Measuring Rheological Properties of Cement-based Materials: State-of-the-Art Report of the RILEM Technical Committee 266-MRP (RILEM State-of-the-Art Reports, 39) [1st ed. 2024] 3031367421, 9783031367427

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RILEM State-of-the-Art Reports

Mohammed Sonebi Dimitri Feys   Editors

Measuring Rheological Properties of Cement-based Materials State-of-the-Art Report of the RILEM Technical Committee 266-MRP

RILEM State-of-the-Art Reports

RILEM STATE-OF-THE-ART REPORTS Volume 39 RILEM, The International Union of Laboratories and Experts in Construction Materials, Systems and Structures, founded in 1947, is a non-governmental scientific association whose goal is to contribute to progress in the construction sciences, techniques and industries, essentially by means of the communication it fosters between research and practice. RILEM’s focus is on construction materials and their use in building and civil engineering structures, covering all phases of the building process from manufacture to use and recycling of materials. More information on RILEM and its previous publications can be found on www.RILEM.net. The RILEM State-of-the-Art Reports (STAR) are produced by the Technical Committees. They represent one of the most important outputs that RILEM generates – high level scientific and engineering reports that provide cutting edge knowledge in a given field. The work of the TCs is one of RILEM’s key functions. Members of a TC are experts in their field and give their time freely to share their expertise. As a result, the broader scientific community benefits greatly from RILEM’s activities. RILEM’s stated objective is to disseminate this information as widely as possible to the scientific community. RILEM therefore considers the STAR reports of its TCs as of highest importance, and encourages their publication whenever possible. The information in this and similar reports is mostly pre-normative in the sense that it provides the underlying scientific fundamentals on which standards and codes of practice are based. Without such a solid scientific basis, construction practice will be less than efficient or economical. It is RILEM’s hope that this information will be of wide use to the scientific community. Indexed in SCOPUS, Google Scholar and SpringerLink.

Mohammed Sonebi · Dimitri Feys Editors

Measuring Rheological Properties of Cement-based Materials State-of-the-Art Report of the RILEM Technical Committee 266-MRP

Editors Mohammed Sonebi School of Natural and Built Environment Queen’s University Belfast Belfast, UK

Dimitri Feys Department of Civil, Architectural and Environmental Engineering Missouri University of Science and Technology Rolla, MO, USA

ISSN 2213-204X ISSN 2213-2031 (electronic) RILEM State-of-the-Art Reports ISBN 978-3-031-36742-7 ISBN 978-3-031-36743-4 (eBook) https://doi.org/10.1007/978-3-031-36743-4 © RILEM 2024 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Permission for use must always be obtained from the owner of the copyright: RILEM. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

Contributing Members

This State-of-the-Art report has been prepared by the RILEM Technical Committee: “Measuring Rheological Properties of Cement-based Materials”, also known as RILEM TC-266-MRP. This report would not have been possible without the contributions of its members: • Mohammed Sonebi, Queen’s University Belfast, United Kingdom (Chair) • Dimitri Feys, Missouri University of Science and Technology, United States (Deputy-Chair) • Sofiane Amziane, Clermont-Ferrand Polytechnique, France • Rolands Cepuritis, Norwegian University of Science and Technology, Norway • Geert De Schutter, Ghent University, Belgium • Chafika Djelal, Université Artois, France • Khadija El-Cheikh, Belgian Building Research Institute, Belgium • Siamak Fakhrayee Nejad, Moghavemsazan Rosha Company, Iran • Shirin Fataei, Technical University Dresden, Germany • Markus Greim, Schleibinger Geräte, Germany • Steffen Grunewald, Technical University Delft, The Netherlands • Michael Haist, Technical University Hannover, Germany • Stefan Jacobsen, Norwegian University of Science and Technology, Norway • Irina Ivanova, Technical University Dresden, Germany • Helena Keller, Schleibinger Geräte, Germany • Kamal Khayat, Missouri University of Science and Technology, USA • Laurent Libessart, Université Artois, France • Karel Lesage, Ghent University, Belgium • Julian Link, Technical University Hannover, Germany • Dirk Lowke, Technical University Braunschweig, Germany • Viktor Mechtcherine, Technical University Dresden, Germany • Ivan Navarrete, Universidad Diego Portales, Chile • Arnaud Perrot, Université de Bretagne-Sud, France • Tilo Proske, Technical University Darmstadt, Germany • Nicolas Roussel, Université Gustave Eiffel, France

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Contributing Members

Wolfram Schmidt, BAM, Germany Egor Secrieru, Heidelberg Cement, Germany Yannick Vanhove, Université Artois, France Jon E. Wallevik, Icelandic Meteorological Office, Iceland Ammar Yahia, Université de Sherbrooke, Canada Jiang Zhu, University of Jinan, China.

Furthermore, the committee would like to acknowledge the contributions of the following individuals who participated in some of the committee’s activities but are not members of the TC: • Chiara “Clarissa” Ferraris, formerly National Institute for Standards and Technology, USA • Faber Fabbris, EQIOM Beton, France • Sarah Leinitz, BAM, Germany • Lars Thrane, Danish Technological Institute, Denmark.

Preface

Although the science of rheology has been applied on cement-based materials since the 1950s, the main increase in research and implementation has only started in the second half of the 1990s. Since then, several different devices have been developed and used in research and in industry, but to date, no comprehensive document has been created focusing on measuring rheological properties of cement-based materials. Therefore, during the 7th international RILEM conference on self-compacting concrete and the first international conference on rheology of construction materials, in Paris in 2013, a group of rheology researchers gathered and discussed the need and intent to start a technical committee, focusing on measuring the rheological properties of concrete. Two years later, on September 1, 2015, RILEM TC-266 Measuring Rheological Properties of Cement-based Materials (MRP) held its official first meeting during the RILEM week in Melbourne, Australia. Since then, the general committee has met over 15 times in different locations in Asia, Europe, and North America, as well as online to progress toward the committee’s final goals. The goals of RILEM TC-266-MRP include this State-of-the-Art Report (STAR), a comprehensive Round-Robin Test on concrete rheometry and two publications focusing on aspects of rheometry of cement-based materials not included in the STAR. The results and interpretation of the Round-Robin Test are discussed in a topical collection in Materials and Structures, and the two publications in RILEM Technical Letters focus on measuring rheological properties of cement paste and viscoelasticity of cement pastes. This State-of-the-Art Report laying in front of you is the result of a 7-year collaboration between researchers and industrials from Asia, the Middle East, Europe, and the Americas since 2015. This report, and all other products of the committee, would not have been possible without the relentless efforts of the committee members and collaborators. A special word of appreciation goes to all chapter leaders, chapter contributors, and chapter reviewers, for their efforts in creating this document, as well as all committee members involved in the Concrete Rheometer Round-Robin

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Preface

Test 3 in Bethune, 2018 (France) and the separate publications. Without them, these tasks would have been impossible to execute and this RILEM report would never have been published. Belfast, UK Rolla, MO, USA

Mohammed Sonebi Dimitri Feys

RILEM Publications

The following list is presenting the global offer of RILEM Publications, sorted by series. Each publication is available in printed version and/or in online version.

RILEM Proceedings (PRO) PRO 1: Durability of High Performance Concrete (ISBN: 2-912143-03-9; e-ISBN: 2-351580-12-5; e-ISBN: 2351580125); Ed. H. Sommer PRO 2: Chloride Penetration into Concrete (ISBN: 2-912143-00-04; e-ISBN: 2912143454); Eds. L.-O. Nilsson and J.-P. Ollivier PRO 3: Evaluation and Strengthening of Existing Masonry Structures (ISBN: 2-912143-02-0; e-ISBN: 2351580141); Eds. L. Binda and C. Modena PRO 4: Concrete: From Material to Structure (ISBN: 2-912143-04-7; e-ISBN: 2351580206); Eds. J.-P. Bournazel and Y. Malier PRO 5: The Role of Admixtures in High Performance Concrete (ISBN: 2-91214305-5; e-ISBN: 2351580214); Eds. J. G. Cabrera and R. Rivera-Villarreal PRO 6: High Performance Fiber Reinforced Cement Composites - HPFRCC 3 (ISBN: 2-912143-06-3; e-ISBN: 2351580222); Eds. H. W. Reinhardt and A. E. Naaman PRO 7: 1st International RILEM Symposium on Self-Compacting Concrete (ISBN: 2-912143-09-8; e-ISBN: 2912143721); Eds. Å. Skarendahl and Ö. Petersson PRO 8: International RILEM Symposium on Timber Engineering (ISBN: 2-91214310-1; e-ISBN: 2351580230); Ed. L. Boström PRO 9: 2nd International RILEM Symposium on Adhesion between Polymers and Concrete ISAP ’99 (ISBN: 2-912143-11-X; e-ISBN: 2351580249); Eds. Y. Ohama and M. Puterman ix

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RILEM Publications

PRO 10: 3rd International RILEM Symposium on Durability of Building and Construction Sealants (ISBN: 2-912143-13-6; e-ISBN: 2351580257); Ed. A. T. Wolf PRO 11: 4th International RILEM Conference on Reflective Cracking in Pavements (ISBN: 2-912143-14-4; e-ISBN: 2351580265); Eds. A. O. Abd El Halim, D. A. Taylor and El H. H. Mohamed PRO 12: International RILEM Workshop on Historic Mortars: Characteristics and Tests (ISBN: 2-912143-15-2; e-ISBN: 2351580273); Eds. P. Bartos, C. Groot and J. J. Hughes PRO 13: 2nd International RILEM Symposium on Hydration and Setting (ISBN: 2-912143-16-0; e-ISBN: 2351580281); Ed. A. Nonat PRO 14: Integrated Life-Cycle Design of Materials and Structures - ILCDES 2000 (ISBN: 951-758-408-3; e-ISBN: 235158029X); (ISSN: 0356-9403); Ed. S. Sarja PRO 15: Fifth RILEM Symposium on Fibre-Reinforced Concretes (FRC) BEFIB’2000 (ISBN: 2-912143-18-7; e-ISBN: 291214373X); Eds. P. Rossi and G. Chanvillard PRO 16: Life Prediction and Management of Concrete Structures (ISBN: 2-91214319-5; e-ISBN: 2351580303); Ed. D. Naus PRO 17: Shrinkage of Concrete – Shrinkage 2000 (ISBN: 2-912143-20-9; e-ISBN: 2351580311); Eds. V. Baroghel-Bouny and P.-C. Aïtcin PRO 18: Measurement and Interpretation of the On-Site Corrosion Rate (ISBN: 2-912143-21-7; e-ISBN: 235158032X); Eds. C. Andrade, C. Alonso, J. Fullea, J. Polimon and J. Rodriguez PRO 19: Testing and Modelling the Chloride Ingress into Concrete (ISBN: 2-912143-22-5; e-ISBN: 2351580338); Eds. C. Andrade and J. Kropp PRO 20: 1st International RILEM Workshop on Microbial Impacts on Building Materials (CD 02) (e-ISBN 978-2-35158-013-4); Ed. M. Ribas Silva PRO 21: International RILEM Symposium on Connections between Steel and Concrete (ISBN: 2-912143-25-X; e-ISBN: 2351580346); Ed. R. Eligehausen PRO 22: International RILEM Symposium on Joints in Timber Structures (ISBN: 2-912143-28-4; e-ISBN: 2351580354); Eds. S. Aicher and H.-W. Reinhardt PRO 23: International RILEM Conference on Early Age Cracking in Cementitious Systems (ISBN: 2-912143-29-2; e-ISBN: 2351580362); Eds. K. Kovler and A. Bentur PRO 24: 2nd International RILEM Workshop on Frost Resistance of Concrete (ISBN: 2-912143-30-6; e-ISBN: 2351580370); Eds. M. J. Setzer, R. Auberg and H.-J. Keck

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PRO 25: International RILEM Workshop on Frost Damage in Concrete (ISBN: 2-912143-31-4; e-ISBN: 2351580389); Eds. D. J. Janssen, M. J. Setzer and M. B. Snyder PRO 26: International RILEM Workshop on On-Site Control and Evaluation of Masonry Structures (ISBN: 2-912143-34-9; e-ISBN: 2351580141); Eds. L. Binda and R. C. de Vekey PRO 27: International RILEM Symposium on Building Joint Sealants (CD03; e-ISBN: 235158015X); Ed. A. T. Wolf PRO 28: 6th International RILEM Symposium on Performance Testing and Evaluation of Bituminous Materials - PTEBM’03 (ISBN: 2-912143-35-7; e-ISBN: 978-2-912143-77-8); Ed. M. N. Partl PRO 29: 2nd International RILEM Workshop on Life Prediction and Ageing Management of Concrete Structures (ISBN: 2-912143-36-5; e-ISBN: 2912143780); Ed. D. J. Naus PRO 30: 4th International RILEM Workshop on High Performance Fiber Reinforced Cement Composites - HPFRCC 4 (ISBN: 2-912143-37-3; e-ISBN: 2912143799); Eds. A. E. Naaman and H. W. Reinhardt PRO 31: International RILEM Workshop on Test and Design Methods for Steel Fibre Reinforced Concrete: Background and Experiences (ISBN: 2-912143-38-1; e-ISBN: 2351580168); Eds. B. Schnütgen and L. Vandewalle PRO 32: International Conference on Advances in Concrete and Structures 2 vol. (ISBN (set): 2-912143-41-1; e-ISBN: 2351580176); Eds. Ying-shu Yuan, Surendra P. Shah and Heng-lin Lü PRO 33: 3rd International Symposium on Self-Compacting Concrete (ISBN: 2-912143-42-X; e-ISBN: 2912143713); Eds. Ó. Wallevik and I. Níelsson PRO 34: International RILEM Conference on Microbial Impact on Building Materials (ISBN: 2-912143-43-8; e-ISBN: 2351580184); Ed. M. Ribas Silva PRO 35: International RILEM TC 186-ISA on Internal Sulphate Attack and Delayed Ettringite Formation (ISBN: 2-912143-44-6; e-ISBN: 2912143802); Eds. K. Scrivener and J. Skalny PRO 36: International RILEM Symposium on Concrete Science and Engineering – A Tribute to Arnon Bentur (ISBN: 2-912143-46-2; e-ISBN: 2912143586); Eds. K. Kovler, J. Marchand, S. Mindess and J. Weiss PRO 37: 5th International RILEM Conference on Cracking in Pavements – Mitigation, Risk Assessment and Prevention (ISBN: 2-912143-47-0; e-ISBN: 2912143764); Eds. C. Petit, I. Al-Qadi and A. Millien PRO 38: 3rd International RILEM Workshop on Testing and Modelling the Chloride Ingress into Concrete (ISBN: 2-912143-48-9; e-ISBN: 2912143578); Eds. C. Andrade and J. Kropp

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RILEM Publications

PRO 39: 6th International RILEM Symposium on Fibre-Reinforced Concretes BEFIB 2004 (ISBN: 2-912143-51-9; e-ISBN: 2912143748); Eds. M. Di Prisco, R. Felicetti and G. A. Plizzari PRO 40: International RILEM Conference on the Use of Recycled Materials in Buildings and Structures (ISBN: 2-912143-52-7; e-ISBN: 2912143756); Eds. E. Vázquez, Ch. F. Hendriks and G. M. T. Janssen PRO 41: RILEM International Symposium on Environment-Conscious Materials and Systems for Sustainable Development (ISBN: 2-912143-55-1; e-ISBN: 2912143640); Eds. N. Kashino and Y. Ohama PRO 42: SCC’2005 - China: 1st International Symposium on Design, Performance and Use of Self-Consolidating Concrete (ISBN: 2-912143-61-6; e-ISBN: 2912143624); Eds. Zhiwu Yu, Caijun Shi, Kamal Henri Khayat and Youjun Xie PRO 43: International RILEM Workshop on Bonded Concrete Overlays (e-ISBN: 2-912143-83-7); Eds. J. L. Granju and J. Silfwerbrand PRO 44: 2nd International RILEM Workshop on Microbial Impacts on Building Materials (CD11) (e-ISBN: 2-912143-84-5); Ed. M. Ribas Silva PRO 45: 2nd International Symposium on Nanotechnology in Construction, Bilbao (ISBN: 2-912143-87-X; e-ISBN: 2912143888); Eds. Peter J. M. Bartos, Yolanda de Miguel and Antonio Porro PRO 46: ConcreteLife’06 - International RILEM-JCI Seminar on Concrete Durability and Service Life Planning: Curing, Crack Control, Performance in Harsh Environments (ISBN: 2-912143-89-6; e-ISBN: 291214390X); Ed. K. Kovler PRO 47: International RILEM Workshop on Performance Based Evaluation and Indicators for Concrete Durability (ISBN: 978-2-912143-95-2; e-ISBN: 9782912143969); Eds. V. Baroghel-Bouny, C. Andrade, R. Torrent and K. Scrivener PRO 48: 1st International RILEM Symposium on Advances in Concrete through Science and Engineering (e-ISBN: 2-912143-92-6); Eds. J. Weiss, K. Kovler, J. Marchand and S. Mindess PRO 49: International RILEM Workshop on High Performance Fiber Reinforced Cementitious Composites in Structural Applications (ISBN: 2-912143-93-4; e-ISBN: 2912143942); Eds. G. Fischer and V. C. Li PRO 50: 1st International RILEM Symposium on Textile Reinforced Concrete (ISBN: 2-912143-97-7; e-ISBN: 2351580087); Eds. Josef Hegger, Wolfgang Brameshuber and Norbert Will PRO 51: 2nd International Symposium on Advances in Concrete through Science and Engineering (ISBN: 2-35158-003-6; e-ISBN: 2-35158-002-8); Eds. J. Marchand, B. Bissonnette, R. Gagné, M. Jolin and F. Paradis PRO 52: Volume Changes of Hardening Concrete: Testing and Mitigation (ISBN: 2-35158-004-4; e-ISBN: 2-35158-005-2); Eds. O. M. Jensen, P. Lura and K. Kovler

RILEM Publications

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PRO 53: High Performance Fiber Reinforced Cement Composites - HPFRCC5 (ISBN: 978-2-35158-046-2; e-ISBN: 978-2-35158-089-9); Eds. H. W. Reinhardt and A. E. Naaman PRO 54: 5th International RILEM Symposium on Self-Compacting Concrete (ISBN: 978-2-35158-047-9; e-ISBN: 978-2-35158-088-2); Eds. G. De Schutter and V. Boel PRO 55: International RILEM Symposium Photocatalysis, Environment and Construction Materials (ISBN: 978-2-35158-056-1; e-ISBN: 978-2-35158-057-8); Eds. P. Baglioni and L. Cassar PRO 56: International RILEM Workshop on Integral Service Life Modelling of Concrete Structures (ISBN 978-2-35158-058-5; e-ISBN: 978-2-35158-090-5); Eds. R. M. Ferreira, J. Gulikers and C. Andrade PRO 57: RILEM Workshop on Performance of cement-based materials in aggressive aqueous environments (e-ISBN: 978-2-35158-059-2); Ed. N. De Belie PRO 58: International RILEM Symposium on Concrete Modelling - CONMOD’08 (ISBN: 978-2-35158-060-8; e-ISBN: 978-2-35158-076-9); Eds. E. Schlangen and G. De Schutter PRO 59: International RILEM Conference on Site Assessment of Concrete, Masonry and Timber Structures - SACoMaTiS 2008 (ISBN set: 978-2-35158-061-5; e-ISBN: 978-2-35158-075-2); Eds. L. Binda, M. di Prisco and R. Felicetti PRO 60: Seventh RILEM International Symposium on Fibre Reinforced Concrete: Design and Applications - BEFIB 2008 (ISBN: 978-2-35158-064-6; e-ISBN: 9782-35158-086-8); Ed. R. Gettu PRO 61: 1st International Conference on Microstructure Related Durability of Cementitious Composites 2 vol., (ISBN: 978-2-35158-065-3; e-ISBN: 978-2-35158084-4); Eds. W. Sun, K. van Breugel, C. Miao, G. Ye and H. Chen PRO 62: NSF/ RILEM Workshop: In-situ Evaluation of Historic Wood and Masonry Structures (e-ISBN: 978-2-35158-068-4); Eds. B. Kasal, R. Anthony and M. Drdácký PRO 63: Concrete in Aggressive Aqueous Environments: Performance, Testing and Modelling, 2 vol., (ISBN: 978-2-35158-071-4; e-ISBN: 978-2-35158-082-0); Eds. M. G. Alexander and A. Bertron PRO 64: Long Term Performance of Cementitious Barriers and Reinforced Concrete in Nuclear Power Plants and Waste Management - NUCPERF 2009 (ISBN: 978-235158-072-1; e-ISBN: 978-2-35158-087-5); Eds. V. L’Hostis, R. Gens and C. Gallé PRO 65: Design Performance and Use of Self-consolidating Concrete - SCC’2009 (ISBN: 978-2-35158-073-8; e-ISBN: 978-2-35158-093-6); Eds. C. Shi, Z. Yu, K. H. Khayat and P. Yan PRO 66: 2nd International RILEM Workshop on Concrete Durability and Service Life Planning - ConcreteLife’09 (ISBN: 978-2-35158-074-5; ISBN: 978-2-35158074-5); Ed. K. Kovler

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RILEM Publications

PRO 67: Repairs Mortars for Historic Masonry (e-ISBN: 978-2-35158-083-7); Ed. C. Groot PRO 68: Proceedings of the 3rd International RILEM Symposium on ‘Rheology of Cement Suspensions such as Fresh Concrete (ISBN 978-2-35158-091-2; e-ISBN: 978-2-35158-092-9); Eds. O. H. Wallevik, S. Kubens and S. Oesterheld PRO 69: 3rd International PhD Student Workshop on ‘Modelling the Durability of Reinforced Concrete (ISBN: 978-2-35158-095-0); Eds. R. M. Ferreira, J. Gulikers and C. Andrade PRO 70: 2nd International Conference on ‘Service Life Design for Infrastructure’ (ISBN set: 978-2-35158-096-7, e-ISBN: 978-2-35158-097-4); Ed. K. van Breugel, G. Ye and Y. Yuan PRO 71: Advances in Civil Engineering Materials - The 50-year Teaching Anniversary of Prof. Sun Wei’ (ISBN: 978-2-35158-098-1; e-ISBN: 978-2-35158-099-8); Eds. C. Miao, G. Ye and H. Chen PRO 72: First International Conference on ‘Advances in Chemically-Activated Materials – CAM’2010’ (2010), 264 pp., ISBN: 978-2-35158-101-8; e-ISBN: 978-2-35158-115-5, Eds. Caijun Shi and Xiaodong Shen PRO 73: 2nd International Conference on ‘Waste Engineering and Management ICWEM 2010’ (2010), 894 pp., ISBN: 978-2-35158-102-5; e-ISBN: 978-2-35158103-2, Eds. J. Zh. Xiao, Y. Zhang, M. S. Cheung and R. Chu PRO 74: International RILEM Conference on ‘Use of Superabsorbent Polymers and Other New Additives in Concrete’ (2010) 374 pp., ISBN: 978-2-35158-104-9; e-ISBN: 978-2-35158-105-6; Eds. O. M. Jensen, M. T. Hasholt and S. Laustsen PRO 75: International Conference on ‘Material Science - 2nd ICTRC - Textile Reinforced Concrete - Theme 1’ (2010) 436 pp., ISBN: 978-2-35158-106-3; e-ISBN: 978-2-35158-107-0; Ed. W. Brameshuber PRO 76: International Conference on ‘Material Science - HetMat - Modelling of Heterogeneous Materials - Theme 2’ (2010) 255 pp., ISBN: 978-2-35158-108-7; e-ISBN: 978-2-35158-109-4; Ed. W. Brameshuber PRO 77: International Conference on ‘Material Science - AdIPoC - Additions Improving Properties of Concrete - Theme 3’ (2010) 459 pp., ISBN: 978-2-35158110-0; e-ISBN: 978-2-35158-111-7; Ed. W. Brameshuber PRO 78: 2nd Historic Mortars Conference and RILEM TC 203-RHM Final Workshop – HMC2010 (2010) 1416 pp., e-ISBN: 978-2-35158-112-4; Eds. J. Válek, C. Groot and J. J. Hughes PRO 79: International RILEM Conference on Advances in Construction Materials Through Science and Engineering (2011) 213 pp., ISBN: 978-2-35158-116-2, e-ISBN: 978-2-35158-117-9; Eds. Christopher Leung and K. T. Wan

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PRO 80: 2nd International RILEM Conference on Concrete Spalling due to Fire Exposure (2011) 453 pp., ISBN: 978-2-35158-118-6, e-ISBN: 978-2-35158-119-3; Eds. E. A. B. Koenders and F. Dehn PRO 81: 2nd International RILEM Conference on Strain Hardening Cementitious Composites (SHCC2-Rio) (2011) 451 pp., ISBN: 978-2-35158-120-9, e-ISBN: 9782-35158-121-6; Eds. R. D. Toledo Filho, F. A. Silva, E. A. B. Koenders and E. M. R. Fairbairn PRO 82: 2nd International RILEM Conference on Progress of Recycling in the Built Environment (2011) 507 pp., e-ISBN: 978-2-35158-122-3; Eds. V. M. John, E. Vazquez, S. C. Angulo and C. Ulsen PRO 83: 2nd International Conference on Microstructural-related Durability of Cementitious Composites (2012) 250 pp., ISBN: 978-2-35158-129-2; e-ISBN: 978-2-35158-123-0; Eds. G. Ye, K. van Breugel, W. Sun and C. Miao PRO 84: CONSEC13 - Seventh International Conference on Concrete under Severe Conditions – Environment and Loading (2013) 1930 pp., ISBN: 978-2-35158-124-7; e-ISBN: 978-2- 35158-134-6; Eds. Z. J. Li, W. Sun, C. W. Miao, K. Sakai, O. E. Gjorv and N. Banthia PRO 85: RILEM-JCI International Workshop on Crack Control of Mass Concrete and Related issues concerning Early-Age of Concrete Structures – ConCrack 3 – Control of Cracking in Concrete Structures 3 (2012) 237 pp., ISBN: 978-2-35158125-4; e-ISBN: 978-2-35158-126-1; Eds. F. Toutlemonde and J.-M. Torrenti PRO 86: International Symposium on Life Cycle Assessment and Construction (2012) 414 pp., ISBN: 978-2-35158-127-8, e-ISBN: 978-2-35158-128-5; Eds. A. Ventura and C. de la Roche PRO 87: UHPFRC 2013 – RILEM-fib-AFGC International Symposium on UltraHigh Performance Fibre-Reinforced Concrete (2013), ISBN: 978-2-35158-130-8, e-ISBN: 978-2-35158-131-5; Ed. F. Toutlemonde PRO 88: 8th RILEM International Symposium on Fibre Reinforced Concrete (2012) 344 pp., ISBN: 978-2-35158-132-2, e-ISBN: 978-2-35158-133-9; Ed. Joaquim A. O. Barros PRO 89: RILEM International workshop on performance-based specification and control of concrete durability (2014) 678 pp., ISBN: 978-2-35158-135-3, e-ISBN: 978-2-35158-136-0; Eds. D. Bjegovi´c, H. Beushausen and M. Serdar PRO 90: 7th RILEM International Conference on Self-Compacting Concrete and of the 1st RILEM International Conference on Rheology and Processing of Construction Materials (2013) 396 pp., ISBN: 978-2-35158-137-7, e-ISBN: 978-2-35158-138-4; Eds. Nicolas Roussel and Hela Bessaies-Bey PRO 91: CONMOD 2014 - RILEM International Symposium on Concrete Modelling (2014), ISBN: 978-2-35158-139-1; e-ISBN: 978-2-35158-140-7; Eds. Kefei Li, Peiyu Yan and Rongwei Yang

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PRO 92: CAM 2014 - 2nd International Conference on advances in chemicallyactivated materials (2014) 392 pp., ISBN: 978-2-35158-141-4; e-ISBN: 978-235158-142-1; Eds. Caijun Shi and Xiadong Shen PRO 93: SCC 2014 - 3rd International Symposium on Design, Performance and Use of Self-Consolidating Concrete (2014) 438 pp., ISBN: 978-2-35158-143-8; e-ISBN: 978-2-35158-144-5; Eds. Caijun Shi, Zhihua Ou and Kamal H. Khayat PRO 94 (online version): HPFRCC-7 - 7th RILEM conference on High performance fiber reinforced cement composites (2015), e-ISBN: 978-2-35158-146-9; Eds. H. W. Reinhardt, G. J. Parra-Montesinos and H. Garrecht PRO 95: International RILEM Conference on Application of superabsorbent polymers and other new admixtures in concrete construction (2014), ISBN: 978-235158-147-6; e-ISBN: 978-2-35158-148-3; Eds. Viktor Mechtcherine and Christof Schroefl PRO 96 (online version): XIII DBMC: XIII International Conference on Durability of Building Materials and Components (2015), e-ISBN: 978-2-35158-149-0; Eds. M. Quattrone and V. M. John PRO 97: SHCC3 – 3rd International RILEM Conference on Strain Hardening Cementitious Composites (2014), ISBN: 978-2-35158-150-6; e-ISBN: 978-235158-151-3; Eds. E. Schlangen, M. G. Sierra Beltran, M. Lukovic and G. Ye PRO 98: FERRO-11 – 11th International Symposium on Ferrocement and 3rd ICTRC - International Conference on Textile Reinforced Concrete (2015), ISBN: 978-2-35158-152-0; e-ISBN: 978-2-35158-153-7; Ed. W. Brameshuber PRO 99 (online version): ICBBM 2015 - 1st International Conference on BioBased Building Materials (2015), e-ISBN: 978-2-35158-154-4; Eds. S. Amziane and M. Sonebi PRO 100: SCC16 - RILEM Self-Consolidating Concrete Conference (2016), ISBN: 978-2-35158-156-8; e-ISBN: 978-2-35158-157-5; Ed. Kamal H. Kayat PRO 101 (online version): III Progress of Recycling in the Built Environment (2015), e-ISBN: 978-2-35158-158-2; Eds. I. Martins, C. Ulsen and S. C. Angulo PRO 102 (online version): RILEM Conference on Microorganisms-Cementitious Materials Interactions (2016), e-ISBN: 978-2-35158-160-5; Eds. Alexandra Bertron, Henk Jonkers and Virginie Wiktor PRO 103 (online version): ACESC’16 - Advances in Civil Engineering and Sustainable Construction (2016), e-ISBN: 978-2-35158-161-2; Eds. T. Ch. Madhavi, G. Prabhakar, Santhosh Ram and P. M. Rameshwaran PRO 104 (online version): SSCS’2015 - Numerical Modeling - Strategies for Sustainable Concrete Structures (2015), e-ISBN: 978-2-35158-162-9

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PRO 105: 1st International Conference on UHPC Materials and Structures (2016), ISBN: 978-2-35158-164-3, e-ISBN: 978-2-35158-165-0 PRO 106: AFGC-ACI-fib-RILEM International Conference on Ultra-HighPerformance Fibre-Reinforced Concrete – UHPFRC 2017 (2017), ISBN: 978-235158-166-7, e-ISBN: 978-2-35158-167-4; Eds. François Toutlemonde and Jacques Resplendino PRO 107 (online version): XIV DBMC – 14th International Conference on Durability of Building Materials and Components (2017), e-ISBN: 978-2-35158-159-9; Eds. Geert De Schutter, Nele De Belie, Arnold Janssens and Nathan Van Den Bossche PRO 108: MSSCE 2016 - Innovation of Teaching in Materials and Structures (2016), ISBN: 978-2-35158-178-0, e-ISBN: 978-2-35158-179-7; Ed. Per Goltermann PRO 109 (2 volumes): MSSCE 2016 - Service Life of Cement-Based Materials and Structures (2016), ISBN Vol. 1: 978-2-35158-170-4, Vol. 2: 978-2-35158-171-4, Set Vol. 1&2: 978-2-35158-172-8, e-ISBN : 978-2-35158-173-5; Eds. Miguel Azenha, Ivan Gabrijel, Dirk Schlicke, Terje Kanstad and Ole Mejlhede Jensen PRO 110: MSSCE 2016 - Historical Masonry (2016), ISBN: 978-2-35158-178-0, e-ISBN: 978-2-35158-179-7; Eds. Inge Rörig-Dalgaard and Ioannis Ioannou PRO 111: MSSCE 2016 - Electrochemistry in Civil Engineering (2016), ISBN: 978-2-35158-176-6, e-ISBN: 978-2-35158-177-3; Ed. Lisbeth M. Ottosen PRO 112: MSSCE 2016 - Moisture in Materials and Structures (2016), ISBN: 9782-35158-178-0, e-ISBN: 978-2-35158-179-7; Eds. Kurt Kielsgaard Hansen, Carsten Rode and Lars-Olof Nilsson PRO 113: MSSCE 2016 - Concrete with Supplementary Cementitious Materials (2016), ISBN: 978-2-35158-178-0, e-ISBN: 978-2-35158-179-7; Eds. Ole Mejlhede Jensen, Konstantin Kovler and Nele De Belie PRO 114: MSSCE 2016 - Frost Action in Concrete (2016), ISBN: 978-2-35158182-7, e-ISBN: 978-2-35158-183-4; Eds. Marianne Tange Hasholt, Katja Fridh and R. Doug Hooton PRO 115: MSSCE 2016 - Fresh Concrete (2016), ISBN: 978-2-35158-184-1, e-ISBN: 978-2-35158-185-8; Eds. Lars N. Thrane, Claus Pade, Oldrich Svec and Nicolas Roussel PRO 116: BEFIB 2016 – 9th RILEM International Symposium on Fiber Reinforced Concrete (2016), ISBN: 978-2-35158-187-2, e-ISBN: 978-2-35158-186-5; Eds. N. Banthia, M. di Prisco and S. Soleimani-Dashtaki PRO 117: 3rd International RILEM Conference on Microstructure Related Durability of Cementitious Composites (2016), ISBN: 978-2-35158-188-9, e-ISBN: 9782-35158-189-6; Eds. Changwen Miao, Wei Sun, Jiaping Liu, Huisu Chen, Guang Ye and Klaas van Breugel

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PRO 118 (4 volumes): International Conference on Advances in Construction Materials and Systems (2017), ISBN Set: 978-2-35158-190-2, Vol. 1: 978-2-35158-193-3, Vol. 2: 978-2-35158-194-0, Vol. 3: ISBN:978-2-35158-195-7, Vol. 4: ISBN:978-235158-196-4, e-ISBN: 978-2-35158-191-9; Eds. Manu Santhanam, Ravindra Gettu, Radhakrishna G. Pillai and Sunitha K. Nayar PRO 119 (online version): ICBBM 2017 - Second International RILEM Conference on Bio-based Building Materials, (2017), e-ISBN: 978-2-35158-192-6; Ed. Sofiane Amziane PRO 120 (2 volumes): EAC-02 - 2nd International RILEM/COST Conference on Early Age Cracking and Serviceability in Cement-based Materials and Structures, (2017), Vol. 1: 978-2-35158-199-5, Vol. 2: 978-2-35158-200-8, Set: 978-2-35158197-1, e-ISBN: 978-2-35158-198-8; Eds. Stéphanie Staquet and Dimitrios Aggelis PRO 121 (2 volumes): SynerCrete18: Interdisciplinary Approaches for Cementbased Materials and Structural Concrete: Synergizing Expertise and Bridging Scales of Space and Time, (2018), Set: 978-2-35158-202-2, Vol.1: 978-2-35158-211-4, Vol.2: 978-2-35158-212-1, e-ISBN: 978-2-35158-203-9; Eds. Miguel Azenha, Dirk Schlicke, Farid Benboudjema and Agnieszka Knoppik PRO 122: SCC’2018 China - Fourth International Symposium on Design, Performance and Use of Self-Consolidating Concrete, (2018), ISBN: 978-2-35158-204-6, e-ISBN: 978-2-35158-205-3; Eds. C. Shi, Z. Zhang and K. H. Khayat PRO 123: Final Conference of RILEM TC 253-MCI: Microorganisms-Cementitious Materials Interactions (2018), Set: 978-2-35158-207-7, Vol.1: 978-2-35158-209-1, Vol.2: 978-2-35158-210-7, e-ISBN: 978-2-35158-206-0; Ed. Alexandra Bertron PRO 124 (online version): Fourth International Conference Progress of Recycling in the Built Environment (2018), e-ISBN: 978-2-35158-208-4; Eds. Isabel M. Martins, Carina Ulsen and Yury Villagran PRO 125 (online version): SLD4 - 4th International Conference on Service Life Design for Infrastructures (2018), e-ISBN: 978-2-35158-213-8; Eds. Guang Ye, Yong Yuan, Claudia Romero Rodriguez, Hongzhi Zhang and Branko Savija PRO 126: Workshop on Concrete Modelling and Material Behaviour in honor of Professor Klaas van Breugel (2018), ISBN: 978-2-35158-214-5, e-ISBN: 978-235158-215-2; Ed. Guang Ye PRO 127 (online version): CONMOD2018 - Symposium on Concrete Modelling (2018), e-ISBN: 978-2-35158-216-9; Eds. Erik Schlangen, Geert de Schutter, Branko Savija, Hongzhi Zhang and Claudia Romero Rodriguez PRO 128: SMSS2019 - International Conference on Sustainable Materials, Systems and Structures (2019), ISBN: 978-2-35158-217-6, e-ISBN: 978-2-35158-218-3 PRO 129: 2nd International Conference on UHPC Materials and Structures (UHPC2018-China), ISBN: 978-2-35158-219-0, e-ISBN: 978-2-35158-220-6;

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PRO 130: 5th Historic Mortars Conference (2019), ISBN: 978-2-35158-221-3, e-ISBN: 978-2-35158-222-0; Eds. José Ignacio Álvarez, José María Fernández, Íñigo Navarro, Adrián Durán and Rafael Sirera PRO 131 (online version): 3rd International Conference on Bio-Based Building Materials (ICBBM2019), e-ISBN: 978-2-35158-229-9; Eds. Mohammed Sonebi, Sofiane Amziane and Jonathan Page PRO 132: IRWRMC’18—International RILEM Workshop on Rheological Measurements of Cement-based Materials (2018), ISBN: 978-2-35158-230-5, e-ISBN: 978-2-35158-231-2; Eds. Chafika Djelal, Yannick Vanhove PRO 133 (online version): CO2STO2019—International Workshop CO2 Storage in Concrete (2019), e-ISBN: 978-2-35158-232-9; Eds. Assia Djerbi, Othman OmikrineMetalssi, Teddy Fen-Chong PRO 134: 3rd ACF/HNU International Conference on UHPC Materials and Structures - UHPC’2020, ISBN: 978-2-35158-233-6, e-ISBN: 978-2-35158-234-3; Eds.Caijun Shi & Jiaping Liu PRO 135: Fourth International Conference on Chemically Activated Materials (CAM2021), ISBN: 978-2-35158-235-0, e-ISBN: 978-2-35158-236-7; Eds.Caijun Shi & Jiaping Liu

