Issue 58

Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is the International Journal of the Italian Group of Fracture (ISSN 1971-8993). It is an open-access journal published online every three months (January, April, July, October). The Journal is financially supported by Italian Group of Fracture and by crowdfunding and is completely free of charge both for readers and for authors. Neither processing charges nor submission charges are required.

Vol XV, Issue 58, October 2021

ISSN 1971 - 8993

Frattura ed Integrità Strutturale, 58 (2021); International Journal of the Italian Group of Fracture

Table of Contents Q.-C Li, L. Zhou, Z.-M. Li, Z.-H. Liu, Y. Fang, L. Zhao, Y. Han.

Factors affecting reorientation of hydraulically induced fracture during fracturing with oriented perforations in shale gas reservoirs ……………………………………………………... 1-20 R. N. da Cunha, C. de Sousa Vieira, D. L. N. de Figueiredo Amorim Lumped damage mechanics as a diagnosis tool of reinforced concrete structures in service: case studies of a former bridge arch and a balcony slab ………………………………………... 21-32 A. Arbaoui, A. Ouahabi, S. Jacques, M. Hamiane Wavelet-based multiresolution analysis coupled with deep learning to efficiently monitor cracks in concrete …………………………………………………………………………....... 33-47 Numerical assessment of reinforced concrete beams strengthened with CFRP sheets under impact loading … ………………………………………………………………………...... 48-64 K. Nabil, M. Djouri, M. Boucherba, M. Kebaili Evaluation of rheological performance of a local modified bitumen by Styrene Butadiene Styrene polymer used in wearing course ………………………………………………………… 65-76 A. Bouaricha, N. Handel, A. Boutouta, S. Djouimaa Load bearing capacity of thin-walled rectangular and I-shaped steel sections of short both empty and concrete-filled columns …………………………………………………………...... 77-85 M. Emara, M. S. Rizk, H.A. Mohamed, M. Zaghlal Enhancement of circular RC columns using steel mesh as internal or external confinement under the influence of axial compression loading………………………………………………... 86-104 B.V. Sunil Kumar, V. Neelakantha Londe, M. Lokesha, S.N. Vasantha Kumar, A.O. Surendranathan Influence of oxidation on fracture toughness of Carbon-Carbon Composites for high-temperature applications …………………………………………………....……………………. 105-113 M. Emara, N. Elkomy, H. Hassan


Fracture and Structural Integrity, 58 (2021); ISSN 1971-9883

J. Wang, Z. Liu, L. Xue Structural model updating based on metamodel using modal frequencies ……………………... 114-127 W. Frenelus, H. Peng, J. Zhang Long-term degradation, damage and fracture in deep rock tunnels: A review on the effect of excavation methods ………..…………………………………………………………. 128-150 E. S. M. M. Soliman Damage severity for cracked simply supported beams ................................................................... 151-165 M. Ravikumar, H.N. Redappa, R. Suresh, E. R. Babu, C. R. Nagaraja Study on micro - nano sized Al 2 O 3 particles on mechanical, wear and fracture behavior of Al7075 Metal Matrix Composites ……………………………………………………. 166-178 A. Talhi, M. Z. Touhami, K. Fedaoui Effect of gaseous carburizing thermochemical treatment on tribological behavior of Ti–6Al–4V alloy ……………………………………………………………………………...... 179-190 S. Doddamani, C. Wang, M. JinnahSheik Mohamed, Md. ArefinKowser Fracture analysis of AA6061-graphite composite for the application of helicopter rotor blade ….. 191-201 I. Elmeguenni Asymptotic response of friction stir welded joint under cyclic loading ……………………….... 202-210 G. Gomes, T. A. A Oliveira, Al. M. D. Neto, L. M. Bezerra A new methodology to predict damage tolerance based on compliance via global-local analysis …... 211-230 A. I. Fezazi, B. Mechab, M. Salem, B. Serier Numerical prediction of the ductile damage for axial cracks in pipe under internal pressure …… 231-241 A. Mishra, A. Vats Supervised machine learning classification algorithms for detection of fracture location in dissimilar friction stir welded joints ……………………………………………………………… 242-253 M. Utzeri, M. Sasso, G. Chiappini, S. Lenci Modelling of low-velocity impacts on composite beams in large displacement ………………….. 254-271


Frattura ed Integrità Strutturale, 58 (2021); International Journal of the Italian Group of Fracture

