A probabilistic approach to characterize coal strength from point load and P-wave velocity tests

Obtaining the values of the uniaxial compressive strength (UCS) of coal is crucial to the design and analysis at a coal mine. The laboratory measurement of the UCS of coal is difficult and may be impossible because of the nature of coal and the sample preparation requirements of uniaxial compression tests, resulting in limited or no UCS test values at most coal sites. To overcome the challenge, a probabilistic characterization of the UCS of coal is developed using results from point load and P-wave velocity tests at a coal mine. The probabilistic characterization is based on Bayesian updating (BU) framework. The framework systematically incorporates prior knowledge and observational data, enabling dynamic updating as new data becomes available, which is an improvement over static empirical model. In addition, the framework provides a transparent method to update and quantify uncertainty in UCS predictions and improves interpretability of results. Using the parameters of point load strength (Is(50)) and P-wave velocity (Vp) from a coal mine together with the ranges of UCS available in literature, the distribution and statistics of the UCS of coal is updated. The BU approach satisfactorily provides probabilistic characterization of the UCS of coal. The approach is further validated using simulated Is(50) and Vp data to investigate how number of input data, and different prior knowledge affect the approach. Such characterization allows mining engineers and practitioners to directly use the values of the UCS of coal from the approach to perform probability-based designs and reliability analyses at coal sites.