Stability Assessment of Shallow Foundations above a Subsurface Cavity: Implications for Natural Hazard Mitigation

Abstract Shallow foundations over subsurface cavities are particularly vulnerable to subsidence, sinkhole formation, and differential settlement, posing significant geotechnical hazards in urban environments. This study investigates the ultimate bearing capacity of shallow foundations above a square subsurface cavity in cohesive–frictional soils using finite-element limit analysis (FELA). The dimensionless stability number ( N s ) is employed to quantify the influence of cavity geometry, depth ( N / B ), lateral offset ( M / B ), and soil properties, including the friction angle ( ϕ ) and unit-weight factor ( γ B / c ), on foundation performance. Results indicate that foundation stability is minimum when the cavity lies directly beneath the footing ( M / B = 0 ) and progressively improves with lateral offset, becoming relatively insignificant beyond M / B ≈ 4 . Low-friction soils ( ϕ ≤ 10 ° ) and high γ B / c exacerbate crown yielding, enlarging the effective influence zone and increasing subsidence risk. Shallow cavities ( N / B ≤ 2 ) significantly reduce N s , whereas deeper cavities ( N / B ≥ 4 ) exhibit minimal influence due to overlying soil confinement and arching effects. Three distinct failure mechanisms are observed: punching failure, where the footing penetrates the cavity roof under minimal soil cover; cylindrical shear wedge, forming asymmetric deformation at moderate offsets ( M / B = 2 – 4 ); and general shear, representing symmetrical plastic wedges for deeper cavities ( N / B ≥ 4 ). Higher friction angles enhance N s , emphasizing the role of soil shear strength in mitigating instability. The study identifies critical cavity positions, depths, and soil conditions for safe foundation design, providing quantitative guidance for hazard mitigation and risk assessment in subsurface cavity-prone regions. The developed stability contours and failure transition maps provide a practical framework for preliminary hazard assessment and safe foundation planning in subsurface cavity-prone regions.