Worldwide Residential Soil Regulatory Guidance Values for Chlorinated Ethanes

Surface soil contamination is often regulated using guidance values that specify the maximum amount of pollutant that can be present without prompting a regulatory response. In the United States, there are at least 89 value sets (and worldwide there are another 29) that provide guidance for at least one of the nine chlorinated ethanes. The most commonly regulated chlorinated ethane is 1,2-dichloroethane (108 values), and it is the third most commonly regulated synthetic organic surface soil contaminant. Pentachloroethane (17 values) is the least regulated chlorinated ethane. Overall, there are at least 690 guidance values for chlorinated ethanes. This analysis explores the origin, magnitude, and form of the variability of these values. Results indicate that the values span from 3.7 to 7.6 orders of magnitude and are distributed in patterns similar to log-normal random variables. Less than 20% of these values are similar to those of national regulatory agencies such as the U.S. EPA or the Canadian Council of Ministers of the Environment, but more than 60% of the values fall within the 95% confidence interval bounds of the uncertainty in U.S. EPA risk model calculations.     

Worldwide Residential Soil Regulatory Guidance Values for Chlorinated Methanes

In many environmental jurisdictions worldwide, surface soil contamination is regulated using guidance values that specify the maximum amount of pollutant that can be present without prompting a regulatory response. Three of the four chlorinated methanes are among the seven most frequently regulated synthetic surface soil contaminants. There are at least 80 U.S. regulatory jurisdictions and at least 30 international jurisdictions with guidance values for at least one of the chlorinated methanes, yielding as many as 106 values (for dichloromethane) for the same regulatory consideration. This analysis explores the variability of these values. Results indicate that the values span at least 5 orders of magnitude and are distributed in patterns similar to a lognormal random variable, but fit distributions that are statistically distinct. The distributions also contain value clusters that may imply emerging consensus about appropriate regulatory levels or demonstrate the impact of regulatory leadership to suppress variability. Simulation based on the current U.S. Environmental Protection Agency risk analysis model are used to estimate the degree to which value ranges may be attributed to uncertainty in exposure models. Approximately 50% of guidance values fall within the 95% confidence interval uncertainty bounds of risk model results.     

Analysis of Regulatory Guidance Values for Residential Surface Soil Arsenic Exposure

Residential surface soil regulatory guidance values (RGVs) specify the threshold at which soil contamination requires action. Usually, RGVs are risk-based values based on child ingestion, inhalation, and dermal exposure. The U.S. Environmental Protection Agency, 45 U.S. states, and 27 other nations have developed arsenic surface soil RGVs. Regulating arsenic poses unusual problems because it presents both cancer and noncancer risks, and its background concentration often exceeds health-based risk levels. Statistical analyses are presented to characterize 119 arsenic surface soil RGVs. State values vary between 0.039 and 200 mg/kg. Worldwide values vary between 1.7 and 687 mg/kg. The U.S. and worldwide values resemble lognormal probability distributions but the data cannot be mingled since worldwide values are significantly higher. An analysis of 40 arsenic background studies yielding averages between 1.3 and 45.1 mg/kg is also presented. Monte Carlo simulations of screening model calculations are used to explore the impact of coefficient uncertainty. Results indicate that 95% of cancer-based results should fall between 0.004 and 2.7 mg/kg and 95% of noncancer results should fall between 1.0 and 40 mg/kg. Although U.S. state arsenic RGVs vary by 3.7 orders of magnitude, most values appear to fall within the bounds of plausible risk- and background-based values.     

