Modelling of Cement Hydration in Concrete Structures with Hybrid Finite Elements - Pham Tien Cuong

UNIVERSIDADE DE LISBOA INSTITUTO SUPERIOR TÉCNICO Modelling of Cement Hydration in Concrete Structures with Hybrid Finite Elements Pham Tien Cuong Supervisor: Doctor João António Teixeira de Freitas Co-supervisor: Doctor Rui Manuel Carvalho Marques de Faria Thesis approved in public session to obtain the PhD Degree in Civil Engineering Jury final classification: Pass with Merit Jury Chairperson: Chairman of the IST Scientific Board Members of the Committee: Doctor João António Teixeira de Freitas Doctor Eduardo Nuno Brito Santos Júlio Doctor Mário Jorge de Seixas Pimentel Doctor Miguel Ângelo Dias Azenha Doctor Carlos Manuel Tiago Tavares Fernandes 2014 UNIVERSIDADE DE LISBOA INSTITUTO SUPERIOR TÉCNICO Modelling of Cement Hydration in Concrete Structures with Hybrid Finite Elements Pham Tien Cuong Supervisor: Doctor João António Teixeira de Freitas Co-supervisor: Doctor Rui Manuel Carvalho Marques de Faria Thesis approved in public session to obtain the PhD Degree in Civil Engineering Jury final classification: Pass with Merit Jury Chairperson: Chairman of the IST Scientific Board Members of the Committee: Doctor João António Teixeira de Freitas Professor Catedrático do Instituto Superior Técnico, da Universidade de Lisboa Doctor Eduardo Nuno Brito Santos Júlio Professor Catedrático do Instituto Superior Técnico, da Universidade de Lisboa Doctor Mário Jorge de Seixas Pimentel Professor Auxiliar da Faculdade de Engenharia, da Universidade do Porto Doctor Miguel Ângelo Dias Azenha Professor Auxiliar da Escola de Engenharia, da Universidade do Minho Doctor Carlos Manuel Tiago Tavares Fernandes Professor Auxiliar do Instituto Superior Técnico, da Universidade de Lisboa Funding institutions Fundação para a Ciência e a Tecnologia (FCT), Grant reference number: SFRH/BD/76632/2011 2014 Abstract The main objective of this work is to develop a hybrid finite element formulation to model cement hydration in concrete structures. First, a hybrid formulation of the finite element method is developed for the solution of heat transfer problems. It is based on the independent approximation of the temperature and heat flux fields in the domain and on the boundary of the element, respectively. The formulation is assessed in terms of convergence and robustness, and is validated using linear and nonlinear steady-state and transient test problems.

Second, the hybrid model is used to simulate the thermo-chemical response of ordinary Portland cement concrete using the hydration degree concept. The hybrid formulation is extended to include the simulation of the effect of the heat source and to approximate directly the hydration degree field. Third, the hybrid model is extended to simulate the coupled processes of heat transfer and moisture transport in concrete. Two fields are approximated in the domain of the element (temperature and relative humidity) and on the boundaries (heat and moisture fluxes).

The model can be used to simulate the hygro-thermo-chemical response of both hardening and hardened concrete and is valid for normal strength concrete and high-performance concrete. Therefore, and besides the hydration reaction, the supporting mathematical model is extended to simulate the effects of the silica fume reaction and silicate polymerization in heat generation and in moisture consumption. The corresponding degrees of reactions are also approximated in the hybrid finite element model. Particular attention is paid to the simulation of the boundary conditions that occur in practical applications, which are typically nonlinear and vary in time and in space.

This is essential to assess the performance of the formulation using laboratory experiments and in situ tests reported in the literature. These tests include one- and two-dimensional problems, as well as axisymmetric and three-dimensional applications. Special attention is also paid to preserving the computational advantages offered by hybrid finite element formulations. The approximation bases are orthogonal and naturally hierarchical, to induce high sparsity indices and enable adaptive p-refinement.

