Causes of cracking in concrete gravity dams

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Background and overview

Concrete, as a material of low tensile strength, has been subject to cracking problems since it was first used in structural applications. Recognition of the importance of cracking in concrete structures has prompted great interest in research on the fracture modelling of concrete. Classical (strength-based) mechanics of materials have been proved to be inadequate to handle severe discontinuities, such as cracks in a material. With the advance of powerful finite element (FE) analysis techniques, intensified research efforts have been made over the past few decades in the application of fracture mechanics (FM) in the modelling of cracking phenomena in concrete and concrete structures. Plain and reinforced concrete structures have been extensively analyzed using this broad FE, FM approach. For example, Valente (2003) used a crack band model to analyze statically and dynamically the collapsed baroque Noto Cathedral in Italy for the purpose of rebuilding the 60-m-high structure. Shi, Ohtsu, Suzuki & Hibino (2001) extended the discrete crack approach to the numerical analysis of multiple cracks in a real-size tunnel specimen which had been experimentally tested. The sudden collapse of the New York Schoharie Creek Bridge in 1987 due to the unstable cracking in the reinforced piers, caused by the rapid flow of a flood, led Swenson & Ingraffea (1991) to adopt discrete cracking models, including linear and non-linear FM, to evaluate the initiation, stability and propagation profile of the crack that caused the failure.
The deadly (loss of ten lives) cracking problems of the bridge can be rationally explained by the use of FE-based models. Other types of plain or reinforced concrete structures that experienced fracture-controlled problems, such as the pullout of anchor bolts, the thick-walled ring, beams, panels, frames, containment vessels and shells, have also been analyzed in the past using FE, FM models (ACI 1997). In an important effort to apply the FM approaches that have been developed to problems of practical significance, concrete dams (which are normally huge, fracture-sensitive concrete structures) have received special attention from researchers and have formed an essential part of this broad area of research on concrete crack modelling. Uncontrolled crack propagation in concrete caused the disastrous failures of Malpasset Dam in France in 1959 (SimScience website). The rapid crack propagation as evidenced in the failure process of the above dam, has emphasized the importance of developing an accurate crack modelling method to safeguard dams. The Kölnbrein arch dam in Austria and Koyna gravity dam in India are representative of the two main types of dam structures which have attracted most research efforts for FM crack modelling of concrete dams. Gravity dams are structures that rely on their own weight for resistance against sliding and overturning to maintain stability. In ancient times dated back as early as 4000 years BC, gravity dams were built using masonry materials such as earth, rock and cut blocks, with both the upstream and downstream faces sloped and the base thickness being many times the height of the dam. Concrete was first used in building a 47-m-high gravity dam called the Lower Crystal Springs Dam in the USA which was completed in 1889. Because they are relatively simple to design and build, concrete gravity dams have become a major dam type throughout the world. With the development of design and analytical expertise, as well as of construction techniques and equipment, dams have become ever larger with regard to both height and volume, e.g. the world’s largest gravity dam so far, Three Gorges Dam in China, has a height of 185 m and a water-storage volume of 39.2 billion m3 . If a dam on this scale were to fail and collapse, this could lead to probably the greatest disaster in human history. Therefore, the safety of huge structures such as concrete gravity dams is of the utmost concern to the engineers involved in the design, construction and post-built safety evaluation of dams. A great deal of research on the numerical modelling of the cracking behaviour of concrete has been carried out during the past few decades. In the process, many concrete crack propagation models have been developed and applied in concrete cracking analyses. The early strength-based model, in which the crack was assumed to propagate when the calculated tensile stresses at the crack tip exceed a specified tensile strength of the concrete, has seldom been used in any recent concrete analyses due to its inherent lack of mesh objectivity (FE mesh discretization has a significant influence on the results).
Linear elastic fracture mechanics (LEFM), in which crack growth occurs when the effective stress intensity factor exceeds the material’s fracture toughness, has been widely used in the analysis of concrete in the past. Models based on non-linear fracture mechanics (NLFM) have now become popular for analysing concrete cracking due to the existence of a fracture process zone (FPZ) at the front of the crack tip. Many concrete gravity dams, which are generally massive, plain concrete structures, have experienced cracking problems to various extents. Crack formation and propagation in concrete gravity dams could influence their structural stability and endanger the safety of the dams. Normally, the huge size of a concrete dam excludes direct experimental tests on the structural cracking behaviour under various loading conditions. Therefore, evaluation of the possible cracking trajectory in concrete dams by means of an accurate constitutive model, in order to simulate the cracking response of the concrete effectively, becomes vital and would be a useful tool for practising engineers to ensure the safety of dam structures. This requires developing a numerical model and techniques that can accurately analyse and appraise a dam structure, either for the purpose of designing a new dam or for evaluating the safety of an existing concrete dam. The need for methods that can accurately predict the behaviour of cracking in concrete dams has led to intensified research in this field. In fact, many attempts have been made to develop a rigorous model to simulate the cracking mechanisms in and the behaviour of concrete dams, especially concrete gravity dams. To name a few, Ingraffea (1990) performed a case study on the Fontana Dam, a gravity dam in the United States, to elucidate the mechanisms for crack initiation and to predict the observed crack trajectory employing a 2-D discrete LEFM method. Bhattacharjee & Leger (1994) applied a 2-D smeared crack model based on NLFM crack propagation criteria to study the static fracture behaviour of the Koyna Dam, a gravity dam in India. A more detailed review of these attempts will be given in Chapter II.
Although many analytical methods based on fracture mechanics have been proposed for concrete dams in the last few decades, they have not yet become part of standard design procedures. In fact, few of the current researches from all over the world are being implemented by practising engineers when evaluating dam safety. Current practice for crack analysis in concrete dams is to implement either the traditional “no-tension” gravity design method, which is based on rigid body equilibrium and strength of materials to determine crack length, assuming horizontal planar crack extension, linear stress distribution and zero stress at crack tip, or a non-linear FE analysis including plasticity models and contact simulation. There are several FE programs that can be used to analyse the cracking response of concrete structures, e.g. MSC.Marc, ABAQUS, ANSYS, DIANA, LUSAS, FRANC2D/3D, FRACDAM and MERLIN, etc. At the Department of Water Affairs and Forestry (DWAF) – the dam authority in South Africa, MSC.Marc is currently the main FE tool used for non-linear analysis, including crack prediction on concrete dams. The cracking analysis in MSC.Marc is limited to linear tensile strain softening and the constant shear retention factor. This means that MSC.Marc lacks the flexibility in analysing cracking behaviour that is offered by more advanced crack models (including multi-linear or non-linear softening, shear retention factor varied with the crack’s normal strain, etc.).
Although some commercial FE programs, such as DIANA include advanced crack models, the codes of these programs are not generally available to be modified/enhanced for research purposes. In addition, the existing programs yield significantly different results on the crack response of a concrete gravity dam, as demonstrated in the benchmark exercise carried out by the European Thematic Network Integrity Assessment of Large Dams between 2003 and 2005 (refer to http://nw-ialad.uibk.ac.at). The different results with regard to peak load, displacement and stress given by the different programs highlight the need to improve the cracking analysis capacity of the existing FE packages by developing, perhaps, a better method of crack analysis and its numerical implementation in an FE program. An improved crack model and method could give a more accurate crack response (crack profile, horizontal crest displacement, etc.) in concrete dams which could be used to evaluate the safety of dams.

