Multi-objective optimization for multi-level anchored bulkhead
Sheet-pile walls are vertical, flexible and quite thin structures, driven into the soil down to a calculated depth with the purpose of providing an additional support for soil stability. Generally, when the wall is over 3 meters in height the structure is stabilized using one or more anchors and/or props, that are otherwise absent. In the former case the structure is called anchored sheet-pile wall or anchored bulkhead.
Case studies
The design of a multi-level anchored structure is investigated, including the different stages of analysis, to define all the features involved in the process and particularly the characteristics of the anchors. All in all, there are two conflicting design targets:
- to obtain the best possible performances;
- to minimize the relatively high costs for the work.
The logic of the design process is expressed as a modeFRONTIER®4 workflow, outling and defining a methodology of design in which all the phases of the analysis are implemented in a single environment and targeted to a multi-objective over all optimization.
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| Figure 1: the modeFRONTIER Workflow |
Model and targets description
The possible configurations of the anchored bulkhead are described by five input parameters, and namely the geometry of the wall and the number of levels of anchors (from two to four). It is worth noting that there are no standard procedures in literature to fix the best number of levels of anchors, and so in practice this value is generally set out under the experience of the engineer.
The above parameters are used to complete the description of the system through an Excel spreadsheet as well as a sequence of two runs of the Paratie®. The Excel spreadsheet gives all the ancillary data of the system, while Paratie allows for a complete answer of the system.
A total of eight output parameters were chosen, grouped into two classes: the first of costs of the work, the second on structural parameters of the system, and namely bending moments as well as displacements. In turn this parameters allowed to define five objectives and four constraints.
Coupling modeFRONTIER with Paratie
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Figure 2: Example of Objective Scatter Chart for two conflicting objectives with representation of the Pareto Frontier where:
• 2 levels of anchor • 3 levels of anchor • 4 levels of anchor |
Coupling the softwares and testing the possibilities of designing a civil construction while considering an optimization of all the factors influencing the project was the major concern of the work. It could be achieved by evaluating in batch mode every single design configuration with Paratie, a simple and powerful tool based on the conceptual model by Winkler, which was created by the CeAS Group to analyze different situations in designing walls, in order to let the optimizer work without human intervention. Since Paratie had never been coupled with modeFRONTIER, it was necessary to create an interface via a DOS BATCH SCRIPT node. Thus only text files are integrated in the workflow created.
Results
Approximately 2000 different configurations of the system were developed by modeFRONTIER, and the optimal Pareto Frontier was obtained. This consists of 102 configurations, which, in the light of an easier interpretation of results, are divided into three groups with respect to the number of levels of anchors integrated into the system (Figure 2).
The choice of the optimal design solution from an engineering perspective has to be guided by further considerations including:
- it is essential to know the environmental conditions of the area where the structure is going to be build; e.g. if this walls are in urban areas, as frequently happens, the design is governed by the displacements of the system.
- In general the overall lateral displacements and main bending moments of the systems are influenting the choice (Figure 3).
Once a group of solutions suitable for the site conditions is selected, it is easy to complete the analysis with Paratie and so to obtain the necessary charts.
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| Figure 3: Example of charts describing the lateral displacement (left) and the bending moments (right) extracted from Paratie |
Conclusions
The model: This way of designing is higly innovative, particularly for the possibility offered by modeFRONTIER to combine different operations in a single work environment. The model created represents not a goal but a starting point, is but to be treated as a starting point and has to be accepted on the basis of engineering judgment.
The softwares: Both softwares proved good performances: Paratie turned out to be the ideal tool for this kind of analysis in terms of operating time and results obtained (the nature of the files it manages), even if the applicability of the Winkler model for the beam-soil interaction has to be accepted by case basis. modeFRONTIER is an excellent platform for both the integration of a variety of CAE tools and to perform MDO tasks in a easy and straightforward manner. Moreover the learning curve of the method is amazingly short.
The optimization results: The objectives and constraints defined allow extraction of a reduced group of results in comparison with all the possible configurations that the structure can assume and the designer can choose the most appropriate solution in according with his/her own sensitivity and experience.
Ing. Fabio Capaldi
Prof. Ing. Quintilio Napoleoni
Università degli Studi di Roma “La Sapienza”, Facoltà di Ingegneria - Dipartimento di Idraulica, Trasporti e Strade, Area di Geologia Applicata e Geotecnica
Article published in the Magazine: EnginSoft Newsletter Year 6 n.2
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