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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

In the last decade, the state departments of transportation in the US have experienced an increase in their construction projects, while the level of their in-house inspection staff and resources has either remained the same or declined. Previous studies have found that one strategy that may reduce the inspection workload is prioritizing construction activities for inspection. However, reducing the number of inspections also has its risks, such as functional failures and reduced design life. Thus, available inspection resources should be allocated to the activities with significant risk consequences if inspection is reduced. The objective of this paper is to develop a risk-based inspection protocol to facilitate efficient allocation of available inspection resources to minimize the risks associated with reduced inspection. First, the risk consequences associated with reduced inspection are identified for various construction activities linked to transportation projects. Based on data collected from 23 state departments of transportation, 58 engineers and inspectors from the Indiana Department of Transportation and 20 inspection consultants in the Midwest, the subjective perceived probabilities associated with the occurrence of each risk consequence are encoded by using fuzzy analysis, from which the risk impacts due to reduced inspection are obtained. The construction activities are prioritized based on the risk impacts associated with reduced inspection into five priority levels. The greater the risk impacts are as a result of reduced inspection, the higher the priority would be for inspection of that activity. Thus, the proposed protocol can be used for resource allocation based on risk impacts. The proposed list of prioritized construction activities can assist project and program managers in state departments of transportation in better allocating their limited inspection resources while reducing the risks due to reduced inspection. [ABSTRACT FROM AUTHOR]

This research investigated the confined flow under hydraulic structures. The hydraulic conductivity of the soil was modeled as a spatially random field, which followed a lognormal distribution. Only porous media that have anisotropic heterogeneity were investigated. Results showed that larger anisotropic heterogeneity ratios (the ratio of horizontal to vertical scale of fluctuation) dramatically increased the seepage flow. This increase of flow was more pronounced at larger coefficients of variations. A similar trend was observed in the case of uplift force, although it was less sensitive to the increase in the anisotropic heterogeneity ratio. Moreover, both the seepage flow and the uplift force tended to their deterministic values as the ratio of anisotropic heterogeneity increased. Results also showed that the exit hydraulic gradient attained its greatest value at particular values of the anisotropic heterogeneity ratio. [ABSTRACT FROM AUTHOR]

Liner systems are increasingly being used to protect the environment from contaminated waste. At the same time, society is increasingly insisting on estimates of the probability that these liner systems will fail to achieve their design objectives, one of which is to limit hydraulic flow from the contaminated region to acceptably small levels. This paper presents a methodology to estimate the probability of excessive hydraulic flow, considering the spatial variability of the soil composing the liner (its mean, variance, and correlation length) as well as the liner thickness. Semiempirical equations predicting the mean and variance of the effective hydraulic conductivity of the liner, based on theory and calibrated by random finite-element method simulations, are presented and used to investigate the probability that a liner exceeds regulatory hydraulic flow requirements. The proposed methodology is illustrated by an example. [ABSTRACT FROM AUTHOR]

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

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

The statistical characteristics of cost overruns experienced from contract award in 276 Australian construction and engineering projects were analyzed. The skewness and kurtosis values of the cost overruns are computed to determine if the empirical distribution of the data follows a normal distribution. The Kolmogorov-Smirnov, Anderson-Darling, and chi-squared nonparametric tests are used to determine the goodness of fit of the selected probability distributions. A three-parameter Frechet probability function is found to describe the behavior of cost overruns and provide the best overall distribution fit. The Frechet distribution is then used to calculate the probability of a cost overrun being experienced. The statistical characteristics of contract size and cost overruns were also analyzed. The Cauchy (), Wakeby (A$1 to 10 million, ) and four-parameter Burr (A$11 to 50 million) tests were found to provide the best distribution fits and used to calculate cost overrun probabilities by contract size. Ascertaining the best fit probability distribution from an empirical distribution at contract award can produce realistic probabilities of cost overruns, which should then be incorporated into a construction cost contingency. [ABSTRACT FROM AUTHOR]

