Estimation of failure probability in braced excavation using Bayesian networks with integrated model updating

A probabilistic model is proposed that uses observation data to estimate failure probabilities during excavations. The model integrates a Bayesian network and distanced-based Bayesian model updating. In the network, the movement of a retaining wall is selected as the indicator of failure, and the observed ground surface settlement is used to update the soil parameters. The responses of wall deflection and ground surface settlement are accurately predicted using finite element analysis. An artificial neural network is employed to construct the response surface relationship using the aforementioned input factors. The proposed model effectively estimates the uncertainty of influential factors. A case study of a braced excavation is presented to demonstrate the feasibility of the proposed approach. The update results facilitate accurate estimates according to the target value, from which the corresponding probabilities of failure are obtained. The proposed model enables failure probabilities to be determined with real-time result updating

PROBABILISTIC APPROACHES TO STABILITY AND DEFORMATION PROBLEMS IN BRACED EXCAVATION

This dissertation is aimed at applying probabilistic approaches to evaluating the basal-heave stability and the excavation-induced wall and ground movements for serviceability assessment of excavation in clays. The focuses herein are the influence of spatial variability of soil parameters and small sample size on the results of the probabilistic analysis, and Bayesian updating of soil parameters using field observations in braced excavations. Simplified approaches for reliability analysis of basal-heave in a braced excavation in clay considering the effect of spatial variability in random fields are presented. The proposed approaches employ the variance reduction technique (or more precisely, equivalent variance method) to consider the effect of spatial variability so that the analysis for the probability of basal-heave failure can be performed using well-established first-order reliability method (FORM). Case studies show that simplified approaches yield results that are nearly identical to those obtained from the conventional random field modeling (RFM). The proposed approaches are shown to be effective and efficient for the probabilistic analysis of basal-heave in a braced excavation considering spatial variability. The variance reduction technique is then used in the probabilistic serviceability assessment in a case study. To characterize the effect of uncertainty in sample statistics and its influence on the results of probabilistic analysis, a simple procedure involving bootstrapping is presented. The procedure is applied to assessing the probability of serviceability failure in a braced excavation. The analysis for the probability of failure, referred to herein as probability of exceeding a specified limiting deformation, necessitates an evaluation of the means and standard deviations of critical soil parameters. In geotechnical practice, these means and standard deviations are often estimated from a very limited data set, which can lead to uncertainty in the derived sample statistics. In this study, bootstrapping is used to characterize the uncertainty or variation of sample statistics and its effect on the failure probability. Through the bootstrapping analysis, the probability of exceedance can be presented as a confidence interval instead of a single, fixed probability. The information gained should enable the engineers to make a more rational assessment of the risk of serviceability failure in a braced excavation. The case study demonstrates the potential of bootstrap method in coping with the problem of having to evaluate failure probability with uncertain sample statistics. Finally, a Bayesian framework using field observations for back analysis and updating of soil parameters in a multi-stage braced excavation is developed. Because of the uncertainties in the initial estimates of soil parameters and in the analysis model and other factors such as construction quality, the updated soil parameters are presented in the form of posterior distributions. In this dissertation, these posterior distributions are derived using Markov chain Monte Carlo (MCMC) sampling method implemented with Metropolis-Hastings algorithm. In the proposed framework, Bayesian updating is first realized with one type of response observation (maximum wall deflection or maximum ground surface settlement), and then this Bayesian framework is extended to allow for simultaneous use of two types of response observations in the updating. The proposed framework is illustrated with a quality excavation case and shown effective regardless of the prior knowledge of soil parameters and type of response observations adopted. The probabilistic approaches presented in this dissertation, ranging from probability-based design of basal heave, to probabilistic analysis of serviceability failure in a braced excavation considering spatial variability of soil parameters, to bootstrapping for characterizing the uncertainty of sample statistics and its effect, and to MCMC-based Bayesian updating of soil parameters during the construction, illustrate the potential of probability/statistics as a tool for enabling more rational solutions in geotechnical fields. The case studies presented in this dissertation demonstrate the usefulness of these tools

