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Despite the clearly stated procedures in current standards, and contrary to its name, nonstandard execution of the standard penetration test (SPT) has been common. The use of different equipment and procedures produces significantly different SPT blow counts. To minimize the effects of these differences, correction factors are applied. Two of these corrections factors, namely hammer energy efficiency ratio (CE) and rod length (CR) corrections, are the scope of this research study. With the intent of quantifying the effects of variabilities and reducing the uncertainties, SPT hammer efficiency measurements were compiled from available literature. Additionally, new hammer energy measurements were performed in the field, controlling the variables of the problem. The resulting database is used to probabilistically develop a set of new CE and CR recommendations. The recommended mean energy ratios for safety hammer and automatic hammers are estimated as 67%±11% and 78%±12% , respectively, which are higher than typically assumed values in engineering practice. The recommended rod length correction values at shallow depths, proven to be also a function of SPT blowcounts, N (SPT-N) values, are higher than typically used values. This suggests less pronounced rod length effects. Additionally, a modified procedure to assess the stress-wave energy at anvil and above the SPT sampler elevations is introduced. [ABSTRACT FROM AUTHOR]

Rainfall infiltration causes the collapse of unsaturated embankments due to loss of suction. In this paper, the Barcelona Basic Model (BBM), a constitutive model developed for unsaturated soils, was implemented in Fast Lagrangian Analysis of Continua (FLAC) for simulating the effect of varying rainfall intensities on compacted embankments. It was observed that large vertical deformations occur and considerably high positive pore-water pressures get developed, accounting for the collapse of an embankment. The results also show that rainfall intensity and duration affect the slope stability. A comparison was made between the results obtained using the Mohr–Coulomb model and BBM. It was found that the soil undergoes larger deformations when modeled using BBM as BBM accurately models the loss of suction upon saturation. Reliability analysis of embankment shows that probabilistic analysis provides a better assessment of slope stability rather than the factor of safety and shows that suction and hydraulic conductivity are critical parameters influencing slope reliability for unsaturated soil slope embankments. [ABSTRACT FROM AUTHOR]

A novel statistical framework was developed to quantify the variability of the fitting parameters of the soil–water characteristic curve (SWCC). Reliable estimation of the mean, standard deviation, and associated probability density function (PDF) of the fitting parameters of SWCC is an important tool for addressing reliability-based designs in unsaturated soil mechanics. The assumption of either Gaussian or lognormal distributions may not be valid for representing a high degree of variability associated with fitting parameters. This study aimed to provide the most appropriate continuous PDFs by optimizing the mean and standard deviation such that errors associated with quantile, percentile, and cumulative distribution function (CDF) were as low as possible. A total of 261 and 111 sample points were collected from the most comprehensive experimental works on the fitting parameters of SWCC for clayey and silty soils, respectively. Optimum distributions suitable to the model fitting parameters of SWCC are highly dependent on the type of soil. The most appropriate PDFs for representing the fitting parameters af , nf , and mf of Fredlund and Xing's model were gamma, Weibull, and inverse Gaussian distributions, respectively. Similarly, fitting parameters af , nf , and mf for silty soils were represented by inverse Gaussian, Gumbel maximum, and Gumbel maximum distributions, respectively. This study found that the selection of inappropriate PDFs overestimated the probability of failure of unsaturated infinite slopes considerably, by 99.49% and 99.76%, respectively, for clayey and silty soils. Recommended mean, coefficient of variation (COV), and PDF are useful in the reliability-based design of unsaturated soil slopes and in judging the performance of existing infinite and finite slopes. [ABSTRACT FROM AUTHOR]

This paper considers the case of a relatively large number of parallel columns that buckle simultaneously. The close proximity between columns results in the possibility of contact between adjacent columns as buckling proceeds, and this brings with it some interesting observations on load-carrying capacity. Some experimental results verify the theoretical development based on the versatility of high-fidelity 3D printing, but also highlights the difficulty of applying purely axial loading. The sensitive nature of initial geometric imperfections (slight lack of straightness) and load eccentricity strongly influence postbuckled contact, load-carrying capacity, and, as the number of columns is increased, a statistically based evaluation of anticipated behavior is explored and ultimately found to be unrealistic. [ABSTRACT FROM AUTHOR]

The design of marine structures requires the simulation of wave parameters that consider sea-state and water-depth transitions. Proper selection of the model coefficients (e.g., alpha and gamma of the JONSWAP spectra) is then required, because of the wave-hydrodynamic nonlinearities during these ocean processes. Therefore, the model coefficient selection should be tested using a nonlinear analysis to assess the effect of the selected spectra coefficients over the modeled wave parameters. The present study performed a design of experiment (DOE)-analysis of variance (ANOVA) and probability analysis to assess the effect of alpha and gamma parameters over the significant wave height (Hs) and peak period (Tp) during sea-state and water-depth transitions. The DOE-ANOVA demonstrated for the mean and extreme wave states of the study area that alpha and gamma parameters positively affect the Hs behavior in deep and intermediate waters. Furthermore, the standardized effects of alpha and gamma over the Tp during extreme wave states suggest quadruplets of wave–wave interactions. The joint and normal probability distributions of alpha and gamma for extreme and normal waves showed a Gaussian distribution, allowing identification of specific alpha and gamma values for the JONSWAP spectra model. The selected alpha and gamma parameters were then validated through the comparison of the modeled Hs (JONSWAP) against other local studies. Considering its relevance in design strategies for offshore structures, this research contributed to the understanding of the nonlinear effects of alpha and gamma parameters over the Hs and Tp during variations of water depth and wave states, easing the selection of the model coefficients. [ABSTRACT FROM AUTHOR]

