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Public transport travel-time variability (PTTV) is essential for understanding the deteriorations in the reliability of travel time, optimizing transit schedules, and route choices. This paper establishes the key definitions of PTTV which firstly include all buses, and secondly include only a single service from a bus route. The paper then analyzes the day-to-day distribution of public transport travel time by using transit signal priority data. A comprehensive approach, using both parametric bootstrapping Kolmogorov-Smirnov test and Bayesian information criterion technique is developed, recommends lognormal distribution as the best descriptor of bus travel time on urban corridors. The probability density function of lognormal distribution is finally used for calculating probability indicators of PTTV. The findings of this study are useful for both traffic managers and statisticians for planning and analyzing the transit systems. [ABSTRACT FROM AUTHOR]

Bridge scour is the loss of soil by erosion because of water flowing around bridge supports. Scour has been the number one cause of bridge failure in the United States with an average annual rate of 22 bridges collapsing or being closed owing to severe deformation. This paper addresses three topics related to bridge scour. First, a set of databases was used to quantify the statistical parameters associated with the scatter between the predicted and measured pier scour depth, as well as the probability that a deterministically predicted pier scour depth will be exceeded. These databases also were used to provide the bias factors in current predictions. Secondly, these statistical parameters were used to develop a reliability-based load and resistance factor design for shallow and deep foundations subjected to scour. The goal was to provide a design procedure where the reliability of the foundation is the same with or without scour. Reliability only addresses the probability of success and, therefore, of failure. Finally, the discussion was broadened by using the concept of risk defined as the probability of failure times the value of the consequences. In this third part, the risk associated with bridge scour was quantified and compared to risks associated with other engineering structures. Target values of acceptable risk were recommended as part of the conclusions. [ABSTRACT FROM AUTHOR]

A model for project budgeting and scheduling with uncertainty is developed. The traditional critical-path method (CPM) misleads because there are few, if any, real-life deterministic situations for which CPM is a great match; program evaluation and review technique (PERT) has been seen to have its problems, too (e.g., merge bias, unavailability of data, difficulty of implementation by practitioners). A dual focus on the distributions of the possible errors in the time and cost estimates and on the reliability of the estimates used as planned values suggests an approach for developing reliable schedules and budgets with buffers for time and cost. This method for budgeting and scheduling is executed through either simulation or a simple analytical approximation. The dynamic buffers provide much-needed flexibility, accounting for the errors in cost and duration estimates associated with planning any real project, thus providing a realistic, practical, and dynamic approach to planning and scheduling. [ABSTRACT FROM AUTHOR]

Response surface methods (RSMs) are attractive approaches for slope reliability analysis because such methods can integrate deterministic numerical slope stability evaluation and reliability analysis. For a slope in layered soils, its performance function is generally nonlinear and the system failure probability could be larger than the failure probability of the most critical slip surface. In this study, the applicability of the kriging-based RSM for system reliability of soil slopes is assessed through its application to two slopes with obvious system effects. It is found that the kriging method combined with Monte Carlo simulation (MCS) can deliver accurate system failure probability estimation. For comparison, the classical RSM based on the iterative local approximation of the performance function may fail to detect the most critical slip surface. The classical RSM can only calculate the failure probability of one slip surface even if the first-order reliability method or MCS is used. Even when the same calibration samples are used, the second-order polynomial-based RSM is not as accurate as the kriging-based RSM. The results in this study show that the kriging-based RSM is an advantageous and promising approach for calculating the system reliability of soil slopes. [ABSTRACT FROM AUTHOR]

The reliability analysis of earth slopes is considered. For slope safety assessment, the first-order reliability method is employed for estimating the probability of failure or reliability index. Since the failure of any slip surfaces implies failure of the slope, the slope is considered as a series system. The system aspect of the slope in the reliability analysis is dealt with by defining a limit state of the system as a function of the minimum of the ratio of the shear strength to the mobilized shear strength for each of all potential slip surfaces. Such a ratio for a given slip surface is evaluated using the extended generalized method of slices. The reliability analysis procedure described is applied to example slopes to illustrate the impact of the probability distribution type, and the spatial variability of the soil properties on the probability of failure of the slopes. [ABSTRACT FROM AUTHOR]