M. Azadi, H. Aroo Bending cyclic behavior and scatter-band analysis of aluminum alloys under beneficial and detrimental conditions through high-cycle fatigue regime …………………………………..... 272-281 F. R. Andreacola, I. Capasso, L. Pilotti, G. Brando Influence of 3D-printing parameters on the mechanical properties of 17-4PH stainless steel produced through Selective Laser Melting ……………………………………………...... 282-295 H. Suiffi, A. El Maliki, F. Majid, O. Cherkaoui The effect of using polypropylene fibers on the durability and fire resistance of concrete …………. 296-307 T.-H. Nguyen, A.-T. Vu Evaluating structural safety of trusses using Machine Learning ……………………………. 308-318 K. Benyahi, Y. Bouafia, M. S. Kachi, A. Hamri , S. Benakli Periodic homogenization and damage evolution in RVE composite material with inclusion ….… 319-343 S. Çal ı ş kan, R. Gürbüz Determining the endurance limit of AISI 4340 steels in terms of different statistical approaches ... 344-364 M. Achoui, F. Sebaa, B. Bouchouicha Influence of themo-mechanical treatments and microstructural state on the fatigue behaviour of a weld seam: case of API X60 steel ………....……………….…………………………... 365-375 M. S ł owik The role of aggregate granulation on testing fracture properties of concrete ……………………. 376-385 R. Capozucca, E. Magagnini, M.V. Vecchietti, S. Khatir RC beams damaged by cracking and strengthened with NSM CFRP/GFRP rods ……..…… 386-401 R. Capozucca, E. Magagnini, M.V. Vecchietti Analysis of static response of RC beams with NSM CFRP/GFRP rods …………………... 402-415 S. Khatir, M. A. Wahab, S. Tiachacht, C. Le Thanh, R. Capozucca, E. Magagnini, B. Benaissa Damage identification in steel plate using FRF and inverse analysis ……………………..…. 416-433


Fracture and Structural Integrity, 58 (2021); ISSN 1971-9883

T. V. Tretyakova, M. P. Tretyakov, E. A. Chechulina Experimental study of the Portevin-Le Chatelier effect under complex loading of Al-Mg alloy: procedure issues …………………………………………………………………….... 434-441 A. Ouladbrahim, I. Belaidi, S. Khatir, M. A. Wahab, E. Magagnini, R. Capozucca Sensitivity analysis of the GTN damage parameters at different temperature for dynamic fracture propagation in X70 pipeline steel using neural network …………………………………... 442-452


Frattura ed Integrità Strutturale, 58 (2021); 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

(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

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 Stavros Kourkoulis Carlo Mapelli Liviu Marsavina

(Military University of Technology, Poland) (National Technical University of Athens, Greece)

(Politecnico di Milano, Italy)

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

Antonio Martin-Meizoso


Fracture and Structural Integrity, 58 (2021); ISSN 1971-9883

Raghu Prakash

(Indian Institute of Technology/Madras in Chennai, India)

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) (Ternopil National Ivan Puluj Technical University, Ukraine)

Tuncay Yalcinkaya

Petro Yasniy

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 Riccardo Fincato 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)

(Osaka University, Japan)

Eugenio Giner Ercan Gürses

(Universitat Politecnica de Valencia, Spain) (Middle East Technical University, Turkey)

Ali Javili

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

Dimitris Karalekas Sergiy Kotrechko Grzegorz Lesiuk Paolo Lonetti Carmine Maletta

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

(Wroclaw University of Science and Technology, Poland)

(Università della Calabria, Italy) (Università della Calabria, Italy)

Sonia Marfia

(Università di Cassino e del Lazio Meridionale, Italy)

Lucas Filipe Martins da Silva

(University of Porto, Portugal)

Tomasz Machniewicz

(AGH University of Science and Technology)

Hisao Matsunaga Milos Milosevic Pedro Moreira

(Kyushu University, Japan)

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

(University of Porto, Portugal) (University of Bristol, UK)

Mahmoud Mostafavi Vasile Nastasescu

(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

(GIDC Degree Engineering College, Abrama-Navsari, Gujarat, India)


Frattura ed Integrità Strutturale, 58 (2021); International Journal of the Italian Group of Fracture

Oleg Plekhov

(Russian Academy of Sciences, Ural Section, Moscow Russian Federation)