Seismic shutoff devices are expected to automatically stop the flow of hazardous gases and liquids through distribution systems that may be damaged by earthquakes. There is some uncertainty in the actuation of these devices; they may actuate when not needed and they may not actuate when needed. Therefore, these devices can only reduce, and not eliminate, the risk of hazardous leaks. It is shown in this paper that shutoff devices can be deployed to meet specific performance goals in seismic design. A cost-benefit analysis is conducted to show that devices are most effective in reducing the risk to weak systems in highly seismic areas. The uncertainty in actuation diminishes the effectiveness of these devices. [ABSTRACT FROM AUTHOR]

Slope stability analysis has traditionally been performed using a deterministic approach. However, it has strongly been debated that the use of only the factor of safety in slope stability analysis does not explicitly account for all the uncertainties in soil parameters. Therefore, to investigate the effect of uncertainties in the stability of a fill slope, this paper uses the finite-element limit analysis methods to conduct a simple probabilistic-based analysis of two-layered undrained clay slopes. The results obtained show that although the recently developed stability charts for two-layered undrained clay may be convenient tools, the factors of safety calculated from the charts may not be sufficient. Particularly, it is shown that the probability of failure of this type of slope can be highly influenced by uncertainties in the soil properties. Various probabilistic charts based on different coefficients of variation in soil properties have been proposed in this paper. Based on this study, the recently developed charts for two-layered undrained clay slopes can be better applied. Additionally, this study also demonstrates the applicability of the finite-element upper and lower bound limit analysis methods to conduct probabilistic slope stability analyses. [ABSTRACT FROM AUTHOR]

Right-turn channelization is used to improve the capacity at busy intersections with a lot of right-turns. However, under heavy traffic conditions the through lane vehicles might backup and block the channelization lane. This will affect the discharge rate of right-turning vehicles and reduce the approach capacity. If the right-turn channelization gets blocked frequently, its advantage is neglected and serious capacity problems can be overlooked. This issue is not addressed in the Highway Capacity Manual (HCM), and no separate model is provided to estimate the capacity of approaches with channelized right-turn lanes. Using conventional methods for estimating the capacity without considering the effect of potential blockage would result in overestimation of the approach capacity. This paper presents a probabilistic capacity model for signalized intersections with channelized right-turn lanes considering the possibility of the right-turn vehicles being blocked from accessing the channelization lane. The capacity model was developed as a function of the short-lane section length and the proportion of right-turn traffic by taking into account the probability of blockage. Subsequently, a model was developed to estimate the probability of blockage with respect to the possible residual queue. The proposed capacity model and the blockage probability model were validated on the basis of VISSIM simulations. For operational purposes, the recommended lengths of the short-lane section were developed to prevent blockage at a certain threshold. The recommended lengths would be useful in evaluating adequacy of the current lengths, identifying the options of extending the short-lane section length, or changing signal timing to reduce the likelihood of blockage. [ABSTRACT FROM AUTHOR]

A maximum entropy (MaxEnt) method is developed to predict mean external and internal flow rates and mean pressure gradients (potential differences) in hydraulic pipe networks, without or with sufficient constraints to enable a closed-form solution. This substantially extends existing methods for the analysis of flow networks (e.g., Hardy Cross), applicable only to deterministic networks. The analysis is based on a continuous relative entropy defined on the space of flow rates, requiring one dimension for each edge and node within the network. This entropy is maximized subject to observable constraints on the mean values of certain flow rates and/or potential differences, and also physical constraints arising from Kirchhoff's first and second laws (node and loop constraints) and the frictional properties of each pipe. A semianalytical and numerical algorithm is developed to solve the equation system, which involves implicit solution of multidimensional integrals and root finding with quasi-Newton and Newton methods. The analysis is demonstrated by application to (1) a simple three-node network, and (2) a 1123-node, 1140-pipe water distribution network in the suburb of Torrens, Australian Capital Territory, Australia. [ABSTRACT FROM AUTHOR]

A methodology for cost-effective design of jet grouted water-sealing bottom plugs is presented in this paper. These massive barriers, made of partially overlapping jet grouted columns, are required to ensure temporary waterproofing to excavation areas and adequate uplift resistance against water loads. Therefore, the proposed calculation procedure simultaneously focuses on the structural performance and continuity of the plug. The design may be optimized by considering the possibility of reducing column length, performing injections only in the lower part of the plug, and leaving the upper part of the plug untreated. The reduction in column length may then result in a very slender slab, and a structural check has to be performed to avoid tension fracturing or overall structural collapse. Additionally, in spite of strict controls, jet grouted columns are never perfectly cylindrical or exactly aligned along their prescribed position, and thus the plug may present imperfections. Statistical evaluation of defects with experimental data from different field trials and their simulation with the Monte Carlo method shows that the imperfections are less relevant for the structural performance of the plug, but must be carefully taken into account in the analysis of seepage. Imperfections have been thus introduced in the structural analysis by means of partial factors evaluated from probabilistic analysis. The latter calculation provides a rule to control the effects of incomplete watertightness of the plug. The introduced relations are expressed with design charts. [ABSTRACT FROM AUTHOR]

Concrete gravity dams are essential infrastructure components and because of earlier design practices, they may be vulnerable to future earthquake events. Therefore, their vulnerability is important to characterize, particularly given the large societal consequences of dam failure. Seismic fragility curves allow a rational safety and vulnerability assessment of existing structures under earthquake hazards offering statements of the conditional probability of reaching a limit state. This paper evaluates the seismic fragility of a case study concrete dam located in northeastern Quebec, improving on existing approaches by including spatial variation of the angle of friction and offering insights regarding the significance of modeling parameters, importance of spatial variation, and overall vulnerability of the dam to two failure modes. Finite-element techniques are used to model the dam system and to fully account for dam-reservoir-foundation interactions. Uncertainties in the ground motions and modeling parameters are included and propagated using a sampling technique. The fragility curves are developed using nonlinear time-history analysis, and the uncertainty related to the spatial variation of the angle of friction is included in the fragility analysis through the incorporation of random fields modeling. The study reveals that this additional source of uncertainty has a slight effect on the fragility of the dam and is mainly critical when severe damage levels are considered. [ABSTRACT FROM AUTHOR]