RILEM Reports (REP) Report 19: Considerations for Use in Managing the Aging of Nuclear Power Plant Concrete Structures (ISBN: 2-912143-07-1); Ed. D. J. Naus Report 20: Engineering and Transport Properties of the Interfacial Transition Zone in Cementitious Composites (ISBN: 2-912143-08-X); Eds. M. G. Alexander, G. Arliguie, G. Ballivy, A. Bentur and J. Marchand Report 21: Durability of Building Sealants (ISBN: 2-912143-12-8); Ed. A. T. Wolf Report 22: Sustainable Raw Materials - Construction and Demolition Waste (ISBN: 2-912143-17-9); Eds. C. F. Hendriks and H. S. Pietersen Report 23: Self-Compacting Concrete state-of-the-art report (ISBN: 2-912143-233); Eds. Å. Skarendahl and Ö. Petersson Report 24: Workability and Rheology of Fresh Concrete: Compendium of Tests (ISBN: 2-912143-32-2); Eds. P. J. M. Bartos, M. Sonebi and A. K. Tamimi Report 25: Early Age Cracking in Cementitious Systems (ISBN: 2-912143-33-0); Ed. A. Bentur Report 26: Towards Sustainable Roofing (Joint Committee CIB/RILEM) (CD 07) (e-ISBN 978-2-912143-65-5); Eds. Thomas W. Hutchinson and Keith Roberts

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Report 27: Condition Assessment of Roofs (Joint Committee CIB/RILEM) (CD 08) (e-ISBN 978-2-912143-66-2); Ed. CIB W 83/RILEM TC166-RMS Report 28: Final report of RILEM TC 167-COM ‘Characterisation of Old Mortars with Respect to Their Repair (ISBN: 978-2-912143-56-3); Eds. C. Groot, G. Ashall and J. Hughes Report 29: Pavement Performance Prediction and Evaluation (PPPE): Interlaboratory Tests (e-ISBN: 2-912143-68-3); Eds. M. Partl and H. Piber Report 30: Final Report of RILEM TC 198-URM ‘Use of Recycled Materials’ (ISBN: 2-912143-82-9; e-ISBN: 2-912143-69-1); Eds. Ch. F. Hendriks, G. M. T. Janssen and E. Vázquez Report 31: Final Report of RILEM TC 185-ATC ‘Advanced testing of cement-based materials during setting and hardening’ (ISBN: 2-912143-81-0; e-ISBN: 2-91214370-5); Eds. H. W. Reinhardt and C. U. Grosse Report 32: Probabilistic Assessment of Existing Structures. A JCSS publication (ISBN 2-912143-24-1); Ed. D. Diamantidis Report 33: State-of-the-Art Report of RILEM Technical Committee TC 184-IFE ‘Industrial Floors’ (ISBN 2-35158-006-0); Ed. P. Seidler Report 34: Report of RILEM Technical Committee TC 147-FMB ‘Fracture mechanics applications to anchorage and bond’ Tension of Reinforced Concrete Prisms – Round Robin Analysis and Tests on Bond (e-ISBN 2-912143-91-8); Eds. L. Elfgren and K. Noghabai Report 35: Final Report of RILEM Technical Committee TC 188-CSC ‘Casting of Self Compacting Concrete’ (ISBN 2-35158-001-X; e-ISBN: 2-912143-98-5); Eds. Å. Skarendahl and P. Billberg Report 36: State-of-the-Art Report of RILEM Technical Committee TC 201-TRC ‘Textile Reinforced Concrete’ (ISBN 2-912143-99-3); Ed. W. Brameshuber Report 37: State-of-the-Art Report of RILEM Technical Committee TC 192-ECM ‘Environment-conscious construction materials and systems’ (ISBN: 978-2-35158053-0); Eds. N. Kashino, D. Van Gemert and K. Imamoto Report 38: State-of-the-Art Report of RILEM Technical Committee TC 205-DSC ‘Durability of Self-Compacting Concrete’ (ISBN: 978-2-35158-048-6); Eds. G. De Schutter and K. Audenaert Report 39: Final Report of RILEM Technical Committee TC 187-SOC ‘Experimental determination of the stress-crack opening curve for concrete in tension’ (ISBN 978-2-35158-049-3); Ed. J. Planas Report 40: State-of-the-Art Report of RILEM Technical Committee TC 189-NEC ‘Non-Destructive Evaluation of the Penetrability and Thickness of the Concrete Cover’ (ISBN 978-2-35158-054-7); Eds. R. Torrent and L. Fernández Luco

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Report 41: State-of-the-Art Report of RILEM Technical Committee TC 196-ICC ‘Internal Curing of Concrete’ (ISBN 978-2-35158-009-7); Eds. K. Kovler and O. M. Jensen Report 42: ‘Acoustic Emission and Related Non-destructive Evaluation Techniques for Crack Detection and Damage Evaluation in Concrete’ - Final Report of RILEM Technical Committee 212-ACD (e-ISBN: 978-2-35158-100-1); Ed. M. Ohtsu Report 45: Repair Mortars for Historic Masonry - State-of-the-Art Report of RILEM Technical Committee TC 203-RHM (e-ISBN: 978-2-35158-163-6); Eds. Paul Maurenbrecher and Caspar Groot Report 46: Surface delamination of concrete industrial floors and other durability related aspects guide - Report of RILEM Technical Committee TC 268-SIF (e-ISBN: 978-2-35158-201-5); Ed. Valerie Pollet

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mohammed Sonebi and Dimitri Feys

1

2 Rheological Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wolfram Schmidt and Julian Link

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3 Concrete Rheometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arnaud Perrot and Sofiane Amziane

33

4 Measuring Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ammar Yahia and Arnaud Perrot

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5 Challenges Encountered During Measuring Rheological Properties of Mortar and Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimitri Feys and Jon E. Wallevik

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6 Empirical Test Methods to Evaluate Rheological Properties of Concrete and Mortar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Kamal Khayat, Jiang Zhu, and Steffen Grunewald 7 State of Knowledge of Interface Rheometers and Tribometers . . . . . . 181 Yannick Vanhove, Chafika Djelal, and Tilo Proske 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Dimitri Feys and Mohammed Sonebi Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

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Symbols

The list below defines commonly used symbols in this state-of-the-art report. However, some of these symbols may have a different meaning in certain contexts. In this case, and if new symbols are introduced in the following chapters, an indication of the property is given. g h m n p r t t50 , t500 v Athix E F G G* H K L N P R S S’ SF

Gravitational acceleration (m/s2 ) Height (m) Mass (g) Consistency index in power law and Herschel-Bulkley models (-) Pressure (Pa) Radial parameter (m) Time (s) Time to reach 500 mm slump flow (s). Also denoted as T50 or T50 (-) Velocity (m/s) Rate of structural build-up, characterized by the increase in static yield stress with time (Pa/s) Energy (J) Force (N) Intercept of linear equation between torque and angular or rotational velocity (Nms) Shear modulus (Pa) Slope of linear equation between torque and angular or rotational velocity (Nms) Consistency factor in power law and Herschel-Bulkley models (Pa sn ) Length (m) Rotational velocity (rps) Power (W) Radius (m) Slump (mm) Dimensionless slump = slump/height of cone (-) Slump flow (mm) xxv

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Symbols

T Torque (Nm) T50 , T50 Time to reach 500 mm slump flow (s). Also denoted as t50 or t500 TV Time for concrete or mortar to flow through the V-Funnel or mini-VFunnel, respectively (-) V Volume (m3 ) γ Strain (-) γ˙ Shear rate or strain rate (s-1 ) η Apparent viscosity (Pa s) μ or μp Viscosity or plastic viscosity (Pa s) ρ Density (kg/m3 ) Relative density = density/density of water at 4°C (-) ρsg σ Normal stress (Pa) √ Yield stress according to von Mises plasticity criterion (Pa) = 3τ0 (-) σ0 τ Shear stress (Pa) Yield stress (Pa) τ0 Dynamic yield stress (Pa) τ0,d Static yield stress (Pa) τ0,s ω Angular velocity (rad/s) Denoting inner (-) Index i Index o Denoting outer (-) Index p Denoting plug (-)

Chapter 1

Introduction Mohammed Sonebi and Dimitri Feys

For more than a century, concrete research has focused on improving the mechanical properties and durability of concrete, focusing on the effects of mix design parameters and exposure conditions on the responses to different mechanical, physical and chemical solicitations. More recently, performance-based approaches are encouraged to meet the criteria. This allows concrete producers to develop their own mixtures outside of typical prescriptive specifications, potentially improving economic efficiency and reducing ecological footprint. Gradually during the last century, research has increasingly concentrated on fresh properties of concrete, in addition to the aforementioned hardened properties. With the development of the last generation of water-reducing agents, a significant increase in research of fresh properties has occurred. Properties of fresh concrete are regularly prescribed, especially for specialty concrete mixtures (self-consolidating concrete, under-water concrete, concrete for 3D printing, architectural concrete, high-performance concrete, etc.), which need to be fulfilled in addition to the requirements for mechanical properties and durability. The concrete producer needs to tailor the fresh concrete properties in order to fulfill requirements related to transportation, placement, consolidation and finishing to ensure an adequate construction process and achieve acceptable properties in the hardened state. The ability to adjust plastic concrete to meet certain requirements is a unique feature of this special construction material. Empirical test methods are continuously developed to evaluate a specific property, or set of properties of fresh concrete, and acceptance criteria are established for M. Sonebi (B) Queen’s University Belfast, Belfast, UK e-mail: [email protected] D. Feys Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Sonebi and D. Feys (eds.), Measuring Rheological Properties of Cement-based Materials, RILEM State-of-the-Art Reports 39, https://doi.org/10.1007/978-3-031-36743-4_1

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M. Sonebi and D. Feys

quality control or quality assurance purposes. The STAR report of RILEM TC145 “Workability and Rheology of Fresh Concrete: Compendium of Tests” was published in 2002 and reports the properties of a selection of fresh special concretes and relevant test methods [1]. However, these methods lack the fundamental aspects of science, and although they are very useful for a large number of applications, a more fundamental approach is essential to fully measure, predict and control fresh properties and placement processes. Rheology, which is defined as the science of the deformation and flow of matter, is a scientific tool which can be used to describe the flow of fresh cement-based materials [2]. It provides a fundamental description of the response (stress, strain, or shear rate) to a solicitation (strain, shear rate or stress). Typically, rheology classifies materials as elastic, viscous, viscoplastic or viscoelastic. While concrete, and any cementbased material, can technically be described by each of these states, the focus of this STAR is on the viscous/viscoplastic response. Concrete and mortar are regarded as homogeneous fluids, for which a number of properties are of interest: the yield stress, the stress which needs to be surpassed to transition between elastic behavior and flow, and the viscosity: the resistance to an increase in flow rate. However, for cement-based materials, these two properties are dependent on time, temperature, and shear-history. One of the more complex behaviors in rheology is the dependency of the material on time and shear-history. Thixotropy is a commonly found phenomenon in the polymer and food industry, with ketchup being a prime example [3]. Thixotropy is defined as the decrease with time of viscosity when shear stress or shear rate is increased, followed by a gradual recovery of viscosity when that stress or shear rate is removed or reduced [2–4]. As such, dependent on the applied shear-history, different properties can be obtained for the same material [5]. Furthermore, ongoing hydration reactions transform the cement-based material from a plastic and sometimes fluid substance into a strong solid artificial rock. As such, thixotropy and hydration cause an even more complex dependency on shear history and time [6]. An additional complexity of the rheology of concrete and mortar is the presence of aggregate particles, as it sometimes nullifies the hypothesis of a homogeneous suspension, or it causes a transition from a suspension into a granular material. In this latter case, the entire concept of measuring needs to be revisited as techniques and technologies are completely different. Neither of the two approaches, suspension, or granular material, is an exception, as typical concrete mix designs cover both areas. Movement of conventional, non-pumpable concrete is typically governed by granular interactions, while for flowable or pumpable concrete, the material is usually behaving as a suspension. The distinction between those two regimes is absolutely essential in selecting rheometers, parameters, and procedures. The tool to measure the rheological properties of a material is called a rheometer, and such tools have been continuously developed, since approximately the 1950s, for mortar and concrete. Due to the particle size of aggregates, larger devices compared to standard tools in polymer and food rheology are required. Comparison campaigns between concrete rheometers have revealed significant differences in measured properties, which can be attributed to calibration and sensing concerns, or to deviations

1 Introduction

3

from the assumed ideal flow behavior. A new round robin test (RRT) was performed in May 2018 in Bethune, France, by this TC, and included new rheological devices, such as the ICAR, Viskomat XL, eBT-V, Rheocad, BML 4 SCC rheometers, as well as the plate test, Sliper, interface rheometer, and tribometer instruments. The measurements were performed on three SCC, two highly flowable concrete and three mortar mixtures. Testing involved the evaluation of flow curves, structural build-up and interface properties and their evolution with time. The outcomes of this RRT are published in a topical collection in the Material and Structures journal. Rheological properties are measured to determine the interaction between mix design, placement, and final properties, although many studies only focus on one or two aspects. Rheology has been used extensively to determine the effect of mix design parameters, including material properties and proportions, on yield stress, viscosity, thixotropy and other time-dependent properties. It has also been used to establish criteria for concrete placement or stability, including flow in formworks, through narrow obstacles, pumping, static and dynamic stability, multi-layer casting, 3-D printing, etc. Finally, it is also used to evaluate whether a specific placement procedure negatively affects the properties of concrete. Moreover, the studies on rheology are analytical, if possible, experimental, or numerical. And while experimental studies allow for the use of empirical tests, analytical and numerical work requires the use of rheology. The report is focused on the rheometry of concrete and mortar and excluded cement pastes. For cement pastes, more “standard tools”, available in the polymer and food rheology industry, can be employed. It was not the intention of the committee to describe all tools and procedures available for cement pastes. Instead, a separate contribution in RILEM Technical Letters was published on rheometry of cement pastes [7]. Similarly, as practically no viscoelastic measurements are performed on mortar and concrete, the topic of viscoelasticity is outside the scope of this STAR. A separate paper on viscoelastic measurements is in preparation at the time this STAR is published. However, the general concepts on rheological properties, rheometry, procedures and challenges that apply to mortar and concrete also apply to cement paste, providing the reader indirectly with useful information on rheometry of cement pastes as well. Although a quick introduction into mix design and applications is given in Chap. 2, this STAR does not discuss how to relate mix design and rheology and which range of rheological properties are best for specific applications. This report also does not provide recommendations on how to measure rheological properties, but it rather delivers a comprehensive overview of: ● ● ● ● ● ●

Rheology definitions, behavior, and parameters (Chap. 2) Rheometers (Chap. 3) Measuring and analysis procedures (Chap. 4) Difficulties and challenges during measurements (Chap. 5) Relationships with specific empirical tests (Chap. 6) Behavior of concrete near a surface (Chap. 7)

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M. Sonebi and D. Feys

In detail, this report is divided into eight chapters. The first is this introduction and the Chap. 2 deals with the rheological properties of cement-based materials. In Chap. 2, several rheological models were reported and thixotropy is defined and described. The mix design composition can be tailored to achieve proper rheological properties and to ensure adequate flow performance and successful casting. Thixotropy of cement-based materials has a direct impact on their placement and compaction performance as well as on the microstructural development and overall performance of the hardened materials. The Chap. 3 describes different concrete rheometers. This chapter describes some rheometers with more details about dimensions and how to use them with some reported literature about challenges. Rheometers included BML 4 SCC rheometer, Viskomat XL, eBT-V, RheoCAD, BML, BT-Rheom, Cemagref, ConTec series, Tattersall Mk-II, Tattersall Mk-III (IBB), squeeze flow and extraction flow rheometers, and the plate test. These rheometers focus on a wide variety of equipment, each suitable for a certain range of concrete mixtures. It cannot be expected that every rheometer can measure every type of concrete. The Chap. 4 is an introductory of measurement procedures used for rheometers. An overview is described on how these rheometers can be used in order to determine rheological parameters from flow curves (dynamic yield stress, viscosity, non-linearity, static yield stress), and how these properties can be calculated from the measured raw data. Chapter 5 focuses on challenges encountered during measuring rheological properties of mortar and concrete. Some challenges that are described in this chapter the influence of aggregates, no-equilibrium, plug flow in case of cylindrical coaxial rheometers, particle migration, evaporation, air content, wall effect, and so forth. Chapter 6 focuses on empirical test methods to evaluate the rheological properties of concrete and mortar and some discuss the relationships between the outcomes from these test methods and the rheological parameters (dynamic and static yield stress, viscosity, and thixotropy). In this chapter, several test methods used to evaluate the free flow of concrete and their relationships with static and dynamic yield stress and viscosity were discussed (e.g., slump, slump flow, spread time, V-funnel, Lbox, and LCPC box, and including the portable vane and inclined plane tests for structural build-up). Some of the specialty tests for extrusion and 3D printing were also mentioned in this chapter with relation to rheological properties. Additionally, the determination of the mixing energy in concrete truck mixtures is also used to estimate the rheological properties of concrete. Some of the limitations associated with empirical test methods are also reported in this chapter. The aim of the Chap. 7 is to give an overview of the state of knowledge of interface rheometry which is very important for pumping concrete (formation of lubrication layer) and interface measurement between concrete and formwork using tribometers. Other devices to measure the interface properties between concrete and wall were also described. The Chap. 8 summarized the conclusion. The committee hopes that the information given in this report on the measurement of rheological properties of complex materials such as concrete is useful, and that

1 Introduction

5

it addressed some challenges on the measuring procedures, the rheological models and some errors and limitations of rheometers used.

References 1. Bartos PJ, Sonebi M, Tamimi AK (eds) (2002) Report 24: workability and rheology of fresh concrete: compendium of tests–report of RILEM Technical Committee TC 145-WSM, vol 24. RILEM publications 2. Macosko CW (1994) Rheology principles. Measurements and applications 3. Barnes HA (1997) Thixotropy—a review. J Nonnewton Fluid Mech 70(1–2):1–33 4. Mewis J, Wagner NJ (2012) Colloidal suspension rheology. Cambridge University Press 5. Cheng DH (1967) Hysteresis loop experiments and the determination of thixotropic properties. Nature 216(5120):1099–1100 6. Roussel N, Ovarlez G, Garrault S, Brumaud C (2012) The origins of thixotropy of fresh cement pastes. Cem Concr Res 42(1):148–157 7. Feys D, Cepuritis R, Jacobsen S, Lesage K, Secrieru E, Yahia A (2018) Measuring rheological properties of cement pastes: most common techniques, procedures and challenges. RILEM Tech Lett 2:129–135

Chapter 2

Rheological Properties Wolfram Schmidt and Julian Link

Abstract This chapter provides an introduction to the rheology of cementitious systems. The non-Newtonian flow behavior of cementitious suspensions is viscoplastic in nature, which is reflected by different flow properties including yield stress, non-linear flow behavior, or shear-rate dependence. The flow properties of mortar and concrete are introduced and influencing parameters are related to the resulting rheological properties. The workability of concrete is controlled by flow phenomena such as flow speed, segregation or blocking, which are affected by the rheological properties. The workability of concrete is also controlled by reversible and non-reversible temporal influences, due to changing particle structure within the suspensions or changing particle connections by the hydration process. The rheology of cementitious systems is controlled by a number of influencing factors, which are described in this chapter.

2.1 Introduction During the last three decades, concrete has transformed from a rather simple mass construction material based on a limited number of constituents, namely cement, water, and aggregates, towards a material with a wide range of performance specifications. It can be tailored for high performance applications and ultimate user specifications. The reason for the rapid evolvement was the increasing awareness With contributions from: Michael Haist, Sarah Leinitz, and Jon Elvar Wallevik. Michael Haist—Technical University Hannover, Germany. Sarah Leinitz—BAM, Germany. Jon E. Wallevik—Icelandic Meteorological Office, Iceland. W. Schmidt (B) Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany e-mail: [email protected] J. Link Technical University Hannover, Hannover, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Sonebi and D. Feys (eds.), Measuring Rheological Properties of Cement-based Materials, RILEM State-of-the-Art Reports 39, https://doi.org/10.1007/978-3-031-36743-4_2

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Fig. 2.1 Evolution of concrete consistencies and strengths [1]

how to benefit from mineral additions and chemical admixtures. In particular, the latter group can be considered as the most influential factor, which yielded a boost of technology as of approximately the 1980s. Figure 2.1 shows the evolution of the history of concrete with the invention of superplasticizers, which played an important role in technology development. This figure also presents the bandwidth of consistencies and feasible utilizations by engineers. At the same time, it can be observed that the widening range of consistencies correlates extremely well with the evolution of concrete compressive strengths. The incorporation of superplasticizers into concrete mixture compositions eventually facilitated concrete engineers to improve the workability properties without need to increase the water-cement-ratio (w/c) and to significantly reduce the w/c or the water-powder-ratio (w/p), which finally resulted in concrete with higher performance and specified properties. Therefore, controlling the rheology of concrete can be considered as the catalyst for the invention of the many recent mortar and concrete innovations such as polymer modified cementitious composites (PCC), self-compacting concrete (SCC), highperformance concrete (HPC), ultra-high-performance concrete (UHPC) or engineered cementitious composites (ECC). Furthermore, it can be seen as the key to the solutions of all future challenges, such as overcoming limited pumping heights, casting at extreme weather conditions, or applications as 3D-printing technologies. Finally, the rheology ensures durability and contributes to increasing sustainability. The majority of construction failures are induced by erroneous application or by improper adjustment of the material to application requirements. The price for the vast technological potentials arising from tailored rheology is that these systems become more sensitive and are more prone to failure, particularly regarding the specified rheological properties. Improperly adjusted rheology or

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scatter in the performances can cause severe problems such as stagnation of flow or segregation with dramatic influence on the structural behavior at later stages. Future additive automated process technologies will further increase the demands on the rheology of concrete, and therefore, reliable control of the rheology as well as tools for the adjustment of robust rheological properties are of utmost importance. Table 2.1 provides an overview of the rheological requirements and the specific rheological challenges that lie within for some challenging concrete technologies. Hence, understanding the rheology of cementitious systems and knowing how to actively control it, are keys to innovation in concrete technology i.e., by external signals to trigger a change in flow behavior [2]. Today, rheometers offer enormous potentials for material developments and quality control on site. However, their use also demands for a higher level of understanding of the flow phenomena. Therefore, this chapter intents to explain basic rheological effects and how they are linked to flow phenomena in cementitious systems. Table 2.1 Rheological challenges for different concrete manufacturing technologies Manufacturing technology

Specifications

Rheological challenge with relevance for function, safety, and durability

3D-printing of concrete elements

Low yield stress with rapid (thixotropic) structural build-up

In-situ measurement of the workability and in-situ counter control required

Self-compacting concrete

Ideal adjustment between yield Effective avoidance of segregation and stress and plastic viscosity stagnation

Ready-mixed concrete Depending upon concrete specification

Suitable workability properties despite transport delays, and high sedimentation resistance

Grouting, esp. Offshore-Grouting

Low yield stress and long workability time

Blockages must be avoided at any case

Pumping concrete

Parallel adjustment of yield stress and plastic viscosity to provide ease pumpability and to avoid pressurized bleeding and blockage

Improper adjustment of rheology causes application issues, i.e., high plastic viscosity means energy intensive pumping, whereas low plastic viscosity/yield stress might result in pressurized bleeding

Fiber concrete/SHCC

Sufficiently high (plastic) viscosity to avoid dynamic segregation, but sufficiently low yield stress to provide workability and fiber dispersion

Heterogeneity of the rheology of pastes can cause poor fiber distribution and agglomeration of fibers

Sprayed concrete

Low viscosity with rapid structural build-up

Small changes to the water/additive content influences the rebound and run out

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2.2 Viscoplastic Properties 2.2.1 Parameters Defining Rheological Properties 2.2.1.1

Newtonian Flow Behavior

Fluids under laminar flow can be described by a plate model (Fig. 2.2), where one plate is fixed and the other plate is displaced at a velocity vi , so that a shear velocity gradient dv/dh occurs between the two plates. The shear stress between the two shear planes can be determined according to:

τ=

F A

(2.1)

where: τ = stress (in Pa), F = force (in N) and A = shear plane area (in m2 ). The derivative of the deformation velocity function over the deformation height is the shear rate γ˙ , which is defined according to: γ˙ =

dv dh

(2.2)

where: γ˙ = shear rate (in s−1 ), v = deformation velocity (in m/s) and h = deformation height (in m). The coefficient that describes the resistance of a fluid against a shear deformation is the dynamic viscosity η. It is defined as: η=

τ γ˙

(2.3)

where: η = dynamic viscosity (in Pa s). Fluids that follow Eq. (2.3) with constant η are so-called Newtonian fluids. They exhibit a linear relation between the shear stress τ and the shear rate γ˙ . The dynamic viscosity η, which is equal to the slope of the flow curve is constant and independent

Fig. 2.2 Plate model for fluids and laminar deformations

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on the shear rate. The stress τ depending upon the shear rate γ˙ can be calculated according to Eq. (2.4). Typical examples for Newtonian fluids are water, or many oils or gases. Newtonian fluids immediately start to flow upon application of a load. τ = ηγ˙

2.2.1.2

(2.4)

Yield Stress

Cementitious systems are suspensions with at least two distinguishable phases, a liquid and a solid phase, which both have different influences on the rheology. Suspensions typically do not instantly flow upon application of a shear stress. Up to a threshold shear stress, these systems behave approximately like a solid, however eventually exhibiting pronounced creep deformation. By exceeding the threshold shear stress, the so-called yield stress, the systems can exhibit viscous flow ehaviour. The experimental determination of the yield stress can be performed by different methods resulting mainly in two types of yield stresses, that can be related to the cement-based material, namely the static yield stress τ 0,s and the dynamic yield stress τ 0,d [3, 4]. The term “dynamic yield stress” is a synonym for “yield stress” [5, 6]. The static yield stress is related to the amount of shear necessary to make the test material start flowing (i.e., the transformation from a solid state to a fluid state). The dynamic yield stress is more responsible for stopping a flowing test material (i.e., the transformation from fluid state back to solid state) and thus τ 0,s ≥ τ 0,d . For concrete casting, often the dynamic yield stress τ 0,d is of larger interest since it is more responsible for stopping of the flowing concrete inside a mould or a formwork [5]. The static yield stress τ s , however is also important for concrete placement, particularly for determining the pressure exerted by the fresh concrete on the formwork or for extrusion-based fabrication to determine increase in stiffness assessing the further processing [7]. The difference or part of the difference Δτ = τ 0,s – τ 0,d can be related to structural rebuild [5, 8]. The structural rebuild (thixotropy) will be explained in Sect. 3.1.1. Thus, during the breakdown process, the difference Δτ is reduced with time. However, the difference or part of it can also be related to the additional resistance, namely the concomitant change in particle packing, when going from zero shear rate to non-zero shear rate [5]. Yield stress phenomena occur when particles in a fluid interact with each other. However, the existence of a yield stress can be critically discussed, particularly for fluids with large Deborah numbers, since the tendency to deform can also depend upon the time the stress is applied [9]. The Deborah number relates the materialdependent relaxation time to the experimental time, indicating the impact of timedependent processes on flow processes resulting in observation of long timescales for large Deborah numbers to detect flow ehaviour. However, for cementitious flowable systems the concept of a yield stress has proven to be a useful concept for scientific and engineering applications. This is particularly valid for systems changing

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their materials ehaviour in a relatively short period of time from fluid towards elastic ehaviour, where different material laws (e.g., Hooke’s law) are valid, and the resistance against deformations is described by the Young’s modulus E, the Poisson’s ratio υ and the shear modulus G. The reader however should be aware of the fact, that when considering segregation phenomena in cementitious systems, the deformation ehaviour of the suspension (or of its constituents) for shear stresses below the yield stress becomes highly relevant.

2.2.1.3

Bingham Flow Behavior

For many fluids, after exceeding a specific or temporary yield stress, there is a linear relationship between shear stress and shear rate like in Newtonian fluids. Fluids that show this kind of behavior are called Bingham fluids after E. C. Bingham, who coined the definition of plastic flow behavior with initial minimum shear force to initiate the flow. This concept clearly distinguished from the popular opinion at that time that plastic flow is equal to incomplete elasticity [10–12]. The shear stress can be calculated according to Eq. (2.5): τ = τ0 + μ p γ˙

(2.5)

where: τ0 = yield stress (in Pa) and μp = plastic viscosity (in Pa s). The shear stress at each shear rate is described by the apparent (dynamic) viscosity ηapp , which can have a viscosity and a yield stress contribution (Fig. 2.3a). Since the yield stress contribution dominates the apparent viscosity at low shear rates, the apparent viscosity becomes infinite at zero shear rate. At high shear rate the apparent viscosity approximates the plastic viscosity (Fig. 2.3b). With regard to concrete, high shear rates occur and differences between apparent and plastic viscosity are minimized. In the following chapters, plastic viscosity will be used as parameter for description of viscosity characteristics.

2.2.1.4

Non-Linear Behavior

Many fluids do not exhibit a constant viscosity. For these fluids the Ostwald-de-Waele relation applies [13, 14] according to Eq. (2.6): τ = K γ˙ n

(2.6)

where: K = consistency factor (in Pa sn ) and n = consistency index (dimensionless). Here a flow consistency factor is introduced as a multiplier to the shear rate and a consistency index is the exponent of the shear rate, which describes how much the flow behavior deviates from Newtonian flow.

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Fig. 2.3 Distinction between plastic and apparent viscosity (a) and shear rate dependency of the viscosity for Newtonian, and Bingham-fluids (b)

In fluids with a consistency index n < 1 the viscosity is reduced with increasing shear rate. The corresponding flow behavior is called shear thinning or pseudoplastic. The reduced viscosity typically arises from polymers or particles that orient themselves in flow direction upon application of a shear deformation. Fluids with a consistency index n > 1 exhibit an increase in viscosity with increasing shear rate. The flow behavior is called shear thickening or dilatant. The effect typically occurs in multi-phase fluids and has its origin in different inertia between heterogeneous phases. In densely packed granular systems (such as concrete) dilatancy often results from a disturbance of the local packing due to shear, resulting in an increased local water demand and thus a reduction in fluidity. Whereas the dimension of K in Eq. 2.6 changes with n, this change in unit is to be seen as a mathematical artifact, resulting from the choice of the fitting function to model the change in viscosity. After all, it is the viscosity, which increases with increasing shear rate.

2.2.1.5

Herschel-Bulkley Behavior

Fluids with yield stress that do not have a constant viscosity coefficient are typically described by the Herschel-Bulkley law [15], which is described by: τ = τ0 + K γ˙ n

(2.7)

This law is equal to the Ostwald-de Waele relation but supplemented with the yield stress τ 0 . Depending upon the characteristic flow behavior, the viscosity in the Herschel-Bulkley model can decrease or increase with increasing shear rate. Since cementitious systems typically exhibit a yield stress the flow performance of these

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Fig. 2.4 Qualitative flow curves following the aforementioned flow laws, see Eqs. (2.5, 2.6), and (2.7) from [16]

systems can be typically well described by a Bingham model or the Herschel-Bulkley model. Their flow curves are illustrated in Fig. 2.4.

2.2.1.6

Shear Rate Dependency

Due to the origin of the flow phenomena, the applicability of the models can strongly depend upon the observed shear rate range. According to Hot and Roussel [17] at low shear rates, attractive Van der Waals forces dominate the particle–particle interactions (Fig. 2.5). They are largely affected by charge interactions on particle surfaces and their separation distance, but not strongly on the shear rate. Therefore, nonNewtonian flow behavior can be observed. At higher shear rates the systems behave Newtonian, whereas the viscosity is mainly driven by the particle volume fraction. At high shear rates the suspending fluid can no longer absorb the inertia of particles, which induces shear thickening effects. The effect is getting more prominent with increased volume fraction.

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Fig. 2.5 Shear rate dependency of the flow behavior of cementitious pastes. Figure after [17]

2.2.2 Relevance of Flow Parameters for Concrete and Mortar Flow 2.2.2.1

Introduction

Rheological model parameters, briefly explained in the sections before, affect the practical ehaviour of cementitious systems during the casting as well as during the early period after placement. Therefore, it is important to understand how the measurable rheological parameters affect the macroscopic flow ehaviour. For flowable concrete types, it is thus of highest importance to understand what underlies viscosity and yield stress changes, and which consequences will affect casting processes.

2.2.2.2

Viscosity

The viscosity determines flow velocity and dynamic effects during the flow. A decreased viscosity comes along with increased flow speed and typically with enhanced de-aeration during the flow process. In return, a viscosity that is too low can cause segregation of aggregates during the flow process, which can also increase the risk of blocking of coarse aggregates at obstacles and can result in heterogeneous concrete components. An overview of yield stress and viscosity of different types of concrete is shown in Fig. 2.6.

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Fig. 2.6 Range of dynamic yield stress and plastic viscosity for various concrete compositions [18]

2.2.2.3

Yield Stress

The dynamic yield stress determines when the flow process will be stopped. It is strongly related to the final shape of flowable concrete. Hence, with decreasing yield stress, the flow diameter or the flow distance becomes wider—assuming the flow is stable. Yield stress therefore significantly affects filling ability and smoothness of the surface. The static yield stress determines at which stress concrete starts flowing. It is thus mainly relevant for formwork pressure and stability of aggregates upon rest.

2.2.2.4

Shear Thinning

Shear thinning is an effect of decreased viscosity with increasing shear rate, which is useful for various applications, particularly in the area of mortar technology. Shear thinning helps to apply cementitious mortars like plasters and renders with ease during the application, when the shear rates are high due to processing, while the system remains stable upon rest due to the higher viscosity at low shear rates when the system is only exposed to gravity forces. Shear thinning also explains that often incongruences are observed between slump flow values, where the shear rate is low, and casting or pumping processes, where high shear rates occur.

2.2.2.5

Shear Thickening

Shear thickening describes an increase in viscosity with increasing shear rate. In comparison to shear thinning, shear thickening cannot be used to enhance the concrete or mortar application. According to the authors’ knowledge, there is no technical process, where shear thickening can be used beneficially. Still, it has to be considered for processes where high shear rates are applied, such as pumping, where shear thickening effects can increase the energy demand and restrict the flow due to limited power of devices.

2 Rheological Properties

2.2.2.6

17

Parameters Affecting Rheology

A majority of rheological phenomena can be attributed to two major influences: the solid volume fraction ϕ and the maximum packing density of the particles ϕ max . These parameters can indirectly be affected by quite many influencing factors, such as the chemical composition of the particles, the temperature, the particle size distribution etc. The solid volume fraction is strongly related to the viscosity. Based on the Einstein equation for non-Brownian, non-colloidal and diluted suspensions of spheres (8) some researchers have developed a number of equations to predict the viscosity of more concentrated suspensions, the mostly applied of which is the Krieger-Dougherty Eq. (2.9) [19]. However, recently more complex equations have been developed (2.10) and applied [20–22]: η = η0 (1 + 2.5ϕ)

(2.8)

  −q η = η0 1 − ϕ ϕmax

(2.9)

     η = η0 f ϕ ϕdiv g(k), ϕ ϕdi v

(2.10)

where: η0 = fluid phase viscosity (in Pa s), ϕ = solid volume fraction (−), ϕ max = maximum solid volume fraction (−), ϕ div = solid volume fraction at which the yield stress diverges (−) k = number of particle contacts (−), q, f, g = functions. Basically, all of the above listed equations have a very narrow range of applicability regarding the maximum phase content (i.e., they are limited to very small phase contents) and thus must be handled with care when applying them to cementitious suspensions. For cement suspensions without superplasticizer Haist presented a model, which predicts the rheological properties of cement suspensions based on the chemical composition of the cement (reflecting the particle interaction behavior) and its granulometry (see Eq. 2.11; [23]). ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨



2  3158·0 τ0 = 391 · ex p −  · φ [Pa] C3 S φmax 

0.358  φ C3 S · φmax μ = 0.001 · ex p 0.373 · [Pa · s] 0 ⎪ ⎪ ⎪  ⎪

0.347  ⎪ φ ⎪ C3 S · φmax ⎪ ⎪ [Pa · s] ⎪ ⎩ η0 = 0.001 · ex p 1.153 · 0

(2.11)

where: τ 0 and μ designate the Bingham yield stress (in Pa) and plastic viscosity (in Pa s), η0 = viscosity for the paste for stresses τ < τ0 , thus considering the fact, that viscous (creep) flow occurs e.g., during sedimentation for stresses below the yield

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stress. ϕ and ϕ max designate the phase content and the maximum packing density of the particles, respectively. C3 S · ϕ · ρcem · cC3 S · O Blaine is a measure for the surface fraction of the cement phase C3 S and can be calculated based on the phase content ϕ, the cement density ρ cem (in g/cm3 , the C3 S mass content cC3 S in the cement determined using Rietveld refinement and OBlaine the Blaine fineness (in cm3 /g). Γ 0 = 1 cm−1 . As can be seen from Eq. 2.11, both the yield stress as well as the plastic viscosity increase exponentially with the ratio ϕ/ϕ max , i.e., the closer the particles get to each other, the more pronounced the effect on rheology. For pure Portland cement suspensions, this effect however depends on the surface fraction of the mineral phase C3 S on the cement particles surface. The dependency of the yield stress on volume fraction, maximum packing, particle sizes, interparticle distances and percolation threshold is described in [24]. This model defines a relationship between the variation of the yield stress and the particle diameter as inversely proportional. The scaling of the yield stress of cementitious materials by addition of noncolloidal particles in a colloidal yield stress fluid is determined by [25] and demonstrates approaches for a tool to predict the yielding behavior of concrete by the constituents. Fundamental theories and experimental verifications on colloidal and noncolloidal contribution to yield stress and thixotropy are given in [26] and [27]. Particle–particle interactions depend upon the forces that act between the particles. Due to differently charged surfaces of the cement particles, and hydrate phases formed as well as the high ion content in the pore solution, cement particles tend to agglomerate rapidly. The agglomerates have different morphologies and surfaces than the primary particles and water is immobilized, thus no longer contributing to dispersion. As results of agglomeration, typically the flow is less stable against segregation and the yield stress is higher. Yield stress can be effectively controlled by dispersing agents such as plasticizers and superplasticizers, that are adsorbed on the surfaces of clinker particles, fillers, and hydrates and minimize attractive forces between particles by steric repulsion and an electrostatic contribution. Since variations in mixture composition typically affect both solid volume fraction and particle interactions, changes in the mixture composition automatically cause changes in the rheology. Some relevant effects are provided by Wallevik and Wallevik [18] for the air pore content, the silica fume content, the water content, as well as the superplasticizer content (Fig. 2.7). However, in general it is complex to simplify the effects, since rheological effects are typically a combination of a variety of parameters that interact in parallel. The rheology depends on multiple effects, some of which are listed in Table 2.2. Concrete is a composition of multiple phases, that interact on multiple scales and that change their character over the course of time. Due to this complexity, the rheological response on a change in the system is difficult to predict. An example is given for SCC at varied temperatures by [28]. It was shown that a stable SCC can show rapid stiffening or segregation at increased temperatures. The reason for the stiffening can be found in the rapid morphology changes and increase of the specific surface area (SSA) of solids caused by the higher temperatures. However, due to the presence of

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19

Fig. 2.7 Effects of various mixture modifications on yield stress and plastic viscosity [18]. SF = silica fume, SP = superplasticizer

superplasticizer, the accelerated hydration process also creates more surfaces for the superplasticizer to be adsorbed, causing higher efficiency of the superplasticizers, thus causing segregation. In addition, the solubility of the set retarder modifications changes with temperature. Which of the two effects dominates depends among other effects upon the cement chemistry and the charge density of the superplasticizer molecule and the dosage of superplasticizer. Particularly the presence of significant amounts of superplasticizers reduces the predictability dramatically, since particle effects are overlapped with superplasticizer adsorption effects, which in return affect the cement hydration process. This is illustrated in Fig. 2.8 for normal concrete and SCC (which typically contains high amounts of superplasticizers). All effects on flowability induced by accelerating or retarding hydration effects occur in SCC in the same way as in normal concrete. However, only for SCC they overlap by effects induced by high dosage of superplasticizers. The way how superplasticizers affect flowable systems depends a lot on the SP dosage and the adsorption efficiency of superplasticizers.