This paper proposes a generalized probabilistic framework for optimum inspection and maintenance planning of deteriorating structures. The proposed framework covers (1) the damage occurrence and propagation and service life prediction under uncertainty, (2) the relation between degree of damage and probability of damage detection of an inspection method, and (3) the effects of inspection and maintenance on service life and life-cycle cost. Optimum inspection and maintenance types and times are obtained through an optimization formulation by maximizing the expected service life and minimizing the expected total life-cycle cost consisting of inspection and maintenance costs. The service life, life-cycle cost, and maintenance delay, along with inspection and maintenance actions, are formulated using a decision tree model. The selection of the appropriate maintenance type depends on the degree of damage. The proposed framework is general and can be applied to any types of deteriorating structures or materials. Applications of the proposed framework may include, but are not limited to, bridges, buildings, aircrafts, and naval ships. [ABSTRACT FROM AUTHOR]

A probabilistic porous model is used to simulate the retention curves of different types of soils. The model is based on the same principles of porous networks models; however, it shows important advantages over them. It considers two different elements: the sites and the bonds. It is able to simulate the retention curves of a material when its pore size distribution is known. It can also be used to interpret more realistically the results of mercury intrusion porosimetry tests. In this paper, the model is used to obtain the pore size distribution of different soils using the retention curve as its data source. The comparison between numerical and experimental results for different soils shows that the model approximately reproduces the pore size distribution obtained from mercury intrusion porosimetry tests. [ABSTRACT FROM AUTHOR]

Maximum seismic shear stresses () have been recognized as one of the important parameters in design practice. This study develops ground-motion parameters for and implements these in probabilistic seismic hazard analysis to provide the distribution of deep soil layers for design purposes. The application of improved ground-motion parameters for is demonstrated at the Oakland International Airport, where a thick Young Bay Mud deposit exists under the artificial fill. Model biases in the predictive equations of seismic shear-stress reduction coefficients () are evaluated by comparison with the site response analyses performed with a wide range of input ground motions. Based on these results, we introduce improved ground-motion parameters for as a linear combination of spectral accelerations, implemented in probabilistic seismic hazard analysis to calculate seismic hazard curves. Conditional mean spectra are calculated, given at 10% in 50 years to illustrate the variations in frequency contents with depth compared with the uniform hazard spectra. Finally, is calculated with depth by using hazard values of and compared with the peak-ground-acceleration-based and uniform-hazard-spectra-based calculations. Analysis results show that will be underestimated for deep soil layers by peak-ground-acceleration-based calculation if the median value of is used in design practice. [ABSTRACT FROM AUTHOR]

Environmental factors directly affect a building's performance and durability. They are particularly detrimental in the case of building envelope materials and systems because these tend to exhibit a large exposed area and relatively narrow thickness. Therefore, tools are needed to model degradation and provide an insight into its occurrence and its relationship with the environmental factors that have the worst effect. In this paper, the degradation of stone wall cladding directly adhered to the substrate is estimated based on the evaluation of the characteristics of 140 wall cladding systems inspected in Lisbon, Portugal. Because it is a complex phenomenon, a probabilistic analysis is developed using multinomial logistic regression. The analysis focuses on the environmental factors that most influence the overall degradation of the façades (condition level). Probabilistic patterns are thus obtained for the evolution over time of each condition level according to their exposure level to outdoor environmental conditions. [ABSTRACT FROM AUTHOR]

A computer program is developed to carry out reliability and optimization analysis with many interconnected probabilistic models. The program is freely available online and it contains a library of versatile models. The user can also implement new models-without any recompilation of the program-by several means, including a powerful scripting option. Other novel features include a comprehensive parameterization that facilitates flexible and effective model communication and the computation of direct-differentiation response sensitivities in multimodel analysis. The new program has already been successfully employed for regional risk analysis with thousands of model objects and hundreds of random variables. This paper presents the software architecture and a multimodel example of a structure that is modeled in an external finite-element program and subjected to multiple hazards, damage, and long-term deterioration. [ABSTRACT FROM AUTHOR]

