Front
Matter, Preface, Table of Contents

Volume 1

Chapter
1. Fracture Energy, Strain Softening, and Fracture Toughness

111

A
Comparative Study of GF Test Results

D.R. Brokenshire and B.I.G. Barr

112 
Determination of
Tension Softening Diagrams of Various Kinds of Concrete by Means
of Numerical Analysis

Y. Uchida, N. Kurihara, K. Rokugo and W. Koyanagi

113 
Fracture Energy
of Normal Strength Concrete, High Strength Concrete and Ultra High
Strength Ductile Steel Fiber Reinforced Concrete

J.P. Ulfkjaer and R. Brincker

114 
Effect of Model
Fracture Law and Porosity on Tensile Softening of Concrete

A. Arslan, E. Schlangen and J.G.M. van Mier

115 
Unified Test
Procedure for Evaluating the Fracture Characteristics of Concrete

A.D. Jefferson and B.I.G. Barr

116 
Influence of Notch
Size, Eccentricity and Rotational Stiffness on Fracture Properties
Determined in Tensile Tests

F.P. Zhou

117 
The Effect of the
Boundary Conditions on the Cylinder Splitting Strength

C. Rocco, G.V. Guinea, J. Planas and M. Elices

118 
Toughness
of Old Plain Concretes

M. Berra and A. Castellani

119 
Rupture Modulus and
Fracture Properties of Concrete

J. Planas, G.V. Guinea and M. Elices

1110 
The Effects of Mix
Variables on Concrete Fracture Mechanics Parameters

Y.C. Kan and S.E. Swartz

1111 
Effect of Concrete
Materials on Fracture Performance

N.Q. Feng, X.H. Ji, Q.F. and J.T. Ding

1112 
Microstructural
Effects on the Brittleness of High Strength Concretes

C. Tasedemir, M.A. Tasedemir, R. Grimm and G. König

1113 
Determination of KS^{IC}
and CTOD_{C} from Peak Loads and Relationship between
TwoParameter Fracture Model and Size Effect Model

T. Tang, S. Yang, C. Ouyang, W. Libardi and S.P. Shah

1114 
Mode I Fracture
Behaviour of Recycled Concrete

S. Ishiguro, S.E. StanzlTschegg, E.K. Tschegg and R. Travnicek

Chapter
2. Fracture Process Zone

121

Simulation and
Observation of the Fracture Process Zone

T. Steiger, H. Sadouki and F.H. Wittmann

122 
Studies of the Length of
Concrete Micro Crack Zone

N.Q. Feng, X.H. Ji, Q.F. Zhuang and J.T. Ding

123 
Further Studies of the
Fracture Process Zone Associated with Mixed Mode Dynamic Fracture
of Concrete

Z.K. Gou, M. Kosai, A.S. Kobayashi and N.M. Hawkins

124 
Fracture Mechanics
Characteristics at Crack Initiation and Propagation and their
Dependence on Structure of Concrete

