Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.     

Seismic hazard assessment in TERESA test areas based on a Bayesian technique

A method based on Bayesian techniques has been applied to evaluate the seismic hazard in the two test areas selected by the participants in the ESC/SC8-TERESA project: Sannio-Matese in Italy and the northern Rhine region (BGN). A prior site occurrence model (prior SOM) is obtain from a seismicity distribution modeled in wide seismic sources. The posterior occurrence model (posterior SOM) is calculated after a Bayesian correction which, basically, recovers the spatial information of the epicenter distribution and considers attenuation and location errors, not using source zones. The uncertainties of the occurrence probabilities are evaluated in both models.The results are displayed in terms of probability and variation coefficient contour maps for a chosen intensity level, and with plots of mean return period versus intensity in selected test sites, including the 90% probability intervals.It turns out that the posterior SOM gives a better resolution in the probability estimate, decreasing its uncertainty, especially in low seismic activity regions.     

Characterizing uncertainty in geotechnical design of energy piles based on Bayesian theorem

It is known that a lot of uncertainties are involved in geotechnical design of energy piles. In this paper, a Bayesian updating framework is presented to characterize those uncertainties. The load-transfer model is developed to predict the thermomechanical response of energy piles. Considering the cross-case variability of the uncertainty in the axial strains of pile, the global model bias is firstly calibrated by establishing a comprehensive database consisting of 12 energy pile cases. Furthermore, the uncertainty in input parameters is considered in the Bayesian updating of model bias in a specific case. The variability of the uncertain parameters is effectively reduced after updating. The coefficient of variation of prediction is decreased from 0.34 to 0.13. The present framework can well quantify uncertain factors and improve the accuracy and reliability of the prediction model.

     

Probabilistic assessment of annual repair rates in pipelines and of direct economic losses in water and sewage networks: application to Manizales,Colombia

A methodology for the development of fully probabilistic seismic risk assessments on water and sewage networks is presented in this paper together with a case study for the system of Manizales, Colombia. These kinds of assessments require the development of probabilistic seismic hazard analysis, the consideration of local site effects, when relevant, the assembly of databases to identify and characterize the exposed elements and the development and assignment of vulnerability models for each type of component. For the case of Manizales, a high-resolution exposure database has been developed (element by element, segment by segment) based on the information and data provided by the owner and operator of the network, Aguas de Manizales. Losses due to earthquakes are obtained after convoluting the hazard and vulnerability inputs in a fully probabilistic manner, using the state-of-the-art methodologies incorporated in the CAPRA risk assessment module. Several risk metrics such as the loss exceedance curve, the loss exceedance probabilities for different time frames and the average annual loss are obtained for the system as a whole as well as disaggregated by component. In addition, repair rates for the pipelines were also calculated. The risk results obtained in this study have been useful for the company in designing and implementing expansion and maintenance plans that explicitly account for seismic risk mitigation issues, as well as to explore and negotiate financial protection alternatives by means of risk transfer and retention schemes, thus becoming a valuable input in the continuous development of good disaster risk management practices in this city.

     

基于IBUNE方法的水文模型不确定性分析

在贝叶斯理论框架下,根据一种可结合多个水文模型给出模拟或预报结果的IBUNE方法探讨了水文模型的输入、参数以及结构的不确定性问题。将SCEM-UA算法和EM算法嵌入新安江和TOPMODEL水文模型用于参数优化和模型平均,进而将输入与参数的综合不确定性处理后得到的预报量后验分布进行多模型综合,据此对水文模型的不确定性及其对水文模拟结果的影响进行评价。以湖南洣水流域龙家山水文站以上集水区域为例进行了应用研究,结果表明,IBUNE方法能够有效估计水文模型的不确定性,并能给出合理的概率预报区间。     

Probabilistic assessment of annual repair rates in pipelines and of direct economic losses in water and sewage networks: application to Manizales,Colombia

A methodology for the development of fully probabilistic seismic risk assessments on water and sewage networks is presented in this paper together with a case study for the system of Manizales, Colombia. These kinds of assessments require the development of probabilistic seismic hazard analysis, the consideration of local site effects, when relevant, the assembly of databases to identify and characterize the exposed elements and the development and assignment of vulnerability models for each type of component. For the case of Manizales, a high-resolution exposure database has been developed (element by element, segment by segment) based on the information and data provided by the owner and operator of the network, Aguas de Manizales. Losses due to earthquakes are obtained after convoluting the hazard and vulnerability inputs in a fully probabilistic manner, using the state-of-the-art methodologies incorporated in the CAPRA risk assessment module. Several risk metrics such as the loss exceedance curve, the loss exceedance probabilities for different time frames and the average annual loss are obtained for the system as a whole as well as disaggregated by component. In addition, repair rates for the pipelines were also calculated. The risk results obtained in this study have been useful for the company in designing and implementing expansion and maintenance plans that explicitly account for seismic risk mitigation issues, as well as to explore and negotiate financial protection alternatives by means of risk transfer and retention schemes, thus becoming a valuable input in the continuous development of good disaster risk management practices in this city.     

