# Axisymmetric adaptive upper-bound finite element limit analysis formulation based on second-order cone programming for bearing capacity of circular footing

## TL;DR

This paper introduces a new computational method to accurately estimate the bearing capacity of circular footings using advanced finite element analysis.

## Contribution

A novel adaptive axisymmetric upper-bound finite element limit analysis formulation is proposed using second-order cone programming.

## Key findings

- The proposed method improves computational efficiency by using second-order cone programming.
- Mesh adaptation based on plastic dissipation enhances accuracy with fewer elements.
- Results show the method provides accurate upper-bound solutions for circular footing bearing capacity.

## Abstract

An adaptive axisymmetric upper bound finite element limit analysis (UB-FELA) formulation has been presented for Mohr-Coulomb (M-C) materials in this paper. The computational domain is discretized using quadratic velocity elements. For the sake of computational efficiency, the axisymmetric UB finite element problem is recast into a model of second-order cone programming (SOCP). To enhance the precision of the proposed UB finite element method using a reduced element count, this study implements a mesh adaptation algorithm grounded in plastic dissipation. The collapse loads for determining the circular footings are then estimated by application of the proposed axisymmetric UB limit analysis formulas. By comparing the results to those reported in the literature, the analysis indicates that the method presented in this paper yields an accurate UB solution.