K. Kolver

125 
Fracture
Parameters for Concrete Based on Polylinear Approximation
Analysis of Tension Softening Diagram

Y. Kitsutaka

126 
A
Method to Evaluate Tension Softening Model for Concrete

N. Nomura and H. Mihashi

127 
A Method for
Determining Fracture Properties of Concrete Through a Single Test

F.P. Zhou

128 
Application of
Electronic Speckle Pattern Interferometry (ESPI) to Observe the
Fracture Process Zone

E. Hack, T. Steiger and H. Sadouki

129 
Use of the
Confocal Microscope to Study PreExisting Microcracks and Crack
Growth in Concrete

H. Sunderland, A. Tolou, E. Denarié, L. Job and C. Huet

Chapter
3. Crack Formation Under Different Conditions

131

Transient Fluid
Fracture Interaction

V. Slowik, V.E. Saouma and Y.S. Roh

132 
Tensile Hydraulic
Fracture of Concrete and Rock

J.H.M. Visser and J.G.M. van Mier

133 
Influence of Stress
Corrosion on Fracture Energy of Cementitious Materials

A. Gerdes and F.H. Wittmann

134 
Tensile
LoadBearing Behaviour of Concrete after LongTerm Static and
Cyclic Tensile Preloading

F. Blaschke and G. Mehlhorn

135 
Influence of the
LongTerm and Repeated Loading on Fracture Mechanics of the
Partially Prestressed Beams

C. Magureanu

136 
Interface
Fracture in Cement Based Materials

A. Vervuurt and J.G.M. van Mier

137 
Interaction of
Plural Cracks in Concrete During Flexural Failure

H. Koide, H. Akita and M. Tomon

138 
Experimental
Measurements of Microfracture in Cement Based Materials

E.N. Landis and S.P Shah

139 
Experimental
and Numerical Investigation of Failure of QuasiBrittle Materials

J. Gao, M.L. Wang and H.L. Schreyer

1310 
On an Efficient New
Numerical Method for Resolution of the Frictionless Contact
Problems with a Variational Inequality Approach

A. Noune, R.M. Courtade and H. Benkhira

1311 
Simulations of
Tensile Fracture in Concrete

A. Vervuurt, M.R.A. van Vliet, J.G.M. van Mier and E. Schlangen

1312 
Interaction of a
Main Crack with Ordered Distributions of Microcracks

A. Brencich and A. Carpinteri

Chapter
4. Concrete Failure under Compression

141

Modelling Compressive
Failure Using Rigid Particle Systems

Y.Q. Liu, H. Hikosaka and J.E. Bolander Jr.

