Evaluation of risk concepts in partial duration series

Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.     

Unbiased estimation of flood risk with the GEV distribution

Conventional flood frequency analysis is concerned with providing an unbiased estimate of the magnitude of the design flow exceeded with the probabilityp, but sampling uncertainties imply that such estimates will, on average, be exceeded more frequently. An alternative approach is therefore, to derive an estimator which gives an unbiased estimate of flow risk: the difference between the two magnitudes reflects uncertainties in parameter estimation. An empirical procedure has been developed to estimate the mean true exceedance probabilities of conventional estimates made using a GEV distribution fitted by probability weighted moments, and adjustment factors have been determined to enable the estimation of flood magnitudes exceeded with, on average, the desired probability.     

Estimation of the Probability of Exceedance of Contaminant Concentrations

Several alternative probability distributions for estimating the probability of exceedance of contaminant concentrations are examined for their appropriateness for developing inputs to risk assessments. The rationale is provided for using the log Pearson Type III distribution, a three-parameter model, for estimation of the exceedance probabilities.     

Seismicity assessment using earthquake catalogues with uncertain and incomplete data: probabilistic formulation

A novel generalized probabilistic formulation is proposed to assess seismicity using earthquake catalogues with uncertain and incomplete data. The seismicity, described by the complete exceedance rate of magnitudes, is estimated starting from a consistent incomplete exceedance rate which is rationally linked to the catalogue data. Complete and incomplete exceedance rates are represented by similar functional forms and they are related by a completeness function, which expresses the probability that an event is included in a data set. Completeness is considered uncertain and it is defined by a suitable, continuous, analytical, magnitude dependent function. The importance of this work lies on its applicability because it can be useful in seismic zones where information about seismic activity is scarce or simply when the catalogue is incomplete in a range of magnitudes that can have a significant influence on the seismic hazard analysis and on the resulting seismic risk assessment. Moreover, it can also be applied in the common case when the catalogue is considered complete above a given magnitude threshold. Numerical examples are presented to illustrate the influence of catalogue incompleteness on the complete exceedance rate estimations. In companion papers, attention is focused on the estimation of completeness probabilities of available catalogues and on parameter estimation of the exceedance rate functions.     

Modeling of transport in groundwater for environmental risk assessment

This paper presents the principles underlying a recently developed numerical technique for modeling transport in heterogeneous porous media. The method is then applied to derive the concentration mean and variance, the concentration CDF, exceedance probabilities and exposure time CDF, which are required by various regulatory agencies for risk and performance assessment calculations. The dependence of the various statistics on elapsed travel time, location in space, the dimension of the detection volume, natural variability and pore-scale dispersion is investigated and discussed.     

Analytical evaluation of structural component limit state probabilities

Probabilistic seismic assessment requires extensive computational effort resulting from variability both in input ground motions and mechanical properties. Nonetheless, such methodologies are of considerable importance, namely for pre-earthquake disaster planning or development of retrofitting programs. A framework for the analytical definition of closed form expressions for exceedance probabilities of structural component limit states, defined by limit values of structural response parameters, is proposed herein. The definition of these expressions is based on the probabilistic representation of the ground motion intensity and on the establishment of suitable expressions characterizing the evolution of structural demand with increasing earthquake intensity. Distinction is made between deformation-based and force-based structural parameters in the definition of such relations. Within the proposed framework, the limit states are defined by single deterministic thresholds of structural response quantities at the component level, as defined in structural codes. Different approaches are also discussed to account for the randomness of the mechanical properties and ground motion input within the proposed methodology. An application of the assessment of different limit state probabilities of members from a reinforced concrete building is presented, for which limit states and limit state capacities are defined according to the upcoming Part 3 of the Eurocode 8. Although the presented application only deals with member chord rotation and shear force limit state probabilities, the proposed methodology can be generalized to other deformation-based and force-based structural parameters.     

Evaluation of a recently proposed record selection and scaling procedure for low‐rise to mid‐rise reinforced concrete buildings and its use for probabilistic risk assessment studies

This paper evaluates a recent record selection and scaling procedure of the authors that can determine the probabilistic structural response of buildings behaving either in the elastic or post‐elastic range. This feature marks a significant strength on the procedure as the probabilistic structural response distribution conveys important information on probability‐based damage assessment. The paper presents case studies that show the utilization of the proposed record selection and scaling procedure as a tool for the estimation of damage states and derivation of site‐specific and region‐specific fragility functions. The method can be used to describe exceedance probabilities of damage limits under a certain target hazard level with known annual exceedance rate (via probabilistic seismic hazard assessment). Thus, the resulting fragility models can relate the seismicity of the region (or a site) with the resulting building performance in a more accurate manner. Under this context, this simple and computationally efficient record selection and scaling procedure can be benefitted significantly by probability‐based risk assessment methods that have started to be considered as indispensable for developing robust earthquake loss models. Copyright © 2013 John Wiley & Sons, Ltd.     

