Issue 64

Frattura ed Integrità Strutturale (Fracture and Structural Integrity): issue 62 (October 2022)

Vol XVII, Issue 64, April 2023

ISSN 1971 - 8993

Frattura ed Integrità Strutturale, 64 (2023); International Journal of the Italian Group of Fracture

Table of Contents

Q. T. Nguyen, R. Livao ğ lu Degradation of the first frequency of an RC frame with damage levels ………………………. 1-10 A. Abdo, H. A. Mohamed, T. Ryad, S. Ahmed The impact of utilizing ultra-high performance fiber-reinforced concrete in beam-column joints with different patterns of transverse reinforcement ……………………………………………... 11-30 D. Derdour, M. Behim, M. Benzerara Effect of date palm and polypropylene fibers on the characteristics of self-compacting concrete: comparative study …………………………………………………………………… 31-50 P. Ghannadi, S. S. Kourehli, S. Mirjalili A review of the application of the simulated annealing algorithm in structural health monitoring (1995-2021) ……………………………………………………………………….. 51-76 M. Ayad, N. Boumechra, K. Hamdaoui Damage identification in RC bridges by confronting two approaches: visual inspection and numerical analysis ….................................................................................................................. 77-92 K. C. Anil, A. B. Hemavathi, A. Adeebpasha Mechanical and fractured surface characterization of epoxy/red mud/fly ash/aluminium powder filled hybrid composites for automotive applications ……………………………………….. 93-103 A. Eraky, A. M. Sharabash, M. H. El-Feky Efficiency of shape memory alloy seismic restrainers for several conditions of bridge joints ………. 104-120 H. K. Tabar, F. Basaligheh, M. Nikkhah Evaluating the safety and the effect of blast loading on the shotcrete together with lattice girder support of tunnels ………………………………………………………….……......... 121-136 M. V. Boniardi, A. Casaroli, L. Sirangelo, S. Monella, M. Mazzola Failure analysis of boron steel components for automotive applications ………………………. 137-147


Fracture and Structural Integrity, 64 (2023); ISSN 1971-9883

A. Abdo, R. Asker, D. Atef, S. Ahmed Experimental and numerical investigations of the flexural behaviour of Green - Ultra High Performance Fiber Reinforced Concrete beams under repeated loads ..……………………….. 148-170 Y. Zhang, W.-H. Ma, H.-Z. Kang, Q. Li Fracture behaviour of concrete with different replacement rates of iron tailings sand based on double-K criterion ....………………………………………………………………… 171-185 H. Zine Laabidine , B. Zeineddine, F. Noureddine The influence of notch connection location on the short-term behaviour of timber-concrete composite beams, modelling of TCC beams and research for optimal locations, a numerical study ………... 186-203 L. Girelli, M. Giovagnoli, M. Tocci, A. Fortini, M. Gelfi, M. Merlin, A. Pola Impact behavior of gravity cast AlSi10Mg alloy: Effect of hot isostatic pressing and innovative high pressure T6 heat treatment ………………………………………………....……... 204-217 F. Gugouch, M. Elghorba, A. Wahid, B. Youssef Fracture analysis of defect Chlorinated Poly Vinyl Chloride pipes based on burst pressure and prediction their fraction of life ...................................................................................................... 218-228 K. Dileep, A. Srinath, N.R. Banapurmath, M. A. Umarfarooq, Ashok M. Sajjan Mechanical and Fracture Characterization of Epoxy/PLA/Graphene/SiO 2 Composites …… 229-239 B. Gudadappanavar, D. K. Kulkarni, P. S. Shivakumar Gouda An assessment of HDPE fillers and fiber wrapping on the strength of reinforced concrete ..…….. 240-249 Y. Li, L. Zou, Z. Zhu Optimization of S-N curve fitting based on neighborhood rough set reduction with improved firefly algorithm ..………………………………………………………………………….. 250-265 M.A. Kenanda, F. Hammadi, Z. Belabed, M.H. Meliani Free vibration analysis of porous functionally graded plates using a novel Quasi-3D hyperbolic high order shear deformation theory …………………………………………………….. 266-282


Frattura ed Integrità Strutturale, 64 (2023); International Journal of the Italian Group of Fracture

Editorial Team

Editor-in-Chief Francesco Iacoviello

(Università di Cassino e del Lazio Meridionale, Italy)

Co-Editor in Chief Filippo Berto

(Università di Roma “La Sapienza”, Italy; Norwegian University of Science and Technology (NTNU), Trondheim, Norway)

Sabrina Vantadori

(Università di Parma, Italy)

Jianying He

(Norwegian University of Science and Technology (NTNU), Trondheim, Norway)

Section Editors Sara Bagherifard

(Politecnico di Milano, Italy) (Politecnico di Milano, Italy) (University of Porto, Portugal) (University of Belgrade, Serbia)

Marco Boniardi

José A.F.O. Correia

Milos Djukic

Stavros Kourkoulis

(National Technical University of Athens, Greece) (University Politehnica Timisoara, Romania)

Liviu Marsavina Pedro Moreira

(INEGI, University of Porto, Portugal) (Chinese Academy of Sciences, China)

Guian Qian

Aleksandar Sedmak

(University of Belgrade, Serbia)

Advisory Editorial Board Harm Askes

(University of Sheffield, Italy) (Tel Aviv University, Israel) (Politecnico di Torino, Italy) (Università di Parma, Italy) (Politecnico di Torino, Italy) (Politecnico di Torino, Italy)

