Finite element reliability analysis of reinforced retaining walls
TL;DR: In this paper, the authors presented the reliability analysis of reinforced retaining wall using finite element method and a first-order reliability method (FORM) is used to evaluate the reliability index.
Abstract: This paper presents the reliability analysis of reinforced retaining wall using finite element method. Response surface approach is used to approximate the performance function and a first-order reliability method (FORM) is used to evaluate the reliability index. In the analysis, displacement response of the reinforced retaining wall is considered as performance function and the corresponding reliability index is evaluated with the aid of a spreadsheet. Uncertainties associated with the soil and reinforcement properties are explicitly taken into account in the analysis. A parametric sensitivity analysis has been performed to bring out the effect of important uncertain parameters by evaluating the sensitivity of the reliability index with respect to each of the uncertain parameters. Results of the response surface method coupled with finite element analysis show the ease and successful implementation of the reliability analysis procedure for the reinforced retaining walls.
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TL;DR: In this article, a new reliability-based design approach was presented to evaluate the performance of a composite tunnel lining using a modified Rosenblueth Point Estimate Method (PEM), First Order Reliability Method (FORM), Monte Carlo sampling method and finite element analysis.
66 citations
TL;DR: This research addresses the issue by representing the cross-section reduction of a buried pipe due to corrosion through a combination of the Gamma process concept and copula and concludes that the proposed method is able to predict the service life of corroding buried pipeline efficiently.
25 citations
TL;DR: In this article, a new reliability-based design (RBD) approach is presented to evaluate the excavation response and support performance for a tunnel in brittle ground, and guidance for the selection of appropriate parameters for variable brittle materials is provided using a combination of the damage initiation and spalling limit method and theories of microcrack initiation.
Abstract: Spalling damage can pose significant risks during the construction of underground excavations in brittle rock. While deterministic analyses have traditionally been used in the design of these structures, reliability-based design (RBD) methods provide a more rational approach to quantify spalling risk by directly incorporating input uncertainty into the design process and quantifying variable ground response. This paper presents a new RBD approach to evaluate the excavation response and support performance for a tunnel in brittle ground. Guidance for the selection of appropriate parameters for variable brittle materials is provided using a combination of the damage initiation and spalling limit method and theories of microcrack initiation. System performance is then evaluated using a proposed global response surface method (GRSM) coupled with the first-order reliability method, random sampling and finite element analysis. The proposed GRSM provides a computationally efficient way to evaluate the probability of failure for various limit states, allowing for the selection of appropriate design parameters such as minimum bolt length and required bolt capacity during early stages of design. To demonstrate the usefulness of this approach, a preliminary design option for a proposed deep geologic repository located in Canada was assessed. Numerical analyses were completed using finite element modeling to determine the depth of spalling around the excavation and support loads over the range of possible rock mass and in situ stress conditions. The results of these analyses were then used to assess support performance and make support recommendations.
22 citations
TL;DR: In this paper, the use of the response surface method (RSM) was used to carry out probabilistic assessment of selected performance features of geosynthetic-reinforced segmental retaining walls under a geodesic environment.
Abstract: The paper demonstrates the use of the response surface method (RSM) to carry out probabilistic assessment of selected performance features of geosynthetic-reinforced segmental retaining walls under...
21 citations
TL;DR: In this paper, the authors proposed a strategy to compute deterministic and probabilistic estimates of maximum outward deformation of mechanically stabilized earth (MSE) modular block wall structures of particular type, materials and boundary conditions.
18 citations
References
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Book•
01 Jan 1987
TL;DR: Measures of Structural Reliability Assessment, including second-Moment and Transformation Methods, and Probabilistic Evaluation of Existing Structures.
Abstract: Measures of Structural Reliability. Structural Reliability Assessment. Integration and Simulation Methods. Second-Moment and Transformation Methods. Reliability of Structural Systems. Time Dependent Reliability. Load and Load Effect Modelling. Resistance Modelling. Codes and Structural Reliability. Probabilistic Evaluation of Existing Structures. Appendices. References. Index.
3,151 citations
"Finite element reliability analysis..." refers background in this paper
...The FORM provides a practical scheme of computing small probabilities of failure at high dimensional space spanned by the random variables in the problem (Hasofer and Lind 1974, Haldar and Mahadevan 2000, Melchers 1999)....
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TL;DR: In this article, a fundamental analysis of the meaning of second-moment reliability in multivariate problems is presented, and the format described is entirely derived from one basic assumption concerning the measurement of reliability.
