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Stochastic mechanics-based Bayesian method calibrating the constitutive parameters of the unified model for clay and sand with CPTU data

Compared with the Cam-Clay model, Clay and Sand Model (CASM) imported the state parameter, which can describe the complicated mechanical behaviors for clay and sand. However, key constitutive parameters ( i.e. , model parameters and geotechnical parameters) are difficult to be determined precisely d...

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Bibliographic Details
Published in:Acta geotechnica 2022-10, Vol.17 (10), p.4577-4598
Main Authors: Fu, Yanbin, Ma, Chengtao, Bian, Yuewei, Lv, Guiyang, Hu, Yu, Wang, Changhong
Format: Article
Language:English
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Summary:Compared with the Cam-Clay model, Clay and Sand Model (CASM) imported the state parameter, which can describe the complicated mechanical behaviors for clay and sand. However, key constitutive parameters ( i.e. , model parameters and geotechnical parameters) are difficult to be determined precisely due to the intrinsic variability and epistemic uncertainty of geomaterial. Based on the CASM and spherical cavity expansion theory, the working mechanism of Piezocone Penetration Test (CPTU) is derived. Key constitutive parameters, such as spacing ratio r ∗ , stress-state coefficient n ( i.e. , two model parameters), critical stress ratio M and overconsolidation ratio OCR ( i.e. , two geotechnical parameters), are calibrated by the stochastic mechanics-based Bayesian method. Firstly, the elastic–plastic theory of spherical cavity expansion based on CASM is analyzed, and the mechanical conversion between the limit stress of cavity expansion and CPTU resistances ( i.e. , cone tip resistance q t and pore water pressure u ) is explained. Secondly, an accelerated sampling algorithm of Markov chain Monte Carlo (MCMC) method is adopted in the Bayesian algorithm. Rationality of the CASM is verified by comparing the numerical results between the CASM and the Modified Cam Clay (MCC) model. Finally, the in situ test data from Bothkennar site of UK are taken as the research objective, the constitutive parameters are calibrated by the above approach, and the accuracies of posterior distributions are evaluated. Coefficient of Variation (COV) of the spacing ratio r ∗ , stress-state coefficient n , critical stress ratio M and overconsolidation ratio OCR are 0.109, 0.368, 0.009 and 0.033, respectively, and statistical correlations exist among the key constitutive parameters. The predicted values of CPTU resistances based on the posterior distribution are closer to the measurements than the prior reconnaissance data, which can verify the effectiveness of the stochastic mechanics-based Bayesian method. And the strength and state parameters which analyzed by predictions of CPTU are consistent with the measured values, which further verify the validity of the method and the reliability of the CPTU predictions. In the engineering perspective, mechanism and statistics between the constitutive parameters of CASM and CPTU resistances are revealed, which put forward a new idea for the parametric calibration according to the in situ investigation.
ISSN:1861-1125
1861-1133
DOI:10.1007/s11440-022-01524-6