Probabilistic Risk Assessment Framework Research Articles

Dynamic Seismic Probabilistic Risk Assessment of Nuclear Power Plants Using Advanced Structural Methodologies

The conditional core damage probability (CCDP) of a representative nuclear power plant is estimated for a beyond design basis earthquake (BDBE) using state-of-the-art structural models within a dynamic probabilistic risk assessment (DPRA) framework. Randomness of seismic excitation and uncertainty of structural parameters are considered using a simulation-based approach. Finite element models are developed for the structure and a liquid container (hydro-accumulator), and fluid–structure interaction is considered with the arbitrary Lagrangian-Eulerian method. The CCDP is evaluated through a time-dependent event tree. Also, correlation among multiple hydro-accumulators is investigated. The results show that operator action and implementation time of mobile safety equipment are critical under BDBE in case of loss of offsite power following an earthquake. It was also found necessary to adopt a DPRA approach to determine the available time for action and core damage timing probabilistically.

Concept design, application and optimization of operational parameters for new forced safety injection tank system

Background The engineered safety systems are designed to execute fundamental safety functions encompassing reactivity confinement, reactivity control and decay heat removal. Failure of any one of these functions can result in severe accident conditions. Passive systems have been implemented as a better option for plant safety. This research proposes a modification of existing safety injection tanks to the new forced safety injection tanks (FSITs) that utilize the backpressure from the pressurizer or steam generator to drive coolant into the reactor core under high pressure conditions. Methods FSITs aim to extend the coping-time during accidents like Station Blackout, providing an extended timing window for deployment of FLEX systems. The mathematical design is proposed and implemented into the thermal-hydraulic input of a nuclear power plant to demonstrate the system’s applicability that was demonstrated by leveraging the conventional PRA approach and risk quantification. Results The suggested system useful when used in the accident scenario of Station black out in-coincident with turbine-driven pumps fail to run. As the proposed design is a conceptual design, the optimization of associated operational parameters and set points is necessary. This optimization is performed using the risk analysis and virtual control environment-based Dynamic Probabilistic Risk Assessment framework. The method and findings of this study affirm that the coping-time for Station Blackout can be significantly extended, ensuring a substantial margin for the effective deployment of the FLEX. Conclusions A concept design of a passive forced safety injection system was suggested and demonstrated by integrating the mathematical model into a thermal-hydraulic model of a nuclear power plant. The parameters were optimized and the results demonstrated that the new system was effective in recovering the nuclear power plant from the accidents such as SBO with turbine-driven pumps fail to operate.

Emissions of polycyclic aromatic hydrocarbons in PM2.5 emitted from motor vehicles exhaust (PAHs-PM2.5-MVE) under the plateau with low oxygen content

Emissions of PAHs and their derivatives from motor vehicles exhaust are mainly due to inadequate combustion of fossil fuels, the combustion efficiency of engine is lower under the plateau with low oxygen content, which will exacerbate the emission of pollutants, especially organic substance. In order to investigate the emission of PAHs-PM2.5-MVE under the plateau with low oxygen content, tunnel experiments and bench tests were conducted in a typical plateau region in Yunnan Province. The study indicated the concentrations of PAHs-PM2.5-MVE in the tunnels of Caohai and Xidu reached 548.11 ± 307.12 and 1241.19 ± 197.54 ng/m3, respectively. The emission factor of PAHs-PM2.5-MVE in the Caohai Tunnel was estimated to be 438.61 ± 296.86 μg/veh/km, and that for gasoline and diesel vehicles in bench tests were 442.83 ± 82.57 and 4098.04 ± 551.21 μg/kg fuel. Meanwhile, the emission factors of carbonaceous component, CO and PAHs-PM2.5-MVE were at a high level that were higher than those in plain which due to the inadequate combustion of fuels in engine. A probabilistic risk assessment framework was integrated to quantitatively estimate the exposure risk for the population of the tunnels, the HPAHs-PM2.5-MVE had potential carcinogenic risk. The study can improve our understanding of the influence of organic substance from inadequate combustion of fuels on the environment and human.