Abstract: A fundamental analysis of the meaning of second-moment reliability in multivariate problems is presented. The format described is entirely derived from one basic assumption concerning the measurement of reliability. All formulations are exact, and approximations involving the assumption of small variance are only introduced to simplify practical equations. The format is fully invariant under any change of formulation of the failure criteria consistent with the laws of algebra and mechanics.
2,702 citations
"Finite element reliability analysis..." refers background in this paper
...f () 30 20% 6 Normal Low and Tang (1997), Phoon and Kulhawy (1999), Hoeg and Muruka (1974) (kN/m(3)) 16 10% 1.6 Normal Low and Tang (1997), Phoon and Kulhawy (1999), Hoeg and Muruka (1974) T (kN/m) 50 10% 5 Normal Low and Tang (1997) () 23 10% 2....
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...4 20% Normal Low and Tang (1997), Phoon and Kulhawy (1999), Hoeg and Muruka (1974) (kN/m(3)) 19 1.9 10% Normal Low and Tang (1997), Phoon and Kulhawy (1999), Hoeg and Muruka (1974) T (kN/m) 60 6 10% Normal Low and Tang (1997) ( ) 15 1....
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...4 20% Normal Low and Tang (1997), Phoon and Kulhawy (1999), Hoeg and Muruka (1974) (kN/m(3)) 19 1....
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...The FORM provides a practical scheme of computing small probabilities of failure at high dimensional space spanned by the random variables in the problem (Hasofer and Lind 1974, Haldar and Mahadevan 2000, Melchers 1999)....
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...f () 30 20% 6 Normal Low and Tang (1997), Phoon and Kulhawy (1999), Hoeg and Muruka (1974) (kN/m(3)) 16 10% 1....
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TL;DR: In this paper, the three primary sources of geotechnical uncertainties are inherent variability, measurem, and measurem uncertainties, and the three main sources of variability are measurem and inherent variability.
Abstract: Geotechnical variability is a complex attribute that results from many disparate sources of uncertainties. The three primary sources of geotechnical uncertainties are inherent variability, measurem...
1,663 citations
Book•
01 Nov 1999
TL;DR: Basic Concept of Reliability, Commonly Used Probability Distributions, and Determination of Distributions and Parameters from Observed Data.
Abstract: Basic Concept of Reliability. Mathematics of Probability. Modeling of Uncertainty. Commonly Used Probability Distributions. Determination of Distributions and Parameters from Observed Data. Randomness in Response Variables. Fundamentals of Reliability Analysis. Advanced Topics on Reliability Analysis. Simulation Techniques. Appendices. Conversion Factors. References. Index.
1,456 citations
"Finite element reliability analysis..." refers background in this paper
...The FORM provides a practical scheme of computing small probabilities of failure at high dimensional space spanned by the random variables in the problem (Hasofer and Lind 1974, Haldar and Mahadevan 2000, Melchers 1999)....
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Book•
01 Jan 2003
TL;DR: In this paper, the authors present a survey of the state of the art in the field of geotechnical reliability analysis, focusing on the following: 1.1 Randomness, uncertainty, and the world. 2.3 Probability.
Abstract: Preface. Part I. 1 Introduction - uncertainty and risk in geotechnical engineering. 1.1 Offshore platforms. 1.2 Pit mine slopes. 1.3 Balancing risk and reliability in a geotechnical design. 1.4 Historical development of reliability methods in civil engineering. 1.5 Some terminological and philosophical issues. 1.6 The organization of this book. 1.7 A comment on notation and nomenclature. 2 Uncertainty. 2.1 Randomness, uncertainty, and the world. 2.2 Modeling uncertainties in risk and reliability analysis. 2.3 Probability. 3 Probability. 3.1 Histograms and frequency diagrams. 3.2 Summary statistics. 3.3 Probability theory. 3.4 Random variables. 3.5 Random process models. 3.6 Fitting mathematical pdf models to data. 3.7 Covariance among variables. 4 Inference. 4.1 Frequentist theory. 4.2 Bayesian theory. 4.3 Prior probabilities. 4.4 Inferences from sampling. 4.5 Regression analysis. 4.6 Hypothesis tests. 4.7 Choice among models. 5 Risk, decisions and judgment. 5.1 Risk. 5.2 Optimizing decisions. 5.3 Non-optimizing decisions. 5.4 Engineering judgment. Part II. 6 Site characterization. 6.1 Developments in site characterization. 6.2 Analytical approaches to site characterization. 6.3 Modeling site characterization activities. 6.4 Some pitfalls of intuitive data evaluation. 6.5 Organization of Part II. 7 Classification and mapping. 