Statistical Analysis of BTEX Surface Soil Regulatory Guidance Values

Residential surface soil regulatory guidance values (RGVs) specify the threshold at which soil contamination requires action. Usually, these are risk-based values based on child ingestion, inhalation, and dermal exposure. Benzene, toluene, ethylbenzene, and xylenes (BTEX) are among the five most commonly regulated soil contaminants in the United States and worldwide. More than 100 regulatory jurisdictions have established surface soil RGVs for BTEX compounds. Analysis of these values indicates that they vary by several orders of magnitude and appear to fit a lognormal random variable model with values well dispersed across the number spans. The RGVs applied to benzene are statistically distinct from those applied to TEX contamination, but the TEX values appear to be statistically indistinguishable. The magnitude of difference between TEX RGVs of different jurisdictions appears to be more significant than differences in the T, E, and X values specified by any one jurisdiction. Although value distributions are dominated by randomness, some contain clusters of points that are unlikely to be random and may represent consensus on appropriate values. Where “consensus clusters” exist, they should be identified and explored. The mechanistic explanations for cluster values may yield methods of reducing RGV variability.     

Identification of Statistically Homogeneous Soil Layers Using Modified Bartlett Statistics

Stationarity or statistical homogeneity is an important prerequisite for subsequent statistical analysis on a given section of a soil profile to be valid. The estimation of important soil statistics such as the variance is likely to be biased if the profile is not properly demarcated into stationary sections. Existing classical statistical tests are inadequate even for simple identification of stationarity in the variance because the spatial variations of soil properties are generally correlated with each other. In this paper, a modified Bartlett statistical test is proposed to provide a more rational basis for rejecting the null hypothesis of stationarity in the correlated case. The accompanying rejection criteria are determined from simulated correlated sample functions and summarized into a convenient form for practical use. A statistical-based soil boundary identification procedure is then developed using the modified Bartlett test statistic. Based on the analysis of a piezocone sounding record, two advantages can be discerned. First, the proposed procedure provides a useful supplement to existing empirical soil classification charts, especially in situations where inherent variability tends to complicate interpretation of soil layers. Second, various key assumptions in geostatistical analysis such as stationarity and choice of trend function can be verified more rigorously using the framework of hypothesis testing.     

Quasi-Monte Carlo Simulation with Low-Discrepancy Sequence for Reinforced Soil Slopes

This paper describes a precise numerical technique to compute the limit state exceedance probability of geosynthetic reinforced soil (GRS) slopes with normally distributed backfill and foundation soils by using the low-discrepancy sequence Monte Carlo (LDSMC) and importance sampling with LDSMC (ISLDSMC) methods. The LDSMC and ISLDSMC methods can effectively compute an accurate limit state exceedance probability of GRS slopes with a limited number of simulations. By using importance sampling, random variables can be generated in an expected failure region, thereby enabling enumeration by the Monte Carlo simulation. The failure region can be searched by the conventional first-order reliability method. To increase the computational efficiency, a low-discrepancy sequence, which is a sequence of quasi-random numbers with uniform distribution, is adopted in this study. The numerical simulation in this study revealed that the LDSMC and ISLDSMC methods can effectively compute an accurate limit state exceedance probability of GRS slopes by performing comparatively fewer simulations than the conventional crude Monte Carlo simulation.     

Postprocessing the Hybrid Method for Addressing Uncertainty in Risk Assessments

In a previous paper in this Journal, a “hybrid method” was proposed for the joint propagation of probability distributions (expressing variability) and possibility distributions (i.e., fuzzy numbers, expressing imprecision or partial ignorance) in the computation of risk. In order to compare the results of the hybrid computation (a random fuzzy set) to a tolerance threshold (a tolerable level of risk), a postprocessing method was proposed. Recent work has highlighted a shortcoming of this postprocessing step which yields overly conservative results. A postprocessing method based on Shafer’s theory of evidence provides a rigorous answer to the problem of comparing a random fuzzy set with a threshold. The principles behind the new postprocessing scheme are presented and illustrated with a synthetic example.     