This paper presents an approach to fatigue reliability assessment of railway bridges based on probabilistic dynamic analysis of a coupled train-bridge system. The fatigue loading from moving trains is investigated through a novel approach in which three-dimensional (3D) numerical models of both the train and the bridge are integrated with a wheel-rail interaction model to perform coupled dynamic analysis. The results of this analysis are used to estimate the long-term fatigue loading and the time-variant fatigue reliability of bridge details. Train speed and track irregularities are selected as random variables in the coupled train-bridge system model. Probabilistic dynamic stress analysis is conducted for each train passage to obtain samples of the stress range and its cycle count. This information is used to identify the probability distributions of the stress range. Fatigue reliability is evaluated by solving a fatigue limit-state function established through the S-N approach. Effects of train speed and track irregularities on the fatigue loading and fatigue reliability are analyzed and discussed. Additionally, the proposed approach is illustrated on an existing steel railway bridge. [ABSTRACT FROM AUTHOR]

A probabilistic cone penetration test (CPT) based liquefaction triggering procedure for cohesionless soils is derived using a maximum likelihood method with an updated case history database. The liquefaction analysis framework includes revised relationships for the magnitude scaling factor (MSF) and for estimating fines contents from CPT data when laboratory test data are not available. The updated case history database and methodology for developing the liquefaction correlation are described. Measurement and estimation uncertainties, the potential effects of false positives and false negatives in the case history database, and the effects of the choice-based sampling bias in the case history database are accounted for. Sensitivity analyses showed that the position of the most likely triggering curve and the magnitude of the total error term are reasonably well constrained by the data. The sensitivity study provides reasonable bounds on the effects of different interpretations, from which probabilistic and deterministic relationships for practice are recommended. [ABSTRACT FROM AUTHOR]

If a contamination event occurs in a water distribution system, sensors in the network may observe water quality changes. The data from these sensors can be used to identify the source of the contamination. The sensors can be binary sensors that record the presence or absence of contamination, fuzzy sensors that measure concentration within a set range, or perfect sensors that measure the exact concentration within the bounds of measurement uncertainty. This work presents an adjoint-based probabilistic approach for identifying the source node, source release time, and source strength for an instantaneous release of contamination based on sensor observations and known system hydraulics. In the adjoint approach, information is propagated upgradient from the sensors to the possible source nodes. EPANET is used to simulate the transient hydraulics of the pipe network and the upgradient propagation of the adjoint state through the network. The resulting adjoint states are related to probability density functions of the source release times at all possible source nodes. For fuzzy or perfect sensors, these probabilities can be used to determine the most likely source node. A hypothetical example is used to show that this method is accurate, even for a small number of sensor observations and complex hydraulics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a decision support tool for contractors before the bidding stage to quantify the probability of delay in construction projects in Turkey by using the relative importance index (RII) method incorporated into fuzzy logic. For this purpose, 83 delay factors were identified, categorized into 9 major groups through a detailed literature review process as well as interviews with experts from the construction industry. The relative importance of these delay factors and groups was quantified by using the relative importance index method. The ranking of the factors and groups was demonstrated according to their level of effect on delay. A delay assessment model was proposed using the fuzzy set theory by taking into account the delay factors characterized in construction projects. The assessment model was developed using a commercial software product. The proposed methodology was tested in a real case study; and the probability of the delay of the project was evaluated by means of the assessment model after the required inputs were entered into the software. The factors and groups that contribute most to the probability of delays were discussed depending on the case study results. The assessment model results were found to be satisfactory. Finally, some recommendations were made in order to minimize and control delays in construction projects. [ABSTRACT FROM AUTHOR]

The determination of a project's cost contingency is a pervasive problem as the amount that is incorporated into an estimate is invariably insufficient to accommodate a project's actual cost overrun. The cost overruns experienced in 49 road construction projects procured using traditional lump contracts are analyzed. The theoretical probability distributions are fitted to cost overrun data derived from the sampled projects whose contract values ranged from AU $0.5 and AU $97 million. Goodness of fit tests are used in conjunction with probability-probability (P-P) plots to compare the sample distribution from the known theoretical distribution. A log logistic probability density function (PDF) was found to best describe the behavior of cost overruns. The cumulative distribution function is then used to determine a realistic probability of a cost overrun being experienced from the point at which a contract is awarded. This is required so that public sector clients can determine an appropriate contingency at contract award, which takes into account the nuances that contribute to increasing project costs. The research findings and methodology adopted to determine the best fit probability distribution provides a more robust approach for governing a construction contingency for road construction projects so that they can be procured successfully. [ABSTRACT FROM AUTHOR]

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]

To quantitatively estimate the contributions of component failure modes to system output, failure-mode importance measures have been proposed in this paper. This issue is discussed in two schemes: in Scheme 1, failure-mode importance is measured by the change in the characteristics of the system output after removal of the interested failure mode; and in Scheme 2, failure-mode importance is measured by the expected change in the characteristics of the system output after fixing the failure mode of interest at nominal values. Properties and the computational strategies of the failure-mode importance measures also are presented. Discussions with numerical and engineering examples demonstrate that the importance measures are of great significance for the purpose of system improvement. [ABSTRACT FROM AUTHOR]