Leslie Banks-Sills Alberto Carpinteri Andrea Carpinteri Giuseppe Ferro

Donato Firrao

Emmanuel Gdoutos

(Democritus University of Thrace, Greece) (Chinese Academy of Sciences, China)

Youshi Hong M. Neil James Gary Marquis

(University of Plymouth, UK)

(Helsinki University of Technology, Finland)

(Ecole Nationale Supérieure d'Arts et Métiers | ENSAM · Institute of Mechanics and Mechanical Engineering (I2M) – Bordeaux, France)

Thierry Palin-Luc Robert O. Ritchie Ashok Saxena Darrell F. Socie Shouwen Yu Cetin Morris Sonsino

(University of California, USA)

(Galgotias University, Greater Noida, UP, India; University of Arkansas, USA)

(University of Illinois at Urbana-Champaign, USA)

(Tsinghua University, China) (Fraunhofer LBF, Germany) (Texas A&M University, USA) (University of Dublin, Ireland)

Ramesh Talreja David Taylor John Yates Shouwen Yu

(The Engineering Integrity Society; Sheffield Fracture Mechanics, UK)

(Tsinghua University, China)

Regional Editorial Board Nicola Bonora

(Università di Cassino e del Lazio Meridionale, Italy)

Raj Das

(RMIT University, Aerospace and Aviation department, Australia)

Dorota Koca ń da

(Military University of Technology, Poland)


Fracture and Structural Integrity, 64 (2023); ISSN 1971-9883

Stavros Kourkoulis Carlo Mapelli Liviu Marsavina

(National Technical University of Athens, Greece)

(Politecnico di Milano, Italy)

(University of Timisoara, Romania) (Tecnun Universidad de Navarra, Spain)

Antonio Martin-Meizoso Mohammed Hadj Meliani

(LPTPM , Hassiba Benbouali University of Chlef. Algeria) (Indian Institute of Technology/Madras in Chennai, India)

Raghu Prakash

Luis Reis Elio Sacco

(Instituto Superior Técnico, Portugal) (Università di Napoli "Federico II", Italy) (University of Belgrade, Serbia) (Tel-Aviv University, Tel-Aviv, Israel)

Aleksandar Sedmak

Dov Sherman Karel Sláme č ka

(Brno University of Technology, Brno, Czech Republic) (Middle East Technical University (METU), Turkey)

Tuncay Yalcinkaya

Editorial Board Jafar Albinmousa Mohammad Azadi Nagamani Jaya Balila

(King Fahd University of Petroleum & Minerals, Saudi Arabia) ( Faculty of Mechanical Engineering, Semnan University, Iran)

(Indian Institute of Technology Bombay, India) (Indian Institute of Technology Kanpur, India)

Sumit Basu

Stefano Beretta Filippo Berto K. N. Bharath

(Politecnico di Milano, Italy)

(Norwegian University of Science and Technology, Norway) (GM Institute of Technology, Dept. Of Mechanical Engg., India)

Elisabeth Bowman

(University of Sheffield)

Alfonso Fernández-Canteli

(University of Oviedo, Spain) (Università di Parma, Italy)

Luca Collini

Antonio Corbo Esposito

(Università di Cassino e del Lazio Meridionale, Italy)

Mauro Corrado

(Politecnico di Torino, Italy)

Dan Mihai Constantinescu

(University Politehnica of Bucharest, Romania)

Manuel de Freitas Abílio de Jesus Vittorio Di Cocco Andrei Dumitrescu Devid Falliano Riccardo Fincato Eugenio Giner Milos Djukic

(EDAM MIT, Portugal)

(University of Porto, Portugal)

(Università di Cassino e del Lazio Meridionale, Italy)

(University of Belgrade, Serbia)

(Petroleum-Gas University of Ploiesti, Romania)

(Dipartimento di Ingegneria Strutturale, Edile e Geotecnica, Politecnico di Torino, Italy)

(Osaka University, Japan)

(Universitat Politecnica de Valencia, Spain) (Université-MCM- Souk Ahras, Algeria) (Middle East Technical University, Turkey) (Hassiba Benbouali University of Chlef, Algeria)

Abdelmoumene Guedri

Ercan Gürses

Abdelkader Hocine

Ali Javili

(Bilkent University, Turkey) (University of Piraeus, Greece)

Dimitris Karalekas Sergiy Kotrechko Grzegorz Lesiuk

(G.V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine, Ukraine)

(Wroclaw University of Science and Technology, Poland)

Paolo Lonetti

(Università della Calabria, Italy)

Tomasz Machniewicz

(AGH University of Science and Technology) (Università Politecnica delle Marche, Italy)

Erica Magagnini Carmine Maletta

(Università della Calabria, Italy)

Fatima Majid Sonia Marfia

(University Chouaib Doukkali, El jadida, Morocco) (Università di Cassino e del Lazio Meridionale, Italy)

Lucas Filipe Martins da Silva

(University of Porto, Portugal) (Kyushu University, Japan)

Hisao Matsunaga Milos Milosevic Pedro Moreira

(Innovation centre of Faculty of Mechanical Engineering in Belgrade, Serbia)

(University of Porto, Portugal)


Frattura ed Integrità Strutturale, 64 (2023); International Journal of the Italian Group of Fracture

Mahmoud Mostafavi Vasile Nastasescu

(University of Bristol, UK)