The use of jet grouting columns to increase the bearing capacity and reduce the settlements of foundations is dealt with, the aim being to formulate a complete design procedure where theoretical analyses and site observations are combined. The study is based on experimental results reported in the literature, which show that jet grouting columns are able to transfer high vertical loads to the surrounding soil but also that structural collapse may locally occur because of a sudden narrowing of their cross sections and/or poor soil cementation. Noticeable attention has been then given to these aspects by interpreting the results of full-scale tests specifically performed to investigate the characteristics of jet grouting columns and their mechanical interaction with the surrounding soil. The results of this analysis form the basis of a numerical method developed to simulate the response of vertically loaded rafts supported by arrays of columns. The nonlinear load-settlement response of axially loaded columns is modeled with the load-transfer curves method customized to account for the irregular shape of jet grouting columns. Extension of the analysis to the whole reinforced foundation is accomplished by considering the mutual interaction between the columns and the upper concrete raft. The variation of column properties is statistically evaluated from the results of field trials, simulated with probabilistic models and introduced into the calculation with a Monte Carlo simulation technique. The main advantages of the proposed method is that the design limit load of the foundation can be expressed in terms of acceptable probability of failure and that the uncertainty arising from the jet grouting process can be experimentally quantified and rationally introduced in the analysis. Benefits and limitations of reinforcement with jet grouting are finally discussed by applying the proposed method to a case study. [ABSTRACT FROM AUTHOR]

To advance the use of reliability-based design procedures, it is necessary to evaluate the sources of the design parameter uncertainty including inherent variability, measurement error, and transformation uncertainty. The results of a probabilistic evaluation of undrained footing bearing performance are discussed in the context of an extensive test site characterization described in a companion paper. Kriged cone tip resistance values are transformed into design parameters using a second-moment probabilistic approach and compared with the parameters obtained from the laboratory test analyses on specimens retrieved from the test site. The spatial, measurement, and transformation uncertainty are incorporated into probabilistic finite-element and bearing capacity analyses in which the results are compared against a full-scale load test performed at the test site. The results indicate that the reliable assessment of the spread footing response depends to a large degree on the assumed strength anisotropy and soil layering. A comparison of the probabilistic estimates of the bearing capacity to deterministic estimates developed from the correlations and average design parameters indicate that the consideration of uncertainty results in a desirable prediction accuracy. [ABSTRACT FROM AUTHOR]

The need for probabilistic slope analysis that takes into account the uncertainty of soil properties has been acknowledged by the geotechnical profession. Traditionally, probabilistic slope analysis involves only single-mode failure that is considered based on the critical slip surface. This may result in underestimating the failure probability. In contrast, system reliability analysis for slopes is deemed more rational. This study aims at improving the existing methods of slope reliability analysis by considering system reliability. A stratified response surface method (stratified RSM) is proposed to describe the performance functions of possible failure modes. The proposed method differs from conventional response-surface-based slope reliability analysis (which constructs a single approximate performance function) by generating a group of (stratified) response surfaces. Based on these stratified response surfaces, system reliability analysis can be efficiently carried out by means of either a first-order reliability method (FORM) or Monte Carlo simulations. The efficient FORM based on the concept of a dispersion ellipsoid in the space of the original variables is used. Application of the proposed approach to probabilistic assessment of slopes is illustrated by case studies, and the results obtained are compared with Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Liquefaction potential of four Pleistocene beach sand deposits in the Greater Charleston area, South Carolina, is assessed. The assessment is based on a review of 51 sites of conspicuous craterlets and horizontal ground displacement that occurred in beach sand deposits during the 1886 Charleston earthquake and an analysis of 82 seismic cone penetration tests with pore-pressure measurements. Of the 51 ground failure sites, 23 are associated with the Ten Mile Hill beds; 13 with the Wando Formation; 13 with the Silver Bluff terrace and younger deposits that lie adjacent to the harbor, rivers, and creeks; and two with the Ladson Formation. Liquefaction potential is analyzed using the seismic cone data with and without correction for age-related processes (diagenesis) and then expressed in terms of the liquefaction potential index (LPI). Probability curves are developed from the LPI calculations for different earthquake ground-shaking parameters. The probability curves for the Wando Formation overpredict liquefaction potential when no corrections for diagenesis are made. When corrections for diagenesis are made, the probability curves for all four sands generally agree with the observed field behavior. [ABSTRACT FROM AUTHOR]

