Seismic safety of RC piers with parameter uncertainties: Assessing dimensionless response using Bayesian linear regression

Both maximum and residual deformations are essential for seismic safety during and following strong earthquakes, especially in the near field. These parameters are often calculated per unidirectional analysis, albeit bidirectional analysis may be carried out for important systems with the availability of growing computational power. However, a pressing challenge in earthquake engineering that continues to exist in the face of several uncertainties is to represent these response statistics – essentially with wide dispersion - in an expressive and effective format. The present paper aims to represent the maximum and residual deformation to unidirectional and bidirectional shaking in a rational format, even when uncertainties in ground motion and structural characteristics are prevalent. To this end, a bridge pier with uncertain material parameters is subjected to a wide range of stochastically simulated near-field motions with forward-directive signature, and the responses are computed to unidirectional and bidirectional shaking. In an attempt to develop predictive models, the responses are regressed first in terms of primary parameters characterizing structural material and ground motions. Next, by standard principles of mechanics, the response is recast in a dimensionless and orientationally consistent format in terms of derived parameters. This reduces the number of independent variables yet connotes a sound basis of mechanics. The predictive model in terms of derived dimensionless parameters is further extended in the Bayesian framework to improve the predictive model in a probabilistic sense.