Rosenblueth's Method Research Articles

Failure Probability and Security Risk Analysis of Gravity-Wharf Structures in Port Engineering

Xie, Y.; Li, P.; Xu, S.; Chen, J., and Feng, H., 2021. Failure probability and security risk analysis of gravity-wharf structures in port engineering. Journal of Coastal Research, 37(5), 1035–1041. Coconut Creek (Florida), ISSN 0749-0208. To assess the security risk of the gravity-wharf overall structure, the failure probability of the overall structure of the gravity wharf is analyzed based on the Rosenblueth method combined with the structural reliability theory. By constructing the serial system of a gravity wharf, a simplified failure model of the overall structure of a gravity wharf is established to obtain the failure probability of the whole wharf structural system. Thus, the security risk assessment of the gravity-wharf structure is realized. The calculation and analysis of the failure risk of a gravity caisson wharf indicates that the reliability index of the gravity-wharf structure at design low water level is much lower than that at design high water level. And at the design low water level, the overall structure has the largest failure probability. The reliability index of antisliding stability of a gravity caisson wharf at design low water level is about 20.6% lower than that at design high water level. And the reliability index of anti-overturning stability at design low water level is about 11.9% lower than that at design high water level. Meanwhile, the failure probability of anti-overturning of the caisson wharf structure is higher than that of antisliding at the same water level. The analysis method in this paper needn't consider the distribution characteristics of each parametric variable, the calculation efficiency of which is high. The analysis conclusions can provide reference for the failure probability and security risk assessment of the gravity-wharf overall structure.

A Suggested Methodology for Assessing the Failure Risk of the Final Slopes of Former Open-Pits in Case of Flooding

Some valuable minerals, such as lignite, are extracted through open-pit mining works. After the cessation of mining activity, large-scale gaps result in the landscape. These gaps, also called “remaining gaps”, represent some of the roughest types of environmental impacts. After the cessation of mining activity, recovery and ecological restoration works are required. However, it is first necessary to carry out risk assessment studies considering the possible future influences on the final slopes. For this study, flooding of the remaining lignite open-pits gaps was considered as the ecological restoration option. The study was based on extensive research, including sampling, laboratory tests, statistical-mathematical processing, hypothesis formulation, evaluations, interpretations, and field observations, regarding the rock behavior and occurrence of negative geotechnical phenomena (geotechnical phenomena that have a negative impact and a risk on the integrity of the environment and local communities, such as landslides, rockfalls, liquefaction, suffosis) during the flooding process. This paper’s originality consists of combining the methods and methodologies developed with the help of classic methods (Fellenius, Janbu, and Bishop methods) and probabilistic ones (Rosenblueth method) existing in the specialized literature for solving the proposed problem and structuring the information similar to a guide.

Effects of Random Variations of Partially Saturated Soils Properties on Site Amplification of Seismic Ground Motions

Based on the principle of random vibration and the Tajimi-Kanai spectrum model, a seismic model with a given magnitude and epicenter distance is used to simulate the seismic motion. For the random variation of soil properties such as shear modulus, mass density, damping ratio and saturation of partially saturated soils, it is assumed that the input seismic wave is SH wave. The random dynamic response analysis of the site is conducted by using the linear wave propagation method and the Rosenblueth method, and the digital features of the amplified power spectral density function, the acceleration power spectrum density, the mean value and the standard deviation are obtained respectively. In a numerical example, a clay ground is considered. For the random variation of soil properties and the different of incident angles, the digital features of the amplified power spectral density function, the acceleration power spectral density, the mean value and the standard deviation are analyzed. The results show that the random variation of quasi saturated soils properties and the different of incident angles have great influence on the site amplification effect.