142 
Softening
Behaviour of Concrete under Uniaxial Compression

M.R.A. van Vliet and J.G.M van Mier

143 
Experimental
Observations of Concrete Behaviour under Uniaxial Compression

Y.H. Lee, K. Willam and H.D. Kang

144 
Failure of Concrete
with Oblique Weak Layer

H. Wang and X.Z. Hu

145 
Compressive Strength
Variation of Concrete Specimens Due to Imperfection Sensitivity.

K. Ikeda and K. Maruyama

146 
A Compressive
Softening Model for Concrete

G. Markeset

147 
Microcracking
in Concrete under Compression: its Gradient Mechanisms and
Reflection in Macro

I. Blechman

148 
A Case of
Compression Failure in Concrete Due to Stress Release

P. Stroeven

Chapter
5. Mixed Mode Fracture

151

A Simple Fracture
Mechanics Model for MixedMode Failure in Concrete

T. Olofsson, U. Ohlsson and M. Klisinski

152 
MixedMode
Fracture in Concrete: a NonLocal Damage Approach

M. di Prisco and J. Mazars

153 
Fracture Behavior of
Concrete to Mixed Loading

S.Y. Peng, N. Shirai and M. Irobe

154 
Influence of Age of
Loading on Mixed Mode Fracture Parameters of Concrete

B. Hu, G. Zhao and Y. Song

Chapter
6. Scaling Theories and Size Effect

161

Scaling Theories
for Quasibrittle Fracture: Recent Advances and New Directions

Z.P. Bazant

162 
Size Effect
Mechanisms in Numerical Concrete Fracture

J.E. Bolander Jr. and Y. Kobashi

163 
Size Effects in the
Biaxial TensileCompressive Behaviour of Concrete: Physical
Mechanisms and Modelling

P. Rossi and F.J. Ulm

164 
A Truncated
Statistical Model for Analyzing the SizeEffect on Tensile
Strength of Concrete Structures

A. Carpinteri, G. Ferro and S. Ivernizzi

165 
Crack
Surface Friction and Size Effect in Mode I Propagation for Mortar
and Concrete

A. Turatsinze and A. Bascoul

166 
Multifractal
Scaling Law for the Fracture Energy Variation of Concrete
Structures

A. Carpinteri and B. Chiaia

167 
A Fractal Study of
the Size Effect of Concrete Fracture Energy

N.Q. Feng, X.H. Ji, Q.F. Zhuang and J.T. Ding

168 
Size Effect and
Stability of Fracture

B. Trunk, H. Sadouki and F.H. Wittmann

169 
Numerical Concrete
Applied to Investigative Size Effect and Stability of Crack
Propagation

H. Sadouki and F.H. Wittman

1610 
Representative Volumes
of Cementitious Materials

Y. Xi 
1611 
Size Effect on
Shear Strength in Reinforced Concrete Beams with Shear
Reinforcement

N. Shirai, K. Moriizumi and K. Ishii 
1612 
Size Effect on
Strength and Deformability of RC Beams Failing in Flexure

H. Adachi, N. Shirai, M. Nakanishi and K. Ogino 
1613 
Size Effect in
Concrete and Reinforced Concrete Structures

J. Ozbolt and R. Eligehausen 
1614 
LargeScale
InSitu Fracture of Ice

J.P. Dempsey, R.M. Adamson and S.V. Mulmule 
1615 
Fracture
Characteristics and Size Effect in Normal and HighStrength
Concrete Beam

S.H. Eo, N.M. Hawkins and G.S. Kwak 
1616 
The Neural
NetworkBased Analysis of Size Effect in Concrete Fracture

A. Arslan and R. Ince

Chapter
7. Rate Effects

171

High Strain
Rate Tensile Behaviour of Concrete: Significant Parameters

F. Toutlemonde, C. Boulay and P. Rossi

172

Effect of
Temperature and Loading Rate on Fracture Behavior of Concrete
Subjected to Uniaxial Tension

V. Mechtcherine, H. Garrecht and H.K. Hilsdorf

173

Dynamic Crack
Propagation in PMMA

R. Jelinek, H.A. Dieterman and L.J. Sluys

Chapter
8. Fibre Reinforced Concrete

181

A Study on
Approximation Method of Tension Softening Curve of Steel Fiber
Reinforced Concrete

S. Matsuo, S. Matsuoka, A. Masuda and H. Yanagi

182 
What is
Interpreted from Fractured Surfaces in Concrete?

H. Mihashi, N. Nomura, H. Nakamura and T. Umeoka

183 
Characterization
of the Toughness of Fiber Reinforced Concrete Using the LoadCMOD
Response

V.S. Gopalaratnam, R. Gettu, S. Carmona and D. Jamet

184 
An RCurve Approach
for PUllOut Fibres From a Matrix

C. Ouyang, A. Pacios and S.P. Shah

185 
Fracture of
FibreReinforced Concrete Beams with Low Fibre Content

J.L. Vitek and P. Vitek

186 
Effects of Fiber on
Fracture Properties of Light Weight Concrete made with FlyAsh
Pelletized Aggregates

T.P. Chang, C.Y. Lin, C.L. Hwang and M.M. Shieh

187 
On Crack
Propagation and Failure Modes in FiberReinforced Concrete Slabs

R. Felicetti, P.G. Gambarova and N. Zanini

Volume 2

Chapter
9. Numerical Models

291

Fictitious
Crack Models: A Classification Aproach

S. Weihe and B. Kröplin

292 
New
Developments in Microplane and Multicrack Models for Concrete

I. Carol and Z.P. Bazant

293 
Enhanced
Microplane Concrete Model

T. Hasegawa

294 
GradientEnhanced
Smeared Crack Models for Finite Element Analysis of Plain and
Reinforced Concrete

J. Pamin and R. de Borst

295 
Holonomic and
Nonholonomic Simulations of QuasiBrittle Fracture: a Comparative
Study of Mathematical Programming Approaches

G. Bolzon, G. Maier and F. TinLoi

296 
Embedded Cohesive
Crack Models Based on Regularized Discontinuous Displacements

R. Larsson, K. Runesson and M. Akesson

297 
Computational
Aspects of Fracture Simulations with Lattice Models

E. Schlangen

298 
A Finite Element
Approach to 3D Crack Growth in Brittle Solids

G. Baker and C.A. Grummitt

299 
An Adaptive Mesh
Strategy Based on the Ale Formation to Transient Finite Element
Analysis of Localisation

L. Bodé, G. PijaudierCabot and A. Huerta

2910 
Particle Model
for Fracture and Statistical MicroMacro Correlation of Material
Constants

M. Jirasek and Z.P. Bazant

2911 
2D and
3DModelling of Concrete as an Assemblage of Spheres Reevaluation
of the Failure Criterion

