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A complex interdisciplinary approach to the reliability assessment of reinforced concrete structures is introduced and demonstrated on a real existing bridge structure. The reliability index of the structure decreases during its life cycle due to material degradation. A retrofitting to the desired reliability level should be performed. This procedure is modeled by advanced life-cycle computer simulation. The main feature of the presented approach is the nonlinear finite-element analysis of the structure employed for the realistic assessment of structural behavior. A suitable technique of statistical sampling, which allows a relatively small number of simulations, is used in this context. Analytical deterioration models combined with in situ monitoring are used to launch the degradation process. The presented methodology for advanced life-cycle analysis is integrated in the innovative decision-making tool that supports maintenance planning of engineering structures. [ABSTRACT FROM AUTHOR]

This study introduces a new probabilistic project control concept to assure an acceptable forecast of final project performance, in terms of not exceeding planned budget and schedule risk levels. This concept consists in the implementation of performance control limit curves for both actual cost and elapsed time, obtained with a probabilistic approach and a graphical representation referred to as Stochastic S curves (SS curves). In order to facilitate the project control process, control limit curves can be used to display and evaluate actual project performance status without the need of actualizing at completion performance forecasts. Three different approaches (quality, benchmarking, and incremental variance) are proposed in this paper for obtaining the project performance control limit curves. In order to find the control limit curve definition with more conservative acceptable performance variations, these approaches are tested in an example project. A further managerial advantage is found in the recommended approach, as it allows monitoring the use of both cost and scheduling contingencies, along the project execution. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for modeling pedestrians’ crossing behavior along an urban trip, as well as an algorithm for the estimation of accident risk along the trip. For that purpose, existing models are exploited and further developed. In particular, a nested logit model and a linear regression model are merged and adapted to develop a hierarchical crossing behavior model, allowing for the estimation of a distribution of crossing probabilities on an urban road link among junctions and various midblock locations. The explanatory variables concern a set of directly measurable geometric and traffic characteristics. A second model is then developed for the estimation of the distribution of crossing probabilities along a trip in relation to the distance from the trip origin. Both models were sufficiently validated by means of appropriate surveys. On the basis of these models, a complete framework for the assessment of pedestrians’ crossing behavior in urban areas is developed. Moreover, a set of formulas for the calculation of accident risk along a trip in relation to the estimated crossing behavior of pedestrians is proposed. [ABSTRACT FROM AUTHOR]

The probabilistic flow within capillary barrier models is evaluated by coupling a first-order reliability (probabilistic) model to a variably saturated flow model. The objective is to determine the most significant uncertain variable to probabilistic flow and the effect of different textural combinations. The model inputs include the mean and standard deviation of each uncertain variable. The van Genuchten curve-fitting model for unsaturated flow is used. The uncertain flow variables are saturated water content, residual water content, saturated hydraulic conductivity, and model parameters alpha (α) and n. A clay loam soil sample overlying a loamy sand sample, a clay loam sample overlying a sand sample, and a loamy sand sample overlying a sand sample are used to represent finer soils overlying coarser soil. Evaluations near the textural interface show that model parameters alpha (α) and n=most significant uncertain variables. These are related to the water entry pressure and the width of pore size distribution of the soils. Generally, soils that have the least uniform pore size distribution are the most effective capillary barriers. In this study, the clay loam overlying loamy sand satisfied this condition and performed better than the other soil combinations. [ABSTRACT FROM AUTHOR]

A model that applies to initial bridge load ratings based on allowable stress, load factor, and load and resistance factor design is presented. The prognostic component calculates bridge load ratings probabilistically considering random variables representative of load and resistance effects. The diagnostic component helps to point out the sensitivity rankings of these input parameters. Monte Carlo simulation and Bayesian networks are the tools employed in this bidirectional model. The model is applied to a beam in a prestressed concrete bridge at the beginning of its service life to demonstrate conclusions related to its applicability as a tool in areas related to bridge design and load rating. [ABSTRACT FROM AUTHOR]

