Reliability analysis and design of cantilever RC retaining walls against sliding failure
01 Apr 2011-International Journal of Geotechnical Engineering (Taylor & Francis)-Vol. 5, Iss: 2, pp 131-141
TL;DR: In this paper, the stability analysis of reinforced concrete (RC) cantilever retaining walls, accounting for uncertainties in the design variables in the framework of probability theory, is presented, where the first order reliability method (FORM), second order reliability (SORM), and Monte Carlo simulation (MCS) method are used as alternative ways to evaluate the probability of failure associated with the sliding failure of retaining walls of various heights (ranging from 4 to 8 m).
Abstract: Among the various modes of failure of reinforced concrete (RC) cantilever retaining walls, the sliding mode of failure is invariably seen to be the critical mode governing the proportions of the wall. Traditionally, a constant factor of safety (usually 1.5) is adopted in the design of cantilever retaining walls against sliding and overturning instability, regardless of the actual uncertainties in the various design variables. This paper presents the stability analysis of cantilever retaining walls, accounting for uncertainties in the design variables in the framework of probability theory. The first order reliability method (FORM), second order reliability method (SORM) and Monte Carlo simulation (MCS) method are used as alternative ways to evaluate the probability of failure associated with the sliding failure of retaining walls of various heights (ranging from 4 to 8 m). Sensitivity analysis has shown that the angle of internal friction (Φ) and the coefficient of friction below the concrete base...
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Journal Article•
23 citations
TL;DR: In this paper, the reliability analysis of basal heave caused by excavation considering uncertainty in the soil properties has been conducted, and the results show that the reliability index decreases with an increase in the coefficient of variation of undrained shear strength.
Abstract: The present study deals with the reliability analysis of basal heave caused by excavation considering uncertainty in the soil properties. The case study considered in the present work has been analyzed deterministically by Hsieh et al. (Can Geotech J 45:788–799, 2008). Taiwan building code is adopted in the method for analyzing the basal heave failure. The random variables (undrained shear strength and total unit weight of clay) are assumed to be normally distributed and uncorrelated. A series of parametric studies have been conducted to calculate the reliability index on the basis of the matrix formulation for the second moment method by Hasofer and Lind (J Eng Mech ASCE 100(1):111–121, 1974) considering different coefficient of variation of undrained shear strength and total unit weight of clay layers. It has been found that for a particular value of coefficient of variation of total unit weight, the reliability index with respect to occurrence of basal heave failure decreases with increase in the coefficient of variation of undrained shear strength. Moreover, the reliability index also decreases when the coefficient of variation of total unit weight increases. It has also been found that the probability of basal heave failure is lower with respect to factor of safety equals to 1.2, as compared to factor of safety equals to 1.0. Sensitivity analysis shows that the undrained shear strength of the bottommost layer and total unit weight of the second layer are the most significant random variables affecting the reliability index. Guidelines are provided for reliability based design where, for ‘target’ reliability index of 2.5 and 3.0, the factor of safety can be chosen such that all the related uncertainties are taken into account, especially with regard to undrained shear strength of the bottommost layer and total unit weight of the second layer. Design guidelines have been provided for this purpose.
11 citations
Cites methods from "Reliability analysis and design of ..."
...Sujit et al. (2011) calculated probability of failure against sliding mode of failure for cantilever retaining wall by first order reliability method (FORM), second order reliability method (SORM) and Monte Carlo simulation (MCS) method....
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TL;DR: It is found that the variation of geotechnical random variables does not have a significant effect on the stability of retaining walls subjected to blast loading.
Abstract: Conventional design methods adopt factor of safety as per practice and experience, which are deterministic in nature. The limit state method, though not completely deterministic, does not take into account effect of design parameters, which are inherently variable such as cohesion, angle of internal friction, etc. for soil. Reliability analysis provides a measure to consider these variations into analysis and hence results in a more realistic design. Several studies have been carried out on reliability of reinforced concrete walls and masonry walls under explosions. Also, reliability analysis of retaining structures against various kinds of failure has been done. However, very few research works are available on reliability analysis of retaining walls subjected to blast loading. Thus, the present paper considers the effect of variation of geotechnical parameters when a retaining wall is subjected to blast loading. However, it is found that the variation of geotechnical random variables does not have a significant effect on the stability of retaining walls subjected to blast loading.
6 citations
TL;DR: The overall performance of the models indicated that ANFIS-PSO provided better results among all four models, while the reliability index was computed using the first-order second-moment (FOSM) method, and the probability of failure was also computed.
Abstract: Gravity retaining walls are a vital structure in the area of geotechnical engineering, and academicians in earlier studies have conveyed substantial uncertainties involved in calculating the factor of safety against overturning, using a deterministic approach. Hence, to enhance the accuracy and eliminate the uncertainties involved, artificial intelligence (AI) was used in the present research. The main aim of this study is to propose a high-performance machine learning (ML) model to determine the factor of safety (FOS) of gravity retaining walls against overturning. The projected methodology included a novel hybrid machine learning model that merged with an adaptive neuro-fuzzy inference system (ANFIS) and meta-heuristic optimization techniques (particle swarm optimization (PSO), genetic algorithm (GA), firefly algorithm (FFA) and grey wolf optimization (GWO)). In this research, four hybrid models, namely ANFIS-PSO, ANFIS-FFA, ANFIS-GA and ANFIS-GWO, were created to estimate the factor of safety against overturning. The proposed hybrid models were evaluated on two distinct datasets (training 70% and testing 30%) with three input combinations, namely cohesion (c), unit weight of soil (Υ) and angle of shearing resistance (φ). To access the prediction power of different hybrid models, various statistical parameters such as R2, AdjR2, VAF, WI, LMI, a-20 index, PI, KGE, RMSE, SI, MAE, NMBE and MBE were computed for training (TR) and testing (TS) datasets. The overall performance of the models indicated that ANFIS-PSO provided better results among all four models. The reliability index was computed using the first-order second-moment (FOSM) method for all models, and the probability of failure was also computed. A Williams plot was drawn to check the applicability domain of the hybrid model and to check the influence of different input parameters on the prediction of the factor of safety, and the Gini index was also computed.
