Predictive equations for rotation and sliding of shallow footings under seismic loads using Bayesian regression and ANN

Accurate estimation of footing movement is essential for evaluating its contribution to story drift, which is a critical metric for seismic design. For this reason, this study develops predictive equations to estimate the rotation and sliding of shallow foundations under the combination of seismic and gravity loads. Archetype low-rise concentrically braced frame buildings with shallow footings are designed for Vancouver, Canada, and are modeled using OpenSees. Uncertainty in demand and capacity of the buildings is considered using incremental Latin hypercube sampling (iLHS). A range of footing sizes, from small foundations designed per the US code to larger capacity-protected (CP) footings following the Canadian code, are analyzed to ensure comprehensive coverage of footing size for deriving reliable equations. Two soil sites are considered to account for varying soil conditions. Bayesian regression is used to develop reliable equations for footing rotation and sliding. An artificial neural network (ANN) model further improves prediction accuracy by incorporating complex variable combinations beyond Bayesian regression. Both new approaches are compared to the guidance in the commentary of CSA A23.3, as there is little guidance in the US and other international standards. This study concludes that both current guidance and the proposed new equations accurately estimate footing rotation for CP footings when sliding is minimal. However, the existing guidance tends to underestimate the rotation of smaller footings and does not adequately estimate the footing movement when significant sliding occurs. Therefore, the equations developed here are recommended for a more accurate estimate of footing movement under seismic load.