Rheology influencing factor

< 1000 nm

Time and temperature Particle morphology

Water-powder ratio

Surface chemistry and charges

Ionic strength and content

Formation of hydrates

Interaction of different polymers

Adsorption of polymers

Solid volume fraction

Particle-solution interface –

Solution and colloid

Observation scale < 4–5 mm

< 100 μm

Air pore content and distribution

Binder to aggregate ratio

Particle shape and surface properties

Particle size distribution

Mortar system

Binder system

Table 2.2 Rheological challenges for different concrete manufacturing technologies [29]

< 8–32 mm

Concrete system

20 W. Schmidt and J. Link

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21

Fig. 2.8 Effects of various mixture modifications on yield stress and plastic viscosity [30]

2.2.3 Flow Phenomena 2.2.3.1

Static Segregation

Static segregation is an effect that can be mainly ascribed to the static yield stress. For lower static yield stresses, the static segregation increases, and phase separation occurs (Fig. 2.9). In the past, it was often believed that segregation stability can be achieved by high viscosity. However, since the viscosity mainly affects the segregation velocity, segregation of the coarse aggregates can only be efficiently avoided, if the resistance against start of flow by static yield stress is appropriate. An accelerated hydration also counteracts static segregation. If the hydration is retarded, e.g., by high amounts of SP, segregation can still occur, if the static yield stress is not sufficiently high.

2.2.3.2

Dynamic Segregation

Dynamic segregation is mainly attributed to the viscosity of the flowable concrete. When the viscosity is too low, coarse aggregates and paste separate, and the paste continues to flow, while aggregates are exposed to a downward orientated flow pattern. Dynamic segregation can be effectively avoided by highly viscous pastes. This, however, does not automatically come along with a high stability against static segregation.

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Fig. 2.9 Effect of yield stress on surface properties and segregation resistance at rest. Reduced yield stress causes larger segregation processes of aggregates, resulting in sinking aggregates

2.2.3.3

Blocking

Blocking of aggregates is typically an effect of viscosity which is not high enough to provide a stable transport of the coarse components, or of the amount of aggregates in the concrete which can be too high for a continuous transport. Once aggregates are blocked at obstacles, e.g., reinforcement bars or a funnel, the aggregates can no longer be transported forward. The effect is typically escalating since blocked aggregates create more blocking effects.

2.2.3.4

Flow Distance/Final Shape

Yield stress is the threshold stress above which flow is initiated or below which the material behaves rather like a solid (see Sect. 2.1.3). Yield stress is a controlling parameter for the initiation and ending of flow processes, and thus it is also linked to the final shape of flowable concrete (Fig. 2.10). Therefore, the slump flow test is an easy method to obtain qualitative information about the yield stress of a concrete. Increasing diameters correlate with reduced yield stresses. The test is relatively independent of the viscosity of the tested concrete. Roussel et al. developed an equation that allows the transformation of the slump

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23

Fig. 2.10 Effect of yield stress on the final flow shape in a flow box with reinforcement obstacles

flow values into fundamental units [31]. The yield stress τ 0 can be calculated from the slump flow according to: τ0 =

225ρgV 2 128π 2 R 5

(2.12)

where: ρ = fresh concrete density (in kg/m3 ), g = gravitational acceleration (in m/ s2 ), V = cone volume (in m3 ) and R = slump flow radius (in m). This approach, however, is only valid as long as the yield stress is very low as in most flowable concrete types, e.g., SCC. For the more complex intermediate regime between slump and slump flow a more complex equation can be found [32]. Alternatively, based on considerations about the shape at rest after flow of a fixed volume, Roussel and co-workers also developed a method to determine the yield stress of flowable concrete [33, 34] based on the shape factors of the concrete at rest. The relation between yield stress τ 0 and the flow length L is defined according to the equation:

l0 ρ · g · l0 l0 · h 0 + · ln τ0 = 2·L 2 l0 + 2h 0

(2.13)

where: l 0 = box width (in m), h0 = height of the concrete at the beginning of the box (in m), L is the flow length at concrete stoppage (in m). Other relationships between slump, slump flow and yield stress are discussed in Chap. 6.

2.2.3.5

Flow Speed

The flow speed can be effectively controlled by the concrete viscosity. With increasing viscosity, the flow speed decreases since the internal friction between solid particles increases. In order to control the flow speed, concrete viscosity can be optimized by usage of viscosity modifying agents. The viscosity of concretes can be tested

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by determination of the flow speed with funnel tests on sites. However, this test is only valid for flowable concretes as SCC. Leemann & Winnefeld [35] quantified the flow speed by usage of a V-Funnel and showed a correlation between flow speed and plastic viscosities.

2.2.3.6

Surface Smoothness

The surface smoothness is largely affected by the dynamic yield stress and the viscosity. The yield stress controls the abilities of maintaining viscous properties until the formwork is filled. Thus, enough fine suspended particles reach the surface and ensure a smooth and homogeneous surface. For concretes with high yield stresses the surface can exhibit air voids due to improper deairing processes, whereas concretes with low yield stresses tend to segregate and develop heterogenous surface properties with bleeding processes on top [36]. The combination of yield stress and viscosity has to be adjusted to the filling process to ensure a homogenous composition after placement resulting in proper surface smoothness.

2.2.4 Practical Test Methods and Their Dependency on Rheological Parameters Rheometers can effectively determine a variety of rheological parameters and visualize non-linear flow behavior. However, also the established more applied test methods provide information on yield stress and plastic viscosity. The methods and the information that can be derived from the measurements are listed in Table 2.3. Distinct test methods clearly provide information on one rheological parameter, as flow distance measurement quantifies effects of yield stress, or the measurement of a flow time or efflux time clearly provides information about the viscosity. However, many test methods show certain flow specifications, that can be valuable for the casting process in question of quality control and boundary conditions, but these tests are affected by combined effects of both yield stress and viscosity. More information on the relationship between empirical test methods and rheological properties can be found in Chap. 6.

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Table 2.3 Different fresh SCC test methods based on [34, 37–43] Method

Measured value

Rheological property

Slump flow

Spread diameter

Yield stress

t500

Flow time for diameter of 500 mm Viscosity

V-funnel

Efflux time

Viscosity

Efflux cone

Efflux time and flow diameter

Viscosity/yield stress

Marsh cone

Efflux time

Viscosity/Mixed information

LCPC box

Flow distance

Yield stress

Orimet

Efflux time

Viscosity

L-Box

Passing ratio

Mixed information

U-Box

Height difference

Mixed information

J-Ring

Step height, spread diameter

Mixed information

Kajima Box

Visual passing ability

Mixed information

Penetration

Penetration depth

Mixed information

Sieve segregation

Percentage of passing laitance

Mixed information

Settlement column Segregation ratio

Mixed information

Rheometer

Yield stress, viscosity, and non-linear flow behavior

Shear stress and shear rate

2.3 Time-Dependent Properties 2.3.1 Reversible Properties 2.3.1.1

Thixotropy

In accordance with [44], thixotropy is defined as “a decrease of the apparent viscosity under constant shear stress or shear rate, followed by a gradual recovery when the stress or shear rate is removed. The effect is time-dependent.” It is often more convenient to work with registered shear stress τ = η γ˙ as a function of time, rather than measured viscosity η. If the shear rate γ˙ is constant, the above definition can immediately be transformed into the following formulation: a decrease in shear stress under constant shear rate with time, followed by a gradual recovery in shear stress when the shear rate is removed. The effect is time dependent. A principle sketch of the thixotropic behavior is shown in Fig. 2.11a. Depending upon whether the shear rate increases or decreases, there is a breakdown part and a rebuild part, respectively, both aiming towards two different equilibrium shear stress values, depending on the value of shear rate. Shear stress τ and shear rate γ˙ cannot be directly measured in a rheometer. The actual measured values are the torque T and the angular velocity ω (of the rheometer’s rotating part). There is usually a one-to-one relationship between the shear stress and the torque, but the relationship between the shear rate and the angular velocity is

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Fig. 2.11 Principle sketch of the thixotropic behavior a and an actual measurement of such of a cement-based material b [18]

generally more complicated. This depends on the type of rheometer. For example, in [18] the relationship between γ˙ and ω were calculated for two types of rheometers, namely the wide gap coaxial cylinders type (i.e., concentric cylinders) and the parallel plates type, both of which show complex shear rate profiles. A further transformation from torque and angular velocity to shear stress and shear rate for arbitrary measurement geometries that are often used for cementitious suspensions with high solid phase contents, show good correlations to wide gap coaxial cylinders and parallel plate types [45]. Thixotropic measurements are conducted by looking at the torque T as a function of different angular velocity conditions ω. An example of this is shown in Fig. 2.11b, in which the rheometer is a coaxial cylinders type [46]. There, a clear breakdown ehaviour is observed for the stepwise increase in angular velocity, while a clear rebuild during the stepwise decrease in angular velocity [46]. Explanations of other tests methods on thixotropy, where torque T and angular velocity ω are used, are available in literature [6, 9, 47–49]. For example, one approach mentioned is by measuring the torque T under a linear increase and then decrease in angular velocity ω (of the rotating part of the rheometer). If the test sample is thixotropic, the two torque curves produced do not coincide, causing rather a hysteresis loop. While hysteresis loops are useful as a preliminary indicator of ehaviour, they do not provide a good basis for quantitative treatments [6, 50]. However, the attempt can be made to quantify thixotropic ehaviour with such torque curves by its integration [6, 50, 51]. Another approach possible in studying the thixotropic ehaviour is by monitoring the decay of the measured torque from an initial value T 0 to an equilibrium value T e with time t, at a constant angular velocity ω [50]. In some cases, simple exponential relationships can be found, but other can be more complicated. For example, Lapasin et al. [52] make use of the aforementioned approach on cement pastes, using three different types of functions, which pointed out to be more complicated than the

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Fig. 2.12 Principle sketch of the anti-thixotropic behavior

simple exponential form. More exact but also more complicated thixotropic material models for cement-based materials can be found in [46, 53, 54].

2.3.1.2

Rheopexy

Rheopexy is also known as anti-thixotropy and as negative thixotropy. In accordance with Barnes et al. [44], rheopexy is defined as “An increase of the apparent viscosity under constant shear stress/rate followed by a gradual recovery when the stress or shear rate is removed. The effect is time-dependent.” Figure 2.12 shows the principle sketch of the anti-thixotropic (i.e., rheopexy) behavior. In general, rheopexy does not apply for cement-based material and thus should not be considered. The term “build-down” in Fig. 2.12 is just used here for explanation. Rheopexy is sometimes confused with shear-thickening behavior. The former is associated with changes in rheological properties with time, even when the applied shear rate is kept constant. In that sense, it is quite different from shear-thickening behavior, which is strictly only shear rate dependent. The same consideration applies for thixotropy and shear-thinning behavior [49]. That is, the former is a time dependent phenomenon, while the shear-thinning is not and thus generating flow curve which is independent of the time of shearing [55, 56]. This distinction has caused some confusion among technologists [55].

2.3.1.3

Non-Reversible Properties

Concrete changes its properties from a visco-elastic fluid after mixing to a solid state after hardening occurs. This process is caused by the reactivity of the cement particles that are exposed to hydration processes after contact with water. The cement

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particles start to dissolve partially in a solution and the ion content increases until supersaturation states are reached, and precipitation of hydration products starts [57]. During hydration calcium silicate and calcium aluminate phases reaction takes place, whereas the silicate reaction causes the mechanical strength with its hydration products Calcium-Silicate-hydrates (CSH) and Portlandite (Ca(OH)2 ). The calcium aluminate reaction is controlled by the addition of sulphate carrier to force the precipitation of AFm during early hydration [57]. Besides time the hydration process is also affected by temperature influencing the kinetic reaction rate. The precipitation of hydration products results in changes of surface properties as well as particle sizes. The ongoing precipitation increases the solid phase content and reduces the liquid phase. The formation of new solid phases can also link single particles by bridging [58]. These processes can cause reversible and irreversible changes to the rheological parameters. Usually, with ongoing hydration processes the stiffness increases resulting in increasing rheological properties e.g., yield stress and viscosity. During later hydration, the influence of non-reversible changes is dominant [59], whereas the gain in stiffness by early hydration products can also be partly reversible since the developed weak structure can be broken by high shear stresses [60]. For rheological measurements within short time periods, the influence of hydration is too small to be detected and can be neglected. For special materials, as 3-D printing materials or geopolymers with short setting time, the influence of hydration processes cannot be disregarded. However, measurements over larger time periods are dominated by hydration processes mostly causing non-reversible changes which control the rheological parameters.

References 1. Schmidt W, Sonebi M, Brouwers HJH, Kühne H-C, Meng B (2013) Rheology modifying admixtures: The key to innovation in concrete technology—a general overview and implications for Africa. Chem Mater Res 5:115–120 2. De Schutter G, Lesage K (2018) Active control of properties of concrete: a (p)review. Mater Struct 51:123 3. Wallevik OH (1990) The rheology of fresh concrete and its application on concrete with and without silica fume. Ph.D. dissertation, The Norwegian university of science and technology (Previously: The Norwegian Institute of Technology), Norway 4. Hakansson U (1993) Rheology of fresh Cement-Based Grouts. Ph.D. Dissertation, R Inst Technol, Sweden 5. Wallevik JE (2003) Rheology of particle suspensions—fresh concrete, mortar and cement paste with various types of lignosulfonates. Ph.D. Dissertation, Nor Univ Sci Technol, Norway. 6. Barnes HA (1997) Thixotropy - a review. J. Non-Newtonian Fluid Mechanics 70:1–33 7. Billberg P (2005) Development of SCC static yield stress at rest and its effect on the lateral form pressure, In: Second North American Conference on the Design and Use of Self-Consolidating Concrete and the Fourth International RILEM Symposium on Self-Compacting Concrete, Chicago, USA, pp 583–589 8. Billberg P (2006) Form pressure generated by Self-Compacting Concrete—Influence of Thixotropy and Structural Behaviour at Rest. Ph.D. Dissertation, R Inst Technol, Sweden.

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9. Barnes HA (1999) The yield stress—a review or ‘παντα ρει’- everything flows? J Nonnewton Fluid Mech 81:133–178 10. Bingham EC (1922) Fluidity and Plasticity. Mcgraw-Hill Book Company Inc., New York 11. Bingham EC (1924) Discussion on plasticity. J Am Ceram Soc 7:375–379 12. Bingham E, Robertson J (1929) Eine methode zur gleichzeitigen messung von plastizität und elastizität. Colloid Polym Sci 47:1–5 13. Ostwald W (1925) Ueber die geschwindigkeitsfunktion der viskosität disperser systeme. I. Colloid & Polymer Science 36:99–117 14. Ostwald W (1925) Ueber die geschwindigkeitsfunktion der viskosität disperser systeme. II. Colloid & Polymer Science 36:157–167 15. Herschel WH, Bulkley W (1926) Konsistenzmessungen von Gummi-Benzollösungen. Kolloid Z 39:291–300 16. Schmidt W (2014) Design concepts for the robustness improvement of Self-Compacting Concrete—Effects of admixtures and mixture components on the rheology and early hydration at varying temperatures. Ph.D. Dissertation, Eindh Univ Technol, The Netherlands 17. Hot J, Roussel (2013) How adsorbing polymers decrease the macroscopic viscosity of concentrated cement pastes? In: Fifth North American Conference on the Design and Use of Self-Consolidating Concrete, Chicago, USA 18. Wallevik OH, Wallevik JE (2011) Rheology as a tool in concrete science: The use of rheographs and workability boxes. Cem Concr Res 41:1279–1288 19. Krieger IM, Dougherty TJ (1959) A mechanism for Non-Newtonian flow in suspensions of rigid spheres. Trans Soc Rheol 34:137–152 20. Mansoutre S, Colombet P, Van Damme H (1999) Water retention and granular rheological behavior of fresh C3S paste as a function of concentration1. Cem Concr Res 29:1441–1453 21. Roussel N, Lemaître A, Flatt RJ, Coussot P (2009) Steady state flow of cement suspensions: A micromechanical state of the art. Cem Concr Res 40:77–84 22. Lemaître A, Roux J-N, Chevoir F (2009) What do dry granular flows tell us about dense non-Brownian suspension rheology? Rheol Acta 48:925–942 23. Haist M (2009) Zur Rheologie und den physikalischen Wechselwirkungen bei Zementsuspensionen (2009 and 2012). Published in: Deutscher Ausschuss für Stahlbeton 605 (2012) 24. Flatt R, Bowen P (2006) Yodel: A yield stress model for suspensions. J Am Ceram Soc 89:1244– 1256 25. Mahaut F, Mokéddem S, Chateau X, Roussel N, Ovarlez G (2008) Effect of coarse particle volume fraction on the yield stress and thixotropy of cementitious materials. Cem Concr Res 38:1276–1285 26. Chateau X, Ovarlez G, Trung KL (2008) Homogenization approach to the behavior of suspensions of noncolloidal particles in yield stress fluids. J Rheol 52:287–313 27. Mahaut F, Chateau X, Coussot P, Ovarlez G (2008) Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids. J Rheol 52:287–313 28. Schmidt W, Brouwers HJH, Kühne H-C, Meng B (2014) Influences of superplasticizer modification and mixture composition on the performance of self-compacting concrete at varied ambient temperatures. Cement Concr Compos 49:111–126 29. Schmidt W, Weimann C, Chabes Weba L (2016) Influences of of hydration effects on the flow phenomena of concrete with admixtures. In: Schmidt W, Msinjili NS, eds Adv Cem Concr Technol Afr, Dar es Salaam, Tanzania. BAM, pp.79–88 30. Schmidt W, Weba L, Silbernagl D, Mota B, Höhne P, Sturm H, Pauli J, Resch-Genger U, Steinborn G, (2016) Influences of nano effects on the flow phenomena of Self-Compacting concrete. In: Khayat K, ed In: SCC 2016 - 8th International RILEM Symposium on SelfCompacting Concrete, Washington DC, USA, pp 245–254 31. Roussel N, Stefani C, Leroy R (2005) From mini-cone test to Abrams cone test: measurement of cement-based materials yield stress using slump tests. Cem Concr Res 35:817–822 32. Pierre A, Lanos C, Estelle P (2013) Extension of Spread-Slump formulae for yield stress evaluation. Appl Rheol, 23

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33. Nguyen TLH, Roussel N, Coussot P (2006) Correlation between L-box test and rheological parameters of a homogeneous yield stress fluid. Cem Concr Res 36:1789–1796 34. Roussel N (2007) The LCPC BOX: a cheap and simple technique for yield stress measurements of SCC. Mater Struct 40:889–896 35. Leemann A, Winnefeld F (2007) The effect of viscosity modifying agents on mortar and concrete. Cement Concr Compos 29(5):341–349 36. Megid W, Khayat KH (2018) Effect of concrete rheological properties on quality of formed surfaces cast with self-consolidating concrete and superworkable concrete. Cement Concr Compos 93:75–84 37. BIBM, CEMBUREAU, EFCA, EFNARC and ERMCO, The european guidelines for SelfCompacting Concrete—Specification, production and Use. http://www.efnarc.org 38. Dafstb-Richtlinie (2003) Selbstverdichtender beton (SVB-Richtlinie). In: Stahlneton, D.A.F. (ed) 39. Dafstb-Richtlinie, 2012. Selbstverdichtender Beton (SVB-Richtlinie)—Schlussentwurf. In: Stahlbeton, D.A.F. (ed) 40. Cussigh F, Sonebi M, De Schutter G (2003) Project testing SCC-segregation test methods. In: 3rd International Symposium on Self-Compacting Concrete, Reykjavik, Iceland. RILEM Publications SARL, pp 311–322 41. Le Roy R, Roussel N (2005) The marsh cone as a viscometer: Theoretical analysis and practical limits. Mater Struct 38:25–30 42. Nguyen VH, Rémond S, Gallias JL, Bigas JP, Muller P (2006) Flow of Herschel-Bulkley fluids through the Marsh cone. J Nonnewton Fluid Mech 139:128–134 43. Roussel N, Le Roy R (2005) The Marsh cone: a test or a rheological apparatus? Cem Concr Res 35:823–830 44. Barnes HA, Hutton JF, Walters K (1989) An introduction to rheology. Elsevier Science B. V, Netherlands 45. Haist M, Link J, Nicia D, Leinitz S, Baumert C, von Bronk T, Cotardo D, Eslami Pirharati M, Fataei S, Garrecht H, Gehlen C (2020) Interlaboratory study on rheological properties of cement pastes and reference substances: comparability of measurements performed with different rheometers and measurement geometries. Mater Struct 53:92 46. Wallevik JE (2009) Rheological properties of cement paste: thixotropic behavior and structural breakdown. Cem Concr Res 39:14–29 47. Mewis J (1979) Thixotropy—a general review. J. Non-Newtonian Fluid Mechanics 6:1–20 48. Mujumdar A, Beris AN, Metzner AB (2002) Transient phenomena in thixotropic systems. J. Non-Newtonian Fluid Mechanics 102:157–178 49. Tanner RI, Walters K (1998) Rheology: an historical perspective. Elsevier Science, Amsterdam 50. Tattersall GH, Banfill PFG (1983) The rheology of fresh concrete. Pitman Books Limited, Great Britain 51. Banfill PFG (1991) The rheology of fresh mortar. Mag Concr Res 43:13–21 52. Lapasin R, Papo A, Rajgelj S (1983) The phenomenological description of the thixotropic behavior of fresh cement pastes. Rheol Acta 22:410–416 53. Roussel N (2006) A thixotropy model for fresh fluid concretes: Theory, validation and applications. Cem Concr Res 36:1797–1806 54. Wallevik JE (2005) Thixotropic investigation on cement paste: experimental and numerical approach. J Nonnewton Fluid Mech 132:86–99 55. Banfill PFG (2006) Rheology of fresh cement and concrete. Br Soc Rheol, Rheology Reviews, p 61 56. British Standards Institution (1975) British Standard BS 5168:1975, Glossary of rheological terms. Br Stand Inst, London 57. Taylor HFW (1997) Cement chemistry, 2nd edn. Thomas Telford Publ, London, p 361

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58. Roussel N, Ovarlez G, Garrault G, Brumaud C (2012) The origins of thixotropy of fresh cement pastes. Cem Concr Res 42:148–157 59. Zhang K, Mezhov A, Schmidt W (2022) Chemical and thixotropic contribution to the structural build-up of cementitious materials. Constr Build Mater 345:128307 60. Link J, Sowoidnich T, Pfitzner C, Gil-Dias T, Heberling F, Lützenkirchen J, Schäfer T, Ludwig H-M, Haist M (2020) The Influences of Cement Hydration and Temperature on the Thixotropy of Cement Paste. Materials 13(8):1853

Chapter 3

Concrete Rheometers Arnaud Perrot and Sofiane Amziane

Abstract The present chapter aims to make an exhaustive presentation of concrete rheometers. After a definition of what can be called a rheometer based on a consensus among the technical committee members, concrete rheometers are presented following a classification that relies on the origin of the solicitation acting on the material and initiating the material flow. Four types of rheometers are listed: the free flow rheometers for which the flow is induced by gravity (i.e. monitored slump or spread flow), the rotational rheometers which are the most used ones and directly refers to conventional rheometry (i.e. concentric cylinders and plate-plate rheometers), the confined flow rheometers that can be useful for zero slump concretes (i.e. capillary extrusion and squeeze flow) and the static rheometers where shear is induced by the concrete’s own settlement and deformation (i.e. the plate test geometry). For each type of rheometer type, the physical principles are presented shortly referring to literature and Chap. 2 of the present book. Then, the different possible existing configurations are presented as well as available technical solutions. This rheometers review shows that there is a large range of devices able to capture and describe part or the entire rheological behavior of concrete mixes. However, each With contributions from: Dimitri Feys, Jon Wallevik, Lars Thrane, Markus Greim, Dirk Lowke and Clarissa Ferraris. Dimitri Feys—Missouri University of Science and Technology, United States. Jon Wallevik—Icelandic Meteorological Office, Iceland. Lars Thrane—Danish Technological Institute, Denmark. Markus Greim—Schleibinger Geräte, Germany. Dirk Lowke—Technical University Braunschweig, Germany. Chiara “Clarissa” Ferraris—Retired, formerly NIST, United States. A. Perrot (B) University Bretagne Sud, UMR CNRS 6027, IRDL, F-56100 Lorient, France e-mail: [email protected] S. Amziane Institut Pascal, UMR 6602, Clermont University, Clermont Ferrand, France e-mail: [email protected]

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Sonebi and D. Feys (eds.), Measuring Rheological Properties of Cement-based Materials, RILEM State-of-the-Art Reports 39, https://doi.org/10.1007/978-3-031-36743-4_3

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rheometer is dedicated to the measurement of specific parameters, is suitable for a range of concrete consistency, and has to be chosen in relation with the targeted parameters and measured concrete type.

3.1 Introduction The definition on what constitute a concrete rheometer is not easy to develop and the boundary of the “rheometers” area is not so clear because lot of devices and tests are used to describe the workability of all kinds of concrete (from self-consolidating to zero-slump). Nevertheless, in the frame of this chapter, to separate rheometers from other semi-empiric field-oriented tests such as slump flow or funnel tests (Orimet, V-funnel, O-Funnel) the following philosophy and definition is adopted: Rheology is the study between stress and strain (or strain rate). Such relationship is characterized with a rheometer and is based on the exploitation of experimental results of complex tests. The sample is loaded by a mastered solicitation (effort or displacement) which induces a recordable answer (displacement or effort). If stress and strain (or strain rate) can be easily calculated from the solicitation and the answer, then fundamental rheology and rheometry is understood. Therefore, this chapter is dedicated to devices designed to estimate the values of parameters of the rheological behavior of mortars and concrete such as viscosity or yield stress by using several models such as Bingham model, Herschel-Bulkley, etc. The first concrete rheometer has been developed by the pioneering work of Tattersall [1] and devices were improved ever since in terms of sensor sensitivity, portability, shearing probes, wall interface (slipping layer) and shape of impellers/Vanes in order to reduce of errors due to shearing segregation, and slippage. The rheometers were classified in different families depending on the flow generated during the measurement. The first family is the free-flow rheometers which are based on the principle of camera recorded spread flow. Using an inverse data analysis, the rheological behavior of a concrete can be described. It can be noted that such family of rheometer is well designed for self- compacting mortars and concretes. The second family is the most conventional one and consists of the rotational rheometers. Such rheometers are well-suited to study a wide range of concrete from conventional to self-compacting but are limited in the study of zero-slump concrete [2, 3]. To study the rheology of such firm concrete, the last family of rheometers, the “confined flow” rheometers are finally presented.

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3.2 Free Flow Rheometers 3.2.1 Introduction Slump flow and t 500 are among the most widely used empirical methods to classify workability of self-compacting concrete and mortar (EN 12,350-8, ASTM C1611) [4, 5]. The slump can be used to estimate the corresponding yield stress of concrete according to Roussel and Coussot [6]. There is, conversely, no trivial way to compute concrete’s plastic viscosity based on t 500 measurements as it depends on the lifting speed of the cone, the yield stress of the material, and the base plate conditions, making plastic viscosity estimations difficult. Many studies deal with the modelling of the slump flow of viscoplastic material such as self-compacting concrete and provide the required theoretical background to transform the slump kinetic (t 500 ) and value into rheological parameters [6–8]. Other geometries such as inclined plate or L-box are also good candidates for the development of free flows into rheometers that are able to provide an accurate estimation of rheological parameters [9, 10].

3.2.2 4C Rheometer The 4C-Rheometer was developed with the goal of determining the plastic viscosity of fluid concretes and mortars based on an automatic and controlled execution of the slump flow test by combining the spread curve information with a database of results obtained from numerical simulations of the slump flow test [11–13]. The reason for choosing the slump flow test was to have an easy-to-use instrument that was easily applied in the lab and the field. Furthermore, the intention was to provide the practitioner with a link between the qualitative behavior observed during testing and the rheological output of the instrument. Figure 3.1 shows the 4C-Rheometer which consists of a dry sand blasted hardened glass base plate, which is levelled to a horizontal position. The Abram’s cone is automatically lifted at a constant speed of 70 mm/s. An industrial grade camera, placed above the glass plate, records the concrete or mortar spread over time. The recorded video is converted into spread as a function of time as depicted in Fig. 3.2. Estimation of the plastic viscosity requires an accurate and detailed information of the flow curve. Using inverse analysis, the experimental flow curve is compared to flow curves based on numerical simulations applying the same conditions as in the experimental test. The simulations assume no-slip conditions in the cone and on the base plate, which is the reason for applying a dry cone and dry sand blasted base plate during the test. The yield stress is computed from the slump flow and the density of the tested material. The execution of a 4C-rheometer test takes approximately two minutes including video acquisition and data analysis. For further reading, including examples of its use, can be found in [6–8].

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Fig. 3.1 4C-rheometer: a base glass plate; b Industrial camera; c Automatic cone lifting system, and d computer

Fig. 3.2 4C-rheometer software interface. Left: recorded and analyzed video. Right: spread as a function of time chart and the resulting yield stress and plastic viscosity

3.2.3 4C-Mini-Rheometer The 4C-mini-rheometer is a scaled-down version of the 4C-rheometer that is tailor made to determine the plastic viscosity and yield stress of various types of cement pastes and mortars by performing an automatic and controlled mini-slump flow test. The setup and execution of the test is shown in Fig. 3.3. It consists of a dry sand blasted

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Fig. 3.3 Testing of a mortar sample with the 4C-mini-rheometer equipment

hardened glass base plate, which is levelled to a horizontal position. The scaled down version of the Abram’s cone is lifted automatically at a constant speed of 38 mm/s. A camera, placed below the glass plate, records the spread of the material over time. The recorded video is converted into spread as a function of time. The execution of a 4C-mini-rheometer test takes up to two minutes including video acquisition and data analysis. The principles of calculating the plastic viscosity and yield stress are the same as applied to the 4C-Rheometer. However, for plastic viscosity new simulations were carried out to establish a new database of results for the inverse analysis applying the same setup as in 4C-mini-Rheometer test.

3.3 Rotational Rheometers 3.3.1 Introduction Rotational rheometers are the most current rheometers used to study concrete rheology. In principle, they all are composed of a container where the concrete is placed, and a spindle immerse in the concrete. Either the spindle or the container rotates at a controlled speed and the resulting torque is measured [14–18]. Rotational rheometers are used to determine the rheological properties of different materials. Often, one is satisfied with values that are only specific to the device in question. Although, such cases do not produced values in fundamental physical quantities (e.g., yield stress and plastic viscosity, for Bingham fluid), such devices can give values that can be compared between different mixes (e.g., like what is done with the slump value). In the case when it is required to obtain rheological values in terms of fundamental physical quantities, one has to identify the relationship between shear stress and shear rate. However, none of the rotational rheometers measure directly shear stress τ or shear rate γ˙ . Instead, torque T, and angular velocity ω measurements are registered and transformed into shear stress τ and shear rate γ˙ values using different theoretical approaches that are described in Chap. 4.

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Many commercial solutions are available ad are listed in this section. It is also important to note there are many labs which have developed their own solutions and devices to measure the rheological behavior of mortars or concrete [8–12]. Some of those devices present interesting or original properties such as pore pressure measurements during shearing [17], high torque capacity [16], etc. In this section, we first present the different families of rotational rheometers and in a second part we present the different existing rotational rheometers dedicated to fresh concrete testing.

3.3.2 Classes of Rotational Rheometers 3.3.2.1

Concentric Cylinder

In this type of rotational rheometer, the spindle is a cylinder whose surface could be smooth or serrated (Fig. 3.4). Analytical solution to convert the rotational speed and torque into fundamental units exist if the ratio between the diameters (container and spindle) are about 1.1. In the case of concrete this is not possible due to the large size of the aggregates, or the diameters will become impractical. Note that one attempt to build such rheometer was done by LCPC in the Cemagref [19]. A three-dimensional and a top view of the coaxial cylinder rheometer is shown in Fig. 3.4. In this case, the outer cylinder (with radius Ro ) rotates at angular velocity ω = ωo [rad/s], while the inner cylinder (with radius Ri ) is stationary and registers the applied torque T [Nm] from the material tested. The term h is the height of the inner cylinder. For a Bingham fluid, the theory behind the coaxial cylinders rheometer, is the socalled Reiner-Riwlin equation given by Eq. (3.1) [13–15, 20]. This equation makes

Fig. 3.4 A three-dimensional- and a top view of a coaxial cylinder (also, concentric cylinders) type rheometer, in which the outer cylinder rotates

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no constraints on the gap size between the two cylinders and thus applies both for the narrow gap- and for the wide gap cylinder system (note that a simpler theoretical setup for the coaxial cylinders system will assume a narrow gap system). In both cases it is assumed that all the material in the gap is sheared. 4π μh

4π τ0 h

(

Rs T = −2 ω + −2 ln −2 −2 Ri Ri − R s Ri − R s

) = Hω + G

(3.1)

The term Rs is the plug radius [21], which is often for simplicity just put equal to the radius of the outer cylinder Rs ≈ Ro . This assumption is usually acceptable for moderate values of τ 0 /μ, where the material over the entire gap is more or less sheared [21, 22] (for a given τ 0 and μ, the plug radius Rs can also be calculated as explained in [22]). Note that Eq. (3.1) is dependent on that the angular velocity ω is in terms of [rad/s] and not in terms of N [rps] (the relationship is simply ω = 2 π N in which N is in terms of [rps]). The Reiner-Riwlin equation Eq. (3.1) applies also for the rotating inner cylinder. In that case, one uses the angular velocity of the inner cylinder ω = ωi . For the case of rotating outer cylinder, a detailed derivation of Eq. (3.1) is available in [21, 22], in which the steps can be repeated for the case of rotating inner cylinder. In either case of rotating inner- or outer cylinder, usually the inner cylinder registers the torque T. For a Bingham fluid, the relationship between measured torque T on the inner cylinder at the different applied angular velocities ω is linear. The slope, H, and the intercept, G, the plastic viscosity μ and the yield stress τ 0 of the tested cementitious material are calculated through Eq. (3.1). Thus, using Reiner-Riwlin equation Eq. (3.1) the raw data, namely the torque T and the angular velocity ω, are directly used to obtain the yield stress τ 0 and plastic viscosity μ. There is no need to convert the raw data into shear rate, γ˙ , and shear stress, τ, in order to obtain the rheological parameters. To avoid slippage between the test material and the cylinders, the surface should be serrated surfaces. The degree of roughness of the serrated surface should be large designed to allow for suspended particles (e.g., coarse aggregates, sand particles or cement particles) to be part of the internal boundary. Including “serrated surfaces”, the designation “protruding vanes”, “ribs”, “protruding ribs” or “roughened surfaces” are also used for such type of boundary settings. As the cementitious materials is viscoplastic (i.e., a yield stress fluid) and bearing in mind that the largest suspended particles will be present in the space between the above-mentioned protruding ribs, the test material and these ribs together behave like a rigid solid. That is, no fluid flow is present inside the serrated surface system. Experimental observation supports this assumption, which is in accordance with the findings made in [23] (see also [24, 25]). The settings described here should not be confused with a four blades-vane rheometer, in which the large distance between the blades is sufficient to allow for a fluid flow to occurs between them, as shown in Fig. 3.5 [26]. In this case, the vanes

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Fig. 3.5 Streamlines inside a vane rheometer (relative to the rotating shaft)

(i.e., the impeller) rotates, while the outer cylinder geometry is stationary (see also the next Sect. 3.2.2). A well-known example of a coaxial cylinders type rheometer (with serrated surfaces), in which the outer cylinder rotates is the ConTec Viscometer (previously known as the BML). This particular device is well explained in [3, 27, 28], with simulation results available in [29]. An example of a rheometer that has a rotating inner cylinder, is the CEMAGREF-IMG rheometer [19].

3.3.2.2

Vane Geometry

A “vane rheometer” is a rotational rheometer with the spindle being a four (or six) blades vane. A spindle with eight or more blades is considered a ribbed cylinder (Sect. 3.2.1). It is assumed that with a large number of blades (eight or more), the material will bridge the vanes in such manner that a cylinder system starts to form. Vane rheometers are often used to obtain rheological flow parameters in the cement-based research and development branch of the concrete industry. As shown in Fig. 3.6, it consists of an impeller system (i.e., a shaft and four vane blades connected to it) rotating in a cylinder geometry (i.e., in a bucket container). This geometry is often selected in an attempt to reduce slippage that could be present when a cylinder is used (Sect. 3.2.1). However, due to the large distance between each blade, an established flow occurs between the blades (previously shown in Fig. 3.5). With this, the impeller’s vane blades will both push and drag the fluid, resulting in non-uniform hydrodynamic pressure exerted on the blades [26, 30]. Thus, in addition to the viscous shear stress, this

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Fig. 3.6 Various vane geometries

pressure will very much influence the measured torque registered by the rheometer (i.e., influence the shaft torque) [26]. Due to its popularity with concrete, there are several simulations of the flow using a vane with 4 or 6 blades. Figure 3.7 shows a simulation result of a large dimension vane rheometer, with the same simulation technique as reported in [30]. In this case, the radius of the impeller system (i.e., the shaft and the four vane blades connected to it) is Ri = 63.5 mm, while the radius of the bucket container is Ro = 143 mm. Height of vane blades is set as h = 127 mm. According to [31] these dimensions correspond to the ICAR rheometer. Here, the blade thickness is set to 5 mm and the clearing between the vanes and the bottom of the bucket is 130 mm. In this simulation, the plastic viscosity μ was set at 120 Pa s, while the yield stress τ 0 was set at 50 Pa (i.e., Bingham fluid). The angular velocity was set as 0.6 rps (i.e., ω = 3.78 rad/s).

Fig. 3.7 Simulation of flow for a 4 blades-vane rheometer (with 251,160 cells)

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Figure 3.7a shows iso-plots of the hydrodynamic pressure acting on the vane blades. The red surface represents 850 Pa gage pressure, while the blue surface represents –850 Pa gage. Both the blue and the red iso-surfaces are contributing to the overall torque, T p . In the horizontal plane of Fig. 3.7b, the color range is also from –850 Pa (blue) to +850 Pa (red). Figure 3.7c shows the velocity vectors, demonstrating the counterclockwise impeller rotation. The largest red arrow shows the maximum velocity vector with the magnitude of Ri ·ω = 0.24 m/s for this example. Simulation results show that the majority of the torque is originating from the hydrodynamic pressure (here, 77%) and not from the viscous torque. Thus, a fundamental difference between the concentric cylinders system (Sect. 3.2.1) and the vane system is evident. That is, the former is a viscous shear stress-based system [12–14], while the latter is mostly a hydrodynamic pressure-based system [26, 30]. However, it should be clear that this does not fail the vane system in any way. This is because there is a direct link between the hydrodynamic pressure and the apparent viscosity η [26]. Therefore, during a rheological test, there will be a direct relationship between the output of the vane rheometer and the apparent viscosity η, giving an accurate measurement [26]. Vane test carried out at a constant low rotational velocity is also very useful for the determination of the static yield stress of cement-based materials and its evolution with time at rest. For example, the portable vane shown in Fig. 3.8 can be used on site for that purpose [32, 33]. For the interested reader, the similarity between the vane and the coaxial cylinders system is also available in [34]. The vane spindles rheometers are very common on the market, for instance ICAR rheometer [35] or CAD rheometer for concrete. But the same geometry is widely used for grouts in any fluid rheometer.