A Bayesian belief network (BBN) can be a powerful tool in decision making processes. Development of a BBN requires data or expert knowledge to assist in determining the structure and probabilistic parameters in the model. As data are seldom available in the engineering decision making domain, a major barrier in using domain experts is that they are often required to supply a huge and intractable number of probabilities. Techniques for using fractional data to develop complete conditional probability tables were examined. The results showed good predictability of the missing data in a linear domain by the piecewise representation method. By using piecewise representation, the number of probabilities to be elicited for a binary child node with k binary parent nodes is now 2k rather than 2k. [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 purpose of this work is to provide a simple, rational basis for combining bridge loads in the extreme event limit state. Classic methods are used to evaluate the probabilities of traffic, seismic, and storm-related bridge loads occurring simultaneously and in various intensities. The loads are modeled using a Poisson distribution, which circumvents problems encountered when using normal- or log-normal distributions. The hazard level is evaluated directly using a negative exponential function in the time domain. An acceptable hazard level for combined events is subjectively based on that deemed acceptable for the strength limit state and extreme events occurring individually, as well as fiscal prudence. It is shown that (1) application of seismic loads to a structure already subjected to the combined effects of degradation, local pier scour, and contraction of the waterway is not justifiable; (2) live loads reduced from the anticipated 75-year maximum to a 2-week maximum are appropriate when designing a bridge in its 100-year “scoured-out” storm configuration; and (3) vehicular live loads are likely to be on a bridge during a seismic event, but other issues need to be considered. [ABSTRACT FROM AUTHOR]

A database of synthetic hurricane wind speeds is developed for a region of the southeastern United States comprising South Carolina, North Carolina, and eastern Virginia. For each zip code in the study region, the database includes a time index (year), duration of strong winds, and peak surface wind speeds (both gust and sustained). Synthetic wind speed records for 15,000 years are developed using an event-based simulation approach (a modeling approach in which each hurricane is simulated as a discrete stochastic event) based on the empirical tracking and central pressure models proposed by Vickery et al. in 2002. The Vickery model considers storm formation and movement including time-varying central pressure from anywhere in the Atlantic Ocean including the Gulf of Mexico. An improved decay model is developed based specifically on statistical analysis of historical hurricane central pressure data from the study region. The results are stored in a database which can be easily mined for site and region-specific hurricane hazard analyses as well as short- and long-term risk studies. Surface wind speed time-histories also were developed at each zip code for a number of recent hurricanes including Fran (1996), Bonnie (1998), Dennis (1999), Floyd (1999), Isabel (2003), and Charley (2004). The wind speed database for these historical hurricanes may be useful for developing hurricane damage (loss) models. [ABSTRACT FROM AUTHOR]

A procedure is presented to develop probabilistic constant-strength ductility demand spectra based on statistical analyses of the results of comprehensive dynamic time history simulations of bilinear single-degree-freedom systems. The procedure offers an approach to estimate both the mean and standard deviation of the ductility demand, given the normalized strength and fundamental system period. The probabilistic distribution of the ductility demands conditional on normalized strength and natural period is validated through goodness-of-fit test. The effects of post-yield stiffness ratio on ductility demand are also investigated. The proposed spectra can allow the treatment of the frequency content and peak intensity measure of the ground motion separately, and describe the state variation of a structure from elastic to inelastic as a function of the peak ground acceleration, which enables its application in stochastic seismic displacement analysis and probabilistic seismic demand analysis. An illustrative example of a seven-story planar frame structure is presented to demonstrate the applicability and utility of the proposed methodology. [ABSTRACT FROM AUTHOR]

A progressive collapse initiates as a result of local structural damage and develops, in a chain reaction mechanism, into a failure that is disproportionate to the initiating local damage. Such collapses can be initiated by many causes. Changes in building practices to address low probability/high consequence events and to lessen building vulnerability to progressive collapse currently are receiving considerable attention in the professional engineering community and in standard-writing groups in the United States, Canada, and Western Europe. Procedures for identifying and screening specific threat scenarios, for assessing the capability of a building to withstand local damage without a general structural collapse developing, and for assessing and mitigating the risk of progressive collapse can be developed using concepts of probabilistic risk assessment. This paper provides a framework for addressing issues related to low probability/high consequence events in building practice, summarizes strategies for progressive collapse risk mitigation, and identifies challenges for implementing general provisions in national standards such as ASCE Standard 7, Minimum design loads for buildings and other structures. [ABSTRACT FROM AUTHOR]

In this paper, the performance of deteriorating bridges is analyzed considering the combination of essential and preventive maintenance actions. Multiobjective optimization under uncertainty is used to find the best combinations of condition, safety, and cost; satisfying all performance constraints of deteriorating bridges during a specified time horizon under multiple maintenance types. The thresholds at which essential maintenance actions are applied and the times of application of preventive maintenance actions are considered as design variables. The evolution in time of nondeterministic performance is modeled as probabilistic condition, safety, and cost profiles, and genetic algorithms are combined with Latin hypercube sampling to optimize the maintenance strategies in a full probabilistic context. Owing to the scarce information on the structural performance effects, due to the interaction among different types of maintenance actions, special attention is paid to the assumptions with respect to the combination of effects of different maintenance types. Examples of application, based on data collected on reinforced concrete bridge crossheads in the United Kingdom, are presented. The benefits of the combination of preventive and essential maintenance actions over single maintenance type strategies are clearly indicated; namely, the reduction in cost for similar condition and safety indices. The use of alternative probabilistic indicators in bridge maintenance, such as the lower percentiles of performance, is also analyzed. [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]

