Cementitious materials, rocks and fibre-reinforced composites commonly termed as quasibrittle, need a different fracture mechanics approach to model the crack propagation study because of the presence of significant size of fracture process zone ahead of the crack-tip. Recent studies show that concrete structures manifest three important stages in fracture process: crack initiation, stable crack propagation and unstable fracture or failure. Fracture Mechanics concept can better explain the above various stages including the concepts of ductility, size-effect, strain softening and post-cracking behavior of concrete and concrete structures. The book presents a basic introduction on the various nonlinear concrete fracture models considering the respective fracture parameters. To this end, a thorough state-of-the-art review on various aspects of the material behavior and development of different concrete fracture models is presented. The development of cohesive crack model for standard test geometries using commonly used softening functions is shown and extensive studies on the behavior of cohesive crack fracture parameters are also carried out. The subsequent chapter contains the extensive study on the double-K and double-G fracture parameters in which some recent developments on the related fracture parameters are illustrated including introduction of weight function method to Double-K Fracture Model and formulization of size-effect behavior of the double-K fracture parameters. The application of weight function approach for determining of the KR-curve associated with cohesive stress distribution in the fracture process zone is also presented. Available test data are used to validate the new approach. Further, effect of specimen geometry, loading condition, size-effect and softening function on various fracture parameters is investigated. Towards the end, a comparative study between different fracture parameters obtained from various models is presented.

FRACTURE MECHANICS OF CONCRETE AND ROCK This book offers engineers a unique opportunity to learn, frominternationally recognized leaders in their field, about the latesttheoretical advances in fracture mechanics in concrete, reinforcedconcrete structures, and rock. At the same time, it functions as asuperb, graduate-level introduction to fracture mechanics conceptsand analytical techniques. Reviews, in depth, the basic theory behind fracture mechanics * Covers the application of fracture mechanics to compressionfailure, creep, fatigue, torsion, and other advanced topics * Extremely well researched, applies experimental evidence ofdamage to a wide range of design cases * Supplies all relevant formulas for stress intensity * Covers state-of-the-art linear elastic fracture mechanics (LEFM)techniques for analyzing deformations and cracking * Describes nonlinear fracture mechanics (NLFM) and the latestRILEM modeling techniques for testing nonlinear quasi-brittlematerials * And much more Over the past few years, researchers employing techniques borrowedfrom fracture mechanics have made many groundbreaking discoveriesconcerning the causes and effects of cracking, damage, andfractures of plain and reinforced concrete structures and rock.This, in turn, has resulted in the further development andrefinement of fracture mechanics concepts and tools. Yet, despitethe field's growth and the growing conviction that fracturemechanics is indispensable to an understanding of material andstructural failure, there continues to be a surprising shortage oftextbooks and professional references on the subject. Written by two of the foremost names in the field, FractureMechanics of Concrete fills that gap. The most comprehensive bookever written on the subject, it consolidates the latest theoreticalresearch from around the world in a single reference that can beused by students and professionals alike. Fracture Mechanics of Concrete is divided into two sections. In thefirst, the authors lay the necessary groundwork with an in-depthreview of fundamental principles. In the second section, theauthors vividly demonstrate how fracture mechanics has beensuccessfully applied to failures occurring in a wide array ofdesign cases. Key topics covered in these sections include: * State-of-the-art linear elastic fracture mechanics (LEFM)techniques for analyzing deformations and cracking * Nonlinear fracture mechanics (NLFM) and the latest RILEM modelingtechniques for testing nonlinear quasi-brittle materials * The use of R-Curves to describe cracking and fracture inquasi-brittle materials * The application of fracture mechanics to compression failure,creep, fatigue, torsion, and other advanced topics The most timely, comprehensive, and authoritative book on thesubject currently available, Fracture Mechanics of Concrete is botha complete instructional tool for academics and students instructural and geotechnical engineering courses, and anindispensable working resource for practicing engineers.

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

Despite tremendous advances made in fracture mechanics of concrete in recent years, very little information has been available on the nature of fracture processes and on reliable test methods for determining parameters for the different models. Moreover, most texts on this topic discuss numerical modeling but fail to consider experimentation. This book fills these gaps and synthesizes progress in the field in a simple, straightforward manner geared to practical applications.

From time to time the International Journal of Fracture has presented matters thought to be of special interest to its readers. The last special topic review was presented by Drs W.G. Knauss and AJ. Rosakis as Guest Editors in four issues, January-April 1990, under the general title of Non Linear Fracture. It contained sections on damage mechanisms, interfaces and creep, time depen dence, and continuum plasticity insofar as they affect the mechanisms of the fracture process. Continuing this policy, which is consistent with our stated objectives, the two September issues deal with the behavior of concrete and cementious materials during fracture initiation and propagation. We hope that the ensuing state-of-the-art review will yield another instructive and timely product which readers will find useful. To assist us in presenting this subject, we have prevailed upon a well-known international expert in concrete behavior, Dr. Z.P. Bazant, Walter P. Murphy Professor of Civil Engineering, of Northwes tern University to act as Guest Editor. On behalf of the editors and publishers, I wish to thank Professor BaZant and his invited authors for undertaking this special effort. M.L. WILLIAMS Pittsburgh, Pennsylvania Editor-in-Chief September 1991 International Journal of Fracture 51: ix-xv, 1991. Z.P. Bafant (ed.), Current Trends in Concrete Fracture Research.

Concrete has traditionally been known as a material used widely in the construction of roads, bridges and buildings. Since cost effectiveness has always been one of the more important aspects of design, concrete, when reinforced and/or prestressed, is finding more use in other areas of application such as floating marine structures, storage tanks, nuclear vessel containments and a host of other structures. Because of the demand for concrete to operate under different loading and environmen tal conditions, increasing attention has been paid to study concrete specimens and structure behavior. A subject of major concern is how the localized segregation of the constituents in concrete would affect its global behavior. The degree of nonhomogeneity due to material property and damage. by yielding and/or cracking depends on the size scale and loading rate under consideration. Segregation or clustering of aggregates at the macroscopic level will affect specimen behavior to a larger degree than it would to a large structure such as a dam. Hence, a knowledge of concrete behavior over a wide range of scale is desired. The parameters governing micro-and macro-cracking and the techniques for evaluating and observing the damage in concrete need to be better understood. This volume is intended to be an attempt in this direction. The application of Linear Elastic Fracture Mechanics to concrete is discussed in several of the chapters.