7.1 Mapping discrete variables. 7.2 Classification. 7.3 Discriminant analysis. 7.4 Mapping. 7.5 Carrying out a discriminant or logistic analysis. 8 Soil variability. 8.1 Soil properties. 8.2 Index tests and classification of soils. 8.3 Consolidation properties. 8.4 Permeability. 8.5 Strength properties. 8.6 Distributional properties. 8.7 Measurement error. 9 Spatial variability within homogeneous deposits. 9.1 Trends and variations about trends. 9.2 Residual variations. 9.3 Estimating autocorrelation and autocovariance. 9.4 Variograms and geostatistics. Appendix: algorithm for maximizing log-likelihood of autocovariance. 10 Random field theory. 10.1 Stationary processes. 10.2 Mathematical properties of autocovariance functions. 10.3 Multivariate (vector) random fields. 10.4 Gaussian random fields. 10.5 Functions of random fields. 11 Spatial sampling. 11.1 Concepts of sampling. 11.2 Common spatial sampling plans. 11.3 Interpolating random fields. 11.4 Sampling for autocorrelation. 12 Search theory. 12.1 Brief history of search theory. 12.2 Logic of a search process. 12.3 Single stage search. 12.4 Grid search. 12.5 Inferring target characteristics. 12.6 Optimal search. 12.7 Sequential search. Part III. 13 Reliability analysis and error propagation. 13.1 Loads, resistances and reliability. 13.2 Results for different distributions of the performance function. 13.3 Steps and approximations in reliability analysis. 13.4 Error propagation - statistical moments of the performance function. 13.5 Solution techniques for practical cases. 13.6 A simple conceptual model of practical significance. 14 First order second moment (FOSM) methods. 14.1 The James Bay dikes. 14.2 Uncertainty in geotechnical parameters. 14.3 FOSM calculations. 14.4 Extrapolations and consequences. 14.5 Conclusions from the James Bay study. 14.6 Final comments. 15 Point estimate methods. 15.1 Mathematical background. 15.2 Rosenblueth's cases and notation. 15.3 Numerical results for simple cases. 15.4 Relation to orthogonal polynomial quadrature. 15.5 Relation with 'Gauss points' in the finite element method. 15.6 Limitations of orthogonal polynomial quadrature. 15.7 Accuracy, or when to use the point-estimate method. 15.8 The problem of the number of computation points. 15.9 Final comments and conclusions. 16 The Hasofer-Lind approach (FORM). 16.1 Justification for improvement - vertical cut in cohesive soil. 16.2 The Hasofer-Lind formulation. 16.3 Linear or non-linear failure criteria and uncorrelated variables. 16.4 Higher order reliability. 16.5 Correlated variables. 16.6 Non-normal variables. 17 Monte Carlo simulation methods. 17.1 Basic considerations. 17.2 Computer programming considerations. 17.3 Simulation of random processes. 17.4 Variance reduction methods. 17.5 Summary. 18 Load and resistance factor design. 18.1 Limit state design and code development. 18.2 Load and resistance factor design. 18.3 Foundation design based on LRFD. 18.4 Concluding remarks. 19 Stochastic finite elements. 19.1 Elementary finite element issues. 19.2 Correlated properties. 19.3 Explicit formulation. 19.4 Monte Carlo study of differential settlement. 19.5 Summary and conclusions. Part IV. 20 Event tree analysis. 20.1 Systems failure. 20.2 Influence diagrams. 20.3 Constructing event trees. 20.4 Branch probabilities. 20.5 Levee example revisited. 21 Expert opinion. 21.1 Expert opinion in geotechnical practice. 21.2 How do people estimate subjective probabilities? 21.3 How well do people estimate subjective probabilities? 21.4 Can people learn to be well-calibrated? 21.5 Protocol for assessing subjective probabilities. 21.6 Conducting a process to elicit quantified judgment. 21.7 Practical suggestions and techniques. 21.8 Summary. 22 System reliability assessment. 22.1 Concepts of system reliability. 22.2 Dependencies among component failures. 22.3 Event tree representations. 22.4 Fault tree representations. 22.5 Simulation approach to system reliability. 22.6 Combined approaches. 22.7 Summary. Appendix A: A primer on probability theory. A.1 Notation and axioms. A.2 Elementary results. A.3 Total probability and Bayes' theorem. A.4 Discrete distributions. A.5 Continuous distributions. A.6 Multiple variables. A.7 Functions of random variables. References. Index.
1,110 citations
"Finite element reliability analysis..." refers background in this paper
...It is to be noted that uncertainties in geotechnical engineering analysis and design are unavoidable and numerous practical advantages are realizable if uncertainties and associated risk can be quantified (Whitman 1984, Low and Tang 1997, Duncan 2000, Christian and Baecher 2003)....
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