Categorisation and Harmonisation of Probabilistic Earthquake Hazard Assessments with Respect to Statistic Representation of Input Data

Probabilistic hazard calculations were tested with respect to input data uncertainties. Statistical approximations of input data allow the regression coefficients and their standard deviations to be determined. Since inaccuracies of the regressions closely depend on the input data uncertainties, the standard deviations of the individual coefficients were used as a measure of input data parametrisation. Differences in the hazard outputs, caused only by various combinations of the regression coefficients and their standard deviations determined for the cumulative recurrence graph and the attenuation law, were studied. It was concluded that the hazard calculation conditions should be (a) strictly defined and always quoted with every hazard assessment, and (b) standardized in order to establish a common liability of earthquake hazard calculations. The established categorisation of the earthquake hazard assessments divides the probabilistic hazard calculations according to their reliability and helps users to apply them in earthquake engineering practice. The credible hazard assessments corresponding to 90% probability can be recommended for common structures whereas the maximum credible hazard assessments coinciding with 95% probability yield values close to hazard assessments of important structures, hospitals, bridges, etc.     

Reliability analysis of soil liquefaction based on standard penetration test

A review of probabilistic and deterministic liquefaction evaluation procedures reveals that there is a need for a comprehensive approach that accounts for different sources of uncertainty in liquefaction evaluations. For the same set of input parameters, different models provide different factors of safety and/or probabilities of liquefaction. To account for the different uncertainties, including both the model and measurement uncertainties, reliability analysis is necessary. This paper presents a review and comparative study of such reliability approaches that can be used to obtain the probability of liquefaction and the corresponding factor of safety. Using a simplified deterministic Seed method, this reliability analysis has been performed. The probability of liquefaction along with the corresponding factor of safety have been determined based on a first order second moment (FOSM) method, an advanced FOSM (Hasofer–Lind) reliability method, a point estimation method (PEM) and a Monte Carlo simulation (MCS) method. A combined method that uses both FOSM and PEM is presented and found to be simple and reliable for liquefaction analysis. Based on the FOSM reliability approach, the minimum safety factor value to be adopted for soil liquefaction analysis (depending on the variability of soil resistance, shear stress parameters and acceptable risk) has been studied and a new design safety factor based on a reliability approach is proposed.     

Seismic Hazard for Selected Sites in Greece: A Bayesian Estimate of Seismic Peak Ground Acceleration

A procedure for estimating maximum values of seismic peak ground accelerationat the examined site and quantiles of its probabilistic distribution in a future timeinterval of a given length is considered. The input information for the method areseismic catalog and regression relation between peak seismic acceleration at a givenpoint and magnitude and distance from the site to epicenter (seismic attenuation law).The method is based on Bayesian approach, which simply accounts for influenceof uncertainties of seismic acceleration values. The main assumptions for the method are Poissonian character of seismic events flow and distribution law of Gutenberg-Richter's type. The method is applied to seismic hazard estimation in six selected sitesin Greece.     

Editorial

The assessment of rock-fall hazards is subject to significant uncertainty, which is not fully considered in general practice and research. This paper reviews and classifies the various sources of the uncertainty. Taking a generic framework for risk assessment as source, a probabilistic model is presented that consistently combines the different types of uncertainties, in order to obtain a unified estimate of rock-fall risk. An important aspect of the model is that it allows for incorporating all available information, including physical and empirical models, observations and expert knowledge, by means of Bayesian updating. Detailed formulations are developed for various types of information. Finally, two examples considering rock-fall risk on roads, with and without protection structures, illustrate the application of the probabilistic modeling framework to practical problems.     