This paper presents methodology and major procedures for the development of analytical urban storm water quality models following derived probability distribution theory, which involves conceptualization of the three major components, i.e., the rainfall–runoff transformation, pollutant buildup, and washoff processes. In this study, two different types of the rainfall–runoff transformations are employed in an attempt to improve model performance by considering spatial variations of parameters associated with runoff generation mechanisms. By integrating different types of the rainfall–runoff transformations and pollutant buildup function with washoff function, two different types of pollutant washoff load models are formulated. Thereby, the probability distributions of the rainfall characteristics are mathematically transformed to create system storm water quality control measures, such as the average pollutant event mean concentration and long-term pollutant loads to receiving waters. These storm water quality control measures are closed-form analytical models and can be employed as alternatives to continuous simulation models for the evaluation of long-term system behavior. The results from case study reveal that with appropriately formulated rainfall–runoff transformation along with pollutant buildup and washoff functions, analytical storm water quality models are capable of providing comparable results to observed data and can serve as effective tools for storm water quality control analysis. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive mathematical model for evaluating the overall performance of a bridge network based on probability analyses of network connectivity, user satisfaction, and structural reliability of the critical bridges in the network. A bridge network consists of all nodes of interest in a geographical region. These nodes of interest are connected to each other through multiple paths. The network performance evaluation in terms of connectivity is formulated by using an event tree technique. The network performance measure of user satisfaction deals with traffic demand and capacity of each link in the network. Moreover, the shortest paths in terms of total traffic costs are identified by network optimization algorithms for each pair of the origin and destination nodes of interest under the specified traffic demands. Using this information, the minimum-weight spanning tree (MST) that consists of the identified shortest paths is constructed. The bridges associated with MST are defined as the critical bridges in the network. The network performance in terms of structural reliability of the critical bridges can be computed from system reliabilities of the critical bridges by using a series-parallel system model. Finally, by combining the above three criteria, a single numerical measure is proposed to evaluate the overall performance of the bridge network. This novel approach is illustrated on a group of fourteen existing bridges with different reliability profiles located in Colorado. This study provides the basis of a network-level bridge management system where lifetime reliability and life-cycle costs are the key considerations for optimal bridge maintenance strategies. [ABSTRACT FROM AUTHOR]

Literature on the probability distribution function (PDF) of annual maximum flood discharges is extensive, yet the literature on the PDF of the flood of record (FOR) is sparse. This is partially due to two facts: (1) the PDF for record events is more complex than the PDF for annual maxima; and (2) data sets for observed FORs are much smaller than for the annual maximum flood series from which they derive. We show that, if annual floods arise from a generalized extreme values (GEV) distribution, then the FOR also arises from another GEV distribution, which we term GEVmax. We also derive the moments and L-moments for the PDF of GEVmax. Using record flood observations at over 1,500 basins in the United States, we compared theoretical and empirical properties of observed values of the FOR. We found that, at both regional and national scales, the FOR values are on average more extreme than would be expected if they occurred randomly, and that they tend to form spatial clusters. [ABSTRACT FROM AUTHOR]

This paper reviews the role of probability density function (PDF) choice on: (1) the statistical characterization of hydraulic conductivity; and (2) the estimation of the local-scale effective hydraulic conductivity. The most widely used skewed PDFs, namely, the lognormal, gamma, and log-gamma PDFs are included in this study. It is shown that the gamma and log-gamma PDFs possess statistical features that render them competitive, if not advantageous, to the more commonly used and better-known lognormal PDF in: (1) the statistical description of hydraulic conductivity; and (2) the estimation of the effective hydraulic conductivity in local-scale groundwater flow. The effective hydraulic conductivity is the parameter relating the average specific discharge to the average hydraulic gradient. Several examples dealing with the statistical analysis of hydraulic conductivity and the estimation of the effective hydraulic conductivity are presented, including a sample of 201 slug-test measurements of hydraulic conductivity in the main clay aquitard underlying Mexico City. [ABSTRACT FROM AUTHOR]

