Crack Analysis in Structural Concrete

Zihai Shi; R&D Centre, Nippon Koei Co., Ltd.; 2304 Inarihara, Tsukuba-shi, Ibaraki 300-1259He has engaged in renovation design of ageing sewers since 1995, and is familiar with resilience theories and practices in structural engineering.

• Preface CHAPTER 1 Introduction1.1 Aims of the Book1.2 Multiple-Crack Problems1.3 Mixed-Mode Crack Problems1.4 Crack Interaction and Localization 1.5 Failure Mode and the Maximum Load 1.6 Outline of this Book ReferencesCHAPTER 2 Linear Elastic and Nonlinear Fracture Mechanics2.1 Elastic Crack-Tip Fields 2.1.1 Equations of Elasticity and Airy Stress Function2.1.2 The Williams Solution of Elastic Stress Fields at the Crack Tip2.1.3 The Complex Stress Function Approach to Elastic Stress Fields at the Crack Tip 2.2 Stress Intensity Factor and K-Controlled Crack-Tip Fields 2.3 The Energy Principles2.3.1 The Griffith Fracture Theory2.3.2 The Energy Release Rate G 2.3.3 Relationship between K and G2.3.4 The Criterion for Crack Propagation2.4 Plastic Zone Theories at Crack Tip 2.4.1 The Irwin Plastic Zone Corrections 2.4.2 Cohesive Zone Models by Dugdale and Barenblatt 2.5 Fracture Process Zone and Tension-Softening Phenomenon in Concrete 2.6 Fracture Energy GF and Tension-Softening Law in Concrete 2.6.1 Fracture Energy GF2.6.2 Tension-Softening LawReferencesCHAPTER 3 The Fictitious Crack Model and its Numerical Implementation 3.1 Introduction 3.2 Hillerborg and Colleagues’ Fictitious Crack Model3.2.1 Modeling Concept 3.2.2 Numerical Formulation by Petersson’s Influence Function Method 3.3 The Principle of Superposition 3.4 The Reciprocity Principle 3.5 The Singularity Issue 3.6 Crack Path Modeling with Dual Nodes 3.7 The Remeshing Scheme for an Arbitrary Crack Path3.8 The Solution Scheme for Incremental Stress Analysis ReferencesCHAPTER 4 Extended Fictitious Crack Model for Multiple-Crack Analysis4.1 Introduction 4.2 Core Issues and Solution Strategy4.3 Numerical Formulation of a Single-Crack Problem4.4 Numerical Formulation of a Multiple-Crack Problem 4.5 Crack Analysis of a Simple Beam under Bending4.5.1 Crack Analysis with a Fixed Crack Path 4.5.2 Crack Analysis with a Curvilinear Crack Path4.6 Crack Analysis of a Fracture Test of a Real-Size Tunnel-Lining Specimen 4.6.1 Fracture Test on a Tunnel-Lining Specimen 4.6.2 Crack Analysis with a Half-FE-Model4.6.3 Crack Analysis with a Full-FE-Model 4.7 Crack Analysis of a Scale-Model Test of a Gravity Dam by Carpinteri and Colleagues 4.7.1 Background4.7.2 Model I: Single-Crack Propagation4.7.3 Model II: Multiple-Crack Propagation4.7.4 Model III: Multiple-Crack PropagationReferencesCHAPTER 5 Crack Interaction and Localization 5.1 Introduction 5.2 Coefficient of Interaction5.2.1 Crack Equations and the Source of Crack Interaction 5.2.2 Coefficient of Interaction and Principal Tip Force Coefficient 5.3 Crack Interactions in Notched Concrete Beams under Four-Point Bending5.3.1 Beams with Small Notches5.3.2 Beams with Both Small and Large Notches5.4 Crack Interactions in Tunnel Linings5.5 Characteristics of Crack Interactions with One and Multiple Tension Zones ReferencesCHAPTER 6 Failure Modes and