Motivations and objectives of this study

This research aims to contribute to the continuing research efforts on mastering the mechanics of cracking in concrete dams. In order to evaluate the stability and safety of concrete dams more accurately, it is necessary to develop a better model and method for analysing cracking problems in concrete dams. The objectives of the research are as follows: • To evaluate the existing constitutive crack models critically and to adopt a suitable constitutive crack model using non-linear smeared fracture mechanics for simulating and investigating the cracking process in concrete dam structures. • To develop a more accurate strain softening relation and to calibrate the parameters. • To develop a numerical program specially for implementing the constitutive model in order to carry out fracture analysis of concrete dams under static loading conditions. • To validate the constitutive model and numerical techniques by investigating the cracking behaviour of concrete structures that have been researched experimentally and/or numerically in the past. • To investigate dam concrete softening parameters. • To investigate the cracking behaviours of concrete gravity dams for better evaluation of dam safety.

Scope of this study

This research is focused on the development of a suitable crack modelling and analysis method for the prediction and study of fracturing in concrete gravity dams, and consequently, for the evaluation of dam safety against cracking. The research is limited to the two-dimensional (2-D) static cracking analysis of concrete gravity dams. The following areas are not covered in this research: • Three-dimensional (3-D) cracking, although the research could be extended from 2-D to 3-D with some additional effort. • Dynamic cracking. • The water pressure that develops inside the crack as the crack grows. • The coupling between different crack modes, and different cracks. • Time dependent behaviour such as creep and shrinkage. 1.4 Methodology of this study The research begins with a thorough literature review of previous investigations into the subject area and similar research. The theory and development of constitutive crack models are followed to establish the material crack model used in this study. The implementation of the proposal crack model is undertaken through the development of a sub-program specially coded for this research. The constitutive crack model proposed and the implementation procedure of the proposed crack model in an FE program are validated by analyzing and comparing the results obtained with the previously investigated concrete beams, gravity dams and model dam.
After the verification process, the crack model and the sub-program are applied to analyze and predict the fracture response and to evaluate the related dam safety against the cracking of an existing, full-size concrete gravity dam. Finally, conclusions are drawn and recommendations are made based on this study. 1.5 Organization of this study Chapter I gives the background, motivation, objectives, scope and methodology of this study. Chapter II is a comprehensive literature review of the development of crack models for application with concrete, especially concrete dams. The review focuses mainly on the evolution of the crack models proposed by other researchers in the world during the past few decades and gives a critical appraisal of the pros and cons of the crack models. A brief description of the analytical and design methods adopted for concrete gravity dams is given for readers who are not familiar with the design and safety evaluation procedure for concrete gravity dams. Past investigations into the fracture analysis of concrete dams are also discussed in Chapter II.