Alessandro Pirondi Maria Cristina Porcu Zoran Radakovi ć D. Mallikarjuna Reddy

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

(University of Belgrade, Faculty of Mechanical Engineering, Serbia) (School of Mechanical Engineering, Vellore Institute of Technology, India)

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

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

Marta S ł owik Cihan Teko ğ lu Dimos Triantis Sabrina Vantadori Natalya D. Vaysfel'd Charles V. White

(TOBB University of Economics and Technology, Ankara, Turkey

(University of West Attica, Greece)

(Università di Parma, Italy)

(Odessa National Mechnikov University, Ukraine)

(Kettering University, Michigan,USA)

Shun-Peng Zhu

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

Special Issue

Steels and Composites for Engineering Structures

Roberto Capozucca

(Polytechnic University of Marche, Italy)

Samir Khatir

(Ghent University, Belgium)

Cuong Le Thanh

(Ho Chi Minh City Open University, Vietnam) (Lublin University of Technology, Poland)

Marta S ł owik

IGF26 - 26th International Conference on Fracture and Structural Integrity

Special Issue Sara Bagherifard Chiara Bertolin Luciana Restuccia Sabrina Vantadori

(Politecnico di Milano, Italy)

(Norwegian University of Science and Technology, Norway)

(Politecnico di Torino, Italy) (Uiversità di Parma, Italy)


Fracture and Structural Integrity, 58 (2021); ISSN 1971-9883

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

Sister Associations help the journal managing 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 Poland: Group of Fatigue and Fracture Mechanics of Materials and Structures Portugal: Portuguese Structural Integrity Society - APFIE Romania: Asociatia Romana de Mecanica Ruperii - ARMR Serbia: Structural Integrity and Life Society "Prof. Stojan Sedmak" - DIVK Spain: Grupo Espanol de Fractura - Sociedad Espanola de Integridad Estructural – GEF Turkey: Turkish Solid Mechanics Group Ukraine: Ukrainian Society on Fracture Mechanics of Materials (USFMM)


Frattura ed Integrità Strutturale, 58 (2021); 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, 58 (2021); ISSN 1971-9883

FIS news

Dear friends, we continuously try to implement new features in our journal. The last ones we activated are: - the list of the most used keywords … it is available as a nice “words salad” (home page, on the right side). Click on one of them … you will obtain the papers connected with the selected keyword! - “Online First” papers are now available also in the home page, in order to improve their visibility. - the number of visitors per country (with flags): the number is only approximative (and the counting started only a few days ago), but the feature offers a nice view of the international level of our journal. - the list of the “Most viewed papers”: this list is available in the home page. Please, in order to further improve our journal, do not hesitate to send us your suggestions using this link: We will really appreciate your help and we will do our best to implement your suggestions. Concerning Citescore, the last update is really interesting: if the 2020 Citescore is 2.0 (calculated on 05 May, 2021), the CiteScoreTracker 2021 is now 2.2 (last update: 04 September 2021)!!! Let’s work all together to further improve the journal Citescore value!! … we only ask you to: - read the papers we will publish in the journal; - help our journal, using its papers in your references, spreading the information in the socials etc.; - suggest any possible improvement you could have in your mind; - submit new papers to be reviewed and published; - help us with the reviews (we activated an agreement with Publons in order to certify your activity as reviewer). Ciao!

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief


Q.-C. Li et alii, Frattura ed Integrità Strutturale, 58 (2021) 1-20; DOI: 10.3221/IGF-ESIS.58.01

Factors affecting reorientation of hydraulically induced fracture during fracturing with oriented perforations in shale gas reservoirs

Qing-Chao Li School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo, Henan 454000, China. School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, Shandong 266580, China.,, Liang Zhou Well Testing Branch, CNPC Bohai Drilling Engineering Company Limited, Langfang, Hebei 065007, China. Zhi-Min Li No.3 Drilling Engineering Company, CNPC Bohai Drilling Engineering Company Limited, Tianjin 300280, China. Zhen-Hua Liu Oil Production Plant No.2, Petrochina Changqing Oilfield Company, Qingcheng, Gansu 745100, China. Yong Fang Well Testing Branch, CNPC Bohai Drilling Engineering Company Limited, Langfang, Hebei 065007, China. Lei Zhao No.4 Drilling Engineering Branch Company, CNPC Bohai Drilling Engineering Company Limited, Renqiu, Hebei 062550, China.