Undrained Bearing Capacity of Two-Strip Footings on Spatially Random Soil

A probabilistic study on the interference of two parallel rough rigid strip footings on a weightless soil with a randomly distributed undrained shear strength performed. The problem is studied using the random finite element method, where nonlinear finite element analysis is merged with random field theory within a Monte Carlo framework. The variability of undrained shear strength is characterized by a lognormal distribution and an exponentially decaying spatial correlation length. The estimated bearing capacity statistics of isolated and two footings cases are compared and the effect of footing interference discussed. Although interference between footings on frictionless materials is not very great, the effect is shown to be increased by soil variability and spatial correlation length.     

Probabilistic Estimation and Allocation of Project Time Contingency

Project managers implement the concept of time contingency to consider uncertainty in duration estimates and prevent project completion delays. Some project managers also build a distribution of the project time contingency into the project activities to create a more manageable schedule. Generally, both the estimation and distribution of the project time contingency are conducted by using subjective approaches. Because the project schedule feasibility mainly depends on the variable behavior of the project activities, the estimate of project time contingency and its allocation at the activity level should be obtained by considering the performance variability of each activity rather than basing on human judgment. In this paper, the stochastic allocation of project allowances method, which is based on Monte?Carlo simulation, is proposed to estimate the project time contingency and allocate it among the project activities. The application of this method to a three-span bridge project results in a fair allocation of the project time contingency and provides practical means to control time contingencies at the activity level.     

Probabilistic Approach to the Solution of Inverse Problems in Civil Engineering

A wide range of important problems in civil engineering can be classified as inverse problems. In such problems, the observational data regarding the performance of a system is known, and the characteristics of the system and/or the input are sought. There are two general approaches to the solution of inverse problems: deterministic and probabilistic. Traditionally, inverse problems in civil engineering have been solved using a deterministic approach. In this approach, the objective is to find a specific model of a system that its theoretical response best fits the observed data. Obtaining the best fit solution, however, does not provide any information regarding the effect of data and/or theoretical uncertainties on the obtained solution. In this paper, a general probabilistic approach to the solution of the inverse problems is introduced, which provides uncertainty measures for the obtained solution. Techniques for direct analytical evaluation and numerical approximation of the probabilistic solution using Monte Carlo Markov Chains, with and without neighborhood algorithm approximation, are introduced and explained. The presented concepts and techniques and their application are then illustrated in practical terms using a simple example of a modulus determination experiment.     

Monte–Carlo Based Method for Predicting Extreme Value Statistics of Uncertain Structures

In the present paper, a simple method is proposed for predicting the extreme response of uncertain structures subjected to stochastic excitation. Many of the currently used approaches to extreme response predictions are based on the asymptotic generalized extreme value distribution, whose parameters are estimated from the observed data. However, in most practical situations, it is not easy to ascertain whether the given response time series contain data above a high level that are truly asymptotic, and hence the obtained parameter values by the adopted estimation methods, which points to the appropriate extreme value distribution, may become inconsequential. In this paper, the extreme value statistics are predicted taking advantage of the regularity of the tail region of the mean upcrossing rate function. This method is instrumental in handling combined uncertainties associated with nonergodic processes (system uncertainties) as well as ergodic ones (stochastic loading). For the specific applications considered, it can be assumed that the considered time series has an extreme value distribution that has the Gumbel distribution as its asymptotic limit. The present method is numerically illustrated through applications to a beam with spatially varying random properties and wind turbines subjected to stochastic loading.     

Stochastic Finite-Element Approach to Quantify and Reduce Uncertainty in Pollutant Transport Modeling

One of the important issues in simulation of contaminant transport in the subsurface is how to quantify the hydraulic properties of soil that are randomly variable in space because of soil heterogeneity. Stochastic approaches have the potential to represent spatially variable parameters, making them an appropriate tool to incorporate the effects of the spatial variability of soil hydraulic properties on contaminant fate. This paper presents development and application of a numerical model for simulation of advective and diffusive-dispersive contaminant transport using a stochastic finite-element approach. Employing the stochastic finite-element method proposed in this study, the response variability is reproduced with a high accuracy. Comparison of the results of the proposed method with the results obtained using the Monte?Carlo approach yields a pronounced reduction in the computation cost while resulting in virtually the same response variability as the Monte?Carlo technique.     

