Numerical limit analysis of three-dimensional slope stability problems in catchment areas

• Published in: Acta geotechnica Vol. 11; no. 6; pp. 1369 - 1383
• Main Authors: Camargo, Júlia, Velloso, Raquel Quadros, Vargas, Euripedes A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2016; Springer Nature B.V
• Subjects: Catchment areas; Catchments; Complex Fluids and Microfluidics; Engineering; Foundations; Geoengineering; Geotechnical Engineering & Applied Earth Sciences; Hydraulics; Mathematical models; Mathematical programming; Numerical analysis; Optimization; Optimization techniques; Pore pressure; Porosity; Pressure effects; Research Paper; Risk analysis; Slope stability; Slopes; Soft and Granular Matter; Soil Science & Conservation; Solid Mechanics; Stability analysis; Water flow; Watersheds; 3D problems; Stability analysis; Numerical limit analysis; Pore pressures
• ISSN: 1861-1125; 1861-1133
• DOI: 10.1007/s11440-016-0459-3

Risk analysis of existing slopes in catchment areas requires quantification of their stability. This quantification becomes particularly difficult when dealing with larger areas under 3D conditions and including saturated and unsaturated water flow. This paper proposes the use of an effective numerical procedure to solve three-dimensional slope stability problems in large areas subjected to pore pressure effects. This numerical approach, numerical limit analysis, utilizes the finite element method and mathematical programming techniques. Mathematical programming is needed because the basic plasticity theorems for limit analysis can be cast as optimization problems. The generated optimization problem is formulated under a second-order cone programming framework, which is known to solve large-scale problems with great computational efficiency. The main objective of this work was to determine the slope safety factor and the collapse mechanism of soils governed by the Drucker–Prager yield criterion for large-scale 3D problems including pore pressure effects. This approach is applied to an experimental catchment in the Oregon Coast Range that failed after an intense rainfall. The results were compared with a previous stability analysis of the area available in the literature that used a novel 3D limit equilibrium method.