Point estimation method: Validation, efficiency improvement, and application to embankment slope stability reliability analysis

Calculating the reliability index is a common approach used in structural reliability analysis. It typically involves a procedure for determining the reliability index of a performance function. The method developed by Rosenblueth only requires calculating the objective functions at selected weighting points. The method is easily implemented and free of numerical iteration. However, it requires large storage space for sign information during coding. In the present study, the problem of large storage space is easily solved by taking the binary bits of integers, which can be achieved with most commercial compilers. By conducting an extensive numerical investigation based of the chi-squared goodness test, it is found that the factors of safety obtained in slope stability analysis follow normal distributions if the uncertainty variables are normally distributed. Meanwhile, the factors of safety obtained in retaining-wall stability analysis follow lognormal distributions. Therefore, the conventional slope stability analysis methods are confirmed not substantially change the distribution form of the performance function, which is a condition that makes the Rosenblueth method applicable. In conjunction with other reliability analysis methods (Monte Carlo and FORM), the Rosenblueth method is shown to be useful for the reliability analysis of slopes and retaining walls with satisfactory accuracy. This study applies the proposed method to the analysis of the 165-m-high earth core rockfill Xiaolangdi Dam in China.

Incorporation of reliability of M-E pavement design using variations of backcalculated pavement layer moduli

This paper describes how the uncertainty of estimated variables of the in situ backcalculated moduli can be incorporated in a mechanistic–empirical (M–E) design procedure to determine pavement design reliability. The mean values and standard deviations of backcalculated layer moduli were used as inputs to predict the variance of mechanical responses from the multilayer pavement system using axle load spectrums. The Rosenblueth method is used to estimate the expected value and variance of the computed strains on the basis of backcalculated layer moduli. The developed FORTRAN program, RELIPAVE, has the capacity to consider the reliability of fatigue cracking. The research shows that the Rosenblueth method can help to clarify a pavement's mechanical response under the influence of loading, traffic, and layer moduli. Therefore, the proposed procedure can be used as an effective decision–making tool for engineers to predict the probability of pavement life using FWD test.

Stochastic Analysis of Thermal Cracking Distress of Asphalt Pavements Using the MEPDG Thermal Cracking Model

The objective of the National Cooperative Highway Research Program (NCHRP) 9-22 project was to develop a Quality Assurance (QA) system for asphalt pavements in conjunction with Performance Related Specifications (PRS). The project was originally intended to use the Mechanistic-Empirical Pavement Design Guide (MEPDG) as the performance prediction simulator. However, since the probabilistic assessment of the MEPDG required hundreds, if not thousands, of solution simulations; the computational time was found to be excessive as a quicker solution was critically necessary. The study presented in this paper has been conducted as part of the effort associated with the development of a rapid thermal cracking (TC) prediction methodology and the estimation of the variance of TC. The Rosenblueth method and the Beta frequency distribution were used to estimate the first and second moments (average and standard deviation) of TC and its service life. The proposed TC stochastic framework showed a successful performance and was accordingly incorporated into the PRS QA system developed under NCHRP 9-22. The ultimate purpose of the developed QA system is to stochastically evaluate the incentive/disincentive for the contractors.

Analysis of uncertainty propagation through model parameters and structure

Estimation of uncertainty propagation in watershed models is challenging but useful to total maximum daily load (TMDL) calculations. This paper presents an effective approach, involving the combined application of Rosenblueth method and sensitivity analysis, to the determination of uncertainty propagation through the parameters and structure of the HSPF (Hydrologic Simulation Program-FORTRAN) model. The sensitivity analysis indicates that the temperature is a major forcing function in the DO-BOD balance and controls the overall dissolved oxygen concentration. The mean and standard deviation from the descriptive statistics of dissolved oxygen data obtained using the HSPF model are compared to those estimated using Rosenblueth's method. The difference is defined as the error propagated from water temperature through dissolved oxygen. The error propagation, while considering the second order sensitivity coefficient in Rosenblueth's method, is observed to have a mean of 0.281 mg/l and a standard deviation of 0.099 mg/l. A relative low error propagation value is attributed to low skewness of dependent and independent variables. The results provide new insights into the uncertainty propagation in the HSPF model commonly used for TMDL development.

