قابلیت اطمینان مبتنی بر طراحی ژئوتکنیکی قوی از پایه های گسترده با استفاده از الگوریتم ژنتیک چند هدفه

This paper presents a new geotechnical design concept, called robust geotechnical design (RGD). The new design methodology seeks to achieve a certain level of design robustness, in addition to meeting safety and cost requirements. Here, a design is considered robust if the variation in the system response is insensitive to the variation of noise factors such as uncertain soil parameters and construction quality. When multiple objectives are considered, a single best design may not exist, and a trade-off may be necessary. In such a case, a genetic algorithm is adopted for multi-objective optimization and a Pareto Front, which describes a trade-off relationship between cost and robustness at a given safety level, is established. The new design methodology is illustrated with an example of spread foundation design. The significance of the RGD methodology is demonstrated.

It is well recognized that uncertainty of soil parameters is usually unavoidable in the geotechnical design [1]. The uncertainty in the soil parameters, as well as the uncertainty in the adopted solution model, can lead to the uncertainty in the solution (e.g., predicted response or performance of a system). In a deterministic approach, the engineer uses factors of safety that have been “calibrated” by experience to cope with the uncertainty in the solution (i.e., predicted response). Of course, the factor of safety adopted in a particular design depends not only on the degree of uncertainties but also on the consequence of failure; in other words, it depends on the “calculated risk” [2] and [3]. To better deal with the uncertainties, the probabilistic or reliability-based approach that considers explicitly the uncertainties in the soil parameters and solution model has been proposed (e.g., [3], [4], [5], [6], [7], [8], [9], [10], [11] and [12]). In a traditional geotechnical design, regardless of whether the deterministic approach or the probabilistic approach is adopted, the design is often based on a trail-and-error process considering safety and cost. Safety is usually checked first to ensure the candidate design satisfying the prescribed “safety” requirements (in terms of factor of safety or probability of failure). Then the design with the least cost is selected from the pool of all acceptable designs that have been screened based on safety requirements [13], [14] and [15]. Thus, the reliability-based design is quite straightforward if the results of the reliability analysis are accurate and precise so that there will be no question whether a given design satisfies the safety requirement. The accuracy and precision of a reliability analysis, however, depends on how well the random soil parameters are characterized. If the knowledge of the statistical distribution of soil parameters is “perfect”, the results of reliability analysis will be accurate and precise and the reliability-based design can be easily implemented with least cost objective constrained with a minimum reliability index requirement. In a real-world geotechnical project, the distribution of a soil parameter is quite uncertain due to lack of data, measurement error, and/or error caused by use of empirical correlations. The variation range of geotechnical parameters is usually quite large [16] and thus the variation can be either overestimated or underestimated. Such overestimation or underestimation of the variation of soil parameters can lead to over-design or under-design. While reduction of the uncertainty in soil parameters is important, which should be pursued whenever it is deemed cost-effective, in this paper, we focus on a different approach by achieving robustness in the design without eliminating the sources of uncertainty. Here, a design is considered robust if the variation in the system response is insensitive to (or robust against) the variation of uncertain soil parameters (called noise factors in this paper). The essence of a robust design is to select a design (through the adoption of a set of design parameters) that yields a minimal variation in the system response without eliminating the sources of uncertainty or reducing the level of uncertainty. In this paper, a robust geotechnical design (RGD) methodology is proposed to fulfill the goal of minimizing the effects of the uncertainty of soil parameters. Robust design was originated from the field of Quality Engineering [17], which has been applied to many structural or mechanical problems in the last two decades [18], [19], [20], [21] and [22]. One widely accepted definition of robust design [18] is manipulating design parameters (i.e., the so-called “easy to control” factors) so that the system response of the design is insensitive to, or robust against, the variation of noise factors (i.e., the so-called “hard to control” factors). In a geotechnical design, the noise factors are the uncertain soil parameters and other factors such as those related to construction. Thus, in a robust design, regions in the design space that yield low variation in the system response should be sought. The robust design will have an acceptable performance even with unexpected variation in soil parameters. In this paper, the design of spread foundation is employed as an example to illustrate the robust design philosophy. In the sections that follow, a brief review of a reliability-based model for design of spread foundation [14] is first provided. Then, the RGD framework is presented with an illustrated example. It should be noted that the RGD methodology presented in this paper does not depend on the reliability-based procedure described by Wang [14]; rather, the latter is used for convenience in presenting a reliability-based RGD methodology. It should be noted that robust geotechnical design (RGD) is not a design methodology to compete with the traditional approach such as the reliability-based design; rather, it is a design strategy to complement the traditional methods. With the RGD approach, the focus is to satisfy three design requirements, namely safety, cost, and robustness (against the variation in system response caused by noise factors). The safety requirement is usually implemented through constraints of reliability, and hence the design becomes a bi-objective optimization problem. For the bi-objective problem examined in this paper, it is possible that no single best solution exists that is most optimal with respect to both objectives (cost and robustness). In such a situation, a detailed study of the trade-offs between these objectives can lead to a more informed design decision.

Robustness as one of the design objectives has been illustrated in this paper. In fact, the concept of robustness is incorporated into the reliability-based design to deal with the uncertainty in the estimated sample statistics of soil parameters, which is often a major problem in a reliability-based design. The significance of design robustness has been demonstrated with a reliability-based design of spread foundations. As demonstrated in this study, there often exists no single best design when multiple design objectives are imposed. Thus, an optimal set of designs, called Pareto Front, in which no design is inferior to others with respect to all objectives, is the best of what an engineer can obtain under such a scenario. The Pareto Front specifies a trade-off relationship between cost and robustness, after satisfying all safety requirements. This trade-off relationship enables the engineer to make a more informed design decision. Finally, it has been demonstrated through the example design of spread foundations that NSGA-II is an effective and efficient tool for performing multi-objective optimization for establishing a Pareto Front. It should be noted that the robust geotechnical design (RGD) is not a methodology to compete with the traditional design approaches; rather, it is a complementary design strategy. With the RGD approach, the focus is to satisfy three design objectives, namely safety, cost, and robustness. In this paper, safety is implemented as a constraint in the form of reliability, and thus the focus of the paper is the reliability-based RGD approach. The RGD methodology is expected to work equally well in a factor-of-safety-based setting. Finally, robustness, which is usually not considered explicitly in a traditional geotechnical design, may have to be achieved at a higher cost, as demonstrated in the example study. Thus, the development of Pareto Front is necessary for trade-off consideration in a robust design. This paper is the first step in developing the RGD methodology. This methodology is being adapted and refined in an ongoing research on design of supported excavation system at Clemson University, which involves challenging numerical and simulation processes within the RGD framework. Further investigations by interested parties are encouraged to advance this design methodolo