Reliability-based analysis of seismic bearing capacity of shallow strip footings resting on soils with randomly varying geotechnical and earthquake parameters

Seismic bearing capacity of strip footings is a challenging task for geotechnical engineers due to its stochastic framework instigated by the natural uncertainties incorporated into geotechnical properties and earthquake parameters. Consequently, the introduction of the random field theory into reliability analysis may provide power tools to succor designers check how reliable their designs. This paper aims to assess the seismic bearing capacity of shallow strip footings resting on soils with randomly varying parameters. Bearing capacity formulas for purely cohesive and cohesive-frictional soils are considered. The influence of the type of the autocorrelation functions (ACFs), the scale of fluctuations (SOFs) and the coefficient of variation (COV) of the random parameters are investigated. Statistical moments, probability density function (PDF) and failure probability (Pf) of the seismic bearing capacity are computed. It is shown that the Single Exponential (SNE) ACF is the most appropriate function to characterize the spatial variability of the soil properties since it provides conservative results. On other hand, the results indicate that the increase in the coefficients of variation (COV) of the cohesion or the friction angle increases the variability of the seismic bearing capacity while this variability remains unaffected when the COV of the seismic coefficient increases. The results also highlight that the effect of the vertical SOF on the PDF and the failure probability is much more significant than that of the horizontal SOF. In addition, the mean seismic bearing capacity fluctuates slightly as the horizontal or vertical SOF increases so that the increment of variation is between 0.4% and 2% for the both two soil types.