[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120314-en":3,"doc-seo-120314-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120314,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Machine Learning-Based Empirical Formulations Properties of Steel Fiber Reinforced Concrete - Strength","The accurate approximation provided by modern machine learning offers a way to reduce shortcomings of traditional empirical methods, including human and technical errors and environmental concerns. While many studies address predicting strength properties of steel fiber reinforced concrete with machine learning, fewer works focus on developing empirical formulations. This paper proposes new empirical formulations to estimate the strength properties of macro steel fiber reinforced concrete using a large 2650 multi-national dataset. A supervised learning workflow compares Ridge, Lasso, and linear regressions, then uses symbolic regression to derive explicit mathematical expressions. Performance is assessed with established error metrics, and formulations are provided for flat, waved, and hooked end fibers.","| \u003Cbr>Journal of Rehabilitation in Civil Engineering\u003Cbr>Journal homepage: [https://civiljournal.semnan.ac.ir/](https://civiljournal.semnan.ac.ir/) |  |  |  |\n| --- | --- | --- | --- |\n| Machine Learning-Based Empirical Formulations Properties of Steel Fiber Reinforced Concrete |  | for | Strength |\n| Mohammad Hossein Taghavi Parsa 1,* ; Mohammad Reza Adlparvar 2; Morteza Esmaeili 3\u003Cbr>1. Ph.D. Candidate, Department of Civil Engineering, Faculty of Engineering, University of Qom, Qom, Iran\u003Cbr>2. Associate Professor, Department of Civil Engineering, Faculty of Engineering, University of Qom, Qom, Iran\u003Cbr>3. Professor, Department of Railway Engineering, Iran University of Science and Technology, Tehran, Iran\u003Cbr>* [Corresponding author:](Corresponding author: mh.taghavi@stu.qom.ac.ir)[ mh.taghavi@stu.qom.ac.ir](Corresponding author: mh.taghavi@stu.qom.ac.ir) (M.H.T.P); [adlparvar@qom.ac.ir](adlparvar@qom.ac.ir) (M.R.A.) |  |  |  |\n| ARTICLE INFO\u003Cbr>Article history:\u003Cbr>Received: 27 December 2023\u003Cbr>Revised: 07 March 2024\u003Cbr>Accepted: 29 April 2024\u003Cbr>Keywords:\u003Cbr>Strength properties;\u003Cbr>Machine learning;\u003Cbr>Empirical formulation;\u003Cbr>Steel fiber reinforced concrete. | ABSTRACT\u003Cbr>The accurate approximation is a benefit of the modern machine learning technique, which also disappeared the problems of traditional empirical methods, such as human and technical errors plus environmental pollution. Although there are many good samples on the state-of-the-art regarding the machine learning prediction of strength properties of steel fiber reinforced concrete, fewer articles are dedicated to proposing empirical formulations. This paper brings some novel empirical formulations to identify the strength properties of macro steel fiber-reinforced concrete. A 2650 multi-national data records are used to perform the regression, which is an exclusive dataset. This archive is the largest available dataset used in the state-of-the-art steel fiber-reinforced concrete prediction process, which is beneficial for supervised learning. Since the user must be careful regarding overtraining with such a vast resource, a successful strategy provided by the authors in previous research is utilized in which various machine learning techniques are compared to forecast the considered properties. So the Ridge, Lasso, and linear methods are used as regressorsto predict the strength properties and the constants. Symbolic regression, a powerful tool for producing empirical formulations, is used for creating mathematical expressions regarding the strength properties. The performance is also evaluated based on well-known error analysis metrics. The formulations are presented for flat, waved, and hooked end fibers, the most common fibers used in construction engineering. The machine learning-driven formulations are exclusive due to the utilized strategy and the resources, and the precision of the relations are denoted, which presents the superiority to traditional methods. |  |  |\n| E-ISSN: 2345-4423\u003Cbr>© 2025 The Authors. Journal of Rehabilitation in Civil Engineering published by Semnan University Press. This is an open access article under the CC-BY 4.0 license. ([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)) |  |  |  |\n| How to cite this article:\u003Cbr>Taghavi Parsa, M. H., Adlparvar, M. R., & Esmaeili, M. (2025) . Machine Learning-Based Empirical Formulations for Strength Properties of Steel Fiber Reinforced Concrete. Journal of Rehabilitation in Civil Engineering, 13(1), 29- 47. [https://doi.org/10.22075/jrce.2024.32743.1963](https://doi.org/10.22075/jrce.2024.32743.1963) |  |  |  |\n\n1. Introduction  \nForecasting the strength properties of a broadly used construction material such as concrete would be possible with both direct and indirect approaches. The direct methods, as it first comes to mind, are methods in which the researchers spend huge costs and time to produce dozens of experimental specimens based on the 28-day","cbCaikeaUom3Mtk7","https://ap.wps.com/l/cbCaikeaUom3Mtk7","pdf",1357748,1,18,"English","en",105,"# Introduction\n## Direct and indirect approaches for strength prediction\n## Limitations of existing regression methods\n## Role of discontinuities and buckling-related objectives\n## Background and motivation for steel fiber reinforced concrete","[{\"question\":\"Why do researchers use machine learning for predicting strength properties of steel fiber reinforced concrete?\",\"answer\":\"Machine learning improves approximation accuracy and can address limitations of traditional empirical approaches, including errors and inefficiencies. It also supports supervised learning using large datasets to better capture relationships between inputs and strength outputs.\"},{\"question\":\"What data and modeling strategies are used to develop the proposed formulations?\",\"answer\":\"The study uses a 2650-record multi-national dataset and applies supervised regression methods including Ridge, Lasso, and linear regression to predict strength properties and constants. Symbolic regression is then used to generate explicit mathematical expressions representing the strength relationships.\"},{\"question\":\"For which steel fiber types are the empirical formulations presented?\",\"answer\":\"The formulations are provided for flat, waved, and hooked end fibers, which are common in construction engineering applications.\"}]","Machine Learning-Based Empirical Formulations Properties of Steel Fiber Reinforced Concrete - Strength | PDF",1785729402,45,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-based-empirical-formulations-properties-of-steel-fiber-reinforced-concrete-strength","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-based-empirical-formulations-properties-of-steel-fiber-reinforced-concrete-strength/120314/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why do researchers use machine learning for predicting strength properties of steel fiber reinforced concrete?","Question",{"text":75,"@type":76},"Machine learning improves approximation accuracy and can address limitations of traditional empirical approaches, including errors and inefficiencies. 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