Small data reliability analysis in concrete three-point bending tests: A Weibull mixture model approach based on Weibull fracture theory

Abstract

Due to the high costs and time-consuming nature of experiments, data from concrete three-point bending tests are usually limited. Additionally, the performance of concrete is influenced by various factors such as mix composition and sample preparation methods, leading to significant variability in test results. This poses a major challenge for the reliability analysis of small data from repeated tests. In reliability analysis, statistical models are particularly important as they allow for the prediction of performance and failure probabilities based on existing data. However, traditional statistical methods require a large number of similar samples for data processing and may need specific adjustments due to the diversity of practical applications. To address these issues, this study proposes a mixture model that combines domain knowledge of concrete with Weibull fracture theory and uses the Clustering-Circular Block Bootstrap method for sample augmentation. By analyzing real data obtained from concrete three-point bending tests, we accurately estimated the failure probability of concrete. Additionally, the study uses Gaussian process regression with a spectral mixture kernel function to fit the threshold fracture strength of concrete and estimate failure probabilities. The results show that the proposed method can accurately fit small datasets, with a RMSE of 0.320 and a MAPE of 0.100. The nominal bending strength range at a 5% failure probability is 2.0 MPa to 6.5 MPa, depending on the sample height and pre-crack length. Statistical learning demonstrates that the proposed method excels in fitting small datasets, providing a solid framework for predicting concrete strength and reliability.