Bayesian Estimation for Probability Distribution of Rock's Elastic Modulus Based on Compression Wave Velocity and Deformation Warning for Large Underground Cavern

The elastic modulus of rock is the key parameter in excavation deformation prediction, support design, and the stability analysis of underground engineering. However, traditional statistical methods require a large number of laboratory or field tests to obtain its probability distribution form and distribution parameters, which is difficult in some projects. To overcome this problem, a new method based on Bayesian theory is developed to infer the rock elastic modulus probability distribution using the compression wave velocity of rock. The test data collected from the Firuzkoy area of Istanbul are used for method validation, the results of the developed method are compared with a traditional regression model to demonstrate the advantage under small sample conditions. And the effects of different prior ranges and forms on the evaluation results of the elastic modulus are also studied. Furthermore, the developed method is applied to obtain the probability distribution of the elastic modulus at the Yingliangbao hydropower station, and the safety warning indexes in the main powerhouse are formulated based on the displacement probability quantile. Compared with the field monitoring data, the consistency in excavation displacement indicates that the acquired elastic modulus of rock is reasonable for deformation probability estimation and safety warning in underground caverns.

Automated summary

The elastic modulus of rock is a crucial parameter in predicting excavation deformation, designing support, and analyzing the stability of underground engineering. A new method based on Bayesian theory is developed to infer the probability distribution of the rock elastic modulus using the compression wave velocity of rock, overcoming the limitations of traditional statistical methods. The method is validated using test data from the Firuzkoy area of Istanbul and compared with a traditional regression model to demonstrate its advantage under small sample conditions. The method is also applied to obtain the probability distribution of the elastic modulus at the Yingliangbao hydropower station, and safety warning indexes are formulated based on the displacement probability quantile.