Multiobjective optimization of post-tensioned concrete box-girder road bridges considering cost, CO2 emissions, and safety

This paper presents a multiobjective optimization of post-tensioned concrete road bridges in terms of cost, CO2 emissions, and overall safety factor. A computer tool links the optimization modulus with a set of modules for the finite-element analysis and limit states verification. This is applied for the case study of a three-span continuous post-tensioned box-girder road bridge, located in a coastal region. A multiobjective harmony search is used to automatically search a set of optimum structural solutions regarding the geometry, concrete strength, reinforcing and post-tensioned steel. Diversification strategies are combined with intensification strategies to improve solution quality. Results indicate that cost and CO2 emissions are close to each other for any safety range. A one-euro reduction, involves a 2.34 kg CO2 emissions reduction. Output identifies the best variables to improve safety and the critical limit states. This tool also provides bridge managers with a set of trade-off optimum solutions, which balance their preferences most closely, and meet the requirements previously defined.The authors acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (BRIDLIFE Project: BIA2014-56574-R) and the Research and Development Support Program of Universitat Politecnica de Valencia (PAID-02-15).García Segura, T.; Yepes, V. (2016). Multiobjective optimization of post-tensioned concrete box-girder road bridges considering cost, CO2 emissions, and safety. Engineering Structures. 125:325-336. https://doi.org/10.1016/j.engstruct.2016.07.012S32533612

A cognitive approach for the multi-objective optimization of RC structural problems

This paper proposes a cognitive approach for analyzing and reducing the Pareto optimal set for multi-objective optimization (MOO) of structural problems by means of jointly incorporating subjective and objective aspects. The approach provides improved knowledge on the decision-making process and makes it possible for the actors involved in the resolution process and its integrated systems to learn from the experience. The methodology consists of four steps: (i) the construction of the Pareto set using MOO models; (ii) the filtering of the Pareto set by compromise programming methods; (iii) the selection of the preferred solutions, utilizing the relative importance of criteria and the Analytic Hierarchy Process (AHP); (iv) the extraction of the relevant knowledge derived from the resolution process. A case study on the reinforced concrete (RC) I-beam has been included to illustrate the methodology. The compromise solutions are obtained through the objectives of economic feasibility, structural safety, and environmental sustainability criteria. The approach further identifies the patterns of behavior and critical points of the resolution process which reflect the relevant knowledge derived from the cognitive perspective. Results indicated that the solutions selected increased the number of years of service life. The procedure produced durable and ecological structures without price trade-offs.The Spanish Ministry of Science and Innovation.Yepes, V.; García Segura, T.; Moreno-Jiménez, J. (2015). A cognitive approach for the multi-objective optimization of RC structural problems. Archives of Civil and Mechanical Engineering. 15(4):1024-1036. https://doi.org/10.1016/j.acme.2015.05.001S1024103615

CO2-Optimization Design of Reinforced Concrete Retaining Walls Based on a VNS-Threshold Acceptance Strategy

This paper presents one approach to a methodology to design reinforced concrete cantilever retaining walls for road construction using a hybrid multistart optimization strategic method based on a variable neighborhood search threshold acceptance strategy (VNS-MTAR) algorithm. This algorithm is applied to two objective functions: the embedded carbon dioxide (CO 2) emissions and the economic cost of reinforced concrete walls at different stages of materials production, transportation, and construction. The problem involved 20 design variables: four geometric variables (thickness of the stem and the base slab; toe and heel lengths), four material types, and 12 variables for the reinforcement setup. Results first indicate that embedded emissions and cost are closely related and that more environmentally friendly solutions than the lowest cost solution are available at a cost increment of less than 1.28%. The analysis also indicated that reducing costs by 1 Euro could save up to 2.28%kg in CO 2 emissions. Finally, the cost-optimized walls require approximately 4.8% more concrete than the best environmental ones, which need 1.9% more steel. © 2012 American Society of Civil Engineers.This work was supported by the Generalitat Valenciana (Research Project GV/2010/086) and by the Universitat Politecnica de Valencia (Research Project PAID-06-09). The authors are grateful to the anonymous reviewers for their constructive comments and useful suggestions. The authors are also grateful Dr. Debra Westall for her thorough revision of the manuscript.10000-01-01Yepes Piqueras, V.; Gonzalez Vidosa, F.; Alcalá González, J.; Villalba Izquierdo, P. (2012). CO2-Optimization Design of Reinforced Concrete Retaining Walls Based on a VNS-Threshold Acceptance Strategy. Journal of Computing in Civil Engineering. 26(3):378-386. doi:10.1061/(ASCE)CP.1943-5487.0000140S37838626