基于贝叶斯网络的梯级水库连溃风险

为研究梯级水库漫坝连溃的风险,并探索贝叶斯网络在水库连溃风险分析中的可行性,通过构建洪水作用下双库连溃的贝叶斯网络模型,并选取四川省大渡河上两相邻梯级水库进行分析,以推求水库漫（溃）坝概率及评估连溃风险。分析过程表明贝叶斯网络方法能直观、简便地分析多风险源共同作用下的水库群连溃风险问题。结果表明,两水库天然洪水漫坝条件概率的数量级均为10-6,洪水引发单库漫坝风险较小;正常蓄水位以上,上游水库溃坝洪水致下游水库漫坝条件概率超0.8,即上游水库溃坝导致水库连溃的风险很大。     

Hazard analysis of seismic submarine slope instability

To assess the risk associated with a submarine landslide, one must estimate the probability of slope failure and its consequences. This paper proposes a procedure to estimate the probability of earthquake-induced submarine slope failure (hazard) based on probabilistic seismic hazard analyses, ground response analyses and advanced laboratory tests. The outcomes from these analyses are treated in a probabilistic framework, with analytical simulations using mathematical techniques such as the first-order reliability method, Monte Carlo simulation and Bayesian updating. Fragility curves of slope failure during the earthquake (co-seismic) and after the earthquake (post-seismic) were developed in this study, and were shown to provide a clear and well-organized procedure to estimate the annual failure probability of a submarine slope under earthquake loading.     

Efficient Monte Carlo Simulation of parameter sensitivity in probabilistic slope stability analysis

Monte Carlo Simulation (MCS) method has been widely used in probabilistic analysis of slope stability, and it provides a robust and simple way to assess failure probability. However, MCS method does not offer insight into the relative contributions of various uncertainties (e.g., inherent spatial variability of soil properties and subsurface stratigraphy) to the failure probability and suffers from a lack of resolution and efficiency at small probability levels. This paper develop a probabilistic failure analysis approach that makes use of the failure samples generated in the MCS and analyzes these failure samples to assess the effects of various uncertainties on slope failure probability. The approach contains two major components: hypothesis tests for prioritizing effects of various uncertainties and Bayesian analysis for further quantifying their effects. Equations are derived for the hypothesis tests and Bayesian analysis. The probabilistic failure analysis requires a large number of failure samples in MCS, and an advanced Monte Carlo Simulation called Subset Simulation is employed to improve efficiency of generating failure samples in MCS. As an illustration, the proposed probabilistic failure analysis approach is applied to study a design scenario of James Bay Dyke. The hypothesis tests show that the uncertainty of undrained shear strength of lacustrine clay has the most significant effect on the slope failure probability, while the uncertainty of the clay crust thickness contributes the least. The effect of the former is then further quantified by a Bayesian analysis. Both hypothesis test results and Bayesian analysis results are validated against independent sensitivity studies. It is shown that probabilistic failure analysis provides results that are equivalent to those from additional sensitivity studies, but it has the advantage of avoiding additional computational times and efforts for repeated runs of MCS in sensitivity studies.     

Probability of serviceability failure in a braced excavation in a spatially random field: Fuzzy finite element approach

A simplified framework is proposed for evaluating the probability of “serviceability failure” in a braced excavation in a spatially random field. Here, the “serviceability failure” is said to occur when the excavation-induced wall or ground movement exceeds specified limiting values. Knowledge of this probability can aid in engineering decision-making to prevent damage to adjacent infrastructures. The proposed framework consists of five elements: (1) finite element method (FEM) for analyzing wall and ground responses in a braced excavation, (2) fuzzy set modeling of parameter uncertainty, (3) spatial averaging technique for handling spatial variability, (4) vertex method for processing fuzzy input through FEM model, and (5) interpretation of fuzzy output. The proposed framework is demonstrated through a well-documented case history. The results show the proposed framework is simple and effective for assessing the probability of serviceability failure in a braced excavation in a spatially random field. To focus on the proposed fuzzy FEM approach, the scope of this paper is limited to one-dimensional modeling of spatial variability with an assumed exponential autocorrelation function.     

A novel agent-based model for tsunami evacuation simulation and risk assessment

Tsunami evacuation is an effective way to save lives from the near-field tsunami. Realistic evacuation simulation can provide valuable information for accurate evacuation risk assessment and effective evacuation planning. Agent-based modeling is ideal for tsunami evacuation simulation due to its capability of capturing the emergent phenomena and modeling the individual-level interactions among agents and the agents’ interactions with the environment. However, existing models usually neglect or simplify some important factors and/or mechanisms in tsunami evacuation. For example, uncertainties in seismic damages to the transportation network are not probabilistically considered (e.g., by simply removing the damaged links (roads/bridges) from the network). Typically a relatively small population (i.e., evacuees) is considered (due to computational challenges) while neglecting population mobility. These simplifications may lead to inaccurate estimation of evacuation risk. Usually, only single traffic mode (e.g., on foot or by car) is considered, while pedestrian speed adjustment and multi-modal evacuation (e.g., on foot and by car) are not considered concurrently. Also, pedestrian–vehicle interaction is usually neglected in the multi-modal evacuation. To address the above limitations, this study proposes a novel and more realistic agent-based tsunami evacuation model for tsunami evacuation simulation and risk assessment. Uncertainties in seismic damages to all links in the transportation network as well as uncertainties in other evacuation parameters are explicitly modeled and considered. A novel and more realistic multi-modal evacuation model is proposed that explicitly considers the pedestrian–vehicle interaction, walking speed variability, and speed adjustment for both the pedestrian and car according to traffic density. In addition, several different population sizes are used to model population mobility and its impact on tsunami evacuation risk. The proposed model is applied within a simulation-based framework to assess the tsunami evacuation risk assessment for Seaside, Oregon.

