Issue 61

Frattura ed Integrità Strutturale (Fracture and Structural Integrity): Issue 61

Vol XVI, Issue 61, July 2022

ISSN 1971 - 8993

Frattura ed Integrità Strutturale, 61 (2022); International Journal of the Italian Group of Fracture

Table of Contents

A. Kostina, M. Zhelnin, O. Plekhov, K.A. Agutin https://youtu.be/12uGZqgEM5E

THM-coupled numerical analysis of temperature and groundwater level in-situ measurements in artificial ground freezing ………………………………………….…………………... 1-19 E. Entezari, J. L. González-Velázquez, D. R. López, M. A. B. Zúñiga, J. A. Szpunar https://youtu.be/QaqWiuUGc6Y Review of current developments on high strength pipeline steels for HIC inducing service ……….. 20-45 V. Shlyannikov, A. Inozemtsev, A. Ratchiev https://youtu.be/LQpcv-JjF8k Couple effects of temperature and fatigue, creep-fatigue interaction and thermo-mechanical loading conditions on crack growth rate of nickel-based alloy ……………………………………... 46-58 H. S. Patil, D. C. Patel https://youtu.be/iuXhhkBAtvM Al 2 O 3 and TiO 2 flux enabling activated tungsten inert gas welding of 304 austenitic stainless steel plates ……………………………………………………………………...…... 59-68 Y. Hadidane, N. Kouider, M. Benzerara https://youtu.be/pwfKzCzr97k Flexural behavior of delta and bi-delta cold-formed steel beams: experimental investigation and numerical analysis .... …………………………………………………………….…... 69-88 F. A. H. Saleh, N. Kaid, K. Ayed, D.-E. Kerdal, N. Chioukh, N. Leklou https://youtu.be/ZC2L2JpEDrg Effects of rubber aggregates on the physical-mechanical, thermal and durability properties of self compacting sand concrete ……………………………………………………………… 89-107 P. O. B. Costa, R. M. Bosse, G. M. S. Gidrão https://youtu.be/gQ7HO6zk3Js Behavior assessment of asymmetrical building with concrete damage plasticity (CDP) under seismic load ………………………………………....……...………………………... 108-118 M. I. Meor Ahmad, M. A. Mohd Sabri, M. F. Mat Tahir, N. A. Abdullah https://youtu.be/phobwclgk2M Predictive modelling of creep crack initiation and growth using Extended Finite Element Method (XFEM) …………………………………………………………………………... 119-129

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Fracture and Structural Integrity, 61 (2022); ISSN 1971-9883

S. Huzni, F. Oktiandar, S. Fonna, F. Rahiem, L. Angriani https://youtu.be/PNAq59jTj6o The use of frictional and bonded contact models in finite element analysis for internal fixation of tibia fracture ………………………………………………………………………... 130-139 M. A. Umarfarooq, P. S. Shivakumar Gouda, K. N. Bharath, G. B. Veereshkumar, N. R. Banapurmath, A. Edacherian https://youtu.be/F9oSkLfFwe0 Effects of residual stresses on interlaminar radial strength of Glass-Epoxy L-bend composite laminates ……………………………………………………………....…………… 140-153 H. Mazighi, M.K. Mihoubi , D. Santillán https://youtu.be/TH9o8Mi3l0M Hybrid phase-field modeling of multi-level concrete gravity dam notched cracks ………….. …... 154-175 R. Andreotti, V. Leggeri, A. Casaroli, M. Quercia, C. Bettin, M. Zanella, M. Boniardi https://youtu.be/3qDb4u7awPs A simplified constitutive model for a SEBS gel muscle simulant - Development and experimental validation for finite elements simulations of handgun and rifle ballistic impacts ………………. 176-197 V.-H. Nguyen, T. Bui-Tien, P. Van Pham, L. Nguyen-Ngoc https://youtu.be/6rHnih9txGI An experimental study and a proposed theoretical solution for the prediction of the ductile/brittle failure modes of reinforced concrete beams strengthened with external steel plates ……………… 198-213 N. Razali, N.B. Masnoor, S. Abdullah, M.F.H.M. Zainaphi https://youtu.be/9hxP90myToY Acoustic analysis using symmetrised implicit midpoint rule ………………………………... 214-229 M. S. Baharin, S. Abdullah, N. Md Nor, M. K. Faidzi, A. Arifin, S. S. K. Singh https://youtu.be/YH7UoIOB3bc Observing the simulation behaviour of Magnesium alloy metal sandwich panel under cyclic loadings ……………………………………………………………………………. 230-243 K. R. Suchendra, M. Sreenivasa Reddy https://youtu.be/Qm-w2NjKxzo Study on microstructure, mechanical and fracture behavior of Al 2 O 3 - MoS 2 reinforced Al6061 hybrid composite …………………………………………………………………….. 244-253 S.M. Firdaus, A. Arifin, S. Abdullah, S.S.K. Singh, N. Md Nor https://youtu.be/S5LalrgofCI Detection of uniaxial fatigue stress under magnetic flux leakage signals using Morlet wavelet …... 254-265 S. Zengah, A. Mankour, S. Abderahmane, H. Salah, A. Mallek, M. M. Bouziane https://youtu.be/o6ZnTHlVds0 Numerical analysis of the crack growth path in the cement of hip spacers ……………………. 266-281

