Probabilistic Back Analysis Research Articles

Probabilistic back analysis of reservoir landslide considering hydro-mechanical coupled observations

Precisely assessing statistical parameters to characterize spatial soil variability presents a significant challenge in probabilistic slope stability analysis, primarily due to inherent soil uncertainties and limited field-specific data. Probabilistic back analysis, recognized as an effective and reliable technique, offers a rational method for utilizing observational data to invert parameters. Nevertheless, previous investigations into parameter inversion for slope stability analysis have seldom considered the coupling of hydro-mechanical characteristics in reservoir landslides. This study proposes a novel integrated Bayesian framework to perform back analysis of reservoir landslides, incorporating the spatial variability of hydro-mechanical parameters. Within this framework, a hypoplastic constitutive model is developed to characterize the step-like deformation of the reservoir slope. The posterior knowledge of the saturated permeability coefficient and shear strength parameters is obtained by collecting field monitoring data of the underground water level and ground displacement. The Maliulin landslide, located in the Three Gorges Reservoir area of China, is used as an illustrative example to validate the proposed framework through back analysis of spatially variable soil parameters and probabilistic stability analysis. The results demonstrate that the proposed Bayesian updating framework significantly reduces the uncertainties associated with statistical values of soil parameters, providing more accurate and reasonable updated soil parameters for probabilistic slope stability analysis.

Improved Bayesian model updating of geomaterial parameters for slope reliability assessment considering spatial variability

In engineering practice, Bayesian model updating using field data is often conducted to reduce the substantial inherent epistemic uncertainties in geomaterial properties resulting from complex geological processes. The Bayesian Updating with Subset simulation (BUS) method is commonly employed for this purpose. However, the wealth of field data available for engineers to interpret can lead to challenges associated with the “curse of dimensionality”. Specifically, the value of the likelihood function in the BUS method can become extremely small as the volume of field data increases, potentially falling below the accuracy threshold of computer floating-point operations. This undermines both the computational efficiency and accuracy of Bayesian model updating. To effectively address this technical challenge, this paper proposes an improved BUS method developed based on parallel system reliability analysis. Leveraging the Cholesky decomposition-based midpoint method, the total failure domain in the original BUS method, which involves a low acceptance rate, is subdivided into several sub-failure domains with a high acceptance rate. Facilitated with an improved Metropolis-Hastings algorithm, the improved BUS method enables the consideration of a large volume of field data and spatial variability of geomaterial properties in the probabilistic back analysis. The results of an illustrative soil slope, involving spatially variable undrained shear strength, demonstrate that the improved BUS method is effective in simultaneously incorporating a substantial volume of field measurements and observations in the model updating process. Through a comparison with the original BUS method, the improved BUS method is shown to be useful for Bayesian model updating of high-dimensional spatially variable geomaterial properties and slope reliability assessment.

Probabilistic Back Analysis Based on Nadam, Bayesian, and Matrix-Variate Deep Gaussian Process for Rock Tunnels

Probabilistic Back Analysis Based on Nadam, Bayesian, and Matrix-Variate Deep Gaussian Process for Rock Tunnels

Probabilistic back analysis of rock strength parameters in heavily jointed rock slopes based on Bayesian inference

Probabilistic back analysis of rock strength parameters in heavily jointed rock slopes based on Bayesian inference

Probabilistic back-analysis of rainfall-induced landslides for slope reliability prediction with multi-source information

Probabilistic back-analysis is an important means to infer the statistics of uncertain soil parameters, making the slope reliability assessment closer to the engineering reality. However, multi-source information (including test data, monitored data, field observation and slope survival records) is rarely used in current probabilistic back-analysis. Conducting the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction under rainfalls by integrating multi-source information is a challenging task since thousands of random variables and high-dimensional likelihood function are usually involved. In this paper, a framework by integrating a modified Bayesian Updating with Subset simulation (mBUS) method with adaptive Conditional Sampling (aCS) algorithm is established for the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction. Within this framework, the high-dimensional probabilistic back-analysis problem can be easily tackled, and the multi-source information (e.g. monitored pressure heads and slope survival records) can be fully used in the back-analysis. A real Taoyuan landslide case in Taiwan, China is investigated to illustrate the effectiveness and performance of the established framework. The findings show that the posterior knowledge of soil parameters obtained from the established framework is in good agreement with the field observations. Furthermore, the updated knowledge of soil parameters can be utilized to reliably predict the occurrence probability of a landslide caused by the heavy rainfall event on September 12, 2004 or forecast the potential landslides under future rainfalls in the Fuhsing District of Taoyuan City, Taiwan, China.