TABLE OF CONTENTS :

• THESIS SUMMARY
• ACKNOWLEDGEMENTS
• TABLE OF CONTENTS
• LIST OF TABLES
• LIST OF FIGURES
• NOTATION
• CHAPTER I INTRODUCTION
  • 1.1 Background and overview
  • 1.2 Motivations and objectives of this study
  • 1.3 Scope of this study
  • 1.4 Methodology of this study
  • 1.5 Organization of this study
• CHAPTER II LITERATURE REVIEW ON GRAVITY DAM DESIGN AND ON THE DEVELOPMENT IN FRACTURE ANALYSIS OF CONCRETE DAMS
  • 2.1 Causes of cracking in concrete gravity dams
  • 2.2 Brief description of methods of analysis and design criteria for concrete gravity dams
  • 2.3 Analysis of cracking in concrete dams
  • 2.4 Finite element approaches for modelling cracking in concrete
  • 2.5 Crack modelling of concrete
    • 2.5.1 Pre-fracture material stress-strain behaviour
    • 2.5.2 Crack initiation
    • 2.5.3 Crack propagation criteria
    • 2.5.4 Crack models
    • 2.5.5 Summary of crack models discussed
    • 2.5.6 Shear resistance of fractured concrete
    • 2.5.7 Post-crack behaviour
  • 2.6 Fracture energy Gf of dam concrete
  • 2.7 Past investigations of the static cracking problems of concrete gravity dams
  • 2.8 Concluding remarks and recommendations
• CHAPTER III CONSTITUTIVE MODELS AND PARAMETERS STUDY
  • 3.1 Pre-softening constitutive relationship
  • 3.2 Crack onset criterion and crack direction
  • 3.3 Constitutive relationship during concrete cracking
    • 3.3.1 Plane stress application used in this research
    • 3.3.2 Plane strain application used in this research
  • 3.4 Mode I tensile softening
  • 3.5 Mode II shear softening
  • 3.6 Fixed/rotating, unloading/reloading and closing/reopening of cracks
  • 3.7 Width of crack blunt front and mesh objectivity
  • 3.8 Element selection for crack analysis
  • 3.9 Concluding remarks
• CHAPTER IV NUMERICAL TECHNIQUE AND PROGRAM FOR FINITE ELEMENT CONSTITUTIVE CRACKING ANALYSIS
  • 4.1 Program framework for the cracking analysis of concrete
  • 4.1.1 Framework for the implementation of the constitutive model in the FE analysis of concrete structures
    • 4.1.2 Sub-pragram coded in MSC.Marc to implement the crack constitutive model
    • 4.1.3 Possible numerical implementation problems
  • 4.2 Verification study with MSC.Marc and other specimens investigated in the past
    • 4.2.1 Built-in crack model in MSC.Marc for specimens 1 and
    • 4.2.2 The smeared model adopted for specimens 1 and
    • 4.2.3 The smeared model adopted for specimens 3 and
    • 4.2.4 FE models benchmarked
    • 4.2.5 Discussion of results of the verification
    • 4.3 Verification study with DIANA
    • 4.3.1 Cracking with linear tensile softening – plane strain
    • 4.3.2 Cracking with bilinear tensile softening – plane strain
    • 4.3.3 Cracking with alternating loading – plane strain
  • 4.4 Concluding remarks
• CHAPTER V STATIC FRACTURE ANALYSIS OF CONCRETE STRUCTURES
  • 5.1 Introduction
  • 5.2 Case 1: three point, centre-loaded, single-notched beam
  • 5.3 Case 2: single-notched shear beam
  • 5.4 Case 3: mesh objectivity and second-order elements validation
  • 5.5 Conclusion
• CHAPTER VI STATIC FRACTURE ANALYSIS OF CONCRETE GRAVITY DAMS
  • 6.1 Introduction
  • 6.2 Model concrete dam
  • 6.3 A concrete gravity dam adopted by NW-IALAD
  • 6.4 Koyna Dam
• CHAPTER VII SAFETY EVALUATION OF A CONCRETE GRAVITY DAM IN SOUTH AFRICA BASED ON FRACTURE ANALYSIS
  • 7.1 Introduction
  • 7.2 Description of the gravity dam and finite element model
  • 7.3 Material properties and constitutive fracture parameters
  • 7.4 Bilinear strain-softening shape parameters
  • 7.5 Fracture analysis and evaluation of the dam safety
    • 7.5.1 Parametric study on the fracture energy of concrete and rock
    • 7.5.2 Parametric study on the bilinear shape parameters α1 and α
    • 7.5.3 Parametric study on the tensile strength of concrete and rock
    • 7.5.4 Parametric study on the crack onset threshold angle φ
    • 7.5.5 Parametric study on the maximum shear retention factor
    • 7.5.6 Comparison with linear elastic and plasticity analyses
  • 7.6 Evaluation of dam safety against sliding (shear)
  • 7.7 Conclusions
• CHAPTER VIII CONCLUSIONS AND RECOMMDATIONS
  • 8.1 Conclusions
  • 8.2 Recommendations
  • 8.3 Closure
  • ANNEXURE
  • REFERENCES/BIBLIOGRAPHY

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