(Military Technical Academy, Bucharest; Technical Science Academy of Romania)

Stefano Natali Andrzej Neimitz

(Università di Roma “La Sapienza”, Italy) (Kielce University of Technology, Poland)

(Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, Ukraine)

Hryhoriy Nykyforchyn

Pavlos Nomikos

(National Technical University of Athens) (IMT Institute for Advanced Studies Lucca, Italy)

Marco Paggi Hiralal Patil Oleg Plekhov

(GIDC Degree Engineering College, Abrama-Navsari, Gujarat, India) (Russian Academy of Sciences, Ural Section, Moscow Russian Federation) (University of Belgrade, Faculty of Mechanical Engineering, Serbia) (School of Mechanical Engineering, Vellore Institute of Technology, India) (Università di Parma, Italy)

Alessandro Pirondi Zoran Radakovi ć D. Mallikarjuna Reddy

Luciana Restuccia Giacomo Risitano Mauro Ricotta Roberto Roberti

(Politecnico di Torino, Italy) (Università di Messina, Italy) (Università di Padova, Italy) (Università di Brescia, Italy)

Elio Sacco

(Università di Napoli "Federico II")

Hossam El-Din M. Sallam

(Jazan University, Kingdom of Saudi Arabia) (Università di Roma "Tor Vergata", Italy)

Pietro Salvini Mauro Sassu

(University of Cagliari, Italy) (Università di Parma, Italy)

Andrea Spagnoli Ilias Stavrakas Marta S ł owik Cihan Teko ğ lu Dimos Triantis

(University of West Attica, Greece) (Lublin University of Technology)

(TOBB University of Economics and Technology, Ankara, Turkey

(University of West Attica, Greece)

Paolo Sebastiano Valvo Natalya D. Vaysfel'd

(Università di Pisa, Italy)

(Odessa National Mechnikov University, Ukraine)

Charles V. White Shun-Peng Zhu

(Kettering University, Michigan,USA)

(University of Electronic Science and Technology of China, China)

Structural Integrity and fatigue mechanisms: applications and recent trends

Special Issue

Rabie Elotmani

(Chouaib Doukkali University, Morocco)


Fracture and Structural Integrity, 64 (2023); ISSN 1971-9883

Frattura ed Integrità Strutturale is an Open Access journal affiliated with ESIS

Sister Associations help the journal managing Algeria: Algerian Association on Fracture Mechanics and Energy -AGFME Australia: Australian Fracture Group – AFG Czech Rep.: Asociace Strojních Inženýr ů (Association of Mechanical Engineers) Greece: Greek Society of Experimental Mechanics of Materials - GSEMM India: Indian Structural Integrity Society - InSIS Israel: Israel Structural Integrity Group - ISIG Italy: Associazione Italiana di Metallurgia - AIM Italy: Associazione Italiana di Meccanica Teorica ed Applicata - AIMETA Italy:

Società Scientifica Italiana di Progettazione Meccanica e Costruzione di Macchine - AIAS Group of Fatigue and Fracture Mechanics of Materials and Structures

Poland: Portugal:

Portuguese Structural Integrity Society - APFIE Romania: Asociatia Romana de Mecanica Ruperii - ARMR Serbia:

Structural Integrity and Life Society "Prof. Stojan Sedmak" - DIVK Grupo Espanol de Fractura - Sociedad Espanola de Integridad Estructural – GEF

Spain: Turkey: Ukraine:

Turkish Solid Mechanics Group

Ukrainian Society on Fracture Mechanics of Materials (USFMM)


Frattura ed Integrità Strutturale, 64 (2023); International Journal of the Italian Group of Fracture

Journal description and aims Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is the official Journal of the Italian Group of Fracture. It is an open-access Journal published on-line every three months (January, April, July, October). Frattura ed Integrità Strutturale encompasses the broad topic of structural integrity, which is based on the mechanics of fatigue and fracture and is concerned with the reliability and effectiveness of structural components. The aim of the Journal is to promote works and researches on fracture phenomena, as well as the development of new materials and new standards for structural integrity assessment. The Journal is interdisciplinary and accepts contributions from engineers, metallurgists, materials scientists, physicists, chemists, and mathematicians. Contributions Frattura ed Integrità Strutturale is a medium for rapid dissemination of original analytical, numerical and experimental contributions on fracture mechanics and structural integrity. Research works which provide improved understanding of the fracture behaviour of conventional and innovative engineering material systems are welcome. Technical notes, letters and review papers may also be accepted depending on their quality. Special issues containing full-length papers presented during selected conferences or symposia are also solicited by the Editorial Board. Manuscript submission Manuscripts have to be written using a standard word file without any specific format and submitted via e-mail to Papers should be written in English. A confirmation of reception will be sent within 48 hours. The review and the on-line publication process will be concluded within three months from the date of submission. Peer review process Frattura ed Integrità Strutturale adopts a single blind reviewing procedure. The Editor in Chief receives the manuscript and, considering the paper’s main topics, the paper is remitted to a panel of referees involved in those research areas. They can be either external or members of the Editorial Board. Each paper is reviewed by two referees. After evaluation, the referees produce reports about the paper, by which the paper can be: a) accepted without modifications; the Editor in Chief forwards to the corresponding author the result of the reviewing process and the paper is directly submitted to the publishing procedure; b) accepted with minor modifications or corrections (a second review process of the modified paper is not mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. c) accepted with major modifications or corrections (a second review process of the modified paper is mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. d) rejected. The final decision concerning the papers publication belongs to the Editor in Chief and to the Associate Editors. The reviewing process is usually completed within three months. The paper is published in the first issue that is available after the end of the reviewing process.