Advanced Bayesian networks for reliability and risk analysis in geotechnical engineering

The stability and deformation problems of soil have been a research topic of great concern since the past decades. The potential catastrophic events are induced by various complex factors, such as uncertain geotechnical conditions, external environment, and anthropogenic influence, etc. To prevent the occurrence of disasters in geotechnical engineering, the main purpose of this study is to enhance the Bayesian networks (BNs) model for quantifying the uncertainty and predicting the risk level in solving the geotechnical problems. The advanced BNs model is effective for analyzing the geotechnical problems in the poor data environment. The advanced BNs approach proposed in this study is applied to solve the stability of soil slopes problem associated with the specific-site data. When probabilistic models for soil properties are adopted, enhanced BNs approach was adopted to cope with continuous input parameters. On the other hand, Credal networks (CNs), developed on the basis of BNs, are specially used for incomplete input information. In addition, the probabilities of slope failure are also investigated for different evidences. A discretization approach for the enhanced BNs is applied in the case of evidence entering into the continuous nodes. Two examples implemented are to demonstrate the feasibility and predictive effectiveness of the BNs model. The results indicate the enhanced BNs show a precisely low risk for the slope studied. Unlike the BNs, the results of CNs are presented with bounds. The comparison of three different input information reveals the more imprecision in input, the more uncertainty in output. Both of them can provide the useful disaster-induced information for decision-makers. According to the information updating in the models, the position of the water table shows a significant role in the slope failure, which is controlled by the drainage states. Also, it discusses how the different types of BNs contribute to assessing the reliability and risk of real slopes, and how new information could be introduced in the analysis. The proposed models in this study illustrate the advanced BN model is a good diagnosis tool for estimating the risk level of the slope failure. In a follow-up study, the BNs model is developed based on its potential capability for the information updating and importance measure. To reduce the influence of uncertainty, with the proposed BN model, the soil parameters are updated accurately during the excavation process, and besides, the contribution of epistemic uncertainty from geotechnical parameters to the potential disaster can be characterized based on the developed BN model. The results of this study indicate the BNs model is an effective and flexible tool for risk analysis and decision making support in geotechnical engineering

Performance Assessment of Masonry School Buildings to Seismic and Flood Hazards Using Bayesian Networks

Performance assessment of schools is an integral part of disaster risk reduction of communities from natural hazards such as earthquakes and floods. In regions of high exposure, these hazards may often act concurrently, whereby yearly flood events weaken masonry school buildings, rendering them more vulnerable to frequent earthquake shaking. This recurring damage, combined with other functional losses, ultimately result in disruption to education delivery, affecting vulnerable schoolchildren. This project examines behaviour of school buildings to seismic and flood loading, and associated disruption to education from a structural and functional perspective. The study is based on a case study of school buildings in Guwahati, India, where the majority of the buildings can be classified into confined masonry (CM) typology. This project presents three stages of analyses to study the performance of these CM school buildings and the system of schools, as summarised in the following. The first stage of the study involves refinement of the World Bank’s Global Library of School Infrastructure taxonomy to widen its scope and to fit the CM school typology. This leads to the identification of index buildings, which are single-story buildings with flexible diaphragms differing mainly in the level of seismic design. In the second stage, a novel numerical modelling platform based on Applied Element Method is used to analyse the index buildings for simplified lateral loads from both the aforementioned hazards. Seismic loading is applied in the form of ground acceleration, while flood loading is applied as hydrostatic pressure. Sequential scenarios are simulated by subjecting the building to varying flood depths followed by lateral ground acceleration, after accounting for the material degradation due to past flooding. Analytical fragility curves are derived for each case of analysis to quantify their physical performance, using a non-linear static procedure (N2 method) and least square error regression. The third stage of the study employs a Bayesian network (BN) based methodology to model the education disruption at the school system level, from exposure of schools to flood and seismic hazards. The methodology integrates the qualitative and quantitative nature of system variables, such as the physical fragility of school buildings (derived in the second stage), accessibility loss, change of use as shelters and socio-economic condition of the users-community. The performance of the education system impacted by the sequential hazards is quantified through the probability of the various states of disruption duration. The BN also explores the effectiveness of non-structural mitigating measures, such as the transfer of students between schools in the system. The framework proves to be a useful tool to assist decision-making, with regard to disaster preparedness and recovery, hence, contributing to the development of resilient education systems