W.J. Beranek and G.J. Hobbelman

Chapter
10. Damage Models

2101

Damage in
Discrete and Continuum Models

G. PijaudierCabot, A. Delaplace and S. Roux

2102 
A ThermoMechanical
Damage Model for Concrete at Elevated Temperatures

G. Baker and R. de Borst

2103 
Some
Considerations on Explicit Damage Models Including Crack Closure
Effects and Anisotropic Behaviour

A. Rouquand and C. Pontiroli

2104 
Gradient Damage
and Reliability: Instability as Limit State Function

J. Carmeliet and R. de Borst

2105 
Additive
VolumetricDeviatoric Split of Finite Strain Tensor and its
Implication for Cracking Models

Z.P. Bazant

2106 
Damage
Evolution Laws for Concrete  a Comparative Study

M. PolancoLoria and S.I. Sørensen

2107 
A Damage Mechanics
Model for Concrete Subjected to Compression

S. Akyüz and M.A. Tasdemir

2108 
Failure
Analysis of PreDamaged Concrete Structural Components

L. Bodé, J.L. Tailhan, G. PijaudierCabit and Ch. La Bordierie

2109

PoroFracture
Analysis of Concrete Using a Damage Mechanics Models 
S.S. Bhattacharjee, F. Ghrib, R. Tinawi and P. Léger

Chapter
11. Fundamental Considerations

2111

Localization and
Mesh Sensitivity in Gradient Dependent Softening Plasticity

F. Meftah, J.M. Reynouard and O. Merabet

2112

Strain
Localization as Bifurcation Behaviour of ElastoPlastic Softening
Materials

H. Yoshikawa, R. Nagano and K. Willam

2113

A Continuum
Thermodynamics Approach for Studying Microstructural Effects on
the NonLinear Fracture Behaviour of Concrete Seen as a
Multicracked Granular Composite Material

C. Huet

Chapter
12: Applications  12.1 Reinforced Concrete and Concrete
Structures 
2121

Approximate
Fracture Mechanical Approach to the Prediction of Ultimate Shear
Strength of RC Beams

B.L. Karihaloo

2122 
HardeningSoftening
Behaviour and Minimum Reinforcement of RC Beams

K. Rokugo, N. Kurihara, T. Ito, Y. Uchida and W. Koyanagi

2123 
Crack Spacing in
Reinforced Elements

L.J Sluys and M.A. Brioschi

2124 
Restrained Shrinkage
 Its Impact on the Response of Reinforced Concrete Members

T.S. Ahn and V.S. Gopalaratnam

2125 
F.E. Analysis of
SFRCT TGirders Submitted to Shear: A Comparison with Experiment

P. Casanova, P. Rossi and A. Elouard

2126 
Fracture of
Lightly Reinforced Concrete Beams: Theory and Experiments

J. Planas, G. Ruiz, M. Elices

2127 
Applications of
Linear Elastic Fracture Mechanics to Reinforced and Prestressed
Concrete Structures

L. Goffi

2128 
Dynamic
Analysis of Reinforced Concrete Slabs: Comparison of Simplified
Methods

F. Toutlemonde and P. Rossi

2129 
Reinforced Normal
and High Strength Concrete Columns  Fracture Mechanics and
Experiments

C. Claeson and K. Gyltoft

21210 
Shock Wave
Loading on Reinforced Concrete Plates: Experimental Results and
Comparisons with Explicit Damage Model Predictions

C. Pontiroli, A. Rouquand and E. Canton

21211 
Simulation of
Punching Failure: Failure Mechanism and SizeEffect

Ph. Menétrey

21212 
Fracture
of Concrete  A New Approach to Predict Crack Propagation

T. Corelius Hansen

21213 
Adaptive Mesh
Refinement Procedure of Finite Element Method for Fracture
Mechanics

L. Liang and Y.M. Lin

21214 
Fictitious
Crack Modelling of Kiln Furniture Ceramics

M.A.J. van Gils, L.J.M.G.Dortmans and G. With

21215 
A Strategy for
Analyzing the Mechanical Behaviour of Concrete Structures under
Various Loadings: the LCPC Experience