Efficient design of post-tensioned concrete box-girder road bridges based on sustainable multi-objective criteria

[EN] Bridges, as an important component of infrastructure, are expected to meet all the requirements for a modern society. Traditionally, the primary aim in bridge design has been to achieve the lowest cost while guaranteeing the structural efficiency. However, concerns regarding building a more sustainable future have change the priorities of society. Ecological and durable structures are increasingly demanded. Under these premises, heuristic optimization methods provide an effective alternative to structural designs based on experience. The emergence of new materials, structural designs and sustainable criteria motivate the need to create a methodology for the automatic and accurate design of a real post-tensioned concrete bridge that considers all these aspects. For the first time, this thesis studies the efficient design of post-tensioned concrete box-girder road bridges from a sustainable point of view. This research integrates environmental, safety and durability criteria into the optimum design of the bridge. The methodology proposed provides multiple trade-off solutions that hardly increase the cost and achieve improved safety and durability. Likewise, this approach quantifies the sustainable criteria in economic terms, and evaluates the effect of these criteria on the best values of the variables. In this context, a multi-objective optimization is formulated to provide multiple trade-off and high-performing solutions that balance economic, ecologic and societal goals. An optimization design program selects the best geometry, concrete type, reinforcement and post-tensioning steel that meet the objectives selected. A three-span continuous box-girder road bridge located in a coastal region is selected for a case study. This approach provides vital knowledge about this type of bridge in the sustainable context. The life-cycle perspective has been included through a lifetime performance evaluation that models the bridge deterioration process due to chloride-induced corrosion. The economic, environmental and societal impacts of maintenance actions required to extend the service life are examined. Therefore, the proposed goals for an efficient design have been switch from initial stage to life-cycle consideration. Faced with the large computational time of multi-objective optimization and finite-element analysis, artificial neural networks (ANNs) are integrated in the proposed methodology. ANNs are trained to predict the structural response based on the design variables, without the need to analyze the bridge response. The multi-objective optimization problem results in a set of trade-off solutions characterized by the presence of conflicting objectives. The final selection of preferred solutions is simplified by a decision-making technique. A rational technique converts a verbal pairwise comparison between criteria with a degree of uncertainty into numerical values that guarantee the consistency of judgments. This thesis gives a guide for the sustainable design of concrete structures. The use of the proposed approach leads to designs with lower life-cycle cost and emissions compared to general design approaches. Both bridge safety and durability can be improved with a little cost increment by choosing the correct design variables. In addition, this methodology is applicable to any type of structure and material.[ES] Los puentes, como parte importante de una infraestructura, se espera que reúnan todos los requisitos de una sociedad moderna. Tradicionalmente, el objetivo principal en el diseño de puentes ha sido lograr el menor coste mientras se garantiza la eficiencia estructural. Sin embargo, la preocupación por construir un futuro más sostenible ha provocado un cambio en las prioridades de la sociedad. Estructuras más ecológicas y duraderas son cada vez más demandadas. Bajo estas premisas, los métodos de optimización heurística proporcionan una alternativa eficaz a los diseños estructurales basados en la experiencia. La aparición de nuevos materiales, diseños estructurales y criterios sostenibles motivan la necesidad de crear una metodología para el diseño automático y preciso de un puente real de hormigón postesado que considere todos estos aspectos. Por primera vez, esta tesis estudia el diseño eficiente de puentes de hormigón postesado con sección en cajón desde un punto de vista sostenible. Esta investigación integra criterios ambientales, de seguridad estructural y durabilidad en el diseño óptimo del puente. La metodología propuesta proporciona múltiples soluciones que apenas encarecen el coste y mejoran la seguridad y durabilidad. Al mismo tiempo, se cuantifica el enfoque sostenible en términos económicos, y se evalúa el efecto que tienen dichos criterios en el valor óptimo de las variables. En este contexto, se formula una optimización multiobjetivo que proporciona soluciones eficientes y de compromiso entre los criterios económicos, ecológicos y sociales. Un programa de optimización del diseño selecciona la mejor combinación de geometría, tipo de hormigón, armadura y postesado que cumpla con los objetivos seleccionados. Se ha escogido como caso de estudio un puente continuo en cajón de tres vanos situado en la costa. Este método proporciona un mayor conocimiento sobre esta tipología de puentes desde un punto de vista sostenible. Se ha estudiado el ciclo de vida a través de la evaluación del deterioro