Probabilistic Back Analysis Research Articles

Bayesian Approach for Sequential Probabilistic Back Analysis of Uncertain Geomechanical Parameters and Reliability Updating of Tunneling‐Induced Ground Settlements

This paper proposes a new sequential probabilistic back analysis approach for probabilistically determining the uncertain geomechanical parameters of shield tunnels by using time‐series monitoring data. The approach is proposed based on the recently developed Bayesian updating with subset simulation. Within the framework of the proposed approach, a complex Bayesian back analysis problem is transformed into an equivalent structural reliability problem based on subset simulation. Hermite polynomial chaos expansion‐based surrogate models are constructed to improve the computational efficiency of probabilistic back analysis. The reliability of tunneling‐induced ground settlements is updated in the process of sequential back analyses. A real shield tunnel project of No. 1 Nanchang Metro Line in China is investigated to assess the effectiveness of the approach. The proposed approach is able to infer the posterior distributions of uncertain geomechanical parameters (i.e., Young’s moduli of surrounding soil layers and ground vehicle load). The reliability of tunneling‐induced ground settlements can be updated in a real‐time manner by fully utilizing the time‐series monitoring data. The results show good agreement with the variation trend of field monitoring data of ground settlement and the post‐event investigations.

Unsaturated soil slope characterization with Karhunen–Loève and polynomial chaos via Bayesian approach

Field measured data reflect real response of soil slopes under rainfall infiltration and can provide representative estimates of in situ soil properties. In this study, an efficient probabilistic back analysis method for characterization of spatial variability of soil properties is used to investigate the effects of field responses with various monitoring schemes on characterization of spatial variability in unsaturated soil slope. A hypothetical heterogeneous slope of spatially varied saturated hydraulic conductivity subjecting to steady-state rainfall infiltration is analyzed as a numerical example. The spatially varied soil saturated hydraulic conductivity is parameterized by the Karhunen–Loeve expansion (KLE) with a given covariance. The random variables corresponding to the truncated KLE terms are considered as variables to be estimated with Bayesian inverse method. Synthetic pore water pressure data corrupted with artificial noise are utilized as measurement data. Nine schemes with various locations, spacings and depths of monitoring sections are discussed. The results show that the local variability can be reduced substantially around the monitoring points of pore pressure. The spatial variability can be estimated more accurately with a smaller spacing of measurement points. When measurement points are installed with a spacing of 16.5 m, the posterior average COV of ks field is around 2% and the RMSE of the MAP field is only 5.90 × 10− 7 m/s. For schemes with different depths, the RMSEs of the MAP field does not change much but the posterior uncertainty of the estimated field is reduced with the increase of borehole depth.

An efficient probabilistic back-analysis method for braced excavations using wall deflection data at multiple points

This paper presents an efficient Bayesian back-analysis procedure for braced excavations using wall deflection data at multiple points. Response surfaces obtained from finite element analyses are adopted to efficiently evaluate the wall responses. Deflection data for 49 wall sections from 11 case histories are collected to characterize the model error of the finite element method for evaluating the deflections at various points. A braced excavation project in Hang Zhou, China is chosen to illustrate the effectiveness of the proposed procedure. The results indicate that the soil parameters could be updated more significantly for the updating that uses the deflection data at multiple points than that only uses the maximum deflection data. The predicted deflections from the updated parameters agree fairly well with the field observations. The main significance of the proposed procedure is that it improves the updating efficiency of the soil parameters without adding monitoring effort compared with the traditional method that uses the maximum deflection data.

A Bayesian framework for updating model parameters while considering spatial variability

ABSTRACTThe study presents a recent slope failure in India which resulted in the burial of a village and claimed large number of lives. Current methods of probabilistic back analysis incorporate uncertainty in the analysis but do not consider spatial variability. In this study, back analysis is performed using Bayesian analysis in conjunction with random field theory. The probabilistic method is shown to be efficient in back-analysing a slope failure. It also provides confidence in parameter values to be used for post-failure slope design. The back analysis method which does not consider spatial variability overestimates the uncertainty in analysis, which can lead to uneconomical slope remediation design and measures.

Probabilistic back analysis of rainfall induced landslide‐ A case study of Malin landslide, India

On 30th July 2014, a devastating landslide resulted in the burial of a village called Malin in western India and led to about 160 deaths. The catastrophic failure was triggered by heavy rainfall over the last 3days. Site investigation was conducted to obtain representative information about the area. To understand the relevant physics, which initiated landslide, seepage and back analysis of the unsaturated slope was performed. Transient seepage analysis was carried out using finite difference method to simulate the slope behavior during rainfall infiltration. A coupled fluid flow analysis was employed to capture the fluid/mechanical interaction in unsaturated soils accurately. The results show that antecedent rainfall played a role in slope instability; rainfall intensity and duration also have a big impact on slope instability. This paper presents a methodology to back analyse the slope so as to identify the mechanisms responsible for landslide initiation. Back analysis is performed using a probabilistic method based on Bayesian analysis. Probabilistic methods can back-analyse numerous sets of uncertain slope stability parameters. The uncertain parameters are imported as random variables in the analysis and are described by their probability distributions. Bayesian analysis updates these distributions based on the observed slope behavior. The method evaluates the reduction in matric suction which initiated landslide in Malin slope. The results show that the decrease in matric suction of about 100% in addition to the development of positive pore pressures is the main mechanism which has triggered the landslide. This amount of reduction in matric suction and the development of positive pore pressures decreases the mobilized shear strength in soil below the threshold value required to maintain equilibrium in the slope and hence the slope failed.

