A. Cibelli

G. Di Luzio

L. Ferrara

P. Kunz

V. Mechtcherine

English

Archivio istituzionale della ricerca - Politecnico di Milano

Fuzzy logic-based approach for the uncertainty treatment in cementitious materials modelling Philipp Kunz1, Antonio Cibelli2, Giovanni Di Luzio2, Liberato Ferrara2, and Viktor Mechtcherine1 1Institute for Building Materials, Faculty of Civil Engineering, Technische Universität Dresden, Dresden (Germany) 2 Department of Civil and Environmental Engineering, Politecnico di Milano, Milan (Italy) philipp.kunz@tu-dresden.de antonio.cibelli@polimi.it Keywords: Fuzzy Logic, Uncertainty Treatment, Material Modelling, Cementitious Materials, Fibre Reinforced Con-crete, Lattice Discrete Particle Model, Hygro-Thermo-Chemical model, ONIX. Abstract In the context of the Horizon 2020 project ReSHEALience, the concept of Ultra High Durability Concrete (UHDC) is introduced to refer to those materials belonging to the wide family of cementitious materials, whose mixture recipe is tailored to enhance the performance in terms of durability compared to ordinary concretes [1]. The target is achieved through the full exploitation of the inherent capacity of autonomously repairing the cracks which characterises the cement-based composites. For this reason, supplementary cementitious materials, such as slag and crystalline admixtures, are included into the mixture [2]. The UHDC concept is validated by means of either extensive and complex experimental programmes in the laboratory, and monitoring campaigns on structures in real service scenarios. However, the disruptive impact of such advanced materials on the construction market can be materialised only by modelling their behaviour accurately, in order to reliably predict the performance in different scenarios.  The behaviour of UHDC is well-captured by physics-based models, of which the Lattice Discrete Particle Model (LDPM) [3], for the mechanical problems, and the Hygro-Thermo-Chemical (HTC) model [4], for the simulation of moisture, heat and chemical phenomena, are two worthy examples. Recently, these models were extended for the autog-enous and stimulated healing in ordinary and fibre-reinforced concretes at the Politecnico di Milano [5, 6]. However, the afore-mentioned models present a significant number of parameters that need to be calibrated against experimental meas-urements, which are almost always unavailable. This represents the most relevant issue to tackle for their use. In addition, accurate small-scale models, such as LDPM and HTC, are particularly suitable for the modelling at the material level. The upscaling to structural members, or even entire structures, requires the identification of bridging parameters, in charge of bringing the small-scale models’ accuracy into the engineering models adopted for the long-term prediction at the structural level. Among other methods for mathematically describing and quantifying uncertainty, the probability theory and fuzzy set theory could be used [7]. The probability theory is a mathematical theory of chance, stating the likelihood that an event will occur, by quantifying it with a number between zero and one. On the other hand, the logic of fuzzy set theory allows the quantification of degrees of truth or membership to a set [8]. Therefore, the latter is used to describe epistemic uncer-tainty, in particular the uncertainty resulting from insufficient information or lack of (experimental) data to deal with in complex systems, such as the cross-influence between the material composition, the chemistry, and environmental con-ditions on the material response. The fuzzy-set theory enables a flexible assessment of the possibility, which is necessary to deal with complex governing parameter systems and limited experimental databases. The content of this paper focuses on the uncertainty featuring the models’ calibration in case of limited experimental data on modelling material properties at microscopic and mesoscopic scales. To the purpose, a fuzzy logic-based approach is presented and tested for one of the UHDC mixtures identified within the activity of the project ReSHEALience. The accuracy of the fuzzy logic-based predictions is compared to the values of the models’ parameters, gained through the calibration against experimental data. In particular, the proposed approach consists of five steps (see Fig 1). 