Publisher Gruppo Italiano Frattura (IGF) ISSN 1971-8993 Reg. Trib. di Cassino n. 729/07, 30/07/2007

Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0)


Fracture and Structural Integrity, 64 (2023); ISSN 1971-9883

FIS news


ear friends, IGF27, the 27 th International Conference on Fracture and Structural Integrity, was a great success! More than 160 presentations, with more than 100 participants in presence and more than 70 in remote, allowed to organize a great event. Soon, the videorecordings of the presentations will be collected in a volume (with ISBN and DOI) and will be available in the IGF YouTube channel and in ESIS-PH ( ESIS Publishing House ) and a volume of papers will be published in Procedia Structural Integrity . Now…let’s talk about the next IGF event: The third European Conference on the Structural Integrity of Additively Manufactured Materials (ESIAM23) The conference will be held in Porto (Portugal) an online in September 4-6, 2023 ( The conference will provide an overview over current scientific knowledge and stimulate ideas for future research directions in this emerging field. Peer-reviewed contributions will be in the form of presentation or a poster. The agenda will allow for extended discussions and for exploring Porto at the end of summer. ESIAM23 is the third event of the ESIAM series following the success of the first event in Trondheim 2019 and the online conference held in 2021. The abstract submission deadline is June 30, 2023 … join us!! Ciao!

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief

P.S. Don’t forget to join the new discussion platform we recently activated… the FIS BLOG:


Q. T. Nguyen et alii, Frattura ed Integrità Strutturale, 64 (2023) 1-10; DOI: 10.3221/IGF-ESIS.64.01

Degradation of the first frequency of an RC frame with damage levels

Quy Thue Nguyen Faculty of Civil Engineering, Nguyen Tat Thanh University, Ho Chi Minh City, Vietnam,, Ramazan Livao ğ lu Department of Civil Engineering, Bursa Uluda ğ University, Bursa City, Türkiye, A BSTRACT . Damage in RC structures causes the degradation of stiffness and frequency. In this study, the relationship between the two coefficients and damage severities is numerically investigated considering a three-dimensional (3D) RC frame in which the concrete damage plasticity model (CDPM) and the elastoplastic model are selected for concrete and reinforcements, respectively. Crack propagation is obtained utilizing a nonlinear static pushover analysis (NSPA). After pushing, according to the base shear force versus top displacement curve, the bending stiffness of the structure is determined rapidly based on the first derivative of the relationship. Thereafter, the degradation of the first frequency is obtained based on the derivative of the nonlinear curve of stiffness, the second derivative of the force- displacement curve viz. As a result, it is observed that the degradation of the first frequency of the RC frame is proportional to the severity of damage but not linearly. More significant damage, a more profound decrease in the frequency. Particularly, the frequency of the frame reduces gradually until the base shear force reaches 70% of the ultimate value at which the parameter is 60% of the healthy counterpart. After that, the reduction gets more significant when the bending capacity approaches the ultimate value. K EYWORDS . Structural Integrity, Structural Health Monitoring, Natural Frequency, Concrete Damage Plasticity Model, Pushover Analysis.

Citation: Nguyen, Q. T., Livao ğ lu, R., Degradation of the first frequency of an RC frame with damage levels, Frattura ed Integrità Strutturale, 64 (2023) 1-10.

Received: 02.11.2022 Accepted: 12.01.2023 Online first: 14.01.2023 Published: 01.04.2023

Copyright: © 2023 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

I NTRODUCTION tructural health monitoring (SHM) has been applied to control regularly the health of RC structures which have deteriorated having been subjected to a sudden loading (Khatir et al. [1]). Systems under service also undergo some faults as a consequence of environmental conditions or accidental events (Ho et al. [2]). It is vital for engineering S