Robust Geotechnical Design - Methodology and Applications

This dissertation is aimed at developing a novel robust geotechnical design methodology and demonstrating this methodology for the design of geotechnical systems. The goal of a robust design is to make the response of a system insensitive to, or robust against, the variation of uncertain geotechnical parameters (termed noise factors in the context of robust design) by carefully adjusting design parameters (those that can be controlled by the designer such as geometry of the design). Through an extensive investigation, a robust geotechnical design methodology that considers explicitly safety, robustness, and cost is developed. Various robustness measures are considered in this study, and the developed methodology is implemented with a multi-objective optimization scheme, in which safety is considered as a constraint and cost and robustness are treated as the objectives. Because the cost and the robustness are conflicting objectives, the robust design optimization does not yield a single best solution. Rather, a Pareto front is obtained, which is a collection of non-dominated optimal designs. The Pareto front reveals a trade-off relationship between cost and robustness, which enables the engineer to make an informed design decision according to a target level of cost or robustness. The significance and versatility of the new design methodology are illustrated with multiple geotechnical applications, including the design of drilled shafts, shallow foundations, and braced excavations

PROBABILISTIC BACK ANALYSIS OF GEOTECHNICAL SYSTEMS

This thesis is aimed at applying the probabilistic approaches for back analysis of geotechnical systems. First, a probabilistic back-analysis of a recent slope failure at a site on Freeway No. 3 in northern Taiwan is presented. The Markov Chain Monte Carlo (MCMC) simulation is used to back-calculate the geotechnical strength parameters and the anchor force. These inverse analysis results, which agree closely with the findings of the post-event investigations, are then used to validate the maximum likelihood 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 elucidate the slope failure mechanism, which provides a basis for a more rational selection of remedial measures. Then the maximum likelihood principle is adapted to formulate an efficient framework for probabilistic back analysis of soil parameters in a braced excavation using multi-stage observations. The soil parameters are updated using the observations of the maximum ground settlement and/or wall deflection measured in a staged excavation. The updated soil parameters are then used to refine the predicted wall and ground responses in the subsequent excavation stages, as well as to assess the building damage potential at the final excavation stage. Case study shows that the proposed approach is effective in improving the predictions of the excavation-induced wall and ground responses. More-accurate predictions of the wall and ground responses, in turn, lead to a more accurate assessment of the damage potential of buildings adjacent to the excavation

FRAMEWORK FOR THE FULLY PROBABILISTIC ANALYSIS OF EXCAVATION-INDUCED SERVICEABILITY DAMAGE TO BUILDINGS IN SOFT CLAYS

In this dissertation, a framework for a fully-probabilistic analysis of the potential for building serviceability damage induced by an excavation in soft clays is established. This analysis framework is established based on the concept of a serviceability limit state where the resistance is represented by the capacity of a building to resist serviceability damage, and the loading is represented by the demand on a building due to excavation-induced ground movements. In this study, both the resistance and the loading are treated as a random variable; the resistance is characterized empirically based on a database of the observed building performance while the loading is estimated for a specific case using semi-empirical models that were created with the results of finite element analysis and field observations. A simplified procedure is developed for estimating the loading on a building induced by an excavation. In this simplified procedure, the loading is expressed in terms of damage potential index (DPI) that is based on the concept of principal strain. On the other hand, the resistance as a random variable is characterized based on observed building performance, also in terms of the DPI. The uncertainties of both the resistance and the loading are fully characterized in this dissertation study to enable a fully probabilistic analysis. The developed framework for the fully-probabilistic assessment of the potential for excavation-induced building damage is demonstrated with the well-known TNEC case history. Finally, since the observational method is commonly applied to the design and construction of excavation systems, a simplified scheme for updating the soil parameters (and consequently DPI) based on the observations of the maximum wall deflection and ground settlement is developed. This updating scheme is demonstrated with an excavation case history and shown to be an effective technique for monitoring the damage potential of buildings adjacent to an excavation. The developed framework allows for fully-probabilistic assessment of the potential of building damage induced by an excavation, and thusly, provides engineers with a more transparent assessment of the risk associated with a particular excavation design and construction. Furthermore, with the observational method, the potential for excavation-induced serviceability damage can be reassessed as the excavation proceeds. With this approach, the excavation system can be monitored as the excavation proceeds and necessary measures can be taken to prevent damage to buildings adjacent to the excavation

