Crack Analysis in Structural Concrete

Theory and Applications

Zihai Shi

• Publisher: Butterworth-Heinemann
• Year: 2009
• Print ISBN: 9780750684460
• eBook ISBN: 9780080942223
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

This new book on the fracture mechanics of concrete focuses on the latest developments in computational theories, and how to apply those theories to solve real engineering problems. Zihai Shi uses his extensive research experience to present detailed examination of multiple-crack analysis and mixed-mode fracture.Compared with other mature engineering disciplines, fracture mechanics of concrete is still a developing field with extensive new research and development. In recent years many different models and applications have been proposed for crack analysis; the author assesses these in turn, identifying their limitations and offering a detailed treatment of those which have been proved to be robust by comprehensive use. After introducing stress singularity in numerical modelling and some basic modelling techniques, the Extended Fictitious Crack Model (EFCM) for multiple-crack analysis is explained with numerical application examples. This theoretical model is then applied to study two important issues in fracture mechanics - crack interaction and localization, and fracture modes and maximum loads. The EFCM is then reformulated to include the shear transfer mechanism on crack surfaces and the method is used to study experimental problems. With a carefully balanced mixture of theory, experiment and application, Crack Analysis in Structural Concrete is an important contribution to this fast-developing field of structural analysis in concrete. - Latest theoretical models analysed and tested - Detailed assessment of multiple crack analysis and multi-mode fractures - Applications designed for solving real-life engineering problems

Chapter 1. Introduction

1.1. Aims of the Book

As research scientists and practicing engineers working in the field of structural engineering and whose responsibilities are almost exclusively confined to analyzing cracked concrete structures for the safety evaluation and renovation design of today's aging infrastructure, we have been studying cracks in various concrete structures through crack analysis for more than a decade. The structures that we have frequently encountered for crack diagnosis include tunnels, dams, bridges, sewage pipes, and so forth, and we need to clarify the various mechanisms by which cracks occur and evaluate the damaging effects that these cracks inflict on these structures. Crack analysis is indispensable in answering these questions, and it is a fascinating field of study in structural concrete. The peculiar nonlinearity that occurs in the fracture process zone (FPZ) ahead of an open crack makes the theory distinctly different from the whole range of problems in classical continuum mechanics. In addition, the frequent encounter of multiple cracks and mixed-mode fracture in real situation problems that require creative approaches highlights the challenging feature of our work, which compels one to advance fracture mechanics of concrete further and to expand its applications wider.

Let us be specific. In Photo 1.1 a large longitudinal crack is shown in the right portion of the arch of an aging highway tunnel. Field surveys showed that the crack-mouth-opening displacement (CMOD) had reached a maximum width of 7 mm, and circumstantial evidence also suggested the existence of another crack in the left portion of the arch from the outer surface of the tunnel lining. Field investigations found that a narrow fault (50 cm in thickness) composed of class D rock mass ran through the tunnel cross section from upper right to lower left direction. A loosening zone with a depth of more than 3 m composed mainly of class CL rock mass was found along the fault. A schematic illustration of the situation is shown in Figure 1.1. Our task may be simple to express, but it is difficult to solve—that is, to determine, through crack analysis, the pressure loads exerted on the tunnel lining by the loosening zone. This information could provide the much needed design load for remedial works to be carried out on the tunnel linings to stabilize the crack and ensure the safety of the tunnel.

Photo 1.1 A highway tunnel with a large longitudinal crack in the right arch area.

Figure 1.1 Schematic cross section of a highway tunnel with large, open cracks based on the results of detailed field investigations.

Now we have a crack analysis problem with two discrete cracks, stemming from an actual engineering situation. Let us specify our solution strategy. First, crack analysis will be carried out using a pseudoshell model to determine the cross-sectional deformation of the tunnel lining as the CMOD of the inner lining crack reaches 7 mm under the earth pressures. Next, assuming a simple elastic loosening zone model and that the ground deformation of the loosening zone is equivalent to the cross-sectional deformation of the tunnel lining at the crack, then the depth of the loosening zone can be determined through iterative computations. Once the size of the loosening zone is known, the pressure loads acting on the tunnel lining can be calculated from its gravity loads. The flow chart for this numerical computation is shown in Figure 1.2.

