Simulation study links hybrid machine learning to ring-foundation capacity in variable soils

A simulation study in Scientific Reports reports that a hybrid finite element limit analysis and machine-learning framework predicted normalized bearing-capacity and safety factors for ring foundations in spatially variable cohesive-frictional soils. According to the abstract, the convolutional neural network achieved an R² above 0.95 and relative errors below 3% across the generated dataset.

The researchers generated the dataset with finite element limit analysis using OptumG2. Their random-field model represented effective cohesion, c′, with a lognormal distribution, a depth-linear mean of µc′ = 10 kPa, a gradient of k = 1 kPa/m and a coefficient of variation of 0.3, together with friction angles, φ′, up to 40°. The simulations examined complete, internal-half, middle-half and external-half loading; inner-to-outer radius ratios from 0 to 0.9; rough and smooth interfaces; and nine anisotropic cases with horizontal scales of fluctuation of 10–60 metres and vertical scales of 2–8 metres.

Within those modeled conditions, complete and external-half loading produced the highest bearing capacities, while internal-half loading reduced capacity by as much as 40%. The abstract further reports that spatial variability in effective cohesion and friction angle contracted modeled failure envelopes by 10–25%. These results are predictions from the simulation dataset rather than measurements from constructed foundations.

The authors describe the framework as a way to support preliminary design, optimization and risk assessment while reducing computational demands relative to traditional finite element limit analysis and Monte Carlo approaches. Its reported performance remains bounded by the simulated soil properties, geometry, interface conditions and loading configurations. The available abstract does not describe a physical field test or independent validation in actual ring foundations, so the findings should be interpreted as model-based evidence rather than demonstrated performance in construction projects.

Subject of Research: Hybrid FELA and machine-learning prediction of ring-foundation bearing capacity in spatially variable cohesive-frictional soils

Article Title: Bearing capacity and safety factors of ring foundations in spatially variable soils: a hybrid FELA-machine learning approach

Article References: Mohammadizadeh, M., & Mohammadizadeh, M. (2026). Bearing capacity and safety factors of ring foundations in spatially variable soils: a hybrid FELA-machine learning approach. Scientific Reports. https://doi.org/10.1038/s41598-026-75645-3

Image Credits: AI Generated

DOI: 10.1038/s41598-026-75645-3

Keywords: ring foundations, bearing capacity, safety factors, finite element limit analysis, machine learning, convolutional neural network, spatially variable soils, random fields, cohesive-frictional soils, geotechnical engineering, Bearing, capacity