Maximum Loads of Notched Concrete Beams6.1 Introduction 6.2 Numerical Analysis of Notched Beams under Various Load Conditions 6.2.1 Maximum Loads with Monotonic Loadings6.2.2 Maximum Load Increase with Higher Density of Initial Notches6.2.3 Maximum Loads with Alternative Loadings 6.3 Critical Initial Notch and Its Influence on Failure Mode and the Maximum Load6.4 Experimental Verifications on Relationships between Failure Modes and the Maximum Loads 6.4.1 Four-Point Bending Tests 6.4.2 Numerical Analyses 6.5 Engineering Implications ReferencesCHAPTER 7 Mixed-Mode Fracture 7.1 Introduction 7.2 Modeling of Cohesive Forces in the FPZ7.3 Reformulation of FCM and EFCM for Mixed-Mode Fracture7.3.1 FCM for Mixed-Mode Fracture7.3.2 EFCM for Mixed-Mode Fracture 7.4 Mode-II Fracture Energy GF II 7.5 Numerical Studies of Arrea and Ingraffea’s Single-Notched Shear Beam 7.5.1 Parametric Studies with Five Shear-COD Relations 7.5.2 Parametric Studies on Mode-II Fracture Energy with Three Shear-COD Relations7.6 Numerical Studies of a Scale-Model Test of a Gravity DamReferencesCHAPTER 8 Applications: Pseudoshell Model for Crack Analysis of Tunnel Linings8.1 Introduction 8.2 Pseudoshell Model 8.2.1 Modeling Concept 8.2.2 Numerical Formulation 8.2.3 Parametric Studies on Uniqueness of Solutions on Tunnel Deformation8.3 Evaluation of Ground Pressure Based on the Quasi Loosening Zone Model 8.4 Numerical Analysis of an Aging Waterway Tunnel (Case A-1) Compared with a Soil Mechanics Approach 8.4.1 Background8.4.2 Numerical Analysis by Adachi-Oka Model8.4.3 Numerical Analysis by the Pseudoshell Model 8.4.4 Evaluation of Ground Pressure8.5 Case Studies of Two Aging Waterway Tunnels8.5.1 Power Plant B (Horseshoe Type): Site B-1 8.5.2 Power Plant B (Horseshoe Type): Site B-2 8.5.3 Power Plant B (Horseshoe Type): Site B-3 8.5.4 Power Plant C (Calash Type): Site C-18.6 Development of Database for Evaluation of Ground Pressure Based on the CMOD8.6.1 Selection of Influential Factors and Cases of Study 8.6.2 Relations between Cross-Sectional Deformation and the CMOD8.6.3 Relations between Pressure Load and Cross-Sectional Deformation8.6.4 Two-Step Procedure for Determining External Loads by the CMOD and Development of Database ReferencesCHAPTER 9 Computer Program for Mode-I Type Crack Analysis inn Concrete Using EFCM (CAIC-M1.FOR)9.1 Overview of the Program 9.2 Structure of the Program 9.3 Main Rules 9.4 Program List9.5 Selected Examples Illustrating the Usage of the Program9.5.1 Crack Analysis of Notched Beam9.5.2 Crack Analysis of Scale Model Dam9.5.3 Crack Analysis of Tunnel LiningReference CHAPTER 10 Computer Program for Mixed-Mode Type Crack Analysis in Concrete Using EFCM (CAIC-M12.FOR) 10.1 Overview of the Program 10.2 Structure of the Program 10.3 Main Rules 10.4 Subroutines with Major Changes 10.4.1 Changes in CAIC-M12.FOR from CAIC-M1.FOR 10.4.2 Subroutines with Major Changes in the Crack Pattern Determination Block (TFORCE) 10.4.3 Subroutines with Major Changes in the Crack Equation Solution Block (EFFECT)10.4.4 Subroutines with Major Changes in the Main Block (MAINCN) 10.5 Selected Example Illustrating the Usage of the Program INDEX