Probabilistic Assessment of Slope Stability That Considers the Spatial Variability of Soil Properties

In this paper, a numerical procedure for probabilistic slope stability analysis is presented. This procedure extends the traditional limit equilibrium method of slices to a probabilistic approach that accounts for the uncertainties and spatial variation of the soil strength parameters. In this study, two-dimensional random fields were generated based on a Karhunen-Loève expansion in a fashion consistent with a specified marginal distribution function and an autocorrelation function. A Monte Carlo simulation was then used to determine the statistical response based on the generated random fields. This approach makes no assumption about the critical failure surface. Rather, the critical failure surface corresponding to the input random fields of soil properties is searched during the process of analysis. A series of analyses was performed to verify the application potential of the proposed method and to study the effects of uncertainty due to the spatial heterogeneity on the stability of slope. The results show that the proposed method can efficiently consider the various failure mechanisms caused by the spatial variability of soil property in the probabilistic slope stability assessment.     

Transitional Markov Chain Monte Carlo Method for Bayesian Model Updating, Model Class Selection, and Model Averaging

This paper presents a newly developed simulation-based approach for Bayesian model updating, model class selection, and model averaging called the transitional Markov chain Monte Carlo (TMCMC) approach. The idea behind TMCMC is to avoid the problem of sampling from difficult target probability density functions (PDFs) but sampling from a series of intermediate PDFs that converge to the target PDF and are easier to sample. The TMCMC approach is motivated by the adaptive Metropolis–Hastings method developed by Beck and Au in 2002 and is based on Markov chain Monte Carlo. It is shown that TMCMC is able to draw samples from some difficult PDFs (e.g., multimodal PDFs, very peaked PDFs, and PDFs with flat manifold). The TMCMC approach can also estimate evidence of the chosen probabilistic model class conditioning on the measured data, a key component for Bayesian model class selection and model averaging. Three examples are used to demonstrate the effectiveness of the TMCMC approach in Bayesian model updating, model class selection, and model averaging.     

Computing Three-Axis Orientations of a Tunnel-Boring Machine through Surveying Observation Points

This research aims to develop an alternative solution to computing the three-axis orientations of a tunnel-boring machine (TBM) during microtunneling and pipe-jacking operations. Comprehensive geometric foundations are given to shed light on the computing mechanism for deriving the TBM’s three rotation angles of yaw, pitch, and roll through surveying a limited quantity of observation points on the TBM. Two well-established computing algorithms in space science are elaborated, including the deterministic triaxis attitude determination (TRIAD) algorithm and the optimal quaternion method. Monte?Carlo simulations are conducted to assess the accuracies on the orientations determined by the two algorithms, given (1)?different levels of point surveying errors and (2)?varying distances between observation points. In relation to microtunneling applications, four layout options for fixing the observation points on the TBM are designed and evaluated. To prove the concept and verify the application value of the proposed computing approach, a practical implementation case is presented, in which the computational method of quaternion was used to fix a working TBM’s orientations on a microtunneling site.     

Assessing the Impacts of Nutrient Load Uncertainties on Predicted Truckee River Water Quality

