Joint Posterior Estimation of Overconsolidation Ratio and Rigidity Index from Co-Located CPTu-DMT Soundings
DOI:
https://doi.org/10.66238/fsrma123Keywords:
Bayesian Inference, Overconsolidation Ratio, Rigidity Index, Site CharacterizationAbstract
The accurate characterization of subsurface soil properties is a fundamental prerequisite for the safe and economical design of geotechnical structures. Among the various state parameters, the overconsolidation ratio and the rigidity index are particularly critical, as they govern the stress history, compressibility, and undrained shear strength of fine-grained soils. Traditional deterministic approaches typically rely on empirical transformation models applied independently to different in-situ tests, which fails to account for inherent geological variability, measurement errors, and transformation uncertainties. This paper presents a comprehensive methodological framework for the joint posterior estimation of the overconsolidation ratio and rigidity index by integrating data from co-located Cone Penetration Tests with pore pressure measurement and Flat Dilatometer Tests. By employing a rigorous Bayesian inference approach, the proposed framework fuses the complementary mechanistic sensitivities of the two sounding methods into a unified probabilistic structure. The methodology relies on Markov Chain Monte Carlo sampling techniques to derive the joint posterior probability distributions, completely characterizing the parameter uncertainties and their cross-correlations. The application of this framework to a well-characterized clay deposit demonstrates that the joint assimilation of co-located sounding data significantly reduces the statistical dispersion of the estimated parameters compared to prior estimates or single-source interpretations. The results underscore the necessity of adopting multiparameter, multi-tool probabilistic methods to achieve more reliable and resilient geotechnical site characterizations.
References
1. Malik, B. A., Jie, S., Zeyu, L., Ouyang, Z., & Wang, D. (2025). Experimental investigation of suction installation behavior of caissons in loose saturated sands. Canadian Geotechnical Journal, 62, 1-21.
2. Ouyang, Z., & Mayne, P. W. (2024). Evaluating friction angles for clays: piezocone tests compared with Atterberg limits. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, 177(2), 147-157.
3. López-Acosta, N. P. (2019, November). Evaluating rigidity index, OCR, and su from dilatometer data in soft to firm clays. In Geotechnical Engineering in the XXI Century: Lessons learned and future challenges: Proceedings of the XVI Pan-American Conference on Soil Mechanics and Geotechnical Engineering (XVI PCSMGE), 17-20 November 2019, Cancun, Mexico (p. 286). IOS Press.
4. Shi, J., Malik, B. A., Liang, Z., Jing, L., Lu, Y., Gao, F., & Ouyang, Z. (2026). Installation effects on the performance of hybrid suction caissons in sand. Ocean Engineering, 359, 126025.
5. Li, Y. Z., Zhang, J. P., Chen, Z. Y., Wang, H. C., Zhang, K. X., Hu, S. S., ... & Dudley, M. (2026, September). Growth and Characterization of High-Quality Thick Epitaxial 4H-SiC Wafers for High Voltage Devices. In Defect and Diffusion Forum (Vol. 452, pp. 79-85). Trans Tech Publications Ltd.
6. Li, X., Wang, P., Li, G., & Zhang, Y. (2023). Design of a novel self-test-on-chip interface ASIC for capacitive accelerometers. IEEE Transactions on Circuits and Systems I: Regular Papers, 70(7), 2834-2843.
7. Xiong, S., Chen, T., Rupendra, A., Clement, C., Gasparri, E., & Lucchi, E. (2026). Embodied Carbon of Progressive Timber Integration in a 47-Storey Tropical High-Rise: A Singapore Public Housing Case Study. Building and Environment, 114910.
8. Yu, A., Huang, Y., Li, S., Wang, Z., & Xia, L. (2023). All fiber optic current sensor based on phase-shift fiber loop ringdown structure. Optics Letters, 48(11), 2925-2928.
9. Zhang, S., & Yan, W. (2025). In-trainNet: A Two-Step Data-Driven Framework for Enhancing Railway In-Train Forces Monitoring. Advanced Engineering Informatics, 65, 103352.
10. Luan, S., Tang, M., Mu, H., Yu, J., Wang, P., & Zhang, L. (2025). A co-precipitation route to produce BaTiO3 nanopowders with high tetragonality for ultra-thin MLCCs application. Journal of Materials Science: Materials in Electronics, 36 (9), 526.
11. Luan, S., Wang, P., Zhang, J., Yu, J., Fu, Z., Cao, X.,... & Sun, R. (2026). Hydrothermal preparation of highly tetragonal BaTiO3 nanopowders for ultra-thin multilayer ceramic capacitors. Journal of Advanced Dielectrics, 16 (01), 2550029.
12. Zhao, R., Zeng, W., Tang, J., Li, Y., Ye, G., Du, J., & Zhao, X. (2025, May). Towards unsupervised entity alignment for highly heterogeneous knowledge graphs. In 2025 IEEE 41St international conference on data engineering (ICDE) (pp. 3792-3806). IEEE.
13. Zhao, R., Xu, D., Jian, S., Tan, T., Sun, X., & Zhang, W. (2023, July). Quadratic Exponential Decrease Roll-Back: An Efficient Gradient Update Mechanism in Proximal Policy Optimization. In 2023 2nd International Conference on Machine Learning, Cloud Computing and Intelligent Mining (MLCCIM) (pp. 65-70). IEEE.
14. Li, Q., Ye, Q., Zhang, N., Zhang, W., & Hu, F. (2025). Digital-twin-enabled industrial IoT: Vision, framework, and future directions. IEEE Wireless Communications, 32(6), 173-181.
15. Wang, S., Zhang, X., Wang, P., & Li, X. (2026). Design of Magnetic Sensor Array-Based PUFs for IoT Security. IEEE Transactions on Instrumentation and Measurement, 75, 1-9.
16. Liang, R., Xu, S., Xie, C., Chen, J., Ren, F., Yang, S., & Yabe, T. (2026). Abstain Mask Retain Core: Time Series Prediction by Adaptive Masking Loss with Representation Consistency. Advances in Neural Information Processing Systems, 38, 99445-99471.
17. Zhao, J., Zhang, C., Qin, M., & Yang, P. (2025). QuantFactor REINFORCE: mining steady formulaic alpha factors with variance-bounded REINFORCE. IEEE Transactions on Signal Processing, 73, 2448-2463.
18. Yang, Z., Liang, B., & Ji, W. (2021). An intelligent end–edge–cloud architecture for visual IoT-assisted healthcare systems. IEEE internet of things journal, 8(23), 16779-16786.
19. Peng, Y., & Li, H. (2023). Benthic foraminiferal morphogroups at the end-Guadalupian extinction in eastern Sichuan Basin, China. Palaeogeography, Palaeoclimatology, Palaeoecology, 618, 111522.
20. Kim, E. H., Huang, H., Wang, Z., Duan, H., Fu, Z., & Pedrycz, W. (2026). Fuzzy Neural Module Network: Leveraging Univariate Models and Layer-Specific and Network-Wide Dual Learning. IEEE Transactions on Cybernetics.
21. Xu, Yuanchao, et al. "Reskoopnet: Learning koopman representations for complex dynamics with spectral residuals." arXiv preprint arXiv:2501.00701 (2025).
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