Ying Han * School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo, Henan 454000, China.

A BSTRACT . Hydraulic fracturing with oriented perforations is an effective technology for gas development from shale reservoirs. However, fracture reorientation during fracturing operation can affect the fracture conductivity and hinder the effective production of shale gas. In addition, factors such as perforation azimuth, in-situ stresses, fracturing fluid viscosity and injection rate can affect fracture reorientation during fracturing operation, and the first

Citation: Li, Q.C., Zhou, L., Li, Z.-M.-, Liu, Z.-H., Fang., Y., Zhao, L., Han., Y., Factors affecting fracture reorientation during fracturing operation with oriented perforations in shale gas reservoirs, Frattura ed Integrità Strutturale, 58 (2021) 1-20.


Q.-C. Li et alii, Frattura ed Integrità Strutturale, 58 (2021) 1-20; DOI: 10.3221/IGF-ESIS.58.01

three factors are controllable factors. In the present work, a numerical simulation model for investigating fracture reorientation during fracturing with oriented perforations was established, and it was verified to be suitable for all investigations in this paper. Based on this simulation model, factors affecting both initiation and reorientation of the hydraulically induced fractures were investigated. The investigation results show that the fluid viscosity has little effect on initiation pressure of hydraulically induced fracture during fracturing operation, and the initiation pressure is mainly affected by perforation azimuth, injection rate and the stress difference. Moreover, the investigation results also show that perforation azimuth and difference between two horizontal principal stresses are the two most important factors affecting fracture reorientation. Based on the investigation results, the optimization of fracturing design can be achieved by adjusting some controllable factors. However, the regret is that the research object herein is a single fracture, and the interaction between fractures during fracturing operation needs to be further explored.

Received: 11.03.2021 Accepted: 03.07.2021 Published: 01.10.2021

Copyright: © 2021 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.

K EYWORDS . Hydraulic fracturing; Oriented perforation; Fracture initiation; Fracture reorientation; Fracture propagation; Shale reservoir.


hale is the fragile and fine grain sedimentary layer that is composed of clastic particles with particle size less than 6.35 × 10 -5 m, clay and organic matter [1]. According to U.S. Energy Information Administration (EIA), the global technically recoverable shale gas resources are 206.68×10 12 m 3 by 2013, and China has the largest recoverable reserves all over the world [2]. Moreover, the EIA predicts that shale gas will be the main driving force for increase of global natural gas production in the future. By 2040, the average daily production of shale gas is expected to be four times that of 2015, reaching 4.76 × 10 9 m 3 [3]. Therefore, although tight shale formations have been generally considered as the caprock of oil and gas reservoirs, they have received increasing attention as unconventional reservoir in recent years. However, shale reservoirs generally have lower permeability (usually between 1.0×10 -21 m 2 and 1.0×10 -19 m 2 ), and belong to ultra-low permeability reservoirs [4]. Hydraulic fracturing operations are generally considered to be effective measures to stimulate the physical properties of shale reservoirs, increasing natural gas production [5, 6]. Perforations around wellbore region can effectively reduce the initiation pressure that is needed to overcome in hydraulic fracturing operations, which is conducive to the initiation of hydraulically induced fractures [7-9]. Accordingly, hydraulic fracturing with oriented perforations has become an effective measure to stimulate shale reservoir. Ideally, to ensure the high fracture conductivity, the direction of perforation should be consistent with the direction of the maximum horizontal main stress. In fact, the geologic conditions of formation are often complicated and it is difficult to accurately determine the direction of the maximum horizontal principal stress σ H [7, 10]. As shown in Fig.1A, stress concentration at the perforation tip due to injection of fracturing fluid results in the micro- hydraulically-induced fracture at the beginning of fracturing operation. As the fracturing fluid continues to be injected, the micro-fracture will propagate along the initial perforation for a certain distance (see Fig.1B). Then, fracture reorientation will occur if there is an angle between the perforation and the maximum horizontal principal stress (Fig.1C). The parameter L in Fig.1C is defined as reorientation radius herein, which is used for describing fracture reorientation. In addition, the bending fractures formed during hydraulic fracturing will lead to retention of proppant in the reorientation position (see Fig.1D), which brings difficulty to the transport of proppant within fracture. Therefore, in-depth investigation on the reorientation of hydraulically induced fractures during hydraulic fracturing operation with oriented perforations is of great importance for the design and optimization of hydraulic fracturing in oilfields. At present, most investigations on hydraulic fracturing technology mainly focus on the analysis of post-fracturing productivity. In comparison, there are fewer studies on the behavioral evolution of fractures during fracturing. Recently, considerable advancements have already been made in behavior evolution of hydraulically induced fractures numerically and/or S