Fig. 3.8 The portable vane test method: square bucket (left) and the vanes (right)

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3.3.2.3

43

Planetary Motion Spindles

Another method is to have a spindle that is rotating not only on its axis but also in a planetary motion. Moving any spindle inserted into a fluid generates a flow around this object. To determine the rheological properties of the fluid, the flow must mathematically be able to be described or the system needs to be calibrated using reference materials. Although there are solutions for several geometries in Newtonian fluids, the situation is much more complex in a yield stress fluid like concrete. 3.3.2.3.1 Ball Rheometer In this rheometer a sphere is moving at very low velocities in a yield stress fluid, the flow can be described based on a modified Stokes law, compare [36–39]. Per Stokes, the resistance F r of a creeping sphere of diameter d is proportional to the velocity vs and the dynamic viscosity η. Fr = 3π dμvs

(3.2)

Assuming the shear rate to γ˙ = vs /d [36, 40, 41] and describing the dynamic viscosity by means of yield stress and plastic viscosity η = τ0 /γ˙ + μ, the resistance can be written as Fr = 3π d 2 τ0 + 3π dμvs

(3.3)

For measurements at very low velocities, the second term can be neglected. Thus, the static yield stress of the fluid can be determined by τ0 =

Fr 3π d 2

(3.4)

A great advantage of this method procedure is that only a small volume amount of the sample around the sphere is sheared. Thus, consecutive measurements of static yield stress for the determination of thixotropy and structural build-up can be carried out on the same sample without significant changes in the microstructure of the suspension, compare [39, 42]. To determine flow curve at varying rotational speeds (e.g., shear rates) the situation becomes more complex. For this case, Schatzmann [43, 44] proposed a semi-empirical solution for suspensions with particles of a diameter up to 10 mm. 3.3.2.3.2 H-Shape Impeller It is important to note that H shape impeller can also be used as a planetary motion spindle just as in the IBB rheometer described in a next section.

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3.3.2.3.3 Other Spindle Geometries Besides spindle geometries like cylinders and vanes, alternate configurations such as spiral double or single, are becoming more popular to measure the rheological properties of particulate fluids with large aggregates. For measurements of concrete, care must be taken to reduce sedimentation, shear induced migration effects. In particular, measuring concrete having a significant fraction larger aggregates there may be a tendency for aggregates to move out radially from the blade and thus reducing the coupling of the blade with fluid making it less homogeneous and as a result the torque measured is reduced for a fixed angular velocity. This could lead to a lower estimate of the viscosity of the fluid. A spiral spindle rheometer has the disadvantage of producing more complex flows that do not readily lend themselves to analytic solutions and the advantage to better mixing of the materials making the fluid system more homogeneous and avoiding sedimentation. Figure 3.9 [45, 46] shows two examples of spirals that were used to develop standard reference materials at NIST. While most modelling of rheometers assume of a continuum fluid, perhaps with at Newtonian fluid matrix, the computational model developed at National Institute of Standards and Technology (NIST) [47, 48] allows for a detailed modelling of the flow of particles in a non-Newtonian fluid matrix. The inputs of the model are the rheological properties of the fluid matrix and the size distribution and shape of the particles. The rheological properties of the suspension can then be determined. Visualization of the flow in rheometer or other geometries can provide a better understanding of the movement of the particles in the fluid. This visualization can help understand some of the artefacts of the measurements and thus improve metrology (Fig. 3.10 for a spiral) Fig. 3.11 provides the comparison flow with a 6-blade vane.

Fig. 3.9 Spiral used for rheometer a for concrete [45], b for mortar [46]

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Fig. 3.10 Flow in a rheometer with spiral spindle. The particles are assigned a color based in their initial placement. a and b the particles are spherical. a Cut view of the spiral inside the mixture before shearing; b View of the particles from A sheared—the particles are clearly mixed and not just shifted; c Initial view of a system with crushed particles

Fig. 3.11 Flow of a mortar with spherical particles (used for the NIST standard reference material 2493 [49]) The particles are assigned a color based in their initial placement. a Initial state; b stage 1 rotation; c after further rotation

3.3.2.3.4 Parallel Plates The simplest geometry for rheological measurement would be two parallel plates, sliding over each other. The stress is the applied force divided by the contact area, while the shear rate corresponds to the velocity difference between the two plates divided by the separation distance of the plates (Fig. 3.12) [50].

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Fig. 3.12 The parallel sliding plates rheometer has simple transformation equations but is practically very difficult to use

Unfortunately, the parallel sliding plates rheometer in Fig. 3.12, is neither practical nor feasible practically. Thus, rotating plate rheometers were designed as an approximate the shearing planes. This geometry needs some adjustment when used for materials other than paste as the gap between the plates needs to be adapted to several time the maximum aggregate size. This would imply that the open surface at the edge of the plates is no longer an option as the material would flow out. A three-dimensional and a top view of the parallel plates rheometer (also, parallel rotating plates rheometer) is shown in Fig. 3.13. In this illustration, it is hollow in the center with radius Ri . One can simply dismiss this hollow center by putting Ri = 0 in the equations that follows. The outer edge of the rheometer has radius Ro . The bottom plate is stationary, while the top plate rotates at angular velocity ω [rad/s] and registers the applied torque T [Nm] from the test material (i.e., from the cement-based material). The term h is the distance between the two plates. For simplicity, the test material between the two plates in Fig. 3.13 is assumed to be a Bingham fluid. A detailed analytical derivation of the flow condition for such case is for example available in [21]. This gives the transformation equations shown with Eqs. (3.5) and (3.6). By plotting the measured torque T as a function of the angular velocities ω, one can connect these measured values with a straight line: T = H·ω + G. From its slope H and its point of intersection with the ordinate G, one can calculate the plastic viscosity μ and the yield value τ 0 of the cement-based material according to Eqs. (3.5) and (3.6).

Fig. 3.13 Principle of the parallel rotating plate rheometer

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μ=

2h H ) π Ro4 − Ri4

(3.5)

τ0 =

3G ) ( 2π Ro3 − Ri3

(3.6)

(

A well-known example of a parallel (rotating) plate rheometer for fresh concrete is the BTRHEOM rheometer [28, 51] with simulation results available in [21, 51].

3.3.3 Commercially Available Rotational Concrete Rheometers 3.3.3.1

Viskomat NT, Viskomat PC, Brabender Viscocorder, Viskomat XL

The Viskomat NT (Fig. 3.14) is a rotational rheometer for paste and mortar with a maximum aggregate size of 2 mm. This instrument is coaxial rheometer geometry (rotating vessel, fixed torque measurement sensor). The Viskomat NT is compatible to the Brabender Viscocorder and the Schleibinger Viskomat PC. The Viscocorder and the Viskomat PC are not produced anymore but were widely used since 1975. The Viskomat NT expands the options of the former Viskomat PC and the Viscocorder. All systems have the same basic geometry: a sample volume of 360 mL and a maximum aggregate size of 2 mm. The stirrer formed probes developed in the early seventies by Teubert [52, 53] are still available. With the standard cylinder-cylinder geometry it follows the ASTM standard C1749 [54]. The torque range is from 0 to 0.5 Nm which can be measured clockwise and anticlockwise. The speed range is from 0.001 to 400 rpm (1.7 10–5 –6.5 s−1 ) also in both directions. Additional to the shear rate and shear stress-controlled operation, also an oscillation mode is available. The range is here from ±0.10 degrees at 0.10 Hz. A double wall vessel connected to a chiller allows temperature control. A RTD sensor, integrated in each probe records the specimen temperature during the test procedure. For sticky pastes and mortars an optional scraper removes the material from the wall of the vessel. The system is divided in 2 units. Unit one is the instrument itself consisting of the motor, the torque sensor, and a lift unit. The electronic unit 2 contains the power and motor control unit as well as an embedded PC running with Linux. The whole system is controlled by a web application via the Internet/Intranet or locally by a classical mouse keyboard or tablet user interface. Actually, there are 4 types of probes available: 1. Stirrer type probes (Fig. 3.14b, c) which are mainly designed for long time tests (10 minutes and more). These probes avoid sedimentation and segregation of the material. These probes are calibrated for Newtonian materials [55, 56]. The calibration coefficients for this type of materials are doubtful, but maybe in the

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Fig. 3.14 Viskomat NT a and measuring probes b Mortar probe c Paste probe d Sphere probe e Vane probe f Basket probe g Cylinder-cylinder probe h Cone-plate probe

future they could be calibrated using new NIST standard Reference Materials (SRM 2492, 2493) [57]. The Paste-Probe (Fig. 3.14c) is for cement paste up to 0.5 mm grain size, the modified Paste-Probe and the Mortar-Probe for aggregates up to 2 mm.

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2. For geometries like a set of sphere probes (Fig. 3.14d) with different diameters (10, 20, 30 mm) [58] or a vane probe with 6 blades (Fig. 3.14e) calibration coefficients [25, 59] have been published in the last 40 years. The Viskomat Vane-Probe with a rectangular vane area of 40 × 60 mm (d × h) mm is specified for aggregates up to 4 mm. Also, the sphere probes are specified for this aggregate size. Both type of probes would not prevent sedimentation or segregation and attention must be paid to the sample homogeneity. 3. The Basket-Probe (Fig. 3.14f) developed by Vogel [60] is a double ring gap probe where the surface of the measuring cup has a metal mesh cylinder placed on the outer rim of the cylindrical spindle. The material inside and outside the cup is gluing together through the holes of the mesh to avoid wall slippage. The double gap probe has a well-defined geometry. There is an analytical solution for the Reiner-Riwlin equation. This geometry would not prevent sedimentation and is only suitable for stable suspensions. 4. The Cylinder-Cylinder probe (Fig. 3.14g) and the Cone-Plate probe (Fig. 3.14h) are geometries well known as standard geometries for nearly all rheometers. The cylinder system is following the ISO 3219 [61] standard with relatively big gap size of 2.1 mm. The maximum recommended particle size is here 0.2 mm. The cone system has a diameter of 100 mm and works with a particle size of 4 mm. Both systems cannot avoid wall slippage, sedimentation, and segregation. So, there is only a limited range of applications for this probe. The cylinder system is applicable for cement paste, according to ASTM C1749 [54] or self-levelling underlayments, the cone-plate system [62] is preferred for pasty systems like tile glues, plaster or UHPC. The Viskomat XL has a sample volume of 3 L and can be used, depending on the probe geometry, with aggregates with a maximum size of 32 mm. The torque range is from 0 to 10 Nm which can be measured clockwise and anti-clockwise. The speed range is from 0.001 to 80 rpm (1.7 10–5 –1.3 s−1 ) also in both directions. Additional to the shear rate and shear stress-controlled operation, also an oscillation mode is available. The range is here from ±0.10 degrees at 0.3 Hz.

3.3.3.2

ICAR Rheometer

The ICAR Rheometer is composed of a container, a driver head that includes an electric motor and torque meter, a four-blade vane that is held by the chuck on the driver, a frame to attach the driver/vane assembly to the top of the container, and a laptop computer (Fig. 3.15). The container has a series of vertical rods around the perimeter to prevent slippage of the concrete along the container wall during the test. The size and length of the vane shaft are selected based on the nominal maximum size of the aggregate. The vane has a diameter and a height of 127 mm. Two types of tests can be performed: (1) stress growth test in which the vane is rotated at a constant slow speed of 0.025 rev/s and the torque is measured as a function of time. The maximum torque measured during the test is used to calculate the static yield stress; (2) flow

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Fig. 3.15 The ICAR rheometer

curve test to determine the dynamic yield stress and the plastic viscosity assuming a Bingham behavior. The flow curve test begins with a “breakdown” period in which the vane is rotated at maximum speed. This is done to breakdown any thixotropic structure that may exist and to provide a consistent shearing history before measuring the Bingham parameters. The vane speed is then decreased in a specified number of steps, which is selected by the user but at least six steps are recommended. During each step the speed is held constant, and the average speed and torque are recorded. The plot of torque versus speed of vane rotation is the flow curve.

3.3.3.3

BTRheom

The BTRheom is the only parallel plates rheometer dedicated for concrete. It was first developed by Hu and De Larrard [51, 63, 64]. During a test, the concrete sample (7 L) is placed in a container between two plates of diameter 200 mm with openings to reduce concrete slippage (Fig. 3.16). The gap between plates is large enough to avoid granular effects (100 mm). In order to consider the flow of a parallel plate tests described in Sect. 3.3.2.3.4. It is also considered that the smooth lateral surfaces of the container allow the material to slip. The rotating plate is the upper one. The rotation of this plate is ensured by a rotating axis (diameter 20 mm) linked to a motor that is located at the basis of the BTRheom. It is important to note that the BTRheom is well adapted to concrete with slump values higher than 100 mm and can be used during vibration even for concrete with lower slump value (50 mm minimum). The torque and the rotation velocity are recorded during the measurement and allow the computation of the shear stress and the shear rate thanks to the theoretical work of Hu et al. [51]. The rotation velocity ranges from 0.63 to 6.3 rad/s and the maximum measurable torque is 14 Nm.

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Fig. 3.16 The BTRheom—schematic view and photos [51]

3.3.3.4

Cemagref

The CEMAGREF-IMG rheometer is a large coaxial-cylinder rheometer that contains approximately 500 L of concrete (Fig. 3.17). The outer cylinder wall is equipped with vertical blades, and the inner one with a metallic grid in order to limit the slippage of concrete. A rubber seal is fitted to the base of the inner cylinder to avoid any materials leakage between the cylinder and the container bottom. This apparatus was originally developed to study mud flow [19]. The primary advantage of this instrument is the large dimensions with respect to the maximum aggregate size. However, the geometry is not a pure Couette one, because the ratio of the inner radius to the outer radius is too large, namely 1.57 instead than 1.1. Therefore, some plug flow is to be expected when testing viscoplastic materials that have a yield stress. It means that for most tests, only the inner part of the concrete sample will be sheared, at least for the lower values of rotation speed.

3.3.3.5

ConTec Viscometer

The ConTec Viscometer 5 is a coaxial cylinders rheometer for coarse particle suspensions such as cement paste, grout, mortars, cement-based repair materials, and concrete. It is based on the concentric cylinders principle already described in Sect. 3.2.2, where the inner cylinder measures torque T and the outer cylinder rotates at variable angular velocities ω. Both cylinders contain ribs (or roughened surfaces) to reduce/prevent slippage. The ConTec rheometer (ConTec BML Viscometer 3) was developed in Norway in 1987 [65, 66] after six years intensive work with the

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Fig. 3.17 The Cemagref rheometer [3]

Tattersall Two-Point test instrument. The ConTec BML Viscometer 3 (often known simply as BML) and the ConTec Viscometer 5 are based on the same principle, but the latter has been upgraded in terms of electronics, engine, and geometric configuration. Figure 3.18 shows both devices, the ConTec BML Viscometer 3 (to the left) and the newer ConTec Viscometer 5 (Fig. 3.18b and c). The right illustration shows parallel run of two ConTec Viscometers 5 with the same fresh concrete batch, as a part of the verification process. The specified performance range of the ConTec Viscometer 5 is for torque 0.27 Nm to 27 Nm and for angular velocity 0.1 rps to 0.6 rps (revolutions per second) under normal testing conditions. The absolute range for both the angular velocity and the torque can be optionally adjusted. The instrument is user-friendly, fully automated, and is controlled by computer software called FreshWin (see [28]). Each test takes about 3 min to 5 min, from filling the bowl/material container to emptying it. More information about these devices (i.e., ConTec Viscometers 3 and 5) can be obtained from www.contec.is and from [28]. There are smaller versions of the ConTec Viscometer 5 available for mortar and cement paste, namely ConTec Viscometers 4 and 6. Results of numerical simulations of the ConTec BML Viscometer 3 are available in [29], in which the so-called bottom effect is investigated and accounted for. Theoretical and analytical description of the ConTec Viscometers (either when using

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Fig. 3.18 The ConTec BML Viscometer 3 (a) and the newer ConTec Viscometer 5 (b and c)

53

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the Bingham model or the modified Bingham model), as well as example of use, is available in [21, 22] See also Sect. 3.2.2. For the standard version of the ConTec Viscometer 5, the maximum aggregate size is 22 mm. When testing larger aggregate size, say 40 mm, the coaxial cylinder system can be replaced with the Coplate 5 (Mark III), which is a special cone–parallel plate system [67]. Figure 3.19 shows the use of such device during parallel testing with the coaxial cylinders system. For the Coplate 5 system, the conversion of the raw data into fundamental physical quantities, like yield stress τ 0 and plastic viscosity μ, is done through the results of series of flow simulations as explained in [67, 68]. Figure 3.20 shows an example of such simulation for the Coplate 5 (Mark III) system. Other similar type of geometry as shown in Fig. 3.16 has been tested for the ConTec Viscometer system [67]. The point is that the ConTec Viscometer is not limited to the coaxial cylinders system and the owner can create their own rheological geometry, thus demonstrating an important flexibility of the ConTec Viscometer 5.

Fig. 3.19 The Coplate 5 system—Mark III (a). Simultaneous testing of the Coplate 5 system (b) and of the coaxial cylinders system (c). Both systems are using the framework of ConTec Viscometer 5

Fig. 3.20 Example of simulation results for the Coplate 5 (Mark III), with the Bingham parameters τ 0 = 120 Pa and μ = 80 Pa s at the angular velocity of 0.4 rps. Dimensions are relative to the extremities of the protruding ribs

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3.3.3.6

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Two-Point Tests or Tattersall Mk-II

The original version of the Two-point workability test was developed by Tattersall (Fig. 3.21). The principle is that an impeller which imparts a stirring action is rotated a bowl of concrete, and the relationship between the impeller speed (N) and driving torque (T ) is determined. This is normally a straight line i.e., of the form T = G + HN demonstrating Bingham behavior. The intercept on the torque axis G is a yield term, and the slope H a viscosity term. Both G and H are dependent on the instrument geometry and the Bingham constants (yield stress, τ 0 and plastic viscosity, μ) of the concrete, but calibration with fluids of known properties has determined the relationships between G and τ 0 , and H and μ. The Tattersall Mk-II rheometer was developed by Tattersall and Bloomer [69], modifying an initial version of their rheometer which could not handle concrete mixtures with high workability [1, 70]. The principle is based on a concentric cylinder system, but the inner cylinder or spindle has the shape of an interrupted helical screw, with four flat blades mounted at a 45° angle. The purpose of the screw was to minimize segregation, while the interruptions were provided to facilitate the filling of the voids in between the blades [69]. The torque was measured by means of the oil pressure developed in the installed hydraulic gear box, while the speed was controlled on the electric motor [69]. The concrete bowl had a diameter of 254 mm, while the height was 304 mm. The bowl is filled up to 75 mm from the top [69]. More recently, a home-made version of the Tattersall Mk-II was modernized at Ghent University (Fig. 3.22) [71, 72]. A new bowl was constructed with a radius of 125 mm. The interrupted helical screw measured 160 mm horizontally and 140 mm vertically between its extremities. A modern torque and velocity sensor was installed, and data was recorded at 5000 Hz, averaging 2000 measuring points as output [71]. The rheometer was calibrated by means of poly-isobutene, which is a viscous, Newtonian oil, and with white honey, which showed Bingham behavior of similar order of magnitude as concrete [71, 72]. The calibration was performed at three different

Fig. 3.21 Two-point workability test—Tattersall

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Fig. 3.22 Ghent University modified Tattersall Mk-II (from Feys et al. [75])

temperatures for oil and four temperatures for honey. The results from the Tattersall Mk-II were compared to the values obtained in a standard cone and plate rheometer at equal temperatures. The calibration revealed a “zone of non-linearity” in the Tattersall Mk-II, in which linear rheological behavior is distorted [71, 72]. A complex analyzing procedure was developed to obtain transformations for torque to shear stress and for velocity to shear rate [71, 72]. Although errors are still suspected in this point-to-point transformation, a comparative study with the Tattersall Mk-II and the ConTec Viscometer 5 revealed that the obtained Herschel-Bulkley parameters were similar [73]. Only for very fluid, near-segregating SCC, the Tattersall Mk-II results deviate from the ConTec data [73]. A majority of the work at Ghent University was executed on SCC and the accuracy of the proposed analyzing method is not applicable for more stiff concrete. Numerical simulations have shown large shear rate concentrations at the tips of the blades [74], while similarly for any other rheometer with vertical or inclined blades, hydrodynamic pressures at the back side of the blades may influence the results [26].

3.3.3.7

Tattersall Mk-III or IBB

The IBB rheometer is an adaptation of the 2-point tests (Fig. 3.23). The IBB rheometer has an H-shaped impeller (130 mm large and 100 mm high) immersed in the concrete placed in a cylindrical container (diameter of 356 mm) [76–78]. The H-shaped probe rotates in a planetary motion at a rotating rate ranging from 0 to 1.2 rps.

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Fig. 3.23 The IBB rheometer and its impeller [78]

3.3.3.8

RheoCAD

The RheoCAD rheometer (Fig. 3.24) is a coaxial cylinder type rheometer which can be equipped with different type of spindles [79, 80]. Different versions of the RheoCAD exist (420, 450 and 500). The smaller one is the RheoCAD 420 which is designed for mortar and the biggest one is the RheoCAD 500 (Fig. 3.24) which is able to test sample volume of 37 L. The RheoCAD rheometers are equipped with a torque meter with a capacity of 10 Nm and a sensitivity of 10 Nm which allows studying self-consolidating concrete. The rotation velocity ranges from 0 to 250 rpm.

3.4 Confined Flow Rheometers 3.4.1 Squeeze Flow Rheometers Squeeze flow is used to describe the rheological behavior of firm concentrated suspensions such as molten polymers, food materials or ceramic pastes [81–83]. It is used for samples that sustain gravity without deformation. The test consists in a simple compression test on a cylindrical sample placed between two coaxial and circular plates. The compression of the sample of radius R height h and at a constant velocity, v, induces an elongational flow essentially in the radial direction (Fig. 3.25). The

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Fig. 3.24 The rheoCAD 500 rheometer

radii of the sample and the plates can be the same or not. In the first case, the mass of the sample remains the same during the test (sample diameter lower than plates diameter) and in the second, the surface between the sample and the test remains constant (sample diameter equal to the plate diameter). In any case, it is important to use rough surface to avoid material slippage at the plates interface [82]. Practically, the test is carried out using a compression device equipped with a load cell and a displacement sensor (Fig. 3.25).

Fig. 3.25 Squeeze flow test. To the left: picture of a test, axisymmetric squeeze flow with constant mass of sample, axisymmetric squeeze flow with constant area of contact between plates and samples

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Fig. 3.26 Squeezed sample, the color heterogeneity highlights the water content gradient within the sample

Squeeze flow has been used on concrete for firm mix such as zero slump concrete, extrudable mix and rendering [84–86]. Common rotational rheometers are not able to describe their rheological behavior due to shear localization, pressure dependency, slippage, or excided torque capacity. Firm mixture is likely to be very dense suspensions that may exhibit internal friction between particles. From a global equilibrium method, Toutou et al. [87] proposes a method to measure the plastic yield stress and friction coefficient (bulk and interfacial) of the materials [87]. The squeeze flow has not been used to estimate the viscosity of mortar or concrete even if analytical model of the squeeze flow of Bingham or Herschel-Bulkley fluids are available in the literature. One of the limitations of the tests is that liquid filtration may appear during the flow especially at low compression velocity [84, 87] when the pressurized interstitial fluid has the time to flow out of the granular network. In this case, the material becomes heterogeneous (Fig. 3.26) and the squeeze flow can no longer be used as a rheometer.

3.4.2 Extrusion Flow Rheometers Extrusion flow is used to estimate the flow properties of mortars (zero slump) for which rotational rheometers are not applicable [85, 88–92]. The methods and techniques used for cement-based materials are inspired by the literature on ceramics, especially the works of Benbow and Bridgwater [93, 94]. Axisymmetric ram extruder is used to characterize the rheological behavior of concrete. The material located inside the extruder barrel is pushed by a ram toward a circular die that gives its final shape to the material. The flow of zero slump concrete or extrudable concrete can always be divided into three parts:

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• A plug flow located in the extruder barrel. It is not clear if friction occurs or if a thin layer of material is sheared just as in concrete pumping. • A tapered static zone where the material remains blocked around the die entry. This area is called the “dead zone”. If the die is conical, the tapered zone might not exist. • A forming zone, located inside the conical dead zone, where the material billet diameter decreases. This zone is also called the “shaping zone” [91]. Within this zone, an elongational flow occurs. Therefore, representative force for each part of the flow where material advance and forming occurs can be introduced (Fig. 3.27): • The shaping force required to give its final shape to the material in the shaping zone denoted Fpl , • The wall friction force, developed along the extruder barrel is linked to the interfacial stress. In Fig. 3.27, a typical extrusion curve is plotted. We can show that the extrusion force decreases as the ram advance. This decrease is due to a reduction of the interfacial surface between the extruder barrel and the cement-based materials. When no material is left in the plug flow zone, the extrusion force is minimal and equal to the shaping force [95]. The shaping force is used to study the bulk rheology of the material using the methodology proposed by Perrot et al. or Zhou et al. [91, 92]. Contrary to rotational rheometry, several tests are needed to describe the whole flow curve of a cementbased material because one extrusion test carried out at a constant ram speed is representative of an average shear rate. This means that an extrusion test provides only one point of the flow curves. The shaping force can be measured by three methods: a load cell located at the ram (deduced from the force when there is no more material in the plug flow zone) [89, 92], two pressures transducers located at the entrance and the exit of the die land [90] or by a system that allows to measure simultaneously the friction force and the total force [91]. As an example, the ram in Fig. 3.28 is equipped with a load cell in order to measure the total extrusion force F required to overcome both frictions on the extruder barrel and shaping force in the die land and the extruder barrel is placed on a novel die system which is fixed on the load frame. This system allows measuring the friction force acting along the barrel wall: the bottom of the extruder barrel and the top of the die system are both equipped with similar circular shoulders which squeeze load cells that allows measuring the force generated by the stress acting along the extruder wall. The friction force is used to measure the tribological behavior (interfacial rheology) of the cement-based materials. Like for squeeze flow, a problem of water filtration may appear leading to a heterogeneous mortar [95–97] as shown in Fig. 3.29. Such filtration is likely to appear for low ram velocity or for mortar or cementitious material which do not contain fine powder or viscosity modifying admixtures and therefore exhibit a high

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a Kw z

wall friction stress

F

σ(L) axial mean stress LB

Zone 1: Plug flow

Kw

Kw

0

Zone 2 and 3: 2: Sheared flow in the shaping zone 3: Dead zone

Fpl

Ldz d

b

D

σ(z)

Fig. 3.27 a Typical evolution of the extrusion force F versus the length of material remaining in the plug flow zone. b Schematic view of an axisymmetric ram extruder (LB is the length of the material in the plug flow zone, Ldz is the length of the dead zone, d is the diameter of the die and D the diameter of the extruder barrel)

permeability [95]. When filtration appears the extrusion force increases instead of decreasing and the technique cannot be used to measure the rheological behavior of studied material.

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Fig. 3.28 Different ram extruder device system measurements. To the left from Alfani et al. [90], Zhou et al. [92] and Perrot et al. [91]

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Fig. 3.29 Map of local hardness (1 mm needle penetration force) of the material remaining in the billet during an extrusion carried out at a too slow ram velocity [96]

3.5 Static Rheometers—The Plate Test The plate test consists in measuring the mass variation of a rough tool (plate or cylinder) immersed in a fresh cement-based material with time. It has been used to study the evolution of the rheological behavior of cement-based materials with time. This device was initially developed to enable a simple measurement of the yield stress increase. Therefore, it can provide an accurate value of the structuration rate during the so-called dormant period and provide an evaluation about the initial setting time. The mass variation of the sample or of the tool is recorded i.e., the apparent mass of the immersed tool or the apparent mass of the sample is continuously monitored versus time by recording the balance output with a computer. It is important to note here that, as opposed to a penetrometer test, the plate is perfectly static. This test is not intrusive because the only movement is due to the changes occurring in the material. In other words, the plate behaves as an additional wall. In the general case, the particles in a suspension move downwards creating a higher density layer at the bottom. In this case, the buoyancy force varies with time. However, if the material remains homogeneous which is the case in most case, the buoyancy remains constant during time. The data analysis is based on the force balance equation of a static cylinder (Fig. 3.30). Three phenomena are acting on the tool: gravity, buoyancy and shearing at the material/plate interface. Before immersion into the cement-based material, the mass plate m0 is only due to gravity and does not change with time: −−−−→ m 0 (t) × g→ = Fgravit y

(3.7)

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Fig. 3.30 Forces acting on the immersed tool

After immersion, the mass measured corresponds to the apparent mass m(t), which can be deduced from the static equilibrium of the tool in a yield stress fluid: −−−−→ −−−−−→ −−−−−→ m(t) × g→ = Fgravit y + Fbuoyancu + Fshear (t)

(3.8)

where F gravity is the constant weight of the plate, F buoyancy is the resistance force due to buoyancy and F shear is the resistance due to shearing at the material/cylinder interface. It is important to note that the bottom end effect is neglected because used tools are very thick (needle) or empty (cylinder) in comparison with the vertical shearing surface. This assumption is not valid for tools with large section [98–100]. In this case, we advise to slightly move the plate upward in order to create an empty space between the bottom end of the immersed tool and the concrete. The mass variation can be expressed as follow: Δm(t) =

) 1( −Fbuoyancy + Fshear (t) g

(3.9)

The shearing force directly depends on the deformation γ at the interface between the material and the immersed tool and can be written as follow: [ ] Fshear (t) = min G(t)γ (t)S; G(t)γc S = τ0 (t)S

(3.10)

where G(t) is the elastic modulus of the studied material, S is the shearing surface, γ c is the critical strain for flow and τ 0 (t) is the yield stress. Equation (3.10) shows that if the critical strain is reached at the interface, it is possible to obtain the evolution of the yield stress of the material with time from the recorded mass variation: τ0 (t) =

g(Δm(t) + ρV ) S

(3.11)

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Going back to the occurring phenomena, it can be interesting to focus on the shear strain γ (t) and to write in as a function of the principal contributions of the volume variation: γ (t) = γcons (t) + γther m (t) + γauto (t)

(3.12)

where γ cons (t) is the contribution of deformation due to consolidation, γ therm (t) is the contribution of deformation due to temperature variation and γ auto (t) is the contribution of deformation linked to autogenous shrinkage and cement phase change. As shown by Eq. (3.10) it seems obvious that controlling the deformation of the sample is paramount for the success of the test because it has to be always larger than the critical deformation of the tested cement-based material. The plate test device can take several forms (Fig. 3.31). It is composed of a tool immersed in a freshly made material (needle or a plate) rigidly attached below a fixed support. The immersed tool used can be a needle with a diameter of 1.13 ± 0.05 mm and 40 mm long (i.e. a roughened Vicat needle) [101], can be a plate covered by sandpaper [102, 103] or also a 10 mm or more diameter rebar [103–106]. The distance between the needle/plate and the container walls is large enough that there is no influence on the stress measured due to the size of the frustum as shown by [107] and Tchamba et al. [102]. Moreover, in order to ensure that the yield stress is fully mobilized

Fig. 3.31 Different configurations of plate tests from a cement paste tested in a Vicat mould to a SCC tested in a column of 100 L

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at the interface with the immersed tool, it is critical to make sure that the critical strain is overcome at the interface. Therefore, as the plate remains static, the vertical settlement of the tested cement-based materials must be sufficient. It can be noted that all types of cement-based materials can be tested from cement paste to concrete [107]. The plate test is therefore an interesting alternative to conventional rheometry as it remains cheap and simple to estimate yield stress initial value and increase with time at rest.

3.6 Summary The present chapter aims to make an exhaustive presentation of concrete rheometers. After a definition of what can be called a rheometer based on a consensus among the technical committee members, concrete rheometers are presented following a classification that relies on the origin of the solicitation acting on the material and initiating the material flow. Four types of rheometers are listed: the free flow rheometers for which the flow are induced by gravity (i.e. monitored slump or spread flow), the rotational rheometers which are the most used and directly refers to conventional rheometry (i.e. concentric cylinders and plate-plate rheometers), the confined flow rheometers that can be useful for no slump concretes (i.e. capillary extrusion and squeeze flow) and the static rheometers where shear is induced by the concrete own settlement and deformation (i.e. the plate test geometry). For each rheometer type, the physical principles are presented shortly referring to literature and Chap. 2 of the present book in a first time. Then, the different possible existing configurations are presented as well as available technical solutions. This rheometers review shows that there is a large range of devices able to capture and describe a part of, or the entire rheological behavior of concrete mixtures. However, each rheometer is typically dedicated to the measurement of specific parameters, is suitable for a certain range of concrete consistencies and has to be chosen in relation to the targeted parameters and measured concrete type.

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102. Tchamba JC, Amziane S, Ovarlez G, Roussel N (2008) Lateral stress exerted by fresh cement paste on formwork: laboratory experiments. Cem Concr Res 38(4):459–466 103. Amziane S, Perrot A, Lecompte T (2008) A novel settling and structural build-up measurement method. Meas Sci Technol 19(10):105702 104. Perrot A, Amziane S, Ovarlez G, Roussel N (2009) SCC formwork pressure: influence of steel rebars. Cem Concr Res 39(6):524–528 105. Billberg PH, Roussel N, Amziane S, Beitzel M, Charitou G, Freund B, Gardner JN, Grampeix G, Graubner CA, Keller L, Khayat KH (2014) Field validation of models for predicting lateral form pressure exerted by SCC. Cement Concr Compos 54:70–79 106. Amziane S, Perrot A (2017) The plate test carried out on fresh cement-based materials: how and why? Cem Concr Res 93:1–7 107. Zhang MH, Ferraris CF, Zhu H, Picandet V, Peltz MA, Stutzman P, De Kee D (2010) Measurement of yield stress for concentrated suspensions using a plate device. Mater Struct 43(1):47–62

Chapter 4

Measuring Procedures Ammar Yahia and Arnaud Perrot

Abstract The interest in developing scientific approaches to assess and predict fresh properties grasped much attention in recent years due to the advent of innovative materials incorporating a variety of admixtures, supplementary cementitious materials and fillers. As a result, rheology has become an essential tool to provide an accurate measurement and characterization of rheological properties. This chapter provides an overview of test procedures commonly employed for rheological analysis and tool geometries, including concentric cylinders, vane geometry, cone plate geometry, parallel plate, and squeeze test, and key rheological properties, including static yield stress, build-up and break down, and principles and measuring techniques involved. Fundamental parameters used in rheology, including shear stress, shear rate, viscosity, and yield stress are presented. Test procedures to assess flow curves, data analysis, and transformation equations are discussed. Additionally, possible measurement artifacts are discussed with strategies for error reduction. Employing appropriate test methods and understanding the underlying principles is important for designing appropriate testing methodologies and interpreting the results effectively, hence allowing good understanding of material behaviour.

With contributions from: Dimitri Feys, Jon Wallevik. Dimitri Feys—Missouri University of Science and Technology, United States. Jon Wallevik—Icelandic Meteorological Office, Iceland. A. Yahia (B) Université de Sherbrooke, Boulevard de L’Université, Sherbrooke, QC 2500, Canada e-mail: [email protected] A. Perrot UMR CNRS 6027, University Bretagne Sud, IRDL, 56100 Lorient, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Sonebi and D. Feys (eds.), Measuring Rheological Properties of Cement-based Materials, RILEM State-of-the-Art Reports 39, https://doi.org/10.1007/978-3-031-36743-4_4

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4.1 Introduction Since the advent of high-performance fluid concrete, such as self-consolidating concrete (SCC), mixtures contain a variety of admixtures to improve fresh and hardened properties. This resulted in an increasing need in developing scientific approaches to measure and predict fresh properties, to properly select materials and to simulate processes and achieve the required performance. As a result, rheology has become a term recognized by technologists worldwide. In recent years, research allowed developing or improving appropriate rheological measurements of fresh cement-based materials (paste, mortar, and concrete) to achieve better understanding of its flow properties. Rheology is the science of the deformation and flow of matter [1] and can be used to optimize the proportions of concrete mixtures in order to achieve proper flow performances. It is well established that cement-based materials exhibit a complex rheological ehaviour, which is affected by various mixture parameters, including water-to-binder ratio, cement type and fineness, mixture composition, presence of admixtures and supplementary cementitious materials, and testing procedures (maximum shear rate, step duration, etc.). The most appropriate way to study the rheological ehaviour of cementitious paste is to determine the relationships between shear stress and shear rate, referred to as the flow curve. Various mathematical models were proposed to adequately fit/describe the flow curve of cement-based materials. The rheological characterization of cement-based materials is challenging because of the wide range of dimension of particles, hence resulting in heterogeneous systems. Furthermore, cementitious materials are colloidal materials that undergo a chemical reaction. The history of loading and solicitation has a great influence on the cementitious particles structuration state and macroscopic rheological ehaviour. Thus, the instantaneous structuration of the cementitious particles assembly has to be controlled in order to obtain a precise estimation of the cementitious material thixotropic ehaviour. The different geometries used in cement-based materials rheological characterization are first presented. A special focus on the generated flow and governing equations is provided. Then, the second part deals with the measurement of viscoplastic properties (flow curves, static yield stress) of cement-based materials. The measurement of viscoelastic properties of cement pastes is outside of the scope of this STAR.

4.2 Measuring Tools and Cement-Based Materials Properties 4.2.1 Rheological Properties The modelling of the rheological behavior of fresh cement-based materials has been presented in detail in the Chap. 2 of the present report. However, it is necessary

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Fig. 4.1 Shear flow of a viscous Newtonian fluid

before going into data analysis and measurement procedures to recall the principal characteristics of the rheological behavior of fresh cement-based materials. For perfectly viscous materials, Isaac Newton (1687) proposed the following relationship: “The resistance which arises from the lack of slipperiness originating in a fluid is proportional to the velocity by which the parts of the fluids are being separated from each other” [2]. In this case, the viscous liquid deforms continuously under constant shear stress. In addition, induced deformation will not be recovered after the removal of applied stress: the material has no memory and the material remains in its final shape. The flow of a perfectly viscous (Newtonian) fluid between two sliding parallel plates is shown in Fig. 4.1. In the case of a constant viscosity with time, a linear relationship between shear stress and shear rate can be obtained according to Eq. (4.1) [2].