Ground‐motion intensity and damage map selection for probabilistic infrastructure network risk assessment using optimization

In many parts of the world, earthquakes threaten regional infrastructure systems. For modeling risk using stochastic earthquake catalogs, random variables include rupture location and the damage state of different components. Thus, there is an infinite set of possible damage maps that a risk modeler could evaluate in an event‐based probabilistic loss model. Even a finite but large number of damage maps may not be practical, because many network performance measures are computationally expensive. Here, we show a computationally efficient method for selecting a subset of damage maps, corresponding ground‐motion intensity maps, and associated occurrence rates that reasonably estimates the full distribution of the ground‐motion intensity and a target performance measure using optimization. The method chooses a subset of maps and associated annual rates of occurrence that minimizes the error in estimating the distribution of a network performance measure as well as the marginal distributions of ground‐motion intensity exceedance. The joint distribution of the ground‐motion intensity is implicitly included in the objective function of the optimization problem via the network performance measure. We then show how to tune the optimization parameters based on consistency checks related to the network performance measure and the ground‐motion hazard. We illustrate the proposed method with a case study of the San Francisco Bay Area road network to estimate the exceedance curve of the average percentage change in morning commute trip time. This work facilitates expanded and risk‐consistent studies of the impacts of infrastructure networks on regional seismic risk and resiliency. Copyright © 2014 John Wiley & Sons, Ltd.     

An exploration of incorporating site response into PSHA—Part I: Issues related to site response analysis methods

This paper presents a series of analyses for the evaluation of the ground response of two NEHRP class D sites, subjected to shaking by a large number of strong ground-motion records. The two investigated sites have very distinct profiles, but they are characterised by almost identical V_s30 values. The site response analyses are performed using various methods of analysis and input parameters in order to explore the sensitivity of the ground response estimates and to identify the dominating parameters. Equivalent linear analysis is performed using different sets of dynamic soil properties curves, while nonlinear analysis is performed using different target dynamic soil curves, viscous damping formulations and fitting procedures for the constitutive model parameters. Particular focus is given to the sensitivity of the response when soil sites are subjected to high-intensity shaking, a subject of particular interest when the prediction of surface ground motions with low annual probabilities of exceedance is the target of probabilistic seismic hazard analyses (PSHA). The site response analysis results of this paper are incorporated into the probabilistic framework of Bazzurro and Cornell [1] in our companion paper in order to assess their impact on the final soil surface hazard calculation.     

Mapped Predictions of Manganese and Arsenic in an Alluvial Aquifer Using Boosted Regression Trees

Manganese (Mn) concentrations and the probability of arsenic (As) exceeding the drinking-water standard of 10 μg/L were predicted in the Mississippi River Valley alluvial aquifer (MRVA) using boosted regression trees (BRT). BRT, a type of ensemble-tree machine-learning model, were created using predictor variables that affect Mn and As distribution in groundwater. These variables included iron (Fe) concentrations and specific conductance predicted from previously developed BRT models, groundwater flux and age estimates from MODFLOW, and hydrologic characteristics. The models also included results from the first airborne geophysical survey conducted in the United States to target an entire aquifer system. Predictions of high Mn and As occurred where Fe was high. Predicted high Mn concentrations were correlated with fraction of young groundwater (less than 65 years) computed from MODFLOW results. High probabilities of As exceedance were predicted where groundwater was relatively old and airborne electromagnetic resistivity was high, typically proximal to streams. Two-variable partial-dependence plots and sensitivity analysis were used to provide insight into the factors controlling Mn and As distribution in groundwater. The maps of predicted Mn concentrations and As exceedance probabilities can be used to identify areas where these constituents may be high, and that could be targeted for further study. This paper shows that incorporation of a selected set of process-informed data, such as MODFLOW results and airborne geophysics, into a machine-learning model improves model interpretability. Incorporation of process-rich information into machine-learning models will likely be useful for addressing a wide range of problems of interest to groundwater hydrologists.     