Probabilistic Validation: Computational Platform and Application to Fire Probabilistic Risk Assessment of Nuclear Power Plants

Abstract Recently, there has been an increasing use of advanced modeling and simulation in the nuclear domain across academia, industry, and regulatory agencies to improve the realism in capturing complex and highly spatiotemporal phenomena within the probabilistic risk assessment (PRA) of existing nuclear power plants (NPPs). Advanced modeling and simulation have also been used to accelerate the risk-informed design, licensing, and operationalization of advanced nuclear reactors. Validation of simulation models traditionally relies on empirical validation approaches which require enough validation data. Such validation data are, however, usually costly to obtain in the contexts of the nuclear industry. To overcome this challenge and to effectively support the use of simulation models in PRA and risk-informed decision-making applications, a systematic and scientifically justifiable validation methodology, namely, the probabilistic validation (PV) methodology, has been developed. This methodology leverages uncertainty analysis to support the validity assessment of the simulation prediction. The theoretical foundation and methodological platform of the PV methodology have been reported in the first paper of this two-part series. The purpose of this second paper is to computationalize the PV methodology, embedded in an integrated PRA framework, and apply it for a hierarchical fire simulation model used in NPP Fire PRA.

Reducing Uncertainty in Site-specific Stress Prediction for CO2 Storage in the North Sea, Norway

Two CO2 storage sites located in the western Norwegian North Sea (NNS), called Aurora and Smeaheia, are currently under construction and assessment respectively. In geological storage of CO2, the in situ minimum horizontal stress is an essential input parameter for assessment of both containment and induced seismic risks [1]. To infer the stress states at certain depths at a site where no data is available, the standard approach is to perform a classical linear regression on stress data versus depth and treat the fitted trend line as the best site-specific stress predictions along depth [2]. However, stress data are often highly limited at CO2 storage sites; for example, Aurora and Smeaheia have only five in situ stress measurements available at best respectively. Such limited data may severely underrepresent the true stress distribution at one site. Data scarcity coupled with measurement error and spatial variability poses a challenge to reliable stress prediction, and hence it is crucial to quantify and reduce uncertainty in site-specific stress prediction for CO2 storage. Stress uncertainty is actually the required input information in the more rational probabilistic risk assessment framework. A natural solution to reducing uncertainty is to integrate stress information from other sources.
 On the Norwegian continental shelf, extensive data has been accumulated from previous petroleum projects. Of the publicly available NPD stress database, Figure 1a shows the distribution of versus depth (< 3,000 m) for each site within the study area containing Aurora and Smeaheia, and reveals a certain degree of similarity between the stress trends at the 11 sites. Such similarity, aligned with other published results [2], may be attributed to the relaxed sedimentary basins where gravitational loading dominates the lateral stress distribution rather than tectonic components, with the between-site variation arising from differences in the geological conditions and pore pressures [3]. When facing limited data for a site like Aurora and Smeaheia, the current approach is often to either directly use the stress trend from other sites having richer data or expand the coverage area to include more data. Such semi-subjective information borrowing approach, although effective in many cases, may lead to overly confident stress predictions as it fails to account for possible between-site heterogeneity in stress trends.
 Bayesian inference has been widely used as a rigorous and powerful statistical approach for quantifying uncertainty, as well as combining information from different sources via informative prior distributions. Hence, historical stress data may be integrated into Bayesian analysis of site-specific data in the form of prior distributions, with stress uncertainties being quantified and updated as the posterior distributions [4, 5]. When developing prior distributions for site-specific stress prediction, it may be tempting to combine all historical stress data for a holistic Bayesian analysis, yet such complete pooling approach may give an overconfident summary of prior information in that it ignores the possible stress heterogeneity between sites.
 This paper presents a Bayesian hierarchical (i.e., partial pooling) model (BHM) that explicitly accounts for between-site heterogeneity/similarity when constructing prior distributions from historical stress data, and demonstrates how the proposed model effectively borrows historical information to reduce uncertainty in site-specific stress prediction for CO2 storage in the NNS study area. Figures 1b illustrates the prior predictions of versus depth at the Aurora site from the Bayesian complete and partial pooling models. Although the complete pooling model gives less uncertain stress predictions than the partial pooling model as indicated by the narrower 90% prediction intervals (PIs), it does not well capture the five unseen stress measurements at Aurora in that two out of five stress values fall outside the 90% PIs. This suggests that complete pooling analysis indeed gives overconfident prior distributions out of the NPD database, and is thus not suitable for integrating historical data into site-specific stress prediction for CO2 storage in the NNS. On the other hand, the partial pooling model gives fairly good prior predictions of the five unseen stress values at Aurora, albeit with larger uncertainties. This result demonstrates the effectiveness of BHM as a framework for formulating proper informative priors from historical data, and an encouraging implication is that probabilistic risk assessment is allowed even with no site-specific stress data at this storage site, which is not possible if external information is not integrated properly. Figure 1c shows the posterior stress predictions updated with the five site-specific stress values from the two Bayesian models in question. After incorporating the site-specific data, the complete pooling model still over-predicts the two stress values at depths with barely noticeable updating, while partial pooling gives considerably more accurate stress predictions with reduced uncertainty.

