# Prediction of Concrete Failure Time Based on Statistical Properties of Compressive Strength
## 1 Introduction  
Reinforced concretes have been applied worldwide in structural engineering since the beginning of the nineteenth century [1; 2; 3; 4; 5]. However, structure damage has increasingly occurred under aggressive service environments, which might be caused by ambient temperature, freeze-thaw cycles, precipitation, carbon dioxide, chloride, and sulfate [6; 7; 8]. Therefore, it is significant to implement effective strategies to guarantee structural safety and strengthen vulnerable buildings. In this paper, a proposed model based on the compressive strength of concrete was applied to predict the concrete failure time. Carbonation is one of the most fundamental triggers of concrete deterioration [9; 10; 11; 12; 13], and carbonation depth is used to describe the level of carbonation-induced corrosion. As presented in the existing paper, the carbonation depth has both favorable and unfavorable effects on the compressive strength of concrete. On the positive side, carbonation-induced corrosion contributes to the increase of the compressive strength and the harnessing of concrete because numerous concrete pores are occupied by the carbonation product, calcium carbonate [14]. On the negative side, too much calcium carbonate that exceeds the limit of concrete pores might cause additional internal pressure andmicro-cracking [15; 16]. In this paper, the relationship between carbonation depth and the compressive strength of concrete is analyzed using a prediction model of carbonation depth [17]. Since the presence of variations associated with climatic factors (e.g., temperature and humidity), concrete materials, and geometric configurations [18; 19], the compressive strength of concrete should be regarded as a variable in order to account for these uncertainties in deterioration. In practical engineering problems, these unavoidable uncertainties are often qualified by probabilistic models [20; 21; 22], among which reliability analyses are widely applied in structural safety assessments [23; 24; 25]. In the existing time-varying reliability models, the probabilities of corrosion initiation and corrosion damage are calculated based on the change in climatic variables [26]. [PERSON] [27] developed a phenomenological constitutive model for obtaining the rebound hardness of a surface concrete as a property of the time-dependent material. Nevertheless, this model has not yet been ratified for practical applications. A previously conducted study [28] exhibits the property of compressive strength in the case of deteriorating concrete in the Tohoku region of Japan; however, the prediction model of compressive strength and the method of structural safety evaluation were not provided. Generally, most existing probabilistic models may not be suitable for evaluating the service life of concrete. Based on a large number of tested data on compressive strength, an effective model based on the reliability to evaluate the service life of concrete was developed. It is noted that different sizes and shapes of the tested components affect the compressive strength of concrete. Therefore, the conversion and standardization of the value of compressive strength may produce an inaccurate result [29]. In this paper, all the shapes and sizes of the experimental members were unified. Additionally, the compressive strengths of all the samples were tested using core pulling. [PERSON] [30] proposed that the compressive strength obeys a normal distribution; however, by analyzing 10,317 datapoints considered in this study, it is observed that a gamma distribution is more appropriate to describe the distribution of compressive strength. Moreover, though [PERSON]'s model serves the purpose of evaluating the compressive strength, only the mean value of compressive strength is considered. Therefore, the probabilistic model may not obtain the precise prediction of concrete failure time.