A probabilistic version of the Idriss and Boulanger standard penetration test (SPT)-based liquefaction triggering correlation is derived using a maximum likelihood approach and an updated case history database. Measurement and estimation uncertainties in the cyclic stress ratio (CSR) and SPT values and the effects of the choice-based sampling bias in the case history database are taken into account. The results of sensitivity analyses show that the position of the most likely triggering curve is well constrained by the case history data and that the magnitude of the total error term is also reasonably constrained. The most likely value for the SD of the error term in the triggering correlation is, however, found to be dependent on the uncertainties assigned to the CSR and . The results of the sensitivity study appear to provide reasonable bounds on the effects of different interpretations on the positions of the triggering curves for various probabilities of liquefaction. Methods for including model and parameter uncertainties in probabilistic liquefaction analyses are briefly discussed. The derived triggering correlation is compared with relationships developed from cyclic laboratory test results for specimens obtained using frozen sampling techniques. [ABSTRACT FROM AUTHOR]

Acceptance procedures are usually defined in terms of the fraction of elements that fall outside certain specification limits, such as the data dispersion around a central tendency. In contrast, design methods usually consider measures of a central tendency or location (i.e., mean) or, occasionally, of a central tendency together with measures of data dispersion. Price adjustments can be derived from data analysis using empirical models or algorithms based on life cycle cost analysis. As a consequence, there is no common logical framework for designing, analyzing, testing, and accepting road and airport pavements. This study analyzes the dependence of pay adjustment on hot mix asphalt air void characteristics using several acceptance procedures. The results demonstrate that the transition from location-based to dispersion-based systems depends on the probability density function describing a given quality characteristic. The drawbacks of several methods, brought to light in the analysis and discussion presented here, informed a new model in which both location and dispersion indicators are considered. The model was applied to a case study, and practical applications are outlined. [ABSTRACT FROM AUTHOR]

A relatively simple technique is presented for estimating the first-passage probability of any stationary Gaussian process. In particular, the technique is shown to give meaningful results for the troublesome case of a process with a bimodal spectral density that cannot be truly classified as either narrowband or broadband. Mathematically, the technique is only a seemingly minor revision of a long-known method for narrowband processes. What is new here is the demonstration of its applicability not only to narrowband processes but also to other spectral densities, including challenging bimodal situations. The fundamental idea is that of a Markovian point process in which the probability of the process never having crossed a given level u is approximated as the probability that all members of the set of amplitude (or envelope) values at a discrete set of time values are below u, along with the assumption that the set of amplitude values has Markovian conditioning. The critical parameter that must be determined is a correlation coefficient that appears in the jointly Rayleigh distribution of the amplitude at two time values. A method involving simple numerical integration (or a series solution) is shown to give an appropriate value for this parameter for a given spectral density and a given value of u. The model is shown to give generally good agreement with simulation results for processes in which the commonly used Vanmarcke approximation is inadequate. [ABSTRACT FROM AUTHOR]

This paper presents a structural health monitoring methodology that uses acoustic emission (AE) features to predict crack growth in structural elements subjected to fatigue. This allows for the prediction of the failure of the structural element at the current load level. The methodology uses Bayesian inference to account for different sources of uncertainty such as uncertainty in the data (AE signal), unknown fracture mechanics parameters, and model inadequacy. The methodology is divided into two main components: a model updating component that uses available data to build a joint probability distribution of the different unknown fracture mechanics parameters, and a prognosis component in which this multivariable probability distribution is sampled to predict the stress intensity factor range at a future number of cycles. The application of the methodology does not require knowledge of the load amplitude nor the initial crack length. The methodology is validated using experimental data from a compact test specimen under cyclic loading. [ABSTRACT FROM AUTHOR]