τ=η

dv = μγ˙ dy

(4.1)

where dv/dy is the velocity gradient or shear rate (dγ /dt), μ is the viscosity, and τ is the shear stress. Viscoelastic materials exhibit both elastic and viscous behaviors when undergoing deformations or stresses. At a constant stress, the viscoelastic material behaves as an elastic material and undergoes an instantaneous strain. Then, with time, strain increases due to the viscous properties. Once the load is removed, only the elastic deformation will be recovered. In other words, these materials can store some of the induced energy and use it for the recovery and dissipate the rest by means of friction [2]. Several tests can be used to investigate the viscoelastic properties. This includes creep, stress relaxation, and oscillatory rheometry tests [3–7]. Cement-based materials are complex materials, which can be considered as ideal elastic for low strain (under a critical shear strain of the order of 10–4 for cementitious paste) and as viscous when a critical stress, called the yield stress, is exceeded. Between both states, the material behavior is more complex and

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viscoelastic modeling is required to describe the material behavior, which is beyond the scope of this STAR. It is important to note that the yield stress is a time-dependent parameter that depends on the state of structuration of the cement particles network that evolves with time. Two characteristic values of yield stress can be defined: the dynamic yield stress related to an unstructured flowing material and the static yield stress that is related to the stress needed to make the material flowing at a specific time.

4.2.1.1

The Viscoplastic Steady-State Flow of Cement-Based Materials

One of the main characteristics of the cement-based materials is their steadystate flow behavior once the yield stress is exceeded [8, 9]. It corresponds to the rheological behavior of the cement-based materials at the unstructured state (nonflocculated cementitious particles assembly and no nucleation points). In order to model this behavior, viscoplastic rheological model, such as the Bingham (Eq. 4.2) and Herschel-Bulkley (Eq. 4.3) models, linking the shear stress τ to the shear rate γ˙ can be used. τ = τ0,d + μγ˙

(4.2)

τ = τ0,d + k γ˙ n

(4.3)

where τ 0,d is the dynamic yield stress in Pa (stress needed to stop the flow), μ is the viscosity in Pa s, k is the consistency factor in Pa.sn , and n is the flow or consistency index. These parameters can be evaluated by inducing flow at different velocities and measuring the material’s resistance to flow.

4.2.1.2

Static Yield Stress, Structural Build-Up and Breakdown

At rest or at low strain rate, the cementitious particles network builds-up with time. Two compounds can be distinguished: one reversible and one irreversible. The reversible structural build-up is commonly known as cementitious materials thixotropic modelling. Flocculation (during few minutes) and cement particles nucleation of hydration products at the contact points (during dozens of minutes) contribute to this phenomenon. This is quasi-reversible at the material fresh state as long as the mixing energy and mixing system is powerful enough [10, 11]. The breakage of the bonds between cementitious particles is called structural breakdown. The shear stress necessary to make the material flow and which is related to the state of structuration of cementitious particles assembly is called the static yield stress τ 0,s . It can be significantly larger than the dynamic yield stress τ 0,d , which is related to a cementitious material network that has been partially or totally broken

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by mixing, shearing or flow. The static yield stress can be considered to linearly evolve with resting time [8, 12] although more sophisticated models can offer a more accurate description of the time evolution of the static yield stress, especially because of hydration [13–15]. Among them, double timescales model can be used to differentiate nucleation and flocculation mechanisms [6, 16] or exponential model can be used to extend the time validity of the modelling [13, 14, 17].

4.2.2 Tools and Geometries An exhaustive review of rheometers dedicated to cement-based materials has been presented in Chap. 3 of the present report. A summary of the principal measurement geometries is given thereafter. Different rheometers can be used to perform the rheological measurements of cement-based suspensions based on their working principles and geometries. In general, the working principle can be divided into a drag or pressure driven flow and uniaxial compression. The following sections will present a summary for the measuring systems inducing a drag flow shear and normal compression that can be used to assess rheology of cement-based suspension. These measurement systems include, but are not limited to, the concentric cylinders, cone-plate (even if this geometry has not been applied at the concrete scale), plate-plate, and vane geometries, as well as uniaxial compression. The general working principle in these systems is to apply a constant simple shear on a trapped sample between two infinite parallel surfaces or a compression of a cylindrical sample between two parallel plates (squeeze test). The applied shear flow could be controlled by means of the shear stress or the shear rate for drag flow shear rheometer types and different amount of rate of normal compression for squeeze rheometers.

4.2.2.1

Concentric Cylinders

The concentric (or coaxial) cylinders measuring geometry consists of an inner cylinder (bob) and an outer cylinder (cup) having the same rotation axis as shown in Fig. 4.2. Two operation techniques could be applied using this geometry, either rotating the inner cylinder while the inner one is at rest (Searle method) or allowing the outer cylinder to rotate while keeping the inner one stationary (Couette). In the case of coaxial cylinder flow, the shear flow can be obtained by allowing a relative rotational velocity between inner and outer cylinders ω and measuring the resulting torque T. From the stress equilibrium equations, the shear stress can be estimated using Eq. (4.4), as follows: τ(r) =

T 2πr 2 h

(4.4)

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Fig. 4.2 Schematic representation of the concentric cylinder geometry

where r is the radius from the vertical axis and h is the height of the cylinder. It is important to consider the fact that Eq. (4.4) does not consider bottom and upside effect where some materials can be also sheared. Other equations can be used to compute the shear stress considering this additional shearing [17] or it is also possible to use geometrical configurations (hollow cylinders, conical end sides, etc.) and experimental adjustments to minimize those end effects. On the other hand, the estimation of the shear rate depends on the gap size [2, 18]. The gap size is defined as the ratio between the outer cylinder radius Ro and the inner cylinder radius Ri . In the case of small gap sizes (Ri /Ro ≥ 0.99), the shear rate can be approximated as constant in the gap. In this case, the shear rate can be calculated as follows [2, 18, 19]: γ˙ =

Ro Ri

ω −1

(4.5)

where ω is the angular velocity (rad/s). Note that the equation can be applied independently of which of the cylinder rotates, i.e., the inner or outer cylinder. If the gap is not small, the shear rate calculation becomes more complex [2]: 2ω γ˙ = γ˙ (Ri ) =   2/n  n 1 − RRoi

(4.6)

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with the parameter n is defined as follow: n=

dln(T) dln(ω)

(4.7)

where n is the slope of the T–ω line in a log–log scale. It corresponds to the flow index n in the power-law model. The use of the small-gap equation Eq. (4.5) can be acceptable if the fluid is close to Newtonian (i.e., ratio of dynamic yield stress to viscosity τ 0,d /μ is low). However, such condition rarely applies for cementitious materials, especially when investigating the rheological behavior as a function of time from the first contact between cementitious particles and water. This equation is also applicable if the ratio Ri /Ro is very close to 1 (say 0.99). But such a configuration cannot be used for mortar or concrete, as the aggregate particles will be too large for the device. Furthermore, even the large-gap equation (Eq. 4.6) is not straightforward to use in case of yield stress materials, as n depends on the rotational velocity. Similar problems are experienced in parallel rotating plate rheometers, in which the determination of the shear stress becomes challenging. However, there is an alternative solution which does not require the calculation of the shear rate in the gap of the rheometer. This transformation procedure is called the Reiner–Riwlin equation (not to be confused with Reiner–Rivlin equation, which is a constitutive equation [20]). Its derivation is detailed in [19–24], and it transforms a relationship between torque and rotational (or angular) velocity into a relationship between shear stress and shear rate. It does not provide a point-to-point transformation, but it expresses the obtained relationship in fundamental units (Pa and Pa s). Hence, in the case of wide gap size, the application of the Reiner-Riwlin equation provides the equations of the yield stress and viscosity of tested cementitious materials [22, 23]: 

 − R1 2  o G τ0,d = 4π hln RRoi   1 1 2 − 2 Ri Ro H μ= 8π2 h 1 Ri 2

(4.8)

(4.9)

where G and H are determined from the torque-rotational velocity curve (T = G + HN). The large-gap concentric cylinder geometry provides a great advantage in the case of fresh concrete where relatively large particles are available in the suspension. In addition, the coaxial cylinders’ geometry is preferred to test low-viscosity suspensions where the tested sample cannot flow out of the gap. However, caution should be taken in this case to ensure minimum effects due to the low instability and

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Fig. 4.3 Picture of 6 and 4 blades vane geometries

turbulent flow that might occur [24]. For example, by verifying the Taylor number and Reynolds number.

4.2.2.2

Vane Geometry

This measuring system is similar to the coaxial cylinders’ geometry, but with a vane tool instead of the cylindrical bob. The vane tool usually consists of 4 or 6 blades. Its main advantage is the avoidances of the wall-depletion or slip artefacts as the tested material works as a tool to induce shearing [25]. It also allows inserting the thin vanes into the sample with a minimum disturbance [26] (Fig. 4.3). The data analysis and the generated flow are considered to be the same as the one obtained with the concentric cylinders [19, 27], even if the shear surface has been shown to be not perfectly cylindrical [28].

4.2.2.3

Cone Plate Geometry

In this measuring system, the tested sample is put between a flat circular cone and a plate (Fig. 4.4). The shear flow is obtained by rotating the cone at a velocity ω (angular velocity) and measuring the resisting torque T. Usually, the cone angle (α) does not exceed 4° while its radius (R) ranges between 10 to 100 mm. A larger plate radius is preferred when testing low viscosity suspensions as this provides a larger shearing area.

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Fig. 4.4 Schematic representation of the cone and plate geometry

As both the gap thickness h(r) and the circumferential velocity v(r) in the coneplate geometry are not constant and varies with the plate radius according to Eqs. (4.10) and (4.11), the shear rate is maintained almost constant (considering small cone angles) within the gap and its value can be given by Eq. (4.12), as follows: h(r) = r tan(α)

(4.10)

v(r) = r ω

(4.11)

where r is the distance from the center. γ˙ =

dv(r) ω ω = ≈ dh(r) tan(α) α

(4.12)

Additionally, from the stress equilibrium equations, in the case of small cone angle, the shear stress τ is uniform within the gap and can be estimated as follows: τ=

3T 2πR3

(4.13)

Indeed, the main advantage of this measuring system is the constant shear rate within the gap, which can ensure homogeneous shearing solicitation [29]. However, this system may have some limitations when testing suspensions that have millimetric or larger particles, such as fibers, aggregates, etc. as the gap thickness at the apex of the cone is in the range of dozens of microns. Usually, the maximum allowed particles size is preferred not to exceed 20% of the edge gap thickness. This greatly hinder the use of this type of geometry for mortars or concretes.

4.2.2.4

Parallel Plate Geometry

This measuring system is similar to the cone-plate geometry but with an upper rotating plate instead of the flat cone (Fig. 4.5). The gap thickness (h) is constant and its value can range between 2 to 10% of the plate diameter 2R. The use of larger gap

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Fig. 4.5 Schematic representation of the parallel plate geometry

thickness promotes the risk of edge failure as well as flow instability and turbulent flows in the case of low-viscosity suspensions subjected to rotational shear [30, 31]. In this geometry and at a given height from the lower plate, the circumferential velocity depends on the distance from the vertical rotational axis. Therefore, the shear rate is not constant, and its value varies linearly within the gap as a function of the distance from the rotation axis. The shear rate and shear stress at 3R/4 can be given from the following approximate equations [32], as follow: 3 ωR 4 H

(4.14)

3T H 2π R3

(4.15)

γ˙ = τ=

This measuring systems allows performing test on suspensions containing relatively large elements. However, caution should be taken to overcome the possible water evaporation and edge failure.

4.2.2.5

Squeeze Flow Rheometer

Most recently, a new class of cement-based materials intended for 3D printing applications, mostly fine mortars, was developed to assess their rheology. Such materials are designed to achieve a high static yield stress and rapid structural build-up to resist the gravitational loads of the upper layers during the printing process. Moreover, the printing materials should be flowable enough to be pumpable and extrudable. Such properties are also demanded for other applications, including shotcrete, plastering, and brick construction applications. For example, the mortar is spread over a surface or squeezed between bricks. The mortar matrix is also locally squeezed between the coarse aggregate during concrete flow. The mortar hence undergoes elongational shear strains and reduction of layer thickness. The rheological evaluation of such type of cement-based suspensions is of interest. However, measuring the rheological properties of such stiff materials using the measuring procedures explained in previous chapters (e.g., coaxial cylinders or parallel-plate systems) can bring some difficulties leading to inaccurate results.

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These include the interfacial slip, disruption of plastic materials, and the difficulty to load stiff materials. One of the main alternatives to avoid such issues is to evaluate the deformation of a given sample under uniaxial compression load, referred to as squeeze test. The squeeze flow test has been recently employed to evaluate the flow behavior of stiff cement-based mixtures [33–38]. This test consists in applying a uniaxial compression in a well-controlled fashion, controlled loading rate or displacement rate, to a cylindrical specimen between two parallel plates (Fig. 4.6). The strain developed within the squeezed material depends on its rheological characteristics, geometry of the squeeze set-up, specimen’s geometry, and material/ plates slip conditions. A typical load vs. displacement profile of a constant velocity (V sq ) squeeze flow is schematically presented in Fig. 4.7. The squeeze flow profile generally includes three main stages, including: (I) small strain, corresponding to viscoelastic behavior of the material; (II) high strain, corresponding to the plastic deformation of materials, reflecting the viscoplastic characteristics of the squeezed material; and (III) strain-hardening stage, corresponding to particles interlock and liquid phase migration, reflected by a high increment in compressional load. The uniaxial compression test results can be fitted to the Herschel-Bulkley model to estimate the rheological properties of the squeezed material. The Eq. 4.16 was proposed to describe the squeeze flow behavior of a Herschel-Bulkley fluid under a constant-radius squeeze instrument with slip condition [37, 39–41]. This relates the applied normal stress (σ N ), shear static yield stress (τ 0 ), extensional consistency (k), and pseudoplastic index (n) of the investigated material, sample radius (R), under a normal force F sq and a squeeze velocity V sq at sample height “h”:

Fig. 4.6 Schematic representation of the squeeze test, a before and b after deformation

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Fig. 4.7 Schematic of typical load vs. displacement curve of a constant velocity squeeze flow test, including three main stages of the material’s behavior: I: elastic state (small strain), II: plastic state (high strain), and III: strain-hardening (high load-increment)

 √ n √ Fsq 3 × Vsq = 3 × τ0 + k × σN = h π × R2

(4.16)

By applying natural-logarithm function to both sides of the Eq. (4.16), the following equation can be obtained:

ln

√ Fsq − 3 × τ0 2 π×R

 = n × ln

 √ n √ 1 + ln 3 × k × 3 × Vsq h

(4.17)

where, as reported by Covey and Stanmore [42], the shear yield stress can be estimated, as follows: τ0,s =

3 × Fsq−hL × hL 2 × π × R3

(4.18)

where hL is the limit height, corresponding to the residual height of the tested sample at the end of the plastic-squeeze flow (Fig. 7b) where the velocity tends to zero, and Fsq−h L is the normal force applied on the sample at the limit-sample height hL . Obtaining the shear yield stress ) usingEq. (4.18), a linear correlation is  values (τ √0   Fsq then established between the ln π ×R 2 − 3 × τ0,s and ln h1 values in the plastic squeeze flow phase for the investigated material when tested with a smooth loading plate. According to Eq. (4.17), the Herschel-Bulkley parameters of the investigated mortars, including the pseudoplastic index (n) and consistency (k) values, can be thus obtained using the slope and intercept of the data shown in Fig. 4.8, respectively:

k=√

eIntercept n √ 3× 3 × Vsq

(4.19)

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 Fig. 4.8 Typical results of linear correlations established between the ln   ln h1 values in the plastic-squeeze flow phase

Fsq π ×R 2

−

 √ 3 × τ0 and

where mean-squeeze velocity (V sq ) can be calculated using the ratio of the changes in sample height to the time duration of the plastic-squeeze flow, as follows: hIEC − hL  Vsq =  t h − th  IEC L

(4.20)

where hIEC and th I EC are the sample height and elapsed-testing time corresponding to the end of the initial elastic compaction phase (or beginning of the plastic squeeze flow), respectively. Moreover, th L is the elapsed testing time corresponding to the limit sample height (hL ), at the end of the plastic squeeze flow. On the other hand, the shear modulus of the squeezed material can also be evaluated through the elastic and strain-hardening phases. According to the von Mises theory, the shear stress τ (t n ) in the sample under the normal force F sq (t n ) and normal stress σ N (t n ) at the elapsed time t n can be calculated, as follows: Fsq (tn ) σN (tn ) τ(tn ) = √ = √ 3 3 × π × R2

(4.21)

On the other hand, the total shear strain γ (t n ) at nth time step, corresponding to the elapsed time t n , can then be evaluated by integration of the shear rate values γ˙ (t) along the testing period (0 to tn ), as follows:

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tn ˙ γ(t).dt = γ(t0 ) +

γ(tn ) =

n 

˙ i−1 ) × (ti − ti−1 ) γ(t

(4.22)

i=1

t0 =0

where γ (t 0 ) is the shear strain at the beginning of the test and equals zero (γ(t0 ) = 0). Moreover, according to Eq. (4.16), the shear-rate values γ˙ (t n ) can be calculated, as follows: √ 3 ˙ n) = × Vsq (tn ) γ(t (4.23) h(tn ) where the sample height h(t n ) and the squeeze velocity V sq (t n ) at the elapsed time “t n ” are obtained, as follows: h(tn ) = h0 × [1 − ε(tn )] Vsq (tn ) =

|h(tn ) − h(tn+1 )| tn+1 − tn

(4.24) (4.25)

where, as shown in Fig. 6a, h0 is the initial sample height, and ε(t n ) is the vertical strain of the sample under the normal force F sq (t n ) at the elapsed time “t n ”, measured using the LVDT. The shear modulus G* of the squeezed material can then be calculated by the slope of the trend line between the shear stress τ and strain γ values, obtained using Eqs. (4.21) and (4.22), respectively.

4.2.2.6

Selection of Geometry

Rheometers are used to identify the relationship between shear stress and shear rate. However, none of the rheometers measure directly shear stress and shear rate. Instead, torque or force, linear or rotational velocity measurements are registered and transformed into shear stress and shear rate values. The simplest geometry for rheological device would be two parallel plates, sliding over each other. The stress is the applied force divided by the contact area, while the shear rate corresponds to the velocity difference between the two plates divided by the separation distance of the plates (Fig. 4.9). However, this type of rheometer is neither practical nor feasible. The only two rheometer types suitable for sufficiently flowable cement-based materials that offer analytical transformation equations that are suitable for cement-based materials (with suspended particles) are the concentric (or coaxial) cylinder and the parallel rotating plate geometries. If the geometry of a rheometer is not similar to one of these two types, the determination of the real rheological properties is more challenging, as no analytical transformation exists. Outside these geometries, potential solutions to deduce rheological parameters may be achieved by comparative measurements

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Fig. 4.9 The parallel sliding plates rheometer has simple transformation equations but is practically very difficult to use

between different devices [20, 30, 43, 44], even like a truck mixer [43], conducting numerical simulations to understand governing shear stress–shear rate values [34, 45] or simply by using the raw data for a given rheometer without the need for transformation equations [23].

4.3 Viscoplastic Properties Measurements 4.3.1 Flow Curves The modelling and prediction of the steady state flow of cement-based materials require the determination of the shear stress τ versus shear rate γ˙ relationship. The plotting of this relationship is commonly named flow curve and can be modelled using viscoplastic constitutive laws, such as Bingham model, modified Bingham model or Herschel-Bulkley model. The determination of the flow curves is made using rheological testing, varying the applied shear rate and measuring the resulting shear stress. It is important to control the degree of structuration of the cementbased materials as it greatly influences the recorded results. This is why flow curves determination is carried out on in equilibrium samples as shown below.

4.3.1.1

Pre-Shear, Hysteresis, and Solicitation History

Cement-based materials at rest undergo particles flocculation, nucleation, and early cement hydration. Such transformation of the system changes the apparent macroscopic behavior of the material and induces an increase in the material static yield stress. A well-known consequence of that is the hysteresis in the recorded torque resulting from an upward and downward ramp of shear rate (Fig. 4.10). As can be observed in Fig. 4.10, the upward and downward curves are not superimposed. Actually, the upward ramp curve is greatly influenced by the initial state of structuration of the cementitious material that may have known a various and uncontrolled period of rest. Then, the first peak can be attributed to the breakdown of the cement particles structuration. On the other hand, the downward curve is related to

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Fig. 4.10 Comparison of downward and upward shear rate ramps. Effect of the microstructure build-up on the flow resistance

the steady-state odelled of the cement-based materials. This curve is obtained with a controlled state of the cement particles network (all bonds are broken during the upward ramp, for a given amount of shear) and can be odelled using a viscoplastic law. Another solution to obtain a controlled structure of cementitious particles is to perform a pre-shearing at the highest shear rate applied during the measurement. In this case, it is important to avoid inducing heterogeneities within the sample during this phase. It is also important to note that even with a downward curve, the recorded data may be influenced by the cementitious materials if the test lasts too long at low shear rate: the structural build-up can be seen as a competition between flocculation rate (and nucleation rate) and shear rate that breaks the structure. If a low shear rate is maintained for too long, the cementitious material will have enough time to create bonds and strength [8, 12].

4.3.1.2

Shear Ramp and Equilibrium State

During the steady-state properties measurement, the way the shear rate is varied is one of the most influential parameters of the test. Conventionally, the shear rate is incrementally varied at different levels by incrementally varying the rotational velocity of the measuring tool. The duration of the level must be sufficient in order to avoid transient effects and the measured torque must be on a plateau at the end of the increment. This equilibrium state provides a couple of values: the torque plateau and the imposed rotational velocity that can be used for the data analysis in order to plot the flow curve. An example of an incremental shear rate ramp can consist of ten decreasing constant rotational velocity plateaus (linear decrease for example from 1 rpm to 0.1 rpm wit 0.1 rpm incremental step). The duration of each plateau must be chosen in order to obtain a constant torque value at the end of the constant shear rate solicitation (steady state reached).

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89

Data Analysis and Transformation Equations

Rheometers record torque and angle of rotation during the measurement. Any other parameter can be computed using adequate transformation equations typically in the shape of “shear rate = constant x rotational velocity” and shear stress = constant x torque [45]. For cement-based materials, the calculation of both shear rate and shear stress in concentric cylinders and in parallel plates are not straightforward. Conventionally, the used equations available in handbooks [2, 29, 30] which have been developed for homogeneous materials and small gap, are not often suited for the case of cementbased materials. Integration procedures such as Reiner-Riwlin method, transforming best-fitting curve parameters (e.g., intercept with T -axis and slope) into rheological parameters (dynamic yield stress and viscosity), instead of a point-to-point transformation of T to shear stress and velocity to shear rate, are probably today the reference method for the determination of flow curves and viscoplastic rheological parameters [21, 22, 38, 46–48]. This method, initially developed for Bingham materials has been extended for modified Bingham [47] and Herschel-Bulkley models [21–23]. Another solution for data analysis is to use the methodology developed by [19, 27, 37]. It consists in computing mean shear rate values from data obtained from two increments of the rotational velocity. This method allows to verify “a posteriori” if plug flow occurs during the measurement and does not require to make assumption on the rheological model of the viscoplastic ehaviour. It is worth noting that if the material presents a high static yield stress value and dilatant ehaviour, shear localization may happen and create a fracture within the sample that may hinder the viscosity measurement as explained by Pierre et al. [37]. The authors proposed a criterion based on the comparison between the sample height and the material dynamic yield stress in order to verify if the material flows under its weight in order to avoid the fracture formation.

4.3.2 Static Yield Stress and Structural Build-Up Assessment As discussed in the previous section, the static yield stress is the stress required to break the cement particles network and make the cementitious material flowing. It is commonly measured using the so-called stress growth procedure [39–41]. This method uses vane and coaxial cylinders geometry and consists in applying a constant and sufficiently low shear rate values in order to make viscous effects negligible. The reported values between 10–2 and 10–1 s−1 can be found in the literature. It is important to note that the applied strain must be sufficient to really yield the material as pointed out by Nerella et al. [49]. If a torque peak T peak is recorded (sufficient strain reached) as shown in Fig. 4.11, static yield stress can be computed from a simple stress balance on the sheared surface:

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Fig. 4.11 Example of stress growth test results

τ0,s =

Tpeak   2π r 2 h + i 3r

(4.26)

where i is an integer value which can be 0, 1 or 2 depending on the shearing conditions at the up and bottom side of the vane or cylinder. For instance, if the cement-based material is sheared above and under the rotating tool i equals 2 (immersed tool). For slender vane or cylinder, i can be taken at 0. Measurement tests must be preferably performed on undisturbed samples left at rest during the targeted duration. However, recent studies have shown that the stress growth procedure can be carried out on the same sample without considerably altering the measured static yield stress (around 10% variation). Such methods using one unique sample, if less accurate, can be used to save materials and time [49–51]. Other methods can also be used to measure the static yield stress of the material, including the linear increasing stress sweep [52] and creep recovery test [7, 53]. Measuring the static yield stress at different resting time allows to describe the structural build-up kinetics of the resting cement-based materials which is a key phenomenon involved in the formwork pressure for self-consolidating concrete [54] or the stability of a printed structure during its fabrication [55–57]. For example, it is possible to compute the structuration rate Athix (Pa/s) [8] of the cement-based materials from the slope of the curve plotting the static yield stress versus the resting time as shown on Fig. 4.12.

4.3.3 From Cementitious Paste to Concrete—Different Scales of Study The difference in particle-size distribution changes the rheological study of cementitious paste, mortars, and concrete. The first consequence is linked to the volume

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Fig. 4.12 Computing the structural build-up rate Athix from the time evolution of the static yield stress

of sample required to obtain results representative of the material ehaviour. It is considered that the gap size of a rheometer geometry must be at least one order of magnitude larger than the largest particle size of the material. Then, studying the concrete rheology leads to preparing samples with volume of several dozens of liters. Moreover, adding centimetric particles to flowable cementitious paste may lead to test-induced heterogeneities than can lead to inaccurate measurements (this point will be discussed in the following section and in Chapter 5 dedicated to measurement errors). Different strategies to limit the volume of tested samples can be found in the literature. One solution is to make a rheological study on cementitious paste and then use homogenization theory to predict the effect of aggregate on the rheological ehaviour of mortars and concretes [40, 58]. The other solution is to substitute the gravel by sand having the same specific surface. This method is known as the concrete equivalent mortar method and can be used to efficiently design concrete mixtures with specified consistency [59].

4.3.4 Possible Measuring Artefacts Rheological measurements are relatively complicated to understand, and some parameters can result in wrong conclusions. This section introduces some of the major issues that can lead to errors during the rheological measurements, hence resulting in wrong interpretation of the obtained results [22]. Presented a general review of rheological principles and measurements and reviewed some of the major issues of rheology measurements to enhance the reliability of rheological measurements. A detailed discussion is provided in Chap. 5. A first measurement artefact is related to the behavior of the material. More precisely, does the mortar or concrete predominantly behave as a suspension or as a granular material? In the latter case, Coulomb’s friction law applies, shearing localizes in typically one plane and establishment of a well-defined shear rate is difficult.

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Similarly, even if the mortar or concrete behave predominantly as a suspension, the size of the measuring domain can be too small compared to the aggregate size, resulting in measurement and interpretation problems. Due to the thixotropic nature of the material, the measuring procedure needs special considerations. Pre-shear, flow curves, and loop curves are discussed in the pre-mentioned chapter (i.e., Chap. 5), and their parameters must be carefully chosen to ensure that thixotropic behavior does not influence the results, unless intended. Inappropriate selection of a measuring protocol could lead to the incorrect conclusion of shear-thickening. The static yield stress of the material can cause some concerns in using transformation equations from standard rheology textbooks, presented earlier in this chapter, or when considering the rheometer software generating shear stress, shear rate and viscosity values as a black box. In geometries based on concentric cylinders, a portion of the material may not be sheared during a part or even the entire measurement. This is called plug flow and needs to be accounted for during the calculation of the rheological properties. Parallel plate and cone and plate rheometers do not pose this issue. Due to the granular nature of the material, even when the mortar or concrete behaves predominantly as a suspension, there is a risk for gravity and shear-induced particle migration. The former is caused by the density difference between the particles and the suspending medium, the latter is caused by the differences in shear rate in the flow domain. The result of these effects is a non-homogeneous material in the rheometer, invalidating the experiment. The risks for non-homogeneity are increased with prolonged measuring time, larger particles, lower suspending medium viscosity and dynamic yield stress, and a larger shear rate. Another consequence of the granular nature of the material is the requirement for roughness on the rheometer surfaces (i.e., serrated surfaces) to avoid wall slip. However, one should be considerate for pressure effects on surfaces perpendicular to the intended flow direction, which could dominate the rheometer’s response. Other measuring issues can occur if there are some compositional changes in the material, or if the measurement could affect the quantities and ratios of constituent materials. Prime examples are the heat of vaporization, removing water when measuring at elevated temperatures and all uncertainties arising with quantity and size of entrained and entrapped air. For static yield stress measurements, there are concerns with successive measurements when using a single batch approach due to changes in shear history induced by previous measurements or local shear-induced particle migration, especially when the measurement continued too long after reaching the peak. Other risks arise due to the formation of a preferential shear plane during static measurements, or when determining the true applied shear rate during the experiment.

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References 1. Barnes HA, Hutton JF, Walters K (1989) An Introduction to Rheology. Elsevier Science B. V, Netherlands 2. Macosko CW (1994) Rheology: principles, measurements, and applications. Wiley-VCH, New York 3. Nair SD, Ferron RD (2016) Real time control of fresh cement paste stiffening: Smart cementbased materials via a magnetorheological approach. Rheol Acta 55(7):571–579 4. Saak AW, Jennings HM, Shah SP (2001) The influence of wall slip on yield stress and viscoelastic measurements of cement paste. Cem Concr Res 31(2):205–212 5. Schultz MA, Struble LJ (1993) Use of oscillatory shear to study flow behavior of fresh cement paste. Cem Concr Res 23(2):273–282 6. Ma S, Qian Y, Kawashima S (2018) Experimental and modeling study on the non-linear structural build-up of fresh cement pastes incorporating viscosity modifying admixtures. Cem Concr Res 108:1–9 7. Qian Y, Kawashima S (2016) Use of creep recovery protocol to measure static yield stress and structural rebuilding of fresh cement pastes. Cem Concr Res 90:73–79 8. Roussel N (2005) Steady and transient flow behaviour of fresh cement pastes. Cem Concr Res 35(9):1656–1664 9. Roussel N, Lemaître A, Flatt RJ, Coussot P (2010) Steady state flow of cement suspensions: A micromechanical state of the art. Cem Concr Res 40(1):77–84 10. Roussel N, Ovarlez G, Garrault S, Brumaud C (2012) The origins of thixotropy of fresh cement pastes. Cem Concr Res 42(1):148–157 11. Wallevik JE (2009) Rheological properties of cement paste: Thixotropic behavior and structural breakdown. Cem Concr Res 39(1):14–29 12. Roussel N (2006) A thixotropy model for fresh fluid concretes: theory, validation and applications. Cem Concr Res 36(10):1797–1806 13. Mantellato S, Palacios M, Flatt RJ (2019) Relating early hydration, specific surface and flow loss of cement pastes. Mater Struct 52(1):1–17 14. Lecompte T, Perrot A (2017) Non-linear modeling of yield stress increase due to SCC structural build-up at rest. Cem Concr Res 92:92–97 15. Subramaniam KV, Wang X (2010) An investigation of microstructure evolution in cement paste through setting using ultrasonic and rheological measurements. Cem Concr Res 40(1):33–44 16. Kruger J, Zeranka S, van Zijl G (2019) 3D concrete printing: A lower bound analytical model for buildability performance quantification. Autom Constr 106:102904 17. Perrot A, Pierre A, Vitaloni S, Picandet V (2015) Prediction of lateral form pressure exerted by concrete at low casting rates. Mater Struct 48(7):2315–2322 18. Schramm, G (1994) A practical approach to rheology and rheometry pp 20–25. Karlsruhe: Haake 19. Estelle P, Lanos C, Perrot A, Amziane S (2008) Processing the vane shear flow data from Couette analogy. Appl Rheol 18(3):34037–34041 20. Wallevik JE (2003) Rheology of particle suspensions—fresh concrete, mortar and cement paste with various types of lignosulfonates. Ph.D. Dissertation, Nor Univ Sci Technol, Norway. 21. Feys D, Wallevik JE, Yahia A, Khayat KH, Wallevik OH (2013) Extension of the Reiner-Riwlin equation to determine modified Bingham parameters measured in coaxial cylinders rheometers. Mater Struct 46(1):289–311 22. Wallevik OH, Feys D, Wallevik JE, Khayat KH (2015) Avoiding inaccurate interpretations of rheological measurements for cement-based materials. Cem Concr Res 78:100–109 23. Heirman G, Vandewalle L, Van Gemert D, Wallevik O (2008) Integration approach of the Couette inverse problem of powder type self-compacting concrete in a wide-gap concentric cylinder rheometer. J Nonnewton Fluid Mech 150(2–3):93–103 24. Pham BT (2019) Caractérisation du potentiel de ségrégation des particules colloidales et noncolloidales des suspensions cimentaires sous cisaillement. Ph.D. Dissertation, Univ Cergy Pontoise, France

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25. Yahia A, Khayat KH (2006) Modification of the concrete rheometer to determine rheological parameters of Self-Consolidating Concrete—Vane Device. In: Proceedings of the 2nd International RILEM Symposium on Advances in Concrete through Science and Engineering, September 11–13, 2006, pp 375–380 26. Barnes HA, Nguyen QD (2001) Rotating vane rheometry—a review. J Nonnewton Fluid Mech 98(1):1–14 27. Estellé P, Lanos C, Perrot A (2008) Processing the Couette viscometry data using a Bingham approximation in shear rate calculation. J Nonnewton Fluid Mech 154(1):31–38 28. Ovarlez G, Mahaut F, Bertrand F, Chateau X (2011) Flows and heterogeneities with a vane tool: Magnetic resonance imaging measurements. J Rheol 55(2):197–223 29. Steffe JF (1996) Rheological methods in food process engineering. Freeman press, East Lansing, MI, USA 30. Mezger TG (2006) The rheology handbook: for users of rotational and oscillatory rheometers. Vincentz Network GmbH & Co KG 31. Haist M, Link J, Nicia D, Leinitz S, Baumert C, von Bronk T, Cotardo D, Eslami Pirharati M, Fataei S, Garrecht H, Gehlen C (2020) Interlaboratory study on rheological properties of cement pastes and reference substances: comparability of measurements performed with different rheometers and measurement geometries. Mater Struct 53(4):1–26 32. Roussel N (ed) (2012) Understanding the rheology of concrete. Woodhead Publ Lted, Cambridge, UK 33. Perrot A, Lanos C, Estellé P, Melinge Y (2006) Ram extrusion force for a frictional plastic material: model prediction and application to cement paste. Rheol Acta 45(4):457–467 34. Perrot A, Lanos C, Melinge Y, Estellé P (2007) Mortar physical properties evolution in extrusion flow. Rheol Acta 46(8):1065–1073 35. Toutou Z, Roussel N, Lanos C (2005) The squeezing test: a tool to identify firm cementbased material’s rheological behaviour and evaluate their extrusion ability. Cem Concr Res 35(10):1891–1899 36. Rabideau BD, Lanos C, Coussot P (2009) An investigation of squeeze flow as a viable technique for determining the yield stress. Rheol Acta 48(5):517–526 37. Pierre A, Perrot A, Histace A, Gharsalli S, Kadri EH (2017) A study on the limitations of a vane rheometer for mineral suspensions using image processing. Rheol Acta 56(4):351–367 38. Moeini MA, Hosseinpoor M, Yahia A (2022) Yield stress of fine cement-based mortars: Challenges and potentials with rotational and compressional testing methods. Constr Build Mater 314:125691 39. Dzuy NQ, Boger DV (1985) Direct yield stress measurement with the vane method. J Rheol 29(3):335–347 40. Mahaut F, Mokéddem S, Chateau X, Roussel N, Ovarlez G (2008) Effect of coarse particle volume fraction on the yield stress and thixotropy of cementitious materials. Cem Concr Res 38(11):1276–1285 41. Perrot A, Lecompte T, Estellé P, Amziane S (2013) Structural build-up of rigid fiber reinforced cement-based materials. Mater Struct 46(9):1561–1568 42. Covey GH, Stanmore BR (1981) Use of the parallel-plate plastometer for the characterisation of viscous fluids with a yield stress. J Nonnewton Fluid Mech 8(3–4):249–260 43. Amziane S, Ferraris CF, Koehler EP (2005) Measurement of workability of fresh concrete using a mixing truck. J Res Nat Inst Stand Technol 110(1):55 44. Wallevik JE (2009) Development of parallel plate-based measuring system for the ConTec viscometer. In: RILEM international symposium on rheology of cement suspensions such as fresh concrete. Chicago, USA. 45. Feys D, Cepuritis R, Jacobsen S, Lesage K, Secrieru E, Yahia A (2018) Measuring rheological properties of cement pastes: most common techniques, procedures and challenges. RILEM technical letters 2:129–135 46. Reiner M (1949) Deformation and flow: an elementary introduction to theoretical rheology. HK Lewis

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47. Yahia A, Khayat KH (2003) Applicability of rheological models to high-performance grouts containing supplementary cementitious materials and viscosity enhancing admixture. Mater Struct 36(6):402–412 48. Yahia A, Khayat KH (2001) Analytical models for estimating yield stress of high-performance pseudoplastic grout. Cem Concr Res 31(5):731–738 49. Nerella VN, Beigh MAB, Fataei S, Mechtcherine V (2019) Strain-based approach for measuring structural build-up of cement pastes in the context of digital construction. Cem Concr Res 115:530–544 50. Ivanova I, Mechtcherine V (2019) Evaluation of structural Build-Up rate of cementitious materials by means of constant shear rate test: Parameter Study. In: Rheol Process Constr Mater. Springer, pp 209–218 51. Khalil N, Aouad G, El Cheikh K, Rémond S (2017) Use of calcium sulfoaluminate cements for setting control of 3D-printing mortars. Constr Build Mater 157:382–391 52. Stokes JR, Telford JH (2004) Measuring the yield behaviour of structured fluids. J Nonnewton Fluid Mech 124(1–3):137–146 53. Qian Y, Kawashima S (2018) Distinguishing dynamic and static yield stress of fresh cement mortars through thixotropy. Cement Concr Compos 86:288–296 54. Billberg PH, Roussel N, Amziane S, Beitzel M, Charitou G, Freund B, Gardner JN, Grampeix G, Graubner CA, Keller L, Khayat KH (2014) Field validation of models for predicting lateral form pressure exerted by SCC. Cement Concr Compos 54:70–79 55. Perrot A, Rangeard D, Pierre A (2016) Structural built-up of cement-based materials used for 3D-printing extrusion techniques. Mater Struct 49(4):1213–1220 56. Wangler T, Lloret E, Reiter L, Hack N, Gramazio F, Kohler M, Bernhard M, Dillenburger B, Buchli J, Roussel N, Flatt R (2016) Digital concrete: opportunities and challenges. RILEM Technical Letters 1:67–75 57. Roussel N (2018) Rheological requirements for printable concretes. Cem Concr Res 112:76–85 58. Martinie L, Rossi P, Roussel N (2010) Rheology of fiber reinforced cementitious materials: classification and prediction. Cem Concr Res 40(2):226–234 59. Schwartzentruber A, Catherine C (2000) Method of the concrete equivalent mortar(CEM)--a new tool to design concrete containing admixture. Mater Struct (France), 33(232), pp 475–482

Chapter 5

Challenges Encountered During Measuring Rheological Properties of Mortar and Concrete Dimitri Feys and Jon E. Wallevik

Abstract Performing rheological measurements of mortar and concrete is not a straightforward task as many challenges can alter or invalidate the outcome of a rheological experiment. This chapter summarizes the most common challenges for flow curve measurements, which are the type of flow behavior, achieving the reference state, plug flow, shear and gravity-induced particle migration, hydrodynamic pressure, heat of vaporization, correct choice of rheological transformation equations and model, air, and wall effects. Some of these challenges are also detailed separately for static yield stress measurements. For each challenge, the physical background, consequence on the measurement outcome and any detection or prevention strategy are described. To adequately perform rheological measurements, all challenges need to be addressed, which can be a daunting task as some prevention strategies can increase the risk for a different challenge to affect the measurement. Developing a suitable measuring and analysis procedure is a critical task to the success of rheological measurements of mortar and concrete.