Tsunami flooding analysis graded-approach framework for tsunami probabilistic risk assessment

ABSTRACT A tsunami probabilistic risk assessment (PRA) is an effective tool that reviews the safety margins for beyond-design-basis events and strengthens the application of the defense-in-depth philosophy. It is recognized that tsunami hazard levels, assumed margins, and assumed risks differ significantly between sites. This paper proposes a framework of risk-based graded approach for a tsunami PRA. Since the predominant sources of uncertainties in an overall tsunami PRA may stem from tsunami hazard analysis, the framework selects a methodology for incorporating the uncertainties of tsunami hazard analysis in subsequent analyses, by grade. The framework provides five grades depending on the level of detail in the assessment. This graded approach framework was experimentally applied to the tsunami PRA for a virtual nuclear power station.

L-moments and Bayesian inference for probabilistic risk assessment with scarce samples that include extremes

In structural applications, uncertainties are unavoidable and play a significant role in risk assessment. Probabilistic risk assessment (PRA) is used to determine the level of risk associated with complex systems such as nuclear power plants, space missions, earthquakes, tornado and floods. The Bayesian inference is often regarded as an effective framework for analysing probabilistic risk and the prior probability and likelihood function are inferred from available data. The traditional approaches usually approximate likelihood functions using conventional moments (C-moments). If data are insufficient, approximations are inadequate, leading to inaccurate conclusions. Therefore in order to determine the amount of risk, it is desirable to develop a PRA framework that is distribution independent and less sensitive or insensitive to extremes in the scarce data. In this paper, L-moments are proposed to characterise or approximate likelihood functions in the Bayesian inference. L-moment ratio diagram is employed to select the appropriate distribution of conditional probabilities. The Bayesian approach is paired with L-moment approach to perform PRA and uncertainty quantification. The efficacy of the proposed approach is demonstrated on three engineering examples. In assessing risk from few samples in the presence of extremes, L-moments based Bayesian inference for PRA framework significantly outperformed its C-moment counterpart.

Distribution of microplastics in freshwater systems in an urbanized region: A case study in Flanders (Belgium)

Microplastics (MPs) are an emerging pollutant of concern in all known aquatic ecosystems. However, studies at a regional scale on MP pollution in freshwater systems and the necessary risk assessments are limited. Therefore, in this study, we examined microplastic concentrations, size distributions, and polymer types in surface waters and sediments in the geographic region Flanders (Belgium), as a case study for a densely populated region and one of the most developed parts of Europe. Samples have been taken on nine different locations, of which five were repeated in a different weather condition. In total 43 aqueous and nine sediment samples have been collected. The quantity and identity of the microplastics in the samples were determined with μFTIR spectroscopy in the range of 25–1000 μm. The MPs' abundances in surface waters and sediments ranged from 0 to 4.8 MP L−1 (average = 0.48 MP L−1) and from 0 to 9558 MP kg−1 dry weight (average = 2774.57 ± 2317.93 MP kg−1 DW), respectively. Polystyrene and polypropylene were the most common polymer compositions found. No correlations were observed between microplastic concentrations in the sediment/the surface water samples and the measured environmental variables rainfall, conductivity, pH, dissolved oxygen content, waterway flow rate and width, and surrounding land use. Risk assessment results for the measured surface water concentrations through the risk quotient (RQ) method and the probabilistic risk assessment framework suggest that most of the sampled sites in Flanders posed negligible risks to freshwater biota, while this was not the case for some of the sediment concentrations. Our results illustrate the need to urgently develop analytical methods that can routinely measure the full size range of MP in environmental samples to adequately assess risks for the environment.

