A Bayesian-based approach for inversion of earth pressures on in-service underground structures

Zhiyao Tian, Shunhua Zhou, Anthony W L Lee, Yu Zhao, Quanmei Gong*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)


This paper presents a Bayesian inversion approach to identify earth pressures 11 on in-service underground structures based on structural deformations. Ill-conditioning and non-uniqueness of solutions are major issues for load inversion problems. Traditional approaches are mostly based on an optimization framework where a smooth solution is uniquely determined using regularization techniques. However, these approaches require tuning of regularization factors that may be subjective and difficult to implement for pressure inversion on in-service underground structures. By contrast, the presented approach is based on a Bayesian framework. Instead of regularization techniques and corresponding tuning procedure, only physically plausible bounds are required for specifying constraints. The complete posterior distribution of feasible solutions is obtained based on Bayes' rules. By inferring the potential pressures with the complete posterior distribution, a natural regularization advantage can be shown. Specifically, this advantage is demonstrated in detail by a series of comparative tests: i) the Bayesian posterior mean exhibits an inherent quality to smooth out ill-conditioned features of inversion solutions; ii) satisfactory inference of the pressures can be made even in the presence of non-uniqueness. These properties are valuable when observed data is noisy or limited. A recorded field example is also presented to show effectiveness of this approach in practical engineering. Finally, deficiencies and potential extensions are discussed.
Original languageEnglish
JournalActa Geotechnica
Early online date10 Jul 2023
Publication statusE-pub ahead of print - 10 Jul 2023

Bibliographical note

Funding Information:
This study was supported by Natural Science Foundation of China (Grant No. 51978523). A.L. acknowledges support from Engineering and Physical Sciences Research Council under the CoSInES (EP/R034710/1). Z.T. acknowledges support from China Scholarship Council.

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


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