As described in Chaps. 2 and 4, mortar and concrete are rheologically speaking complicated materials. Not only do they show non-Newtonian behavior, with the presence of a yield stress and potential non-linear flow curves, but the properties With contributions from: Irina Ivanova, Viktor Mechtcherine, Arnaud Perrot, and Ammar Yahia. I. Ivanova−Technical University, Dresden, Germany. V. Mechtcherine−Technical University, Dresden, Germany. A. Perrot−Universite Bretagne Sud, France. A. Yahia−Universite de Sherbrooke, Canada. D. Feys (B) Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO, USA e-mail: [email protected] J. E. Wallevik Division of Processing and Research, Icelandic Meteorological Office, Reykjavík, Iceland e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Sonebi and D. Feys (eds.), Measuring Rheological Properties of Cement-based Materials, RILEM State-of-the-Art Reports 39, https://doi.org/10.1007/978-3-031-36743-4_5

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are also dependent on time and shear: the shear-history. Furthermore, mortar and concrete are three phase fluids, composed of air, water and a large volume fraction of solid particles. These particles differ in reactivity, size, and shape, which affects the rheology of the material. The particle size can vary from several nanometer to millimeter or centimeter size. The particle size distribution can cover up to six orders of magnitude, substantially complicating the behavior. A platelet shaped colloidal nanoclay particle will show distinctly different behavior compared to a roughly spherical inert coarse aggregate. As such, due to the intrinsic composition and properties of mortar and concrete, performing rheological measurements is not a simple task. Chapter 3 has already described the variety in rheometers, for which the development has undergone a series of iterations to assure the equipment is able to adequately capture the rheological behavior. However, even with this research on optimizing the rheometers, one cannot consider those tools as black boxes. Numerous measurement artefacts can alter or invalidate the rheological test, and unawareness of those can lead to surprising or illogical results. The following chapter describes a number of measurement artefacts, their physical origin, and solution strategies proposed in literature on how to observe their (in)existence, and ways to avoid/minimize the impact of these artefacts on test results.

5.1 Homogeneous Suspension or Granular Material The first distinction that should be made is the nature of the movement. Does the mortar or concrete behave as a suspension, or does it act as a granular or a soillike material? This distinction is crucial to determine testing protocols and can have marked effect on the validity of the measurements and the interpretation of results. Furthermore, due to relatively large size of the aggregates, at which extent can the sample be regarded as homogeneous? In other words, what is the desired size of the flow domain and what are the consequences if the flow domain is too small?

5.1.1 Physical Background Granular movement is dominated by friction at contact surfaces of the aggregates. In order to secure movement of mortar or concrete, particles need to pass by each other in a rubbing fashion, where the dominant force is the frictional stress [1–3]. As for any frictional phenomenon, the sliding stress is proportional to the normal stress. As a result, the rheological properties of mortar or concrete dominated by friction are dependent on the height of the material on top of the measuring zone [4, 5], or they are dependent on any applied pressure [6, 7]. Browne and Bamforth have demonstrated this transition between a suspension and a granular material in the framework of pumpability, showing the difficulties in pumping of a granular concrete [6]. The transition from suspension flow to frictional behavior occurs at the critical volume

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fraction for friction, which is an aggregate parameter. Below this threshold, the aggregates in the mortar or concrete amplify the rheological behavior of the cement paste. Above this critical volume fraction, the yield stress increases dramatically in a short range of volume fractions, as demonstrated by Yammine et al. [8] and Perrot et al. [9]. Although more research is needed on the topic, flowable concrete mixtures, including self-consolidating concrete can be regarded as suspensions, while most conventional vibrated concrete mixtures are controlled by friction. The main exception to this classification would be pumpable conventional concrete, as the mix design is modified to avoid the occurrence of friction. When the material can be considered as a suspension, a homogeneous material is assumed to be able to apply conversion equations, and to interpret the data. Rheology textbooks recommend that the smallest dimension in the rheometer is larger than 10 times the particle size. However, if this needs to be applied on cement-based materials, very large geometries would be required, which could increase the negative effect of shear-induced particle migration and of plug flow. Early studies on suspensions show that the streamlines of the fluid surrounding particles are substantially deformed, leading to an increase in viscosity. If suspensions become more concentrated, there are significant interactions between particles, which at a certain volume fraction can lead to dilation effects: an increase in volume due to shearing. This is caused by particles needing to move perpendicular to the flow direction in order to be able to pass each other. To ensure a rheological measurement of a homogeneous material, the local disturbances caused by the presence of particles must be sufficiently “averaged” in the measured volume.

5.1.2 Consequences If mortar or concrete behaves as a granular material, the shearing is mostly localized in one shearing plane, accompanied by dilatancy of the system as particles need to pass each other. In this case, the measurement of viscosity in conventional rotational rheometers is not viable, as the macroscopic shear rate across the gap is localized in one microscopic shearing plane. A static yield stress can still be measured, as long as no preferential shearing plane has formed prior to the measurement, which may happen during pre-shearing. Other parameters related to flow can be determined with alternative devices, such as ram extruders or penetration devices for very stiff mixtures, or interface rheometers (see Chap. 7) to determine the lubrication layer properties [9, 10]. If the dimensions of the rheometer are not sufficiently large to average the local disturbances in the flow field in case of suspension flow, a lot of variation in torque is observed at constant velocity as well.

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5.1.3 Detection Detection of friction-dominated behavior is not straightforward in a rheometer. The following part is more inspired by experience of the authors of this chapter, rather than literature. A first indication of friction can be detected when intercept (G) is high and the slope (H) is low in the torque-rotational velocity-curve (T-N), although this observation is no guarantee for frictional behavior. Yammine et al. have shown a strong increase in concrete yield stress when the volume fraction threshold for friction was exceeded [1, 8]. Large fluctuations in the torque signal at constant velocity could also be an indication of friction, as well as vertical walls in the mortar or concrete when removing the inner cylinder after the measurement (Fig. 5.1). A separate way to detect friction, is to add a dispersing admixture to the mixture and detect changes in (static) yield stress or slump. If no significant changes are noted, the behavior is dominated by friction. In this case, standard rotational rheological measurements as described in this STAR do not apply. Extrusion measurements or experiments adapted from soil mechanics may be more suitable to characterize the material [9– 20]. Also, any of the following artefacts that are described in this chapter do not apply since they are based on mortar or concrete behaving as a suspension.

Fig. 5.1 Example of vertical standing walls after removal of the inner cylinder of the rheometer, which could be an indication of the presence of friction. Figure from Salinas [21]

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For mortar or concrete behaving as a suspension, large fluctuations in the measurements can be observed when there are too large particles, relative to the rheometer dimensions. Standard concrete rheometers have a recommended ratio of rheometer dimension to maximum particle size of at least 3 or 4. If rheological measurements are required on concrete mixtures with large aggregates, it is recommended to re-consider the effects on shear and gravity-induced particle migration first, and preferentially downscale maximum particle size. If necessary, an increase in rheometer gap could be considered as well, but temporary jamming should be avoided to ensure the load cell does not get overloaded.

5.2 Reference State As mentioned above, the rheological properties of mortar or concrete are dependent on the shear-history. As such, when performing a rheological measurement, the shearhistory can influence the results, and efforts must be taken to ensure consistency when comparing different measurements and when using the results of measurements in experimental and numerical applications.

5.2.1 Physical Background In theory, for every (macroscopic) shear rate applied for a sufficiently long time, there exists an equilibrium condition for which the rheological properties no longer vary with time [22–26], although this could be compromised in the longer term by hydration [27]. It should be kept in mind that there is a critical minimum shear rate below which shearing helps building internal structure [28]. In that case, the equilibrium condition is a fully structured material. Also, breakdown of internal structure typically happens faster than build-up [23]. As a consequence, when changing the shear rate, the material wants to evolve to its new equilibrium state. In case of breakdown (going from low to high shear rate), this evolution is typically relatively quick, but dependent on the difference between initial and equilibrium structure, this can take a time of the order of 101 s. In case of build-up (going from high to low shear rate), this evolution can be substantially longer. Although the flocculation time is of the same order of magnitude as breakdown (101 s), the rebuilding of hydration connections can take 102 –103 s [29]. To avoid the influence of breakdown on the measurements, it is commonly accepted to bring the material into its reference state first, and then perform the measurement quickly [30–67].

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Fig. 5.2 How non-equilibrium could lead to erroneous interpretation of shear-thickening. Figure adapted from Petit et al. [38], inspired by the results from Geiker et al. [33]

5.2.2 Consequences If breakdown is neglected, and the process is still ongoing during the measurement, the torque values at the beginning of the measurement period will be over-estimated compared to equilibrium values, with a decrease of this over-estimation with elapsed shearing time (Fig. 5.2). As a result of this artefact, the flow curve will most likely show non-linear shear-thickening behavior (Fig. 5.2) [33, 39, 68]. And although this behavior has been confirmed for concrete [39, 69], it is rather an exception than the rule, as it only occurs in specific conditions. If any shear-thickening is observed, and the results are to be reported, investigation of the equilibrium condition is essential to ensure the quality of the data.

5.2.3 Detection and Prevention To prevent the influence of breakdown on the rheological measurement, it is advised to pre-shear the sample at the highest possible shear rate that which will be used during the measurement. Typical pre-shear times reported in literature vary between 20 and 180 s for mortar and concrete [30–67], although extended shearing can be disadvantageous for shear and gravity-induced particle migration (see Sect. 5.4). It is thus advised to keep the pre-shear time to the minimum required to achieve equilibrium. Following the pre-shear, a down-curve (decreasing shear rate with time) is recommended. Ideally, a stepwise function of the shear rate with time is imposed, as this allows for an additional verification of the equilibrium condition at each shear rate step. A decreasing ramp in shear rate is also possible, but the verification purely depends on the observation of equilibrium during the pre-shear period. In case of

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a stepwise profile, one can manually remove each step which is not in equilibrium and proceed with the analysis with the remaining data points. In case of a ramp, the entire measurement would be invalid if no equilibrium is achieved in the pre-shear period. It should though be noted that when deleting a different number of steps in the stepwise procedure, not exactly the same reference state is imposed on the material for different measurements. The stepwise profile or decreasing ramp should be executed relatively quickly to reduce the risk of particle migration. However, it should be noted that the shear rate during the pre-shear should (at least) be the highest shear rate applied during the measurement, and it is advised that no resting period be inserted between the pre-shear and the measurement. Several authors have reported the use of loop curves in an attempt to quantify the flow curve and any thixotropic behavior simultaneously [70–80]. This is not without risk, especially when the duration of each step in the loop curve is short. It is likely that equilibrium is not yet achieved at the highest shear rate in the loop curve, compromising the flow curve measurement. Here, one can apply the same strategy as described above by eliminating any step in the down curve which has not yet achieved equilibrium. When using up and down ramps, that verification is not possible, and indirectly invalidates the flow curve measurement. According to the authors of this chapter, the only solution to use a loop curve to combine flow curve and thixotropic measurements, is to have a tunable (or pre-identified) sufficiently long step at the highest shear rate to ensure equilibrium before the down curve is started.

5.3 Plug Flow In concentric cylinders rheometers, and theoretically also in capillary rheometers, the shear stress profile is a non-constant function over the flow domain [81]. If the shear stress does not exceed the yield stress in a part of the flow domain, the transformation equations need to be adjusted to accommodate for this measurement artefact [47, 49, 68, 82]. For parallel plate rheometers, this effect should not occur, as this rheometer principle imposes a velocity function over the gap, guaranteeing a non-zero shear rate in the entire flow domain, except at the exact central axis of the rheometer.

5.3.1 Physical Background In concentric cylinders rheometers, the shear stress evolves as a function of 1/r2 . The highest shear stress is always occurring at the inner cylinder, the lowest at the outer cylinder. If the shear stress at the outer cylinder is smaller than the yield stress, part of the flow domain does not shear. This means that in this zone, called the plug zone, the rotational/angular velocity is either zero (in the case that the inner cylinder rotates), or constant and equal to the rotational/angular velocity of the outer radius

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Fig. 5.3 Presence (left) and absence (right) of plug flow in a concentric cylinders rheometer. If the shear stress is lower than the yield stress, plug flow occurs. Ωo stands for the angular velocity at the outer cylinder. Figure adapted from Feys et al. [47]

(in the case that the outer cylinder rotates). The division of the plug and shearing zones occurs at the plug radius (Rp ), which can be calculated based on the torque value (T ) and the yield stress of the concrete (τ 0 ) as: Rp =

√

T /2π τ0 h

(5.1)

For any radius larger than Rp , the material is not sheared. Note that Rp is a function of T and is thus a variable during the measurement. If a stepwise measurement is executed, Rp changes with each change in rotational velocity. If Rp > Ro , there is no plug flow (Fig. 5.3).

5.3.2 Consequence If plug flow is neglected, the transformation of the results into fundamental units is compromised. Regardless of whether a point-to-point transformation or an integration approach (e.g., Reiner-Riwlin) is used, the transformation requires the boundaries of the flow domain to be used in the equations. Neglecting plug flow will result in a lower estimation of the shear stress-shear rate relationship for the part of the measurement in plug flow. This can lead to apparent shear-thinning behavior, or it can enhance the observation of shear-thinning (Fig. 5.4). Manually transforming the raw data into fundamental units allows for this correction. However, automatic transformation equations in most rheometer software do not account for this effect.

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Fig. 5.4 Transformation from raw data to fundamental units with plug flow correction using the Bingham model. The two points at the lowest angular velocities are in plug flow. The percentages indicate the deviation from the best-fitting linear relationship [58]

5.3.3 Detection and Prevention The likelihood of plug flow increases with increasing yield stress, decreasing viscosity, increasing gap in the rheometer and at low rotational velocity. Plug flow cannot be prevented without compromising the quality of the measurement. Deleting points in plug flow or adjusting the measurement procedure to avoid plug flow could lead to large extrapolation ranges to obtain the dynamic yield stress, which affects the accuracy of this value. Plug flow can be easily detected by calculating Rp at each T value. In fact, one can calculate Rp first at the lowest T value. If Rp remains larger than Ro , there is no plug flow, and no correction is needed. If plug flow occurs, an iterative procedure is necessary, as the correction requires the input of the unknown yield stress of the material. Based on an initial set of rheological properties, one can calculate Rp at each velocity step, adjust the flow domain and the shear rate equation (Eq. 5.2 is for Bingham materials), and re-calculate the rheological properties. In Eq. (5.2), Rs represents the outer boundary of the flow domain: Rp in case of plug flow, Ro in case the entire domain is sheared. γ˙ (Ri ) =

2 Ri2

(

1 1 − 2 Rs Ri2

)−1 ( ( )) τ0 τ0 Rs 2π N + ln − μ Ri μ

(5.2)

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If the initial values are properly chosen, convergence should be achieved [68, 82]. In case of materials with high yield stress and low viscosity, or in case non-linearity is observed, this correction can be more of a challenge [47].

5.3.4 Size of Flow Domain Especially for high yield stress—low viscosity materials, a verification of the size of the flow domain may be useful after plug flow correction. The distance between Ri and Rp should be compared to the maximum particle size of the material. If the particle size is larger than the flow domain, the measurement is compromised most likely due to shear-induced particle migration (Fig. 5.5) [58]. As such, measurements of conventional vibrated concrete, even when the concrete behaves as a suspension, might not be straightforward to execute. An alternative measurement with a different rheometer might be required in this case, although this does not guarantee the validity of the results. The other condition, in which the particle size is smaller than the flow domain does not guarantee that no shear-induced particle migration has occurred.

Fig. 5.5 Boundary between sheared and unsheared zones indicates whether the thickness of the sheared zone is sufficiently large. Measurements performed in a coaxial cylinders rheometer with Ri = 63.5 mm, Ro = 143 mm, and a maximum size aggregate (Dmax ) of 12.5 mm [68]

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5.4 Particle Migration 5.4.1 Gravity-Induced Particle Migration 5.4.1.1

Physical Background

The cause for gravity-induced particle migration is the density difference between the components in the material. Considering concrete as coarse aggregates suspended in mortar, or all aggregates suspended in paste, the particles are heavier than the medium which results in sinking of the particles. In case of lightweight aggregates, this would induce floating of the aggregates if the particles are lighter than the medium. The stabilizing forces are the yield stress and its increase with time due to internal structure development, and the particle lattice effect [83–86]. The particle lattice effect can stabilize particles which would be unstable individually in the suspending medium. An elevated viscosity reduces the velocity at which the particles sink [87–90], which aids in stabilization as the yield stress increases with time at rest. However, under shearing conditions, the yield stress is exceeded in at least a part of the measurement domain, removing the primary stabilizing force. It has been shown that particles sink faster with an increase in applied shear rate, and their settling speed is reduced with increasing yield stress of the suspending medium [91]. However, particles settling cannot be avoided when the yield stress is exceeded. As such, during a dynamic rheological measurement, the particles are intrinsically unstable. The effect is identical to dynamic segregation during other placement operations with cement-based materials [92–94].

5.4.1.2

Consequence

The consequence of gravity-induced particle migration is that a concentration gradient of particles is generated over the vertical dimension of the rheometer. Whether this leads to an increase or decrease in rheological properties depends on whether the bottom zone with more particles [90, 91, 95], or the top zone with less particles is more prominent in the effective flow domain. As such, the outcome depends on the geometry. If there is significant particle migration, this will invalidate the measurement without the possibility to salvage the results.

5.4.1.3

Detection and Prevention

The detection of gravity-induced particle migration is mainly visual in nature, as one needs to assess bleeding and segregation after the measurement. If a significantly larger number of particles can be found at the bottom of the rheometer bucket, the measurement is likely to be invalid. More elaborate detection procedures can be performed, by changing the position of the inner cylinder in the rheometer [96], or

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by a washing procedure to determine coarse aggregate volume fractions in samples from the top and bottom of the rheometer after testing. Gravity-induced particle migration cannot be prevented, as the yield stress needs to be exceeded to perform a measurement. The settlement speed of the particles increases with the decrease in viscosity of the suspending medium, the increase in particle size, and a reduced particle lattice effect [83, 84]. To prevent gravity-induced particle migration, the main solution is to limit measuring time, including the pre-shear period, as it is a dynamic process. Reducing the shear rate or rotational velocity can be beneficial as well.

5.4.2 Shear-Induced Particle Migration When a concentrated suspension is subjected to a shear-rate gradient, particles tend to migrate away from the zones with the highest shear rates [97, 98]. It is this mechanism that eases/enables pumping of concrete by forming a thin lubricating layer at the vicinity of the pipe wall [99–101]. This layer is depleted of coarse aggregates and has, potentially, a reduction in the quantity of coarse sand particles, causing a decrease in rheological properties. As a consequence, a higher shear rate is observed in this layer, resulting in a larger flow rate at equal pressure loss. However, if this same phenomenon would occur during rheometer tests, the entire data set could be compromised.

5.4.2.1

Physical Background

The physical cause of shear-induced particle migration is an increased collision frequency between particles in zones with high shear rates compared to zones with low shear rates [98]. If a shear rate gradient is applied to a suspension, particles will be bumped into zones with lower shear rates. With increased migration, the volume fraction of particles increases in the zones with low shear rates, increasing the collision frequency on that side of the particles, resulting in a countering effect. Similarly, due to the increased rheological properties as a consequence of the increased concentration of particles, the particles are pushed back into zones with higher shear rates. After sufficient time (or more correctly: strain), these motions cause a dynamic equilibrium in particle fluxes, resulting in a concentration gradient of particles in the flow domain. A second theory for shear-induced particle migration does not require physical collisions but attributes the particle migration due to the chaoticity of the hydrodynamic interactions in concentrated suspensions, amplifying small perturbations to particle motion [102].

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The rate of shear-induced particle migration is proportional to the particle radius squared, causing coarse particles to migrate (much) faster than fine particles [98, 103]. If a particle size distribution is used in the suspension, the coarser particles will cause the main observation of migration, potentially reducing or hindering the movement of smaller particles.

5.4.2.2

Consequence

The consequence of shear-induced particle migration is a non-homogeneous distribution of aggregates in horizontal direction in the flow domain of the rheometer. As particle migration is dependent on the particle size squared, concrete is much more susceptible to shear-induced particle migration than mortars or cement pastes, although the effect cannot be excluded for the latter two systems. If migration has occurred before the measurement (during the pre-shear period), lower rheological properties, compared to the homogeneous system, will be measured. If the migration occurs during the measurement, apparent shear-thickening could be observed [68].

5.4.2.3

Detection and Prevention

Shear-induced particle migration is probably the most difficult artefact to detect. Unfortunately for concrete measurements, its occurrence is possible (or even likely) within the duration of the measurements. Interface rheometers, used to mimic pumping conditions, can create the lubrication layer in a duration of the order of 100 –102 s. It should be noted that shear-induced particle migration was enhanced due to the smooth surface for interface rheometers, but the speed at which it develops is indicative for the risk. Feys and Khayat have executed a number of measurements of mortar and concrete mixtures with different consistencies and aggregate contents to evaluate the occurrence of shear-induced particle migration [58]. A part of the measurements consisted of comparing the rheological properties of mixtures with the standard ConTec Viscometer 5, and with the same rheometer with a slightly larger bucket. As the hardware for the measurements (apart from the bucket) was identical, measurements with the standard and larger bucket should, statistically, be identical. This was generally true for the mortar, indicating either no particle migration, or equal particle migration in the system. However, for the concrete mixtures, a decrease in rheological properties was observed for the larger geometry, indicating potentially more particle migration due to a larger gap width. The difference between the two geometries was enhanced with increased coarse aggregate content and with increased yield stressto-plastic viscosity ratio. This latter term is related to the potential and magnitude for plug flow. Preventing particle migration is impossible, due to the nature of the phenomenon and the principles of rheometer experiments. The effect is unavoidable, but its impact could be limited. Reducing the duration of the experiment could limit the effect,

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although no guarantee. As such, an experiment with a pre-shear period followed by short steps is preferred to an experiment without pre-shear and longer steps. Secondly, the applied rotational velocity should be limited, as the effect is dependent on the shear rate gradient. Reducing the rotational velocity also reduces the number of collisions, slowing down the effect, but not preventing it. Following the results from Feys and Khayat, reducing the maximum particle size will extend the measuring period during which the material is minimally affected by shear-induced particle migration. Performing rheological experiments on concrete mixtures with large coarse aggregates is not recommended due to the dependency of shear-induced particle migration on the particle size squared, and due to the larger rheometer size, increasing the room for particles to migrate and the potential for plug flow.

5.5 Effect of Hydrodynamic Pressure in Rheological Devices The hydrodynamic pressure is an important factor to an object every time there is a flow normal to it (here, the object is the sensor system of a rheometer). In some rheometers, the flow will be able to act perpendicular to the given blade system and thus resulting in an important pressure contribution to the registered torque. This is an important factor for 4-blades vane rheometers, while not so significant in other types of rheometers. Examples of the latter are the parallel plates rheometer and the concentric cylinders rheometers, in which registered torque is largely dominated by the shear stress. Thus, there exists a fundamental physical difference between rheometers, which can be important to understand.

5.5.1 Physical Background For the simple case of flow of cement-based materials in a “wind tunnel”, where an arbitrary object is present in the flow path, two types of forces will apply to that object, namely a viscous force and a pressure force (or force by the hydrodynamic pressure). To correctly calculate the total force applied to this object, the theory of continuum mechanics must be applied. First, this is done by calculating the traction vector [104, 105] applied to the object, given by t = n · σ = n · (– p I + T), where n is the unit normal vector on the surface of the object (pointing outward into the fluid), σ is the (total) stress tensor of the flow, p is the hydrodynamic pressure, I the unit dyadic and T is the extra stress tensor [106]. Thereafter, the overall force is calculated by the following integration: ¨ Ftot =

t d A = Fv + F p A

(5.3)

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where the term A represents the area of the object and dA the corresponding integrand. Furthermore, the term Ftot is the total force applied to the object, Fv is the viscous contribution and Fp is the contribution by the hydrodynamic pressure. It should be clear that the force by the viscous contribution has both a normal (i.e., perpendicular) component as well as a parallel (i.e., shear) component, while the force by pressure Fp consists only of a normal component (i.e., acts only normal to the surface of the object surface). An example of the above case is shown in Fig. 5.6 (OpenFOAM calculation). In this case, a Bingham fluid is flowing past an elliptic shaped object (14 cm in height, 12 cm wide and 16 cm in length), with the yield stress τ 0 = 94 Pa and a plastic viscosity of μ = 47 Pa s. With an inflow velocity of 0.5 m/s, the viscous force is F vx = ix · Fv = 34 N and the force by pressure is F px = ix · Fp = 20 N, c.f. Equation (5.3). The term ix is the unit vector in the x-direction (i.e., in the flow direction). The sum is F x = F vx + F px = 54 N. The point with the above exercise is to show that a large portion of the total force F x = F vx + F px is attributed to the effect from hydrodynamic pressure. In some rheometers, the flow will be able to act perpendicular to the given blade system and thus result in an important pressure contribution in the same manner as explained above. An example of this is the 4-blades rheometer, which are frequently used to obtain rheological flow parameters of the cement-based materials. As shown

Fig. 5.6 Flow of Bingham fluid past an elliptic shaped object: Streamlines with speed color (blue 0 m/s, red 0.3 m/s); hydrodynamic pressure p in Pa (reference value is set as zero at the outflow √ area); von Mises shear stress T : T/2 in Pa

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in Fig. 5.7, the device consists of an impeller (the rotor) rotating in a cylinder geometry (the stator). With rotation, the impeller’s vane blades will both push and drag the fluid, resulting in non-uniform hydrodynamic pressure exerted on the blades [107, 108]. Thus, in addition to the viscous shear stress, this pressure will influence the measured torque registered by the rheometer (i.e., influence the shaft torque), basically in the same manner as described for the case of Fig. 5.6. Similar to Eq. (5.3), the torque is calculated with the following equation [107, 108]:

Fig. 5.7 Three different types of 4-blades vanes rheometers: Top left is from Wallevik [107], top right is from Wallevik [108] and the bottom illustration is reproduced from Fig. 3.7 in Sect. 3.2

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¨ Ttot =

r × td A = Tv + Tp

(5.4)

A

where the term A represents the area of the object (say, the blade system) and dA the corresponding integrand. The term r is the vector location of the solid boundary of the impeller system and t is traction vector, previously explained. In the above equation, the term T tot is the total shaft torque, T v is the viscous contribution and T p is the contribution by the hydrodynamic pressure. Three different vane rheometers are shown in Fig. 5.7. The top left illustration shows the velocity vector of the cement-based material, while the remaining illustrations show iso-plots of the hydrodynamic pressure acting on the vane blades. For the top right illustration of Fig. 5.7, the edge-to-edge diameter of the blades (including the shaft diameter) is only 28 mm and thus apply for finer cement suspensions. The red surface represents 20 Pa gage (contributing to friction), while the blue surface represents –20 Pa gage (contributing to drag) [108]. In this particular example, the material model is Herschel-Bulkley with the yield stress τ 0 = 0.1 Pa, consistency factor k = 10 Pa sn , consistency index n = 0.5 and rotational velocity 0.5 rps. In this case, the effect of hydrodynamic pressure constitutes for about 80% of the overall torque T tot registered by the rheometer [108]. The same conclusion is made for the concrete vane rheometer shown at the bottom in Fig. 5.7. In this case the edge-to-edge diameter of the blades (including the shaft diameter) is 127 mm. The material model is Bingham, with plastic viscosity μ = 120 Pa s, yield stress τ 0 = 50 Pa and rotational velocity at 0.6 rps. With these parameters, the red surface represents 850 Pa gage (contributing to friction), while the blue surface represents –850 Pa gage (contributing to drag).

5.5.2 Consequence Analysis has shown that some rheological devices, like the vane system, are very much influenced by the hydrodynamic pressure [107, 108]. Other devices, like the concentric cylinder system, are not significantly affected by this [47, 109, 110] (for the interested reader, the similarity between the vane and the coaxial cylinders system is available in Zhu et al. [111]). However, it should be clear that the effect of hydrodynamic pressure does not fail the vane system in any way. This is because in Wallevik [107, 108], it has been shown that there is a direct link between the hydrodynamic pressure and the apparent viscosity η. Thus, during a rheological test, there will be a direct relationship between the output of the vane rheometer and the apparent viscosity η. For other pressure-based devices, this is possibly also the case, but this needs to be verified.

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5.5.3 Detection Since the registered shaft torque is the result of the combined effect of the viscous stress and hydrodynamic pressure, one cannot differentiate between the two. Only the total torque T tot expressed by Eq. (5.4) is registered by the vane rheometer and not the two effects of T v and T p . If the effect of hydrodynamic pressure T p is to be specifically measured, the vanes must be mounted with collection of pressure sensors. The network-of-pressuresensors-system would have to be able to resolve hydrodynamic pressure as a function of location on the blades in such manner that the integration in Eq. (5.4) could be estimated with confidence (i.e., the pressure-sensor-network would have to be of high resolution).

5.6 Uncontrolled Reduction in Temperature Due to Heat of Vaporization In some cases, it is desirable to make rheological laboratory measurements in the higher temperature range, for example at 40 °C, to emulate prevailing conditions where rheological values are needed. The obvious approach would be to store everything (all materials, aggregates, cement, water, etc.) in a 40 °C room, as well as mixing and measuring in the same environment. The water has to be stored in a closed container. Although, all constituents (of the cement-based material) have separately the same temperature (here 40 °C), as soon as mixing starts (say in Gustav Eirich- or Hobart mixer), the mixture will start to cool down by the heat of vaporization [112]. This is an uncontrolled reduction in temperature, which can compromise the results, sometimes designated as “evaporative cooling” [112]. Depending on the relative humidity, the drop in temperature can be several degrees Celsius. More specifically, during mixing, a larger area of the test sample becomes exposed to the air, meaning a larger rate of vaporization and thus a faster cooling (relative to if the material is at rest). During a rheological measurement, the test sample is usually less exposed to the air (relative to the mixing phase), and thus less vaporization may occur. Thus, the highest danger for losing control over temperature is during the mixing phase. One way to solve this is by increasing the relative humidity in the laboratory close to 100%, and by this avoiding vaporization altogether. However, such working conditions for the scientist as well as for the electrical equipment would be impossible. Another way is by keeping the mixer in a closed container with 100% relative humidity. In any case, the temperature reduction will decrease with higher relative humidity of the air.

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Fig. 5.8 The parallel sliding plates rheometer has simple transformation equations but is practically difficult to use

5.7 Rheometers and Transformation Equations 5.7.1 Rheometer Geometries Rheometers are used to determine the rheological properties of different materials, thus to identify the relationship between shear stress and shear rate. However, none of the rheometers measure directly shear stress and shear rate. Instead, torque or force, linear or rotational velocity measurements are registered and transformed into shear stress and shear rate values. The simplest geometry for rheological device would be two parallel plates, sliding over each other. The stress is the applied force divided by the contact area, while the shear rate corresponds to the velocity difference between the two plates divided by the separation distance of the plates (Fig. 5.8) [81]. However, this type of rheometer is neither practical nor feasible. The only two rheometer types that offer analytical transformation equations that are suitable for cement-based materials (with suspended particles) are the concentric (or coaxial) cylinder and the parallel rotating plate geometries. If the geometry of a rheometer is not similar to one of these two types, the determination of the real rheological properties is more challenging, as no analytical transformation exists. Outsides these geometries, potential solutions to deduce rheological parameters may be achieved by comparative measurements between different devices [113], conducting numerical simulations to understand governing shear stress—shear rate values [114] or simply by using the raw data for a given rheometer without the need for transformation equations.

5.7.2 Importance of Transformation Equations When a concentric cylinder rheometer is employed, shear stress can be calculated as [82]: τ (r ) =

T 2πr 2 h

(5.5)

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where τ = shear stress (Pa), T = torque (Nm), r = radial parameter (m) and corresponds to the spread between inner radius Ri and outer radius Ro and h = height of the cylinder (m). The shear rate is, however, not straightforward to calculate. As the shear stress already evolves with 1/r 2 , the shear rate is also a complex function of r, dependent on the (unknown) rheological model. In the rheology literature, two solutions are proposed: • The gap is considered small (Ri /Ro ≥ 0.99), then the shear rate can be approximated as constant in the gap. In this case [81, 115]: γ (Ri )= ˙

2ωo Ro2 Ro2 − Ri2

(5.6)

where ωo = angular velocity at the outer cylinder (rad/s). Note that the equation is similar if the inner cylinder rotates. • If the gap is not small, the shear rate calculation becomes more complex [81]: 2ωi γ˙i = ( ( )2/n ) n 1 − RRol

(5.7)

Supposing the inner cylinder rotates in this case, and with n=

dln(T ) dln(ωi )

(5.8)

In fact, n is the slope of the T – ω line in a log–log scale. It corresponds thus to the power “n” in the power-law model. The use of the small-gap equation Eq. (5.6) can be acceptable if the fluid is close to Newtonian (i.e., ratio of yield stress to plastic viscosity τ 0 /μp is low). But such condition rarely applies for cementitious materials, especially when investigating rheological behavior as a function of time from water addition. This equation is also applicable for small-gap conditions when the ratio Ri /Ro is close to 1 (say 0.99). But such a configuration cannot be used for mortar or concrete, as the aggregate particles will be too large for the device. Furthermore, even the large-gap equation (Eq. (5.7)) is not straightforward to use in case of a yield stress materials, as “n” depends on the rotational velocity. Similar problems are experienced in parallel rotating plate rheometers, in which the determination of the shear stress becomes challenging. However, there is an alternative solution which does not require the calculation of the shear rate in the gap of the rheometer. This transformation procedure is called the Reiner-Riwlin equation (not to be confused with Reiner-Rivlin equation, which is a constitutive equation [82]). The derivation of the Reiner-Riwlin transformation equations is, for example, available in Feys et al. [47], Wallevik [82], Heirman et al. [116],

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and it transforms a relationship between torque and rotational (or angular) velocity into a relationship between shear stress and shear rate. It does not provide a point-topoint transformation, but it expresses the obtained relationship in fundamental units (Pa and Pa s): (

) − R1 2 ( o )G τ0 = 4π hln RRoi ( ) 1 1 2 − 2 Ri Ro H μ= 8π2 h 1 Ri 2

(5.9)

(5.10)

where G and H are determined from the torque—rotational velocity relationship (T = G + H N). In order to illustrate the utility of the Reiner-Riwlin equation and the importance of using adequate set ups in rheological testing, a series of experiments was carried out using a commercially available rheometer to evaluate viscosity of a vegetable oil that exhibits a Newtonian behavior. The data obtained using coaxial cylinders rheometer of different geometries are reported in Table 5.1 [68]. Data obtained with the two narrow gap systems with Ri /Ro of 0.922 are similar even though one inner coaxial cylinder had a smooth surface compared to a sandblasted one for the other system. The wide-gap system had a Ri /Ro ratio of 0.576 and smooth inner surface. A linear decrease in shear rate from 100 to 1 s−1 during 60 s was used, registering data every 0.5 s. Data between 10 and 90 s−1 were retained for analysis. Four procedures were used to determine viscosity, as follows: • Average of all apparent viscosities, based on the viscosity output of the rheometer. • Average of all apparent viscosities, based on narrow gap equation to calculate shear rate. • Average of all apparent viscosities, based on large gap equation to calculate shear rate (n = 1, as the material is Newtonian). • Calculation of the (differential) viscosity, based on the T –N relationship and applying the Reiner-Riwlin equation for various geometries. Since the material is Newtonian, the apparent viscosity and the differential viscosity, which is the slope of the line at each shear rate, are equal. Technically, Table 5.1 Different coaxial cylindrical geometries used to evaluate commercially available rheometer for polymers and similar materials [68] Smooth CC narrow

Smooth CC wide

Sandblasted CC narrow

Inner radius (mm)

13.335

8.329

13.331

Outer radius (mm)

14.458

14.458

14.457

Height (mm)

40.001

25.019

40.002

0.922

0.576

0.922

Ri /Ro (−)

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Fig. 5.9 Evaluation of viscosity of a Newtonian vegetable oil with the three different geometries from Table 5.1 and the four analyzing procedures discussed [68]

all measurements should deliver the same viscosity value, or at least a viscosity value independent of the geometry. However, Fig. 5.9 shows the opposite, clearly indicating significant problems interpreting the data when narrow gap equations are used, and when the rheometer is used as a black box system. The Reiner-Riwlin procedure appears to deliver the smallest variation in viscosity assessment. It should be noted that these observations were made with a “standard rheometer” from the polymer industry, and that a Newtonian material was used. As is shown further, complexity increases when using non-Newtonian materials, such as cement-based materials, and more complex rheometers. The above example is carried out for coaxial cylinders rheometer, not applicable for mortar or concrete. For concrete/mortar rheometers (i.e., of much larger dimension), the implementation of the wrong shear rate formulas (as shown above) can lead to more dramatic errors. For example, for typical rheological parameters for concrete (e.g., μ = 25 Pa s and τ 0 = 385 Pa), the variation of torque (T ) as a function rotational velocity (N) can be illustrated in Fig. 5.10a. The slight non-linearity in the curve is due to plug propagation. As already mentioned, it is easy to convert the torque values T into shear stress, τ. Because of the difficulties in generating correct shear rate values, γ˙ , software programmers are tempted to use equations like proposed by HAAKE, i.e., Eq. (5.6) [115]. Figure 5.10b shows the error in using this approach, with the line marked as “wrong”. For comparison, the line marked as “right” is calculated using plug flow correction. By curve fitting (in the least-squares sense) the “wrong” line, the obtained plastic viscosity is μ = 29.3 Pa s and yield stress τ 0 = 502 Pa (plastic viscosity is overestimated by 4.3 Pa s and the yield stress by 117 Pa). Doing the same for the “right” line, the correct values are obtained, namely μ = 25 Pa s and τ 0 = 385 Pa.