A method of assessing the probability of failure of shallow foundations in saturated fine-grained soil under multidirectional seismic loading is presented. The method uses the distributions of two variables, the spectral acceleration at the fundamental period of the structure and the shear strength of the foundation soil, to form the joint probability density function. The performance function, which defines the required soil strength for the foundation to equilibrate the applied loading, is mapped on this domain. Numerical integration is used to ascertain the probability of failure. A bounded probability density function is used, namely a Pearson Type 1 (Beta) distribution, for soil strength. This distribution provides an upper and lower limit to in situ shear strength. The spectral acceleration is represented by the complementary cumulative distribution function of a Type 1 asymptotic extreme value (Gumble) distribution. Such a distribution is shown to be an accurate representation of real earthquake loading and may be found by a probabilistic seismic hazard analysis for a region. The method is based on pseudostatic seismic loading of the foundation and accounts for spectral acceleration acting along the two horizontal axes. The influence of the orientation of the foundation to the earthquake source is incorporated using the concept of principal directions of ground motion. The performance function is formulated for shallow foundations under eccentric and inclined loading using the recommendations in Eurocode 7. The function is shown to be nonlinear and compound, one part pertaining to the bearing mode of failure (for lower values of acceleration) and the remaining part pertaining to the sliding mode of failure (for higher values of acceleration). An equation is presented for the transition acceleration that separates the performance function into the two parts. A case study is presented and conclusions are drawn about the role of the bearing and sliding modes of failure. [ABSTRACT FROM AUTHOR]

A simple model for evaluating liquefaction probability using cone penetration test (CPT) data is developed based on logistic regression analyses of 396 case histories. The proposed model uses the normalized cone penetration resistance and soil behavior type index as input parameters; therefore, only CPT testing is necessary for evaluating the liquefaction probability of a site. The selection of the model parameters and the expression of equations are based on results of probability examinations and rigorous statistical analyses. Moreover, the derivation of the logistic regression model is presented in a system of equations. The incorporation of these procedures in developing the model not only fully satisfies the statistic requirements but also highlights the physical meanings of the model parameters. Comparisons of the proposed probability model with previously proposed deterministic and probabilistic approaches are performed to demonstrate the improvements. For practical purposes, the developed model is implemented to establish the relationship between the factor of safety against liquefaction and the probability of liquefaction. [ABSTRACT FROM AUTHOR]

Ground motions recorded during earthquakes are often used to assess the seismic performance of structures affected by those ground motions. However, it is necessary to first establish the return period of the recorded ground motion, because structures are expected to perform better for frequently occurring ground motions than for rare ground motions. A systematic approach is presented to establish the return period of ground motion recorded at the base of the Templeton Community Hospital during the 2003 San Simeon California Earthquake. A similar approach can be used for any other ground motion. [ABSTRACT FROM AUTHOR]

The main objective of a bridge manager is to find the best maintenance plan for a group of bridges over a prescribed time horizon. The bridge manager usually faces conflicting objectives, as maintenance plans resulting in safer and less deteriorated structures also lead to higher costs. In general, the problem is posed as a deterministic single-objective optimization where cost is minimized keeping performance above predefined thresholds. However, single-objective optimization results in only one optimal solution that does not provide the advantages of considering other objectives and constraints. In addition, the effects of uncertainties are not taken into account or are included in a very simplified way. The bridge manager obtains, in this way, only one deterministic optimum maintenance plan, and not a set of different probabilistic maintenance solutions from which the best, for each particular situation, can be chosen. In this paper, a full probabilistic multiobjective approach to bridge maintenance considering single maintenance types is developed. This approach is based on the latest developments in bridge management by considering probabilistic continuous performance indicators and probabilistically defined objectives and constraints. The problem is solved using multiobjective genetic algorithms and a Latin hypercube sampling technique. Multiobjective applications to existing reinforced concrete bridge components under probabilistic deterioration and probabilistic-defined single maintenance types are presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper the problem of calculating the probability of failure of linear dynamic systems subjected to random vibrations is considered. This is a very important and challenging problem in structural reliability. The failure domain in this case can be described as a union of linear failure domains whose boundaries are hyperplanes. Each linear limit state function can be completely described by its own design point, which can be analytically determined, allowing for an exact analytical calculation of the corresponding failure probability. The difficulty in calculating the overall failure probability arises from the overlapping of the different linear failure domains, the degree of which is unknown and needs to be determined. A novel robust reliability methodology, referred to as the domain decomposition method (DDM), is proposed to calculate the probability that the response of a linear system exceeds specified target thresholds. It exploits the special structure of the failure domain, given by the union of a large number of linear failure regions, to obtain an extremely efficient and highly accurate estimate of the failure probability. The number of dynamic analyses to be performed in order to determine the failure probability is as low as the number of independent random excitations driving the system. Furthermore, calculating the reliability of the same structure under different performance objectives does not require any additional dynamic analyses. Two numerical examples are given demonstrating the proposed method, both of which show that the method offers dramatic improvement over standard Monte Carlo simulations, while a comparison with the ISEE algorithm shows that the DDM is at least as efficient as the ISEE. [ABSTRACT FROM AUTHOR]

