# Geotechnical Seismic Design Code Calibration

### A probabilistic study of seismic design code safety

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## Abstract

Seismic design codes are currently moving from a force-based design approach to a performance-based design approach. For example, in a performance-based design approach it could be specified how many lanes must be available during the lifetime of a bridge given a certain earthquake intensity.The problem with this approach is that it is not specified what the probability must be that the performance criterion is satisfied. This raises the question whether the design codes are acceptably safe or not. Focus is laid on the Canadian Highway Bridge Design Code (CHBDC), in which a total resistance factor approach is used. Because the total resistance factor in the CHBDC is a multiplicative factor, lower resistance factors lead to stronger foundation designs. The goal of this thesis is to calibrate the design procedure in the CHBDC for geotechnical systems under seismic loading, by finding a relationship between resistance factors and the lifetime probabilities of failure of said systems. The resistance factor can then be fine-tuned to a lifetime probability of failure that is consistent with the lifetime probability of failure targeted in static design. As an example problem, the bearing capacity of a shallow foundation on a clay with a pseudo-dynamic earthquake load is tested. The research question that is answered in this thesis is: "What should the resistance factors for geotechnical seismic design be in order to achieve a target lifetime probability of failure that is consistent with static design targets?'' Not every possible combination of soil strengths and forces on the superstructure can be taken into account, and therefore the random finite element method is used in a Monte Carlo simulation. Thousands of realization sare performed for each resistance factor, design return period, and "actual''return period that the designed foundations are tested against. By seeing how many realizations of the Monte Carlo simulation fail given a certain earthquake intensity, the conditional probability of failure given that earthquake intensity can be estimated. The total lifetime probability of failure can then be estimated from the conditional probabilities of failure with the total probability theorem. As part of a parametric study, the lifetime probabilities of failure are estimated for six different scenarios, each of which has different sources of uncertainty. The resulting lifetime probabilities of failure are interpolated in order to find a resistance factor that targets a lifetime probability of failure consistent with static design targets. Currently, the resistance factor that the CHBDC recommends for geotechnical systems under seismic loading are defined as the static resistance factor for that geotechnical system incremented with 0.20, meaning that compared to static design, weaker foundations are designed for seismic load cases. The resistance factor found in this thesis is closer to the resistance factor for static design than to the resistance factor for seismic design. It should therefore be considered to lower the seismic resistance factor to the value of the static resistance factor so that a sufficient lifetime reliability can be targeted.