Gradient-based design robustness measure for robust geotechnical design

This paper presents a gradient-based robustness measure for robust geotechnical design (RGD) that considers safety, design robustness, and cost efficiency simultaneously. In the context of robust design, a design is deemed robust if the system response of concern is insensitive, to a certain degree, to the variation of noise factors (i.e., uncertain geotechnical parameters, loading parameters, construction variation, and model biases or errors). The key to a robust design is a quantifiable robustness measure with which the robust design optimization can be effectively and efficiently implemented. Based on the developed gradient-based robustness measure, a robust design optimization framework is proposed. In this framework, the design (safety) constraint is analyzed using advanced first-order second-moment (AFOSM) method, considering the variation in the noise factors. The design robustness, in terms of sensitivity index (SI), is evaluated using the normalized gradient of the system response to the noise factors, which can be efficiently computed from the by-product of AFOSM analysis. Within the proposed framework, robust design optimization is performed with two objectives, design robustness and cost efficiency, while the design (safety) constraint is satisfied by meeting a target reliability index. Generally, cost efficiency and design robustness are conflicting objectives and the robust design optimization yields a Pareto front, which reveals a tradeoff between the two objectives. Through an illustrative example of a shallow foundation design, the effectiveness and significance of this new robust design approach is demonstrated.