Solving the Fokker-Planck-Kolmogorov (FPK) equation is one of the most important and challenging problems in high-dimensional nonlinear stochastic dynamics, which is widely encountered in various science and engineering disciplines. To date, no method available is capable of dealing with systems of dimensions higher than eight. The present paper aims at tackling this problem in a different way, i.e., reducing the dimension of the FPK equation by constructing an equivalent probability flux. In the paper, two different treatments for multidimensional stochastic dynamical systems, the FPK equation and the probability density evolution method (PDEM), are outlined. Particularly, the FPK equation is revisited in a completely new way by constructing the probability fluxes based on the embedded dynamics mechanism and then invoking the principle of preservation of probability. The FPK equation is then marginalized to reduce the dimension, resulting in a flux-form equation involving unknown probability flux caused by the drift effect. On the basis of the equivalence of the two treatments, this unknown probability flux could be replaced by an equivalent probability flux, which is available using the PDEM. An algorithm is proposed to adopt the data from the solution of the generalized density evolution equation in PDEM to construct the numerical equivalent flux. Consequently, a one-dimensional parabolic partial differential equation, i.e., the flux-equivalent probability density evolution equation, could then be solved to yield the probability density function of the response of concern. By doing so, a high-dimensional FPK equation is reduced to a one-dimensional partial differential equation, for which the numerical solution is quite easy. Several numerical examples are studied to verify and validate the proposed method. Problems to be further studied are discussed. [ABSTRACT FROM AUTHOR]

The steel strands in posttensioned (PT) concrete systems are typically embedded inside cementitious grout for protection from the environment. However, strands not embedded in grout have been observed in PT systems. The exposed strand is susceptible to corrosion, and particularly the location where the strand protrudes from the grout (i.e., grout-air-steel interface) is more vulnerable to corrosion. Prediction of the tension capacity () of strands with such interfaces under various exposure conditions is necessary for structural assessment. This prediction could be accomplished by using the data from an experimental program that includes the exposure of strands to various corrosive environments and testing to determine the time-variant residual of these strands. However, these tests are cumbersome and expensive, especially when it is necessary to maintain very high tensile stress conditions during the exposure period to simulate the in-service stress conditions on the strands in PT systems. Similar investigations of unstressed single wires are simpler and less expensive. This paper presents an experimental investigation of the corrosion-induced losses in the of unstressed wires, unstressed strands, and stressed strands. Based on these data, this paper develops probabilistic models to predict the of unstressed wires with grout-air-steel interfaces and subjected to various moisture and chloride conditions. By using these models for wires and the experimental data on strands, two probabilistic models are then developed to predict the of stressed strands based on the of unstressed wires. The developed models can be used to determine the of strands with grout-air-steel interfaces subjected to various exposure conditions, provided the of corresponding wires under those conditions is estimated. [ABSTRACT FROM AUTHOR]

Drinking water distribution system models have been increasingly utilized in the development and implementation of contaminant warning systems. This study proposes a Bayesian approach for probabilistic contamination source identification using a beta-binomial conjugate pair framework to identify contaminant source locations and times and compares the performance of this algorithm to previous work based on a Bayes' rule approach. The proposed algorithm is capable of directly assigning a probability to a potential source location and updating the probability through the use of a backtracking algorithm and Bayesian statistics. The evaluation of the performance associated with the two algorithms was conducted by a simple comparison, as well as a simulation study in terms of a conservative chemical intrusion event through both a small skeletonized network and a large all-pipe distribution system network. Results from the simple comparison showed that the beta-binomial approach was more responsive to changes in sensor signals. In terms of intrusion events, the beta-binomial approach was more selective than the Bayes' rule approach in identifying potential source node-time pairs and provided the flexibility to account for multiple possible injection locations. [ABSTRACT FROM AUTHOR]

The statistical characteristics of design error rectification costs experienced in 139 Australian construction projects are analyzed. Theoretical probability distributions are fitted to the design error cost data. A generalized Pareto probability function was found to provide the best overall distribution fit for design error costs. The generalized Pareto distribution is used to calculate the probability of design error costs being experienced for the selected sample. A mean design error cost of 14.2% of a project's contract value is reported. A significant difference between mean design error costs and project types was found for civil engineering (23.44%) and fit-out (22.50%) projects. Projects Australian dollars (A$)101M were found to experience significantly higher mean design error costs (26.18%) than other projects. Being able to determine the likelihood of design error rectification costs from the derived empirical probability distribution will provide an ameliorated assessment of risk before the commencement of construction. Strategies to reduce design error rectification costs are also discussed. [ABSTRACT FROM AUTHOR]

The previously developed cyclic void growth model (CVGM) has been demonstrated to accurately simulate ductile fracture initiation under monotonic and ultralow cycle fatigue loading for a variety of steel materials and geometric configurations. Prediction of ductile fracture initiation involves significant uncertainty, particularly where there is high variability in the material (e.g., welded connections) subjected to irregular cyclic loading. The reliability of the model predictions is improved through a probabilistic formulation based on maximum likelihood parameter estimation. The probabilistic formulation, which incorporates information from both the failure and nonfailure loading cycles, has the following features: (1) the calibration of model parameters provides the maximum likelihood of agreement for a given set of cyclic fracture observations, and (2) fracture predictions are provided in a probabilistic sense by generating a distribution of the expected instant of fracture. The benefit of the approach is twofold. First, it eliminates an inconsistency that is inherent in the deterministic calibration procedure, as proposed in the original development of the CVGM. Second, the degree of certainty of fracture predictions is quantified. In combination, these features significantly enhance the robustness of the framework within which the model is implemented. Although this paper applies this approach in the specific context of the CVGM, the method can be generalized to other models that share similar characteristics. [ABSTRACT FROM AUTHOR]

Planning retrofit actions on bridge networks under tight budget constraints is a challenging process. Because of the uncertainties associated with this process, a probabilistic approach is necessary. In this paper, a probabilistic methodology to establish optimum pre-earthquake retrofit plans for bridge networks based on sustainability is developed. A multicriteria optimization problem is formulated to find the optimum timing of retrofit actions for bridges within a network. The sustainability of a bridge network and the total cost of retrofit actions are considered as conflicting criteria. The sustainability is quantified in terms of the expected economic losses. The uncertainties associated with seismic hazard and structural vulnerability are considered. The methodology is illustrated on an existing bridge network. Genetic algorithms are used to solve the multicriteria optimization problem. The effects of deterioration on bridge seismic performance are considered. The effects of the time horizon on the Pareto optimal solutions are also investigated. [ABSTRACT FROM AUTHOR]