Assessment of uncertainty sources in water quality modeling in the Niagara River

This paper presents a framework to quantify the overall variability of the model estimations of Total Polychlorinated Biphenyls (Total PCBs) concentrations in the Niagara River on the basis of the uncertainty of few model parameters and the natural variability embedded in some of the model input variables. The results of the uncertainty analysis are used to understand the importance of stochastic model components and their effect on the overall reliability of the model output and to evaluate multiple sources of uncertainty that might need to be further studied. The uncertainty analysis is performed using a newly developed point estimate method, the Modified Rosenblueth method. The water quality along the Niagara River is simulated by coupling two numerical models the Environmental Fluid Dynamic Code (EFDC) – for the hydrodynamic portion of the study and the Water Quality Analysis and Simulation Program (WASP) – for the fate and transport of contaminants. For the monitoring period from May 1995 to March 1997, the inflow Total PCBs concentration from Lake Erie is the stochastic component that most influences the variability of the modeling results for the simulated concentrations at the exit of the Niagara River. Other significant stochastic components in order are as follows: the suspended sediments concentration, the point source loadings and to a minor degree the atmospheric deposition, the flow and the non-point source loadings. Model results that include estimates of uncertainty provide more comprehensive information about the variability of contaminant concentrations, such as confidence intervals, and, in general offer a better approach to compare model results with measured data.

Statistical Applications and Stochastic Analysis for Performance-Related Specification of Asphalt Quality Assurance

Performance-related specification (PRS) is known as the most advanced specification type in asphalt pavement quality assurance (QA). One major feature of PRS QA is the consideration of material variability in performance prediction models through the application of several essential statistical techniques. The uncertainty in material properties can consequently be encoded in the evaluation of asphalt mix quality. For this reason, it is of critical significance to use the statistical applications correctly in PRS QA. One product of the NCHRP 9-22 project is a computerized quality assurance tool, quality-related specification software (QRSS). This computer program can quantitatively evaluate the as-constructed asphalt mix quality against the as-designed mix quality to predict service life. To quantify stochastically the quality of both the as-designed and as-built mixes with the consideration of material variability, several essential statistical techniques were applied to the QA procedure. This paper presents the techniques used and the applications implemented in the QRSS. It includes statistical methods to estimate variance of a multivariate function (e.g., Monte Carlo simulation and Rosenblueth method), conversion methods from distress to service life, expression of predicted distress as well as its service life by using probability distributions, and a method to quantify the relative difference in predicted service life between as-designed and as-constructed mixes with the use of cumulative frequency distributions.

Calculation of reinforced concrete corrosion initiation probabilities using the Rosenblueth method

The Rosenblueth method is used to analyse stochastic parameters in a numerical model to calculate the solution for independent variables. By replacing all or a part of the independent variables with random variables, the solution becomes itself random. The Rosenblueth method simplifies this passage, while being limited to dichotomous random variables. This avoids the complex and computer-intensive Monte Carlo simulation method. A specific example is developed in this article using a non-linear transport model to simulate chloride ion penetration into reinforced concrete and to predict the development of corrosion in the civil structure. The taking into consideration of complex physical chemical processes and a reconstituted climate increases considerably the simulation time, making impossible the usual use of the Monte Carlo method. The two numerical examples show that the exposure degree affects in a dominating way the appearance of structural damage.

Incorporating Reliability into the Definition of the Margin of Safety in Total Maximum Daily Load Calculations

In the calculation of the total maximum daily load (TMDL), the margin of safety (MOS) is an attempt to account for the uncertainties related to the conceptual representation of the system and the inherently random nature of the processes under study. In general, the MOS is often the result of arbitrary or poorly supported decisions that have little to do with the reliability of the system. To improve the current practice in TMDL calculations, an enhanced reliability-based MOS is proposed here. The Modified Rosenblueth point estimate method is proposed in this paper as a valuable means to assess the uncertainty of a system, and, thus, its probability of failure. The Modified Rosenblueth method is a less computationally demanding uncertainty analysis technique, and can be easily coupled with deterministic hydraulic and water quality numerical models. A case study on arsenic concentrations in the Niagara River is discussed in this paper. The results of the uncertainty analysis are used to compute the effecti...

Evaluation of Probabilistic Point Estimate Methods in Uncertainty Analysis for Environmental Engineering Applications

This paper begins with a comprehensive review of various point estimate methods, with an emphasis on their differences and similarities in theory and application. The Rosenblueth probabilistic point estimate method is a computationally straightforward technique for the uncertainty analysis of engineering problems. It is capable of estimating a statistical moment of any order of a model output involving several stochastic variables that are correlated or uncorrelated, symmetric, or asymmetric. However, in multivariate problems with more than two stochastic variables involved, the Rosenblueth method is not able to provide a unique solution, rather an approximate solution to indeterminate problems. This is attributed to the fact that the number of unknowns to be solved is larger than the number of governing equations provided. An improved modified Rosenblueth point estimate method is proposed to circumvent the drawback of the nonunique solution of the original Rosenblueth method and to increase the computational efficiency in modeling. One example application on the particle terminal velocity computation is presented for illustration. A quantitative performance index is introduced to assess the performance of various point estimate methods. It is concluded in this study that the modified Rosenblueth method has a comparable performance to the Rosenblueth method and yet resolves the nonuniqueness problem in solutions.

