Risk management of BTEX contamination in ground water--an integrated fuzzy approach

An integrated fuzzy simulation-assessment method (FSAM) was developed for assessing environmental risks from petroleum hydrocarbon contamination in ground water. In the FSAM, techniques of fuzzy simulation and fuzzy risk assessment were coupled into a general framework to reflect a variety of system uncertainties. A petroleum-contaminated site located in western Canada was selected as a study case for demonstrating applicability of the proposed method. The risk assessment results demonstrated that system uncertainties would significantly impact expressions of risk-level outputs. A relatively deterministic expression of the risks would have clearer representations of the study problem but may miss valuable uncertain information; conversely, an assessment under vaguer system conditions would help reveal potential consequences of adverse effects but would suffer from a higher degree of fuzziness in presenting the modeling outputs. Based on the risk assessment results, a decision analysis procedure was used to calculate a general risk index (GRI) to help identify proper responsive actions. The proposed method was useful for evaluating risks within a system containing multiple factors with complicated uncertainties and interactions and providing support for identifying proper site management strategies.     

An integrated fuzzy-stochastic modeling approach for assessing health-impact risk from air pollution

High concentrations of air pollutants in the ambient environment can result in breathing problems with human communities. Effective assessment of health-impact risk from air pollution is important for supporting decisions of the related detection, prevention, and correction efforts. However, the quality of information available for environmental/health risk assessment is often not satisfactory enough to be presented as deterministic numbers. Stochastic method is one of the methods for tackling those uncertainties, by which uncertain information can be presented as probability distributions. However, if the uncertainties can not be presented as probabilities, they can then be handled through fuzzy membership functions. In this study, an integrated fuzzy-stochastic modeling (IFSM) approach is developed for assessing air pollution impacts towards asthma susceptibility. This development is based on Monte Carlo simulation for the fate of SO₂ in the ambient environment, examination of SO₂ concentrations based on the simulation results, quantification of evaluation criteria using fuzzy membership functions, and risk assessment based on the combined fuzzy-stochastic information. The IFSM entails (a) simulation for the fate of pollutants in ambient environment, with the consideration of source/medium uncertainties, (b) formulation of fuzzy air quality management criteria under uncertain human-exposure pathways, exposure dynamics, and SPG-response variations, and (c) integrated risk assessment under complexities of the combined fuzzy/stochastic inputs of contamination level and health effect (i.e., asthma susceptibility). The developed IFSM is applied to a study of regional air quality management. Reasonable results have been generated, which are useful for evaluating health risks from air pollution. They also provide support for regional environmental management and urban planning.     

Probabilistic-fuzzy health risk modeling

Health risk analysis of multi-pathway exposure to contaminated water involves the use of mechanistic models that include many uncertain and highly variable parameters. Currently, the uncertainties in these models are treated using statistical approaches. However, not all uncertainties in data or model parameters are due to randomness. Other sources of imprecision that may lead to uncertainty include scarce or incomplete data, measurement error, data obtained from expert judgment, or subjective interpretation of available information. These kinds of uncertainties and also the non-random uncertainty cannot be treated solely by statistical methods. In this paper we propose the use of fuzzy set theory together with probability theory to incorporate uncertainties into the health risk analysis. We identify this approach as probabilistic-fuzzy risk assessment (PFRA). Based on the form of available information, fuzzy set theory, probability theory, or a combination of both can be used to incorporate parameter uncertainty and variability into mechanistic risk assessment models. In this study, tap water concentration is used as the source of contamination in the human exposure model. Ingestion, inhalation and dermal contact are considered as multiple exposure pathways. The tap water concentration of the contaminant and cancer potency factors for ingestion, inhalation and dermal contact are treated as fuzzy variables while the remaining model parameters are treated using probability density functions. Combined utilization of fuzzy and random variables produces membership functions of risk to individuals at different fractiles of risk as well as probability distributions of risk for various alpha-cut levels of the membership function. The proposed method provides a robust approach in evaluating human health risk to exposure when there is both uncertainty and variability in model parameters. PFRA allows utilization of certain types of information which have not been used directly in existing risk assessment methods.     