Q. T. Nguyen et alii, Frattura ed Integrità Strutturale, 64 (2023) 1-10; DOI: 10.3221/IGF-ESIS.64.01

applications (Benaissa et al. [3]). Since maintenance and repair of existing structures are essentially required (Ho et al. [4]). Evaluating the vibrations of buildings possibly leads to an indication of the extent of faults that may transpire in the incoming earthquake events of as stated by Kristiawan et al. [5]. Khatir et al. [6] claimed that cracks are among the most commonly witnessed failure types in engineering structures and materials. Crack propagation plays a decisive role in the residual lifetime of any structure (Khatir and Wahab [7], Thobiani et al. [8]). After damage occurrence or crack presence , stiffness parameters of monitored structures reduce, leading to changes in terms of modal characteristics such as frequency and mode shape. Vibration-based damage detection methods have played an important role among current non-destructive evaluation testing techniques (Gillich et al. [9]). The modal information is targeted in various damage assessment methods (Gentile et al. [10], Tiachacht et al. [11], Saisi et al. [12], Iacovino et al. [13], Khatir et al. [14]). Compared to mode shape generations, frequency measurements are cheap, quickly conducted, and often reliable. Therefore, it has been focused on in literature. Non destructive methods assessing the integrity of structures based on natural frequencies have been mentioned in many studies (Cerri and Vestroni [15], Yang and Wang [16]). Natural frequency is considered a diagnostic parameter in structural assessment procedures using vibration monitoring, particularly an analysis of periodical frequency in Salawu [17]. In general, natural frequency shifts are sensitive damage indicators of damage occurrence. Loss of the structural stiffness caused by the damage of materials directly leads to natural frequency degradation. It means the natural frequencies that are straightforwardly identified in practice contain information about the damage severities or declination of stiffness parameters of complicated structures like RC buildings. Hence, the relationship between the two parameters has also taken a lot of interest but not adequately. For instance, changes in resonant frequency with increasing loads of a simply supported RC beam with multiple cracks using different dynamic excitations for various damage levels were evaluated by Hamad et al. [18]. The author showed that at 30% of the ultimate load, the resonant frequency decreases an amount of 10% from the counterpart of the intact one and then gradually reduces. The amount of reduction is about 25% as the beam is loaded by 70% of the ultimate load. Targeting larger and more complicated structures than an RC beam, this current study is to investigate the fundamental frequency degradation due to damage severity of a 3D RC frame. More importantly, the proposed two-step derivative procedure allows us to figure out the full relationship between stiffness degradation and the fundamental frequency. From the authors’ point of view, such a study has not been considered adequately. The suggested approach requires a full curvature of loading and top displacement but there are indeed some difficulties to set up an investigation on real specimens like RC frames. Hence, the investigation is conducted by simulating the RC frame whose materials have been validated in order to reach reliable results. Meanwhile, numerical investigations have taken interest from researchers such as Roumaissa et al. [19], Le Thanh et al. [20], Saadatmorad et al. [21], Shirazi et al. [22]. For more enormous and complex structures, the presented derivative procedure is promising for similar examinations on the frequency declination caused by damage, especially RC buildings regardless of numerical or experimental studies.



n SHM of RC buildings, structural damage causes degradation in terms of stiffness while the mass parameter keeps unchanged. Therefore, at each mode, the frequency degradation depends only on the stiffness parameter as seen in Eqn. 1, making it can be captured once the declination of stiffness is determined. Particularly, the natural frequency reduction is proportional to the square root of the stiffness coefficient degradation.







Changes in terms of frequency caused by different damage severities on RC structures can be obtained completely considering its nonlinear behavior. The frequency degradation is then can be determined using the 2-step derivative as demonstrated in Fig. 1. Initially, a nonlinear static pushover analysis is implemented on monitored RC frames to capture the relationship between base-shear force versus top displacement. The relationship in a specific range is then formulated to build an original equation. Thereafter, the stiffness degradation according to damage levels is directly determined from the 1 st derivative of the equation. The declination of the corresponding natural frequency is finally reached based on the 2 nd derivative of the original formulation.


Q. T. Nguyen et alii, Frattura ed Integrità Strutturale, 64 (2023) 1-10; DOI: 10.3221/IGF-ESIS.64.01

Figure 1: Flowchart of frequency degradation determination from NSPA.



iming at a realistic behavior of RC structures, especially at inelastic stages, the material models of concrete and reinforcement should be selected appropriately. In the commercial software, ABAQUS CAE®, the CDPM is conducted according to Kupfer et al. [23] and Lubliner et al. [24]. The software is capable of capturing the nonlinear behaviour of concrete due to a refined constitutive model of damage coupled with plasticity (see Batista da Costa et al. [25]). Nguyen and Livao ğ lu [26] successfully validated the model using a four-point bending test on an RC beam conducted by Perera and Huerta [27]. Particularly, the required parameters utilized to define the CDPM (see Tab. 1) are built based on previous studies (Kupfer et al. [23], Ren et al. [28], and Najafgholipour et al. [29]). As demonstrated in Fig. 2, the uniaxial behavior in compression is exploited based on Hsu and Hsu [30] and Carreira [31] whereas the tensile regime is delineated following Aslani and Jowkarmeimandi [32]. In Fig. 2a, β is a parameter related to the shape of the compressive branch in the inelastic range, further information about this parameter can be followed in Carreira [31].

(a) (b) Figure 2: Uniaxial stress-strain curve of concrete (a) in compression and (b) in tension.


Q. T. Nguyen et alii, Frattura ed Integrità Strutturale, 64 (2023) 1-10; DOI: 10.3221/IGF-ESIS.64.01

Parameter Dilation angle Eccentricity


35 0.1 2/3 1.16


f bo / f co

Viscosity parameter

0.007985 Table 1: Parameters of CDPM.

The mechanical properties of concrete whose compressive strength is 32 MPa are listed in Tab. 2. In particular, the Poisson’s ratio is set as 0.18 according to Kupfer et al. [23] and Lee and Fenves [33]. The tensile capacity is indicated as 10% of the ultimate compressive strength according to Aslani and Jowkarmeimandi [32] but a percentage of 12 is selected since it leads to a good agreement with empirical data (see Nguyen and Livao ğ lu [26]). On the other hand, the elastoplastic model is selected to define the reinforcements. The detailed mechanical characteristics of reinforcements are listed in Tab. 3.

Properties (cylindrical specimen at 28-day age)


Ultimate compressive strength

32 MPa

Tensile capacity

3.84 MPa 2.3 t/m 3


Elastic modulus Poisson’s ratio

17953.3 MPa


Table 2: Mechanical properties of concrete.