Q.-C. Li et alii, Frattura ed Integrità Strutturale, 58 (2021) 1-20; DOI: 10.3221/IGF-ESIS.58.01

experimentally during hydraulic fracturing operations. Li et al. [11] numerically investigated factors affecting fracture propagation during the multi-cluster staged fracturing for shale reservoir using cohesive elements with ABAQUS FEM software. The investigation reveals that the cluster spacing between the adjacent hydraulic-induced fractures is the most important factor. Chang et al. [12] carried out a series of laboratory experiments to investigate the effectiveness of oriented perforation fracturing, and it showed that the fractures formed by oriented perforation fracturing technology tend to stimulate more reservoir volume. Zhu et al. [13] studied the factors affecting initiation pressure of unconventional reservoirs with a finite element model of hydraulic-induced fracture for the cased wells with the oriented perforations. Li et al. [14] analyzed the reorientation mechanism of hydraulically induced fracture with the coupling finite element model, and the investigation results showed that difference between the maximum and the minimum horizontal principal stresses affects the fracture morphology large. Although these investigations are particularly useful and helpful, there is a lack of detailed research on factors affecting reorientation of fractures during hydraulic fracturing operations with oriented perforation in shale reservoirs. In other words, investigation on the fracture reorientation during reservoir stimulation through hydraulic fracturing is not deep enough. Therefore, it is important and necessary to conduct relevant research.

Figure 1: Schematic of fracture reorientation during hydraulic fracturing operation with oriented perforations. A: fracture initiation; B: fracture propagation; C: fracture reorientation; D: proppant retention within fracture.

In addition, the interaction between fractures during fracturing operation is also an important factor affecting the final fracture morphology in reservoir. Therefore, in-depth analysis of the interaction between fractures is valuable for understanding the formation mechanism of complex fracture network during the fracturing operation. Up till now, some progress has been made by so many scholars in this area. However, current investigations focus on the interaction between natural fractures and hydraulic fractures during fracturing operation, rather than interaction between hydraulically induced fractures. Zhou et al. [15] analyzed crack coalescence in rocks with defects by uniaxial compression experiments and found that crack coalescence can occur in nearly all samples, but the mechanism is different for different types of rocks. Yu et al. [16] numerically analyzed the interaction between fractures during fracturing in tight sandstone reservoir. It was found that obvious interaction occurs between hydraulically induced fractures, and the reservoir pressure is the dominant factor affecting the interaction between fractures. Zhang et al. [17] analyzed factors affecting propagation of natural fracture by XFEM method, it is found that natural fracture propagates easily with the decrease of dip angle and stress difference. Arash [18] investigated the effect of natural fracture on propagation of hydraulically induced fractures, and the investigation results show that interaction between natural fracture and hydraulically induced fracture is the key condition resulting in complex fracture network. Nevertheless, considering that interaction between hydraulic fractures is not the focus of the present work, so related investigation is not carried out herein. In the present work, the coupled finite element model (FEM) used for investigating reorientation of the hydraulically induced fracture in shale reservoirs was developed by using the extended finite element method (XFEM). In this coupled model, some important aspects in the


Q.-C. Li et alii, Frattura ed Integrità Strutturale, 58 (2021) 1-20; DOI: 10.3221/IGF-ESIS.58.01

hydraulic fracturing operations (such as injection of fracturing fluid, fluid flow in hydraulically induced fractures and fracture reorientation) were considered. Based on this, factors affecting fracture reorientation during fracturing in shale reservoirs are then studied, regarding fracture initiation pressure and reorientation radius as the research target. The study in this paper will provide reference for fracturing design of unconventional oil and gas reservoirs.


