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1、. . . _ . - . . . . _ . _i _ _ . .- . . .- : - - . * . . : . . . . :- . . -. - Fracture Mechanics: Application to Concrete Victor C. Li Zdenek E! Bazant Ed tors SP-118 B C PI* American Concrete Institute, Detroit PI2 A COPYRIGHT ACI International (American Concrete Institute) Licensed by Information
2、 Handling Services COPYRIGHT ACI International (American Concrete Institute) Licensed by Information Handling Services rn f DISCUSSION of individual papers in this symposium may be submitted in accordance with general requirements of the AC1 Fublication Policy to AC1 headquarters at the address give
3、n below. Closing date for submission of discussion is May 1, 1990. All discussion approved by the Technical Activities Committee along with closing remarks by the authors will be published in the September-October 1990 issue of either AGI Structural Journal or AGI Materials Journal depending on the
4、subject emphasis of the individual paper. The Institute is not responsible for the statements or opinions expressed in its publications. Institute publications are not able to, nor intended to, supplant individual training, responsibility, or judgment of the user, or the supplier, of the information
5、 presented. The papers in this volume have been reviewed under Institute publication procedures by individuals expert in the subject areas of the papers. Copyright1989 APEXICAN CONCRETE INSTITUTE P.O. Box 19150 Redford Station Detroit, Michigan 48219 All rights reserved including rights of reproduct
6、ion and use in any form or by any means, including the making of copies by any photo process, or by any electronic or mechanical device, printed or written or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing i
7、s obtained from the copyright proprietors. Printed in the United States of America Editorial production: Patricia Kost LIBRARY OF CONGRESS CATALOG CARD NUMBER 89-80358 COPYRIGHT ACI International (American Concrete Institute) Licensed by Information Handling Services COPYRIGHT ACI International (Ame
8、rican Concrete Institute) Licensed by Information Handling Services PREFACE Recent advances i n concrete fracture mechanics involving fracture characterization, fracture resistance measurements, sophisticated numerical/computational tools, and material intrinsic toughness development have brought ab
9、out certain consensus among researchers that fracture mechanics could help i n improving concrete structural performance. There is a sense of urgency t h a t researchers should provide assistance i n bringing research results to bear on practical concerns related t o the safety and economy of concre
10、te structural design. This is the motivation behind the formation of AC1 TechncalCommttee446whosegoalstorevewtheapplcatons of fracture mechanics to concrete structures. A s part of its activities, Committee 446 sponsored two technical sessions on this topic a t the Seattle f a l l meeting of the Ame
11、rican Concrete Institute i n November, 1987. This book is a collection of most of t h e papers from that meeting, and some additional invited papers. It is hoped that the book w i l l stimulate greater interaction between researchers i n concrete fracture mechanics and practitioners of concrete stru
12、ctural design, especiallythose concernedwithmcdernizing the design codes. It is not easy t o divorce discussion of fracture failure from discussion of the fracture behavior of cementitious materials. This book is, therefore, divided into two sections: the f i r s t section is on applications of frac
13、ture mechanics t o cementitious materials, and the second is on applications of fracture mechanics t o concrete structures. The synergism of these two sections can be seen i n the introductory chapter. W e wish t o acknowledge with appreciation the many valuable contributions fromthecommitteemembers
14、, many of whomassisted in reviewing manuscripts. Victor C. Li and Zdenek P. Bazant AC1 Committee 446 . 111 COPYRIGHT ACI International (American Concrete Institute) Licensed by Information Handling Services COPYRIGHT ACI International (American Concrete Institute) Licensed by Information Handling Se
15、rvices A C 1 SP-3Z 87 Obb297 0008383 AC1 Conunittee 446 Fracture Mechanics Zdenek P. Bazant m a i m O r a l wiyukozturk riligi Cedolin David Darwin Manuel Elices ShuJin Fang N e i l M. Hawkins Hideyuki H o r i i Anthony R. Ingraffea Jeremy Isenberg Vidor C. Li Feng-Bao Lin Sheng-Taw M a u consulting
16、 Member Boris Bresler Vellore S. Gopalaratnam Secretary Sidney MindeSc Antoine E. Naaman C. fiber reinforced concretes; fracture woperties; research; reviews; tensile stress; structural design build% codes; concretes; cmckhq (fracturing) ; 1 COPYRIGHT ACI International (American Concrete Institute)
17、Licensed by Information Handling Services COPYRIGHT ACI International (American Concrete Institute) Licensed by Information Handling Services 2 Li Victor C. Li has done research in non-linear fracture analysis, frachire testing method and micro/meso-mechanics of concrete. He is pursuing the advancem
