Probabilistic Inverse Analysis Of Geotechnical Parameters And Deformation Prediction Based On Bayesian Theory

With the rapid urbanization in China,the distribution of buildings and structures has become fairly dense in urban areas.More attention is needed to the geotechnical deformation and its impact on the surrounding environment.Accordingly,there is an increasing demand for more accurate deformation calculation methods.The traditional prediction methods directly use the soil parameters measured by field or laboratory tests,resulting in predictions that frequently deviate from monitoring data due to various geotechnical uncertainties,including the inherent variability of soil and the imperfection of the prediction model.The Bayesian method provides an effective way to reduce uncertainties and improve the accuracy of deformation prediction.It can incorporate the field monitoring data to achieve a rational and reasonable parameter estimation.Based on Bayesian theory,this study investigates and develops efficient probabilistic inverse analysis methods to make full use of the multiple observation data of geotechnical structures.The proposed methods can quickly update the soil properties and model parameters with quantified uncertainties,subsequently improving the accuracy of deformation prediction.The methods of assimilating the monitoring data are of great practical interest to risk management and construction safety.The main work and achievements of this paper are as follows:(1)A probabilistic inverse analysis method is proposed to infer the spatially varying parameter of soil by incorporating the deformation monitoring data into the random finite element method.Karhunen-Loève is used to simulate the random field and reduce the unknown dimension.The interface between the inverse analysis method and finite element software ABAQUS is established.Different unknown variables and observation spacings are used to study their effects on parameter estimation.The results show that the site-specific spatial variability can be estimated efficiently and reasonably.Reducing the number of variables to be inferred results in inferior estimations of the parameter field and is detrimental to identifying the local spatial variability,especially when unknown coefficients are selected directly according to the magnitude of KL eigenvalues.It is necessary to select important variables based on a sensitivity analysis.A reduction in the observation spacing is helpful to improve the accuracy of estimation.(2)An inverse analysis approach based on ensemble Kalman filtering(En KF)is proposed to evaluate the soil settlement with quantified uncertainty using time-varying observation data.The Sobol method is adopted to study the sensitivity of model parameters and to explain the inverse analysis results.Detailed parameter studies are conducted to study the influence of ensemble size,the value range of the initial ensemble and the observation error.The practical effectiveness of this approach is demonstrated through a realistic application of the Saga airport road embankment.The results show that this method can effectively improve the accuracy of settlement prediction by incorporating time-varying monitoring data.The reduction of uncertainty is more significant for parameters with higher sensitivity.The ensemble size has little effect on the inverse analysis results as it is within the typical range.The range of the initial ensemble has a significant impact in the early assimilation process but gradually decreases with the increase of observation data.The increase in observation error results in a wider prediction interval of settlement.(3)Using the MCMC-based Bayesian updating as a benchmark,the performance of En KF and En KF-MDA is comprehensively evaluated from the perspectives of data-matching quality,uncertainty quantification,and computational cost.A settlement prediction software is developed for a specific engineering project.The results show that En KF can reasonably estimate the mean value.However,when the observation data is not dense in time,the En KF tends to overcorrect the parameters due to its single linear update,resulting in an overestimation of the variance.En KF-MDA can lead to roughly the same mean and variance as MCMC but require considerably less computational cost.(4)Based on the equality and inequality between soil parameters,an ensemble Kalman filter method considering additional constraint information is proposed,named regularized ensemble Kalman filter with multiple data assimilation(REnKF-MDA).The proposed method is compared with the MCMC-based Bayesian method,MCMC-based Bayesian method with constraints,and REn KF.The results indicate that assimilating the additional constraint information is helpful to improve the rationality and confidence of the inferred parameters.The REnKF-MDA can accurately evaluate the mean and the uncertainty by recursing the likelihood conjugated with an inflated error in each update.(5)An efficient Bayesian approach for excavation responses is proposed to update the soil properties and the model bias factor based on observation data at multiple points.Bidirectional long short-term memory(BiLSTM)neural networks are constructed to act as a substitute for the finite-element method to achieve higher computational efficiency.To evaluate the depth-dependent characteristic of model uncertainty,the model factor is quantified by a constant part and a trending component.An excavation project in Taipei is used to illustrate the proposed approach.The results demonstrate that the accuracy of BiLSTM is higher than the traditional neural network commonly used in geotechnical problems,and their difference increases with the increase of the number of observation points.The trending component of the model factor can calibrate the underestimation of deflection at the shallow depth and the overestimation at the deeper depth in the early stages.The prediction of the subsequent responses can be significantly improved by using the updated soil parameters and model factors.