hale reservoirs are generally heterogeneous and anisotropic, which brings difficulties to practical research [19]. To highlight the research focus, the research model for investigating fracture reorientation in shale reservoirs is assumed to be a homogeneous, isotropic 2D plane strain model. Furthermore, it is considered that the fracture propagation is quasi-static and there is no fluid hysteresis within fractures. Finally, the incompressible Newton fracturing fluid is injected into the wellbore at a constant flow rate during fracturing. Therefore, in-depth study of fracture reorientation in hydraulic fracturing process needs to thoroughly understand the basic theories of seepage mechanics, rock mechanics and damage mechanics involved in the process. In this section, the elementary theories were presented. Stress balance equation of rock in shale reservoir Rock deformation occurs under the dual action of the in-situ stresses and the fluid pressure during fracturing. Weak form is the ultimate equation form for solving multi-field coupling problems by using finite element method. Therefore, the weak form of equations for both the seepage field (pore pressure) and the deformation field (stress and displacement) were obtained herein. The weak form of stress balance equation can be expressed by Eqn. (1) when seepage in porous media of shale reservoir was considered [20, 21]. S where, σ is the effective stress, MPa; f is the unit body force, MPa; t is the unit surface force, MPa; p w is the fluid pressure at the fracture, MPa; δ ε is the virtual stain, dimensionless; δ u is the virtual displacement, m; dV is the volume of the micro-element, m 3 ; and dS is the area of the micro-element, m 2 . Seepage flow equation in shale gas reservoir Simulation of fluid seepage in shale reservoir can be realized by applying pore pressure at each node and then applying the boundary condition of pore pressure at a certain boundary. The law of mass conservation is the law that all physical processes follow. Therefore, the mass conservation equation of fracturing fluid in porous medium can be written as [22, 23] ( )  : σ I ε - p  dV dS =   t u f u +     w V S V dV (1)

   

   


  w


  w

 n v









where, ρ w is the density of fracturing fluid, kg/m

3 ; φ is the porosity, dimensionless; n is the normal vector of surface S ,

dimensionless . At present, only single-phase incompressible seepage can be properly realized in ABAQUS software, and the calculation of complex multi-phase seepage cannot be achieved. Just as Eqn. (3), the seepage of fracturing fluid in shale reservoir is assumed to satisfy Darcy's law [21].


= −





  g


where, v is the seepage velocity, m/s; k is the permeability of shale reservoir, m 2 ; g is gravity acceleration, 9.8 m/s 2 ; dp is pressure difference between two ends of micro-element, MPa.


Q.-C. Li et alii, Frattura ed Integrità Strutturale, 58 (2021) 1-20; DOI: 10.3221/IGF-ESIS.58.01

Initiation and propagation of hydraulically induced fracture The constitutive model of elements used for simulating fracture initiation satisfies the traction-separation criteria. That is to say, the constitutive relationship of elements within the investigation model herein is linear elastic before damage, and its stiffness drops to zero when the damage occurs. Up till now, a variety of different damage criteria (such as the maximum principal stress and the maximum principal strain criterion) have been embedded in the ABAQUS finite element software [11, 24]. Among them, the maximum stress criterion has been proved to be more effective and accurate [24]. Therefore, in this paper, the maximum principal stress criterion shown in Eqn. (4) is used as the damage criterion [25].

    =     max 0 max



where, σ 0 max and σ max are the critical maximum principal stress and the maximum principal stress respectively, MPa. Once the principal stress criterion was adopted, the critical maximum principal stress should be given, and the element damage begins to occur when the maximum principal stress σ max exceeds the critical maximum principal stress σ 0 max . The damage evolution of the unit follows the Benzeggagh-Kenane criteria [25, 26] shown in the following equation

  G




+ − G G G

=   G






  T G

where, G nc , G sc , G S and G T are the normal critical energy release rate, tangential critical energy release rate, the first tangential fracture energy release rate and the second tangential fracture energy release rates respectively, MPa·m; η is a constant, 2.284. Fluid flow in fracture during fracturing Fluid flow in fracture can be divided into the normal flow and the tangential flow. The tangential flow ensures the continuous propagation of fracture during fracturing, and the following Cubic-Law can be adopted to describe the tangential flow in hydraulically induced fracture.

 =  3 - 12 d




where, q is the fluid flow required for 1m of fracture propagation, m 3 ; d is the fracture width, m; μ is the fluid viscosity, Pa·s. Normal fluid flow within the hydraulically induced fracture results in the leak-off of fracturing fluid, and the leak-off of fracturing fluid from fracture into reservoir is defined as




− leak off w Surf C p p −




where, v leak-off is the leak-off velocity, m/s; C leak-off is the leak-off coefficient, m/(MPa · s); p Surf is the pore pressure in shale reservoir adjacent to the fracture surfaces, MPa.


