Lower Bound Finite Element Limit Analysis of Geo-Structures with Non-Associated Flow Rule

• Published in: Computers and geotechnics Vol. 147; p. 104803
• Main Authors: Payan, Meghdad, Fathipour, Hessam, Hosseini, Maryam, Jamshidi Chenari, Reza, Shiau, Jim S.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.07.2022; Elsevier BV
• Subjects: Analysis; Bearing capacity; Constitutive models; Design; Finite element limit analysis (FELA); Finite element method; Flow stability; Friction; Internal friction; Lateral earth pressure; Limit analysis; Lower bound; Lower bounds; Mathematical models; Non-associated flow rule; Objective function; Optimization; Second-order cone programming (SOCP); Shallow foundations; Soil; Soil conservation; Soil stability; Soils; Stability; Stability analysis; Structural stability; Structures; Finite element limit analysis (FELA); Lower bound; Lateral earth pressure; Bearing capacity; Second-order cone programming (SOCP); Non-associated flow rule
• ISSN: 0266-352X; 1873-7633
• DOI: 10.1016/j.compgeo.2022.104803

The use of finite elements and limit analysis in the stability analysis of geo-structures is not uncommon nowadays, with the assumption of associated flow rule and rigid perfectly plastic constitutive soil model. Nevertheless, the simplified assumption may lead to misevaluation of the objective function for the nonlinear optimisation solution, thus giving rise to uncertainty in the design of geo-structures. In this study, the influence of non-associated flow rule on the stability evaluations for obliquely- and eccentrically-loaded shallow foundations, as well as for retaining structures with cohesionless granular backfill, is examined using lower bound finite elements and second-order cone programming (SOCP). A wide range of dilation angles (ψ) is considered for the study (e.g., from zero to a maximum of soil internal friction angle φ), and it is generally observed that failing to consider the non-associated flow rule in the soil constitutive model would yield non-conservative designs of geo-structures. These inaccurate predictions and subsequent unreliable stability analysis are more pronounced in cases of large soil internal friction angles. The findings in this study would be of great importance for practical design applications.