P. Rossi and F.J. Ulm

21216 
Discrete Crack
Modeling in Concrete Structures

J. Cervenka and V.E. Saouma

21217 
Similarity
Laws for Concrete Structures under Dynamic Loading

J. Mazars, J.F. Dubé and S. Ghavamian

21218 
Crack
Propagation in Concrete Specimens Subjected to Sustained Loads

A. Carpinteri, S. Valente, F.P. Zhou, G. Ferrara and G. Melchiorri

21219 
Interfacial Fracture
Toughness of Concrete Repair Materials

V.C. Li, Y.M. Lim and D.J. Foremsky

21220 
Application of
Fracture Mechanics to Design of SFRC Tunnel Linings and
Development of StrainHardening Cementitious Composites

H. Horii, P. Nanakorn and P. Kabele

21221 
Strength of a
Concrete Element under the Action of Concentrated Tensile or Shear
Force

V.I. Yagust and D.Z. Yankelevsky

21222 
Simulation of 3D
ConcreteFrame Collapses Due to Dynamic Loading

M. Hakuno

21223 
Linear or
Nonlinear Fracture Mechanics of Concrete

G.A. Plizzari and V.E. Saouma

21224 
Mesh Sensitivity
Effects in Smeared Finite Element Analysis of Concrete Fracture

V. Cervenka, R. Pukl, J. Ozbold and R. Eligehausen

21225 
Seismic
Localization of Softening Cracking Damage in Concrete Frames

Z.P. Bazant and M. Jirasek

21226 
Application of
NonLinear Fracture Mechanics to the Seismic Assessment of
Concrete Gravity Dams

M. Galli, G. Feltrin and H. Bachmann

12.2
Hygral and Thermal Gradients and Crack Formations

21227

Crack Formation
under Hygral or Thermal Gradients

A.M. Alvaredo

21228 
Modelling of Early
Age Concrete Cracking Due to ThermoChemoMechanical Couplings

F.J. Ulm, A. Elouard and P. Rossi

21229 
Bonded High
Strength Concrete Overlays Exposed to Autogenous and Drying
Shrinkage

T. Kanstad

21230 
Experimental
and Numerical Study of DryingInduced Warping of Concrete Slabs

A.M. Alvaredo, S. Gallo and F.H. Wittmann

21231 
Optimization
of Mortars by Means of Fracture Mechanics

G. Martinola and F.H. Wittmann

21232 
An Insight in
the Reduction of Drying Shrinkage of Concrete Due to Skin
MicroCracking

L. Granger and P. Rossi

21233 
Water Movement
within Mortar Analyzed as Capillary Flow

H. Akita and T. Fujiwara

21234 
Evaluation of
Concrete Durability Based on Crack Growth Kinetics Data under
influence of Elevated Temperatures

Y. Zaitsev, V. Shevchenko and T. Cherednichenko

21235 
Influence
of Drying Induced Damage on the Hygral Diffusion Coefficient

F.H. Wittmann

12.3
Anchor Bolts

21236

Anchor PullOut
Tests  Influence of Boundary Conditions and Material Properties

V. Slowik, A.M. Alvaredo and F.H. Wittmann

21237 
Fracture
Behaviour of Normal and High Strength Concrete in Anchor PullOut

R. Zeitler and J.D. Wörner

21238 
Anchor Bolts in
Concrete Structures  Finite Element Calculations Based on
Inner Softening Bands

U. Ohlsson and T. Olofsson

21239 
Fatigue Behaviour
of Anchor Bolts in Concrete

E. Cadoni

21240 
FEM Analysis of
Tensile Fracture Phenomena in Concrete Structures

A. Ali

21241 
Splitting of
Concrete Covers  A Fracture Mechanics Approach

K. Noghabai

21242 
Computer Simulation
of Fasteners in Concrete Under Fire

R. Pukl, M. Reick and R. Eligehausen

Volume 3

Front
Matter, Preface, Table of Contents 
Workshop
1. Numerical Modelling and Determination of Fracture Mechanics
Parameters

311

Numerical
Modelling and Determination of Fracture Mechanics Parameters for
Concrete and Rock: Introduction