Common probabilistic scores are used to evaluate the performance and reliability of interpolated rainfall scenarios based on geostatistics. The kriging variance is used jointly with the best linear unbiased estimator at the interpolation sites to render an ensemble of rainfall depth at each time step, providing dynamic information about the uncertainty of the interpolated field. Tests are conducted with rainfall data, extending from June 1, 2000, to October 31, 2005, from 50 stations located in the Saint Lawrence Valley, Canada. Three categories of variograms are examined: automated variograms that change at each time step; variable variograms that associate an average variogram to a specific interval of mean areal rainfall; and unique variograms, which are averages over the whole series. Simple, ordinary, and universal kriging are also examined. Rainfall scenarios constructed from automated variograms, simple kriging, and 30 neighboring stations presented acceptable sharpness and overall performance, including reliable exceedance probability and confidence intervals. An optimal choice of neighborhood is critical to performance and reliability. [ABSTRACT FROM AUTHOR]

A nonlinear relationship between peak discharge and runoff volume (or depth = volume per unit area or rainfall amount), reported in the literature, was derived based on the standardized peak discharge distribution (SPDD) with regression analysis. However, the SPDD regression-based runoff model may only predict the mean behavior of peak discharge for a given runoff depth (i.e., the conditional expectation of peak discharge for a given runoff depth). This study proposes the application of entropy theory to derive the joint frequency distribution of peak discharge and runoff depth and the distribution of peak discharge conditioned on runoff depth. The conditional expectation of peak discharge (i.e., predicted peak discharge) for a given runoff depth is then compared with that obtained from the second-order SPDD regression-based runoff model. The entropy-based method is validated using data from 27 watersheds of different areas located in different climate regions in the United States. The results show that (1) with properly defined constraints, the entropy-based method may properly model the joint distribution of runoff depth and peak discharge and conditional distribution of peak discharge given runoff depth, and (2) the proposed method performs better than the regression-based method in terms of representation of extreme values that otherwise may be considered outliers. [ABSTRACT FROM AUTHOR]

At any location, flood magnitudes can result from multiple causes (e.g., riverine flooding, tidal surges, snowmelt runoff, pluvial flooding, etc.) that occur simultaneously or independently. Analyzing flood data that resulted from simultaneous occurrences but treating the individual magnitudes as independent factors can lead to inaccurate estimates of flood depths, probability, and risk. While the assumption of independence is computationally convenient, it can be hydrologically incorrect. A method of joint flood frequency analysis that is based on copulas is proposed to address cases where the assumption of independence does not apply. For example, flooding at a coastal site can be the result of high riverine flows that simultaneously happen with high storm surges. The individual flood records would not adequately describe flood depths where both flood types occurred. The proposed method can be applied with two or more causes of flooding. The method is demonstrated using data from a site in coastal Florida, with the results showing that differences in flood estimates can be significant when independence is assumed for cases when a dependency exists. [ABSTRACT FROM AUTHOR]

In this work, a conceptual lumped model was developed to simulate runoff and analyze hydrological processes with the goal of incorporating the morphological information into a probability-distributed model (PDM). PDMs usually describe the process of runoff generation as the result of soil saturation excess caused by precipitation with soil storage capacity represented by a spatially distributed quantity and described by a probability distribution. The proposed model, called topography-based probability distributed model (TOPDM), based on a simple water balance whose components are basin soil moisture storage, precipitation, drainage to groundwater, evapotranspiration, and Dunnian and Hortonian surface runoff, is the result of the combination and integration of the topographic index within a PDM. A TOPDM was applied to the Baron Fork basin in Oklahoma in this research, and simulation results show that it provides a reasonably good estimation of runoff and a realistic representation of physical process in the catchment confirmed by the comparison with soil moisture data and with the results provided by a more complex, physically based distributed hydrological model. [ABSTRACT FROM AUTHOR]

Probabilistic deterioration models such as state-based and time-based models are only capable of predicting future bridge-condition ratings when a sufficient amount of condition data and reasonable data distribution are available. However, such are usually difficult to acquire from limited bridge-inspection records. As a result, these probabilistic models cannot guarantee reliable long-term prediction for each of the bridge elements concerned. To minimize this shortcoming, this paper proposes an advanced integrated method to construct workable transition probabilities for predicting long-term bridge performance. A selection process within this method automatically chooses a suitable prediction procedure for a given situation in terms of available inspection data. The backward prediction model (BPM) is also incorporated to effectively predict the bridge performance when sufficient inspection data are unavailable. Four different situations in regard to the available inspection data are predefined in this study to demonstrate the capabilities of the proposed integrated method. The outcomes show that the method can help develop an effective prediction model for various situations in terms of the quantity and distribution of available condition-rating data. [ABSTRACT FROM AUTHOR]

Seismic fragility analysis is a complex process involving different sources of uncertainties. In this paper, an alternative procedure for seismic fragility analysis based on the uniform design method (UD) is proposed. UD is used to generate a reasonable sample to build probabilistic seismic demand models (PSDMs), which are used to generate the fragility curves of a cable-stayed bridge. Sensitivity analyses of different uncertainties are carried out by comparison of the fragility curves for different components. It is concluded that (1) the UD method can consider different sources of uncertainties in fragility analysis with reasonable accuracy; (2) the bridge system is more fragile than any component of bridges; and (3) the damage probability of fragility considering uncertainty in the ground motion, geometry, and material is larger than that considering only the uncertainty in the ground motion. [ABSTRACT FROM AUTHOR]

