Numerical Modeling of AAR

This reference book presents the theory and methodology to conduct a finite element assessment of concrete structures subjected to chemically induced volumetric expansion in general and alkali aggregate reaction in particular. It is limited to models developed by the author, and focuses on how to best address a simple question: if a structure suffers from AAR, how is its structural integrity jeopardized, and when would the reaction end. Subjects treated are: • Brief overview of AAR: nature of the chemical reactions, AAR in both dams and nuclear power plants, and how does it impact the mechanical properties of concrete. • Constitutive model for both the AAR expansion, and concrete nonlinearities (both smeared and discrete crack models). • Validation of the model along with a parametric study to assess what are the critical parameters in a study. • Selection of material properties for an AAR finite element simulation, followed by applications in dams and massive reinforced concrete structures. • Micro Model for improved understanding of the essence of the reaction, along with a newly proposed mathematical model for the kinetics of the reaction. • Review of relevant procedures to estimate the residual expansion of a structure suffering from AAR, along with a proposed approach to determine when the reaction will end. The book is extensively illustrated with numerous figures and provides guidance to engineers confronted with swelling in concrete infrastructures.

Table of Contents:
Chapter 1 Introduction 1.1 Concrete Composition 1.2 Alkali Aggregate Reactions 1.2.1 What is AAR 1.2.2 Consequences of AAR 1.2.3 Testing Methods 1.2.4 Correlation Between Test Results and Field Observations 1.2.5 in-situ Measurement: Crack Index 1.2.6 LCPC Experimental Work 1.2.7 Partial Field Validation of LCPC Tests 1.2.8 AAR and Creep 1.2.9 AAR in Dams 1.2.10 AAR in Nuclear Power Plants 1.2.10.1 Structural Deterioration 1.2.10.2 Role of Irradiation 1.2.10.3 Life Extension 1.2.10.4 Seabrook Nuclear Power Plant 1.3 A Brief Review of Finite Element 1.3.1 Element Formulation 1.3.2 Isoparametric Elements 1.3.3 Nonlinear System 1.3.4 Constitutive Model D 1.4 A Brief Review of Heat Transfer 1.4.1 Modes of Heat Transfer and Boundary Conditions 1.4.2 Governing Partial Differential Equation 1.5 Finite Element Modeling of AAR 1.5.1 Scale and Models 1.5.2 Overview of Coupled Chemo-Mechanical Models 1.6 Book Content 1.7 Summary Chapter 2 AAR Constitutive Model 2.1 Minimum Requirements for a “Modern” AAR Numerical Model 2.2 The Model 2.3 Kinetics 2.3.1 Sensitivity to Temperature 2.3.2 Sensitivity to Integration Scheme 2.3.3 Sensitivity to Activation Energies 2.3.4 Sensitivity to Time 2.4 Retardation 2.4.1 Hydrostatic Compressive Stress 2.4.2 Role of Cracking 2.4.2.1 Tensile Macrocrack 2.4.2.2 Compressive Microcracks 2.5 Humidity 2.6 AAR Strain 2.6.1 Weights 2.6.2 AAR Linear Strains 2.6.3 Deterioration 2.7 Summary Chapter 3 Constitutive Model; Concrete 3.1 Introduction 3.2 Nonlinear response of concrete 3.2.1 Concrete in tension 3.2.2 Hillerborg’s Model 3.2.2.1 ợ-COD Diagram, Hillerborg’s Model 3.2.2.2 Localization 3.2.3 Concrete in compression 3.2.4 Concrete in shear 3.3 The nonlinear continuum model 3.3.1 Material model formulation 3.3.2 Rankine-Fracturing Model for concrete cracking 3.3.3 Plasticity model for concrete crushing 3.3.4 Combination of plasticity and fracture model 3.4 Nonlinear Discrete Joint Element 3.4.1 Introduction 3.4.2 Interface Crack Model 3.5 Summary Chapter 4 Validation 4.0.1 Benchmarks 4.1 Benchmark Results 4.1.1 P1: Constitutive Model 4.1.2 P2: Drying and Shrinkage 4.1.3 P3: Creep 4.1.4 P4: Effect of Temperature 4.1.5 P5: Relative Humidity 4.1.6 P6: Confinement 4.1.7 P7: Presence of Reinforcement 4.1.8 P8: Dams 4.1.8.1 2D 4.1.8.2 3D case: AAR only 4.2 Summary Chapter 5 Parametric Study 5.1 Preliminary 5.1.1 Problem definition 5.1.2 Primary units 5.1.3 Elastic and Thermal Properties 5.1.4 Preliminary thermal analysis 5.2 Results 5.2.1 Without a foundation/dam interface 5.2.1.1 (G+T+H)-(G+T); Role of the hydrostatic load 5.2.1.2 (G+T+H+A)-(G+T+H); Role of AAR expansion 5.2.1.3 (G+T+A+H)-(G+T+A): Role of the hydrostatic load (revisited) 5.2.1.4 (G+T+H+A)-(G+T+H’+A): Role of the hydrostatic model 5.2.2 (G+T+A)-(G+T’+A): Role of the temperature model 5.2.2.1 (E)-(E’): Effect of concrete deterioration 5.2.2.2 (G+T+H+A)-(G+T+H+A’): Effect of modeling internal and external concretes 5.2.2.3 (G+T+A): Effect of time discretization 5.2.2.4 Role of the kinetic model 5.2.3 Model with inclusion of joint 5.2.3.1 Effect of hydrostatic load 5.2.3.2 Effect of the kinetic model 5.3 Summary Chapter 6 Material Properties 6.1 Introduction 6.1.1 On the Randomness of Properties 6.1.2 Units & Conversion Factors 6.2 Elastic properties 6.2.1 Elastic modulus 6.2.2 Tensile strength 6.2.3 Poisson’s ratio 6.2.4 Fracture properties 6.3 AAR properties 6.4 Thermal properties 6.4.1 Temperatures 6.4.1.1 Air temperature 6.4.1.2 Pool temperature 6.4.2 Concrete thermal properties 6.5 Reclamation study 6.5.1 Elastic properties 6.5.1.1 Effect of confinement 6.5.2 Compressive strength 6.5.3 Tensile strength 6.5.4 Case studies 6.6 AAR properties through system identification 6.6.1 Algorithm 6.7 On the Importance of Proper Calibration 6.8 Summary Chapter 7 Applications 7.1 Arch Gravity Dam; Isola 7.1.1 Data Preparation 7.1.2 Stress Analysis 7.1.3 Results 7.2 Hollow Buttress Dam; Poglia 7.2.1 Transient Thermal Analysis 7.2.2 Stress Analysis 7.2.3 Analysis and Results 7.3 Arch Dam, Amir-Kabir 7.3.1 Dam description 7.3.2 Analysis Results and Discussion 7.4 Arch Dam, Kariba 7.4.1 Concrete Constitutive Model 7.4.2 Description of the Dam 7.4.3 Analysis 7.4.4 Observations 7.5 Massive Reinforced Concrete Structure 7.5.1 Description 7.5.2 Model 7.5.3 Results 7.5.4 Seismic Analysis Following AAR Expansion 7.6 Summary Chapter 8 Micro Model 8.1 A Diffusion-Based Micro Model 8.1.1 Analytical Model 8.1.1.1 Diffusion Models 8.1.1.1.1 Macro-Ion Diffusion of Alkali 8.1.1.1.2 Micro-Ion Diffusion Model of Alkali 8.1.1.1.3 Micro-Diffusion of Gel 8.1.2 Numerical Model 8.1.2.1 Macro-Ion Diffusion Analysis 8.1.2.2 Micro-Coupled Chemo-Mechanical Analysis 8.1.2.3 Macro-Stress Analysis 8.1.3 Example 8.1.3.1 Model 8.1.3.2 Analysis Procedure 8.1.3.3 Investigation Results 8.1.3.3.1 Micro-Modeling 8.1.4 From Diffusion to the Kinetic Curve 8.1.4.1 Preliminary Model 8.1.4.2 Refined Model 8.1.4.2.1 Formulation 8.1.4.2.2 Applications 8.2 A Mathematical Model for the Kinetics of the Alkali-Silica Reaction 8.3 Summary Chapter 9 Prediction of Residual Expansion 9.1 Literature Survey 9.1.1 Estimation of previous AAR expansion, Berube et al. (2005) 9.1.2 Value of Asymptotic Expansion, Multon et al. 2008 9.1.3 Estimation of Residual Expansion, Sellier et. al. (2009) 9.1.3.1 Preliminary Observations 9.1.3.2 Proposed Procedure 9.1.3.2.1 Field work 9.1.3.2.2 Laboratory tests 9.1.3.2.3 Inverse finite element simulation 9.2 Expansion Curve from Delayed Laboratory Testing 9.2.1 Numerical Formulation 9.2.2 Assessment 9.3 Summary Chapter A Numerical Benchmark for the Finite Element Simulation of Expansive Concrete A.1 Introduction A.1.1 Objectives A.1.2 Important Factors in Reactive Concrete A.2 Test Problems A.2.1 P0: Finite Element Model Description A.2.2 Materials A.2.2.1 P1: Constitutive Models A.2.2.1.1 Constitutive Model Calibration A.2.2.1.2 Prediction A.2.2.2 P2: Drying and Shrinkage A.2.2.2.1 Constitutive Model Calibration A.2.2.2.2 Prediction A.2.2.3 P3: Basic Creep A.2.2.3.1 Constitutive Model Calibration A.2.2.3.2 Prediction A.2.2.4 P4: AAR Expansion; Temperature Effect A.2.2.4.1 Constitutive Model Calibration A.2.2.4.2 Prediction A.2.2.5 P5: Free AAR Expansion; Effect of RH A.2.2.5.1 Constitutive Model Calibration A.2.2.5.2 Prediction A.2.2.6 P6: AAR Expansion; Effect of Confinement A.2.2.6.1 Constitutive Model Calibration A.2.2.6.2 Prediction A.2.3 Structures A.2.3.1 P7: Effect of Internal Reinforcement A.2.3.2 P8: AAR Expansion; Idealized Dam A.3 Presentation of Results A.4 Results Submission and Workshop A.5 Acknowledgements Chapter B Merlin B.1 Introduction B.2 Arch Dam Preprocessor: Beaver B.3 Preprocessor: KumoNoSu B.4 Analysis: Merlin B.5 Post-Processor: Spider B.5.1 Integration Chapter C Brief Review of Reaction Rate C.1 Definitions C.2 Examples of Simple Reactions C.2.1 Zero-order reactions C.2.2 First-order reactions C.2.3 Second-order reactions C.3 Complex Reactions C.3.1 Competitive or parallel reactions C.3.2 Consecutive or series reactions C.3.3 Chain reactions Author Index Index