Gradient-based design robustness measure for robust geotechnical design

Abstract

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.

R-LRFD: Load and resistance factor design considering robustness

“…The robustness or insensitivity of the system response [f(d, θ)] to the variation in noise 284 factors (θ) can be measured with its gradient (G), which is formulated as the variation of the 285 system response caused by one unit change in noise factors (Gong et al 2014b). The plots in 286 Figure 1(a) and 1(c) illustrate the gradient-based robustness concept: two designs (i.e., d 1 and 287 d 2 ) with the same noise factors ( 1 ) exhibit different patterns of system response, one (i.e., d 1 in 288 Figure 1a) yields high variation in the system response and the other (i.e., d 2 in Figure 1c) 289 yields low variation in the system response.…”

“…This unique characteristic of the gradient-based robustness 294 measure is a perfect match with LRFD, in which the uncertainties in input parameters and the 295 solution model are recognized but unquantified. Note that while the existing gradient-based 296 robustness measure (Gong et al 2014b) is applicable for the scenario involving a system with 297 quantified uncertain parameters, the modified gradient-based robustness measure, outlined 298 below, is intended for the scenario involving a system with recognized but unquantified 299 uncertainty. The latter is uniquely suitable for integration with the standard LRFD.…”

“…For example, the mean 570 of the resulting shaft diameter (B) and shaft depth (D) are 0.9 m and 8.0 m, respectively; 571 whereas, the COV of the resulting B and D values are only 1.05% and 0.75%, respectively. 572 Further, given the statistical characterization of uncertain parameters in Table 2, this 573 drilled shaft is readily designed with RBD and reliability-based RGD (Gong et al 2014b); and, 574 the derived designs are also included in Table 2. For illustration purposes, the target reliability 575 index ( T ) is set to 2.6 and the reliability index () of each candidate design is analyzed with 576 first order reliability method (FORM) (Low and Tang 2007).…”

Robust design in geotechnical engineering – an update

“…The more recent applications are found in various fields such as mechanical, structural and aeronautical design (e.g., Chen et al 1996;Chen et al 1999;Lee and Park 2001;Doltsinis et al 2005;Park et al 2006;Brik et al 2006;Lagaros and Fragiadakis 2007;Kumar et al 2008;Marano et al 2008;Lee et al 2010). Applications to geotechnical problems were introduced by Juang and his co-workers (Juang et al 2012(Juang et al , 2013a(Juang et al , 2013bJuang and Wang 2013;Wang et al 2013Wang et al , 2014Gong et al 2014aGong et al , 2014bGong et al , 2014c. Because of the distinct characteristic of geotechnical problems, which often involves high coefficients of variation (COVs) in the noise factors (i.e., uncertain input parameters and imperfect models), the term 'RGD' was coined by Juang et al (2013b) for use in these geotechnical applications.…”

“…To reduce the computational effort, Gong et al (2014a) proposed a gradient-based robustness measure. For a system with design parameters d and noise factors θ as inputs, its system response can be denoted as g(d, θ).…”