estructural del puente debido al ataque por cloruros. Se examina el impacto económico, ambiental y social que produce el mantenimiento necesario para extender la vida útil del puente. Por lo tanto, los objetivos propuestos para un diseño eficiente han sido trasladados desde la etapa inicial hasta la consideración del ciclo de vida. Para solucionar el problema del elevado tiempo de cálculo debido a la optimización multiobjetivo y el análisis por elementos finitos, se han integrado redes neuronales en la metodología propuesta. Las redes neuronales son entrenadas para predecir la respuesta estructural a partir de las variables de diseño, sin la necesidad de analizar el puente. El problema de optimización multiobjetivo se traduce en un conjunto de soluciones de compromiso que representan objetivos contrapuestos. La selección final de las soluciones preferidas se simplifica mediante una técnica de toma de decisiones. Una técnica estructurada convierte los juicios basados en comparaciones por pares de elementos con un grado de incertidumbre en valores numéricos que garantizan la consistencia de dichos juicios. Esta tesis proporciona una guía que extiende y mejora las recomendaciones sobre el diseño de estructuras de hormigón dentro del contexto de desarrollo sostenible. El uso de la metodología propuesta lleva a diseños con menor coste y emisiones del ciclo de vida, comparado con diseños que siguen metodologías generales. Los resultados demuestran que mediante una correcta elección del valor de las variables se puede mejorar la seguridad y durabilidad del puente con un pequeño incremento del coste. Además, esta metodología es aplicable a cualquier tipo de estructura y material.[CA] Els ponts, com a part important d'una infraestructura, s'espera que reunisquen tots els requisits d'una societat moderna. Tradicionalment, l'objectiu principal en el disseny de ponts ha sigut aconseguir el menor cost mentres es garantix l'eficiència estructural. No obstant això, la preocupació per construir un futur més sostenible ha provocat un canvi en les prioritats de la societat. Estructures més ecològiques i durables són cada vegada més demandades. Davall estes premisses, els mètodes d'optimització heurística proporcionen una alternativa eficaç als dissenys estructurals basats en l'experiència. L'aparició de nous materials, dissenys estructurals i criteris sostenibles motiven la necessitat de crear una metodologia per al disseny automàtic i precís d'un pont real de formigó posttesat que considere tots estos aspectos. Per primera vegada, esta tesi estudia el disseny eficient de ponts de formigó posttesat amb secció en calaix des d'un punt de vista sostenible. Esta investigació integra criteris ambientals, de seguretat estructural i durabilitat en el disseny òptim del pont. La metodologia proposada proporciona múltiples solucions que a penes encarixen el cost i milloren la seguretat i durabilitat. Al mateix temps, es quantifica l'enfocament sostenible en termes econòmics, i s'avalua l'efecte que tenen els dits criteris en el valor òptim de les variables. En este context, es formula una optimització multiobjetivo que proporciona solucions eficients i de compromís entre els criteris econòmics, ecològics i socials. Un programa d'optimització del disseny selecciona la millor geometria, tipus de formigó, armadura i posttesat que complisquen amb els objectius seleccionats. S'ha triat com a cas d'estudi un pont continu en calaix de tres vans situat en la costa. Este mètode proporciona un major coneixement sobre esta tipologia de ponts des d'un punt de vista sostenible. S'ha estudiat el cicle de vida a través de l'avaluació del deteriorament estructural del pont a causa de l'atac per clorurs. S'examina l'impacte econòmic, ambiental i social que produïx el manteniment necessari per a estendre la vida útil del pont. Per tant, els objectius proposats per a un disseny eficient han sigut traslladats des de l'etapa inicial fins a la consideració del cicle de vida. Per a solucionar el problema de l'elevat temps de càlcul degut a l'optimització multiobjetivo i l'anàlisi per elements finits, s'han integrat xarxes neuronals en la metodologia proposada. Les xarxes neuronals són entrenades per a predir la resposta estructural a partir de les variables de disseny, sense la necessitat d'analitzar el pont. El problema d'optimització multiobjetivo es traduïx en un conjunt de solucions de compromís que representen objectius contraposats. La selecció final de les solucions preferides se simplifica per mitjà d'una tècnica de presa de decisions. Una tècnica estructurada convertix els juís basats en comparacions per parells d'elements amb un grau d'incertesa en valors numèrics que garantixen la consistència dels dits juís. Esta tesi proporciona una guia que estén i millora les recomanacions sobre el disseny d'estructures de formigó dins del context de desenrotllament sostenible. L'ús de la metodologia proposada porta a dissenys amb menor cost i emissions del cicle de vida, comparat amb dissenys que seguixen metodologies generals. Els resultats demostren que per mitjà d'una correcta elecció del valor de les variables es pot millorar la seguretat i durabilitat del pont amb un xicotet increment del cost. A més, esta metodologia és aplicable a qualsevol tipus d'estructura i material.García Segura, T. (2016). Efficient design of post-tensioned concrete box-girder road bridges based on sustainable multi-objective criteria [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/73147TESI

