Probabilistic Analysis of the Stress-Strain State of Shallow Foundation Considering Non-linear Soil Properties

The evaluation of the stress-strain state of shallow foundations, taking into account the heterogeneity and non-linearity of soil deformation and the requirements for ensuring the reliability and safety of the foundations using a probabilistic approach, allows the full use of the bearing capacity. The objective of this study is to improve the methodology for probabilistic analysis of the stress-strain state of foundations with a computational technique using random sampling, a validated non-linear method and computer programming. It is proposed to use probabilistic analysis to determine the allowable pressure in terms of both ultimate and serviceability limit states, namely ultimate bearing capacity, settlement exceedance and deformation. Calculations of square spread footings to support column loads on sandy and clay soils were carried out using both probabilistic and deterministic approaches. Probabilistic calculations yielded the following values of variation coefficients: ν(S)=0.06–0.17, ν(∆S/L)=0.74–0.79, ν(R)=0.08–0.14, ν(Pu)=0.10–0.18. In the case of heterogeneous soil mechanical properties with variation coefficients v ≥ 0.15 – 0.2, and with these variations taken into account in the probabilistic calculations, the allowable pressures on the footings did not exceed the calculated resistance as the limit of linearity. At higher pressures, the probability of soil failure also increases, and from the point at which 40-60 % of the bearing capacity is reached, it rises rapidly to values exceeding the allowable limits. According to the results of probabilistic analysis, the values of allowable pressures are 5-50 % lower than those obtained from deterministic calculations, which confirms the need to take into account the heterogeneity of soil characteristics, especially when assessing the possibility of the foundation's operation in the nonlinear stage of deformation due to their bearing capacity reserves.