A new three-dimensional limit analysis formulation that uses the recently developed discontinuity layout optimization (DLO) procedure is described. With DLO, limit analysis problems are formulated purely in terms of discontinuities, which take the form of polygons when three-dimensional problems are involved. Efficient second-order cone programming techniques can be used to obtain solutions for problems involving Tresca and Mohr-Coulomb yield criteria. This allows traditional 'upper bound' translational collapse mechanisms to be identified automatically. A number of simple benchmark problems are considered, demonstrating that good results can be obtained even when coarse numerical discretizations are employed.

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Switches and crossings are a critical part of railway infrastructure and have a complex superstructure, creating variable support and bending stiffness along the track length. These variable structural and loading effects lead to faster rates of track geometry deterioration compared with plain line. Multibody vehicle-track interaction and finite element models combined with empirical predictions have been used to assess the likely benefits and improvements of using an asphalt layer combined with reduced ballast depth under S&C, in terms of long-term ballast differential settlement as well as in terms of reducing stress levels within the ballast and the subgrade layers. The assessment is primarily comparative against a baseline scenario site without asphalt layer. The introduction of asphalt track configurations reduced the variation in trackbed stiffness and increased stiffness throughout the switch panel. Using stresses calculated from finite element modelling, the ballast settlement was calculated using a semi-empirical equation to account for higher load cycles. The introduction of the asphalt layer reduced both maximum and differential settlements, originating from the ballast layer, in the switch panel with respect to the baseline scenario. Furthermore, the maximum stresses transmitted to the subgrade are generally reduced for both asphalt thicknesses with respect to the baseline.