Risk tolerance measure for decision-making in fuzzy analysis: a health risk assessment perspective

In risk assessment studies it is important to determine how uncertain and imprecise knowledge should be included into the simulation and assessment models. Thus, proper evaluation of uncertainties has become a major concern in environmental and health risk assessment studies. Previously, researchers have used probability theory, more commonly Monte Carlo analysis, to incorporate uncertainty analysis in health risk assessment studies. However, in conducting probabilistic health risk assessment, risk analyst often suffers from lack of data or the presence of imperfect or incomplete knowledge about the process modeled and also the process parameters. Fuzzy set theory is a tool that has been used in propagating imperfect and incomplete information in health risk assessment studies. Such analysis result in fuzzy risks which are associated with membership functions. Since possibilistic health risk assessment studies are relatively new, standard procedures for decision-making about the acceptability of the resulting fuzzy risk with respect to a crisp standard set by the regulatory agency are not fully established. In this paper, we are providing a review of several available approaches which may be used in decision-making. These approaches involve defuzzification techniques, the possibility and the necessity measures. In this study, we also propose a new measure, the risk tolerance measure, which can be used in decision making. The risk tolerance measure provides an effective metric for evaluating the acceptability of a fuzzy risk with respect to a crisp compliance criterion. Fuzzy risks with different membership functions are evaluated with respect to a crisp compliance criterion by using the possibility, the necessity, and the risk tolerance measures and the results are discussed comparatively.     

Joint Monte Carlo and possibilistic simulation for flood damage assessment

A joint Monte Carlo and fuzzy possibilistic simulation (MC-FPS) approach was proposed for flood risk assessment. Monte Carlo simulation was used to evaluate parameter uncertainties associated with inundation modeling, and fuzzy vertex analysis was applied for promulgating human-induced uncertainty in flood damage estimation. A study case was selected to show how to apply the proposed method. The results indicate that the outputs from MC-FPS would present as fuzzy flood damage estimate and probabilistic-possibilistic damage contour maps. The stochastic uncertainty in the flood inundation model and fuzziness in the depth-damage functions derivation would cause similar levels of influence on the final flood damage estimate. Under the worst scenario (i.e. a combined probabilistic and possibilistic uncertainty), the estimated flood damage could be 2.4 times higher than that computed from conventional deterministic approach; considering only the pure stochastic effect, the flood loss would be 1.4 times higher. It was also indicated that uncertainty in the flood inundation modeling has a major influence on the standard deviation of the simulated damage, and that in the damage-depth function has more notable impact on the mean of the fitted distributions. Through applying MC-FPS, rich information could be derived under various α-cut levels and cumulative probabilities, and it forms an important basis for supporting rational decision making for flood risk management under complex uncertainties.     

An inexact fuzzy-random-chance-constrained air quality management model

An inexact fuzzy-random-chance-constrained programming model (IFRCCMM) was developed for supporting regional air quality management under uncertainty. IFRCCMM was formulated through integrating interval linear programming within fuzzy-random-chance-constrained programming framework. It could deal with parameter uncertainties expressed as not only fuzzy random variables but also discrete intervals. Based on the stochastic and fuzzy chance-constrained programming algorithms, IFRCCMM was solved when constraints was satisfied under different satisfaction and violation levels of constraints, leading to interval solutions with different risk and cost implications. The proposed model was applied to a regional air quality management problem for demonstration. The obtained results indicated that the proposed model could effectively reflect uncertain components within air quality management system through employing multiple uncertainty-characterization techniques (in random, fuzzy and interval forms), and help decision makers analyze trade-offs between system economy and reliability. In fact, many types of solutions (i.e. conservative solutions with lower risks and optimistic solutions with higher risks) provided by IFRCCMM were suitable for local decision makers to make more applicable decision schemes according to their understanding and preference about the risk and economy. In addition, the modeling philosophy is general and applicable to many other environmental problems that may be complicated with multiple forms of uncertainties.     

Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site

Today, in different countries, there exist sites with contaminated groundwater formed as a result of inappropriate handling or disposal of hazardous materials or wastes. Numerical modeling of such sites is an important tool for a correct prediction of contamination plume spreading and an assessment of environmental risks associated with the site. Many uncertainties are associated with a part of the parameters and the initial conditions of such environmental numerical models. Statistical techniques are useful to deal with these uncertainties. This paper describes the methods of uncertainty propagation and global sensitivity analysis that are applied to a numerical model of radionuclide migration in a sandy aquifer in the area of the RRC “Kurchatov Institute” radwaste disposal site in Moscow, Russia. We consider 20 uncertain input parameters of the model and 20 output variables (contaminant concentration in the observation wells predicted by the model for the end of 2010). Monte Carlo simulations allow calculating uncertainty in the output values and analyzing the linearity and the monotony of the relations between input and output variables. For the non monotonic relations, sensitivity analyses are classically done with the Sobol sensitivity indices. The originality of this study is the use of modern surrogate models (called response surfaces), the boosting regression trees, constructed for each output variable, to calculate the Sobol indices by the Monte Carlo method. It is thus shown that the most influential parameters of the model are distribution coefficients and infiltration rate in the zone of strong pipe leaks on the site. Improvement of these parameters would considerably reduce the model prediction uncertainty.     

Coupling fuzzy-chance constrained program with minimax regret analysis for water quality management

Mathematical modeling technique plays an important role for regionalization assessment of integrated economy and environment problems, resulting in provision of decision makers with break-through insights and risk-informed strategies. However, such a planning effort is complicated with a variety of uncertain and dynamic factors as well as their interactions. In this study, a fuzzy-chance constrained programming (FCP) method is firstly developed for addressing uncertainties characterized as fuzzy sets and random variables and, then, minimax regret (MMR) analysis technique is advanced to determine desired alternative that can reflect compromises between maximized system benefit and minimized system-failure risk. FCP coupled with MMR is applied to a real-case study of water quality management through optimizing chemical industry activities of the New Binhai District, an economically and industrially fast growing region in the center of northern China. Modeling formulation can analyze interactions among criteria of industry layout, economic benefit, pollution mitigation, and water quality security. Solutions for planning the water quality management have been generated, reflecting that there is trade-off among industrial structure, environmental protection, and economic development.     

Dual inexact fuzzy chance-constrained programming for planning waste management systems

This study develops a dual inexact fuzzy chance-constrained programming (DIFCCP) method for planning municipal solid waste (MSW) management systems. The concept of random boundary interval (RBI) is introduced to address the high uncertain parameters in the studied system. Fuzzy flexible programming and chance-constrained programming are also introduced to take into account the uncertainties of RBIs and various uncertainties in MSW management system. Compared with the existing methods, the developed method could deal with the uncertainty without simplification and thus is more robust. Moreover, the potential system-failure risks in MSW management system due to the existing uncertainties could be quantified by means of violation levels and satisfaction levels in DIFCCP. The developed method then is applied to a MSW management system. The obtained solutions could be used for generating efficient management schemes. The values of violation and satisfaction levels could help decision makers understand the tradeoffs between system cost and system-failure risk, and identify desired strategy according to the practical economic and environmental situation.     

Risk and uncertainty analysis of gas pipeline failure and gas combustion consequence

Taking into account a general concept of risk parameters and knowing that natural gas provides very significant portion of energy, firstly, it is important to insure that the infrastructure remains as robust and reliable as possible. For this purpose, authors present available statistical information and probabilistic analysis related to failures of natural gas pipelines. Presented historical failure data is used to model age-dependent reliability of pipelines in terms of Bayesian methods, which have advantages of being capable to manage scarcity and rareness of data and of being easily interpretable for engineers. The performed probabilistic analysis enables to investigate uncertainty and failure rates of pipelines when age-dependence is significant and when it is not relevant. The results of age-dependent modeling and analysis of gas pipeline reliability and uncertainty are applied to estimate frequency of combustions due to natural gas release when pipeline failure occurs. Estimated age-dependent combustion frequency is compared and proposed to be used instead of conservative and age-independent estimate. The rupture of a high-pressure natural gas pipeline can lead to consequences that can pose a significant threat to people and property in the close vicinity to the pipeline fault location. The dominant hazard is combustion and thermal radiation from a sustained fire. The second purpose of the paper is to present the combustion consequence assessment and application of probabilistic uncertainty analysis for modeling of gas pipeline combustion effects. The related work includes performance of the following tasks: to study gas pipeline combustion model, to identify uncertainty of model inputs noting their variation range, and to apply uncertainty and sensitivity analysis for results of this model. The performed uncertainty analysis is the part of safety assessment that focuses on the combustion consequence analysis. Important components of such uncertainty analysis are qualitative and quantitative analysis that identifies the most uncertain parameters of combustion model, assessment of uncertainty, analysis of the impact of uncertain parameters on the modeling results, and communication of the results’ uncertainty. As outcome of uncertainty analysis the tolerance limits and distribution function of thermal radiation intensity are given. The measures of uncertainty and sensitivity analysis were estimated and outcomes presented applying software system for uncertainty and sensitivity analysis. Conclusions on the importance of the parameters and sensitivity of the results are obtained using a linear approximation of the model under analysis. The outcome of sensitivity analysis confirms that distance from the fire center has the greatest influence on the heat flux caused by gas pipeline combustion.     