Probabilistic risk assessment framework for predicting large woody debris accumulations and scour near bridges

The accumulation of waterborne large woody debris is a critical issue facing bridges spanning active waterways. In addition to collision forces, drift buildup constricts flow, producing increased hydraulic pressures and exacerbating scour, the cause of nearly one-third of bridge failures. Accurate methods of predicting debris generation, transport, entrapment, and dimensions are consequently necessary to improve public safety, bridge designs, and informed decision-making. However, debris buildup characteristics are site-specific, varying with the regional vegetative, hydraulic, topographical, and geotechnical properties. As sufficient data on these properties is limited to create empirical predictive models, a probabilistic physics-based framework incorporating the risk assessment of local vegetation to estimate debris accumulation and scour is developed. Based on the upstream tree, soil, weather, and river conditions, fragility assessment of the riparian trees from landslides and windthrow is conducted to estimate the probability of debris generation and subsequent entrapment. The framework is demonstrated in a case study of a bridge in Vermont subject to Hurricane Irene. Sensitivity analysis is conducted to quantify the importance of various contributing factors, including slope, rainfall, wind gust, flow rate, and pier geometry. The experimental results highlight the importance of including the debris accumulation in the scour projections.

Global damage evaluation of a dry storage structure subjected to postulated aircraft crashes

This paper describes an assessment of vulnerability to global damage of a dry storage structure subjected to postulated commercial aircraft crashes. The vulnerability from plausible collisions of an aircraft is expressed by failed volume fraction in distribution curves obtained from an integrated deterministic and probabilistic approach. Nonlinear dynamic analyses are performed using smoothed particle hydrodynamics and finite element method to simulate the aircraft impact and the subsequent reinforced concrete damage. The response surface method, polynomial regressions and Monte Carlo simulation are employed for the probabilistic assessment. Failure probabilities of damage for three predefined response modes are estimated at side and upper impact locations. Resultant probabilities under these scenarios were relatively high and, thus, global resistance of the structure to withstand aircraft crashes is generally low. The outcomes of this study can be incorporated into quantitative evaluation within a probabilistic risk assessment framework and associated with further numerical analysis methodologies.

Rockburst and Gas Outburst Forecasting using a Probabilistic Risk Assessment Framework in Longwall Top Coal Caving Faces

A probabilistic risk assessment framework was developed to mathematically represent the complex engineering phenomena of rock bursts and gas outbursts for a heterogeneous coal seam. An innovative object-based non-conditional simulation approach was used to distribute lithological heterogeneity present in the coal seam to respect their geological origin. The changing mining conditions during longwall top coal caving mining (LTCC) were extracted from a coupled numerical model to provide statistically sufficient data for probabilistic analysis. The complex interdependencies among abutment stress, pore pressure, the volume of total gas emission and incremental energy release rate, their stochastic variations and uncertainty were realistically implemented in the GoldSim software, and 100,000 equally likely scenarios were simulated using the Monte Carlo method to determine the probability of rock bursts and gas outbursts. The results obtained from the analysis incorporate the variability in mechanical, elastic and reservoir properties of coal due to lithological heterogeneity and result in the probability of the occurrence of rock bursts, coal and gas outbursts, and safe mining conditions. The framework realistically represents the complex mining environment, is resilient and results are reliable. The framework is generic and can be suitably modified to be used in different underground mining scenarios, overcoming the limitations of earlier empirical indices used.

Of critical importance: Toward a quantitative probabilistic risk assessment framework for critical infrastructure

AbstractCritical comments can be made to the current risk assessment framework for critical infrastructure used in The Netherlands: the Dutch National Risk Assessment (DNRA). The DNRA uses a qualitative approach to risk assessment, based on, for example, ordinal risk scoring and the risk matrix. Even though qualitative risk assessment methods are internationally popular, there is no scientific evidence that a qualitative approach to risk assessment actually works. In the case of the DNRA, the main points of criticisms relate to the usage of a subjective concept of risk, dependency on subjective risk experts, the use of risk matrices and the absence of decision rules. To combat these criticisms, this article proposes a quantitative probabilistic risk assessment framework for critical infrastructure based upon four design principles, that a methodologically justified risk assessment method for critical infrastructure should meet. The proposal made for the quantitative risk assessment framework uses a Bayesian approach, a standardized measure for negligible risk in the form of a yearly mortality probability of 10−6, and Disability Adjusted Life Years to quantify human life years for social cost–benefit analysis. Finally, the proposed quantitative method is demonstrated in a case study.