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Frattura ed Integrità Strutturale, 61 (2022); International Journal of the Italian Group of Fracture

L. Arfaoui, A. Samet, A. Znaidi https://youtu.be/UbO_OnBMZho Identification of the anisotropic behavior of the laser welded Interstitial Free steels subjected to off axis tensile tests ……………………………………………………………………... 282-293 R. A. El-Sadany, S. H. Al-Tersawy, H. El-Din M. Sallam https://youtu.be/c_BM5s-gX1k Effect of GFRP and steel reinforcement bars on the flexural behavior of RC beams containing recycled aggregate …………………………………………………………………...... 294-307 M. Khalaf, A. El-Shihy, E. El-Kasaby, A. Youssef https://youtu.be/gSnCbvHksEE Experimental behavior based on effective slab width acting as a flange with supporting steel beams in composite floors with openings ………………………………………………………. 308-326 T. Achour, F. Mili https://youtu.be/tIjZBTlRkdE Composite lay-up configuration effect on double and single sided bonded patch repairs …………. 327-337 P. S. Joshi, S.K. Panigrahi https://youtu.be/UP28yBafIps Evaluation of tensile properties of FRP composite laminates under varying strain rates and temperatures ……………………………………………………..………………….. 338-351 A.A. ELShami, N. Essam, ES. M. Yousry https://youtu.be/_q4l2Apbiwg Improvement of hydration products for self-compacting concrete by using magnetized water ……... 352-371 K. Belkaid, N. Boutasseta, H. Aouaichia, D. E. Gaagaia, B. Boubir , A. Deliou https://youtu.be/222XnMsjFzM A simple and efficient eight node finite element for multilayer sandwich composite plates bending behavior analysis …………………………………………………………………….. 372-393 A. Y. Rahmani, S. H. Boukhalkhal, M. Badaoui https://youtu.be/BzQXb75_UJQ Effect of beam-column joints flexibility on the seismic response of setback RC buildings designed according to the Algerian seismic code …………………………………………………... 394-409 C. Bellini, V. Di Cocco, F. Iacoviello, L. P. Mocanu https://youtu.be/9KI6qZrkDSg Fracture micrographic analysis of a carbon FML under three-point bending load …………….. 410-418 A. Kostina, M. Zhelnin, E. Gachegova, A. Prokhorov, A. Vshivkov, O. Plekhov, S. Swaroop https://youtu.be/82FI_rWZrlQ Finite-element study of residual stress distribution in Ti-6Al-4V alloy treated by laser shock peening with varying parameters ……………………………………………………….. 419-436

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Fracture and Structural Integrity, 61 (2022); ISSN 1971-9883

K. K. Espoir, X. Fuzhe, C. Lu, I. Offei https://youtu.be/xpOBWr6POP8 Experimental and numerical assessment of the location-based impact of grouting defects on the tensile performance of the fully grouted sleeve connection …………………………………… 437-460 T. Salem, A. Eraky, A. Elmesallamy https://youtu.be/BCjf6XyGgfs Locating and quantifying necking in piles through numerical simulation of PIT …………….... 461-472 E. Ashoka, C. M. Sharanaprabhu, G. K. Krishnaraja https://youtu.be/wxsRJEEIc18 Effect of cenosphere and specimen crack lengths on the fracture toughness of Al6061-SiC composites ………………………………………………………………………….. 473-486 T. G. Sreekanth, M. Senthilkumar, S. M. Reddy https://youtu.be/BltRDFMywx4 Natural Frequency based delamination estimation in GFRP beams using RSM and ANN …. 487-495 F. Ferrian, P. Cornetti, L. Marsavina, A. Sapora https://youtu.be/a8x2B52dn5M Finite Fracture Mechanics and Cohesive Crack Model: Size effects through a unified formulation 496-509 N. H. Ononiwu, C. G. Ozoegwu, I. O. Jacobs, V. C. Nwachukwu, E. T. Akinlabi https://youtu.be/9oIgY5bvxog The influence of sustainable reinforcing particulates on the density, hardness and corrosion resistance of AA 6063 matrix composites ……………………………………………… 510-518 A.D. Basso, M. Caldera, N. E. Tenaglia, D. O. Fernandino, R. E. Boeri https://youtu.be/nCtrLZ8y3P0 Influence of free ferrite on the mechanical properties of high strength intercritical Austempered Ductile Iron ……………………………………………………………………….... 519-529 M. E. Kerkar, M. K. Mihoubi https://youtu.be/rOHITv6l6wo Study of structural stability of a concrete gravity dam using a reliability approach …………….. 530-544