The solving system is not condensed at element level to enhance parallel processing. The approximations of the state variables and of the geometry are uncoupled to enable the use of unstructured, coarse meshes of high-degree elements. Approximation of the state variables is also uncoupled directionally in space to implement elements with high aspect ratios, frequently needed in the simulation of staged construction of concrete structures. Keywords: Cement hydration; Heat transfer; Moisture transport; Normal strength concrete; High-performance concrete; Hybrid finite elements.

iii Resumo O objectivo central deste trabalho é desenvolver uma formulação híbrida do método dos elementos finitos para simular a hidratação do cimento em estruturas de betão. Começa-se por desenvolver uma formulação híbrida para problemas de transferência de calor, a qual é baseada na aproximação independente da temperatura no domínio do elemento e do fluxo de calor nas fronteiras. O desempenho da formulação é avaliado em termos de convergência e robustez, sendo validado recorrendo a problemas em regime estacionário e transitório, lineares e não-lineares. A formulação é depois aplicada à simulação da hidratação do cimento Portland em betões de resistência normal.

A reacção e a fonte de calor associada ao processo termo-químico são descritas usando o conceito de grau de hidratação, sendo esse campo também directamente aproximado na formulação por elementos finitos híbridos. Seguidamente procede-se à generalização da formulação para simular o acoplamento dos processos de transferência de calor e de transporte de humidade. O modelo utilizado pode ser usado para simular o comportamento higro-termo-químico do betão nas diferentes fases de hidratação e de endurecimento, e é também válido para betões de alto desempenho, pois a formulação desenvolvida contempla as reacções de fumo de sílica e de polimerização dos silicatos. Os correspondentes graus de reacção são também directamente aproximados na formulação híbrida desenvolvida.

A formulação é validada recorrendo aos resultados publicados sobre testes laboratoriais e ensaios in situ de provetes e estruturas de betão. Dá-se, por isso, particular atenção à adequada simulação das condições de fronteira que ocorrem nos ensaios simulados numericamente, as quais são frequentemente não-lineares e variáveis no espaço e no tempo. Os testes de validação cobrem problemas unidimensionais, planos, axi-simétricos e tridimensionais. Procura-se, também, conceber e implementar a formulação preservando as vantagens computacionais inerentes às variantes híbridas do método dos elementos finitos.

As bases de aproximação são ortogonais e naturalmente hierárquicas, por forma a obter sistemas resolventes com elevados índices de esparsidade e facilitar a aplicação de processos de refinamento adaptativos. O sistema resolvente não é condensado a nível do elemento, a fim de potenciar a solução em processamento paralelo. A aproximação das variáveis de estado é desacoplada da aproximação da geometria, para permitir o uso de malhas não estruturadas envolvendo relativamente poucos elementos mas com elevado grau de aproximação. A aproximação das variáveis de estado é também desacoplada direccionalmente, para permitir a utilização de elementos com relações de dimensões características muito elevadas, cuja utilização é muito útil na simulação do processo construtivo de estruturas de betão.

Palavras-chave: Hidratação do cimento; Transferência de calor; Transporte de humidade; Betão de resistência normal; Betão de alto desempenho; Elementos finitos híbridos. v Acknowledgements The work done in this thesis would not have been possible without the help and contribution of many people. I would like to express my deep gratitude to all of them. First, I would like to express my deepest gratitude to my supervisor, Prof.

João António Teixeira de Freitas for giving me the opportunity to do a PhD at Departamento de Engenharia Civil, Arquitectura e Georecursos (DECivil) with his great scientific guidance, advice, and invaluable support throughout my PhD period. He did his best to clarify my understanding of the non-conventional formulations of finite elements which were new to me. His scientific knowledge contributed to this thesis in many ways. He was always to help me solve not only problems in my work but also any difficulties during my stay in Portugal.

Furthermore, he always received me with sympathy for the long period of my stay. I admire him for his profound knowledge, experience and his passion for research. I will always be grateful for the lessons that I learned from our discussions. Finally, I would like to thank him for the friendship that we have developed.