ASTM E1300-09 uses a glass failure prediction model (GFPM) to quantify the probability that a critical surface flaw with a certain location and orientation will initiate a facture in the glass for a given lite geometry and uniform design load. The nonfactored load charts in ASTM E1300-09 are calibrated to a GFPM probability of breakage of at the first occurrence of the design load. The GFPM probability of breakage only addresses the material properties of the annealed monolithic window glass and does not incorporate the probability of the occurrence of the design load. Because window glass is typically designed to resist wind loads, the probability of the occurrence of the design load was based on ASCE 7-05. Using a Monte Carlo simulation to evaluate the limit-state equation, this paper presents a procedure to quantify the probability of failure incorporating the probability of the wind load and the probability of the window glass load resistance from the GFPM for window glass lites loaded with a 3-s uniform lateral wind load. A series of figures are presented illustrating the large variations in the probability of failure as the nominal glass thickness changes with varying rectangular dimensions. The probabilities of failure tend to be an order of magnitude smaller than the corresponding probabilities of breakage. [ABSTRACT FROM AUTHOR]

Liquefaction of sandy soils has led to catastrophic damage to structures during past earthquakes. Implementing simplified procedures such as the shear-stress method is the most prevalent current practice in assessing liquefaction. Because there may be no perfect single simplified procedure, use of multiple methods is reasonable to minimize the risk of uncertainty. This paper presents an alternative simplified method for assessing soil liquefaction that is based on the cumulative kinetic energy density (CKED). Strong ground-motion data were employed, and with the aid of a genetic programming tool, an attenuation relationship was developed for estimating the CKED in liquefiable sites. CKED at a given layer depth was estimated by applying a depth-reduction factor. A simple correlation was developed for estimating the depth-reduction factor by way of equivalent linear site-response analysis on actual liquefiable soil profiles. The performance of the model presented herein was evaluated by implementing two databases of field liquefaction case histories. Probabilistic and deterministic curves are suggested for practice application. [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]

This investigation presents results of the statistical and probabilistic analyses of 3,269 normal weight concrete cylinder compression tests used for recently constructed highway bridges in California. A new model for in-place strength of concrete structures is proposed as a function of the specified compressive strength, the normalized 28-day cylinder strength, and age of the structure based on a realistic strength-age relation for hardened concrete. The model prediction indicates that concretes in cast-in-place bridge structures designed with specified compressive strengths of 25 MPa (3.6 ksi), 28 MPa (4.0 ksi), and 35 MPa (5.0 ksi) reach their maximum strengths at about 40 years, with approximately 98% of the maximum strength occurring during the first 10 years. Also, through significance testing on the 28-day cylinder strengths, it was established that the California Department of Transportation practice of using an expected concrete strength instead of the specified strength for seismic design of bridge components is justified. An expression for predicting the 28-day strength of concrete cylinders as a function of the strength of companion cylinders, also proposed herein, could prove a useful tool for quality control of concrete during construction. [ABSTRACT FROM AUTHOR]

Water distribution system (WDS) models may improve system control when applied using real-time data, and in doing so, help meet consumer and regulatory demands. Such real-time modeling often overlooks the multiple sources of system uncertainty that cascade into model forecasts and affect the identification of robust operational solutions. This paper considers key uncertainties in WDS modeling and reviews promising approaches for uncertainty quantification and reduction in the modeling cascade from calibration, through data assimilation, to model forecasting. An uncertainty framework exemplifying how such methods may be applied to propagate uncertainty through the real-time control process is outlined. Innovative methods to constrain uncertainty when the time-horizon and data availability limit such thorough analysis are also discussed, alongside challenges that need to be addressed to incorporate uncertain information into the control decision. Further work evaluating the value of these methods in light of computational resources, and the nature of model errors in real WDS, is required. Such work is necessary to demonstrate the benefits of considering model and data uncertainty, leading to robust control decisions. [ABSTRACT FROM AUTHOR]

The emergence of performance-based wind engineering calls for improved probabilistic modeling of wind effects on buildings. This paper focuses on the development of probabilistic models of the peak distribution and peak factor for non-Gaussian processes and explores the applications of this development in wind engineering. The closed-form expressions for the mean, SD, and fractile levels of extremes are derived for a random process whose peaks are modeled by the parametric Weibull distribution. A new translated-peak-process method is then developed for the estimation of the peak distribution, peak factor, and variability of extremes, based on the Weibull distribution and point-to-point mapping procedure. The proposed translated-peak-process method is validated by wind-tunnel pressure measurements on a standard tall building and is shown to be more robust and practical than many existing methods in analyzing non-Gaussian wind pressure data. [ABSTRACT FROM AUTHOR]

Soil consolidation by prefabricated vertical drains (PVDs) relies on some soil properties that are spatially variable, such as the coefficient of permeability. However, the design of soil consolidation via PVDs has been traditionally carried out deterministically and thus can be misleading because of the ignorance of the uncertainty associated with the inherent spatial variation of soil properties. In this paper, the effects of spatial variability of soil permeability on soil consolidation by PVDs are investigated stochastically, and the corresponding uncertainty associated with the degree of consolidation is statistically quantified and analyzed. [ABSTRACT FROM AUTHOR]

The ability to accurately predict traffic loading is essential for cost-effective bridge maintenance and repair programs. The traffic load model currently used in the United States for the design of long-span bridges was developed over three decades ago. In the meantime, vehicle characteristics and traffic patterns have changed. The Eurocode for traffic loading is more recent, but was calibrated only for bridges up to 200 m long. In this work, weigh-in-motion traffic records from 11 different sites across Alabama are used to establish congested traffic loading. Traffic microsimulation is used to generate congestion based on real traffic data. Influence lines for two typical long-span bridges, one cable-stayed bridge, and one suspension bridge are determined using finite-element models. These are used in the microsimulation model to estimate the bridge-load effects caused by congested traffic. These results are extrapolated to find the characteristic lifetime maximum values that are used to evaluate the Eurocode load model to assess its suitability for long-span bridges. In a similar way, the current American load model for long-span bridges, commonly known as the ASCE model, is evaluated to see if it accurately reflects the congested traffic loading that is currently found on American highways. Recent research has suggested the use of the AASHTO HL-93 load model to estimate the effects of traffic loading on long-span bridges, and this model is also evaluated in this work. [ABSTRACT FROM AUTHOR]