Probability-credibility health risk assessment under uncertain environment

The ability to describe variables in a health risk model through probability theory enables us to estimate human health risk. These types of risk assessment are interpreted as probabilistic risk assessment (PRA). Generally, PRA requires specific estimate of the parameters of the probability density of the input variables. In all circumstances, such estimates of the parameters may not be available due to the lack of knowledge or information. Such types of variables are treated as uncertain variables. These types of information are often termed uncertainty which are interpreted through fuzzy theory. The ability to describe uncertainty through fuzzy set theory enables us to process both random variable and fuzzy variable in a single framework. The method of processing aleatory and epistemic uncertainties into a same framework is coined as hybrid method. In this paper, we are going to talk about such type of hybrid methodology for human health risk assessment. Risk assessment on human health through different pathways of exposure has been attempted many a times combining Monte Carlo analysis and extension principle of fuzzy set theory. The emergence of credibility theory enables transforming fuzzy variable into credibility distribution function which can be used in those hybrid analyses. Hence, an attempt, for the first time, has been made to combine probability theory and credibility theory to estimate risk in human health exposure. This method of risk assessment in the presence of credibility theory and probability theory is identified as probabilistic-credibility method (PCM). The results obtained are then interpreted through probability theory, unlike the other hybrid methodology where the results are interpreted in terms of possibility theory. The results obtained are then compared with probability-fuzzy risk assessment (PFRA) method. Generally, decision under hybrid methodology is made on the index of optimism. An optimistic decision maker estimates from the \(\alpha\)-cut at 1, whereas a pessimistic decision maker estimates from the \(\alpha\)-cut at 0. The PCM is an optimistic approach as the decision is always made at \(\alpha\)=1.     

Risk analysis for water resources management under dual uncertainties through factorial analysis and fuzzy random value-at-risk

Water resources systems are associated with a variety of complexities and uncertainties due to socio-economic and hydro-environmental impacts. Such complexities and uncertainties lead to challenges in evaluating the water resources management alternatives and the associated risks. In this study, the factorial analysis and fuzzy random value-at-risk are incorporated into a two-stage stochastic programming framework, leading to a factorial-based two-stage programming with fuzzy random value-at-risk (FTSPF). The proposed FTSPF approach aims to reveal the impacts of uncertainty parameters on water resources management strategies and the corresponding risks. In detail, fuzzy random value-at-risk is to reflect the potential risk about financial cost under dual uncertainties, while a multi-level factorial design approach is used to reveal the interaction between feasibility degrees and risk levels, as well as the relationships (including curvilinear relationship) between these factors and the responses. The application of water resources system planning makes it possible to balance the satisfaction of system benefit, the risk levels of penalty and the feasibility degrees of constraints. The results indicate that decision makers would pay more attention to the tradeoffs between the system benefit and feasibility degree, and the water allocation for agricultural section contributes most to control the financial loss of water. Moreover, FTSPF can generate a higher system benefit and more alternatives under various risk levels. Therefore, FTSPF could provide more useful information for enabling water managers to identify desired policies with maximized system benefit under different system-feasibility degrees and risk levels.     