I express my sincerest gratitude to my co-supervisor Prof. Rui Manuel Carvalho Marques de Faria from the University of Porto for all his advice, support, guidance and special contribution for this thesis. He always received me warmly whenever we had meetings in Porto and he suggested many good ideas in our discussions. I would like to express my thanks to the Departamento de Engenharia Civil, Arquitectura e Georecursos where I pursued my doctoral degree and to the Portuguese Foundation for Science and Technology (FCT) for their financial support through R&D project PTDC/ECM/70781/2006 launched at IST and research contract SFRH/BD/76632/2011.

My thanks are also extended to “O Núcleo de Pós-Graduação e Formação Contínua” for their kind help for my PhD’s procedure at IST. I would like to thank all the staff and professors of the Structural Mechanics and Structures Section, especially Maria da Conceição Melo, Paula Cristina, Prof. Moitinho de Almeida, Prof. Luís Castro, Prof.

Orlando Pereira and Prof. Eduardo Júlio for all their assistance and support. My special thanks are conveyed to Prof. Carlos Manuel Tiago Tavares Fernandes, from whom I received great help, support and encouragement as well as for the many daily talks about many aspects of life that we had, in particular, cycling and football discussions.

I sincerely wish to thank Prof. João José Rio Tinto de Azevedo and his aunt, Ms. Maria Tinto for letting me stay in her apartment without paying during my last year of my PhD. I want to take this opportunity to thank Prof.

Miguel Ângelo Dias Azenha from the School of Engineering of the University of Minho. He never hesitated to share his scientific expertise, particularly in early-age concrete behaviour. Additionally, he gave me many good comments and suggestions, as well as many test data used in this work. vii Acknowledgements viii I would also like to thank Prof.

Giovanni Di Luzio at Department of Structural Engineering, Politecnico di Milano, Italy, for his kind help with many discussions about the mathematical model of moisture as well as the data used in this thesis. I gratefully acknowledge Maria Cristina (my supervisor’s wife) for her kindness, encouragement as well as her regular and kind regards to my family in Vietnam. I would like to thank her for the close friendship that we have built. My thanks also go to my colleagues at DECivil: Cristina Lopez, Vasco Mano, Júlio Pargana and Maria José.

I will always remember the fun moments we had together. My particular gratitude to Luís Mendes, my office mate, who helped me a lot, namely with Matlab programing, and we also had a lot of fun during the first two years of my PhD. I express many thanks to another office mate, Vladimir Ivannikov, a Russian PhD student who shared with me many types of fun for almost three years and half, such as watching together many games of European football cups, going to watch the games in Estádio da Luz, the home of the Benfica team, and travelling. I have also spent many great moments with Vietnamese friends, who were studying and working in Lisbon: Hoàng Văn Xiêm, Trần Nguyễn Nguyên Khôi, Lê Hồng Trang, Hàn Thế Anh, Đinh Thanh Giang, Trần Thế Hùng, Nguyễn Thành Trung, Nguyễn Hà Anh Tuấn, Nguyễn Hoàng Sơn and Prof.

Phan Thành An. Thank you all for sharing a good time with me during my stay in Lisbon. My thanks also go to other friends: Diego Felix de Souza, Sanchit Singh, Mauricio Ramalho, Suresh, Dhiraj K. Shah, Berner Panti and João Matos Cardoso for the great times of relaxing and travelling during my stay in Portugal, especially with all the funny things they did that I cannot forget.

Furthermore, I am particularly grateful to my close friend, Cao Đức Toàn, without whose help I may not have been to Lisbon. I would like to thank my mother, mother-in-law, sisters, brothers, sisters-in-law and brothers- in-law, who encouraged, motivated and supported me throughout my years of study. They admire me and I deeply love them. Finally, my most special words are for my wife, Lê Thị Tuyết Chinh and my son, Phạm Gia Hoàng, for having me in their hearts.

Nothing could have been possible without their love, encouragement and patience.