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Fig. 5.10 Illustration a: raw data in rheometer for concrete with μp = 25 Pa s, τ 0 = 385 Pa, Ri = 100 mm, Ro = 145 mm, and h = 199 mm. Illustration. b: “right” and “wrong” interpretation of data as a consequence of the transformation equations

The problem of using the plug flow correction in generating the “right” curve in Fig. 5.10b, is that it relies on information that the rheometer is trying to obtain (i.e., an unknown quantity). Also, it assumes that the plug radius (Rs ) is known at each rotational velocity beforehand (if plug is present). By plotting the measured torque T as a function of rotational velocity N (as done in Fig. 5.10a), one can connect these measured values with a straight line: T = G + H N. From its slope H and its point of intersection with the ordinate G, one can calculate the plastic viscosity μ and the yield stress τ 0 by the above-mentioned Reiner-Riwlin equation (i.e., Eqs. (5.9) and (5.10)). Here, the presence of plug has been ignored altogether by putting Rs = Ro in the two above equations. This will generate some error in the analysis. By Eqs. (5.9) and (5.10), the obtained plastic viscosity is μ = 29.3 Pa s and yield stress τ 0 = 354 Pa. That is, the plastic viscosity is overestimated by 4.3 Pa s (same error as before by Eq. (5.6)), and the yield stress is underestimated by 31 Pa. Previously by Eq. (5.6), the yield stress was overestimated by 117 Pa, thus Eqs. (5.9) and (5.10) represent a significant improvement.

5.7.3 Importance of Rheological Model As discussed in Chap. 2, there are occasions where the rheological results do not follow the Bingham model. Both shear-thinning and shear-thickening have been confirmed in literature for mortar and concrete. Applying a linear model to a nonlinear data set could be an adequate solution, as long as the deviation from linearity is not too pronounced. However, as soon as the non-linearity is no longer negligible, applying the Bingham model will deliver some non-desirable data. The yield stress is the main parameter affected by applying Bingham on a non-linear data set. In case of shear-thinning, the linear model over-estimates the yield stress, while for shear-thickening, the Bingham equation delivers a lower yield stress. In some cases,

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especially with more severe shear-thickening and low yield stress materials, the Bingham model can deliver a negative value for the yield stress, which is physically impossible. Feys et al. compared four different yield stress values generated by different models applied to the same data set [47]. They also developed a procedure to investigate which model would be most applicable to their mixtures, by comparing the yield stress values from the rheometer to the yield stresses derived from the slump flow data. If the ratio of rheometer yield stress to slump flow yield stress does not show an increasing or decreasing trend with the degree of shear-thickening, an applicable model is found. In case a non-linear data set is obtained, the transformation of data might become even more complicated. As mentioned in Sect. 5.3, the correction for plug flow for non-linear rheological properties seems to be mathematically and computationally a lot more challenging. If someone prefers to employ the large gap equations for shear-rate transformation in concentric cylinders, similar issues with yield stress as for the Bingham model arise. For the Reiner-Riwlin equations, extensions for the Hershel-Bulkley and modified Bingham model were developed. Due to the sensitivity of rheological parameters to the choice of rheological model, one must be consistent in applying the same model when comparing different measurements.

5.8 Air As mentioned in the introduction of this chapter, cement-based materials are threephase materials, containing solid particles, liquid, and air. Of those three components, the air content and air bubble distribution are the least controlled as they are strongly dependent on mixing. One can increase the air content by adding an air-entraining agent, and reduce air content by consolidation, but often, the increase or decrease in air content are not as precisely controlled as for any other ingredient.

5.8.1 Physical Background The main concept of adding air is that it decreases yield stress and viscosity [25]. However, the behavior of the air bubbles depends on the capillary number (Ca), which is the ratio of the shearing forces to the surface tension [117]: Ca =

aηm γ˙ Γ

(5.11)

where a = bubble diameter (m), ηm = viscosity of the suspending medium (Pa s), γ˙ = shear rate (s−1 ) and Γ is the surface tension between gas and liquid (N/m).

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If the applied shearing forces are sufficient to overcome surface tension, the bubble deforms and decreases the macroscopic viscosity of the material. If the surface tension cannot be overcome, the bubble remains spherical and can be considered as a rigid particle in the suspension, increasing the viscosity of the material [117]. Assuming a surface tension of 0.04 N/m for air in water, Ca equals 10 for a 4 mm air bubble, for concrete with an apparent viscosity of 10 Pa s at a shear rate of 10 s−1 . However, for a 400 μm air bubble in cement paste with a viscosity of 0.1 Pa s sheared at 100 s−1 , Ca = 0.1 [118]. As such, dependent on the bubble size, mixture rheology and applied shear rate, different outcomes can be observed. This is the reason why there is a discrepancy between results in literature on the influence of air on the rheological properties of cement-based materials [117–120].

5.8.2 Consequence Having an uncontrolled, and especially an unknown air content (and fresh concrete air-void distribution) makes it hard to predict the outcome of the rheological properties. Typically, changes in air content are considered as part of the intrinsic variability of the rheological properties. However, it is also unknown how much air characteristics change during rheological measurements. Air can escape from the concrete volume, it can migrate towards zones with high shear rates, it can be broken into smaller air bubbles due to the locally elevated shear rates, etc.

5.8.3 Detection and Prevention As mentioned before, measuring the air content of the fresh material should be done with each measurement if one wants to detect changes in rheology due to air. Measuring the air-void distribution for each sample might be a more arduous task though. To prevent the influence of uncontrolled air contents on rheology, one can consider consolidating (consistently) the concrete prior to each measurement, but this means that the sample is no longer fully representative for the concrete application. In terms of mix design, a possible solution to prevent significant influences of air content on rheology is to employ mixtures with self-consolidating characteristics.

5.9 Wall Effects As can be seen in Chaps. 3 and 7 of this report, standard rheometers for mortar and concrete are either equipped with ribs, consist of a vane system, or contain special geometry where smooth surfaces are avoided. Interface rheometers do contain a smooth surface.

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5.9.1 Physical Background The underlying principle of having some kind of roughness is to ensure the material is homogeneous during the measurement and slippage between the material and the rheometer surfaces is avoided. As demonstrated in Chap. 7, a smooth surface induces the geometrical wall effect: a gradual reduction in particle concentration when approaching a smooth wall. Shear-induced particle migration is enhanced due to the geometrical wall effect, leading to the formation of a lubrication layer. Slippage occurs when the frictional stress transfer between the rheometer surfaces and the material is lower than the stress necessary to shear the material.

5.9.2 Consequence The geometrical wall effect, combined with shear-induced particle migration, will quickly compromise the measurement results. Knowing that the lubrication layer forms relatively fast during shear, it is deemed impossible to perform a rheological measurement of a homogeneous material if the rheometer surfaces have insufficient roughness. In case of slippage, a local velocity difference between the material and the rheometer surface is present, preventing the determination of the real velocity gradient in the material. If slippage occurs, the measurement is invalid.

5.9.3 Prevention The only way to prevent the influence of the geometrical wall effect and slippage is to provide roughness to the rheometer surfaces, sufficiently large to contain the largest particle intended for the instrument (suggested to be at least d max /2). However, other effects, such as pressure effects, should also be considered when ribs or vane blades are moving in the fluid (see Sect. 5.5).

5.10 Challenges When Determining Static Yield Stress 5.10.1 Main Challenges In its fresh state a cement-based material is a non-Newtonian, yield-stress fluid with time-dependent behavior, like thixotropy and structural breakdown. This time dependency results from flocculation and the reactivity of cement when mixed with water. In the case of mortar and concrete, i.e., when a material also contains aggregates, it can be described as a suspension of irregularly shaped polydisperse particles in such

5 Challenges Encountered During Measuring Rheological Properties … 1000

none at 10 min; 10 1/s at 10 min; 30 1/s at 19 min; 10 1/s

900

static yield stress [Pa]

Fig. 5.11 Effect of shear history on structuration rate of mortar [123]

123

800 700 600 500 400 300 200 100 0 0

20

40

60

80

age of material [min]

a fluid [121]. In static yield stress (SYS) measurements, this rheological complexity of cement-based materials leads to the following consequences: • Intensive shearing of material prior to the static measurement may result in nonuniformity of the sample’s properties due to shear-induced particle migration [58, 122]. The extent of such effect depends on the applied shear rate, aggregate size and on the rheological properties of suspending medium (cement paste). • Another effect which can be observed for very stiff cement-based materials, e.g., 3D-printable concrete, is formation of a shear plane between the probe with material in between the blades and the main bulk. Subsequent SYS measurements performed on the same sample generally show underestimated results. • Each shearing of material breaks its structure formed due to time-dependent thixotropic behavior. The time at which the sample was sheared prior to SYS measurement and the intensity of this shearing affects the value of maximum torque and the resultant SYS, see example in Fig. 5.11 [123]. The above-mentioned challenges can be solved as follows: • If both dynamic and static measurements must be conducted using the same sample, it can be recommended to carefully homogenize it after the dynamic test and before the static test to ensure the uniformity of material in the rheometer cell. • Testing procedure must be designed under consideration of material’s application. For example, if the material is not exposed to any notable loads after its placement, it should not be pre-sheared in the rheometer either, especially at high rotational velocities.

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5.10.2 Selection of Applied Constant Rotational Velocity and Test Duration In any SYS measurement, there are two main setting parameters, i.e., applied constant rotational velocity (CRV) and test duration, which must be meaningfully selected to avoid erroneous results. Ideally, the applied CRV must be as low as possible in order to simulate static conditions during the measurement. Concurrently, it should be considered that a certain time is required for the effective rotational velocity to reach the applied CRV, see Fig. 5.12 [124, 125]. This time lag exists due to inertia and differs depending on the design features of a particular rheometer and, in some cases, on the stiffness of the tested material. It must be ensured that, firstly, the applied CRV is high enough to be achieved for a material at all ages of interest and, secondly, that this applied CRV can be reached in a relatively short time. Otherwise, the resultant SYS cannot be attributed to the age, at which the measurement started [123]. Test duration can be defined as time from the start of a test to the moment when SYS is reached. If a sample is still being loaded after this moment, it is subjected to a notable excess shear. If the goal of the test is to evaluate the structuration rate by performing multiple SYS measurements of a single sample, such excess shear must be avoided. This is due to high sensitivity of the SYS measurements to shear history of the sample: each time it is exceedingly loaded, the formed structure of the material in the vicinity of the rheometer probe is damaged, leading to underestimated resultant structuration rate [123, 124]. Nevertheless, if the goal of investigation is different, e.g., measurement of equilibrium shear stress is required, or a sample is sheared before each measurement according to the testing protocol, this recommendation can be ignored.

Fig. 5.12 Representative curves resulting from a single SYS measurement of a cement-based material performed with a rheometer HAAKE MARS II and b rheometer Viskomat XL. T is torque, Nap is applied CRV, Ne f is effective rotational velocity, td is test duration [124]

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5.10.3 Correct Implementation of Single-Batch Protocol For assessing the structuration rate of cement-based materials, a single-batch or a multi-batch protocol can be used. In the case of multi-batch protocol, a discrete sample is prepared for every age under investigation. Immediately after the sample’s preparation the probe is immersed in the material and kept motionless until the specified age of the material is reached; then the SYS measurement is performed. This protocol supposedly provides more accurate results due to conducting the measurement of an entirely undisturbed sample [123, 124]. On the other hand, it is considerably time-, material- and labor-consuming, and is improper for field conditions. Single-batch protocol means performing SYS measurements at all ages of a single sample. It can be considered as more suitable approach for in-situ control of structuration rate. At the same time, there is a risk of underestimating the structuration rate due to multiple disturbances of the material during testing. A conventional method to avoid this excess disturbance would be manually stopping each individual SYS measurement after observing a peak or a plateau on the torque-time curve. However, it requires operator’s presence at the device and is dependent on the operator’s response speed. To exclude the effect of human factor, SYS measurement can be stopped automatically by applying a breaking criterion, see Eq. (5.12): Ne f (td ) = Nap (td ) ⇒ T (td ) = Tmax

(5.12)

where N ef is effective rotational velocity, N ap is applied CRV, td is test duration, T is torque and T max is maximum torque [124]. Equation (5.12) means that the peak value of torque is obtained at the moment of the effective rotational velocity becoming equal to the applied CRV for the first time, see Fig. 5.12. Each individual SYS measurement can be terminated at this point (Fig. 5.13). The resultant torque T(t d ) is used to calculate the value of SYS, while excessive loading of the sample is avoided [124].

5.10.4 Uniformity of Sample in Static Conditions In the case when the yield stress of the constitutive cement paste is not enough to adequately suspend the aggregate particles, segregation of aggregate in concrete can occur, leading to non-uniformity of the sample. Since volume fraction and composition of aggregate has an effect on the SYS of concrete [126], this non-uniformity may result into a SYS gradient in the sample, and thus to erroneous SYS measurement results. It is recommended to control segregation in the tested sample, which can be done by dividing it into two or three horizontal segments after the end of the test and evaluating the aggregate content in each segment. Segregation control is especially important for flowable concrete.

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Fig. 5.13 Representative curves resulting from SYS measurements of a cement-based material performed with a rheometer HAAKE MARS II and b rheometer Viskomat XL. T is torque, Nap is applied CRV, Ne f is effective rotational velocity, td is test duration

5.11 Summary This chapter describes a number of challenges which can be encountered during the measurement or interpretation of rheological data. To ensure high quality of data, these challenges should be considered when performing measurements, and the detection and prevention methods should be consulted. Some measurement artefacts can be corrected for afterwards, others invalidate a measurement right away. A first challenge which should be considered is the nature of flow. Does the mortar or concrete behave as a suspension, or as a granular material? In case of a granular material, one is more suited to refer to squeeze flow and penetration tests, while for suspension flow, rotational rheometry can be applied. In case of suspension flows, one can adjust the rheometer, the measuring and interpretation procedure to avoid the effects of: • non-equilibrium: leading to apparent shear-thickening behavior • plug flow: under-estimating yield stress and over-estimating viscosity • appropriate choice of data transformation procedure and rheological model, otherwise, different rheological values are obtained • pressure effects: although related to apparent viscosity for vertical blades, the assumed shearing behavior is not fully satisfied • slippage due to a lack of roughness: invalidating the measurement However, some challenges are inherently connected to the nature of the material and might be much more difficult to mitigate. Their occurrence typically invalidates the measurement, and the main preventative action is to limit the exposure of the sample to shearing:

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• gravity and shear-induced particle migration, rendering the sample nonhomogeneous, both for dynamic and static measurements • heat of vaporization, changing the temperature of the sample A last effect which is difficult to control is the air content and air-void distribution of the material. It is typically not considered for most rheological measurements, but can have a tremendous, and variable, effect on the rheological properties. The authors are aware that the prevention techniques provided in this chapter can be contradictory dependent on which challenges need to be addressed. It is up to the researcher to develop a technique and procedure which works for their materials. Simply copying a procedure described in literature is no guarantee for success, but it is recommended to investigate why certain choices were made in the development of a measurement procedure. There is no one-fits-all procedure for rheological measurements, but procedures should be adapted based on the descriptions in this chapter and in this report overall.

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107. Wallevik JE (2014) Effect of the hydrodynamic pressure on shaft torque for a 4-blades vane rheometer. Int J Heat Fluid Flow 50:95–102 108. Wallevik JE (2016) Influence of hydrodynamic pressure in a 4-blades vane rheometer. In: Khayat K (ed) SCC 2016—8th international RILEM symposium on self-compacting concrete, Washington, DC, USA, pp 389–396 109. Wallevik JE (2008) Minimizing end-effects in the coaxial cylinders viscometer: viscoplastic flow inside the ConTec BML Viscometer 3. J Nonnewton Fluid Mech 155(3):116–123 110. Reiner M (1949) Deformation and flow: an elementary introduction to theoretical rheology. HK Lewis 111. Zhu H, Martys NS, Ferraris C, De Kee D (2010) A numerical study of the flow of Binghamlike fluids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics (SPH) based method. J Nonnewton Fluid Mech 165(7–8):362–375 112. Zumdahl SS (1998) Chemical principles, 3rd edn.. Houghton Mifflin Company, Boston, USA 113. Feys D, Verhoeven R, De Schutter G (2007) Evaluation of time independent rheological models applicable to fresh self-compacting concrete. Appl Rheol 17(5):56244–56251 114. Wallevik JE (2009) Development of parallel plate-based measuring system for the ConTec viscometer. In: Proceedings of the 3rd international RILEM symposium on rheology of cement suspensions such as fresh concrete, Reykjavik, Iceland. RILEM Publications S.A.R.L 115. Schramm G (1994) The HAAKE handbook. A practical approach to rheology and rheometry. Gebrueder HAAKE GmbH, Karlsruhe, Federal Republic of Germany 116. Heirman G, Vandewalle L, Van Gemert D, Wallevik O (2008) Integration approach of the Couette inverse problem of powder type self-compacting concrete in a wide-gap concentric cylinder rheometer. J Nonnewton Fluid Mech 150(2–3):93–103 117. Rust AC, Manga M (2002) Effects of bubble deformation on the viscosity of dilute suspensions. J Nonnewton Fluid Mech 104(1):53–63 118. Gálvez-Moreno D, Feys D, Riding K (2019) Characterization of air dissolution and reappearance under pressure in cement pastes by means of rheology. Front Mater 6:73 119. Struble LJ, Jiang Q (2004) Effects of air entrainment on rheology. Mater J 101(6):448–456 120. Feys D, Roussel N, Verhoeven R, De Schutter G (2009) Influence of air bubbles size and volume fraction on rheological properties of fresh self-compacting concrete. In: 3rd international RILEM symposium on rheology of cement suspensions such as fresh concrete. RILEM Publications, pp 113–120 121. Roussel N (ed) (2012) Understanding the rheology of concrete. Woodhead Publishing Ltd., Cambridge, UK 122. Qian Y, Kawashima S (2016) Flow onset of fresh mortars in rheometers: contribution of paste deflocculation and sand particle migration. Cem Concr Res 90:97–103 123. Ivanova I, Mechtcherine V (2019) Evaluation of structural build-up rate of cementitious materials by means of constant shear rate test: parameter study. In: Rheology and processing of construction materials; RILEM book series, Springer, Cham, Switzerland, pp 209–218 124. Ivanova I, Mechtcherine V (2020) Possibilities and challenges of constant shear rate test for evaluation of structural build-up rate of cementitious materials. Cem Concr Res 130:105974 125. Nerella VN, Beigh MAB, Fataei S, Mechtcherine V (2019) Strain-based approach for measuring structural build-up of cement pastes in the context of digital construction. Cem Concr Res 115:530–544 126. Ivanova I, Mechtcherine V (2020) Effects of volume fraction and surface area of aggregates on the static yield stress and structural build-up of fresh concrete. Materials 13(7):1551

Chapter 6

Empirical Test Methods to Evaluate Rheological Properties of Concrete and Mortar Kamal Khayat, Jiang Zhu, and Steffen Grunewald

Abstract Several empirical test methods used to measure the workability of cementbased materials under field conditions can be employed to evaluate the fundamental rheological properties of these materials. This chapter summarized some of the analytical solutions of different workability test methods for concrete and mortar from the rheological basis. Many of the relationships between the various workability parameters of concrete and mortar determined using empirical tests and their corresponding rheological properties, namely yield stress, plastic viscosity, and thixotropy are evaluated. Limitations of the applicability of the various empirical methods are highlighted to avoid erroneous estimates of rheological characteristics. Established relations between flow properties of 3D printing mortar measured by empirical squeeze and penetration tests and the rheological characteristics are also presented. Other test methods for monitoring the output of concrete mixing trucks, including the imposed load and hydraulic pressure, and the correlations between the rheological performance are discussed for the application of in-drum measurement systems.

With contributions from: Jon Wallevik, Mohammed Sonebi, Sofiane Amziane and Markus Greim Jon Wallevik—Icelandic Meteorological Office, Iceland. Mohammed Sonebi—Queen’s University Belfast, United Kingdom. Sofiane Amziane—Clermont-Ferrand Polytechnique, France. Markus Greim—Schleibinger Gerate, Germany. K. Khayat (B) Missouri University of Science and Technology, Rolla, MO, USA e-mail: [email protected] J. Zhu University of Jinan, Jinan, China e-mail: [email protected] S. Grunewald Technical University Delft, Delft, The Netherlands e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Sonebi and D. Feys (eds.), Measuring Rheological Properties of Cement-based Materials, RILEM State-of-the-Art Reports 39, https://doi.org/10.1007/978-3-031-36743-4_6

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6.1 Objective and Scope A variety of empirical test methods have been applied to evaluate the workability of concrete. A comprehensive list of empirical test methods for workability with accompanying test description has been documented by some compendia documents, such as RILEM TC 145 Workability and Rheology of Fresh Concrete [1] and ACI 238.1R-08: Report on Measurement of Workability and Rheology of Fresh Concrete [2]. There is a growing interest in using such empirical test methods to evaluate rheological properties that are essential for the design and control of complex materials with specific rheological property requirements to ensure proper performance. This includes self-consolidating concrete (SCC) where a relatively low yield stress and a moderate viscosity are necessary to secure proper workability. However, it is difficult with a single test method to assess all the functional characteristics of SCC that include filling ability (flowability), passing ability (free from blocking at reinforcement and in the mould), and stability (resistance to bleeding, segregation, and surface settlement). The objective of this chapter is to present some of the main empirical test methods that can be used to evaluate the rheological parameters of concrete and mortar and to discuss the relationships between the responses that can be established from these test methods and the rheological parameters. Rheological parameters include dynamic and static yield stress, viscosity, and thixotropy. It is important to note that yield stress in this chapter refers to dynamic yield stress determined using flow curves. On the other hand, static yield stress is referred to as such in this chapter. Various test methods used to evaluate the free flow of concrete and their relationships with static and dynamic yield stress and viscosity are discussed. Such tests include the slump, slump flow, spread time, V-funnel, L-box, and LCPC box. The chapter also presents test methods that can be used to assess the structural build-up of concrete, including the portable vane and inclined plane tests. Relationships between changes of concrete properties determined using empirical test methods, such as slump flow after different rest times, and the structural build-up measured using a concrete rheometer are also established. Free fall empirical tests that can be employed to evaluate the rheological parameters of mortar and the test methods that can be used to assess the structural build-up of mortar are also presented. This includes some of the specialty tests for extrusion and 3D printing. Some of the limitations associated with empirical test methods are also discussed. Finally, the determination of the mixing energy in concrete truck mixtures is also used to estimate rheological properties of concrete by applying certain in-drum measurement systems. Such systems enable to correlate the pressure or force applied on the probe with the slump and rheological parameters of the concrete. Hereafter, several equations expressing correlations are presented. Not in all cases the authors used the same notation for the same test parameter. Where applicable, reference is made in the text to the more common version of notation.

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6.2 Free Flow Tests for Concrete with Direct Relationship to Rheology This section describes the main test methods used to evaluate the flowability or deformability of concrete and attempts to present correlations between these methods and the rheological parameters. The latter includes dynamic and static yield stress, plastic viscosity, and thixotropy. Table 6.1 summarizes some of the studies that have proposed correlations between workability characteristics determined from different empirical workability test methods and rheological parameters of concrete. Some of the relationships that are cited in Table 6.1 are further elaborated below, and examples of some of the established correlations between empirical tests to determine free flow properties of concrete and dynamic and static yield stress and viscosity are presented.

6.2.1 Slump Versus Yield Stress The slump test is the most used test method for concrete with normal consistency to characterize the workability of fresh concrete. The test method is widely standardized throughout the world, including ASTM C143/C143M [26] and EN12350-2 [27]. The slump test is not considered applicable for concrete with a maximum aggregate size larger than 37.5 mm [2] and concrete types with a low or very high workability. For concrete with coarse aggregates greater than 40 mm in size, the slump can still be determined after sieving of the concrete to remove aggregate particles larger than 40 mm in size. The slump of concrete is influenced by yield stress and plastic viscosity; however, for most cases, the effect of plastic viscosity on slump is negligible. Equations relating yield stress and slump have been developed based on either analytical or experimental analyses. Because different rheometers measure different absolute yield stress values of identical samples of concrete, the experimental equations largely depend on the specific rheometer in use to measure yield stress. In the report of Brower and Ferraris [28], the measurements of yield stress using different rheometers were compared for 12 concrete mixtures with slump values ranging from 110 to 240 mm. The spread in yield stress measured using the BML and Two-Point rheometers for a given concrete mixture with a fixed slump value were reported to range from a relatively low value of 330 Pa to a high value of 1300 Pa. Several authors have proposed and discussed relationships between slump/slump flow and yield stress. In general, more flowable mixtures can exhibit better relationships between the yield stress and slump than those having a lower consistency. The rheometer in use has a significant influence on the correlations with slump/ slump flow, as discussed earlier. The following presents a summary of empirical relationships correlating slump/slump flow and yield stress.

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Table 6.1 List of references with studies relating rheological parameters to workability characteristics Rheological characteristic versus empirical workability characteristics

Dynamic yield stress

Static yield stress

Plastic viscosity

Slump Murata and Kikukawa, 1973 (Coaxial cylinder viscometer) [3]

X

Hu, 1995 (Numerical simulation) [4]

X

Ferraris and de Larrard, 1998 (BTRHEOM) [5]

X

Wallevik, 2006 (BML Viscometer) [6]

X

Saak et al., 2004 (Analytical solution) [7]

X

Roussel and Coussot, 2005 (Analytical solution) [8]

X

Roussel, 2006 (Numerical simulation BML and BTRHEOM) [9]

X

Feys et al., 2016 (ConTec 5) [10]

X

Slump flow Feys et al., 2016 (ConTec 5) [10]

X

Müller et al., 2014 (BML) [11]

X

Coussot et al., 1996 (Analytical solution) [12]

X

Sedran, 1999 (BTRHEOM) [13]

X

González-Taboada et al., 2017 (ICAR) [14]

X

Kokado and Miyagaw, 1999 (Analytical solution) [15]

X

Roussel and Coussot (2005) (Analytical solution) [8]

X

X

Slumping time Ferraris and de Larrard, 1998 (BTRHEOM) [5]

X

Kurokawa et al., 1994 (Analytical solution) [16]

X

T 50 /T 500 Kurokawa et al., 1994 (Analytical solution of slumping curve with time) [16]

X

Sedran, 1999 (BTRHEOM) [13]

X

Sedran and de Larrard, 1999 (BTRHEOM) [17]

X

Grünewald, 2004 (BML) [18]

X

González-Taboada et al., 2017 (ICAR) [14]

X

Khayat (Contec 5, unpublished work)

X

Long et al., 2017 (Modified Tattersall MK-III two-point workability rheometer with vane device) [19]

X

T 40 Mikanovic et al., 2010 (ICAR) [20]

X

Rouis, 2017 (Contec 6) [21]

X (continued)

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Table 6.1 (continued) Rheological characteristic versus empirical workability characteristics

Dynamic yield stress

Static yield stress

Plastic viscosity

V-funnel Feys et al., 2016 (ConTec 5) [10]

X

Long et al., 2017 (Modified Tattersall MK-III two-point workability rheometer with vane device) [19]

X

Benaicha, 2013 (Analytical solution) [22]

X

X

Benaicha et al., 2016 (Analytical solution) [23]

X

X

Grünewald, 2004 (BML) [18]

X

L-box blocking ratio Nguyen et al., 2006 (Analytical solution, HAAKE ViscoTester—Vane) [24]

X

González-Taboada et al., 2017 (ICAR)

X

Long et al., 2017 (Modified Tattersall MK-III two-point workability rheometer with vane device) [14]

X

Khayat and Mitchell, 2008 (Modified Tattersall MK III rheometer with vane device) [25]

X

L-box flow time Long et al., 2017 (Modified Tattersall MK-III two-point workability rheometer with vane device) [19]

X

LCPC box Nguyen et al., 2006 (Analytical solution) [24]

X

Murata and Kikukawa [3] proposed the following equation for yield stress obtained with a co-axial cylinder rheometer in terms of slump. The equation is applicable to concrete mixtures with a slump ranging from 125 to 260 mm. ( τ0 = 714 − 473 · log

S 10

) (6.1)

where τ 0 is the dynamic yield stress (by default in this chapter yield stress is the dynamic yield stress) in Pa, and S is the slump in mm. With a finite element model of a slump test, Hu [4] proposed a relationship between yield stress obtained using the BTRHEOM and slump of concrete with slump values ranging from 125 to 250 mm. The equation is appropriate for concrete with a plastic viscosity lower than 300 Pa·s. τ0 = 3.70 · ρsg · (300 − S)

(6.2)

where τ 0 is the yield stress in Pa, S is the slump in mm, and ρ sg is the relative density of fresh concrete related to the density of water at 4 °C (i.e., 1000 kg/m3 ).

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Ferraris and de Larrard [5] improved Hu’s model by adding a constant term and modifying the slope term based on experimental measurements carried out with the BTRHEOM. Equation (6.3) applies to concrete with slump values below 260 mm: τ0 = 2.88 · ρsg · (300 − S) + 212

(6.3)

where τ 0 is the yield stress in Pa, S is the slump in mm, and ρ sg is the relative density of fresh concrete related to the density of water at 4 °C (i.e., 1000 kg/m3 ). Wallevik [6] altered Eq. (6.3) by measuring the yield stress with the BML viscometer for concrete with slump values below 275 mm, as shown in Eq. (6.4): τ0 = 2.40 · ρsg · (300 − S) + 394

(6.4)

where τ 0 is the yield stress in Pa, S is the slump in mm, and ρ sg is the relative density of fresh concrete related to the density of water at 4 °C (i.e., 1000 kg/m3 ). Wallevik [6] also proposed an empirical relationship between yield stress obtained with the BML viscometer and slump of concrete below 275 mm by considering the relative density of concrete, the lubrication and volume fraction of the matrix, and the fact that a different viscometer is used, as shown in Eq. (6.5): S = 300 − 0.416 ·

) ( ( ) (τ0 + 394) ref · Vm − Vmr e f + α · τ0 − τ0 ρsg

(6.5)

where τ 0 is the yield stress in Pa, S is the slump in mm, ρ sg is the relative density of fresh concrete related to the density of water at 4 °C (i.e., 1000 kg/m3 ), V m is the volume fraction of the matrix in m3 , and α is an empirical coefficient in mm/(Pa·m3 ). ref ref The term τ0 −τ0 refers to the lubrication effect, and the term Vm −Vm considers the effect of matrix which ) implies the distance of suspended particles. ) ( ( volume fraction, ref ref · Vm − Vm is only based on empirical consideration The term α · τ0 − τ0 depending on the angularity, density, and grading of the aggregate. Saak et al. [7] developed a dimensionless model relating slump to static yield stress based on an analytical solution of a slump test, which is generalized as a function of the cone geometry (Fig. 6.1), as shown in Eq. (6.6): S ' = S/H = 1 − h 0 /H − h 1 /H with h1 =

2H τ y'

[ ( ) ( 2 )] H H + 3h t (H + h t ) ln + ln h0 h 20 + 3h t (h 0 + h t )

(6.6)

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Fig. 6.1 a Slump cone and b stress distribution before lifting the cone [7]

)2 ( h 0 = 2H τ y + 2H τ y /a + a − h t h t = Hrt /(r H − rt ) [ ( )] / [ ] 1/3 )3 ) ( ( 1 3 3 a= h + 16 H τ y + h 3t h 3t + 32 H τ y 2 t where S ' is the dimensionless slump related to the height H of the cone, h0 is the thickness of a section from the top of the cone that generates the static yield stress of the concrete, h1 is the height of the deformed section of the slumped concrete, ht is the height of the missing top of the cone, τ y is the shear stress at h0 equal to the static yield stress, τ y' is the dimensionless static yield stress, and r t and r H are the radii at the top and bottom of the slump cone, respectively. Based on analytical solutions of a slump test for the ASTM Abrams cone, Roussel and Coussot [8] proposed two relationships between yield stress and slump for two different cases of the slump of concrete: (1) the height of slumped concrete is considerably lower than the bottom radius of slumped concrete, and (2) the height of slumped concrete is much larger than the bottom radius of slumped concrete. The relationships are given as shown in Eqs. (6.7) and (6.8): τ0 = For H > R :

) ( τ0 S √ / 3 = 1− ρg H0 H

(6.8)

where τ 0 is the yield stress in Pa, ρ is the density of fresh concrete in kg/m3 , g is the gravity acceleration in m/s2 , H 0 is the height of ASTM Abrams cone in m, and H and R are the height and bottom radius of concrete at the end of the slump test in m, respectively. Using numerical simulation of a slump test for the ASTM Abrams cone, Roussel [9] established a linear correlation between slump and yield stress for concrete with slump values ranging between 50 and 250 mm, as shown by Eq. (6.9): τ0 = 5.68 · ρsg · (255 − S)

(6.9)

where τ 0 is the yield stress in Pa, S is the slump in mm, and ρ sg is the relative density of fresh concrete related to the density of water at 4 °C (i.e., 1000 kg/m3 ). Feys et al. [10] established relationships between yield stress and slump and slump flow, respectively, as shown in Fig. 6.2. The yield stress was determined with the ICAR rheometer and was transformed into values calculated for a Contec 5 co-axial rheometer. The concrete mixtures varied in consistency from a conventional vibrated concrete (CVC) with a slump flow 550 mm. Mixtures were identified as segregated if the sieve stability value exceeded 20%. A linear correlation between slump and yield stress measured using the Contec 5 rheometer can be obtained, as shown in Eq. (6.10): ( ) τ0 = 1239.00 − 4.27 · S R2 = 0.84

(6.10)

where τ 0 is the yield stress in Pa, and S is the slump in mm.

6.2.2 Slump Flow Versus Yield Stress Slump flow, i.e., the total spread diameter at the conclusion of the slump test, is often used in SCC literature to describe the filling ability of the concrete. There is a strong correlation between slump flow and yield stress; however, as in the case of slump, the relationship is dependent on the rheometer type. ASTM C 1611 [29] covers the slump flow measurement in addition to T 50 and the visual stability index (VSI). The T 50 value corresponds to the elapsed time from the lifting of Abrams cone to the time when the concrete has flowed to a diameter of 500 mm. T 50 , is proportional to the viscosity of the concrete, as discussed below. In some documents instead of T 50 , the value t 500 is applied, both representing an identical measurement (flow time in seconds in the slump flow test between the lifting of the cone and the concrete reaches the prescribed diameter of 500 mm). In the relevant equations T 50, T 50 , T 500 and t 500 are interchangeable. The VSI (Visual Stability Index) offers a visual

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1000

Yield stress (Pa)

800 CVC (slump!) HWC SCC

600

Segregated

400 y = 2 678.96e-0.01x R² = 0.85 200

y = -4.27x + 1 239.00 R² = 0.84

0 0

100

200

300

400 500 600 Slump / Slump flow (mm)

700

800

900

1000

Fig. 6.2 Relationships between slump/slump flow and yield stress [10]

assessment of bleeding and segregation of the concrete during the slump flow test [29]. Highly stable SCC can be homogenous and stable with a VSI of 0 (values of VSI: 0, 1, 2 or 3). As shown in Fig. 6.2, Feys et al. [10] proposed a relationship between slump flow and yield stress measurements determined using a Contec 5 co-axial rheometer: ) ( τ0 = 2678.96 · e−0.01·S F R2 = 0.85

(6.11)

where τ 0 is the yield stress in Pa, and SF is the slump flow in mm. Müller et al. [11] compared and discussed relationships that link the slump flow of three different SCC mixtures with the yield stress obtained with the BML viscometer, as shown in Eq. (6.12): ( S F = 2R2 exp V gρα1 ·

{

[( ) ] }α2 ) H + A C1 + D · τ0,B M L + C2 ρsg

(6.12)

where SF is the slump flow in m, R2 is the lower radius of the slump cone in m, V is the volume of the cone in m3 , ρ is the density of fresh concrete in kg/m3 , ρ sg is the relative density of fresh concrete related to the density of water at 4 °C (i.e., 1000 kg/ m3 ), H is the height of the cone in m, α 1 and α 2 are correction factors that are related

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to the density of fresh concrete, and τ 0,BML is the yield stress in Pa obtained with the BML viscometer. The parameters of A, C 1 , D, and C 2 are listed in Table 6.2. By analytically studying the spread file of fine particle suspensions, Coussot et al. [12] (also referenced in Sedran [13]) proposed the following relationship between slump flow and yield stress. τ0 =

ρ

(6.13)

(S F/279)5

where τ 0 is the yield stress in Pa, SF is the slump flow in mm, and ρ is the density of fresh concrete in kg/m3 . Sedran [13] established the following empirical relation between slump flow and yield stress determined using the BTRHEOM, as shown in Eq. (6.14). For SCC with a slump flow larger than 500 mm, the average error was reported to be 46 mm (Series 2), 44 mm (Series 3), and 86 mm (Series 4). τ0 =

ρ (808 − S F) 1174

(6.14)

where τ 0 is the yield stress in Pa, SF is the slump flow in mm, and ρ is the density of fresh concrete in kg/m3 . González-Taboada et al. [14] obtained the following relationship between static yield stress measured with the ICAR rheometer with a vane geometry and the empirical slump flow for SCC, as shown in Eq. (6.15): τ0,s = 2.71 × 10−4 ·

ρ (S F/2000)

5

( 2 ) R = 0.76

(6.15)

where τ 0,s is the static yield stress in Pa, SF is the slump flow in mm, and ρ is the density of fresh concrete in kg/m3 . By a theoretical analysis of the slump flow test, Kokado and Miyagaw [15] proposed a relationship between yield stress and slump flow of highly flowable concrete, as shown in Eq. (6.16): τ0 =

225ρgV 2 4π 2 S F 5

(6.16)

Table 6.2 Parameters of Eq. (6.12) for different models Model

α1

α2

H (m)

A

C1

D

C2

M1

0.61

3.2

0.3

−0.347

244

2

−212

M2

0.61

3.2

0.3

−0.347

350

3

−212

M3

0.61

3.2

0.3

−0.180

480

3.8

−212

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where τ 0 is the yield stress in Pa, ρ is the density of fresh concrete in g/mm3 , g is the gravity acceleration in mm/s2 , V is the sample volume in mm3 , and SF is the slump flow in mm. Based on an analytical solution of the shape at stoppage, Roussel and Coussot [8] proposed the following model to determine the yield stress of SCC from a slump flow measurement as shown in Eq. (6.17): ( h=

2τ0 (R − r ) ρg

)1/2 (6.17)

where τ 0 is the yield stress in Pa, h is the thickness of the tested material in m, R is the radius of the materials at stoppage in m, r is the radius of the top horizontal solid surface of the sample in m, ρ is the density of fresh concrete in kg/m3 , and g is the gravity acceleration in m/s2 . The authors further computed the expression for the yield stress as a function of the slump flow and material volume, as shown in Eq. (6.18): τ0 =

225ρgV 2 128π 2 R 5

(6.18)

where τ 0 is the yield stress in Pa, ρ is the density of fresh concrete in kg/m3 , g is the gravity acceleration in m/s2 , V is the sample volume in m3 , and R is the radius of the materials at stoppage in m.