Yielding strength

510 MPa 7.85 t/m 3


Elastic modulus Poisson’s ratio

210000 MPa

0.3 Table 3: Mechanical properties of reinforcement.

Another verification of the material models is also conducted herein as another contribution of this study. Xiao [34] applied a concentrated load at the right center of a 1200-mm-square RC slab whose thickness is 150 mm as seen in Fig. 3a. The load-carrying capacity of the slab that depends on loading rates was examined. A detailed description of the experiment such as specimen properties, test setup and procedures, instrumentation, and can be followed in the original study. Some key information about the specimen is mentioned herein for a better understanding of the numerical model. The experiment is imitated in ABAQUS CAE® to verify the material models utilized in this current study based on the failure mechanism and the load carrying capacity of the slab under a monotonic pushing procedure. It should be noted that the aforementioned material models are also implemented to simulate the slab. The compressive strength of concrete is 42.9 MPa and the yield strength of reinforcing bars is 443 MPa. Although the classes of materials are different from those of the beam, they can be defined in the same manner as done for the beam. In the experiment, the four sides of the slab were bolted to a supporting system using 24 high-tension bolts (6 ones for each side). Besides that, the supporting system is a 1200×1200 mm steel support composed of a series of H-shaped steel beams (Fig. 3b). The system was constrained to a strong floor with high-tension bolts to provide enough rigidity during testing. It is seen that bolting was chosen to constraint the supporting system to the floor below and the slab above it. It is assumed that a completely fixed boundary conditions of the slab may not be attained. Therefore, in the numerical model, two kinds of conditions were examined, simply supported and fully fixed. Similar to Nguyen and Livao ğ lu [26], in the simulation, linear hexahedral elements of type C3D8R and linear line elements of type T3D2 were utilized to define concrete and reinforcements, respectively. The meshing size of 50 mm for both types of materials was defined. As a result, the numerical model of the slab is composed of 2628 elements and 3400 nodes. They are formed by 1728 C3D8R elements and 900 T3D2 elements.


Q. T. Nguyen et alii, Frattura ed Integrità Strutturale, 64 (2023) 1-10; DOI: 10.3221/IGF-ESIS.64.01




(d) (e) Figure 3: Verification of material models on a RC slab conducted by Xiao [34] (a) Test set up (b) Supporting system (c) Real damage mode (d) Numerical damage mode and (e) Comparison of load carrying capacity. The bending capacity and damage mechanism are considered when comparing the experimental and numerical slabs. The real slab was pushed under different loading rates, a static loading rate of 0.0004 m/s (Experiment_Slow) and a high loading rate of 2 m/s (Experiment_High). Displacement sensors and load cells were arranged to collect the applied load and the movement of the mid-span of the slab during pushing. The damage mechanism captured at the low surface of the slab under Experiment_High is shown in Fig. 3c. On the other hand, damage is captured on the top and bottom of the numerical specimen in the case of fully fixed conditions as seen in Fig. 3d. It can be seen that damage mechanisms in the numerical and experimental specimens are in harmony with each other. Moreover, the nonlinear behavior of the two numerical cases is generally similar to that of Experiment_Slow as picturized in Fig. 3e. It initiates from a linear tendency and then gradually falls into a nonlinear range until reaching a peak followed by a significant downward trend. Subsequently, stagnation is witnessed. Meanwhile, dynamic effects were observed in the case of Experiment_High. The numerical result is in harmony with that of Experiment_Slow since the pushing procedure is defined in a Static Step. However, some disagreements are witnessed among them. The numerical specimens seem to be stiffer than the real one as seen in their linear range. Furthermore, the load-carrying capacity of the two numerical specimens is higher than that of Experiment_Slow, especially Numerical_Fixed. The issues may be attributed to many reasons. For example, the real boundary conditions in the real text may be different from the two cases defined in the simulation. Moreover, steel bolts arranged to restrict the real slab to the supporting system can be deformed during loading, especially under high levels, making the boundary condition of the real slab may change during testing. It is true that different boundary conditions possibly lead to significant deviation. Even with no change in the boundary conditions, the notably different behaviors of the two numerical models can be taken as an example. Although they perform approximately in the same tendency in the elastic stage, they start deviating when falling into the inelastic stage. The carrying capacity of Numerical_Simply supported is remarkably lower than that of Numerical_Fixed. More importantly, a perfect bond using ‘‘embedded constraint’’ is utilized to define the interaction


Q. T. Nguyen et alii, Frattura ed Integrità Strutturale, 64 (2023) 1-10; DOI: 10.3221/IGF-ESIS.64.01

between concrete and reinforcements whereas reinforcing bars may delaminate from their surrounding concrete in practice, especially under high levels of loading. That directly lowers the carrying capacity of the actual slab compared to that of the numerical specimens. It can be concluded that although the result of the verification on the slab is not good as seen for that of the beam, it is not bad and does not contain any problematic issues. The above-mentioned deviation can be lessened considering the potential reasons but that is not the main target of this study. Hence, the selected material models are also acceptable for further investigation.



3D RC frame is simulated in the commercial program as one solid body. The finished dimensions and cross section of columns (300 mm x 300 mm) and beams (250 mm x 300 mm) are shown in Fig. 4. It is noted that in all cross-sections, there are 4 longitudinal reinforcing bars whose diameter is 14 mm. On the other hand, 8 mm is the diameter of stirrups that are placed with intervals of 150 mm for both columns and beams. The clear cover of the concrete is 26 mm. The bottom surfaces of the bases are completely fixed.