Probabilistic back analysis of slope parameters and reliability evaluation using improved Bayesian updating method

Probabilistic back analysis of slope parameters and reliability evaluation using improved Bayesian updating method

Back analysis of cohesion and friction angle of failed slopes using probabilistic approach: two case studies

In general, geotechnical investigations deal with the back analysis of the geotechnical parameters on the basis of the field observation. According to the back analysis method introduced in the present study, geometry of a number of failed slopes have been carefully mapped and then statistical features of the groundwater level, the bulk unit weight and other measurable parameters have been determined. After that, a series of two-dimensional models for back analysis of the failures have been established. Moreover, statistical analyses based on probabilistic approaches have been utilized to estimate the variation ranges of the shear strength variables. The study provided the probabilistic back analysis of the slope failure with the two case studies in the copper mines of Anjerd and Daraloo. Results indicated that the approach to the probabilistic back analysis has been effective in the analysis of the slope failures wherein considerable uncertainty has been observed in the shear strength and other influential variables. Furthermore, the probabilistic back analysis presented a lot of information in comparison to the approach to the deterministic back analysis and thus had more reasonable matching with the practice of geotechnical engineering in the real world. Therefore, this method would be beneficial and practical for stability analysis, redesigning the slopes, designing the new slopes under the same geotechnical conditions and promote the construction safety. The probabilistic back analysis could be also used to estimate the shear parameters and analyze the stability of slopes as a cost-effective and high reliability method.

Probabilistic Back Analysis Based on Adam, Bayesian and Multi-output Gaussian Process for Deep Soft-Rock Tunnel

Probabilistic Back Analysis Based on Adam, Bayesian and Multi-output Gaussian Process for Deep Soft-Rock Tunnel

Estimation of Uncertainties in Soil Using MCMC Simulation and Effect of Model Uncertainty

The simulation of field conditions for seismically induced slope failures incorporates model uncertainties, which account for the difference between simulated and observed slope behaviour. The quantification of this uncertainty is mandatory to understand the field response of the geotechnical system and make decisions for geotechnical systems. Previous studies have partially studied uncertainty for slope systems under seismic loading. To this aim, this study proposes a methodology based on probabilistic back analysis to estimate uncertainties in soil parameters considering the observed slope response under seismic loading. The proposed method involves support vector regression (SVR) model to map the relationship between soil parameters and seismically induced slope displacement. The SVR model is generated using the data from the numerical simulation of slope system under seismic loading using FLAC 2D. Further, the developed SVR model is used for probabilistic back analysis using Markov Chain Monte Carlo (MCMC) simulation. The Noto Hanto earthquake in 2007 and the subsequent slope failure along Noto Yuryo Road, Japan, are considered as a case study to validate the proposed methodology. The results of the case study show that the updated or inferred soil parameters have less variability than the prior distribution. Further, the uncertainties in the slope system influence the inferred soil parameters. Hence, a parametric study is conducted to investigate the effect of model uncertainty on the posterior statistics of soil parameters. The study results facilitate a better understanding of the slope deformation mechanism and the effect of model uncertainty on the updated statistics of soil parameters.

Probabilistic back analysis of rainfall-induced slope failure considering slope survival records from past rainfall events

Many rainfall-induced landslides occur on slopes that have limited, or even no, site investigation data before failure. Probabilistic back analysis of slope failure provides an effective tool to back analyze possible pre-failure soil parameters, thus gaining insights into the mechanism of slope failure. For a slope failure induced by rainfall, the actual factor of safety (FS) is time-variant when time-variant rainfall and infiltration are explicitly modeled. This study proposes a novel probabilistic back analysis method that models explicitly the rainfall triggering mechanism for a rainfall-induced slope failure. Unlike existing methods that are based on a constant FS = 1, the proposed method utilizes FS inequality information for probabilistic back analysis, including slope failure record with FS < 1 and slope survival records from past rainfall events with FS > 1. The proposed method is suitable for high-dimensional problems when soil hydraulic properties are also back analyzed. The proposed method converges to the conventional methods with FS = 1 when the time span of slope failure is narrowed down to a few hours and slope survival records are ignored. Incorporating both slope failure and survival records effectively reduces uncertainties in soil strength and hydraulic parameters.

Development and application of a novel probabilistic back-analysis framework for geotechnical parameters in shield tunneling based on the surrogate model and Bayesian theory

Development and application of a novel probabilistic back-analysis framework for geotechnical parameters in shield tunneling based on the surrogate model and Bayesian theory

Multi-objective probabilistic back analysis for selecting the optimal updating strategy based on multi-source observations

Accurate prediction of geotechnical performance is essential to safety control and risk mitigation in an uncertain environment. In situ observation could be incorporated into the Bayesian inference to improve the reliability of prediction for a rational treatment of various geotechnical-related uncertainties. However, due to technical limitations and cost-efficiency, previous studies generally adopted one or two types of observations in Bayesian updating and focused only on the prediction fidelity. Thus, a fixed updating strategy is usually prescribed according to the engineer’s experience, which may lead to the unreliability of prediction. This paper proposes a novel multi-objective probabilistic back analysis approach for determining the optimal updating strategy, based on multi-source observations, to improve the reliability of subsequent predictions. The features of this approach include three aspects: (1) more than two types of observations are incorporated into the Bayesian updating, (2) prediction fidelity and prediction variability are both considered for determining the optimal strategy, and (3) multi-objective optimization results in a set of non-dominated optimal strategies in the pool of candidate updating strategies. A diaphragm wall-supported excavation in clay is analyzed to demonstrate the effectiveness of the proposed approach.