Metaheuristic algorithms in optimum design of reinforced concrete beam by investigating strength of concrete

The locations of structural members can be provided according to architectural projects in the design of reinforced concrete (RC) structures. The design of dimensions is the subject of civil engineering, and these designs are done according to the experience of the designer by considering the regulation suggestions, but these dimensions and the required reinforcement plan may not be optimum. For that reason, the dimensions and detailed reinforcement design of RC structures can be found by using optimization methods. To reach optimum results, metaheuristic algorithms can be used. In this study, several metaheuristic algorithms such as harmony search, bat algorithm and teaching learning-based optimization are used in the design of several RC beams for cost minimization. The optimum results are presented for different strength of concrete. The results show that using high strength material for high flexural moment capacity has lower cost than low stretch concrete since doubly reinforced design is not an optimum choice. The results prove that a definite metaheuristic algorithm cannot be proposed for the best optimum design of an engineering problem. According to the investigation of compressive strength of concrete, it can be said that a low strength material are optimum for low flexural moment, while a high strength material may be the optimum one by the increase of the flexural moment as expected

CO2-Optimization of Post-Tensioned Concrete Slab-Bridge Decks Using Surrogate Modeling

[EN] This paper deals with optimizing embedded carbon dioxide (CO2) emissions using surrogate modeling, whether it is the deck of a post-tensioned cast-in-place concrete slab bridge or any other design structure. The main contribution of this proposal is that it allows optimizing structures methodically and sequentially. The approach presents two sequential phases of optimization, the first one of diversification and the second one of intensification of the search for optimums. Finally, with the amount of CO2 emissions and the differentiating characteristics of each design, a heuristic optimization based on a Kriging metamodel is performed. An optimized solution with lower emissions than the analyzed sample is obtained. If CO2 emissions were to be reduced, design recommendations would be to use slendernesses as high as possible, in the range of 1/30, which implies a more significant amount of passive reinforcement. This increase in passive reinforcement is compensated by reducing the measurement of concrete and active reinforcement. Another important conclusion is that reducing emissions is related to cost savings. Furthermore, it has been corroborated that for a cost increase of less than 1%, decreases in emissions emitted into the atmosphere of more than 2% can be achieved.Grant PID2020-117056RB-I00 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe".Yepes-Bellver, L.; Brun-Izquierdo, A.; Alcalá-González, J.; Yepes, V. (2022). CO2-Optimization of Post-Tensioned Concrete Slab-Bridge Decks Using Surrogate Modeling. Materials. 15(14):1-15. https://doi.org/10.3390/ma15144776115151

Seismic design of reinforced concrete frames for minimum embodied CO2 emissions

Optimum structural design of reinforced concrete (RC) frames has been the focus of extensive research. Typically, previous studies set economic cost as the main design objective despite the fact that RC structures are major contributors of CO2 emissions. The limited number of studies examining optimum design of RC frames for minimum CO2 emissions do not address seismic design considerations. However, in many countries around the world, including most of the top-10 countries in CO2 emissions from cement production, RC structures must be designed against earthquake threat. To bridge this gap, the present study develops optimum seismic designs of RC frames for minimum cradle to gate embodied CO2 emissions and compares them with optimum designs based on construction cost. The aim is to identify efficient design practices that minimize the environmental impact of earthquake-resistant RC frames and examine the trade-offs between their cost and CO2 footprint. To serve this goal, an RC frame is optimally designed according to all ductility classes of Eurocode 8 and for various design peak ground accelerations (PGAs), concrete classes and materials embodied CO2 footprint scenarios. It is found that the minimum feasible CO2 emissions of RC frames strongly depend on the adopted ductility class in regions of high seismicity, where low ductility seismic design can generate up to 60% more CO2 emissions than designs for medium and high ductility. The differences reduce, however, as the level of seismicity decreases. Furthermore, CO2 emissions increase significantly with the design PGA. On the other hand, they are less sensitive to the applied concrete class. It is also concluded that, for medium to high values of the ratio of the unit environmental impact of reinforcing steel to the respective impact of concrete, the minimum CO2 seismic designs are very closely related to the minimum cost designs. However, for low values of the same ratio, the minimum cost design solutions can generate up to 13% more emissions than the minimum CO2 designs