This paper demonstrates the size effect on the shear strength of reinforced concrete (RC) beams with stirrups and does so in two separate and independent ways: (1) by fracture mechanics, based on finite-element analysis calibrated by a large beam test; and (2) by purely statistical analysis in which a newly assembled database of 234 tests is filtered to eliminate spurious size effects caused by nonuniformity of secondary influencing parameters. Both ways show that stirrups, whether minimum or heavier, cannot suppress the size effect completely, although they can mitigate it significantly for beam depth d<1 m (39.4 in.). The effect of stirrups is to push the size effect curve in logarithmic scale into sizes larger by about one order of magnitude. For beam depths d<0.5 m, 1, 2, and 6 m (19.7, 39.4, 78.7, and 236.2 in.), the percentages of beams whose shear strength is below the code limit are calculated as 3.5, 6.5, 15.7, and 55.1%, respectively. The corresponding failure probabilities are 10-6, 10-5, 10-4, and 10-3, whereas 10-6 is the generally accepted standard for a tolerable maximum in risk analysis. It follows that, for beams with stirrups having depth >1 m (39.4 in.), the size effect cannot be neglected. [ABSTRACT FROM AUTHOR]

A model using lifetime functions is used to evaluate the probability of survival of bridge components. The possible outcomes associated with nondestructive inspections (NDIs) are incorporated in an event-tree model. Each time a bridge component is inspected, different decisions can be made. The use of a lifetime function for each component of the structural system enables one to express the probability that the component survives. In theory (i.e., perfect inspection), each NDI should be associated with two possible outcomes: survival or failure. In the first case, no damage is detected and the probability density function of time to failure is updated knowing that the component has survived until the inspection. In the second case, damage is detected and maintenance action is planned. In practice, NDIs are subjected to uncertainties (i.e., imperfect inspections) and detecting or not detecting damage depends on the inspection quality (i.e., probability of detection). For poor-quality inspections, there is a significant risk to overestimate the probability of safe performance. The aim of this paper is to provide a practical methodology for determining optimal NDI strategies for different components of steel bridges. The different types of inspections considered in this paper are visual, magnetic particle, and ultrasonic. An economic analysis is performed and NDI strategies are optimized by simultaneously minimizing both the expected inspection/maintenance cost (i.e., the sum of inspection and maintenance costs) and the expected failure cost. The proposed approach is applied to an existing steel bridge. [ABSTRACT FROM AUTHOR]

The Bernoulli pulse process has been used in the past for modeling snow loads. However, it is not an appropriate model for heavy snow-load areas as the snow accumulation cannot be simulated, which may lead to an underconservative assessment of buildings in such areas. In this study, a filtered Poisson process (FPP) is investigated and demonstrated to be an effective stochastic model capable of simulating snow loads with or without accumulation. Weather records obtained from the National Climatic Data Center are used to calibrate the simulated ground snow-load records using the FPP model. A genetic algorithm is employed to determine the parameters of the FPP model. Illustrated by three selected sites in the United States, the annual maximum and daily ground snow-load characteristics are well captured by the FPP model. Potential applications of the model in reliability analysis and risk assessment are discussed. [ABSTRACT FROM AUTHOR]

