of the procedure. The stochastic linear programming problems which are produced by introducing random variables in lower bound limit analysis is solved by Monte Carlo simulation techniques in corporation with the using of MATHCA quicksheet. The stochastic linear programming becomes a distribution problem when random variables appear only on the right hand of the equation, and a more efficient program is proposed to obtain the reliability index based on the method of the probability of intervals.