Study of Size Effect in Concrete Using Fictitious Crack Model

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Abstract
A boundary element program based on a fictitious crack‐model (FCM) was used to study the size effect in concrete during mode‐I nonlinear fracturing. Series of numerical parametric studies were performed to examine the effects of specimen size, loading configuration (three‐point beam and double cantilever beam), and initial notch size on the nonlinear fracture characteristics. The results of numerical simulations confirmed the curve‐fitting procedure proposed by Bažant and his coworkers in their size‐effect law method. However, two notable exceptions were observed: (1) Small size specimens where bending strengthening may be pronounced; and (2) specimens with small initial notch. In addition to examining the range of applicability of Bažant's size‐effect law method, this paper provides empirical equations for determination of the maximum process‐zone length under three‐point bending or double cantilever beam (DCB) loading condition. Finally, the normalized R‐curves expressed in terms of the energy release rate versus the normalized effective crack extension have been shown to be independent of specimen size, initial notch size, and loading configurations. Therefore, the normalized R‐curves are recommended as a proper way of representing the nonlinear resistance of beam structures to mode‐I fracture.

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