Model geometry and mesh generation lthough the establishment of simulation model is the basic for investigation of fracture reorientation during fracturing operation, a series of assumptions need to be made before the model is constructed. Firstly, shale reservoir is assumed to be homogeneous, and the reservoir properties at any node within the model are the same. Secondly, only single-phase seepage of fracturing fluid occurs in shale, and it satisfies Darcy's law. Moreover, shale is A


Q.-C. Li et alii, Frattura ed Integrità Strutturale, 58 (2021) 1-20; DOI: 10.3221/IGF-ESIS.58.01

assumed to be elastic and its plastic failure during fracturing is ignored. Finally, wellbore used for shale gas production and fracturing operation is a vertical one (see Fig.2A). Based on these assumptions, a 2D plane strain model for investigating fracture reorientation during hydraulic fracturing with oriented perforations in shale reservoirs is established with ABAQUS finite element software (see Fig.2). Therefore, only the maximum and the minimum horizontal principal stress exist within the 2D simulation model before simulation. As shown in Fig.2B, the investigation model is a full-size square model, and its side length is200 m. Generally speaking, the half-length of fractures during fracturing operation is within 100 meters [11]. Therefore, the model size in this paper is sufficient to avoid the influence of boundary effects on the simulation results [11, 27-29]. Moreover, the borehole with a radius of 0.2 m is located in the center of the simulation model. As can be seen from Fig.2A and Fig.2B, the simulation area "abcd" corresponds to a plane in shale reservoir that is perpendicular to the wellbore axis. In order to improve the simulation accuracy, the element size at the outer boundaries is 25 times as large as that around wellbore (see Fig.2B and Fig.2C), and the reservoir model is finally discretized into 17,500 CPE4P elements. The CPE4P elements can realize coupling analysis of fracturing fluid seepage and borehole deformation in simulation of hydraulic fracturing. Another important reason for meshing in this way is that both the initiation and propagation of fractures mainly occur in the near-wellbore region around wellbore. As can be seen in Fig.2C, two perforations are designed centrosymmetrically in different azimuth angles around borehole herein, and the perforation depth is 0.50 m. In the model, reservoir and two perforations are three separate parts, and the perforations should be discretized separately during simulation. Therefore, two centrosymmetrical perforations around wellbore are discretized into 10 T2D2 elements and interact with the reservoir elements. During simulation with this model, when the pressure in perforation reaches reservoir strength, the fracture will initiate at the perforation tip.

Load type


Type and value

Fluid injection

Two injection nodes in Fig.2C

Injection rate Q =10m 3 /min

Boundary ab and cd

Displacement U 1=0

Boundary bc and da

Displacement U 2=0

Boundary conditions

Boundary ab, bc, cd and da

Pore Pressure Pp =18MPa


Displacement U 1= U 2=0

Whole model

Pore Pressure Pp =18MPa

Initial conditions

Whole model

σ H =43MPa, σ H =33MPa and σ V =35MPa

Table 1: The loads, boundary conditions and initial conditions in the investigation.

Boundary conditions and basic simulation parameters The loads, boundary conditions and initial conditions adopted herein have been presented in Tab.1. As can be seen in Tab.1, The normal displacement of both the outer boundaries and the borehole should all be set to 0 throughout the simulation, and the pore pressure at the outer boundaries should also be fixed to the original reservoir pressure. Before the fracturing simulation, the initial in-situ stresses and reservoir pressure within the model need to be initialized. Furthermore, it should be emphasized that the two perforation tips are regarded as injection points of fracturing fluid. The fracturing fluid is injected into the perforation holes at a constant rate during the fracturing operation.


Q.-C. Li et alii, Frattura ed Integrità Strutturale, 58 (2021) 1-20; DOI: 10.3221/IGF-ESIS.58.01

Figure 2: Schematic diagram of hydraulic fracturing with oriented perforation in shale reservoir and the established finite element model. (the perforation azimuth angle is 30 ° , and the perforation depth is 0.50 m) (A): Formation model; (B): 2D finite element meshing model; (C): Meshing elements around borehole.