Figure 1.2 Evaluation of the pressure loads based on a crack analysis of the tunnel lining.

Before starting this numerical analysis, we must choose a numerical method for modeling cracks. In fracture mechanics of concrete, there are two generally accepted computational theories used in the finite element method (FEM) analysis to represent cracking in structural concrete: the smeared crack approach (Rashid, 1968) and the discrete crack approach (Ngo and Scordelis, 1967Nilson, 1967Nilson, 1968 and Hillerborg et al., 1976). The smeared crack approach treats the cracked solid as a continuum and represents cracks by changing the constitutive relations of the finite elements. The wisdom of this approach lies in its full exploitation of the fundamental concepts of the FEM, which can be summarized as (1) subdivide a problem into elements, (2) analyze this problem through these elements, and (3) reassemble these elements into the whole to obtain the solution to the original problem.

In some sense, the smeared crack approach may be considered as a straightforward way to express cracks with the FEM, because the stress-strain relations of the elements can be easily altered to reflect the effects of cracking, which is a very convenient feature not only for static crack analysis but also for dynamic crack analysis, such as simulations of dynamic crack propagation during earthquakes. A different modeling concept is adopted in the discrete crack approach, in which a crack is treated as a geometric entity and the FPZ forms a part of the boundary condition, including the geometric shapes and cohesive forces acting on the crack surface.

From a macroscopic-material point of view, this is the most accurate physical model to study cracks because the approach reflects most closely the physical reality of the cracked concrete. It seems that these two modeling concepts emerged naturally in the 1960s through the great efforts of engineers attempting to analyze concrete structures using the FEM, following the advent of computers in the 1940s and the subsequent rapid development of the FEM in the 1950s. Due to its continuum assumption for cracked concrete materials, the smeared crack approach is computationally much more convenient than the discrete crack approach.

The method has been widely accepted in practice as one of the most effective means for crack analysis in concrete structures to predict general structural behaviors. However, the limitations of this approach are just as obvious as its merits. In principle, the approach can only predict cracking behavior approximately, and the continuum assumption makes it impossible to obtain any specific information related to the crack-opening displacement (COD) of any individual crack. Therefore, the smeared crack approach is unfit for our present task. On the other hand, the modeling concept of the discrete crack approach makes it possible to analyze cracking behavior in a concrete structure as physically accurately as possible, including the crack path and the CMOD. For this reason, the discrete crack approach, which is the focus of this book, will be chosen to solve our present problem.

Over the years, various other analytical concepts and modeling techniques have also been proposed for specific research purposes, such as the microplane theory by Bazant and Ozbolt (1990), the particle model by Bazant et al. (1990) and the lattice model by van Mier (1997), to name but a few, reflecting the complex and diverse mechanisms of various fracture phenomena in concrete structures. In practice, applications of these models are limited due to the...

Table of contents

• Cover Image
• Table of Contents
• Copyright
• Dedication
• Preface
• Chapter 1. Introduction
• Chapter 2. Linear Elastic and Nonlinear Fracture Mechanics
• Chapter 3. The Fictitious Crack Model and Its Numerical Implementation
• Chapter 4. Extended Fictitious Crack Model for Multiple-Crack Analysis
• Chapter 5. Crack Interaction and Localization
• Chapter 6. Failure Modes and Maximum Loads of Notched Concrete Beams
• Chapter 7. Mixed-Mode Fracture
• Chapter 8. Applications
• Chapter 9. Computer Program for Mode-1 Type Crack Analysis in Concrete Using EFCM (CAIC-M1.FOR)
• Chapter 10. Computer Program for Mixed-Mode Type Crack Analysis in Concrete Using EFCM (CAIC-M12.FOR)
• Index