Probabilistic Structural System Response to Differential Settlement Resulting from Spatially Variable Soil

Abstract

The role of spatially variable soil stiffness and strength on structural performance has been increasingly recognized with the rapid development of geotechnical reliability-based design tools. Performance criteria linked to the angular distortion between foundations and the probability of exceeding certain limit states as a function of linear-elastic soil property autocorrelation have shed light on the link between foundation soils and potential structural damage. However, the role of soil-structure interaction (SSI), especially considering nonlinearity in soil and structural elements, to redistribute shear and flexure within structures that result from differential foundation movements, has been largely neglected. This study presents a critical examination of the effect of nonlinear SSI to redistribute flexural demands within a steel structure founded in soils exhibiting spatial variability and the corresponding differential settlements through a comparison of uncoupled and coupled Monte Carlo simulations (MCS). This study shows that the differential settlement, Δs, computed using coupled (i.e., SSI) analyses are significantly smaller than those derived from the uncoupled analyses for the random field models (RFMs) used to simulate soil spatial variability. The effect of SSI is to substantially reduce the probability of exceeding selected limit state criteria due to differential movements that vary in magnitude with the level of stringency of the limit state criteria; the most significant reduction corresponds to the structural ultimate limit state (ULS). Furthermore, the effect of SSI on structural performance and the critical scale of fluctuation, δcrit, becomes more apparent and beneficial as the severity of differential movement increases. Smaller and/or “allowable” angular distortions are governed by the local footing-to-footing distance, whereas the probability of exceeding the ULS (i.e., yielding of beams) is controlled by the entire structure working to redistribute the flexural demands. Limit state severity appears to control the critical soil autocorrelation length for angular distortion, indicating that the role of SSI in the performance of structures in spatially varying soils cannot be ignored.