Rain gardens have increasingly been used to control the adverse effects of urbanization on storm-water quantity and quality. The ratio or percentage of storm water generated from the contributing area of a rain garden that is captured by the surface depression of the rain garden is known as its storm-water capture efficiency. This capture efficiency is an important indicator of a rain garden's performance for storm-water management. Based on the probability distributions of local rainfall event characteristics and the hydrologic operation of rain gardens, an explicit analytical equation is derived for estimating the long-term average storm-water capture efficiency of a rain garden. The validity of the analytical equation is demonstrated by comparing its outcomes with results from a series of continuous simulations. Example applications of this equation are made for two locations. [ABSTRACT FROM AUTHOR]

A probabilistic analysis of the face stability of a pressurized tunnel is undertaken in this article. First, two existing velocity fields based on the limit analysis theory are briefly described. They allow one to compute the values of the critical pressures of collapse and blowout of a pressurized tunnel face in cases of both frictional and nonfrictional soils. These models, which have the great advantage of a low computational cost, are validated by comparison with a computationally expensive numerical model. Then, an efficient probabilistic method called collocation-based stochastic response surface methodology (CSRSM) is applied on these velocity fields to perform the uncertainty propagation. This method makes it possible to compute the probability of failure of the tunnel face against both collapse and blowout. In the case of a frictional soil, it appears that the blowout of the face is extremely unlikely and that the collapse is the only probable failure mode. On the contrary, in a purely cohesive soil, it appears that both failure modes are likely to appear and should be considered in the analysis. Finally, this paper presents a discussion concerning the application of the proposed probabilistic method for an economic and safe design of a pressurized shield. [ABSTRACT FROM AUTHOR]

The collection of floating woody debris at flow control structures, such as spillways and weirs, can potentially result in reduced discharge efficiency (higher upstream head for a given weir discharge). Compared to less hydraulically-efficient control structures, piano key weirs have higher discharge efficiency (lower upstream heads for a given discharge), which may increase the likelihood of woody debris collection. A systematic laboratory study was conducted to evaluate the interaction between various piano key weir geometries and woody debris types and sizes. The results of individual (noncumulative) debris tests indicated that floating debris blockage probability is highly influenced by trunk diameter and upstream head. The effects of debris accumulation on the upstream head varied with the value of the debris-free reference upstream head condition. At lower upstream reference head values, the cumulative debris tests indicated a relative increase of the debris-associated upstream head of approximately 70%; higher upstream reference head values produced upstream head increases limited to approximately 20%. [ABSTRACT FROM AUTHOR]

A methodology is presented to assess the effect of wind directionality on the vulnerability of rural houses to cyclonic wind speed, and also to provide cyclonic risk assessment of coastal regions. The effect of wind directionality is incorporated in two different ways. In the first case, an equivalent directional effect is used to modify the component failure velocities. In the second case, component failure velocities are converted into direction-dependent failure velocities by finding a wind directional factor for the 16 orthants directly from the data downloaded from the NIST website. For each direction, the vulnerability curve is obtained by a component-based approach in which a damage probability matrix showing the conditional probability of failure of each different component is determined. The final vulnerability curve is drawn for each direction by the convolution technique. The same approach is used for obtaining the vulnerability curve when the average directional effect is considered. The comparison between the vulnerability curves obtained for some of the 16 orthants and that for average direction are compared for an example problem of a coastal region having 100 rural houses. [ABSTRACT FROM AUTHOR]

This study examines the probability for sediment entrainment to bed load and the probability for the threshold condition of sediment to be in suspension. The theoretical analysis is based on a simple one-sided exponential distribution of probability function. The probability distributions are derived from a truncated universal Gram-Charlier series expansion based on the exponential or Laplace-type distributions for turbulent velocity fluctuations. The key criterion of sediment entrainment is the hydrodynamic lift acting on a solitary particle to exceed submerged weight of the particle. In this way, a simple probability function for sediment entrainment to bed load in terms of Shields parameter containing the lift coefficient is obtained. It was found that the value of lift coefficient as 0.15 satisfactorily fitted the probability function versus Shields parameter curve with the experimental data. On the other hand, the key criterion of the threshold of sediment suspension is the fluctuations of the vertical velocity component to exceed terminal fall velocity of the particle. The probability function for the threshold of a sediment particle to be in suspension is obtained in terms of Shields parameter as a function of shear Reynolds number. Curves for different values of probabilities are drawn in respect to a Shields diagram. For the value of probability 0.05, the threshold of sediment suspension is indicated. The prediction curves for the threshold of sediment suspension are proposed in terms of Rouse number versus Shields parameter and also Shields parameter versus shear Reynolds number. [ABSTRACT FROM AUTHOR]

Fatigue assessment of several steel bridge details, having equivalent stress range below the constant amplitude fatigue threshold (CAFT), showed that many of these details are free of cracks, although the remaining life calculations predicted that they should have already been suffering from cracks. This shows that the current methods for predicting the fatigue remaining life of steel bridges can be conservative and may lead to unnecessary retrofit and rehabilitation actions. For a better fatigue life prediction, a bilinear approach has been proposed. In this approach, the bilinear lines have different slopes above and below the CAFT. This paper addresses fatigue assessment and service life prediction of existing fatigue-prone steel bridges by integrating structural health monitoring (SHM) data into a probabilistic bilinear approach. The effect of changing the value of the slope of the AASHTO lines below the CAFT on the fatigue life is investigated through a parametric study. In addition, an existing steel bridge is used to illustrate the proposed probabilistic approach. [ABSTRACT FROM AUTHOR]

