# Acoustic Emission Analysis of Fracture and Size Effect in Cementitious Mortars
## 1 Introduction
[PERSON] and [PERSON] [13] performed tensile tests on notched concrete samples with varying sizes. Additionally in their work, the size of FPZ was found to increase with sample size, but the rate of growth was less than the sample size. [PERSON] and [PERSON] [14] observed that the size of the FPZ was more affected by the type of rock used than the sample size increase rate. [PERSON] et al. [11] also found sample size to have no significant effect on the width of the located AE clusters (FPZ) when performing Brazilian splitting tests on quasi-brittle materials. Hence, in this paper, this ambiguous relation between sample size, AE source locations, and the size of FPZ is investigated. A straightforward test that can induce a brittle failure is a Brazilian splitting test [8]. In this test, a cylindrical sample is diametrically compressed. For a linear elastic brittle material, this will generate a nearly uniform tensile stress at the center plane that passes along the loading direction [2]. The tensile stress at failure will split the sample, and this stress is used to measure the tensile splitting strength (\(f_{\text{ct}}\)) [22]. The relation between the \(f_{\text{ct}}\) and the sample diameter (D) is often contradictory in the literature. [PERSON] [23] (for D = 150 mm to 600 mm) observed the \(f_{\text{ct}}\) to increase with diameter. However, [PERSON] et al. [24] (for D = 37 mm to 300 mm) and [PERSON] et al. [8] (for D = 19 mm to 508 mm) found the \(f_{\text{ct}}\) to decrease as sample size increases. Yet, in the study of [PERSON] et al. [8], this effect was reversed when passing above a specific diameter, while [PERSON] et al. [24] observed the \(f_{\text{ct}}\) to reach asymptotically a minimum value as the diameter increases. From these literature analyses, it can be inferred that the correlation between sample diameter and the tensile splitting strength depends on the range of the compared specimens' diameter. In addition to the sample size, the boundary condition was found to affect the \(f_{\text{ct}}\)[24]. In the current paper, the Brazilian splitting test method is adopted not only to clarify the impact of size on strength, but also on fracture initiation and development. The focus will be on the smaller diameter range (27-106 mm) and constant boundary conditions. This paper aims at studying the causes of size effect phenomena with the AE technique. It is clear from the literature study that researchers have investigated the size effect in the Brazilian splitting test. However, to the authors' knowledge, simultaneous direct and derived AE parameters and waveform analyses have not been applied for size effect investigation in the Brazilian splitting test of cementitious mortars. Hence, the AE analysis is used to validate prior extensive theoretical and experimental analyses found in the literature. The size effect is analyzed by comparing the failure strength and the AE-based fracture analysis. The paper is organized as follows: the second section describes the experimental test program and the overall methodology. The third section presents observations on mechanical behavior of cementitious mortars in a Brazilian splitting test in relation to sample size and boundary conditions. In the fourth section, the size effect is investigated by means of AE analysis: AE amplitude, AE hit count, AE-based FPZ, and \(b\)-value analysis are reported and linked to the fracture process.