Stochastic numerical approach to the bearing capacity of adjacent footings on spatially variable soils

Abstract The interaction of adjacent footings in spatially variable soils presents significant challenges in geotechnical engineering, particularly when soil heterogeneity introduces uncertainty into foundation performance. Traditional deterministic methods provide valuable insights into bearing capacity (BC) and settlement behaviour; however, they capture the complex interactions arising from spatial variability. This study employs the random finite element method to investigate how anisotropic random fields affect the BC of adjacent footings. The problem is considered in three distinct soil types: perfectly cohesive, purely frictional, and cohesive-frictional. A series of numerical simulations is conducted to examine the effects of foundation spacing and the spatial variability of soil properties. Deterministic results indicate that BC increases at the critical spacing but gradually diminishes as the spacing increases further. Probabilistic analyses reveal that soil heterogeneity significantly impacts foundation behaviour, particularly in non-cohesive soils, where the coefficient of variation of BC is highly sensitive to spatial fluctuations. Reliability-based assessments reveal that failure probabilities vary significantly depending on soil type and correlation structure, underscoring the importance of stochastic modelling in geotechnical design. These findings contribute to the development of risk-informed design methodologies, highlighting the importance of modelling spatial variability using stationary random fields. As shown, such approaches enhance foundation reliability assessments and informed engineering decision-making.