Fuzzy rule based seismic risk assessment of one-story precast industrial buildings

Efficient tools capable of using uncertain data to produce fast and approximate results are more practical in rapid decision-making applications when compared to conventional methods. From this point of view, this study introduces a risk assessment model for one-story precast industrial buildings by fuzzy logic which builds a bridge between uncertainty and precision. The input, output and relations of the fuzzy based risk assessment model(FBRAM) were determined by reference buildings. The Monte Carlo simulation method was used to handle uncertainties associated with the structural characteristics of the reference buildings. Section dimension, longitudinal reinforcement ratio, column height related to building elevation, confinement ratio and seismic hazard are regarded as input and the plastic demand ratio is considered as the output parameter by the mathematical formulation of strength and deformation capacity of the buildings. The supervised learning method was used to determine the membership function of fuzzy sets. Fuzzy rules of FBRAM were constructed from Monte Carlo simulation by mapping of inputs and output. FBRAM was evaluated by a group of simulated buildings and two existing precast industrial buildings. Comparisons have shown significant agreement with analytical model results in both cases. Consequently, it is anticipated that the proposed model can be used for the seismic risk mitigation of precast buildings.     

Dealing with uncertainty in risk assessments in early stages of a CO<Subscript>2</Subscript> geological storage project: comparison of pure-probabilistic and fuzzy-probabilistic frameworks

CO₂ capture and storage is recognized as a promising solution among others to tackle greenhouse gas emissions. This technology requires robust risk assessment and management from the early stages of the project (i.e. during the site selection phase, prior to injection), which is a challenging task due to the high level of aleatory and epistemic uncertainties. This paper aims at implementing and comparing two frameworks for dealing with uncertainties: a classical probabilistic framework and a probabilistic-fuzzy-based (i.e. jointly combining fuzzy sets and probabilities) one. The comparison of both frameworks is illustrated for assessing the risk related to leakage of brine through an abandoned well on a realistic site in the Paris basin (France). For brine leakage flow computation, a semi-analytical model, requiring 25 input parameters, is used. Depending on the framework, available data is represented in a different manner (either using classical probability laws or interval-valued tools). Though the fuzzy-probabilistic framework for uncertainty propagation is computationally more expensive, it presents the major advantage to highlight situations of high degree of epistemic uncertainty: this enables nuancing a too-optimistic decision-making only supported by a single probabilistic curve (i.e. using the Monte-Carlo results). On this basis, we demonstrate how fuzzy-based sensitivity analysis can help identifying how to reduce the imprecision in an effective way, which has useful applications for additional studies. This study highlights the importance of choices in the mathematical tools for representing the lack of knowledge especially in the early phases of the project, where data is scarce, incomplete and imprecise.     

Accounting for source location errors in the bayesian analysis of seismicity and seismic hazard

A method is presented for incorporating the uncertainties associated with hypocentral locations in the formulation of probabilistic models of the time and space distributions of the activity of potential seismic sources, as well as of the resulting seismic hazard functions at sites in their vicinity. For this purpose, a bayesian framework of analysis is adopted, where the probabilistic models considered are assumed to have known forms and uncertain parameters, the distribution of the latter being the result of an a priori assessment and its updating through the incorporation of the direct statistical information, including the uncertainty associated with the relations between the actual hypocentral locations and the reported data. This uncertainty is incorporated in the evaluation of the likelihood function of the parameters to be estimated for a given sample of recorded locations. For the purpose of illustration, the method proposed is applied to the modelling of the seismic sources near a site close to the southern coast of Mexico. The results of two alternate algorithms for the incorporation of location uncertainties are compared with those arising from neglecting those uncertainties. One of them makes use of Monte Carlo simulation, while the other is based on a closed-form analytical integration following the introduction of some simplifying assumptions. For the particular case studied, accounting for location uncertainties gives place to significant changes in the probabilistic models of the seismic sources. Deviations of the same order of magnitude can be ascribed to differences in the mathematical and/or numerical tools used in the uncertainty analysis. The resulting variability of the seismic hazard at the site of interest is less pronounced than that affecting the estimates of activity of individual seismic sources.     