Assessment of Slope Stability in the Monitoring Parameter Space

AbstractSlope monitoring is routinely conducted, and observational information such as surface/underground displacements, groundwater levels, and rock bolt forces at multiple locations is collected. How to make use of the monitoring information to reveal failure mechanisms and assess the slope stability is a key issue in slope engineering. This paper presents a method for assessing the slope stability by integrating monitoring parameters with physical analysis. The observed information first was used to back analyze the strength and loading parameters, and then the updated basic parameters were used to calculate the factor of safety or failure probability of the slope. The dominant basic parameters whose uncertainties influence the observed results the most were identified from the probabilistic back analysis. Alert levels were defined in the monitoring parameter space on the basis of a factor of safety or failure probability criterion. A rock slope example was worked out to illustrate the application of ...

Bayesian Updating Approach for Flexible Pavements Considering Fatigue and Rutting Failures

Abstract In this paper, an efficient approach for Bayesian updating of design parameters of flexible pavements is developed. Using Bayesian theorem, the updated design parameters are the integration of the prior knowledge and the observed information on the pavement failure. Two primary failure modes of flexible pavements, fatigue and rutting, are simulated using mechanistic–empirical approaches. The mechanistic–empirical models and the Bayesian framework are implemented in spreadsheets for the ease of engineering applications. The developed spreadsheet-based approach is demonstrated to be effective in the probabilistic back-analysis using the observed fatigue and rutting failures. This developed Bayesian updating approach is based on optimization method and, thus, it requires much less sophisticated modeling and much less computational effort. The updated design parameters as well as the associated variability will significantly contribute to the decision-making process of pavement maintenance and rehabilitation.

Probabilistic back analysis for geotechnical engineering based on Bayesian and support vector machine

Geomechanical parameters are complex and uncertain. In order to take this complexity and uncertainty into account, a probabilistic back-analysis method combining the Bayesian probability with the least squares support vector machine (LS-SVM) technique was proposed. The Bayesian probability was used to deal with the uncertainties in the geomechanical parameters, and an LS-SVM was utilized to establish the relationship between the displacement and the geomechanical parameters. The proposed approach was applied to the geomechanical parameter identification in a slope stability case study which was related to the permanent ship lock within the Three Gorges project in China. The results indicate that the proposed method presents the uncertainties in the geomechanical parameters reasonably well, and also improves the understanding that the monitored information is important in real projects.

Probabilistic back analysis based on Bayesian and multi-output support vector machine for a high cut rock slope

Uncertainty of geomechanical parameters is an important consideration for rock engineering and has a very important influence on safety evaluation, design, and construction. Back analysis is a common method of determining geomechanical parameters but traditional deterministic back analysis cannot allow for consideration of this uncertainty. In this study, a new probabilistic back analysis method is proposed that integrates Bayesian methods and a multi-output support vector machine (B–MSVM). In this B–MSVM back analysis method, Bayesian was used to deal with the uncertainty of geomechanical parameters and a multi-output support vector machine (MSVM) was adopted to build the relationships between displacements and those parameters. The proposed method was applied to a high abutment rock slope at the Longtan hydropower station, China. At Longtan, the uncertainty of the two types of geomechanical parameters, Young's modulus and lateral pressure coefficients of in situ stress, were modeled as random variables. Based on the parameters identified by probabilistic back analysis, the computed displacements agreed closely with the measured displacement data monitored in the field. The result showed that B–MSVM presented the uncertainty of the geomechanical parameters reasonably. Further study indicated that the performance of B–MSVM could be improved greatly by updating field monitoring information regularly. The proposed method provides a significant new approach for probabilistic back analysis and contributes to the determination of realistic geomechanical parameters.

Probabilistic Back Analysis of Landslides in Arakli-Tasonu Quarry, Northeast Turkey

This study evaluates the landslides that occurred on 3 October 2005, 20 March 2006, and 19 October 2006 in Tasonu Limestone Quarry, Trabzon, and Northeast Turkey. The failure plane of the three landslides occurred on the same clay layer. Back analyses using probabilistic technique were carried out in order to assess the failure mechanism, determine the range of shear strength mobilized in the failure plane, estimate the groundwater condition at the time of failure and evaluate the influence of blasting. The values of shear strength parameters c and ϕ obtained by direct shear tests were considered as prior information about the input parameters. It was determined that the results of the probabilistic back analysis could be exploited in evaluating the formation conditions of previous landslides and the potential for future landslides in that area.