6.2.3 Slump and Slump Time Versus Plastic Viscosity The plastic viscosity of slumped concrete can be estimated by adding a parameter related to time to the standard slump test. As shown below, several authors have proposed and discussed relationships between slump, slump time (or slumping time), and plastic viscosity. Ferraris and de Larrard [5] expressed a semi-empirical model of plastic viscosity with the BTRHEOM as a function of final slump, slump time, and concrete density, as shown in Eqs. (6.19) and (6.20), respectively: For 200 mm < S < 260 mm : μ = 1.08 × 10−3 · ρT (S − 175) For S < 200 mm : μ = 1.08 × 10−3 · ρT (S − 175)

(6.19) (6.20)

where μ is the plastic viscosity in Pa·s, ρ is the density of fresh concrete in kg/m3 , T is the slump time in s, and S is the slump in mm. By assumption that the ratio of top to bottom radii after slump is constant to the initial situation, Kurokawa et al. [16] estimated the plastic viscosity by comparison

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of the measured slumping curve corresponding to the variation of slump height with time with a theoretical one that is expressed by the hyperbola function of time. The authors proposed a theoretical expression of plastic viscosity relating with slump, slump flow, and the time required to reach a certain slump or slump flow value, as shown in Eq. (6.21, for slump) and Eq. (6.22 for slump flow), respectively: ] [ 7ρgS s f 2 · (S − H ) + D 2 H ( ) μ= · Ts f 7200 s f 2 H − D 2 H )( ) ( 7ρg D 2 H S F 2 − D 2 S F 2 − s f 2 ( ) μ= · Ts f 7200 · S F 4 s f 2 − D 2

(6.21)

(6.22)

where μ is the plastic viscosity in Pa·s, ρ is the density of fresh concrete in kg/m3 , g is the gravity acceleration in m/s2 , S is the slump in cm, sf is the slumping value in mm at a slumping time of T sf in s, SF is the slump flow at stoppage in mm, H = 300 mm and D = 200 mm are the height and the upper diameter of Abrams slump cone, respectively.

6.2.4 T50 and Slump Flow Versus Plastic Viscosity For concrete with high flowability, the time to reach a slump flow spread of 50 cm or 500 mm (i.e., T 50 or T 500 ) is proportional to the plastic viscosity of the concrete. The plastic viscosity of concrete can be expressed using equations based on the experimental results of the slump flow test. T 50, T 50 , T 500 and t 500 represent the same value of the same measurement, as discussed before. Kurokawa et al. [16] proposed a relationship between plastic viscosity and slump flow, T 500 , and the bulk density of concrete for a slump flow larger than 300 mm, as shown in Eq. (6.23): ) ( ) ( 25000 40000 · 1− · T500 μ = 0.0545ρ · 1 − SF2 SF2

(6.23)

where μ is the plastic viscosity in Pa·s, ρ is the density of fresh concrete in kg/m3 , SF is the slump flow at stoppage in mm, T 500 is the time reaching a slump flow of 500 mm after lifting of the cone. By adjusting the multiplier term in Eq. (6.23), Sedran [13] proposed the following equation that applies to SCC with a slump flow greater than 500 mm, as shown in Eq. (6.24). The average error for SCC is 50 Pa·s. ) ( ) ( 25000 40000 · 1− · T500 μ = 0.0414ρ · 1 − SF2 SF2

(6.24)

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where μ is the plastic viscosity in Pa·s determined using the BTRHEOM, ρ is the density of fresh concrete in kg/m3 , SF is the slump flow at stoppage in mm, T 500 is the time reaching a slump flow spread of 500 mm. Based on a dimensional analysis, Sedran and de Larrard [17] established an equation predicting the plastic viscosity of the SCC for slump flows greater than 500 mm, as shown in Eq. (6.25). The average error is 35 Pa·s. μ=

ρg · (0.026 · S F − 2.39)T500 10000

(6.25)

where μ is the plastic viscosity in Pa·s determined using the BTRHEOM, ρ is the density of fresh concrete in kg/m3 , g is the gravity acceleration in m/s2 , SF is the slump flow at stoppage in mm, and T 500 is the time reaching a slump flow spread of 500 mm in s. Grünewald [18] proposed an empirical relationship between the experimental plastic viscosity determined using with the BML viscometer and T 50 of selfconsolidating fiber-reinforced concrete, as shown in Eq. (6.26). The mean error is 0.65 s (STD: 0.54 s). μ = 52.08 · T50 − 69.27

(6.26)

where μ is the plastic viscosity in Pa·s, and T 50 is the time reaching the flow spread of 50 cm in s. González-Taboada et al. [14] obtained the following relation between plastic viscosity measured with the ICAR rheometer with vane geometry and T 500 for SCC, as shown in Eq. (6.27): ( ) μ = 13.07 · T500 + 5.88 R2 = 0.76

(6.27)

where μ is the plastic viscosity in Pa·s, and T 500 is the time reaching slump flow of 500 mm in s. Figure 6.3 shows a relationship between T 50 and plastic viscosity of SCC measured with the Contec 5 rheometer. Within the increase of T 50 from about 2–7 s, the plastic viscosity of SCC increased linearly from approximately 20–100 Pa·s. It is important to note that a high flow time can also be associated with a low deformability due to a high plastic viscosity and with high inter-particle friction and even segregation and blockage in extreme cases. As the flow rate of concrete decreases at the end of the slump flow test, with a slump flow of not much more than 500 mm (for example 580 mm), a relatively higher flow time can be obtained that suggests a higher plastic viscosity, which is not the case in reality. Long et al. [19] investigated the relationship between T 50 and plastic viscosity of stable SCC made with different maximum size aggregates (MSAs). The plastic viscosity was determined with a modified Tattersall MK III rheometer with a vane device. Figure 6.4 shows a relationship between T 50 and the plastic viscosity of SCC with slump flows in the range of 615–760 mm and different MSAs of 9.5–19 mm.

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Fig. 6.3 Relationship between T 50 and plastic viscosity (Khayat, personal communication, unpublished work)

Fig. 6.4 Relationship between plastic viscosity, T 50 , and V-funnel flow time values measured at 10 min [19]

Relative higher values obtained with the V-funnel might indicate a more pronounced effect of reduced passing ability, which can be either the result of larger aggregates or segregation taking place inside the funnel, which increases the volume of coarser grains in the vicinity of the outlet of the V-funnel.

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6.2.5 T40 Versus Plastic Viscosity For super-workable concrete (SWC) with a slump flow of 400–550 mm, the time to reach the slump flow spread of 40 cm, i.e., T 40 , is proportional to the plastic viscosity of the concrete. The plastic viscosity of concrete can be expressed using equations based on the experimental results of the slump flow test as illustrated in Mikanovic et al. [20] and Rouis [21]. For example, Rouis [21] proposed an empirical relationship between the experimental plastic viscosity determined with the Contec 5 rheometer and T 40 of concrete, as shown in Eq. (6.28). ( ) μ = 22.03 · T40 − 2.34 R2 = 0.71

(6.28)

where μ is the plastic viscosity in Pa·s, and T 40 is the time reaching a slump flow of 40 cm in s.

6.2.6 V-Funnel Flow Time Versus Plastic Viscosity The V-funnel test can be used to determine the plastic viscosity of SCC, and to a certain degree the resistance to segregation of the fresh concrete that can lead to blockage and an increase of the V-funnel time. As shown in Fig. 6.4, Long et al. [19] established a relationship between V-funnel flow time and plastic viscosity of stable SCC made with MSA of 9.5–19 mm. The plastic viscosity was obtained with a modified Tattersall MK III rheometer with vane device. The slump flow of the investigated mixtures ranged from 615 to 760 mm. It is important to note that the V-funnel flow time also is affected by the yield stress of the SCC. Therefore, changes in slump flow or yield stress can affect the V-funnel test results. Feys et al. [10] proposed a relationship between plastic viscosity and V-funnel flow time of SCC with a slump flow >550 mm using a V-funnel test with an outlet of 65 × 75 mm2 , as shown in Eq. (6.29) and Fig. 6.5. The SCC was prepared with a maximum aggregate size of 20 mm. The plastic viscosity was determined with the ICAR rheometer and was transformed into values calculated for a Contec 5 coaxial rheometer. The figure also shows the data for highly workable concrete (HWC) with a slump flow of 300 to 550 mm. A relationship was obtained for the SCC mixtures; however, with the increase in yield stress for the HWC mixtures, a poor relationship can be obtained between the plastic viscosity and the V-funnel flow time since the yield stress has a significant effect on the V-funnel flow. As mentioned before, it is important to note that a high flow time can also be associated with low deformability due to a high plastic viscosity and with high inter-particle friction and even segregation and blockage in extreme cases. ( ) μ = 7.58 · TV + 6.31 R2 = 0.91

(6.29)

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180 160

Plastic viscosity (Pa s)

140 120 100 80 60

HWC

40

SCC

20 0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

V-funnel (s)

Fig. 6.5 Relationship between V-Funnel flow time and plastic viscosity, proving the additional influence of the yield stress for mixtures with lower slump flow values (HWC) [10]

where μ is the plastic viscosity in Pa·s, and T V is the V-funnel flow time in s. Based on an analytical solution of the V-funnel flow time of SCC, Benaicha [22] and Benaicha et al. [23] proposed a correlation between the plastic viscosity, the V-funnel flow time, and the density of concrete, as shown in Eq. (6.30). The proposed approach showed that for 32 SCC mixtures with V-funnel times of 9–35 s, the maximum error between the experimental plastic viscosity determined using a Brookfield R/S rheometer and the theoretical value was 28 Pa·s. ( [( ) 8H τ0 2(z · tanα + d) + e dt μ= − + ρgz 3 dz (z · tanα + d) · e ) ]−1 ( )] [ ) ( dz 16H [2(z · tanα + d) + e]4 z · tanα + d 2 · −ς +ρ 1 − · d 2 · dt π [(z · tanα + d) · e]3

(6.30) where μ is the plastic viscosity in Pa·s, τ 0 is the yield stress in Pa, ρ is the density of concrete in kg/m3 , g is the gravity in m/s2 , dt/dz is the flow velocity (emptying velocity of V-funnel), H, z, α, d, and e are the geometric parameters of the V-funnel in m given in Fig. 6.6, and ζ is the loss coefficient. Grünewald [18] pointed that, if a funnel is sufficiently large and concrete has a low yield stress, a relationship is obtained between plastic viscosity determined with

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Fig. 6.6 Dimensions of V-funnel. x is the coefficient of singular head losses [23]

the BML viscometer and the the fiber funnel flow-time T V-fiber of self-compacting fiber reinforced concrete, as shown in Eq. (6.31). A relatively large funnel (fiber funnel) with a square opening at the bottom of 125 mm was used to establish this relationship; the opening corresponds to about twice the maximum fiber length. μ = 118.90 · TV − f iber − 265.16

(6.31)

where μ is the plastic viscosity in Pa·s, and T V-fiber is the fiber funnel flow-time in s. The mean error of this relationship is 0.37 s.

6.2.7 L-Box Blocking Ratio Versus Yield Stress The passing ability of SCC can be evaluated with the L-box test. The method enables the evaluation of the filling ability and resistance to segregation and blockage of the SCC. The blocking ratio (h 2 / h 1 ), also referred to as the blocking ratio, corresponding to the ratio of the heights of concrete at the end of the horizontal portion of the L-box test, h2 , and in the vertical section, h1 , indicates the passing ability, or the degree to which the passage of concrete through the bars is restricted. The slope of concrete in the L-box also depends on the yield stress, accordingly, potentially higher blocking ratios can be obtained with a more flowable concrete. It is important to note that the L-box test is a passing ability test and is not designed to determine yield stress. Based on an analytical approach, Nguyen et al. [24] showed that the blocking ratio (h 2 / h 1 ) of the standard L-box can be related with the static yield stress, as expressed in Eqs. (6.32) and (6.33). The analytical models were validated using a HAAKE ViscoTester VT550 equipped with a vane-type sensor (HAAKE FL10) on limestone powder suspensions with static yield stress values ranging between those that can be obtained with SCC mixtures and stiffer concrete mixtures. The model suspension did not contain sand or coarse aggregates, so the effect of passing ability on the blocking ratio was minimized.

150

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2h avg − (h 1 − h 2 ) ∼ ρg − 100 · τ0,s h2 = (in case of L − box with 3 bars) = h1 2h avg + (h 1 + h 2 ) ρg + 100 · τ0,s (6.32) 2h avg − (h 1 − h 2 ) ∼ ρg − 84 · τ0,s h2 = (in case without bars) = h1 2h avg + (h 1 + h 2 ) ρg + 84 · τ0,s

(6.33)

with h avg =

V h1 + h2 = 2 l0 L 0

where h1 is the height of concrete in the vertical section in m, h2 is the height of concrete at the end of the horizontal portion in m, ρ is the density of fresh concrete in kg/m3 , g is the gravity in m/s2 , τ 0,s is the static yield stress in Pa, V is the volume of tested concrete in m3 , l 0 is the width of the L-box in m, and L 0 is the horizontal length of the L-box in m. The blocking ratio of SCC is affected by the rheological properties of the SCC at the time of testing, which vary with rest time. González-Taboada et al. [14] established a relationship between the blocking ratio of SCC and the static yield stress at the time of L-box testing, as shown in Eq. (6.34). The static yield stress was determined using the ICAR rheometer after 15 and 45 min of rest time. ) ( τ0,s = −501.13 · (h 2 / h 1 ) + 532.92 R2 = 0.82

(6.34)

where τ 0,s is the static yield stress in Pa, and h 2 / h 1 is the L-box blocking ratio.

6.2.8 L-Box Blocking Ratio Versus Plastic Viscosity The blocking ratio (h 2 / h 1 ) determined from the L-box test can be related to the viscosity of SCC. Khayat and Mitchel [25] investigated the relationship between the L-box test results and plastic viscosity of stable SCC made with different maximum size aggregates (MSAs) of 9.5–19 mm and slump flow values of 615–760 mm. The plastic viscosity was determined with a modified Tattersall MK III rheometer with vane device. The results were further analyzed by Long et al. [19] and shown in Fig. 6.7. Both crushed aggregates (C) and gravels (G) were used in the testing program. In addition to the blocking ratio, the time to reach the end of the horizontal section of the L-box can be correlated to the plastic viscosity of the SCC. This is shown in Fig. 6.8 for SCC made with different coarse aggregate characteristics (crushed coarse aggregates (C) and gravels (G) with different MSA values). The plastic viscosity was obtained with a modified Tattersall MK-III two-point workability rheometer equipped with a four-blade vane impeller.

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Fig. 6.7 Relationship between plastic viscosity and L-box blocking ratio [19]

Fig. 6.8 Relationship between plastic viscosity and L-box flow time [19]

6.2.9 LCPC-Box Spread Length Versus Yield Stress Based on the analytical solution of LCPC-box flow and the time of stoppage, Nguyen et al. [24] proposed the relationship between the spread length and yield stress, as shown in Eq. (6.35). The analysis takes into account the shear stress at the lateral walls and bottom surface to predict the shape of a given volume of concrete at stoppage for a yield stress fluid flowing slowly enough so any inertia effect can be negligible. The width and length of the channel are 20 and 120 cm, respectively. The studied volume (limestone powder suspensions) is the same as the one used for the slump flow test (i.e., 6 L). ) ( l0 l0 h0 + ln L= A 2A l0 + 2h 0 with

(6.35)

152

K. Khayat et al.

A = 2τ0,s /(ρgl0 ) where L is the spread length at stoppage in cm, h0 is the thickness in cm of the sample at the extremity of the LCPC-box where the concrete is cast, l0 is the width of the channel in cm (l0 = 20 cm), τ 0,s is the static yield stress of the model fluid (limestone powder suspensions) in Pa, ρ is the density of fresh concrete in kg/m3 , and g is the gravity in m/s2 .

6.3 Structural Build-Up at Rest of Concrete Empirical test methods have been used to determine the structural build-up of concrete at rest, such as portable vane, inclined plane, and plate tests. This section describes the main test methods used to evaluate the structural build-up and workability loss of concrete and attempts to present correlations between these methods and the thixotropic parameters. The latter includes the increase of static yield stress and apparent viscosity at rest. Table 6.3 summarizes some of the studies that have proposed correlations between empirical test methods and structural build-up at rest of concrete. Some of the relationships that are cited in Table 6.3 are further elaborated below, and examples of some of the established correlations between empirical tests to evaluate the structural build-up of concrete and the increase of static yield stress and apparent viscosity at rest are presented.

6.3.1 Portable Vane The portable vane (PV) test method is described in Chap. 3. The test consists of determining the change in the static yield stress at rest (τ 0,s-PV ). Good correlations are established between the indexes of structural build-up determined from the PV and concrete rheometer [30, 31]. For example, Omran et al. [31] compared the τ 0rest measurements obtained from the PV test to those determined using a vane rheometer for SCC mixtures. As shown in Fig. 6.9, the test results determined after 15 min of rest and those between 15 and 60 min of rest (i.e., 30, 45, and 60 min) are presented. The correlations reported in Fig. 6.9 for concrete tested after 15 min of rest and those between 30 and 60 min have correlation coefficients (R2 ) of 0.86 and 0.93, respectively. However, the relationship between the PVτ 0rest and Rheometerτ 0rest at 15 min of rest is close to a 1:1 relationship since both rheometers are testing undisturbed samples. ( ) P V τ0r est@15 min = 1.11 · Rheometer τ0r est@15 min R2 = 0.86, n = 50

(6.36)

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Table 6.3 List of references with relations of structural build-up at rest and workability Rheological characteristic versus empirical workability test

Static yield stress

Athix

Portable vane Khayat and Omran, 2010 (Modified Tattersall MK-III X two-point workability rheometer with vane device) [30]

X

Omran et al., 2011 (Modified Tattersall MK-III two-point workability rheometer with vane device) [31]

X

X

Khayat et al., 2012 (Modified Tattersall MK-III two-point workability rheometer with vane device) [32]

X

Inclined plane Khayat and Omran, 2010 (Modified Tattersall MK-III X two-point workability rheometer with vane device) [30]

X

Omran et al., 2011 (Modified Tattersall MK-III two-point workability rheometer with vane device) [31]

X

X

Khayat et al., 2012 (Modified Tattersall MK-III two-point workability rheometer with vane device) [32]

X

Megid and Khayat, 2018 (Modified Tattersall MK-III X two-point workability rheometer with vane device) [33]

X

Workability loss of undisturbed samples Megid and Khayat, 2018 (undisturbed slump flow, T 50 ) [33]

X

X

where PVτ 0rest@15min is the static yield stress obtained from the PV test at 15 min of rest in Pa, Rheometerτ 0rest@15min is the static yield stress obtained from rheometric testing using a coaxial concrete rheometer in Pa, and n is the number of investigated SCC. The overestimation of 11% of the PVτ 0rest@15min compared to the Rheometerτ 0rest@15min can be due to the difference in the gap between the outer edge of the vane and the concrete container used in the two test methods as well as differences in torque sensors and rotational velocity. The ratio between the container’s width and vane’s diameter (DT/D) for the PV test is 3.2 (i.e., 240/75 mm = 3.2). The corresponding ratio between the bowel’s diameter and the vane’s diameter (DT/D) used for the concrete rheometer is 4.0 (i.e., 360/90 mm = 4.0). As shown in Eq. (6.37) and Fig. 6.9, the correlation between the τ 0rest for all data between 15 and 60 min of the rheometer and PV test methods (n = 146) deviates significantly from the 1:1 line. ) ( P V τ0r est = 1.55 · Rheometer τ0r est R2 = 0.93, n = 146

(6.37)

154

K. Khayat et al.

Fig. 6.9 Correlation between initial static yield stress obtained with a concrete rheometer and PV test [31]

where PVτ 0rest is the static yield stress obtained from the PV test of rest in Pa, and Rheometerτ 0rest is the static yield stress obtained from rheometric testing using a coaxial concrete rheometer in Pa. The increase of 55% of τ 0rest of the PV test compared to the rheometer test can be explained by the fact that the shearing histories of the two tests were not the same. In the portable vane test, the measurements were determined on four “virgin”, undisturbed, samples, while the concrete tested in the rheometer was subjected to successive shearing over a 60-min testing period in which the concrete samples were also used for the rheometer testing. The samples were manually re-homogenized for one minute following each measurement and left to rest until the next measurement (typically 15 min of rest). Omran et al. [31] also proposed a relationship between the time-dependent static yield stress determined using the PV test [PVτ 0rest (t)] and the rheometric test determined using the Modified Tattersall-type MK-III concrete rheometer [Rheometerτ 0rest (t)], as shown in Fig. 6.10. The correlation is given in Eq. (6.38) with a R2 value of 0.96. The evolution of static yield stress with time was determined for 30 SCC mixtures. As expected, this relationship deviated from the 1:1 line due to the difference in shear histories of the two testing approaches. The PV test exhibits a higher rate of change in static yield stress with growing rest time compared to that obtained with the concrete rheometer. As noted before, this is because the SCC in the concrete rheometer is disturbed between subsequent measurements, which is not the case for the PV test where four undisturbed samples were tested in an undisturbed state. ) ( Rheometer τ0r est (t) = 0.39 · P V τ0r est (t) R2 = 0.96, n = 30

(6.38)

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Fig. 6.10 Relationship between the time-dependent change of static yield stress as well as the drop in apparent viscosity at 0.7 rps obtained using the PV test and a concrete rheometer [31]

where PVτ 0rest (t) and Rheometerτ 0rest (t) are the time-dependent static yield stresses determined using the PV test and the rheometric test in Pa/min, respectively. Figure 6.10 also shows a correlation between the time-dependent change in static yield stress determined from the PV test [PVτ 0rest (t)] and the time-dependent change of the drop in apparent viscosity at a rotational velocity of 0.7 rps [Δη[email protected] (t)]. The relationship is given by Eq. (6.39). ) ( Δη[email protected] ps (t) = 0.28 · P V τ0r est (t) R2 = 0.96, n = 30

(6.39)

where Δη[email protected] (t) is the time-dependent change of the drop in apparent viscosity at a rotational velocity of 0.7 rps in Pa·s/min, and PVτ 0rest (t) is the time-dependent static yield stress determined using the PV test in Pa/min.

6.3.2 Inclined Plane The inclined plane (IP) test is described in Chap. 3. The test involves casting concrete in a cylindrical mould resting on a horizontal plate of a given roughness, followed by lifting the mould to allow the concrete to spread [30–32]. The static yield stress is determined (τ s−IP ) at different times of rest and can be correlated to similar measurements from a rheometer. For example, Megid and Khayat [33] compared the static yield stress at rest that can be obtained using the Modified Tattersall-type MK-III concrete rheometer and the IP test. The relationship is given in Eq. (6.40): ( 2 ) 0.52 R = 0.89 τ0,s−M K −I I I = 21.31 · τ0,s(Field−oriented)

(6.40)

where τ 0,s−MK −III is the static yield stress obtained with the MK-III rheometer in Pa,

156

K. Khayat et al.

τ 0,s(Field −oriented) is the static yield stress obtained using the IP test in Pa. The relationship between time-dependent static yield stress determined using the MK-III rheometer and IP test is given in Eq. (6.41). )( ( ) Athi x−M K −I I I = 666.17 · exp 0.0003 · Athi x(Field−oriented) R2 = 0.93

(6.41)

where Athix−MK −III is the thixotropic index obtained from MK-III rheometer in Pa·Pa/ min, Athix(Field −oriented) is the thixotropic parameter using the IP test in Pa·Pa/min.

6.3.3 Workability Loss of Undisturbed Samples With the aid of the above-mentioned relationships between static yield stress and slump or slump flow that are presented in Sect. 6.2, the thixotropy and workability loss with time of concrete can be evaluated. Schipper [34] estimated the structural build-up of 18 concrete mixtures by calculating the static yield stress based on the relationships between static yield stress and slump or slump flow values. Using the above PV and IP test methods, Megid and Khayat [33] proposed the following correlations derived from statistical models relating the variations with time of the τ 0,s−IP and τ 0,s−PV with the variations of slump flow and T 50 values of seven undisturbed samples measured over approximately 1 h of age, as shown in Eqs. (6.42) and (6.43): τs−I P(t) = 5700 · [T50 (t)/S F(t)]0.55

(6.42)

τs−P V (t) = 335 · [T50 (t)]375/S F(t)

(6.43)

where τ 0,s−IP is the static yield stress measured using the IP test method in Pa, τ 0,s−PV is the static yield stress measured using the PV test method in Pa, t is the rest time in min (15 ≤ t ≤ 60), SF(t) is the slump flow determined after rest in mm, and T 50 (t) is the T 50 determined after rest in s.

6.4 Free Flow Tests for Mortar with Direct Relationship to Rheology This section describes the main test methods used to evaluate the flowability or deformability of mortar and attempts to present correlations between empirical test methods and rheological parameters. The latter includes static and dynamic yield stress, plastic viscosity, and structural build-up. Similar test methods can also be applied for cement paste; however, these test methods are not discussed in this chapter.

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Table 6.4 List of references with studies on mortar relating rheological parameters to free flow properties Dynamic yield stress

Rheological characteristic

Plastic viscosity

Mini cone Kokado and Miyagaw, 1999 (Analytical solution) [15]

X

Roussel et al., 2005 (Analytical solution) [35]

X

Rouis, 2017 (ConTec 6) [21]

X

Choi et al., 2016 (Computational fluid dynamics analysis) [36]

X

X

Mini V-funnel Mikanovic et al., 2010 (ConTec 6) [37]

X

Meng and Khayat, 2017 (ConTec 6 and ConTec 5) [38]

X

Teng et al., 2020 (ConTec 5) [39]

X

Table 6.4 summarizes some of the studies that have proposed correlations between free flow properties and rheological parameters of mortar. Some of the relationships that are cited in Table 6.4 are further elaborated below, and examples of some of the established correlations between empirical tests to determine free flow properties of mortar and dynamic yield stress, viscosity, and structural build up are presented. Table 6.5 presents a summary of the influencing parameters of the empirical test methods in Table 6.4.

6.4.1 Flow Spread Versus Yield Stress The shape of cementitious materials at stoppage of flow can be related to the yield stress. Several studies were executed to quantitatively obtain reliable relations between dynamic yield stress values and either spread flow or slump tests. By a theoretical analysis of the mini-slump flow test, Kokado and Miyagaw [15] proposed a relationship between yield stress and mini-slump flow, as shown in Eq. (6.44) that also applies to mortar: τ0 =

225 · ρg · V 2 4 · π2SF5

(6.44)

where τ 0 is the yield stress in Pa, ρ is the density of fresh mortar in g/mm3 , g is the gravity acceleration in mm/s2 , V is the sample volume in mm3 , and SF is the mini-slump flow in mm. Based on a theoretical analysis of mini-cone tests, Roussel et al. [35] proposed the expression for the spreading distance as a function of the yield stress and material

X

Teng et al., 2020 (ConTec 5) [39]

Flow time

X

X

Spread time

Meng and Khayat, 2017 (ConTec 6 and ConTec 5) [38]

X

Surface tension

X

X

X

Volume

Mikanovic et al., 2010 (ConTec 6) [37]

Mini V-funnel

X

Choi et al., 2016 (Computational fluid dynamics analysis) [36]

X

X

X

Roussel et al., 2005 (Analytical solution) [35]

X

Flow spread

Rouis, 2017 (ConTec 6) [21]

X

Density

Kokado and Miyagaw, 1999 (Analytical solution) [15]

Mini cone

Influence parameter

X

X

X

X

Dynamic yield stress

X

X

X

X

Plastic viscosity

Table 6.5 List of references with studies on mortar relating rheological parameters to influence parameters of free flow properties

X

Fit parameters

158 K. Khayat et al.

6 Empirical Test Methods to Evaluate Rheological Properties of Concrete …

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Fig. 6.11 Relationship between yield stress and slump spread of concrete equivalent mortar [21]

volume, as shown in Eq. (6.45): τ0 =

225 · ρgV 2 π R2 − const. 128π 2 · R 5 V

(6.45)

where τ 0 is the yield stress in Pa, ρ is the density of fresh mortar in kg/m3 , g is the gravity acceleration in m/s2 , V is the sample volume in m3 , R is the radius of flow spread in m, and const. coefficient is a function of both the unknown tested fluid surface tension and contact angle in N/m. A practical form of the above relationship is shown in Eq. (6.46): τ0 = 1.747 · ρV 2 R −5 − λ ·

R2 V

(6.46)

where τ 0 is the yield stress in Pa, ρ is the fresh mortar density in kg/m3 , V is the sample volume in m3 , R is the half of mini-slump flow in m, and λ is a parameter considering the surface tension effect and contact angle in N/m. Rouis [21] established a correlation between the mini slump flow and yield stress determined using the Contec 6 rheometer for concrete-equivalent mortar (CEM) made with different mixture proportions, as shown in Fig. 6.11.

6.4.2 Flow Spread/flow Time Versus Plastic Viscosity Choi et al. [36] determined the flow spread-time curves of ultra-high-performance concrete (UHPC) mixtures using a mini cone with computational fluid dynamics (CFD) simulations. The plastic viscosity and yield stress can be correlated with two calibrating parameters (λ and γ ) obtained from the flow spread-time curves, respectively, as is shown in Eqs. (6.47)–(6.49): ( D(t) = α + 29.8 · ln(t + γ ) − λ

t 0.842 13.5 + t 0.842

) (6.47)

160

K. Khayat et al.

μ= (

γ + 0.0165 0.00395

μ τ0 = λ 0.48μ + 124

(6.48) ) (6.49)

where D(t) is the change in the spreading diameter in mm with time t in s, α is a fitting constant in mm, μ is the plastic viscosity in Pa·s, τ 0 is the yield stress in Pa, γ and λ are the fitting parameters.

6.4.3 Mini V-Funnel Versus Plastic Viscosity Mikanovic et al. [37] proposed a relationship between V-funnel flow time and plastic viscosity of concrete-equivalent mortar (CEM) of SCC using a Contec 6 rheometer, as shown in Eq. (6.50). The opening of the V-funnel is 30 × 30 mm2 . ( ) μ = 1.39 · TV − 0.60 R2 = 0.90

(6.50)

where μ is the plastic viscosity in Pa·s, and T V is the mini-V-funnel flow time in s. Meng and Khayat [38] established a correlation between mini-V-funnel flow time and plastic viscosity for UHPC suspending mortar and UHPC. The opening of the V-funnel is 30 × 30 mm2 . The mini-V-funnel flow times were in the range from 10 to 100 s. The viscosity of the suspending mortar (matrix) and UHPC composite materials were evaluated using the co-axial viscometers Contec 6 and Contec 5, respectively, and they were in the range of 10 to 120 Pa·s: ( ) For suspending mortar of UHPC : μ = 1.05 · TV + 3.83 R2 = 1.00 ( ) For UHPC : μ = 1.10 · TV + 3.10 R2 = 0.99

(6.51) (6.52)

where μ is the plastic viscosity in Pa·s, and T V is the mini-V-funnel flow time in s. Teng et al. [39] reported a relationship between mini-V-funnel flow time and plastic viscosity for UHPC mortar. The data included the results of the UHPC suspending mortar reported by Meng and Khayat [38]. The UHPC mortar by Teng et al. [39] was prepared with a fixed mini-slump flow of 270 ± 10 mm. The opening of the V-funnel is 30 × 30 mm2 . The mini-V-funnel flow time ranged from 12 to 59 s. The plastic viscosity of the UHPC mortar evaluated using the co-axial viscometers Contec 5 was in the range of 10–66 Pa·s. ( ) μ = 0.92 · TV − 1.46 R2 = 0.99, n = 9

(6.53)

where μ is the plastic viscosity in Pa·s, and T V is the mini-V-funnel flow time in s.

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6.5 Structural Build-Up of Mortar As discussed earlier, empirical test methods also have been used to determine the structural build-up of mortar, such as portable vane, inclined plane, undisturbed slump spread (USS), and cone penetration (CP) tests. This section describes the main test methods used to evaluate the structural build-up and workability loss of mortar and attempts to present correlations between these methods and the structural buildup parameters. The latter includes the increase of static yield stress and apparent viscosity at rest. Table 6.6 summarizes some of the studies that have proposed correlations between empirical test methods and structural build-up of mortar. Some of the relationships that are cited in Table 6.6 are further elaborated below, and examples of some of the established correlations between empirical tests to evaluate the structural build-up of mortar and the increase of static yield stress and apparent viscosity at rest are presented.

6.5.1 Portable Vane For the concrete-equivalent mortars (CEM) of SCC mixtures, Khayat et al. [32] validated the structural build-up index of the portable vane (PV) test using the static yield stress of the modified Tattersall MK-III rheometer equipped with an eightbladed vane. The PVτ 0rest@15min × PVτ 0rest (t) index from the PV test is correlated to the time-dependent static yield stress of the rheometer [Rheometerτ 0rest (t)], as shown in Eq. (6.54): ) ( P V τ0r est@15min × P V τ0r est (t) = 340 · Rheometer τ0r est (t) R2 = 0.96

(6.54)

where PVτ 0rest@15min is the static yield stress obtained from the PV test at 15 min of rest in Pa, PVτ 0rest (t) is the time-dependent static yield stress determined using Table 6.6 List of references with studies on mortar relating structural build-up at rest and workability Rheological characteristic versus empirical workability test

Static yield stress

Athix / τ 0rest (t)

X

X

X

X

Portable vane Khayat et al., 2012 (Modified Tattersall MK-III rheometer equipped with eight-bladed vane, undisturbed slump flow) [32] Thixotropy of undisturbed samples Khayat et al., 2012 (Modified Tattersall MK-III rheometer equipped with an eight-bladed vane, undisturbed slump flow) [32]

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K. Khayat et al.

the PV test in Pa/s (also known as Athix ), and Rheometerτ 0rest (t) is the yield stress obtained from rheometric testing using a coaxial rheometer in Pa.

6.5.2 Structural Build-Up of Undisturbed Samples Khayat et al. [32] proposed the following correlations derived from statistical models relating the variations with time of the τ 0,s−IP and τ 0,s−PV with the variations of undisturbed slump spread (USS) of concrete-equivalent mortars (CEM) of SCC measured on samples being at rest over up to 70 min. The USS of CEM was tested using a cylinder with an inner diameter of 78 mm and a height of 110 mm. ( ) τ0,s−I P = −150 · ln(U SS) + 940 R2 = 0.88

(6.55)

( ) τ0,s−P V = −3.53 · U SS + 1169 R2 = 0.84

(6.56)

where τ 0,s−IP is the static yield stress measured using the inclined plane test method in Pa, τ 0,s−PV is the static yield stress measured using the portable vane test method in Pa, and USS is the undisturbed slump spread in mm. Khayat et al. [32] also proposed the following correlation derived from statistical models relating the variations with time of the τ 0,s−PV with the variations of penetration depth (PD) of the CEM measured being at rest over up to 70 min. The penetration depth of CEM were tested using the cone penetration (CP) test referring to ASTM D3441 [40]. ) ( τs−P V = 3563.1 · e−0.11·P D R2 = 0.89

(6.57)

where τ 0,s−PV is the static yield stress measured using the penetration depth test method in Pa, and PD is the penetration depth of the cone penetration test in mm.

6.6 Tests for Extrusion and 3DP This section describes the main test methods used to evaluate the flowability or deformability of highly concentrated building materials, such as mortar, and attempts to present correlations between empirical test methods and the rheological parameters. The latter includes yield stress, apparent/plastic viscosity, and consistency index. Table 6.7 summarizes some of the studies that have proposed correlations between flow properties and rheological parameters of mortar. Some of the relationships that are cited in Table 6.7 are further elaborated below, and examples of some of the established correlations between flow properties of mortar and stress and viscosity/

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Table 6.7 List of references with studies relating rheological parameters to flow properties of mortar Rheological characteristic

Yield stress

Viscosity/ consistency index

Compression force/stress

Penetration force/depth

Squeeze test Toutou et al., 2005 (Analytical solution) [41]

X

Sherwood and Durban, 1996 (Analytical solution) [42]

X

Grandes et al., 2018 (Analytical solution) [43]

X X

X

X

X

Penetration test Lootens et al., 2009 (Analytical solution and numerical simulation) [44]

X

X

Mazhould et al. 2019 (Cone penetrometer) [45]

X

X

consistency index are presented. Table 6.8 presents a summary of the influencing parameters of the empirical test methods in Table 6.7.

6.6.1 Squeeze Tests The Squeeze test method is described in Chap. 3. Such test is often used to assess the flow behavior of highly concentrated building materials, such as mortar [41, 43, 46]. Such materials behave as highly viscous or quasi-plastic fluids and can be described as Bingham fluids as a first approximation. Squeeze flows are similar to some conditions involved in processing and the application of paste, mortar, and concrete. Examples of processing and application of these materials include material flow through a narrow nozzle during pumping, injection or spraying, spreading over a surface, and then finishing, squeezing between bricks, tiles or aggregates, extrusion and 3D printing [41, 43, 47, 48]. In practical applications, the squeeze test can be applied over different substrates that vary in roughness, porosity, and water absorption capacity. It is important to note that the flow behavior can be greatly affected by the roughness of the plate and substrate. Based on a theoretical analysis of the squeeze test for Bingham suspensions, Toutou et al. [41] proposed two models for the perfect plastic flow and the Drucker– Prager plastic behavior, respectively. In the former case, the compression force is calculated from the energy dissipation, and a relationship between the compression load and yield stress is then given as shown in Eq. (6.58):

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K. Khayat et al.

Table 6.8 List of references with studies on mortars relating rheological parameters to influencing parameters of free flow properties Influence parameter

Height/ Motion Yield Viscosity/ Fit/ Compression Penetration depth speed stress consistency apparatus force/stress force index parameters

Squeeze test Toutou et al., 2005 (Analytical solution) [41]

X

X

Sherwood and X Durban, 1996 (Analytical solution) [42]

X

Grandes et al., X 2018 (Analytical solution) [43]

X

X

X

X

X

X

X

X

X

X

Penetration test Lootens et al., 2009 (Analytical solution and numerical simulation) [44]

X

Mazhould X et al., 2019 (Cone penetrometer) [45]

X

F∗ = −

X

2σ0 2π σ0 h Fh = √ · + π R3 R 3 3

(6.58)

with F =−

2π σ0 R 2 Fh 2π σ0 R 3 = − − √ π R3 3h 3

( ) where F * is the reduced compression load defined by Fh/ π R 3 in Pa, F is the compression force applied on the plates in N, h is the sample height or plate separation in m, R is the plate radius in m, and σ 0 is the yield stress defined according to the Von Mises criterion in Pa. It is worth noting that according to the Von Mises√plasticity criterion, the yield stress is linked to the shear yield stress through σ0 = 3τ0 . In the case of the Drucker–Prager plastic behavior, the average compression stress (p) is calculated, as shown in Eq. (6.59):

6 Empirical Test Methods to Evaluate Rheological Properties of Concrete …

) ) ( ( h F h2 h 2fR − p0 · · 1+ p= = p0 · · ex p π R2 2 f 2 R2 h fR 2fR

165

(6.59)

where p is the average compression stress in Pa, F is the compression force applied on the plates in N, R is the plate radius in m, p0 is the pressure in Pa at the boundary R = 0 of the plate, h is the sample height or plate separation in m, f is the Coulomb apparent friction parameter. In the case of a Bingham fluid flow with a no-slip condition, based on the lubrication theory, Sherwood and Durban [42] gave the expression for the compression force as shown in Eq. (6.60): F=

4π σ0 R 3 √ 2π σ0 R 3 + · 2g + O(g) 3h 7h

(6.60)

For g = ηc R/(τi h 2 )