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Frattura ed Integrità Strutturale, 61 (2022); 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)

Sabrina Vantadori

(Università di Parma, Italy)

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 Stavros Kourkoulis

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

Carlo Mapelli

(Politecnico di Milano, Italy)

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Fracture and Structural Integrity, 61 (2022); ISSN 1971-9883

Liviu Marsavina

(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)

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

Hisao Matsunaga Milos Milosevic Pedro Moreira

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

Mahmoud Mostafavi Vasile Nastasescu

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

Stefano Natali

(Università di Roma “La Sapienza”, Italy)

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Frattura ed Integrità Strutturale, 61 (2022); International Journal of the Italian Group of Fracture

Andrzej Neimitz

(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)

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 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)

Special Issue Salvinder Singh Shahrum Abdullah Roberto Capozuzza

Failure Analysis of Materials and Structures

(Universiti Kebangsaan, Malaysia) (Universiti Kebangsaan, Malaysia)

(Polytechnic University of Marche, Italy)

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) (Università di Parma, Italy)

Special Issue

Russian mechanics contributions for Structural Integrity (Mechanical Engineering Research Institute of the Russian Academy of Sciences, Russia) (Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Russia)

Valerii Pavlovich Matveenko

Oleg Plekhov

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Fracture and Structural Integrity, 61 (2022); 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)

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Frattura ed Integrità Strutturale, 61 (2022); 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 gruppofrattura@gmail.com. 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) http://www.gruppofrattura.it 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)

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Fracture and Structural Integrity, 61 (2022); ISSN 1971-9883

FIS news

D

ear friends, we have great news about Frattura ed Integrità Strutturale – Fracture and Structural Integrity . First of all, our Journal is now classified in 2021 as a Q2 journal in three different categories:  Civil and Structural Engineering;

 Mechanical Engineering;  Mechanics of Materials. There are two interesting diagrams that should be focused: “Citations per document” and “Cited and Uncited documents”:

All the authors are kindly requested to “push” the visibility of their papers, for example linking the published papers in Facebook, ResearchGate and in all the social media they think could be useful for our goal: improve the visibility and the usefulness of our journal! We have a second important news: we adopted iThenticate as antiplagiarism software. We are grateful to iThenticate for the “special prize” they applied to FIS as Diamond Open Journal. Ad maiora semper!

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief

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A. Kostina et alii, Frattura ed Integrità Strutturale, 61 (2022) 1-19; DOI: 10.3221/IGF-ESIS.61.01

THM-coupled numerical analysis of temperature and groundwater level in-situ measurements in artificial ground freezing

A. Kostina, M. Zhelnin, O. Plekhov Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Russia kostina@icmm.ru, http://orcid.org/0000-0002-5721-3301 zhelnin.m@icmm.ru, http://orcid.org/0000-0003-4498-450X poa@icmm.ru, http://orcid.org/0000-0002-0378-8249 K.A. Agutin Institute of Nature Management of the National Academy of Sciences of Belarus, Belarus kirill.agutin@gmail.com, http://orcid.org/0000-0002-2345-6790 A BSTRACT . Belarusian Potash salt deposits are bedded under aquifers and unstable soil layers. Therefore, to develop the deposits a vertical mine shaft sinking is performed using the artificial ground freezing technology. Nowadays, real-time observations of ground temperature and groundwater level is applied to control the ground freezing process. Numerical simulation can be used for a comprehensive analysis of measurements results. In this paper, a thermo-hydro-mechanical model of freezing for water-saturated soil is proposed. The governing equations of the model are based on balance laws for mass, energy and momentum for a fully saturated porous media. Clausius Clayperon equation and poroelastic constitutive relations are adopted to describe coupled processes in water and ice pore pressure, porosity and a stress-strain state of freezing soil. The proposed model was used to predict equivalent water content measured in Mizoguchi’s test and frost heave in a one-sided freezing test. Numerical simulation of ground freezing in the Petrikov mining complex located in Belarus has shown that the model is able to describe field measurements of pore pressure inside a forming frozen wall. Furthermore, the mismatch between hydro- and thermo-monitoring data obtained during the artificial freezing is analyzed. K EYWORDS . Saturated freezing soil; Artificial ground freezing; Thermo hydro-mechanical model; In-situ measurements; Ice wall integrity.