A methodology to perform dynamic risk assessment using system theory and modeling and simulation: Application to nuclear batteries

Accidents may occur as a result of complex dynamic processes in interconnected socio-technical systems. Such accidents cannot be explained solely in terms of static chains of failures. Therefore, the traditional Probabilistic Risk Assessment (PRA) framework, which stands on the consideration that accidents are caused by direct failures or chains of events, is not apt to describe the dynamic behavior of the relevant Systems, Structures and Components (SSCs) and assess the risk. This work proposes a novel framework that embeds (i) System-Theoretic Accident Model and Processes (STAMP) principles to guide a qualitative exploration of the SSC threats and hazards, (ii) Modeling and Simulation (M&S) to investigate the SSC dynamic behavior during accidental scenarios, and (iii) the Goal-Tree Success-Tree Master Logic Diagram (GTST-MLD) framework to assess risk quantitatively. The integration of STAMP, M&S and GTST-MLD allows a systematic analysis to provide risk insights, with due account to the SSC dependencies and interactions, and enables a dynamic assessment of the risk profile.The effectiveness of the proposed framework is shown by means of its application to the safety assessment of Nuclear Batteries (NBs), a unique class of nuclear micro-reactors which is gaining attention as a transportable, flexible, affordable, and distributed low-carbon power source.

Commuter welfare-based probabilistic seismic risk assessment of regional road networks

This study integrates welfare, a measure of the impact of road network disruption on individual commuters’ well-being, with a probabilistic seismic risk assessment framework in a computationally tractable way. Welfare is a network performance measure that reflects the differential impacts of changes in commute time on various groups. For a case study of the San Francisco Bay Area, welfare loss is computed by augmenting an origin–destination matrix with publicly available information about commuters’ income levels, residences, and workplaces. While commuters from all income groups have similar risk of drivers’ delay due to road network disruption, commuters with low incomes have a substantially higher risk of welfare loss than those with high incomes. A comparison of bridge retrofit policies shows that disaggregation of welfare loss by income group is necessary to examine whether such policies reduce risk equitably. While a retrofit policy determined using drivers’ delay reduces the expected drivers’ delay, it increases the disparity in the per-capita welfare loss of commuters with low and high incomes relative to the network’s baseline state. In contrast, a retrofit policy that prioritizes low-income commuters reduces the difference in welfare loss of commuters with low and high incomes compared to the baseline network state.

Conceptualizing a probabilistic risk and loss assessment framework for wildfires

Conceptualizing a probabilistic risk and loss assessment framework for wildfires

Fragility analysis for performance-based blast design of FRP-strengthened RC columns using artificial neural network

In this paper, fragility analysis for performance-based blast design of FRP-strengthened RC columns is carried out. The blast intensity levels, performance levels and performance objectives of the RC columns are defined. A simplified probabilistic risk assessment framework incorporating the performance-based design concept and fragility analysis is established. Since fragility analysis is the most important but time-consuming process of probabilistic assessment risk, an artificial neural network (ANN) based fragility analysis framework is proposed to improve its computational efficiency. Based on the rapid fragility analysis method, fragility curves of several typical RC columns with or without FRP strengthening are calculated to analyze their damage probabilities. This study provides avenues for engineers to estimate the failure probabilities of RC columns with or without FRP strengthening under blast loads and make decisions quickly.

Health risk assessment of volatile organic compounds exposure among nail salon workers in Vietnam

Purpose The objective of this study is to assess the carcinogen and non-carcinogen risks due to exposure to volatile organic compounds including methyl methacrylate (MMA), benzene, toluene, and xylene among Vietnamese nail salon workers, using probabilistic health risk assessment. Methods This study applied the probabilistic health risk assessment framework to assess the health risk due to exposure to four types of volatile organic compounds among nail salon workers. Forty-two passive personal samples of full-shift female nail workers from 15 salons in Da Nang city were monitored and analyzed by GC-FID in the Thammasat laboratory. Exposure parameters were collected by interviewing nail salon workers. Monte Carlo simulation was used to characterize the risk and its uncertainty. Results The mean of concentrations of MMA, benzene, toluene, and xylene were 20.62, 0.21, 2.49, and 0.58 mg m−3, respectively. The 95th percentile hazard quotients calculated for MMA, benzene, toluene, and xylene were 33.14, 7.49, 0.54, and 2.07, respectively. The 95th percentile lifetime cancer risk for benzene was 198 times higher than the EPA recommendation for cancer risk (10−6). Conclusions Non-cancer risks from exposure to MMA, benzene, and xylene were many times higher than the acceptable limit, which indicated a possible risk of adverse health effects among nail salon workers. Nail salon workers may also be at risk of leukemia or cancer of the blood-forming organs because the cancer risk due to exposure to benzene is higher than the recommended level.