This paper presents a general approach to the probabilistic prediction of the structural service life and to the maintenance planning of deteriorating concrete structures. The proposed formulation is based on a novel methodology for the assessment of the time-variant structural performance under the diffusive attack of external aggressive agents. Based on this methodology, Monte Carlo simulation is used to account for the randomness of the main structural parameters, including material properties, geometrical parameters, area and location of the reinforcement, material diffusivity and damage rates. The time-variant reliability is then computed with respect to proper measures of structural performance. The results of the lifetime durability analysis are finally used to select, among different maintenance scenarios, the most economical rehabilitation strategy leading to a prescribed target value of the structural service life. Two numerical applications, a box-girder bridge deck and a pier of an existing bridge, show the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

A probabilistic approach is proposed to help select the most suitable nondestructive inspection (NDI) technique and associated optimal schedule for fracture-critical member/detail fatigue inspections on a specific steel bridge. The probability of detection (POD) function for the NDI technique, which is a measure of the detection accuracy, is employed. By combining probability calculations based on use of the POD function together with numerical Monte Carlo simulations of the crack propagation of the fracture-critical detail, a cost function is formulated that includes the expected cost of inspections and failure resulting from the chosen NDI technique and alternative inspection schedules. In summary, the selection of an NDI technique with an associated inspection schedule for fracture-critical inspections is formulated as an optimization problem that can guarantee minimum total cost. The inspection frequency is determined as part of the optimization that utilizes appropriate constraints on inspection intervals and a minimum acceptable (target) structural safety level. A case study for a box girder bridge is presented to demonstrate the application of the proposed probabilistic method. [ABSTRACT FROM AUTHOR]

This paper summarizes methods and results for a recent precipitation frequency study of the Kansas City metropolitan area. The study was motivated by prevalent concern that frequency estimates used for hydrologic design and analysis are based on studies published decades ago. Data currently used for design were extracted from National Weather Service (NWS) rainfall atlases TP-40 and HYDRO-35, published in 1961 and 1977, respectively. Results of this study are compared to those two atlases and a third regional study published by Huff and Angel in 1992. In general, the rainfall depths predicted by this study are higher than TP-40 and HYDRO-35 for return periods longer than 10 years, yet for short durations and low return periods, the converse is true. For the most part, rainfall depths from this study are within a few percent of NWS estimates. [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]

This paper describes a stochastic simulation-based scheduling system (S3) that: (1) integrates the deterministic critical path method (CPM), the probabilistic program evaluation and review technique (PERT), and the stochastic discrete event simulation (DES) approaches into a single system and lets the scheduler make an informed decision as to which method is better suited to the company’s risk-taking culture; (2) automatically determines the minimum number of simulation runs in DES mode and therefore optimizes the simulation process; and (3) provides a terminal method that tests the statistical significance of the differences between simulations, hence eliminating outliers and therefore increasing the accuracy of the DES process. The system is based on an earlier version of the system called stochastic project scheduling simulation and makes use of all the capabilities of this system. The study is of value to practitioners because S3 produces a realistic prediction of the probability of completing a project in a specified time. The study is also of relevance to researchers in that it allows researchers to compare the outcome of CPM, PERT, and DES under different conditions such as different variability or skewness in the activity duration data, the configuration of the network, or the distribution of the activity durations. [ABSTRACT FROM AUTHOR]

Accurate prediction of the current and future conditions of wastewater systems using available assessment data is crucial for developing appropriate proactive maintenance and rehabilitation strategies for an aging wastewater collection and conveyance system. This paper proposes a method to estimate the transition probabilities of different condition states in Markov chain-based deterioration models for wastewater systems using an ordered probit model. The proposed model is applied and evaluated using the condition data of sewer pipes managed by the City of San Diego’s Metropolitan Wastewater Department. The developed model presents some advantages in estimating transition probabilities over the approaches developed in the past, including the nonlinear optimization-based approach, in terms of versatility in the implementation, precision of the estimated data, and appropriateness of the assumptions in the model. The paper concludes that the ordered probit model approach is a statistically sound and robust method; however, in order to gain greater accuracy in deterioration modeling, periodic assessment of the wastewater systems with more data types is desirable. [ABSTRACT FROM AUTHOR]

Many earth structures, including foundations, retaining walls, and road embankments, exhibit signs of distress, such as excessive vertical or lateral movements and cracking. Rotation or tilting and cracking of the structural components in retaining walls are quite common and constitute the majority of cases of concern in built-up areas. This paper describes a general iterative methodology for the diagnosis of existing civil infrastructure, with emphasis on geotechnical problems. The term diagnosis, as used in this paper, refers to the process of determining a set of technical explanations for the occurrence of the observed defects. Using probability theory, the investigating engineer is in a better position to make informed decisions rather than simply relying on experience and intuition. Engineering decisions include the correctness of a given hypothesis; whether further investigations are necessary or a terminal decision can be made; and whether appropriate corrective action can be undertaken. A case study is used to demonstrate the application of the methodology. [ABSTRACT FROM AUTHOR]