18、ent of high strength/high ductility concrete as a construction material of the future. Victor Li is an Associate Professor of Civil Engineering at the Massachusetts Institute of Technology, Cambridge, MA 02139, USA. INTRODUCTION Extensive experiments have revealed the dependence of concrete structur
19、al component strength on its size. This size dependence cannot be explained by the Weibull distribution of flaw size alone, Instead, it has been shown thrit the qwsi- brittle nature leading to a . fracture mode of failure in concrete is responsible for this phenomenon. Current reinforced concrete de
20、sign codes (e.g. AC1 318 Building Code Requirements for Reinforced Concrete) are based on strength or similar concepts. Is the code over-conservative and economically wasteful? Is the code under-conservative and represents potentid hazards? Does the code reflect modem design concerns such as structu
21、ral durability and the introduction of concrete with higher strength but perhaps more brittle behavior? In addition, increasing observational evidence of macroscopic fracture failure in concrete structures suggests a need for new tools beyond the traditional mecans of concrete structural analysis un
22、der certain circumstances. “HAT CAUSES TENSILE FAILURE IN CONCRETE STRUCTURES? What causes tensile stress in the concrete if the smicture is reinforced or even prestressed? The origin of tensile stresses may come from several sources - applied loading such as in the flexing of a beam and that due to
23、 punching on a slab, material shrinkage during curing of the concrete, stress concentration related to structural geometry as in shear keys (such as those in precast concrete bridge se,ments i), and ironically, even from the reinforcing bar itself. This last source has been documented as spalls deve
24、loped on concrete covers caused by the propagation of cracks in the concrete as the steel bxr corrodes and expands (NCHRP Synthesis No. 57, 1979). In addition, when a reinforced concrete beam or slab is loaded in excessive bending, the reinforcing bar may slip. The ribs of a re-bar cm cause local te
25、nsile stresses in adjacent concrete when the re- bar deforms in tension 2. Given the wide variety of situations when tensile 1o:ids we directly or indirectly induced in concrete, and that concrete is a brittle niaterial (concrete has 0.1 to 1 % of the tensile strength of striictural steel, and COPYR
26、IGHT ACI International (American Concrete Institute) Licensed by Information Handling Services COPYRIGHT ACI International (American Concrete Institute) Licensed by Information Handling Services Fracture Mechanics 3 only 0.2 to 4 % of its fracture toughness), it is no wonder why cracks develop in co
27、ncrete structures. It should be noted that even predominantly compressive loading, such as caused by post-tensioning in certain concrete structures, can generate tensile cracks in the transverse direction which leads to surface spalling. This is, after all, the failure mechanism of an unconfined con
28、crete cylinder under compressive loading. WHY SHOULD TENSILE CRACKS BE OF CONCERN? Are cracks benign in reinforced concrete smictures? It depends on many factors. It is rather rare, at least fi-om past experience, that reinforced concrete structiues collapse from a brittle fiacture failure in concre
29、te. In some metal structures, a small crack may grow rapidly and rather suddenly lead to a catastrophic structural collapse. In reinforced concrete structures, failure associated with cracks may occur in different manners. For example, cracks increase the permeability of concrete and allow greater p
30、enemtion of chloride ioiis and other agents which cause the corrosion of the reinforcing steel. Concrete bridge deck delamination and spalling have been traced to tensile cracking near corroding re-bars which expand with time (Figure 1). Thus certain poor durability of reinforced concrete structures
31、 may be associated with the lack of tensile load bearin; capacity of concrete. Thermal loading has been known to be responsible for tensile crack development leading to failure of concrete dams 3. Failure of the Kolnbrein dam has also been traced to excessive loading and its acute geometry, in combi
32、nation with low fracture resistance of the material. resulting ir1 large fractures at the base of this arch dam 4 . For certain structures, especially thin wall structures such as concrete pipes and shells, the reinforcement ratio could be very low or none at all due to difficulty in placing the rei
33、nforcing bars. In this case, the potential of fracture failure and structural collapse becomes more likely 5 . Even in reinforced structures, there are locations where reinforcement may be difficult to place due to the structural geometry. This is the case near the shear keys of concrete segments in
