Mahmoud A. Issa

Fractal dimension––a measure of fracture roughness and toughness of concrete

Abstract The quantitative description of rough surfaces and interfaces has been an important challenge for many years. This paper addresses the potential application of fractal geometry to characterize the fracture surface and to determine whether there is any correlation between fracture properties and the roughness of the fracture surface. Fractured surfaces of three different size wedge-splitting specimens, dimensions varying from ( width × total depth × thickness ) 420×420×50 mm to 1680×1680×200 mm with four different maximum aggregate sizes of 9.5, 19, 38, and 76 mm, were analyzed using a modified slit-island technique. It was found that fractal dimension, i.e., roughness, increases with an increase in both specimen and maximum aggregate size. A clear correlation exists between roughness (fractal dimension) and fracture toughness: the tougher the material, the higher the fractal dimension.

Correlation between crack tortuosity and fracture toughness in cementitious material

This paper proposes a new technique for the evaluation of fractal dimension (D) of fracture surface and a quantitative correlation between D and fracture toughness of cementitious materials. The experimental program has been performed on compact tension (CT) specimens (600 × 525 × 125 mm) with three different aggregate sizes (dmax=4.7 mm, 18.8 mm and 37.5 mm). The fractal geometry concept is utilized in the evaluation of fracture surface roughness. To avoid indirect or destructive experimental procedures that are prohibitively laborious and time consuming, a new non-destructive technique is presented. Results of the analysis indicate that the concept of fractal geometry provides a useful tool in the fracture surface characterization. The results also suggest that the fracture toughness can be correlated with the fractal dimension of fracture surface.

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76 mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125 mm/min (0.005 in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G1). There is a well pronounced general trend observed: G1 increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G1 increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G1, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.

Size effects in concrete fracture: Part I, experimental setup and observations

AbstractThis paper presents an experimental investigation on the influence of microstructural parameters, such as aggregate size, and macroscopic parameters, such as specimen dimensions, on brittle fracture. Maximum aggregate size was used as a representative parameter of aggregate distribution in agreement with ASTM C 136 standards. Six groups of geometrically similar concrete specimens with various dimensions and aggregate sizes were prepared. Similarity of the specimens was strictly maintained by scaling the specimen dimensions from one group to another by a factor of two starting from a specimen size of (width × total depth × thickness) 105×105×12.5 mm to 1680×1680×200 mm. Two separate sets of removable pre-cast notches were designed to determine the effect of initial notch size. A considerable effort was devoted to the design of the loading fixture to have a reproducible crack initiation and controlled crack growth. Several loading fixtures were evaluated prior to selection of the one used in the experimental program. Quasi-static splitting cyclic loading in edge cleavage configuration was applied. A servo-hydraulic Instron machine was used for testing. The fracture process was monitored by optical and acoustic imaging techniques. Three forms of comparisons of the test results with respect to the specimen and aggregate sizes were adopted. The first corresponded to the various specimen sizes cast with the same maximum aggregate size. The second comparison was based on the geometrically identical specimens cast with various maximum aggregate sizes. The third form of comparison dealt with complete geometrical similarity, i.e., all dimensionless geometrical characteristics including specimen thickness to maximum aggregate size ratio were identical. Results from this study indicated that as the specimen size decreases, the envelope becomes larger within the first and third forms of comparison. In the second form of comparison, i.e., geometrically identical specimens cast with various maximum aggregate sizes, the area under the envelope was greater as the maximum aggregate size increased. The existence of a trend in dimensionless critical load-CMOD envelopes despite the apparent geometrical and physical similarity of the test conditions is the direct indication of a scale effect, i.e., the modified fracture energy,

SPECIMEN AND AGGREGATE SIZE EFFECT ON CONCRETE COMPRESSIVE STRENGTH

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FIELD PERFORMANCE OF FULL DEPTH PRECAST CONCRETE PANELS IN BRIDGE DECK RECONSTRUCTION

indicates the existence of a strong scale effect:

Analysis of full depth precast concrete bridge deck panels

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