In this paper, the issue of model uncertainty is examined in detail within the framework of the first-order reliability method (FORM). The focus of the paper is on the characterization of the uncertainty of a shear wave velocity-based simplified model for liquefaction potential evaluation developed by Andrus and Stokoe. This simplified model is expressed as a boundary curve that defines liquefaction resistance as a function of the corrected shear wave velocity. The uncertainty of this simplified model is represented by a lognormal random variable, and characterization of the model uncertainty mainly involves the determination of its two statistics, namely, the mean and the coefficient of variation. A trial-and-error procedure is used to determine the two statistics of the model uncertainty based on a Bayesian mapping function that is calibrated with a database of case histories. This procedure is shown to be effective in the present study, and the uncertainty of the Andrus and Stokoe’s model is characterized. With the known model and parameter uncertainties, the probability of liquefaction can be determined through a routine FORM analysis. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of determining the optimal daily operating policy of a small reservoir subject to yearly probabilistic constraints on floods and shortages. The problem is difficult to solve because the reservoir inflows on day k are stochastic and correlated with those on days k-1,k-2,...,k-n. The problem is broken down into two subproblems that are solved with a set of inflow scenarios and not with the conditional probability distributions of the inflows. The first subproblem determines the conditions to be respected each day for the yearly probabilistic constraints to be satisfied. The second finds the reservoir’s optimal feedback operating policy for each day of the year that respects those conditions. This method is applied to the Kenogami reservoir located in Quebec, Canada, and the results are presented. The method is robust, fast to execute, and easy to program. Furthermore, it does not require that the problem be linear or differentiable. [ABSTRACT FROM AUTHOR]

This paper describes a study to develop site-specific probabilistic snow load models for use in reliability analyses of structures in the United States. Annual maximum snow water-equivalent depth data measured at 93 first-order weather stations was obtained from the National Climatic Data Center. These were then converted to annual maximum ground snow loads and statistics at each site were obtained using graphical fitting techniques. The 50 year maximum roof snow load values (in ratio to code-specified nominal values) were then evaluated site by site using the statistics for annual maximum ground snow, extreme value theory, Monte Carlo simulation, statistics for ground to roof conversion factors, and the nominal ground snow load values in ASCE 7. Finally, the 84 sites in the continental United States (excluding nine sites in Alaska) were grouped on the basis of the 5% exclusion values of actual to nominal 50 year maximum roof snow load. Aggregated statistics for 50 year roof snow load in three geographic regions (designated Northeast, Midwest/Mid-Atlantic, and Northern Midwest/Mountain West) were determined. The roof snow load models developed in this study can be used in code calibration studies and development of next-generation partial safety factors. Snow load models such as those developed herein are developed using data from weather stations typically located at airport or military base locations. Therefore, they are not applicable to special locations such as mountainous regions or gorges. ASCE 7 suggests that design snow loads in such cases should be based on local snow information with consideration given to the orientation, elevation, and records available at each location. Using the state of Oregon as an example, this study also develops county-scale design ground snow load curves and then postprocesses this information into snow hazard curves. Both the design ground snow load curves and the snow hazard curves are presented as functions of elevation for each county area (defined as areas having similar ground snow load versus elevation relationships). To evaluate structural performance of a building subjected to snow load in a performance-based framework, snow hazard curves can be convolved with fragility curves for the building. This study demonstrates one approach for developing snow hazard curves for special regions (mountain areas and gorges) for use in such performance-based design applications. [ABSTRACT FROM AUTHOR]

The time-varying performance of deteriorating materials and structures can be simulated using probabilistic methods. The propagation of performance uncertainties is affected by the characteristics of input random variables. In general, the number of samples and/or their quality do not satisfy the rigorous statistical constraints required to obtain reliable probability distributions. This deficiency encountered at the beginning of assessment process can be alleviated later by investigating the importance of variables through variability and sensitivity analyses. These analyses help the identification of significant variables in a quantitative way. In this paper, evaluation of the time-varying performance of deteriorating materials and its effect on structures measured by the reliability index profile is addressed based on three aspects: (1) acquisition of statistical characteristics of input random variables from imperfect samples; (2) model-based simulation; and (3) evaluation of variability and sensitivity measures of the nondeterministic performance model. Examples are presented to illustrate these aspects. [ABSTRACT FROM AUTHOR]

