Convex Programming-Based Robust Optimization Procedure for Blast-Excited Structures with Bounded Uncertainty

Application of the robust optimization (RO) technique to ensure the least possible deviation of structural performance is gaining increasing attention in recent years. However, most RO studies have been conducted in the probabilistic domain, where sufficient uncertainty information is available to construct probability distribution functions of response parameters. But, in many cases, such as for structures under underground blast excitation, hazard parameters like charge weight and charge center distance do not have any definite probability density function. Only their ranges of variations are known to an engineer. Hence, it is more logical to model these parameters as uncertain-but-bounded (UBB) type, which requires only bounds of variations to characterize the uncertainty. The available RO studies in the UBB-domain mainly deal with static loads. Studies on time-variant dynamic loads, such as blast load, are scarce in the existing literature. Also, blast load time-histories show record-to-record variations in their signatures, even with the same setup of hazard parameters. This aspect cannot be considered by the conventional convex programming approaches of RO in the UBB domain. To address all these issues, a new RO procedure is proposed in the present study, which is based on the dual response surface method. The proposed RO procedure can transform the complex simulation-based RO procedure under dynamic blast load to an equivalent deterministic problem with explicit constraints. Thereby, the RO can be easily solved by a gradient-based optimizer. The effectiveness of the proposed approach is elucidated by the complex real-world problems of a multistory building and an underground reinforced concrete bunker. The results are compared with conventional RO approaches. The results show that the proposed approach consistently yields more economic as well as robust solutions in a computationally efficient way.

This research provides a computationally efficient and easy means to yield economic and robust design solutions of structures subjected to stochastic underground blast excitation. The obtained solutions are robust, as these are least affected due to various sources of parameter uncertainty. The proposed approach is valid even for cases where no statistical distribution of input parameters is available. The efficiency of the proposed approach is tested for a multistory building and a reinforced concrete (RC) bunker, which are practical and complex structures. Material nonlinearity and soil–structure interaction have been considered. The proposed approach uses conventional easy industrial software SAP2000 and Matlab. The method, being generic in nature, can be applied for any form of load application, any type of structure, and any material and analysis type. The charts have been developed for the 20-story building and RC bunker, from which one can work out a budget and risk of explosion for an anticipated explosive charge weight, and charge center distance from the structure.