In this paper, the excavation-induced settlement determined by the KJHH model, a recently developed semiempirical model, is used to assess the serviceability reliability of adjacent buildings. The calculated settlement, considered as the load in the context of reliability analyses in this paper, is compared with a tolerable settlement, considered as the resistance herein. The reliability of the adjacent building against “damage” (defined herein as the violation of serviceability requirements such as having intolerable settlement) is first analyzed and the probability of exceedance (i.e., exceeding the tolerable settlement) is calculated. Furthermore, as the excavation proceeds, observed settlement at the current excavation stage is used to update the prediction of settlement at subsequent stages, and the probability of exceedance is updated accordingly. [ABSTRACT FROM AUTHOR]

The evaluation of crossing probability for a given threshold level of a discrete process is an important modeling issue in stochastic hydrology. Rice’s formula is a tool to measure the instantaneous crossing rate for a given threshold level in a continuous Gaussian process. This paper examines the discrete application of Rice’s formula to estimating the up-crossing probability in typical discrete stationary univariate Gaussian processes. The results based on Rice’s formula are found to follow a biased pattern relative to the exact solutions, and perform poorly in important scenarios, particularly for estimating resilience in these numerical experiments. [ABSTRACT FROM AUTHOR]

This paper presents a reliability-based approach for the analysis and design of a shallow strip footing subjected to a vertical load with or without pseudostatic seismic loading. Only the punching failure mode of the ultimate limit state is studied. The deterministic models are based on the upper-bound method of the limit analysis theory. The random variables used are the soil shear strength parameters and the horizontal seismic coefficient. The Hasofer-Lind reliability index and the failure probability are determined. A sensitivity analysis is also performed. The influence of the applied footing load on the reliability index and the corresponding design point is presented and discussed. It was shown that the negative correlation between the soil shear strength parameters highly increases the reliability of the foundation and that the failure probability is highly influenced by the coefficient of variation of the angle of internal friction of the soil and the horizontal seismic coefficient. For design, an iterative procedure is performed to determine the breadth of the footing for a target failure probability. [ABSTRACT FROM AUTHOR]

A reliability-based structural control design approach is presented that optimizes a control system explicitly to minimize the probability of structural failure. Failure is interpreted as the system’s state trajectory exiting a safe region within a given time duration. This safe region is bounded by hyperplanes in the system state space, each of them corresponding to an important response quantity. An efficient approximation is discussed for the analytical evaluation of this probability, and for its optimization through feedback control. This analytical approximation facilitates theoretical discussions regarding the characteristics of reliability-optimal controllers. Versions of the controller design are described for the case using a nominal model of the system, as well as for the case with uncertain model parameters. For the latter case, knowledge about the relative plausibility of the different possible values of the uncertain parameters is quantified through the use of probability distributions on the uncertain parameter space. The influence of the excitation time duration on feedback control design is discussed and a probabilistic treatment of this time duration is suggested. The relationship to H2 (i.e., minimum variance) controller synthesis is also examined. [ABSTRACT FROM AUTHOR]

The mean-value first-order second-moment (MFOSM) method is the main method for estimating the reliability of slopes in practice. It is well recognized that the method occasionally underestimates the probability of failure for inhomogeneous soil slopes, but there is as of yet no commonly accepted procedure to identify this problem. This study presents a solution by projecting MFOSM results to obtain an equivalent most probable failure point in the material space as defined by Hasofer and Lind. A stability analysis using this material point then provides a check for the validity of the MFOSM solution. If the resulting critical factor of safety is one, the MFOSM results are valid; whereas, if a factor of safety of less than one is obtained, the reliability index is overestimated and the failure probability underestimated. [ABSTRACT FROM AUTHOR]