Citation: Kostina, A., Zhelnin, M., Plekhov, O., Agutin, K., THM-coupled numerical analysis of temperature and groundwater level in-situ measurements in artificial ground freezing, Frattura ed Integrità Strutturale, 61 (2022) 1-19.

Received: 18.01.2022 Accepted: 04.04.2022 Online first: 06.04.2022 Published: 01.07.2022

Copyright: © 2022 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.

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A. Kostina et alii, Frattura ed Integrità Strutturale, 61 (2022) 1-19; DOI: 10.3221/IGF-ESIS.61.01

I NTRODUCTION

O

verlying stratums of potash salt deposits in Belarus consist of aquifers and unstable soils. Therefore, artificial ground freezing (AGF) technology is required to provide groundwater control and enhance the mechanical properties of such soils. AGF is performed before and during the shaft sinking by a series of freezing wells drilled around the projected contour of the shaft. A circulation of refrigerant in the pipes placed into the wells induces heat extraction from the soils and the formation of a frozen wall. For a safe shaft sink operation, it is required to achieve a solid impermeable frozen wall of the designed thickness. Nowadays control of a frozen wall state is carried out by field measurements of ground temperature and groundwater level. However, analysis of the measurements is frequently complicated by a lack of data on initial hydrogeological conditions in the excavation site and freezing conditions. A promising way to study the freezing process and analyze the monitoring data is through mathematical modeling of AGF. Research of soil freezing was begun about one hundred years ago. The pioneering works of [1-3] were related to studies of unfrozen water content in soils at negative temperatures. Taber [4] and Beskow [5] observed that the frost heave in freezing soil was induced by ice lens formation associated with water migration from the unfrozen zone to the freezing front. Further efforts were intended to detailed investigation and a quantitative description of such processes as cryogenic suction in soils at negative temperatures [6-7], the dependence of unfrozen water content on temperature [8-9], frost heave of freezing soils [10-12] and mechanical behavior of frozen soils [13-14]. As a result, coupled model of heat-fluid transport in freezing soil [15-16], the ice rigid model [17], and a conception of the segregation potential [18-19] were developed. These models provide a theoretical foundation for evaluation of temperature, water velocity and frost heave strain due to ice segregation in freezing soils. It is assumed that water and ice coexist in phase equilibrium. The unfrozen water content is expressed by soil-freezing characteristic curves. The studies related to the soil-freezing characteristic curves can be found in many works [20-23]. Modern thermo-hydraulic models are able to predict temperature evolution and distribution of water, and ice content in laboratory tests [24-26] and in engineering applications of the AGF [27-28]. However, analysis of frost heave effect on surrounding unfrozen soil and structures requires stress and strain fields evaluation. Currently, fully coupled thermo-hydro mechanical models for geotechnical application are derived using the theory of porous media. A model proposed by Nishimura et al. [29] was applied to a study of a frost heave effect on buried pipelines. In the model, the mechanical behaviour of freezing soil is described by extended Barcelona Basic Model with two-stress variable constitutive relations. In Liu and Yu [30] performance of a thermo-hydro-mechanical model was tested on field data collected in pavement of seasonally frozen soils. A volumetric expansion of freezing soil is incorporated through additional inelastic strains. Fully coupled thermo-hydro-mechanical models of AGF are presented in [31-34]. According to these models, the stress-strain state of the freezing ground is simulated using constitutive relations of poroelasticity proposed by Coussy [35-36]. In the studies of Zhou and Meschke [31] and Tounsi et al. [34] numerical simulation of AGF is performed for horizontal excavations. Panteleev et al. [32-33] consider AGF for a vertical shaft sinking in the Petrikov potash deposit. However, in the model, the mass balance law is considered only for unfrozen soil. This work is a continuation of [37-38] where the pure mechanical behavior of ice wall at the Petrikov mining complex (Republic of Belarus) has been investigated. In this paper, a thermo-hydro-mechanical model of freezing for saturated soil is proposed. The model was applied to the analysis of field measurements of ground temperature and groundwater level obtained by hydro-observation wells. The governing equations of the model include the mass balance equation, the energy conservation equation, and the momentum balance equation. According to thermo-hydro-mechanical models of frost heave developed by Zhou et al. [39] and Lai et al. [40], the mechanical behavior of the freezing soil is described by a change in porosity which is defined by the mass balance equation. Soil porosity, equivalent pore pressure, and a stress-strain state of the freezing soil are evaluated using constitutive relations of poroelasticity proposed by Coussy [35-36] and effective stress conception developed by Bishop [41]. Clausius – Clapeyron equation is used for estimation of pore ice pressure and cryogenic suction. Phase transition of water into ice is incorporated in the model by a soil freezing characteristics curve. Coupled set of nonlinear equations of the model were implemented in Comsol Multiphysics software. The effectiveness of the proposed model was demonstrated by numerical simulation of two laboratory tests. The first one is a well-known Mizoguchi’s test in which an evolution of equivalent water content in sandy loam samples was measured during freezing in a closed system. The second test is one-sided freezing of silty sand samples in an open system to measure frost heave displacement. The validated model was applied to numerical simulation of pore pressure evolution in unfrozen soil inside a closed cylindrical frozen wall. Numerical predictions were compared to field measurements of groundwater level recorded by two hydro-observation wells of different depths during AGF in the Petrikov mining complex (Republic of Belarus). A mismatch between field measurements of temperature and groundwater level collected in different layers is analyzed. In addition, an effect of water migration to the inner boundary of the frozen wall on the pore pressure inside the frozen wall is discussed.