J.G.M. van Mier

312

Numerical Modelling
and Determination of Fracture Mechanics Parameters. Hillerborg
Type Models

M. Elices and J. Planas

313 
On Fracture
Mechanics in General and Discrete Cracks in Particular

V.E. Saouma

314 
Softening, Damage
and HigherOrder Continua

R. de Borst

315 
Numerical
Modelling and Determination of Fracture Mechanics Parameters for
Concrete and Rock: Probabilistic Aspects

J. Carmeliet

316 
The Need for Standard
Test Models

B.I.G. Barr and S.E. Swartz

317 
Numerical
Modelling and Determination of Fracture Mechanics Parameters:
Workshop Summary Report

E. Schlangen

Workshop
2. Fracture Mechanics and Design of Concrete Structures

321

Approximate
Analytical Fracture Mechanics Approach to the Design of Concrete
Structures

A. Carpinteri and R. Massabó

322 
Applications of
Fracture Mechanics to Anchors and Bond

L. Elfgren, K. Noghabai, U. Ohlsson and Th. Olofsson

323 
Fracture Mechanics in the Design
of Concrete Pipes

P.J. Gustafsson and O. Dahlblom

324 
Using Fracture
Mechanics Concepts to Predict the Shear Strength of Concrete
Structures

S. Kono, N.M. Hawkins and A.S. Kobayashi

325 
Application of
Computational Fracture Mechanics to Repair of Large Concrete
Structures

A. Ingraffea, B. Carter and P. Wawrzynek

326 
Application
of Fracture Mechanics to High Strength and Offshore Concrete
Structures

M. Modéer

327 
Fracture
Mechanics and Design of Concrete Structures  Workshop Summary
Report

B.L. Karihaloo

Workshop
3. Size Effects: Theoretical Concepts, Experimental Verifications,
and Implications in Structural Design

331 
Size Effect Aspects
of Measurement of Fracture Characteristics of Quasibrittle
Material

Z.P. Bazant

332 
A Multifractal Approach to the
Strength and Toughness Scaling of Concrete Structures

A. Carpinteri and B. Chiaia

333 
Intrinsic Material
Law for Predicting Size Effect in Concrete Structures

H. Mihashi and N. Nomura

334 
Size Effects in
Cracking of Concrete: Physical Explanations and Design
Consequences

P. Rossi

335 
Size Effect on
Strength and Deformation of RC Beams Failing in Flexure

H. Adachi, N. Shirai, M. Nakanishi and K. Ogino 
336 
Size Effects:
Theoretical Concepts, Experimental Verifications, and Implications
in Structural Design  Conclusive Remarks

F.J. Ulm

Workshop
4. Experimental Methods

341

Strain Softening of
Concrete in Compression

S.P. Shah, S. Choi and D.C. Jansen

342 
Effect of
Confinement on the Fracture Behavior of Concrete under Compression

K.M. Nemati and P.J.M. Monteiro

343 
An Experimental
Study of the Microstructural Mechanism Influencing Crack Closure
Stresses in a FineSand Mortar

R. Dasgupta, J.C. Hay, J. McConell, K.W White and C. Vipulanandan

344 
Uniaxial Tension

H.W. Reinhardt

Workshop
5. Smeared Versus Discrete Failure Analysis with Application to
PullOut Problems

351

Discrete Versus
Smeared Crack Analysis

K. Willam and I. Carol

352 
Fastening
Elements in Concrete Structures

R. Eligehausen and J. Oûbolt

353 
PullOut Failure
Mechanisms in Concrete

D.V. Phillips, D.R. Green, B.S. Zhang, C.J. Pearce and N. Bicanic

354 
Application of
the Finite Element Method to Anchoring Technology in Concrete

J. Nienstedt and Ch. Dietrich

355 
Bridges Between
Damage and Fracture Mechanics

J. Mazars and G. PijaudierCabot

356 
Discrete
Crack Analysis of Anchor Bolt PullOut

J. Cervenka and V.E. Saouma

357 
Smeared Versus
Discrete Failure Analysis with Application to PullOut Problems 
Concluding Remarks

J. Ozbolt and R. Pukl

Author
Index