On the treatment of uncertainty in seismic vulnerability and portfolio risk assessment

In a related study developed by the authors, building fragility is represented by intensity‐specific distributions of damage exceedance probability of various damage states. The contribution of the latter has been demonstrated in the context of loss estimation of building portfolios, where it is shown that the proposed concept of conditional fragility functions provides the link between seismic intensity and the uncertainty in damage exceedance probabilities. In the present study, this methodology is extended to the definition of building vulnerability, whereby vulnerability functions are characterized by hazard‐consistent distributions of damage ratio per level of primary seismic intensity parameter—Sa(T₁). The latter is further included in a loss assessment framework, in which the impact of variability and spatial correlation of damage ratio in the probabilistic evaluation of seismic loss is accounted for, using test‐bed portfolios of 2, 5, and 8‐story precode reinforced concrete buildings located in the district of Lisbon, Portugal. This methodology is evaluated in comparison with current state‐of‐the‐art methods of vulnerability and loss calculation, highlighting the discrepancies that can arise in loss estimates when the variability and spatial distributions of damage ratio, influenced by ground motion properties other than the considered primary intensity measure, are not taken into account.     

北京地区不同超越概率水准下基岩峰值加速度分析

基于中国地震动参数区划图、华北平原地震带和汾渭地震带地震活动性参数、华北地区地震动参数衰减关系,计算北京地区50年、70年、100年不同超越概率水准下基岩峰值加速度.并分析不同年限各超越概率水准下的峰值加速度与该年限超越概率10％的峰值加速度比值,发现各计算格点的比值普遍偏小,按照当前抗震设防标准,所考虑的地震作用偏于保守且安全.     

软土地基深开挖对场地设计地震动的影响

本文根据南京河西地区所处的地震地质环境、地震活动环境及基岩地震动衰减规律,在场址区地震危险性分析基础上确定该地区的基岩地震动参数,并选取河西地区某个典型工程场地,根据场地上的静、动力性能参数的测试结果,进行场地上层地震反应分析,研究软土地基条件下地基深开挖场地的地震动效应及其对场地设计地震动参数的影响．文中给出了设计基准期为５０年及１００年时对应不同抗震设防水准的设计地震动参数,该结果对河西地区其它高层建筑的抗震设计也有一定的参考价值．     

Optimization and uncertainty analysis of operational policies for multipurpose reservoir system

This paper presents optimization and uncertainty analysis of operation policies for Hirakud reservoir system in Orissa state, India. The Hirakud reservoir project serves multiple purposes such as flood control, irrigation and power generation in that order of priority. A 10-daily reservoir operation model is formulated to maximize annual hydropower production subjected to satisfying flood control restrictions, irrigation requirements, and various other physical and technical constraints. The reservoir operational model is solved by using elitist-mutated particle swarm optimization (EMPSO) method, and the uncertainty in release decisions and end-storages are analyzed. On comparing the annual hydropower production obtained by EMPSO method with historical annual hydropower, it is found that there is a greater chance of improving the system performance by optimally operating the reservoir system. The analysis also reveals that the inflow into reservoir is highly uncertain variable, which significantly influences the operational decisions for reservoir system. Hence, in order to account uncertainty in inflow, the reservoir operation model is solved for different exceedance probabilities of inflows. The uncertainty in inflows is represented through probability distributions such as normal, lognormal, exponential and generalized extreme value distributions; and the best fit model is selected to obtain inflows for different exceedance probabilities. Then the reservoir operation model is solved using EMPSO method to arrive at suitable operational policies corresponding to various inflow scenarios. The results show that the amount of annual hydropower generated decreases as the value of inflow exceedance probability increases. The obtained operational polices provides confidence in release decisions, therefore these could be useful for reservoir operation.     

Seismic hazard assessment for Iceland in terms of macroseismic intensity using a site approach

We present the results of probabilistic seismic hazard assessment for Iceland in the framework of the EU project UPStrat-MAFA using the so-called site approach implemented in the SASHA computational code. This approach estimates seismic hazard in terms of macroseismic intensity by basically relying on local information about documented effects of past seismic events in the framework of a formally coherent and complete treatment of intensity data. In the case of Iceland, due to the lack of observed intensities for past earthquakes, local seismic histories were built using indirect macroseismic estimates deduced from epicentral information through an empirical attenuation relationship in probabilistic form. Seismic hazard was computed for four exceedance probabilities for an exposure time of 50 years, equivalent to average return periods of 50, 200, 475 and 975 years. For some localities, further return periods were examined and deaggregation analysis was performed. Results appear significantly different from previous seismic hazard maps, though just a semi-qualitative comparison is possible because of the different shaking measure considered (peak ground acceleration versus intensity), and the different computational methodology and input data used in these studies.     