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A. Kostina et alii, Frattura ed Integrità Strutturale, 61 (2022) 1-19; DOI: 10.3221/IGF-ESIS.61.01

T HERMO - HYDRO - MECHANICAL MODEL OF SOIL FREEZING

F

reezing soil is modelled as a fully saturated three-phase porous medium consisting of solid grains (index s ), liquid water (index l ) and ice (index i ). In the initial state, the pore space is filled only with water. The air phase is ignored. According to [31], [34] the following hypotheses are applied: 1. All phases of the porous media are in the local thermal equilibrium, so the temperature of all phases is the same. 2. Phase densities are assumed to be constant during freezing. 3. Effects of pore water salinity and external load on the freezing temperature are not considered. 4. Ice moves together with solid grains, so a velocity of ice relative to solid grains is zero. 5. Ice lens formation is negligible. 6. The soil is elastic and isotropic. Deformation of the soil is estimated using the small strain formalism. Balance equations for a three-phase porous media can be formulated on the base of these hypotheses. The mass balance equation is written as                 0 l l i i l l S n S n div t t v (1) where  j S j n is the mass content per unit of volume of water ( j = l ) and ice ( j = i ) at time t ;  j is the density of the phase j ; S j is saturation of the phase j ; n is the porosity; v l is the velocity of water relative to the solid skeleton. The energy conservation law has the following form where T is the temperature of the porous media, C and λ are the volumetric heat capacity and the thermal conductivity of the porous media; С l is the volumetric heat capacity of water; Q ph is the heat source related to the latent heat due the water phase change. The momentum balance equation for the porous media is given as:   0 div σ γ (3) σ is the total stress tensor; γ is the unit weight of the porous media. The ice saturation S i is determined by a soil freezing characteristic curve which is expressed as a power function of the temperature T [42]:                  1 1 , 0 ph ph i ph T T T T S T T (4) where T ph is the freezing temperature of pore water and α is the experimental parameter. The water saturation is found from the condition of the full saturation S l = 1 – S i . The relative velocity of water v l can be described by the Darcy law as where k is the hydraulic conductivity and ψ is the soil-water potential. Following Nixon [43], the hydraulic conductivity k is given as                 0 0 1 , ph ph ph T T k T T k T T k (6)    l kgrad v (5)  C T div gradT С     l l v  gradT Q  ph t (2)

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A. Kostina et alii, Frattura ed Integrità Strutturale, 61 (2022) 1-19; DOI: 10.3221/IGF-ESIS.61.01

where k 0 is the hydraulic conductivity of the unfrozen soil, β is the experimental parameter. The soil water potential ψ driving pore water migration is defined according to Bernoulli's equation:

p z g

   l l

(7)

where p l is the pressure of the pore water; g is the gravitational acceleration; z is the vertical coordinate. The volumetric heat sources in the energy conservation Eqn. (2) are written as       i ph i nS Q L t (8) where L is the latent heat. The volumetric heat capacity C and the thermal conductivity λ are determined as [44]        1 s s l l l C n c nS c (9)