Probabilistic back analysis for rainfall-induced slope failure using MLS-SVR and Bayesian analysis

ABSTRACT Measurement and model uncertainties in soil parameters account for the difference between slope behaviour in the field and expected behaviour. The probabilistic back analysis is an effective approach to quantify these uncertainties in soil parameters. A new methodology for probabilistic back analysis is proposed to evaluate the uncertainties in soil parameters for observed data for slope. The proposed methodology implements multi-output least square support vector regression (MLS-SVR) to replicate the numerical model for slope under precipitation. This methodology also utilises a multi-objective genetic algorithm and Bayesian analysis to estimate updated statistics of soil parameters for observed data for slope. The rainfall-induced slope failure at Malin, Pune, India, in 2014 is used as a case study to validate the proposed methodology. The mean values of soil parameters are updated using multi-objective genetic algorithm for the expected values of safety factor. The uncertainties in soil parameters are estimated using Bayesian analysis. The updated statistics of input parameters suggest that matric suction governs the slope behaviour under rainfall precipitation. The results of the study suggest that continuous updating of the observations reduces the uncertainties involved in soil parameters. It is noted that the values of safety factor calculated using updated parameters are consistent with the slope failure observed in the field. Hence, results of the study can be used for the reliability-based design of slopes and the provision of remedial measures.

Efficient probabilistic back analysis of spatially varying soil parameters based on monitored displacements

Efficient probabilistic back analysis of spatially varying soil parameters based on monitored displacements

Glacial burst triggered by triangular wedge collapse: a study from Trisul Mountain near Ronti glacier valley

Himalayan mountain ranges separate the Tibetan plateau from the Indian subcontinent, where challenging topography, ongoing orogeny, and weather conditions are significant factors behind mass movements. The detachment of a composite rock-ice mass occurred on 7-Feb-2021 over the north-eastern slope of the Trisul mountain resulting in devastation along the Rishiganga-Dhauliganga valley, Uttarakhand. In this study, an attempt is made to understand the failure mechanism of the overhang wedge, where prolonged glacial mobility is seen as a possible factor behind the formation of such a structure. The temporal movement (2020–2021; annual & seasonal) of metamorphosed ice is assessed using sub-pixel offset tracking of Sentinel-1A-GRD data. Kinematic analysis checks failure susceptibility due to joint sets within the rockmass. Slope stability analysis is performed using probabilistic back analysis for three values of coefficient of variation (CoV), i.e., 10%, 15%, and 20% considering cohesion (c) and angle of internal friction (ϕ) as random variables. The detachment impact is quantified using rockfall simulation and parameters such as maximum bounce height, total kinetic energy, and translational velocity. Finally, probabilistic analysis of parameters is performed that may be useful in developing a mitigation system.

Bayesian selection of slope hydraulic model and identification of model parameters using monitoring data and subset simulation

Accurate prediction of pore water pressure responses in soils is critical for predicting stability of a slope when subjected to rainstorms. Slope hydraulic model and soil hydraulic parameters have been widely used in prediction of pore water pressure responses under rainfall infiltration, but establishing a suitable slope hydraulic model and accurately identifying its parameters for a specific slope are often challenging due to a lack of knowledge and site investigation data on the slope, particularly the subsurface conditions. In-situ monitoring data (e.g., time series of pore water pressure under rainfall infiltration) from a slope provide valuable information about subsurface conditions of the slope. This study proposes a probabilistic back analysis method, using Bayesian updating with subset simulation (BUSS) and slope monitoring data, to determine the most suitable slope hydraulic model from a group of candidate models with different settings (i.e., governing equations, boundary conditions, and initial conditions). The most probable soil hydraulic parameters (e.g., spatially variable soil properties used in the slope hydraulic model) are identified simultaneously in the proposed method. The most suitable slope hydraulic model significantly improves quantification of uncertainties in soil hydraulic parameters and prediction of pore water pressure responses in slopes during rainfalls.