Effects of random variations of soil properties on site amplification of seismic ground motions

This paper investigates the effects of random variations of soil properties on site amplification of seismic waves. First, based on attenuation laws and the filtered Tajimi–Kanai spectrum, seismic motion at the base rock of a soil site is stochastically generated according to an assumed earthquake with a given magnitude and epicentral distance. Motions on the surface of this layered random soil site are calculated by nonlinear wave propagation methods, and by assuming the incoming seismic wave consisting of SH wave or combined P and SV waves. Soil properties, including shear modulus, damping ratio and mass density, as well as ground water level are considered as random in the numerical calculation. The Rosenblueth method is used to solve the random dynamic responses of the soil site. Parametric calculations are performed to investigate the effects of various parameters on site amplification of seismic waves. The mean and maximum ground motions on surface of the site are estimated. Numerical results indicate that the estimated surface motions differ substantially if the random variations of soil properties and soil saturation level are taken into consideration in the analysis.

Uncertainty Analysis by Point Estimate Methods Incorporating Marginal Distributions

The model performance of an engineering system is affected by many variables subject to uncer­ tainty. Point estimate (PE) methods are practical tools to assess the uncertainty features of a model involving multivariate stochastic parameters. Two PE methods have been developed for engineering applications. One is Rosenblueth's PE method, which preserves the first three moments of random variables and the other is Hare's PE method, which reduces the computations of Rosenblueth's method but only as appropriate for application to random variables with normal distributions. In this study, two algorithms are proposed to encompass the advantages of the two PE methods: computational practicality and the handling of mixture distributions. Through a numerical experiment, the proposed methods yielded more accurate estimations than those of Rosenblueth's method with about the same amount of computation as Hare's method. The two proposed methods were also applied to estimate statistical moments of a pier scouring model output to demonstrate their performance in an engineering application.

Reliability Design of Flexible Airfield Pavements: Elastic Layered Method

A design procedure was developed for layered elastic flexible airfield pavement systems in terms of probability and reliability. A user-friendly computer program, RELIFLEX, was prepared to carry out the computations. The Rosenblueth method is used to estimate the expected value and variance of the computed strains (dependent parameters) on the basis of the input mean values of independent parameters (i.e., aircraft load, layer thicknesses, and material moduli). RELIFLEX has the capability of considering the strain distribution to be normal, lognormal, or beta, and a capacity-demand analysis is included. Only normal distribution is presented. Environmental effects and the lack of fit of the prediction models are not considered in RELIFLEX. The relationships between the reliability level and the allowable strain repetition of the designed system, established using RELIFLEX, provide a decision-making tool for engineers to design pavement at the desired reliability level. For a desired reliability level of the design system, pavement thickness can be varied to agree with the designed coverage or the allowable coverage can be modified for a given pavement thickness.

Point‐Estimate Method for Calculating Statistical Moments

A number of approximate methods exist in the literature for estimating the statistical moments of a random function. The usual approach is based on Taylor series expansion about the mean values of the random variables. This approach requires the calculation of the derivatives of the random function. For complex functions or functions that cannot be expressed in an explicit form, it is desirable to use the so-called point-estimate methods, which do not require the calculation of the derivatives. Point-estimate methods enable the calculation of the expectation of a random function to be calculated based on the values of the function at a specific set of input parameters. In this paper, an efficient point-estimate method is developed, which requires only (\In\N²+3\In\N+2)/2 evaluations of a random function with \In\N random variables. The method is applicable to correlated random variables, and is more accurate than the commonly used Rosenblueth method, which requires a total of 2\I\un\N evaluations of the random function.