Probabilistic techniques are of vital use in predicting the seismic story drifts of buildings, which vary due to uncertainties in the characteristics of future earthquake motions. This paper proposes a procedure for evaluating the expected mean and standard deviation of seismic story drifts of reinforced concrete buildings by considering both total and story failure mechanisms. The estimation process consists of a pushover analysis of the structure against inverted triangular forces to evaluate the most probable mechanism during earthquakes, followed by consideration of the relative reserve strengths to evaluate the probability of other mechanisms. The relative reserve strengths against story and total mechanisms are expressed by two newly defined story-safety and total-reduction factors, respectively. In this paper, the proposed procedure is verified by conducting dynamic response analyses of 9-story wall and frame structures with various story-safety and total-reduction factors using 36 records from 14 different earthquakes. The proposed procedure well predicted the mean and standard deviation of story drifts of the structures. Application to wall-frame structures is also discussed. [ABSTRACT FROM AUTHOR]

A fragility analysis methodology is developed for assessing the response of light-frame wood construction exposed to stipulated extreme windstorms and earthquakes. Performance goals and limit states (structural and nonstructural) are identified from a review of the performance of residential construction during recent hurricanes and earthquakes in the United States. Advanced numerical modeling tools provide a computational platform for risk analysis of light-frame wood building structural systems. The analysis is demonstrated for selected common building configurations and construction (defined, e.g., by roof sheathing, truss spacing, and roof or shear wall nailing patterns). Limit state probabilities of structural systems for the performance levels identified above are developed as a function of 3-s gust wind speed (hurricanes) and spectral acceleration (earthquakes), leading to a relation between limit state probabilities and the hazard stipulated in ASCE Standard 7, "Minimum design loads for buildings and other structures." [ABSTRACT FROM AUTHOR]

This paper presents an analytical probabilistic based design procedure for concentrically loaded compression members of fiber-reinforced polymeric composite materials. Resistance factors for use in a load and resistance factor design format are developed for flexural buckling of doubly symmetric sections, both flexural buckling and flexural-torsional buckling of equal leg angles, and material failure. The developed resistance factors are a function of the coefficient of variation of the appropriate material properties. The proposed resistance factors were determined to provide a reliability index of 3.0 for buckling limit states and a reliability index of 3.5 for the material fracture limit state. A proposed method of developing an allowable stress design code is also given. [ABSTRACT FROM AUTHOR]

A new way of incorporating fuzzy logic concepts is introduced in order to better capture and manage some uncertainties in applying stochastic dynamic programming (SDP) formulations for reservoir operation. A model called fuzzy-state stochastic dynamic programming (FSDP), which takes into account both uncertainties due to random nature of hydrological variables and imprecision due to variable discretization is introduced in this study. In this model, fuzzy transition probabilities for stochastic hydrologic state variables are calculated by defining a fuzzy Markov chain. These fuzzy probabilities are derived based on fuzzy frequency concept considering different frequencies for different points of a class interval. In order to show how effective the proposed method is, FSDP was applied to the Zayandeh–Rud river–reservoir system in Isfahan, in the central part of Iran, and was compared with a demand driven stochastic dynamic programming model. The results show the robustness of the FSDP solutions with respect to the type of discretization scheme used in calculating the transition probabilities. [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]

Persistence is the most important property in any hydrologic design concerning the storage capacity of reservoirs, average return periods, failure risks, and drought properties. Its consideration in analytical derivations of design criteria presents difficulties, especially in autocorrelated hydrologic processes, and for this reason, most often the analytical expressions are obtained on the basis of non-persistent (independent) cases. Although the conventional autocorrelation coefficients and function are used in many hydrological design problems, the very definition of the autocorrelation function requires that the underlying hydrologic process generating mechanism abide with normal (Gaussian) probability distribution function in addition to other restrictive assumptions. Since almost all of the analytical stochastic approaches are based on the normality assumption, it is necessary to transform non-Gaussian distributions to the normal distribution to use analytical expressions. During the transformation process, the very genuine persistence property of the basic hydrologic variables is not preserved, even when the statistical parameters such as the average, standard deviation, skewness coefficient, kurtosis, etc., are maintained in the transformed data. This shortcoming in the autocorrelation function is by-passed by the introduction and use of an autorun function, which is probability distribution free and a robust parameter. Its basis is the conditional probability statement which does not require any assumptions in practical applications. Various practical and simple hydrological design quantities are developed on the basis of the autorun coefficients without considering the conventional autocorrelation structure. The application of methodology is presented for John’s river in Florida. [ABSTRACT FROM AUTHOR]

The paper illustrates the procedures for computing the probability of failure occurrence that represents the potential that a slope can undergo failure due to both the spatial variability of the structural and geomechanical aspects of the joint sets and the existing boundary conditions. The presented approach to a global probabilistic assessment of the rock slopes stability conditions is based on the analysis of the spatial variability of structural aspects of the rock mass, of the uncertainty in geomechanical properties, and of the occurrence probabilities of certain values of seismic forces and rainfall intensities. Finally, the probability of failure recurrence is computed taking into account occurrences, in time, of the external acting forces, so providing an evaluation of the rock slope landslide hazard, that is the probability that an instability event with a given intensity may occur within a reference time period. [ABSTRACT FROM AUTHOR]