Probabilistic back analysis for improved reliability of geotechnical predictions considering parameters uncertainty, model bias, and observation error

The predicted performance of a geotechnical system may deviate from the in situ observation due to the uncertainties in the input geotechnical parameters, solution model, and observation error. A precise characterization of these uncertainties is a significant challenge primarily because of limited data availability. The Bayesian theory provides a means for updating these uncertainties by incorporating prior statistical information and observations. However, conventional Bayesian inference focuses on limited sources of uncertainties. This paper presents a probabilistic back analysis method for improved reliability of subsequent predictions that considers all the uncertainties. Three distinct features of this new method include: (1) multiple observations are incorporated into the Bayesian updating, (2) the statistical information of the uncertain variables is updated in a stage-by-stage manner, and (3) the posterior distributions of uncertain variables are derived with Markov Chain Monte Carlo (MCMC) simulation that is based on the Hamiltonian Monte Carlo (HMC) algorithm. Two case histories, including a braced excavation problem and a tunnel excavation problem, are analyzed to demonstrate the effectiveness of the new method. The advantages of this new back analysis method over the conventional Bayesian updating analyses are documented.

From probabilistic back analyses to probabilistic run-out predictions of landslides: A case study of Heifangtai terrace, Gansu Province, China

The input parameters of dynamic numerical models for landslide run-out distance simulations cannot be measured accurately, which results in significant uncertainties in the predictions obtained using these models. To address this issue, a novel framework combining probabilistic back analyses and probabilistic predictions of landslide run-out distance is developed in this study, with the aim of ensuring the reliability of run-out predictions in risk assessments. First, a probabilistic back analysis method is applied to calibrate the input parameters and quantify their uncertainties; the calibrated parameters are then used for a probabilistic forward run-out prediction. Unlike the trial and error calibration approach, the back analysis method is implemented probabilistically by modeling the input parameters as random variables and efficiently improving their distributions through Markov chain Monte Carlo-based Bayesian inference using the observed run-out distance of a previous landslide event. These improved posterior distributions are employed to obtain the run-out distance exceedance probability curve of a potential landslide similar to the previous event; this curve can be used to estimate the probability of the run-out distance being exceeded at different locations along the landslide's path. By selecting different threshold values for the exceedance probabilities, a landslide hazard zoning map can be generated, serving as a valuable tool for landslide risk assessment and management. Moreover, a Kriging-based surrogate model is used to approximate the dynamic numerical model employed in this study, which significantly improves the computational efficiency of the proposed methodology. Finally, two sequential landslides that have occurred in the Heifangtai terrace of Gansu Province, China, are considered as a case study to demonstrate the performance of the proposed methodology.

Bayesian back analysis of landslides considering slip surface uncertainty

Previous studies about probabilistic back analysis for shear strength parameters of landslides generally adopted a fixed slip surface. This setting may lead to unreliable results due to the uncertainty of slip surface location speculated by limited observations. Based on Bayes’ theorem, this paper proposes a probabilistic framework for the back analysis of landslides considering slip surface uncertainty. The posterior distributions of shear strength parameters in Bayesian inference are solved by Markov chain Monte Carlo simulation method. To improve computational efficiency, a response surface function based on extreme learning machine is constructed to approximate the relationship between shear strength parameters and the corresponding factor of safety and critical slip surface. A synthetic slope, for which the actual shear strength parameters and slip surface are known, is used to compare the proposed and traditional methods. The effects of measurement error of slip surface and prior distribution of shear strength parameters on probabilistic back analysis results are also investigated. Results show that the shear strength parameters obtained from traditional probabilistic back analyses neglecting slip surface uncertainty significantly deviate from actual values, and are greatly affected by prior mean of shear strength parameters. The proposed method performs better than traditional method and is less affected by the prior distributions of shear strength parameters, and the smaller the measurement error of slip surface, the higher the Bayesian back analysis accuracy. A practical landslide is applied to further verify the effectiveness of the proposed method.

Efficient probabilistic back analysis of spatially varying soil parameters for slope reliability assessment

The probability distributions of soil parameters can be updated with limited site-specific information via probabilistic back analyses. The updated probability distributions can be further used for a more realistic slope reliability assessment. However, few attempts have been made to conduct probabilistic back analyses accounting for the inherent spatial variability of soil properties. The main challenge is the so-called curse of dimensionality encountered when thousands of random variables are used to model spatial variability. The BUS approach (Bayesian Updating with Structural reliability methods) can tackle the high-dimensional back analysis problem by transforming it into an equivalent structural reliability problem, but it requires an evaluation of the likelihood multiplier that is tedious and time-consuming. This paper proposes a modified BUS approach for the probabilistic back analysis of soil parameters and reliability updating of slopes in spatially variable soils. With this approach, the curse of dimensionality and evaluation of the likelihood multiplier can be effectively avoided, and the computational accuracy is significantly improved. Two slope examples are investigated to illustrate the effectiveness of the proposed approach. The soil parameters and their probability distributions for a slope section can be well determined through a probabilistic back analysis, which facilitates an accurate identification of the causes of slope failures and a deep understanding of the actual performance of in-service slopes.