Analysis of historic fires to determine most frequent challenging events

The fire probabilistic risk assessment framework for nuclear power plants relies on experimental data to determine expected fire behavior or to validate models to predict fire conditions in the plant. To support reducing the uncertainty in this experimental data, a research effort was conducted to identify the most frequent and challenging fire scenarios using historic fire data from nuclear power plants in the United States. To support this effort, an electronic version of the publicly available Updated Fire Event Database developed by Electric Power Research Institute was produced resulting in data on 2111 fire events, 540 events were labelled as being challenging fires with 74.2% of these challenging fire events being due to eleven selected fire types. Of these fire types, electrical and electronic equipment, transient combustibles, and liquid fires were the most frequent of the challenging fires. The fire scenario specifics were characterized for each of the eleven selected types and then related to existing fire experiments.

A Critical Look at the Need for Performing Multi-Hazard Probabilistic Risk Assessment for Nuclear Power Plants

Probabilistic Risk Assessment (PRA) is one of the technologies that is used to inform the design, licensing, operation, and maintenance activities of nuclear power plants (NPPs). A PRA can be performed by considering the single hazard (e.g., earthquake, flood, high wind, landslide) or by considering multi-hazards (e.g., earthquake and tsunami, high wind and internal fire). Single hazard PRA was thought sufficient to cover the analysis of a severe accident until the Fukushima Daiichi NPP accident in 2011. Since then, efforts were made to consider multi-hazards as well; thus, multi-hazard PRAs are starting to be seen as being indispensable for NPPs. In addition to the changing frequency of global and local natural hazards, other reasons to be highlighted are that the number and diversity of NPPs will probably increase. Moreover, advanced reactors are close to becoming a reality by designing them with passive safety systems, smaller, standardized, and even transportable to make them cheaper across the design, licensing construction, and operation stages. Thus, multi-hazards should be addressed in any future full-scope PRA. Although we found a few studies discussing multi-hazards, a general framework for multi-hazard PRA is still missing. In this paper, we argue that the starting point for any multi-hazard PRA general framework should be the Advanced Non-LWR Licensing Basis Event Selection (LBE) Approach and Probabilistic Risk Assessment Standard for Non-Light Water Reactor (non-LWR) Nuclear Power Plants. For Probabilistic Risk Assessment (PRA), history has shown us the path forward before, with Three Mile Accident being seen as one milestone to understand the necessity of PRA. The Fukushima Daiichi NPP Accident is another milestone in the development of PRA, showing the need for performing multi-hazard PRA for the current and future NPPs.

Predictive capacity of topological measures in evaluating seismic risk and resilience of electric power networks

Electric Power Networks (EPNs) play a fundamental role in the wellbeing of modern societies and recovery of societal functions after an earthquake. Risk and resilience analyses may identify useful network characteristics to improve EPN response and recovery during and after a severe seismic event. This work computes different functional measures in order to: (i) estimate the actual risk and resilience of EPNs; and (ii) evaluate the predictive capacity of different topological measures (TMs) relative to the EPN earthquake risk performance. The analysis is carried out on the Chilean EPN at the national, regional and substation level, by using a detailed model of the network. EPN operation was modeled using the DC optimal power flow model from the time of earthquake occurrence until full system recovery using the Seismic Probabilistic Risk Assessment framework. Seismic risk and resilience estimations of Energy Not Supplied (ENS) and number of hours with ENS have been correlated with six network TMs. Linear correlation results show that TMs provide, in general, limited insight into the criticality of the Chilean EPN. In spite of that, the strongest correlation was observed for the degree TM. Moreover, the Damage Consequence Index confirmed the rather uniformly distributed seismic risk along the country.