Optimum Seismic Design of RC Frames Using Multi-Level Performance-Based Design Method

Despite much research efforts and new generations of seismic design guidelines, structures still experience extensive damage and incur significant economic losses during earthquakes (e.g. 2011 Christchurch earthquake) due to inefficient design and construction practices. This research aims to reduce the structural damage of reinforced concrete (RC) frames, particularly under major to severe earthquakes, which in turn assists to save economic losses caused by the potential structural and non-structural damage. The aim is achieved by providing a multi-level performance-based optimisation methodology.

This study develops a performance-based optimisation framework for minimising the initial material usages (costs) of multi-storey RC frames, while minimising structural damage by satisfying multiple performance objectives. The proposed methodology is characterised by computational efficiency, as optimum results can typically be achieved within a few iterative steps. This efficiency saves computational efforts particularly when non-linear time history analysis is involved in the optimisation, compared to conventional optimisation methodologies which often require thousands of analysis iterations. The optimisation method employs the concept of Uniform Damage Distribution (UDD). The novelty of the proposed optimisation framework lies in its implementation of the UDD approach to (i) simultaneously control both local structural seismic responses (plastic hinge rotations) and more global responses (inter-storey drifts); (ii) consider different hazard levels, ranging from minor (i.e. 50% probability of exceedance in 50 years) to major (i.e. 10% and 2% probabilities of exceedance in 50 years) earthquakes; and (iii) iteratively modify both section dimensions and longitudinal reinforcement ratios according to the performance results until that material capacities are fully exploited in each storey, achieving more uniform distributions of the response and satisfying multi performance targets. In addition to performance-based constraints, design constraints required in design guidelines (i.e. Eurocode) and practical design practices are also incorporated in the optimisation framework.

The efficiency of the proposed method is initially demonstrated through optimum designs of 3-, 5-, 10- and 15-storey RC frames under six spectrum-comparable artificial earthquakes. The results show that compared to conventionally designed counterparts, optimum structures exhibit lower maximum inter-storey drift and maximum plastic rotations by up to 58% and 78%, respectively, along with reduced global structural damage (up to 88%), while both responses are more uniformly distributed along storey levels. Sensitivity analysis of the optimum designs to the earthquake record selections shows that (i) using a single earthquake record may not lead to an acceptable seismic design, particularly for tall buildings, and (ii) both artificial and natural earthquakes can lead to optimum frames with similarly and satisfactory performances. Compared to code-based designs, the optimum designs reduce initial construction costs, including material and construction costs of concrete, reinforcement and formworks, by up to 15%, while reducing total life-cycle costs (the sum of initial construction costs and expected life-cycle damage losses) by up to 64%. The optimum designs consistently experience less global damage (up to 82%) when considering uncertainties in material (i.e. concrete and steel strengths) and geometry properties (i.e. area of longitudinal rebar). The effect of earthquake records variability is efficiently managed in this optimisation framework.