Study of the Stress Concentration Factor Under Circular Surface Loading as Affected by Soil Strength Properties: Finite Element Simulation and Experimental Validation

The theory of stress distribution in soil based on continuum mechanics introduces a stress concentration factor (ξ) of 3 for a purely elastic soil and larger than 3 for an elastic–plastic soil material. However, the experimental estimation of ξ as a function of loading geometry and soil properties is a challenge. Furthermore, the insertion of a stress probe into the soil exacerbates the stress concentration due to the arching effect.

The aim of this study is to model ξ under circular surface (uniform) loading as a function of soil strength, loading area, and depth using finite element method.

The simulations were performed using a model of stress propagation under circular uniform loading in two parts: with and without a stress probe. Simulations were carried out for combinations of 21 soil properties of varying water content and cone index (CI), surface loading radius (R), soil depth (z), and surface stress (q). For each combination, the stress at a given depth (σ_z) and the resulting concentration factor (ξ) were analyzed.

A total of 1512 values were obtained for ξ from simulations. Regression models were developed and validated for with-probe and without-probe ξ as a function of CI, R, z, soil yield stress (σ_yield), and vertical stress (σ_z). Experimental data of stress measurements under plate sinkage loading for samples of a clay loam soil at two levels of water content each at two levels of bulk density were used to validate the with-probe regression model.

The values obtained from the model and those from the experimental tests showed a relatively good correlation with R² of 0.7. ξ varied between 3.5 and 14 which is much larger than the values obtained for the without-probe model or reported in the literature.