The uncertainty in material properties and traffic characterization in the design of flexible pavements has led to significant efforts in recent years to incorporate reliability methods and probabilistic design procedures for the design, rehabilitation, and maintenance of pavements. In the mechanistic-empirical (ME) design of pavements, despite the fact that there are multiple failure modes, the design criteria applied in the majority of analytical pavement design methods guard only against fatigue cracking and subgrade rutting, which are usually considered as independent failure events. This study carries out the reliability analysis for a flexible pavement section for these failure criteria based on the first-order reliability method (FORM) and the second-order reliability method (SORM) techniques and the crude Monte Carlo simulation. Through a sensitivity analysis, the most critical parameter affecting the design reliability for both fatigue and rutting failure criteria was identified as the surface layer thickness. However, reliability analysis in pavement design is most useful if it can be efficiently and accurately applied to components of pavement design and the combination of these components in an overall system analysis. The study shows that for the pavement section considered, there is a high degree of dependence between the two failure modes, and demonstrates that the probability of simultaneous occurrence of failures can be almost as high as the probability of component failures. Thus, the need to consider the system reliability in the pavement analysis is highlighted, and the study indicates that the improvement of pavement performance should be tackled in the light of reducing this undesirable event of simultaneous failure and not merely the consideration of the more critical failure mode. Furthermore, this probability of simultaneous occurrence of failures is seen to increase considerably with small increments in the mean traffic loads, which also results in wider system reliability bounds. The study also advocates the use of narrow bounds to the probability of failure, which provides a better estimate of the probability of failure, as validated from the results obtained from Monte Carlo simulation (MCS). [ABSTRACT FROM AUTHOR]

This paper presents probabilistic models for the structural performance of rounded dovetail joints. The models are developed with a Bayesian technique, which implies that the model uncertainty is explicitly characterized by random variables. The Bayesian approach also promotes model updating when new test results become available in the future. Practical insight is gained from the modeling process, which includes a novel search for influential parameters, and from the subsequent probabilistic analysis with the models. The models are based on 80 tests of single and double dovetail joints with varying geometric parameters, specifically the flange angle and the dovetail height. A significant effort was made to record variables that conceivably influence the performance of this type of joint, including a series of material parameters: tension strength perpendicular to grain, shear strength parallel to grain, moisture content, density, growth ring density, and growth ring orientation. This paper explores the significance of each parameter and proposes models that include the most significant parameters while retaining a measure of the model uncertainty. In contrast to most models used in structural design, the probabilistic models presented herein are unbiased and suitable for future reliability-based calibration of code equations. [ABSTRACT FROM AUTHOR]

Probabilistic seismic demand models are developed for bridges elevated with steel pedestals by adding correction and error terms to commonly used models. Separate probabilistic demand models are developed for the force demand on steel pedestals and the shear and deformation demands on concrete columns. Nonlinear time history analyses on detailed, three-dimensional finite-element models are used to generate virtual experimental data. By applying a Bayesian updating method to the generated data, parameters of the probabilistic models and their correlations are estimated. Comparisons between the demands from the developed probabilistic demand models and the demands from their corresponding demand models without correction and error terms reveal that the developed probabilistic models provide more accurate and unbiased predictions of the demands of interest. As an illustration of the developed framework, fragilities are estimated for a two-span bridge. The results show that pedestals are more vulnerable in the longitudinal direction, and columns are more vulnerable in the transverse direction. A sensitivity analysis on the studied bridges shows that decreasing the pedestal height, increasing the length of the pedestal anchor bolts within the concrete bent, and increasing the concrete cover on the anchor bolts are the most effective ways to decrease the probability of failure. [ABSTRACT FROM AUTHOR]

Recent research has shown that the dynamic amplification factor (DAF) to be applied to free-flowing traffic-induced load effect may not be as high as previously thought. Therefore, congested traffic states may govern extreme load effect at lower bridge lengths than currently assumed. Thus, there is a need for a methodology that incorporates both free-flowing and congested traffic states in the calculation of lifetime load effect. It should allow for the relative frequency of occurrence of the different forms of traffic and any form of DAF function that may arise. This paper presents such an approach and also presents a general probabilistic DAF formulation for inclusion. Using measured traffic, the approach is applied to a range of bridge lengths and load effects employing a variety of DAF approaches from the literature, in addition to the new DAF formulation. Using a critical traffic index, it is shown that the governing form of traffic is very sensitive to the dynamic amplification model used. Further, depending on this model, congested traffic can govern short spans, and for other spans, a combination of free- and congested-flow traffic states must be considered. [ABSTRACT FROM AUTHOR]

This paper presents an efficient stochastic buckling model for studying the structural reliability of layered composite columns with interlayer slip between the layers and random material and loading parameters. The model is based on the exact buckling model, response surface method, and Monte Carlo simulations. The probability of failure is investigated for a different number of random variables, sample points, and various degrees of response surfaces. The results show that the probability of failure is considerably affected by the type (deterministic or probabilistic) of the loading and its distribution. [ABSTRACT FROM AUTHOR]

This paper presents an overview and a recap of basic equations of structural reliability as applied to structural condition assessment. Common sources of uncertainties in structural design parameters are explained, and methods to quantify uncertainties are reviewed and presented. Through two illustrative examples, it is demonstrated that in certain cases, even though an acceptable factor of safety may be obtained, in the presence of uncertainty, there may be a rather undesirable probability of failure associated with the factor of safety. The paper is intended to offer a practical and simple, yet logical, approach in treating uncertainties in structural condition assessment. [ABSTRACT FROM AUTHOR]