The concept of safety factor is nearly universally applied in structural engineering. There are presently several approaches for probabilistic interpretation of the safety factors in the literature. Herein we generalize the above approaches to derive four possible definitions of safety factor that are based on fuzzy sets: (1) the central fuzzy safety factor is defined as the ratio of the centroid abscissas of the membership functions, respectively, of the capacity and the demand of the structure; (2) the characteristic value of fuzzy safety factor as the lower bound of the α cut of the fuzzy safety factor for a specified level of the membership function; (3) the mean value of fuzzy safety factor as the centroid abscissa of the fuzzy capacity-to-demand ratio; and (4) the fuzzy multiplicative safety factor is defined as the abscissa of the centroid of the capacity multiplying to the abscissa of the centroid of the inverse of the demand. Fundamental problem of the strength of materials, namely, tension of an element subjected to an axial load, is analyzed in the context of the above four fuzzy safety factors. [ABSTRACT FROM AUTHOR]

The potential for liquefaction triggering of a soil under a given seismic loading is measured herein by probability of liquefaction. The first order reliability method (FORM) is used to calculate reliability index, from which the probability of liquefaction is obtained. This approach requires the knowledge of parameter and model uncertainties; the latter is the focus of this paper. An empirical model for determining liquefaction resistance based on cone penetration test (CPT) is established through “neural network learning” of case histories. This resistance model along with a reference seismic loading model forms a performance function or limit state for liquefaction triggering analysis. Within the framework of the FORM, the uncertainty of this limit state model is characterized through an extensive series of sensitivity studies using Bayesian mapping functions that have been calibrated with a set of quality case histories. In addition, a deterministic model for assessing liquefaction potential in terms of factor of safety is presented, and the probability-safety factor mapping functions for estimating the probability of liquefaction for a given factor of safety in the absence of the knowledge of parameter uncertainty are also established. Examples are presented to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

A conditional reliability model (CRM) is presented for assessing reliabilities for meeting water needs over the next several months, conditioned upon current reservoir storage contents. The CRM procedure was developed in conjunction with a generalized river/reservoir system model called the Water Rights Analysis Package (WRAP). The CRM methodology is presented in the context of the WRAP model, but the process is applicable to other models as well. A new concept of conditional frequency duration curves, representing probability distributions of naturalized streamflows conditioned on preceding simulated reservoir storage, is incorporated in the CRM methodology. The results of the model are probability-weighted values of storage or diversion from many short-term simulations that start with the same storage condition. Applications of the model in annual operational planning, drought contingency planning, and reservoir resilience analysis are presented, along with pertinent discussions of the fundamental concepts of the model and comparison with the alternative, simpler approach of assuming each short-term simulation is equally likely to occur. [ABSTRACT FROM AUTHOR]

Uncertainty and risk are central features of geotechnical and geological engineering. Engineers can deal with uncertainty by ignoring it, by being conservative, by using the observational method, or by quantifying it. In recent years, reliability analysis and probabilistic methods have found wide application in geotechnical engineering and related fields. The tools are well known, including methods of reliability analysis and decision trees. Analytical models for deterministic geotechnical applications are also widely available, even if their underlying reliability is sometimes suspect. The major issues involve input and output. In order to develop appropriate input, the engineer must understand the nature of uncertainty and probability. Most geotechnical uncertainty reflects lack of knowledge, and probability based on the engineer’s degree of belief comes closest to the profession’s practical approach. Bayesian approaches are especially powerful because they provide probabilities on the state of nature rather than on the observations. The first point in developing a model from geotechnical data is that the distinction between the trend or systematic error and the spatial error is a modeling choice, not a property of nature. Second, properties estimated from small samples may be seriously in error, whether they are used probabilistically or deterministically. Third, experts generally estimate mean trends well but tend to underestimate uncertainty and to be overconfident in their estimates. In this context, engineering judgment should be based on a demonstrable chain of reasoning and not on speculation. One difficulty in interpreting results is that most people, including engineers, have difficulty establishing an allowable probability of failure or dealing with low values of probability. The F–N plot is one useful vehicle for comparing calculated probabilities with observed frequencies of failure of comparable facilities. In any comparison it must be noted that a calculated probability is a lower bound because it must fail to incorporate the factors that are ignored in the analysis. It is useful to compare probabilities of failure for alternative designs, and the reliability methods reveal the contributions of different components to the uncertainty in the probability of failure. Probability is not a property of the world but a state of mind; geotechnical uncertainty is primarily epistemic, Bayesian, and belief based. The current challenges to the profession are to make use of probabilistic methods in practice and to sharpen our investigations and analyses so that each additional data point provides maximal information. [ABSTRACT FROM AUTHOR]

