# Crack Analysis in Structural Concrete

This book is an outgrowth of my research in the broad field of fracture mechanics over a period of twenty years, the past fifteen years of which I have spent focusing on a subbranch of the discipline—that is, fracture mechanics of concrete. My late decision to focus on this field of study was motivated by two factors, namely, a surging demand for crack analysis in structural concrete and a keen personal interest in the subject. Compared with other mature engineering disciplines, fracture mechanics of concrete is still a developing field that is wonderfully rich in scope and diversity and full of challenging issues to be studied.

In recent years a wide range of models and applications have been proposed for crack analysis, and an impressive array of useful information has been accumulated. As a result, the theoretical basis of the discipline has been strengthened; a number of fundamental issues solved; and the range of applications widened. As the subject is approaching its early stage of maturity, it is imperative for students to learn the fundamental theoretical advances that have been made, and engineers need to familiarize themselves with newly developed numerical solution techniques.

I have written this book to summarize the recent theoretical advances in the computationalfracture mechanics of concrete, especially regarding the discrete approach to multiple-crack analysis and mixed-mode fracture. The extension of the Fictitious Crack Model (FCM) to address these problems has greatly expanded the range of crack analysis in structural concrete.

The book begins with a brief introduction to the fundamental theories of linear elastic fracture mechanics and nonlinear fracture mechanics of concrete. Then, after addressing the issue of stress singularity in numerical modeling and introducing some basic modeling techniques, the Extended Fictitious Crack Model (EFCM) for multiple-crack analysis is explained with numerical application examples. This theoretical model is then used to study two important issues in fracture mechanics:

(1) crack interaction and localization and (2) failure modes and maximum loads. The EFCM is subsequently reformulated to include the shear transfer mechanism on crack surfaces and the method is used to study experimental problems. Following these theoretical developments, an application example in tunnel engineering is discussed, which shows how the EFCM can be built
into a pseudoshell model for crack analysis of tunnel linings that takes the earth–tunnel interaction into account. Because the book is written both for students and practicing engineers, an effort has been made to present a balanced mixture of theory, experiment, and application.

The companion website for the book contains the source code of two computer programs developed by the author’s team, with which the numerical solutions of numerous sample problems discussed can be verified. The purpose of publishing these programs is threefold. First, students can use them to resolve some of the sample problems as exercises to gain a more indepth understanding of the subject. Second, practicing engineers can use them to solve real engineering problems as this book fully demonstrates. Third, research scientists can use or modify them for specific research purposes. Although great effort has been made to verify the programs, the user must be solely responsible for their performance in practice.