Incorporating the LCIA concept into fuzzy risk assessment as a tool for environmental impact assessment

Environmental impact assessment (EIA) is a procedural tool for environmental management that identifies, predicts, evaluates and mitigates the environmental impact of development proposals. In the process of EIA, EIA reports, prepared by developers, are expected to delineate the environmental impact, but in practice they usually determine whether the amounts or concentrations of pollutants comply with the relevant standards. Actually, many analytical tools can improve the analysis of environmental impact in EIA reports, such as life cycle assessment (LCA) and environmental risk assessment (ERA). Life cycle impact assessment (LCIA) is one of steps in LCA that takes account of the causal relationships between environmental hazards and damage. Incorporating the concept of LCIA into an ERA as an integrated tool for the preparation of EIA reports extends the focus of the reports from the regulatory compliance of the environmental impact, to determine the significance of the environmental impact. Sometimes, when using integrated tools, it is necessary to consider fuzzy situations, because of a lack of sufficient information; therefore, so ERA should be generalized to a fuzzy risk assessment (FRA). Therefore, this paper proposes the integration of a LCIA and a FRA as an assessment tool for the preparation of EIA reports, whereby the LCIA clearly identifies the causal linkage for hazard–pathway–receptor–damage and then better explain the significance of the impact; furthermore, a FRA copes with fuzzy and probabilistic situations in the assessment of pollution severity and the estimation of exposure probability. Finally, the use of the proposed methodology is demonstrated in a case study of the expansion plan for the world’s largest plastics processing factory.     

Probabilistic failure analysis of riprap as riverbank protection under flood uncertainties

Existing riverbank riprap could face the risk of failure if the flood regime changes in future. Additionally, changed sediment transport in rivers, as a possible result of climate change, impacts the failure risk of flood protection measures. Evaluation of this potential failure is the primary issue of riprap stability and safety assessment. The consequences of the bank failure are probably uncontrolled erosion and flooding with disastrous consequences in residential areas or damage to infrastructures. Thus, a probabilistic analysis of riprap failure considering different mechanisms due to the flood and sediment transport uncertainties is required to assess embankment stability. In this article, the concept of a probabilistic assessment model based on Monte Carlo simulation method, moment analysis methods, and Rosenblueth point estimation method are presented to define the failure risk of riprap as the river bank protection. The probability of failure in different modes, namely direct block erosion, toe scouring and overtopping, has been defined by taking into account the river bed level variation based on bedload transport described with a probabilistic function of the peak discharge. The result of three models comparison revealed a good agreement (the average deviation of less than 2%) in estimation of riprap failure probability. This model is a strategical tool to search the critical river reaches and helps to evaluate the risk maps. So that, the model could cover the engineering aspect of environmental stability in the rivers with riprap as the bank protections.     

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.     

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.     

Multi‐objective risk‐informed design of floor isolation systems

The design of floor isolation systems (FISs) for the protection of acceleration sensitive contents is examined considering multiple objectives, all quantified in terms of the probabilistic system performance. The competing objectives considered correspond to (i) maximization of the level of protection offered to the sensitive content (acceleration reduction) and (ii) minimization of the demand for the isolator displacement capacity and, more importantly, for the appropriate clearance to avoid collisions with surrounding objects (floor displacement reduction). Both of these objectives are probabilistically characterized utilizing a versatile, simulation‐based framework for quantifying seismic risk, addressing all important uncertainties related to the seismic hazard and the structural model. FIS performance is assessed through time‐history analysis, allowing for all important sources of nonlinearity to be directly addressed in the design framework. The seismic hazard is described through a stochastic ground motion model. For efficiently performing the multi‐objective optimization, an augmented surrogate modeling methodology is established, considering development of a single metamodel with respect to both the uncertain model parameters and the design variables for the FIS system. This surrogate model is then utilized to simultaneously support the probabilistic risk assessment and the design optimization to provide the Pareto front of dominant designs. Each of these designs establishes a different compromise between the considered risk‐related objectives offering a variety of potential options to the designer. Within the illustrative example, the efficiency of the established framework is exploited to compare three different FIS implementations, whereas the impact of structural uncertainties on the optimal design is also evaluated. Copyright © 2016 John Wiley & Sons, Ltd.