(a) (c) Figure 4: Numerical model (a) Finished dimensions, (b) beam and column sections, and (c) meshing. (b)



he NSPA procedure as shown in Fig. 5a is defined in ABAQUS CAE® as a displacement-control procedure. It should be noted that the analysis consists of two main steps. Step 1 is used to account for the response against the constant normal loading as profoundly illustrated by the purple components. In particular, the value of the axial load of 5.97 N/mm 2 (equal to about 19% of the normal capacity of structural members) is imparted constantly in the Y axis at the top of the four columns. The gravitational load is also considered in Y-axis in the same direction. It is noted that the effects of this loading are propagated into the next step. In Step 2, the structure is subjected to a monotonically pushing procedure, red components. In Fig. 5a, a monotonic lateral pushing procedure is applied on two columns with respect to the X-axis using a displacement control approach. the lateral displacement is applied incrementally until the drift ratio is equal to 3.5% as stipulated by ACI Committee 374.1 [35]. That makes the target of lateral displacement equal to 87.75mm. Step 1 works separately from Step 2 and then the results of the former step are propagated into the latter one. Moreover, during the both steps, the foot is restrained spatially by assigning the “fixed boundary condition” option to the surfaces at the bottom surfaces of the bases. In general, 50 mm x 50 mm x 50 mm size meshing is utilized to solid elements (see Fig. 4c) whereas the size of 50 mm is selected for truss elements. The numerical model is composed of 27796 linear hexahedral elements of type C3D8R for concrete and 7080 linear line elements of type T3D2 for reinforcements, producing 43896


Q. T. Nguyen et alii, Frattura ed Integrità Strutturale, 64 (2023) 1-10; DOI: 10.3221/IGF-ESIS.64.01

nodes. After the determination of the base-shear force versus top lateral displacement, the displacement ductility factor of the RC frame can be determined in Fig. 5b according to Park [26].

(a) (b) Figure 5: Numerical NSPA (a) Test set up and (b) displacement ductility factor determination.


(b) (c) Figure 6: Product of NSPA (a) Crack propagation (b) Roof-displacement versus Base-shear force and (c) Bending stiffness degradation.


Q. T. Nguyen et alii, Frattura ed Integrità Strutturale, 64 (2023) 1-10; DOI: 10.3221/IGF-ESIS.64.01



he product of NSPA is illustrated in Fig. 6. The crack propagation as well as the roof displacement versus the base shear force curve, depicted in Fig. 6a, b emphasizes the nonlinear behavior of the RC structure. In general, the numerical test leads to reliable results. In each column, the first and most severe crack transpire at the section just above the base. Afterward, the crack propagates into the section and new cracks appear at higher sections. Meanwhile, in the beams, cracks take place at the sections just beside the connections with columns. The visualization of tensile damage at the final stage demonstrates a spectrum that seems to be realistic. Furthermore, the nonlinear behavior is also observed in Fig. 6b. One of the more prominent takeaways of the line graph is that the nonlinear behavior is appropriate to that of typical RC structures. The product of NSPA initiates with an upward trend in the elastic stage followed by another increasing regime but with a continuous stiffness reduction until hitting peaks starting a declined curve and then ending up at a base shear-force of 85% of the peak. The elastic regime ends up at 11.723 mm and then starts transforming to the nonlinear stage in which the ultimate shear force is determined at 30.218 mm while the fracture occurs at 65.431mm lateral displacement. The displacement ductility factor of the structure is about 4.2 falling into the range of 3 to 6 for typical RC frames according to Park [36]. As a result, it can be concluded that the behavior of the considered RC frame is reliable and can be taken advantage of to evaluate the reducing tendency of its fundamental frequency. After the determination of the bending capacity based on the base-shear force versus the top lateral displacement graph (Fig. 6b), the stiffness degradation and the reduction of the fundamental frequency of the RC frame can be pointed out rapidly as illustrated in Fig. 6c and Fig. 7, respectively. First of all, the curve that starts from the elastic range to the nonlinear regime until the ultimate point is numerically formulated through an equation. Afterward, the first derivative of this equation at each point stands for the stiffness of the structure at that moment as seen in Fig. 6c. Subsequently, the degraded stiffness corresponding to each level of fault is normalized to the stiffness at the intact state (about 30 kN/mm). Finally, the normalized frequency which is the fraction of the frequency at each loading level to the one determined at the pristine stage is equal to the square root of the normalized stiffness. As a result, the degradation of the first frequency is graphically demonstrated in Fig. 7. It is noted that normalized lateral loading on the horizontal axis is the ratio of the lateral load at each point and the ultimate value. Compared to the investigation on an RC beam conducted by Hamad et al. [18], the degradation of the fundamental frequency of the considered RC frame is slightly different. For instance, at the moment of 30% of the ultimate load, the declination is 15% for the frame, slightly higher than the 10% value for the beam. When the applied load reaches 70% of the ultimate value, the degradation slightly surpasses 40% for the frame where the amount of reduction of only about 25% is witnessed for the beam. It can be seen that the frequency degradation of the frame seems to be more significant than that of the beam based on the desired moments of loading. In comparison with the approach utilized for the beam, this study gives more sufficient investigation as the fundamental frequency declination can be picturized more thoroughly.

Figure 7: Frequency declination.