1. Collection of the expert knowledge on the material itself and on the relationships between peculiar aspects, such as material composition, environmental conditions, loading regimes, and the models governing parameters. 2. Definition of a fuzzy cognitive map, namely a fuzzy graph for representing causal reasoning [9], which allows the extraction, analysis, and visualisation of the knowledge based on hard evidence as well as subjective expert judge-ment. 3. Implementation of a fuzzy rule base with if-then conditions. This fuzzy rule base is serving as the main combina-tion between the membership functions, the causal relations, as it is stated in the cognitive map, and the expert knowledge provided by surveys or literature of similar materials. 322 4. Fuzzification of the parameters, which govern the models adopted, by associating a membership function to each of them. This operation is carried-out for those parameters whose value is affected by a scenario-related uncer-tainty. 5. De-fuzzification process: the membership functions, interval limitations and expert knowledge are combined into an inference system to identify a crisp value for each models governing parameter.   Fig. 1. Fuzzy logic and set theory-based approach for the calibration of the governing parameters in five steps. References 1. Di Luzio, G., Ferrara, L., Alonso, M.C., Kunz, P., Mechtcherine, V., Schroefl, C.: Predicting the long term performance of struc-tures made with advanced cement based materials in extremely aggressive environments: current state of practice and research needs. The approach of the H2020 Project ReSHEALience. In: Schlangen, E., De Schutter, G., Savija, B., Zhang, H., Romero Rodriguez, C. (eds.) Proceedings of Symposium on Concrete Modelling CONMOD2018, pp. 467-477. RILEM Publications SARL, Delft, the Netherlands (2018). 2. Cuenca, E., Mezzena, A., Ferrara, L.: Synergy between crystalline admixtures and nano-constituents in enhancing autogenous healing capacity of cementitious composites under cracking and healing cycles. Construction and Building Materials 266(B), 121447 (2021). 3. Cusatis, G., Pelessone, D., Mencarelli, A.: Lattice Discrete Particle Model (LDPM) for failure behaviour of concrete. I: Theory. Cement and Concrete Composites 33, 881-890 (2011). 4. Di Luzio, G., Cusatis, G.: Hygro-thermo-chemical modeling of high performance concrete. I: Theory. Cement and Concrete Com-posites 74, 120-135 (2009). 5. Cibelli, A., Pathirage, M., Cusatis, G., Ferrara, L., Di Luzio, G.: A discrete numerical model for the effects of crack healing on the behaviour of ordinary plain concrete: Implementation, Calibration, and Validation. Engineering Fracture Mechanics. In Review. 6. Cibelli, A., Ferrara, L., Di Luzio, G.: A discrete numerical model for the effects of crack healing on the behaviour of  fibre reinforced concrete: Implementation, Calibration, and Validation. Unpublished. 7. Altmann, F., Mechtcherine, V.: Modelling chloride ingress into cracked and crack-free strain-hardening cement-based composites (SHCC). In: Ferreira, R.M., Gulikers, J., Andrade, C. (eds.) 3rd International PhD Workshop on Modelling the Durability of Re-inforced Concrete, pp. 75-83. RILEM Publications SARL, Guimarães, Portugal (2009). 8. Möller, B., Beer, M.: Fuzzy randomness. Uncertainty in Civil Engineering and Computational Mechanics. Springer, Berlin, Ger-many (2004).  9. Altmann, F.: A Durability Concept for Strain-Hardening Cement-Based Composites, PhD Thesis, Institute for Building Materials, Faculty of Civil Engineering, Technische Universität Dresden, Dresden, Germany (2012).  M-LDPM -basedcoupled modelgoverning parameters set case study input data setstep 4 - fuzzificationstep 1 - expert knowledgestep 2 - fuzzy cognitive mapstep 3 - fuzzy rule basestep 5 - de-fuzzificationmembership functions for each parameterranges, average values,cross-dependecies among parameters and between parameters and different scenariosvisualisation of the harnessed knwoledge “if - then” statements correlatingparameters to each other and to eventual scenariosinference system to result in crisp valuesfor a given scenario33

Fuzzy logic-based approach for the uncertainty treatment in cementitious materials modelling

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Fuzzy logic-based approach for the uncertainty treatment in cementitious materials modelling

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