Adaptive Reliability Analysis of Excavation Problems

Excavation activities like open cutting and tunneling work may cause ground movements. Many of these activities are performed in urban areas where many structures and facilities already exist. These activities are close enough to affect adjacent structures. It is therefore important to understand how the ground movements due to excavations influence nearby structures. The goal of the proposed research is to investigate and develop analytical methods for addressing uncertainty during observation-based, adaptive design of deep excavation and tunneling projects. Computational procedures based on a Bayesian probabilistic framework are developed for comparative analysis between observed and predicted soil and structure response during construction phases. This analysis couples the adaptive design capabilities of the observational method with updated reliability indices, to be used in risk-based design decisions. A probabilistic framework is developed to predict three-dimensional deformation profiles due to supported excavations using a semi-empirical approach. The key advantage of this approach for practicing engineers is that an already common semi-empirical chart can be used together with a few additional simple calculations to better evaluate three-dimensional displacement profiles. A reliability analysis framework is also developed to assess the fragility of excavation-induced infrastructure system damage for multiple serviceability limit states. Finally, a reliability analysis of a shallow circular tunnel driven by a pressurized shield in a frictional and cohesive soil is developed to consider the inherent uncertainty in the input parameters and the proposed model. The ultimate limit state for the face stability is considered in the analysis. The probability of failure that exceeding a specified applied pressure at the tunnel face is estimated. Sensitivity and importance measures are computed to identify the key parameters and random variables in the model

Application of new observational method on deep excavation retaining wall design in London Clay

Ground engineering in urban areas faces the great challenge of balancing the increasing demand for underground space against safety and asset protection while avoiding high construction costs. This study shows savings can be achieved on embedded retaining wall design for deep excavation in London Clay through the observational method, without compromising safety. Despite the inherent benefits of the method and its acceptance by design codes, the application of the observational method for excavation design has been slow and inconsistent due to the lack of guidance, in addition to other difficulties. This research aims to promote the application of the observational method in excavation design by proposing a new framework. The framework with four design approaches is established based on the review of historical excavation case histories and four Crossrail station excavations using the observational method. The term Ab initio is used for excavation design from the beginning of construction, covering Optimistic Approach A and Cautious Approach B. The term Ipso-tempore is introduced for excavation redesign after construction starts, comprising a newly defined Pro-active Approach C and the ‘best-way-out’ or Reactive Approach D. Back-analysis is critical in the observational method. The whole process of back analysis is examining monitoring systems (observations) and predictions by the numerical analysis with the adopted soil constitutive models. Three Crossrail excavation cases are back-analysed by the Mohr-Coulomb model using FEMs from Pseudo-FEM to 2D and 3D FEMs. The Crossrail Tottenham Court Road Station, Western Ticket Hall deep box excavation is also back-analysed by the BRICK model using the 3D FEM, representing the advanced soil model. The above back-analysis results are presented including the calibrated most probable soil model parameters. The different results indicate the back-analysis is subject to the type of numerical analysis, the adopted soil constitutive model, also it needs to be tailored to the monitoring data used for comparison. A reassessment of the TCR-WTH excavation design by Approach A is carried out using the semi-FEM with the Mohr-Coulomb model. The optimistic design with the calibrated most probable Mohr-Coulomb parameters shows over 30% saving in construction materials, which is supported by the contingency plan with the characteristic Mohr-Coulomb parameters if the excavation does not encounter the expected conditions. Improvements of specifications for the instruments and monitoring data are recommended to provide more reliable monitoring data.Ove Arup and Partner