34、 segmental bridge construction i. It is often in such locations where tensile stress and concrete cracking occurs. Cracks growing from such a region may extend into an initially compressive zone where there is litde or no reinforcement iii the structural member. Such cracking development could compr
35、omise the structural integrity of the joint. In addition, it has been shown 161 that the post- tensioning of steel tendons in precast concrete segmental bridges could cause high tensile stresses in the direction trhnsverse to the steel tendons which may lead to COPYRIGHT ACI International (American
36、Concrete Institute) Licensed by Information Handling Services COPYRIGHT ACI International (American Concrete Institute) Licensed by Information Handling Services A C 1 SP-LIB 87 W Obb29q7 0008188 7 W 4 . Li surface spalling. The loss of anchorage and bond of a re-bar has been associated with the dev
37、elopment of tensile cracks in the concrete 2. Moreover, it is known that reinforced concrete structures often develop dangerous surface spalls iiiider impact loads. The above observations represent a spectrum of problems in concrete structures related to the lack of tensile bearing capacity of concr
38、ete. These problems can be avoided if we understand how the tensile stresses arise, how the material responds to these tensile stresses, and how the material may be engineered to perform adequately under tensile loading. STATE OF THE ART IN RESEARCH IN CONCRETE FRACTURE It is the recognition of the
39、importance of cracking in concrete structures that research of concrete and concrete smctures in the tensile field has intensified in recent yeears (e.g. NATO Advanced Research Workshop on Application of Fracture Mechanics to Cementitious Composites, Evanston, 1984; Internatioriiil Conference on Fra
40、cture of Concrete and Rock sponsored by RILEM American Concrete Institute Symposium on Applications of Fracture Mechanics to Concrete Structures, Seattle, U.S.A., 1987; MRS International Meeting on Advanced Materials: Symposium on Fracture of Rock and Concrete, Tokyo, Japan, 1988; International Conf
41、erence on Fracture and Damage of Concrete and Rock, Vienna, Austria, 1988; International Workshop on Fracture Toughness and Fracture Energy - Test Methods for Concrete and Rock, Sendai, Japan, 1988). Since concrete is a brittle material, it has become common place to study concrete failure in tensio
42、n by means of fracture mechanics. Here several issues arise: Does fracture mechanics accurately describe concrete failure in tension? How does one accurately characterize and measure the fratture resistance of the material? How does one apply the appropriate fracture mechanics theory and the measure
43、d fracture resistance of the material to predict the performance of a reinforced or unreinforced concrete structure? How can one improve the structura1 performance by improving the mechanical behavior of the material? In spite of extensive research in recent years, these questions have only been par
44、tially answered, There is, however, growing convergence of opinion. For example, it is now generally agreed that linear elastic fracture mechanics may not Ix directly applicable to concrete, unless the structure or laboratory specimen size is very Inrge 7, and that a non-linear fracture mechanics th
45、eory accounting for the growth of a fracture process zone and subsequently a structural size effect coiild be used instead 7,8,9,10,11,12. However, the issue of fracture resistance COPYRIGHT ACI International (American Concrete Institute) Licensed by Information Handling Services COPYRIGHT ACI Inter
46、national (American Concrete Institute) Licensed by Information Handling Services Fracture Mechanics 5 characterization and measurement is still much debated and a standard test method has yet to be established. Apart from theories, there are also recent advances in numerical methodology, especially
47、in finite element method, and to a lesser extent, boundary element method, in incorporating these theories in the analyses of increasingly more complex structures. Successful modelling of concrete structurai behavior using fracture based finite element codes have been achieved by various researchers
48、 e.g. 4,5,13,14,15,16. Additional work in fracture resistance characterization and measurement, and in numerical simulation of simultaneous tension-softening and slip-weakening mixed mode concrete fracture appears to be necessary to deal with structures subjected to mixed mode loading. Introduction
49、of new construction materials such as high strength concrete and polymer concrete having different fracture characteristics from normal concrete, demands further investigations into how such materials influence structural performance, especially when they are subjected to tensile stresses. With the recognition of fracture resistance as an important material parcameter for concrete, there is increasing research in improving this property through materials engineering. At present the most successful technique of achieving fracture resist
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