Poisson's ratio υ , Dimensionless

Elastic Modulus E , GPa



Maximum horizontal principal stress σ H , MPa

Minimum horizontal principal stress σ h , MPa



Vertical principal stress σ V , MPa


Water saturation Sw , %


Initial porosity φ , %

Tensile strength Ts , MPa



Leak-off coefficient C leak-off , m/(MPa · s)

Initial pore pressure P p0 , MPa




Permeability k , m 2

5×10 -17

Side length L , m


Viscosity of fracturing fluid μ , mPa · s


Injection rate Q , m 3 /min


Borehole radius r, m


Perforation depth P d , m


Total fracturing time T , min


Reservoir depth D, m


Perforation azimuth θ , °


Table 2: Basic parameters for simulation.

Although Tab.1 has presented how loads, boundary conditions and initial conditions are applied, no specific values are given. For this purpose, Tab.2 gives the basic data required for simulation. Based on these data, the simulation can be conducted in this paper. Implementation of fracture initiation and reorientation in ABAQUS Although most of the simulation involved in this paper can be done directly by CAE interface in ABAQUS software, secondary development is required for some settings. In this work, a text file with extension .inp is outputted after inputting basic parameters to the simulation software, and secondary development can be conducted by manually modifying this file. Fig.3 shows what needs to be modified in the *.inp file. As can be clearly seen in Fig.3, two contents need to be modified to achieve secondary development: ➢ The fluid injection parameters need to be added into the *.inp file. The content (1) in Fig.3 means that the fracturing fluid is continuously injected at a rate of 5×10 -6 m 3 /s at two nodes numbered 180 and 181 within the instance named Part-1-1.


Q.-C. Li et alii, Frattura ed Integrità Strutturale, 58 (2021) 1-20; DOI: 10.3221/IGF-ESIS.58.01

(A) Before modification

(B) After modification Figure 3: Comparison of the *.inp file before and after modification .

➢ In addition, some simulation results need to be manually outputted. Contents (2) in Fig.3 are some output variables that need to be manually edited in file with extension .inp. Modification (2) in Fig.3 are PFOPENXFEM: width of the hydraulically induced fracture; LEAKVRTXFEM and LEAKVRBXFEM: Leak-off flow rate of two interfaces of fracture in 2D model; ALEAKVRTXFEM and ALEAKVRBXFEM: Total leak-off flow volume from two interfaces of fracture within a 2D model; PORPRES: Pore pressure of the element damaged by the hydraulically induced fracture. The relevant results of hydraulically induced fracture are read from the result file in the form of *.odb when the simulation has been completed, thereby obtaining the initiation pressure and the reorientation radius. In addition, as can be seen in Tab.2, the injection rate is a constant value. However, in order to prevent the non-convergence caused by the sudden change of injection rate at the beginning of simulation, some measures need to be taken. As shown in Fig.4, the injection rate is gradually increased from 0 to the set value during the first 10 seconds. In this way, injection evolution of fracturing fluid at the beginning of fracturing operation becomes smoother, and the simulation process is more stable. Of course, the injection pattern displayed in Fig.4 needs to be realized by the amplitude function.


Q.-C. Li et alii, Frattura ed Integrità Strutturale, 58 (2021) 1-20; DOI: 10.3221/IGF-ESIS.58.01

Figure 4: Evolution of injection rate during fracturing operation .

Verification of the simulation model Model validation refers to exploring the applicability of the established model to investigations. The applicability of the investigation model used in this paper has been verified numerically and/or experimentally in several studies [14, 30]. In the present work, the applicability of the investigation model given in Fig.2 is verified by comparing the experiment in References [31] with the simulation in this paper. However, it should be noted that the simulation conditions (Of course, numerical scaling is required according to dimensional analysis.) should be all consistent with experimental conditions in reference [31]. The experimental conditions are summarized in Tab.3.

Figure 5: Comparison of the experimental result in reference [31] with the simulation result.

Fig.5 illustrates the comparison of the experimental result with the simulation result. By Fig.5, we can clearly see that the fracture morphology obtained by experiment (see Fig.5A) and simulation (see Fig.5B) is similar, which can qualitatively verify the applicability of the investigation model. In order to quantitatively verify the applicability, Tab.4 compares the experiment and the simulation by two parameters, i.e. initiation pressure and reorientation radius. By comparison, it can be found that the initiation pressure in simulation is only 0.29MPa lower than that in experiment, and the redirection radius in simulation is also only 0.18cm shorter than that in experiment. All the above comparisons show that the investigation model in this paper can be used for analysis of both the initiation and the redirection of hydraulically induced fractures during fracturing operation.


Made with FlippingBook flipbook maker