Over 10,000 failures have occurred in US oil and gas pipelines in the past 15 years, highlighting the significance of safety measures for such facilities. Various models have been proposed by researchers to predict different failure parameters. Despite such efforts, no comprehensive review has yet been conducted in this domain. The objective of this study is to provide a detailed review of the methodologies proposed to predict failure parameters for oil and gas pipelines. Such a review gathers, organizes, classifies, and analyzes previous contributions in this domain and highlights the gaps associated with different failure prediction models. In addition, the current code-based methodologies for predicting the failure of oil and gas pipelines and their corresponding limitations are discussed. As such, this study provides pipeline operators and researchers with a comprehensive overview of the research and practices in oil and gas pipeline failure and safety. In conclusion, several avenues for future research are discussed. In particular, a maintenance planning procedure directed by pipeline availability analysis is proposed to address the existing gaps and limitations. [ABSTRACT FROM AUTHOR]

Seismic reliability analysis of wood structures has to take into consideration the uncertainties from many sources. This paper presented three methods to deal with the uncertainties from ground motion records, intensity measure, and resistance. The application of the methods in analyzing wood shear walls was also discussed. The traditional method calculates the exceeding probability of drift demand from conditional distributions given intensity levels. The second method determines the exceeding probability of drift demand from conditional distributions given ground motion records. The second method is computationally efficient and relatively accurate by using the mean of conditional exceeding probabilities. The third method is the quasi-Monte Carlo simulation method. Sequence numbers can be used to improve the efficiency of simulation analysis. These methods were used to analyze three wood shear walls. The shear wall model is a mechanics-based nail analogue with parameters validated by test results. The results from the three methods are very similar, which indicates that the three methods may be equally used in seismic reliability analysis of wood shear walls. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for evaluating fitness-for-service (i.e., safety, serviceability, and reliability) of corroded metal pipelines. A model for predicting pipe failure pressure is developed from a series of nonlinear finite-element analyses of metal pipes of different diameters and wall thicknesses with corrosion defects of different sizes and depths. The strength limit state (burst) and service limit states (yield and leakage) both are investigated in the pipe fitness-for-service analyses. Uncertainties associated with in situ measurement of flaw size, pipe geometry, pipe material properties, operating pressures, and corrosion in exposure environments are considered in a time-dependent reliability analysis of pipe performance over a service life of 50 years. Engineering variables that have the most significant impact on the reliability of a corroded pipe are identified through Monte Carlo-based sensitivity studies. Finally, a set of simple reliability-based evaluation tools are presented for assessing pipeline safety. The procedure and the results presented in this paper can be used to support decisions related to continued safe operation of pipes, optimal pipe inspection intervals, and maintenance schedules. [ABSTRACT FROM AUTHOR]

Concrete sewer pipes encounter corrosion as a predominant form of deterioration that reduces the service life of the pipeline system and increases the costs of maintenance and rehabilitation. Reliability analysis can help pipeline owners and sewer-system managers to predict the service life of the pipes and the time for repair or replacement. To include uncertainties in the reliability analysis, the corrosion process can be considered a stochastic process. This paper presents a stochastic gamma process model to account for temporal variability and uncertainties associated with the corrosion process in concrete sewer pipes that typically increase the probability of failure with the aging of the pipe. The proposed methodology is then applied to a specific concrete sewer system. The key element of the proposed method is the use of the gamma process concept. A gamma process can model the monotonic behavior of the ageing and deteriorating process. The application of the gamma process presented in this paper can potentially contribute to widening the use of stochastic processes for the modeling of structural degradation processes such as wear, fatigue, corrosion, crack, erosion, and creep. [ABSTRACT FROM AUTHOR]