Probabilistic back analysis of slope failure – A case study in Taiwan

In this paper, the authors present a probabilistic back-analysis of a recent slope failure at a site on Freeway No. 3 in northern Taiwan. Post-event investigations of this failure found uncertain strength parameters and deteriorating anchor systems as the most likely causes for failure. Field measurement after the event indicated an average slip surface of inclination 15°. To account for the uncertainties in input parameters, the probabilistic back analysis approach was adopted. First, the Markov Chain Monte Carlo (MCMC) simulation was used to back-calculate the geotechnical strength parameters and the anchor force. These inverse analysis results, which agreed closely with the findings of the post-event investigations, were then used to validate the maximum likelihood (ML) method, a computationally more efficient back-analysis approach. The improved knowledge of the geotechnical strength parameters and the anchor force gained through the probabilistic inverse analysis better elucidated the slope failure mechanism, which provides a basis for a more rational selection of remedial measures.

Probabilistic parameter estimation and predictive uncertainty based on field measurements for unsaturated soil slope

A key issue in assessment of rainfall-induced slope failure is a reliable evaluation of pore water pressure distribution and its variations during rainstorm, which in turn requires accurate estimation of soil hydraulic parameters. In this study, the uncertainties of soil hydraulic parameters and their effects on slope stability prediction are evaluated, within the Bayesian framework, using the field measured temporal pore-water pressure data. The probabilistic back analysis and parameter uncertainty estimation is conducted using the Markov Chain Monte Carlo simulation. A case study of a natural terrain site is presented to illustrate the proposed method. The 95% total uncertainty bounds for the calibration period are relatively narrow, indicating an overall good performance of the infiltration model for the calibration period. The posterior uncertainty bounds of slope safety factors are much narrower than the prior ones, implying that the reduction of uncertainty in soil hydraulic parameters significantly reduces the uncertainty of slope stability.

Methodology for Pavement Design Reliability and Back Analysis Using Markov Chain Monte Carlo Simulation

AbstractGiven the increasing cost of designing and building new highway pavements, reliability analysis has become vital to ensure that a given pavement performs as expected in the field. Recognizing the importance of failure analysis to safety, reliability, performance, and economy, back analysis has been employed in various engineering applications to evaluate the inherent uncertainties of the design and analysis. The probabilistic back analysis method formulated on Bayes’ theorem and solved using the Markov chain Monte Carlo simulation method with a Metropolis-Hastings algorithm has proved to be highly efficient to address this issue. It is also quite flexible and is applicable to any type of prior information. In this paper, this method has been used to back-analyze the parameters that influence the pavement life and to consider the uncertainty of the mechanistic-empirical pavement design model. The load-induced pavement structural responses (e.g., stresses, strains, and deflections) used to predict t...

Efficient Probabilistic Back-Analysis of Slope Stability Model Parameters

Back-analysis of slope failure is often performed to improve one's knowledge on parameters of a slope stability analysis model. In a failed slope, the slip surface may pass through several layers of soil. Therefore, several sets of model parameters need to be back-analyzed. To back-analyze multiple sets of slope stability parameters simultaneously under uncertainty, the back-analysis can be implemented in a probabilistic way, in which uncertain parameters are modeled as random variables, and their distributions are improved based on the observed slope failure information. In this paper, two methods are presented for probabilistic back-analysis of slope failure. For a general slope stability model, its uncertain parameters can be back-analyzed with an optimization procedure that can be implemented in a spreadsheet. When the slope stability model is approximately linear, its parameters can be back-analyzed with sensitivity analysis instead. A feature of these two methods is that they are easy to apply. Two case studies are used to illustrate the proposed methods. The case studies show that the degrees of improvement achieved by the back-analysis are different for different parameters, and that the parameter contributing most to the uncertainty in factor of safety is updated most.

An application of the rock engineering systems (RES) methodology in rockfall hazard assessment on the Chengdu-Lhasa Highway, China

In the evaluation of rock slope stability, there are many kinds of uncertainties including the input parameters uncertainty, the calculations uncertainty, and the procedure. Slope stability analysis can be classified into deterministic analysis or probabilistic analysis depending on how uncertainty is incorporated and evaluated. Probabilistic method takes into consideration the inherent variability and uncertainties in the analysis parameter. In this study, rock slope stability analysis, especially probability analyzes will be reviewed. In addition, probabilistic slope stability analysis and probabilistic back-analysis was applied to landslides which occurred at the Arakli-Tasonu quarry, NE Turkey, on October 3, 2005, March 20, 2006, and October 19, 2006. The sliding plane of the landslides passed through the thick clay layer. The tension cracks developed behind and are parallel to these landslides scarps. Considering these information, it is thought that the new failure can develop in these slopes. For this, no technical entry was allowed for this part of the quarry area. Therefore, the probabilistic stability analysis of these new slopes was performed. The values input parameters, shear strength parameters, and depth of the water in the tension crack used in these analyses are obtained by probabilistic back-analyses.