6 citations
TL;DR: The numerical results indicated that the effects of spatial correlation length of the soil/wall base friction coefficient on the probability of failure (Pf) were greater than those of cohesion on the possibility of slip failure, and the antislip factor of safety is essentially equal to 1 when the values of normalized spatial correlations length are relatively large.
Abstract: In this paper, the antislip stability assessment of a gravity retaining wall is analyzed by considering the spatial variability of soils based on the theory of random fields. The effects of spatial correlation lengths of the soil/wall base friction coefficient and cohesion on the antislip safety factor of a gravity retaining wall were investigated. The numerical results indicated that the effects of spatial correlation length of the soil/wall base friction coefficient on the probability of failure (Pf) were greater than those of cohesion on the probability of slip failure. Moreover, when comparing different levels of failure probability, the antislip factor of safety corresponded to different constants when values of normalized spatial correlation length were relatively small. In other words, the antislip factor of safety increases with a decreasing failure probability, whereas the antislip factor of safety is essentially equal to 1 when the values of normalized spatial correlation length are relatively large. In addition, the numerical results obtained using the proposed method were in good agreement with those obtained using Monte Carlo simulation. DOI: 10.1061/(ASCE)GM.1943-5622.0001413. © 2019 American Society of Civil Engineers. Author keywords: Gravity retaining wall; Antislip safety factor; Random fields; Markov process.
5 citations
Cites methods from "Reliability analysis and design of ..."
...The FORM, SORM, and MCS were used to evaluate the Pf associated with the sliding failure of retaining walls of various heights (Sujith et al. 2011)....
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References
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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
"Reliability analysis and design of ..." refers background in this paper
...Hasofer and Lind (1974) defined the reliability index β as the shortest distance from the origin O to the failure surface in the normalized coordinate system....
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...This problem of ‘lack of invariance’ was resolved by Hasofer and Lind (1974), by transforming the X variables into an equivalent set of uncorrelated standard unit normal U variables....
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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
TL;DR: In this paper, simple reliability analyses, involving neither complex theory nor unfamiliar terms, can be used in routine geotechnical engineering practice to evaluate the combined effects of uncertainties in the parameters involved in the calculations, and they offer a useful supplement to conventional analyses.
Abstract: Simple reliability analyses, involving neither complex theory nor unfamiliar terms, can be used in routine geotechnical engineering practice. These simple reliability analyses require little effort beyond that involved in conventional geotechnical analyses. They provide a means of evaluating the combined effects of uncertainties in the parameters involved in the calculations, and they offer a useful supplement to conventional analyses. The additional parameters needed for the reliability analyses—standard deviations of the parameters—can be evaluated using the same amount of data and types of correlations that are widely used in geotechnical engineering practice. Example applications to stability and settlement problems illustrate the simplicity and practical usefulness of the method.
979 citations
"Reliability analysis and design of ..." refers background or methods in this paper
...Attempts have been made to account for these uncertainties in a more rational manner using probability theory by geotechnical engineers (Whitman, 1984; 2000; Duncan, 2000; Phoon et al., 1999; Christian, 2004)....
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...Duncan (2000) opined that ‘factor of safety’ alone is not sufficient for risk assessment and it should be used in conjunction with ‘reliability index’....
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...Past experience shows that apparently conservative designs (based on the traditional ‘factor of safety concept’) are not always safe against failure (Hoeg and Muruka, 1974; Duncan, 2000; Christian, 2004)....
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Book•
03 Mar 2006
TL;DR: This book discusses the foundations of Probability Models, computer-Based Numerical and Simulation Methods in Probability, and Elements of Quality Assurance and Acceptance Sampling.
Abstract: Chapter 1 - Role of Probability and Statistics in Engineering Chapter 2 -- Fundamentals of Probability Models Chapter 3 -- Analytical Models of Random Phenomena Chapter 4 -- Functions of Random Variables Chapter 5 - Computer-Based Numerical and Simulation Methods in Probability Chapter 6 -- Statistical Inferences from Observational Data Chapter 7 -- Determination of Probability Distribution Models Chapter 8 -- Regression and Correlation Analyses Chapter 9 -- The Bayesian Approach Chapter 10 - Elements of Quality Assurance and Acceptance Sampling (Available only online at the Wiley web site) Appendices: Table A.1 -- Standard Normal Probabilities Table A.2 - CDF of the Binomial Distribution Table A.3 - Critical Values of t Distribution at Confidence Level (1- a)=p Table A.4 - Critical Values of the c2 Distribution at Confidence Level (1-a)=pTable A.5 - Critical Values of Dna at Significance Level a in the K-S Test Table A.6 - Critical Values of the Anderson-Darling Goodness-of-fit Test (for 4 specific distributions)
909 citations