Empirical Models to Formulate the Nonlinear Response of Rocking Shallow Foundations

This paper aims to introduce a simplified moment-rotation backbone model for exploring the nonlinear behavior of shallow foundations subjected to rocking. The model is developed based on parametric numerical investigations of rectangular footings on dense dry sand, taking advantage of a nonlinear macro-element model verified based on a set of experimental results. Empirical expressions are proposed for rocking stiffness degradation due to gravity loads and foundation rotation as a function of the factor of safety against vertical loads and aspect ratio of foundations. Similar to previous researches, the uplift reference rotation was introduced to explore a new closedform expression appropriate for normalizing the foundation response in a non-dimensional form. The proposed approach for stiffness degradation and nonlinear backbone model of rocking foundations aims to be simple, to minimize the dependence on the variable parameters, and to provide physically sound selections for engineering applications.

Modeling of Seismic Energy Dissipation of Rocking Foundations Using Nonparametric Machine Learning Algorithms

The objective of this study is to develop data-driven predictive models for seismic energy dissipation of rocking shallow foundations during earthquake loading using multiple machine learning (ML) algorithms and experimental data from a rocking foundations database. Three nonlinear, nonparametric ML algorithms are considered: k-nearest neighbors regression (KNN), support vector regression (SVR) and decision tree regression (DTR). The input features to ML algorithms include critical contact area ratio, slenderness ratio and rocking coefficient of rocking system, and peak ground acceleration and Arias intensity of earthquake motion. A randomly split pair of training and testing datasets is used for initial evaluation of the models and hyperparameter tuning. Repeated k-fold cross validation technique is used to further evaluate the performance of ML models in terms of bias and variance using mean absolute percentage error. It is found that all three ML models perform better than multivariate linear regression model, and that both KNN and SVR models consistently outperform DTR model. On average, the accuracy of KNN model is about 16% higher than that of SVR model, while the variance of SVR model is about 27% smaller than that of KNN model, making them both excellent candidates for modeling the problem considered.

Seismic fragility analysis for tall pier bridges with rocking foundations

Costal bridge systems usually contain tall piers with heights over 40 m, due to the engineering site exposed to deep water circumstances. Note that the conventional seismic isolation devices (e.g., isolation bearings) are not that effective for tall piers, since their dynamic performance is significantly affected by the distributed mass and vibration modes of columns; therefore, base isolation design philosophy could be a promising alternative for mitigating seismic demands of this type of bridges. This paper mainly investigates the efficiency of rocking foundations in improving seismic performance of tall pier bridges, with the results presented in the format of fragility curves. Finite element model of the prototype tall pier bridge is developed, and the responses subjected to near-fault motions are obtained using nonlinear time history analysis. Probability seismic demand models and fragility curves are then developed accordingly, based on which the performance of tall pier bridges are assessed. The results show that employment of rocking foundations could significantly reduce the demands of tall piers and the probability of being damaged. Before the initiation of uplifting at pier base, the behavior of rocking piers resembles that of conventional ones with integrated foundation. While rocking initiates under strong excitations, the demands of rocking piers reduce drastically compared with integrated ones and tend to be similar under different motions, which benefits the post-earthquake performance assessment of these bridges.