## Bridges: Nonlinear Analyses, Probability Theory and Optimization Theory

Cosic M., Folic R., Folic B.: Bridges: Nonlinear Analyses, Probability Theory and Optimization Theory (poster)

The poster shows a multidisciplinary approach to the assessment of seismic performances based on the Performance-Based Earthquake Engineering (PBEE), taking into account the multi-criteria optimization theory in analyzing the priority methods for bridge rehabilitation/strengthening. One bridge model was subjected to nonlinear static pushover analyses (NSPA), target displacement analyses using the spectrum capacity method (CSM), vulnerability analyses, and reliability analyses, while for a damaged bridge, in addition to be considered using the above methods, was also analyzed using the VIKOR method of multi-criteria optimization.

## Soil-Pile-Pier Performance

Cosic M., Folic B., Folic R.: Soil-Pile-Pier Performance (presentation)

In the presentation is shown a discrete numerical solid pile model with a discontinuity and defects. Model included performance-based seismic evaluation of the soil-pile-bridge pier interaction. The pile discontinuity and defects are modelled by reducing the specific finite elements and elastic modulus of concrete. The wave-propagation response of the pile was analyzed based on a step-by-step numerical integration using the Hilber-Hughes-Taylor (HHT) method in time domain (THA). The response analysis is performed with an integration of individual reflectograms into a reflectogram surface, which is generated in a 3D cylindrical coordinate system. Non-linear response of the system is considered using the incremental-iterative Newton-Raphson`s method, while the stability analysis is performed according to the modified geometrical nonlinearity analysis of stability. Determination of critical load and effective length of the pile are performed based on numerical solution and using regression analysis of the power function. The procedure of the soil-pile-bridge pier performance evaluation is based on the incremental nonlinear dynamic analysis (INDA). The system’s input signal is treated through the generated artificial accelerograms, which were subsequently processed by soil layers and for the bedrock. Fragility curves were constructed based on solutions of the regression analysis and the probability theory of log-normal distribution, while the generation of reliability curves is based on a solution of vulnerability.