      1 l i nS nS n s l i

(10)

where c j , λ j ( j = s,l,i ) are the specific heat capacities and the thermal conductivities of the phase j . Unit weight of the saturated porous media γ is written as                1 s l l i i n n S S γ g

(11)

The total stress σ of the porous media is defined as   ' bp σ σ I

(12)

where σ′ is the effective stress; p is the equivalent pore pressure; b is the effective Biot coefficient; I is the identity tensor. The effective stress σ′ is given by the Hooke’s law for isotropic linear-elastic media

2 3

  

  

 e

e

 

(13)

K G

G

'

2

σ

I

ε

vol

where K is the effective bulk modulus; G is the effective shear modulus;  e is the elastic strain tensor;  e vol is the volumetric part of the tensor. According to the additive decomposition of the total strain  , the elastic strain  e can be expressed as

  e th ε ε ε

(14)

where  th is the thermal strain. Total strain  is defined by the geometric relation for an infinitesimal deformation:

1 2

 T grad grad u u

(15)

ε

where u is the displacement vector. Thermal strain is written as      0 th T T T ε I

(16)

where a T is the volumetric thermal dilation coefficient and T 0 is the initial temperature of the unfrozen soil.

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A. Kostina et alii, Frattura ed Integrità Strutturale, 61 (2022) 1-19; DOI: 10.3221/IGF-ESIS.61.01

The equivalent pore pressure p is assumed to be the weighted sum of the pore water pressure p l and the pore ice pressure p i [17], [41]:        1 l i p p p (17)

where χ is the pore pressure parameter defined as

1.5

   1

i S

(18)

The pore ice pressure p i is expressed by the Clausius-Clapeyron equation as follows

   

      ph T T

 

i

l

  i p

(19)

p

p

L

ln

i

hydr

i

i

 l

 l

where p hydr is the reference pressure in soil before the freezing process. Following [39-40], expression for the pore water pressure p l can be obtained from (18), (20) as

  

  

T

     

   1

    i l

 l

p

L

p

1

ln

T

i

l

hydr

ph

p

(20)

   1

  

l



l

i

According to theory of poroelasticity [31], [35], [36] the equivalent pore pressure p can be expressed by the porosity and the volumetric strain              0 0 0 3 e vol T p N n n b b n T T (21)

where n 0 is the initial porosity; N is the effective Biot tangent modulus . The effective mechanical properties are estimated as [31]        1 fr un X X X

(22)

where X is the effective value, X fr and X un are the values for the frozen and the unfrozen states.

C OMPUTER IMPLEMENTATION OF THE MODEL

T

he Eqns. (1)-(22) were solved in finite-element software Comsol Multiphysics® using Weak Form PDE Interface, Heat Transfer Module and Solid Mechanics Module. The porosity n , the temperature T and the displacement u were chosen as primary variables. In [39-40] have been shown that solution of the mass balance equation relative to the porosity n enables accurate prediction of water and ice distributions. To incorporate the mass balance Eqn. (1) in Comsol a weak form of the equation was obtained. By taking partial derivative with respect to time, using condition of fully saturation of the porous media and the Darcy’s law (5) we can rewrite the Eqn. (1) as

 S n S S n 

i

  l l

    

  i i

div kgrad

0

(23)

i

l

l

t

t

Eqn. (23) was multiplied by a test function F and integrated over the domain Ω using integration by parts to obtain the weak form. The final form of the equation is

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A. Kostina et alii, Frattura ed Integrità Strutturale, 61 (2022) 1-19; DOI: 10.3221/IGF-ESIS.61.01

      F F x x y y           

S

n







i

   l l

 

   Fd

 

 

 l

i i S S Fd

n

k

d

i

l

t

t

(24)

  

  

   kF m m d x y     x y

 

