Materials and Structures

, Volume 43, Issue 6, pp 857–874 | Cite as

Evaluation of fracture parameters of concrete from bending test using inverse analysis approach

Original Article


In this study, an inverse analysis approach is developed to obtain the fracture parameters of concrete, including stress–crack opening relationship, cracking and tensile strength as well as fracture energy, from the results of a three-point bending test. Using this approach, the effects of coarse aggregate size (5–10, 10–16, 16–20 and 20–25 mm) and matrix strength (compressive strength of 40 and 80 MPa, respectively) on the fracture parameters are evaluated. For normal strength concrete, coarse aggregate size and cement matrix strength significantly influence the shape of σ–w curve. For a given total aggregate content, small aggregate size leads to a high tensile strength and a sharp post-peak stress drop. The smaller the coarse aggregate, the steeper is the post-peak σ–w curve. By contrast, in high strength concrete, a similar σ–w relationship is obtained for various aggregate sizes. The post-peak stress drop for high strength concrete is more abrupt than that for normal strength concrete. Also, the smaller the coarse aggregate size, the higher is the flexural strength. For both normal and high strength concrete, fracture energy and characteristic length are found to increase with increase of coarse aggregate size.


Bending test Inverse analysis Stress–crack width relationship Fracture energy Aggregate 



Support from the National Natural Science Foundation of China (Nos. 50438010 and 50178043) is gratefully acknowledged.


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Copyright information

© RILEM 2009

Authors and Affiliations

  • Jun Zhang
    • 1
  • Christopher K. Y. Leung
    • 2
  • Shilang Xu
    • 3
  1. 1.Department of Civil EngineeringTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.Department of Civil EngineeringHong Kong University of Science and TechnologyKowloon, Hong KongPeople’s Republic of China
  3. 3.Department of Civil EngineeringDalian Institute of TechnologyDalianPeople’s Republic of China

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