This paper presents the formulation of a time-dependent seismic fragility format for bridges, as well as new insights into the potential effects of aging and deterioration on seismic vulnerability traditionally neglected in fragility modeling, including joint impacts of multiple component deterioration not investigated to date. The study evaluates the impact of lifetime exposure to chlorides from deicing salts on the seismic performance of multispan continuous highway bridges, considering corrosion of reinforced concrete columns and steel bridge bearings. The components' degradation and their influence on seismic response are illustrated through three-dimensional nonlinear dynamic analysis. A full probabilistic analysis accounting for variation in bridge, ground motion, and corrosion parameters is conducted to develop time-dependent seismic fragility curves. These fragility curves indicate the evolving potential for component and system damage under seismic loading considering time-dependent corrosion-induced deterioration. The results indicate that while corrosion may actually decrease the seismic vulnerability of some components, most critical components suffer an increase in vulnerability. Quadratic models depicting the change in lognormal seismic fragility parameters are proposed to capture the time-dependent effect of aging on the fragility of the bridge system. Overall, the seismic vulnerability significantly increases throughout the lifetime of the representative bridge geometry, with a 32% shift in the median value of complete damage fragility near the end of the bridge's life. [ABSTRACT FROM AUTHOR]

In this paper, the mean-centered first-order second-moment (FOSM) method is employed to perform probabilistic push-over analysis (POA) of structural and/or soil-structure systems. Approximations of first and second statistical moments (FSSMs) of engineering demand parameters (EDPs) of structural and/or geotechnical systems with random material parameters are computed based on finite-element (FE) response and response sensitivity analysis (RSA) results. The FE RSA is performed accurately and efficiently by using the direct differentiation method (DDM) and is employed to evaluate the relative importance (RI) of the various modeling material parameters in influencing the variability of the EDPs. The proposed approximate methodology is illustrated through probabilistic POA results for nonlinear inelastic FE models of: (1) a three-story reinforced-concrete (RC) frame building and (2) a soil-foundation-structure interaction system consisting of a RC frame structure founded on layered soil. FSSMs of EDPs computed through the FOSM method are compared with the corresponding accurate estimates obtained via Monte Carlo simulation. Results obtained from 'exact' (or 'local') and 'averaged' (or 'global') response sensitivities are also compared. The RI of the material parameters describing the systems is studied in both the deterministic and probabilistic sense, and presented in the form of tornado diagrams. Effects of statistical correlation between material parameters are also considered and analyzed by the FOSM method. A simple approximation of the probability density function and cumulative distribution function of EDPs due to a single random parameter at a time (while all the other parameters are fixed to their mean values) is also proposed. Conclusions are drawn on both the appropriateness of using local RSA for simplified probabilistic POA and on the application limits of the FOSM method. It is observed that the FOSM method combined with the DDM provides accurate estimates of FSSMs of EDPs for low-to-moderate level of inelastic structural or system behavior and useful qualitative information on the RI ranking of material parameters on the structural or system response for high level of inelastic behavior. [ABSTRACT FROM AUTHOR]

The presence of air voids, moisture, and chlorides inside tendon systems on segmental posttensioned (PT) bridges has been cited as a reason for the early age corrosion and failure of strands in these bridges. This paper develops probabilistic models to predict the time-variant tension capacity of PT strands exposed to wet-dry conditions. A total of 384 unstressed and 162 stressed strand test specimens were exposed to various void, moisture, and chloride conditions for 0, 12, 16, and 21 months; the residual tension capacities of the strands were then determined. Using these experimental data, a Bayesian approach is used to develop probabilistic capacity models for unstressed and stressed strands. The tension capacities of stressed strands under potential void, wet-dry, and chloride conditions in the field are predicted using the developed models. Probabilistic time-variant models are formulated in such a way that they can be updated by other researchers using additional information from the testing of unstressed strands only, avoiding expensive and cumbersome testing of stressed strands. The mean absolute percentage errors of these models are less than 3.2%, indicating good overall model accuracy. [ABSTRACT FROM AUTHOR]