 

 l

0

where m =( m x ; m y ) is the outward unit normal to the boundary Γ of the domain Ω . Eqn. (24) was solved in Comsol using Weak Form PDE Interface. The energy conservation Eqn. (2) was solved using Heat Transfer in Solids Interface where the heat source Q ph and the convective term c l v l ·grad T were included by Heat Source nodes. The momentum balance Eqn. (3) together with constitutive relations (13)-(16) were solved by Solid Mechanics Interface. Influence of the pore pressure p on a stress-strain state was taking into account by External Stress node. Thermal strain  th was added to the total strain  by Thermal Expansion node. For the spatial discretization of the porosity Eqn. (24), quadratic Lagrange shape functions were used whereas linear Lagrange shape functions were applied for the heat transfer equation. Displacement vector u was approximated using quadratic serendipity shape functions. Optimal element sizes were achieved by successive refinement of the mesh in each calculation. Time-dependent problem (1)-(22) was integrated according to the Backward Differentiation Formula. Segregated solver was used for the computation, where the temperature field T was defined in the first step while the porosity n and displacement u were obtained in the second step. System of non-linear algebraic equations in every step was solved by a damped Newton method with a constant damping factor. Direct PARDISO solver was employed for the linearized system of equations. he validation of the proposed model has been carried out by simulation of two different laboratory tests. The first is the benchmark test carried out by Mizoguchi [24-25], [30]. This test gives us information about water and ice content during one-sided freezing of four identical cylindrical samples packed with sandy loam in a closed system. One cylinder was taken as a reference, the rest were frozen for 12, 24, and 50 hours. The test was conducted in a closed system under the following conditions. The cylindrical sample had a height of 20 cm and a radius of 4 cm. In the initial time moment, the soil was fully saturated with water. Volumetric water content which coincided in this case with the porosity was uniformly distributed along the sample height and was equal to 0.35. Initial temperature of the cylinder was 6.7 O C. The top surface of the cylinder was subjected to a constant temperature of –6 O C. The other surfaces were thermally insulated. Due to the radial symmetry of the problem, half of the cylinder’s cross-section was simulated. Therefore, a computational domain had a rectangular shape with a width of 4 cm and a height of 20 cm. According to Zhou et al. (2012) it is assumed that the top surface of the soil was subjected to instantaneous freezing without water migration. The difference in the densities of the water and ice induces increase in the volume of the pore water by 9%. Therefore, the value of the porosity at the top boundary of the sample is assumed to be 1.09· n 0 =0.3815, where n 0 =0.35. Zero flux boundary condition was applied at the other sides of the domain. The displacement vector at the bottom boundary was constrained in all directions. Symmetry boundary condition was given at the axis of the symmetry and only vertical displacement was permitted at the lateral boundary. The parameters of the soil used in the simulation are listed in Tab. 1. The considered area was divided into quadrilateral elements. The optimal mesh size was determined by series of calculations with various element sizes. Reference numerical solution was obtained on a computational mesh with 30000 elements which ensures sufficiently fine partition of the computational domain. The relative tolerance tol has been determined by a formula: T V ALIDATION OF THE PROPOSED MODEL

 L

 n n dL

r

,

(25)

tol

100%

 L

n dL

r

where subscript r denotes the reference solution, L represents the middle line of the computational domain along which the porosity n has been defined.

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A. Kostina et alii, Frattura ed Integrità Strutturale, 61 (2022) 1-19; DOI: 10.3221/IGF-ESIS.61.01

Parameter

Value 1000

Unit

kg/m kg/m kg/m

 l  i  s

3

917

3

2215 4180 2090 850 0.58 2.22 1.62

3

c l c i c s λ l λ i λ s L

J/(kg·K) J/(kg·K) J/(kg·K) W/(m·K) W/(m·K) W/(m·K)

334560 1.4·10 -10

J/kg m/s

k 0

-5.5

- -

 

-2

a T

5·10 -7

1/K MPa MPa MPa

K fr

4.4 1.9 2.9

K un G fr G un

1.25 MPa Table 1: Parameters of soil used for the simulation of the Mizoguchi’s test.

Fig. 1 shows the effect of the mesh size on the relative tolerance. The results demonstrate that the relative error decreases with the increase in number of elements. The relative tolerance becomes constant when total number of elements exceeds 1875 which corresponds to the 75 elements along the lateral side of the computational domain and 25 elements along the top of the computational domain.

Figure 1: Relative tolerance vs number of elements.

Fig. 2 presents porosity distribution along the sample height measured in the test and obtained by numerical simulation for 12, 24, and 50 hours of the freezing. The presented plots can be divided into three stages. In the first stage, the porosity rises and the temperature of the soil is less than the freezing temperature T ph . Therefore, at this stage frost heave of the soil is occurred due to the phase transition of water into ice and water inflow. In the second stage, the temperature is also less than T ph , but the porosity significantly reduces to a minimum value. It indicates that there is an intensive water migration

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A. Kostina et alii, Frattura ed Integrità Strutturale, 61 (2022) 1-19; DOI: 10.3221/IGF-ESIS.61.01

into the freezing front induced by cryogenic suction. The water migration together with the mechanical impact of the frozen zone leads to a volumetric shrinkage of the soil. Since a temperature gradient in the sample decreases in the process of freezing, the length of this stage increases. The third stage corresponds to unfrozen soil. At this stage the porosity is also reduced by water migration to the freezing front.

