Classical upper bound slip-line mechanisms can be accurately and robustly generated using Discontinuity Layout Optimization (DLO) methods for any geometry of problem, using a wide range of failure criteria relevant to geotechnical problems  including Mohr-Coulomb and Tresca.

At the heart of the DLO procedure is a simple yet robust and highly efficient algorithm that can identify the critical failure mechanism from a very large number of possibilities, such that the upper bound solution is typically very close to the true plastic solution.

Furthermore, the core optimization goals can also be 'reversed' to generate powerful geotechnical design tools. 

Key Publications

Smith C & Gilbert M (2007) Application of discontinuity layout optimization to plane plasticity problems. Proceedings Royal Society A, 463(2086), 2461-2484. 

Smith CC & Gilbert M (2013) Identification of rotational failure mechanisms in cohesive media using discontinuity layout optimization. Geotechnique: International Journal of Soil Mechanics, 63(14), 1194-1208. 

Smith CC & Gilbert M (2015) Modelling rotational failure in confined geometries using DLO. Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics, 168(4), 155-168. 

Smith CC & Cubrinovski M (2011) Pseudo-static limit analysis by discontinuity layout optimization: Application to seismic analysis of retaining walls. Soil Dynamics and Earthquake Engineering, 31(10), 1311-1323.