The degradation of the first frequency of the RC frame is more extreme as the damage severity increases and can be divided into three main regimes. The modal characteristic decreases about 20% of the counterpart of the pristine frame when the lateral normalized lateral load increase from 0 to 0.4. However, after that, the increase of normalized load from 0.4 to 0.7 causes a degradation of approximately 22%, a more significant reduction compared to the previous state. After this defect


Q. T. Nguyen et alii, Frattura ed Integrità Strutturale, 64 (2023) 1-10; DOI: 10.3221/IGF-ESIS.64.01

level, extreme degradation of the frequency is witnessed, about 33% when the normalized lateral load is increased by an amount of only 0.2, from 0.7 to 0.9.



he current study numerically evaluates the degradation of the fundamental frequency of an RC frame due to the stiffness declination. In general, the two parameters are proportional to each other but not linearly. The relationship contains some different ranges. It is observed that the first frequency decreases gradually until the lateral load reaches 70% of the ultimate value. At that level of loading, the fundamental frequency lowers to about 60% of the counterpart at the pristine state. From this point, the reduction gets more significant. The coefficient loses an amount of about 30% when increasing the horizontal load from 70% to 90% of the ultimate value. In general, the relationship between the fundamental frequency degradation and fault levels is illustrated effectively and completely using the proposed approach without using data from vibration measurements. The numerical results obtained in this study are useful for further investigation of the effects of damage occurrence on the changes in frequency parameters not only at the fundamental modes but also at higher modes of multiple-storey RC structures. However, the proposed method is only suitable for investigations on each separate mode. The observation in this study is obtained based on the fundamental mode while more slender RC buildings may be damaged at higher modes. Damage may be caused by a single mode or combinations of modes, making the presented method in the current version not adequate. [1] Khatir, A., Capozucca, R., Khatir, S., Magagnini, E. (2022). Vibration-based crack prediction on a beam model using hybrid butterfly optimization algorithm with artificial neural network. Front. Struct. Civ. Eng., 16(8), pp. 976–989. DOI: 10.1007/s11709-022-0840-2. [2] Ho, L.V., Nguyen, D.H., Mousavi, M., Roeck, G.D., Bui-Tien, T., Gandomi, A.H., Wahab, M.A. (2021). A hybrid computational intelligence approach for structural damage detection using marine predator algorithm and feedforward neural networks, Comput. Struct., 252, 106568. DOI: 10.1016/j.compstruc.2021.106568. [3] Benaissa, B., Hocine, N.A., Khatir, S., Riahi, M.K., Mirjalili, S. (2021). YUKI Algorithm and POD-RBF for Elastostatic and dynamic crack identification, J. Comput. Sci., 55, 101451. DOI: 10.1016/j.jocs.2021.101451. [4] Ho, L.V., Trinh, T.T., Roeck, G.D., Bui-Tien, T., Nguyen-Ngoc, L., Wahab, M.A. (2022). An efficient stochastic-based coupled model for damage identification in plate structures, Eng. Fail. Anal., 131, 105866. DOI: 10.1016/j.engfailanal.2021.105866. [5] Kristiawan, S.A., Hapsari, I.R., Purwanto, E., Marwahyudi, M. (2022). Evaluation of Damage Limit State for RC Frame Based on FE Modeling, Buildings-Basel, 12(1), 21. DOI: 10.3390/buildings12010021. [6] Khatir, S., Boutchicha, D., Le Thanh, C., Tran-Ngoc, H., Nguyen, T.N., Wahab, M.A. (2020). Improved ANN technique combined with Jaya algorithm for crack identification in plates using XIGA and experimental analysis, Theor. Appl. Fract. Mech., 107, 102554. DOI: 10.1016/j.tafmec.2020.102554. [7] Khatir, S., Wahab, M.A. (2019). Fast simulations for solving fracture mechanics inverse problems using POD-RBF XIGA and Jaya algorithm, Eng. Fract. Mech., 205, pp. 285–300. DOI: 10.1016/j.engfracmech.2018.09.032. [8] Thobiani, F.A., Khatir, S., Benaissa, B., Ghandourah, E., Mirjalili, S., Wahab, M.A. (2021). A hybrid PSO and Grey Wolf Optimization algorithm for static and dynamic crack identification. Theor. Appl. Fract. Mech., 118, 103213. DOI: 10.1016/j.tafmec.2021.103213. [9] Gillich, G.R., Furdui, H., Waha, M.A., Korka, Z.I. (2019). A robust damage detection method based on multi modalanalysis in variable temperature conditions. Mech. Syst. Signal Proc., 115, pp. 361–379. DOI: 10.1016/j.ymssp.2018.05.037. [10] Gentile, C., Saisi, A., Cabboi, A. (2015). Structural Identification of a Masonry Tower Based on Operational Modal Analysis, Int. J. Archit. Herit., 9, pp. 98–110. DOI: 10.1080/15583058.2014.951792. [11] Tiachacht, S., Khatir, S., Le-Thanh, C., Rao, R.V., Mirjalili, S., Wahab, M.A. (2021). Inverse problem for dynamic structural health monitoring based on slime mould algorithm, Eng. Comput., 38, pp. 2205–2228. DOI: 10.1007/s00366-021-01378-8. [12] Saisi, A., Gentile, C., Guidobaldi, M. (2015). Post-earthquake continuous dynamic monitoring of the Gabbia Tower in Mantua, Italy, Constr. Build. Mater., 81, pp. 101–112. DOI: 10.1016/j.conbuildmat.2015.02.010. R EFERENCES


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