A deductive model of karst evolution based on hydrological probability

Combination of a conduit flow law with the exceedance probability of stream discharge allows the estimation of the exceedance probability of water level in a simple conduit aquifer. The probability of water levels higher than available relief is interpreted as the probability of surface as opposed to underground runoff. Very high probability of surface runoff implies a fluvial environment, whereas very low probabilities define a mature karst or ‘holokarst’, Intermediate probabilities identify ‘fluviokarst’. Overflow probability depends on available relief, mean discharge, and especially conduit radius. Growth rate of the underground conduit depends on saturation deficit which thus controls the rate of evolution of the fluvial landscape, through fluviokarst to holokarst. However, variations of discharge and sedimentation through time can cause dramatic reversion of karst drainage into less mature states. Landscapes experiencing such periodic rejuvenation will have a confused morphology. A functional definition of landscape may be more objective and pertinent than arbitrary interpretation of form.     

Probabilistic seismic hazard assessment for Thailand

A set of probabilistic seismic hazard maps for Thailand has been derived using procedures developed for the latest US National Seismic Hazard Maps. In contrast to earlier hazard maps for this region, which are mostly computed using seismic source zone delineations, the presented maps are based on the combination of smoothed gridded seismicity, crustal-fault, and subduction source models. Thailand’s composite earthquake catalogue is revisited and expanded, covering a study area limited by 0°–30°N Latitude and 88°–110°E Longitude and the instrumental period from 1912 to 2007. The long-term slip rates and estimates of earthquake size from paleoseismological studies are incorporated through a crustal fault source model. Furthermore, the subduction source model is used to model the megathrust Sunda subduction zones, with variable characteristics along the strike of the faults. Epistemic uncertainty is taken into consideration by the logic tree framework incorporating basic quantities, such as different source modelling, maximum cut-off magnitudes and ground motion prediction equations. The ground motion hazard map is presented over a 10 km grid in terms of peak ground acceleration and spectral acceleration at 0.2, 1.0, and 2.0 undamped natural periods and a 5% critical damping ratio for 10 and 2% probabilities of exceedance in 50 years. The presented maps give expected ground motions that are based on more extensive data sources than applied in the development of previous maps. The main findings are that northern and western Thailand are subjected to the highest hazard. The largest contributors to short- and long-period ground motion hazard in the Bangkok region are from the nearby active faults and Sunda subduction zones, respectively.     

Model-based geostatistical interpolation of the annual number of ozone exceedance days in the Netherlands

This paper discusses two model-based geostatistical methods for spatial interpolation of the number of days that ground level ozone exceeds a threshold level. The first method assumes counts to approximately follow a Poisson distribution, while the second method assumes a log-Normal distribution. First, these methods were compared using an extensive data set covering the Netherlands, Belgium and Germany. Second, the focus was placed on only the Netherlands, where only a small data set was used. Bayesian techniques were used for parameter estimation and interpolation. Parameter estimates are comparable due to the log-link in both models. Incorporating data from adjacent countries improves parameter estimation. The Poisson model predicts more accurately (maximum kriging standard deviation of 2.16 compared to 2.69) but shows smoother surfaces than the log-Normal model. The log-Normal approach ensures a better representation of the observations and gives more realistic patterns (an RMSE of 2.26 compared to 2.44). Model-based geostatistical procedures are useful to interpolate limited data sets of counts of ozone exceedance days. Spatial risk estimates using existing prior information can be made relating health effects to environmental thresholds.     

Ground motion evaluation procedures for performance-based design

The objective of performance-based earthquake engineering (PBEE) is the analysis of performance objectives with a specified annual probability of exceedance. Increasingly undesirable performance is caused by increasing levels of strong ground motion having decreasing annual probabilities of exceedance. Accordingly, the evaluation of ground motion intensity measures is a vital component of PBEE. This paper provides a brief synthesis of ground motion analysis procedures within a performance-based design framework, and is a summary of a recent report to which the reader is referred for details. The principal topics addressed are probabilistic characterizations of source, path, and site effects, with the discussion of these effects focusing principally on applications in active regions such as California.     

Seismic evaluation of rocking structures through performance assessment and fragility analysis

Numerical studies have been conducted for low- and medium-rise rocking structures to investigate their efficiency as earthquake-resisting systems in comparison with conventional structures. Several non-linear time-history analyses have been performed to evaluate seismic performance of selected cases at desired ground shaking levels, based on key parameters such as total and flexural story drifts and residual deformations. The Far-field record set is selected as input ground motions and median peak values of key parameters are taken as best estimates of system response. In addition, in order to evaluate the probability of exceeding relevant damage states, analytical fragility curves have been developed based on the results of the incremental dynamic analysis procedure. Small exceedance probabilities and acceptable margins against collapse, together with minor associated damages in main structural members, can be considered as superior seismic performance for medium-rise rocking systems. Low-rise rocking systems could provide significant performance improvement over their conventional counterparts notwithstanding certain weaknesses in their seismic response.