Abstract
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.
Highlights
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A method based on Bayesian framework is developed to estimate the distribution of rock’s elastic modulus using the wave velocity, which can effectively improve the evaluation ability under the conditions of small samples.
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The effects of different input data, different prior ranges, and different prior forms on the evaluation results of elastic modulus are studied, which show that the advantage of the proposed method is general and applicable for different amounts of input data and different types of prior.
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A probability warning index is proposed based on the occurrence probability of displacement, which can be used to recognize the unstable deformation of surrounding rock in the underground cavern, and the proposed method is verified with the field monitoring data.
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Acknowledgements
The authors gratefully acknowledge the financial support from National Natural Science Foundation of China (No. U1965205 and No. 51779251), and the Science and Technology department of China Huaneng Corporation Limited (No. HNKJ21-HF317).
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Liu carried out the calculation, data analysis and wrote the content, Jiang designed the study and wrote the content; Yan, Chen, Yin, and Xiong took part in the field data collection and analysis; Zheng organized experiment and technical analysis. All authors have read and approved the final manuscript.
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Appendices
Appendix A: Matlab Code of Bayesian Method
Appendix B: Matlab Code of Random Field Generation of Elastic Modulus
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Liu, J., Jiang, Q., Chen, T. et al. Bayesian Estimation for Probability Distribution of Rock’s Elastic Modulus Based on Compression Wave Velocity and Deformation Warning for Large Underground Cavern. Rock Mech Rock Eng 55, 3749–3767 (2022). https://doi.org/10.1007/s00603-022-02801-2
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DOI: https://doi.org/10.1007/s00603-022-02801-2