This study examined the effects of uncertain model boundary conditions on dissolved oxygen (DO) predictions for the lower Truckee River, Nevada using an augmented version of the EPA’s Water Quality Analysis Simulation Program Version 5 (WASP5) that included periphyton, or attached algae, in eutrophication kinetics. Uncertainty analyses were performed on selected organic nitrogen (ON) and carbonaceous biochemical oxygen demand boundary conditions using Monte Carlo techniques. The stochastic model was run using boundary concentrations assigned from observed probability distributions. Ranges of simulated values were used to construct confidence intervals, the magnitudes of which indicated the uncertainty associated with model predictions. Uncertainty in agricultural ditch return concentrations had minimal effects on in-stream model predictions, as predicted values of daily minimum and maximum DOs, daily average ON, and periphyton biomass all failed to show significant variability as a result of ditch concentration uncertainty. This result indicates that while ditch return nutrient loads are not trivial, their exact concentrations are not needed to make relatively accurate predictions of in-stream DO. However, uncertainty in the upstream ON boundary did result in significant uncertainty during summer months with regard to in-stream model predictions of ON, periphyton biomass, and DO. The model is clearly more sensitive to changes in this boundary than to changes in agricultural ditch concentrations.     

Stochastic Six-Degree-of-Freedom Flight Simulator for Passively Controlled High-Power Rockets

This paper presents a method for simulating the flight of a passively controlled rocket in six degrees of freedom, and the descent under parachute in three degrees of freedom. Also presented is a method for modeling the uncertainty in both the rocket dynamics and the atmospheric conditions using stochastic parameters and the Monte Carlo method. Included within this, we present a method for quantifying the uncertainty in the atmospheric conditions using historical atmospheric data. The core simulation algorithm is a numerical integration of the rocket’s equations of motion using the Runge-Kutta-Fehlberg method. The position of the rocket’s center of mass is described using three dimensional Cartesian coordinates and the rocket’s orientation is described using quaternions. Input parameters to the simulator are made stochastic by adding Gaussian noise. In the case of atmospheric parameters, the variance of the noise is a function of altitude and noise at adjacent altitudes is correlated. The core simulation algorithm, with stochastic parameters, is run within a Monte Carlo wrapper to evaluate the overall uncertainty in the rocket’s flight path. The results of a demonstration of the simulator, where it was used to predict the flight of real rocket, show the rocket landing within the 1σ area predicted by the simulation. Also lateral acceleration during weather cocking, which was measured in the test, shows a strong correlation with simulated values.     

Statistical Modeling of Coupled Shear-Moment Resistance for RC Bridge Girders

Many reinforced concrete bridges are posted or restricted to traffic, and repair or replacement decisions for these bridges involves both economical and safety considerations. To avoid the high costs of unnecessary replacement or repair, safety evaluation should be done with the most accurate methods available. Due to variability in material properties, geometrical properties, and methods of analysis, load carrying capacity evaluation may lead to uncertain outcomes. This paper presents a statistical model for combined shear-moment resistance of conventionally reinforced concrete bridge girders with common vintage design details and properties. New statistical data on stirrup spacing variability were developed from field measurements on in-service deck-girder bridges and these were combined with available data in the literature to model resistance uncertainty. The model offers bias factor and coefficient of variation for combined moment and shear carrying capacity per modified compression field theory. AASHTO-LRFD and ACI-318 were utilized to calculate capacity of the selected sections and strength reduction factors in AASHTO-LRFD and ACI-318 were compared using the obtained statistical parameters.     

Finite Difference Method for Computation of 1D Pollutant Migration through Saturated Homogeneous Soil Media

The physical processes such as advection, dispersion, and diffusion and interaction between the solution and the soil solids such as sorption, biodegradation, and retention processes have been considered in the governing equation used in the present study. Finite difference method has been adopted herein to solve the one-dimensional contaminant transport model to predict the pollutant migration through soil in waste landfill. In the finite difference technique, the velocity field is first determined within a hydrologic system, and these velocities are then used to calculate the rate of contaminant migration by solving the governing equation. A total of seven contaminants have been chosen for analysis to represent a wide variety of wastes both organic and inorganic. A computer software CONTAMINATE has been developed for solution of the contaminant transport model. Results of this study have been compared with existing analytical solution for validation of the proposed solution technique. Design charts for liners have also been developed to facilitate the designers. The liner thickness has been optimized by considering the effect of velocity of advection, dispersion coefficient, and geochemical reactions for all the contaminants of this study.