This paper proposes a newapproach, entitled discrete event simulation with probabilistic event list (DESPEL), for approximating the project completion time and the critical path in a stochastic resource-constrained project network. Unlike the traditional discrete event simulation approach, which is based on replications to find the project completion time, this approach only requires one simulation run. This approach is similar to the programevaluation and review technique (PERT) approach in the sense that it considers the path with the highest expected activity duration as the critical path. However, it extends the capability of the PERT by considering the resource constraints when finding the critical activities and project completion time. [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]

In this paper, a hydrometeorological approach to the probabilistic simulation of soil moisture is proposed. The time series of in situ soil moisture and meteorological variables at a monthly scale from different monitoring stations across India are utilized. Preliminary investigation with both precipitation and near-surface air temperature as meteorological variables reveals that the strength of association between soil moisture and precipitation is more significant compared to that between soil moisture and temperature. Precipitation-based probabilistic estimation of soil moisture using the proposed hydrometeorological approach is tested with in situ observed soil moisture data and with soil moisture data of the Climate Change Initiative project, funded by the European Space Agency. The results are found to be promising. In addition, the proposed hydrometeorological approach is able to provide the information on uncertainty associated with the estimation. It is also shown that the parameter of the developed model is linked to the predominant soil textural class. Higher values of the model parameter [dependence parameter () for the selected copula] correspond to clay loam, medium values correspond to loamy sand or loam, and low values correspond to sandy loam to sandy soil. Three stations outside India, which are widely separated across the globe with known soil textural class, are also considered, and the performance of the proposed model is tested by estimation of the model parameter depending on the soil textural class. The results are found to be reasonably good, indicating the spatial transferability of the proposed approach. [ABSTRACT FROM AUTHOR]

Based on a wind-vehicle-bridge analysis system and quasi-steady pneumatic force coefficient data obtained from wind tunnel tests, the problem of moving vehicles on a cable-stayed bridge deck overturning in a strong wind environment is studied, with the probability evaluation as the emphasis. It is put forward that the evaluation of a vehicle's overturning is a probability problem that a stochastic process overpasses a threshold level, and the influence of the statistic process characteristics of excitations on driving safety is profoundly discussed in the paper. The analysis shows that the higher the driving speed, the more obvious the effect of statistic process characteristics tends to be. Moreover, the influence degree of stochastic process characteristics is relevant to the wind velocity range of the dynamic reliability curve and the range of the probability distribution for the mean wind velocity. When the range of the former is broad enough and overlaps with the range of the latter, the influence of stochastic process characteristics should be considered. Wind barriers can promote a safe driving velocity from 80 to under normal weather conditions. Under extreme weather conditions, traffic control measures should be implemented to maintain the bridge's traffic service. Wind barriers together with the speed limitation () can ensure that a truck passes the bridge safely during storm conditions (, Beaufort Scale 10). When the natural wind is a violent storm (, Beaufort Scale 11), the speed limitation should be . [ABSTRACT FROM AUTHOR]

Corrosion of steel reinforcement due to chloride penetration is a major deterioration mechanism of reinforced concrete (RC) structures exposed to marine environments. In the present paper, a probabilistic model is presented to predict the chloride penetration profile in concrete and the risk of steel corrosion considering the time dependence of both the diffusion coefficient and the surface chloride concentration of concrete. Abundant field data from two projects in China and Japan are respectively collected. The consistency between these field data and the model prediction verified the reliability of this probabilistic model, based on which further parametric analyses were carried out to investigate the effects of different design variables on the probability of steel corrosion. [ABSTRACT FROM AUTHOR]

Earthquakes are rare natural catastrophes, causing severe impacts on society due to loss of lives, damage to built facilities, and business interruptions. After a large earthquake (mainshock), many induced events (aftershocks) may be triggered and cause additional damage or even collapse to mainshock-damaged buildings. To reduce seismic hazard and risk of aftershocks and extend the current performance-based earthquake engineering framework, the effects of aftershocks on the seismic performance of structures should be incorporated. Considering an extensive set of real and artificial mainshock-aftershocks sequences, the vulnerability of residential wood-frame houses in southwestern British Columbia, Canada, is examined analytically using incremental dynamic analysis. Subsequently, seismic loss estimation is conducted for four wood-frame house types with different seismic capacities. The analysis results indicate: (1) moderate effects of aftershocks (5-20%) on maximum structural response and damage extent, and (2) significant impact of structural seismic capacity on estimated seismic loss. [ABSTRACT FROM AUTHOR]