Optimization of reinforced concrete building frames with automated grouping of columns

[EN] In structural design, it is common practice to adopt the same cross-section dimensions for a group of elements. This procedure is mainly for practical and aesthetic reasons, as well as to reduce labour costs, but it also has a positive effect of reducing the number of variables, which simplifies the usual trial and error design process. On the other hand, the total materials cost obtained is closely related to this grouping. Based on this, the present work aims to minimize the cost of reinforced concrete plane frames considering the automated grouping of columns. To achieve this objective, an optimization software was developed by the association of matrix structural analysis, dimensioning and optimization. The sections dimensions, the area of steel and the concrete strength of beams and columns were taken as design variables. For a given maximum number of groups, the optimum grouping and the corresponding values to design variables are obtained. The strategy proposed in this paper to obtain the grouping reduces significantly the number of infeasible candidate solutions during the search process and avoid the proposition of unrealistic designs. For the optimization, a variant of the Harmony Search method was adopted. Some structures were analyzed in order to validate the application of the proposed formulation, as well as to verify the influence of the grouping of elements on the final results. In these structures, it was possible to observe a significant additional reduction in the total cost when automated grouping is performed regarding a uniform grouping, even when a small number of groups is considered. For the 20-floor building frame analyzed, the cost reduction from uniform to automated grouping varied from 5.53 to 7.35%. The influence of the concrete strength on optimal results was also investigated, indicating a cost reduction of 9.74% from best (40 MPa) to worst case (20 MPa). In general, it can be concluded that, when applied in conjunction with the usual design variables, the proposed procedure can enable a significant additional economy, without affecting the structural safety.The authors acknowledge the financial support of the Brazilian Council for Scientific and Technological Development CNPq (Grant: 302736/2017-4) and of the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (Project: BIA2017-85098-R).Boscardin, J.; Yepes, V.; Kripka, M. (2019). Optimization of reinforced concrete building frames with automated grouping of columns. Automation in Construction. 104:331-340. https://doi.org/10.1016/j.autcon.2019.04.024S33134010

Carbon embodied optimization for buttressed earth-retaining walls: Implications for low-carbon conceptual designs

[EN] This paper shows the differences between the design of a reinforced concrete structure considering two objectives to minimize; economic cost and CO2 emissions. Both objectives depend on the amount of two high carbon intensive materials: cement in the concrete and steel; therefore, these objectives are related. As the balance between steel and cement per m3 of concrete depends on several factors such as the type of structure, this study focuses on buttressed earth-retaining walls. Another factor that determines the balance between steel and concrete is the height of the wall. Thus, the methodology considers a parametric study for optimal designs of buttressed earth-retaining walls, where one of the parameters is the wall height. One of the objectives is to show the variation in cost when CO2 is minimized, respectful of minimizing the economic cost. The findings show that wall elements under bending-compressive strains (i.e. the stem of the buttressed retaining wall) perform differently depending on the target function. On one hand, the study reveals an upward trend of steel per unit volume of concrete in emission-optimized earth-retaining buttressed walls, compared to the cost-optimized. On the other hand, it is checked that unlike the cost-optimized walls, emission-optimized walls opt for a higher concrete class than the minimum class available. These findings indicate that emission-optimized walls penalize not only concrete volume, but also the cement content, to the extent that a higher concrete class outperforms in reduced emissions. Additionally, the paper outlines how and to what extent the design of this typology varies for the two analyzed objectives in terms of geometry and amount of materials. Some relevant differences influencing the geometry of design strategies are found.This research was funded by the European Institute of Innovation and Technology under grant agreement no 20140262 Low Carbon Strategy in the Construction Industry (PGA_A-PED0094_2014-2.1-278_P066-10) and the Spanish Ministry of Economy and Competitiveness along with FEDER funding (Project BIA2014-56574-R). The authors are grateful for the through revision of the manuscript by Tatiana Garcia-Segura.Molina Moreno, F.; Martí Albiñana, JV.; Yepes Piqueras, V. (2017). Carbon embodied optimization for buttressed earth-retaining walls: Implications for low-carbon conceptual designs. JOURNAL OF CLEANER PRODUCTION. 164:872-884. https://doi.org/10.1016/j.jclepro.2017.06.246S87288416