# Effects of Fineness and Dosage of Fly Ash on the Fracture Properties and Strength of Concrete
## 1 Introduction  
Incorporating fly ash in concrete may affect the rate of hydration reaction and improve its microstructure [1; 2]. The improvement in microstructure occurs due to grain and pore refinements, especially in the interfacial transition zone (ITZ) [3]. The improved microstructure can cause enhancement in the mechanical and durability-related properties of concrete. For the replacement amounts normally used, most fly ashes tend to reduce the early strength up to 28 days but increase the long term strength [4]. It is generally recognized that the use of finer fly ash may increase the properties of concrete [5] [PERSON] [6] reported that the majority of the reactive particles in fly ash are actually less than 10 micrometers in diameter. Studies [3; 4; 5; 6] showed that increasing the fineness of fly ash by grinding improves the reactivity to some extent and increases the strength of the concrete, but eventually leads to increased water demand. [PERSON] et al. [7] tested ultra-fine fly ash with a mean particle diameter of about 3 \(\upmu\)m and found that significant improvements in the concrete strength and durability without loss in workability could be achieved with a commercially available ultra-fine fly ash. It could be primarily concluded that increasing the fineness of fly ash may increase the strength of concrete attributed to the micro-cracking resistance of cement paste, particularly in the ITZ. The interfacial transition zone in concrete, which is often considered to be a three-phase material, is represented as the third phase [8; 9]. Existing as a thin shell around the larger aggregate, the ITZ is generally weaker than either of the two main components of the concrete, which are the hydrated cement paste and the aggregate. The ITZ has less crack resistance, leading to the preferential occurrence of cracking. A major factor responsible for the poor strength of the ITZ is the presence of micro-cracks. Much of the physical nature of the response of concrete under loading can be described in terms of micro-cracks that can be observed at relatively low magnification. Cracking in concrete is mostly due to the tensile stress that occurs under load or environmental changes. As such, the failure of concrete in tension is governed by micro-cracks, which are associated particularly with the ITZ [10; 11]. The tensile strength of concrete is a very essential property. Not only the tensile strength but also the behavior at the tensile fracture is of importance, particularly the fracture toughness. When concrete fails in tension, its behavior is characterized by both the peak stress and the energy required to fully generate a crack. Fracture mechanics can, in principle, be a suitable basis for analyzing the fracture toughness of concrete [12]. The defects and stress concentrations are the main factors causing failure. Concrete with defects or stress concentrations is more prone to cracking, which results in reduced strength. A structure made with high-strength concrete may fail under critical stress when small cracks simultaneously occur. It is essential, therefore, to determine fracture behavior and toughness for the widely used high-strength high-performance concretes that normally contain fly ash or furnace slag [13; 14]. Due to the non-homogeneous characteristics of concrete, its fracture behavior is quite complicated. It has been proved that the methods developed in conventional fracture mechanics are unsuitable for the analysis of the influence of fracture toughness on the behavior of concrete structures [15; 16]. Many theoretical models have been developed to make such an analysis possible. Among them, three well-known models are the fictitious crack model, the crack band model, and the two-parameter fracture model. By means of numerical techniques, for example, the finite element method, it is possible to use these models to make a theoretical analysis for the development of the damage zone and the complete behavior of the structure.