One of the greatest challenges in the United States today is overcoming the deterioration of an aging infrastructure system. In particular, the highway/bridge infrastructure system has traditionally been neglected of maintenance and repair. One of the most concerning degrading mechanisms in the bridge infrastructure is corrosion, and it is compounded by the fact that much of the older infrastructure is not consistent with current seismic code requirements. The research presented here determines the effects of corrosion on the seismic response of a typical reinforced concrete bridge designed according to recent standards, predominantly governed by flexural deformations, and based on realistic lifetime deteriorations in strength due to the reduction in cross-sectional area of the reinforcement and in stiffness due to concrete cover spalling. The findings of the research, given the noted modeling assumptions, are that the losses in strength and stiffness only marginally influence the seismic fragility of the selected bridge. [ABSTRACT FROM AUTHOR]

Flutter-critical velocity is usually estimated from deterministic analyses by assuming that physical and geometrical parameters are perfectly known. However, aleatory and epistemic uncertainties, especially those associated with the definition of material properties, are intrinsically present partly because of the random nature of every physical system and partly because those properties are evaluated from a finite number of observations. The paper focuses on the combination of structural reliability analysis with aeroelastic simulation to give a correct flutter speed evaluation for design purposes. Two typical aeronautical test cases have been considered: (1) an isotropic material structure and (2) a composite material structure. Different computational methodologies (classical and developed by authors) have been coupled with a simple two-dimensional aeroelastic model to study the qualitative consequences of uncertainty in determination of critical flutter speed and to provide a comparison between different reliability methods such as Monte Carlo (MC) simulation, first-order reliability method (FORM), second-order reliability method (SORM), and response surface by fixed or adaptive order regressor coupled with FORM and MC. For the isotropic case best prediction of MC results is always obtained with high-order response surface (HORS) (coupled with both MC and FORM) above all for low levels of coefficient of variation (C.V.) (10% or under) for which results are basically equivalent. FORM and SORM give acceptable results only above cumulative distribution function values of 35-40%. Only response surface with a fixed polynomial order always gives totally misrepresentative results even for very low variability of basic physical quantities. For the composite case, no generic conclusion can be made about the influence of physical quantities on uncertainty propagation because it strongly depends on layup configuration. From a design point of view, variability in composite materials is even more important because, in a general sense, more variables are involved. The flutter speed reductions reveal greater slope of the linear regressors with respect to the isotropic counterpart, with stronger differences when the uncertainty afflicting the basic random variables is higher. [ABSTRACT FROM AUTHOR]

The low-bid method, typically used for competitive bidding in the United States, may result in a contract with a firm that submits either accidentally or deliberately an unrealistically low-bid price. Such an occurrence hurts both the owner and the contractor by promoting disputes, increased costs, and schedule delays. To address this problem, other countries have adopted bidding methods based on the average of the bids submitted. One such approach is the below-average method where the winning bid is closest to but below the average of all bids. A competitive bidding model for the below-average-bid method is presented and its merits relative to the average-bid method and the low-bid method are explored. The below-average-bid process is investigated analytically and through Monte Carlo simulation. The results of bidding models for the below-average, the average, and the low-bid methods are presented in four easy-to-use nomograms which allow contractors to determine the optimal lump-sum bid price for each method without the need for complicated analysis. A comparison of the three methods provides information and insights to help owners with the difficult choice of a suitable bidding method for the project at hand. [ABSTRACT FROM AUTHOR]

In this paper swarm intelligence based methodology is proposed for optimal and reliable design of irrigation channels. The input parameters involved in channel design are prone to uncertainty and the solution of deterministic model may result in flooding risk and affect the stability of the channel. To provide reliability in the design, an overtopping probability constrained design is presented in this study. The deterministic equivalent of the probabilistic constraint is derived by following the principle of first order uncertainty analysis. In order to account for the uncertainty of design parameters in the objective function, a modified cost function is proposed. A methodology is propounded to solve it in a metaheuristic environment and solved it using elitist-mutated particle swarm optimization (EMPSO) method. The EMPSO based solutions are found to be quite successful and better than the classical optimization methods. Finally, it is concluded that the proposed methodology has a good potential for reliable design of composite channels for designer specified reliability values. [ABSTRACT FROM AUTHOR]