Reliability Design Procedures for Flexible Pavements

A procedure is developed to analyze layered elastic flexible pavement systems in terms of reliability. Rosenblueth's method is used to estimate the expected value and variance of the strains (dependent parameters), based on the input mean values of independent parameters, i.e., aircraft load, layer thicknesses, and material moduli. Relationships between reliability level and allowable strain repetition of the designed system provide a decision‐making tool for engineers to design pavements at a desired reliability level. The design can be optimized by selecting thicknesses of bituminous concrete and base layers so that the pavement fails in fatigue cracking of the bituminous concrete and subgrade at nearly the same traffic level for a given reliability level. The performance of conventional flexible pavement is sensitive, in descending order, to variations of gear load P, thickness of the granular base h2, subgrade modulus E3, and thickness and modulus of the bituminous‐concrete surface course h1 and E1, r...

A study on entrainment in various forms of tachycardias.

In order to study the entrainment phenomenon in various forms of clinical and experimental tachycardia, overdrive pacing was performed in clinical paroxysmal supraventricular tachycardia (PSVT) of Wolff-Parkinson-White syndrome (6 cases), atrial flutter (AF-6 cases), ventricular tachycardia (VT-2 cases), experimental AF induced by Rosenblueth's method (5 dogs), and in VT induced by aconitine (5 dogs). Progressive fusion was demonstrated in all but aconitine-induced VT. After cessation of pacing, the first tachycardia complex showed no fusion at all, but the timing of the complex varied depending on the recording sites of the electrogram. The tachycardia complex occurred at the pacing rate only when the electrogram was recorded at the upstream of the pacing site along the reentry circuit in PSVT and experimental AF. In clinical VT, the complex appeared progressively later as the pacing rate was increased. In aconitine-induced experimental VT, the complex occurred at its original tachycardia rate originating from the site where aconitine was applied. In reentrant tachycardia, entrainment could be observed even when all three of the diagnostic criteria proposed by Brugada et al. were not fulfilled. The mechanism of tachycardia can be assessed by entrainment, although the proposed criteria should be reevaluated.

Sensitivity analysis, calibration and predictive uncertainty of the Institute of Hydrology Distributed Model

The physically based Institute of Hydrology Distributed Model is briefly described and its sensitivity to the parameters of the surface and subsurface flow components is examined for the Tanllwyth catchment, Powys, Wales. Model predictions are most sensitive to a surface flow roughness parameter and the saturated hydraulic conductivity of the soil. Uncertainty in the effective values of these parameters is assessed by comparing observed and predicted discharges for a number of storms. The effect of uncertainty in the effective parameter values on the predicted discharges for two additional storms is assessed using the Rosenblueth method.

Simulation for risk analysis with correlated variables

A Monte-Carlo simulation technique for geotechnical risk analysis with correlated random variables is presented. The proposed method is illustrated by an example of time required for water-table draw-down near a box cut of an open strip coal mine. The permeability and storage coefficient are considered as correlated stochastic variables. The results are compared with those achieved by using Rosenblueth's point estimate method for finding statistical moments as well as the well-known Taylor series approach. Excellent agreement is achieved for the first two moments. For higher moments the Rosenblueth method provides a better approximation to the simulation solution than does the Taylor series method. The role of a valid risk analysis technique for correlated variables is discussed and the application of the Paper to stability analysis of slopes is highlighted. L'article présente une technique de simulation type Monte-Carlo pour l'analyse géotechnique des risques avec des variables aléatoires corrélatives. La méthode proposée est illustrée à l'aide de l'exemple du temps nécessaire pour le rabattement de la nappe aquifére dans le voisinage d'une tranchée rectangulaire dans une mine à ciel découvert. La perméabilité et le coefficient d'accumulation sont considérés comme des variables aléatoires corrélatives. On compare les résultats avec ceux obtenus par la méthode d'évaluation par pointes (Rosenblueth) pour découvrir les moments statistiques aussi bien qu'avec la méthode connue des séries de Taylor. Pour les deux premiers moments on obtient un accord excellent. Pour des moments supérieurs la méthode de Rosenblueth offre une meilleure approximation à la solution par simulation que ne le fait la méthode des séries de Taylor. L'article discute le rôle joué par une technique analytique valable des risques pour les variables aléatoires corrélatives et souligne la validité de la méthode présentée pour l'analyse de la stabilité des talus