(a)

(b)

(c)

(d)

(e) (f) Figure 2: Simulation results of the Mizoguchi`s test. Computed porosity distributions in partially frozen samples corresponding to 12 (a), 24 (c), 50 (e) hours of the freezing (left); White line corresponds to the freezing front position. Computed (solid line) and experimental (points) porosity profiles along the middle line in the sample for 12 (b), 24 (d), 50 (f) hours of the freezing (right). The sizes of computational domain are in meters [m].

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A. Kostina et alii, Frattura ed Integrità Strutturale, 61 (2022) 1-19; DOI: 10.3221/IGF-ESIS.61.01

Comparison of the numerical results and experimental data has shown that the proposed model is able qualitatively to describe both a porosity reduction due to water migration and thermal shrinkage of the solid skeleton as well as porosity rise in the frozen zone induced by the frost heave. The second and third stages show better agreement between calculated and experimental results than the first one. In the first stage, maximum deviation between the plots is observed for 24 hours of the freezing and is equal to 0.04. As regards the second stage, the maximum deviation is 0.016 and also corresponds to the freezing for 24 hours. The obtained deviation is less than 10 %, which indicates an acceptable agreement between numerical results and experimental measurements. The second laboratory test used for verification of the model is one-sided freezing of silty sand cylindrical samples in an open system. The experiment was carried out by the Institute of Nature Management of the National Academy of Sciences of Belarus (INM of NAS) according to Russian union standard GOST 28622-2012. Such tests are an essential part of the experimental program for preparation for a shaft sinking. The silty sand water-saturated cylindrical samples were taken from a stratum laid at the depth of 75 m in the Petrikov potash deposit. Initial water content of the soil was 0.4. The soil was packed in cylindrical samples. The samples had a height of 10 cm and a radius of 5 cm. Initial temperature was 1 O C. Freezing of the samples was performed at the temperature of –6 O C controlled on the top surface. A positive temperature of 1 O C was maintained at the bottom surface. The lateral surface was thermally insulated. The test was ended when a freezing front propagated to about 90% of the sample height. At the end of the test, a displacement of 4.6 mm of the top surface was measured. The freezing of the soil proceeded with the formation a massive cryogenic structure [45]. Any thick ice lenses were not observed in the frozen zone of the soil. Similar to Mizoguchi’s test, only a cross-sectional area of the cylinder was simulated. Boundary conditions for the energy conservation equation corresponded to the experimental conditions. A constant porosity of 1.09· n 0 =0.436 was given at the top boundary, where n 0 =0.4. Horizontal displacement was suppressed at the lateral boundary. Symmetry boundary condition was given to the symmetry line. The bottom boundary was fixed while the top boundary was free from kinematic constraints. The model parameters of the soil used in the simulation are presented in Tab. 2. Mesh convergence analysis was performed similarly to Mizoguchi’s test. The optimal mesh consists of 620 quadrilateral elements.

Parameter

Value 1870

Unit

kg/m

 s

3

c s

720

J/(kg·K) W/(m·K)

λ s

1.2

k 0

1.4·10 -12

m/s

-5

- -

 

-15

a T K fr

5·10 -6

1/K GPa GPa GPa

2.13 1.67 1.94

K un G fr G un

6.6 MPa Table 2: Parameters of soil used for the simulation of the frost heave.

Fig. 3 presents the distribution of the vertical displacement along the sample after 2 hours of the freezing (Fig. 3(a)) and variation of the vertical displacement of the top surface with time (Fig. 3(b)). It can be seen that shrinkage of the soil arises near the freezing front. On the other hand, a frost heave induces a vertical uplift of the soil in the frozen zone. The mechanical behavior indicates a rise in the equivalent pore pressure of the frozen zone and a decrease in the pressure of the unfrozen zone. Similar distributions were obtained by [39]. Fig. 3 (b) shows that upward displacement induced by frost heave achieved 4.6 mm as it was measured at the end of the freezing test. Calculated evolution of the vertical displacement qualitatively close to experimental curves recorded in one-sided freezing experiments carried out by Lai et al. [40]. At the beginning of the freezing, a small frozen shrinkage of the soil occurs. After that, the frost heave strain increases due to the freezing of the initial and migrated water.

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