# Analytical Study on the Load-Bearing Performance of RC Beams Subjected to ASR Expansion
## 1 Introduction  
The alkali-silica reaction (hereinafter referred to as ASR), one of the deterioration phenomena of concrete, causes cracks in concrete and is a significant problem in the maintenance of concrete structures. The alkali-silica gel has high water absorption and expansion properties, so it expands when water is supplied from outside the concrete, causing internal stresses in the concrete, breaking down the surrounding cement paste, and causing microcracks and cracks over time as shown in Figure 1[1, 2, 3]. Figure 1(a) shows the results of the observation of cracks around aggregate due to aggregate expansion under black light irradiation with fluorescent resin impregnation (meso-observation), and Figure 1(b) shows the results of the observation of cracks, typically cracks in the shape of a tortoiseshell, on RC members and structures due to ASR (macro-observation). Although the observation scales are different, it is important to clarify the effects of these cracks on durability and load-carrying capacity to realize rational maintenance management and to select appropriate repair and reinforcement measures. In summary, the evaluation of the internal expansion phenomena caused by ASR is still under research, and the inability to evaluate and predict the performance of deteriorated structures caused by internal expansion phenomena such as ASR is also an issue. As an overview of the existing research, many studies on the durability of concrete due to deterioration have been conducted to date, focusing on deterioration due to salt damage and other factors [4; 5; 6]. However, the risks associated with internal swelling reactions (ISRs), including ASR, have attracted attention both domestically and internationally, and research on the evaluation and prediction of these expansion phenomena is still in its infancy. The Japan Concrete Institute (JCI) has established the research committee (JCI-TC-211A). The main topics of the research on the internal expansion reaction are the modeling of expansion prediction and the modeling of mechanical performance degradation due to expansion. Regarding the modeling of expansion prediction, a model that takes into account the effect of temperature and humidity and the diffusion of alkali ions in the reaction process has been proposed. However, few expansion models consider the effect of reinforcing steel bars, and there are only a few cases in which structural performance evaluation is possible. In addition, structural models that describe macroscopic behavior (cracking, loss of bearing capacity, etc.) corresponding to microscopic expansion phenomena are still under study, making it difficult to evaluate ASR deterioration in real structures. [PERSON] et al. [7] cut RC slab members from a railroad viaduct damaged by ASR approximately 24 years after completion, observed the appearance, and conducted material strength tests. The results showed the compressive strength and static modulus of elasticity had dropped to 50-70% and 53-60%, respectively, due to cracking. [PERSON] et al. [8] fabricated cylindrical specimens  
Figure 1: General expansion mechanism of ASR. **(a)** Generation of the alkali–silica gel; **(b)** water absorption expansion of gel; **(c)** occurrence of cracking. Figure 2: Cracks due to ASR: **(a)** Cracks around aggregate (mesoscopic observation); **(b)** cracks on bridge abutment surface (macroscopic observation). and RC beam specimens, accelerated ASR, and observed the structural and mechanical behavior of the specimens. At 6 months of age, the compressive strength, tensile strength, and dynamic modulus of the cylindrical specimens were 24, 38, and 31% lower, respectively, than the corresponding values at 28 days of age. ASR caused visible cracking in the RC beams, but the flexural load-carrying capacity was similar to that of the non-reactive beams.