     

Probabilistic flood risk analysis considering morphological dynamics and dike failure

A comprehensive flood risk assessment should aim not only at quantifying uncertainties but also the variability of risk over time. In this study, an efficient modelling framework was proposed to perform probabilistic hazard and risk analysis in dike-protected river systems accounting for morphological variability and uncertainty. The modelling framework combined the use of: (1) continuous synthetic discharge forcing, (2) a stochastic dike breach model dynamically coupled to a stochastic unsteady one-dimensional hydraulic model (MIKE1D) describing river flows, (3) a catalogue of pre-run probabilistic inundation maps (MIKE SHE) and (4) a damage and loss model (CAPRA). The methodology was applied using continuous simulations to a 45-km reach of the Upper Koshi River, Nepal, to investigate the changes in breach and flood hazards and subsequent risks after 2 and 5 years of probable river bed aggradation. The study results indicated an increase in annual average loss of 4% per year driven by changes in loss distribution in the most frequent loss return periods (20–500 years). The use of continuous simulations and dike breach model also provided a more robust estimation of risk metrics as compared to traditional binary treatment of flood defence and/or the direct association of flow with loss return periods. The results were helpful to illustrate the potential impacts of dynamic river morphology, dike failure and continuous simulation and their significance when devising flood risk study methodologies.     

Probabilistic seismic hazard assessment for the Horn of Africa based on seismotectonic regionalisation

A probabilistic seismic hazard analysis (PSHA) for the Horn of Africa is presented. Our seismicity database consists of a revised and up-to-date regional catalogue compiled from different agencies, checked for completeness with respect to time and homogenized with respect to magnitude (M_s). The seismic source zones are based on our present day knowledge of the regional seismotectonics. Among the results we present regional hazard maps for 0.01 annual probability for intensity and Peak Ground Acceleration (PGA) and hazard curves and response spectra for six economical significant sites within the region. The model uncertainties with respect to seismicity are analysed in a novel approach and form part of a sensitivity analysis that quantifies our PSHA modelling uncertainties.

For 0.01 annual probability we find randomly oriented horizontal PGA that exceed just 0.2 g and MM-scale intensity VIII in the Afar depression and southern Sudan. Uncertainties amount to 20% g PGA in some cases, mainly due to attenuation uncertainties. Intensity uncertainties seldom exceed 0.5 intensity units. Relatively large seismic hazard is found for Djibouti (VIII for 0.01 annual probability), slightly lower for the port of Massawa (between VII and VIII for 0.01 annual probability) and low for the port of Assab (between VI and VII for 0.01 annual probability).     

The Importance of Prehistoric Data and Variability of Hazard Regimes in Natural Hazard Risk Assessment – Examples from Australia

Natural hazards are normally viewed as events that occur randomly overtime. This precept usually forms the basis for the development of the hazardmagnitude-recurrence interval relationship used in risk assessments. However,hazard variability does not always conform to this relationship especially overlonger time intervals. Non-stationarity can be common with some hazards andthose periods where the variability and/or mean (magnitude/frequency) remainconstant are referred to here as hazard regimes. Shifts from one regime to anotheroccur at a variety of time scales from centuries to millennia. Regime shifts areoften only discernible by examining longer-term records which usually includeprehistoric data. Risk assessments frequently ignore these regime shifts andestimates of the risks associated with tropical cyclones, tsunami, terrestrialfloods and landslides in Australia have been both under-estimated and exaggeratedwhen such assessments have been based solely upon short historical records.Examples of these regime shifts and their significance for natural hazard riskassessment are presented here.     

Bayesian techniques for seismic hazard assessment using imprecise data

Some Bayesian methods of dealing with inaccurate or vague data are introduced in the framework of seismic hazard assessment. Inaccurate data affected by heterogeneous errors are modeled by a probability distribution instead of the usual value plus a random error representation; these data are generically called imprecise. The earthquake size and the number of events in a certain time are modeled as imprecise data. Imprecise data allow us to introduce into the estimation procedures the uncertainty inherent in the inaccuracy and heterogeneity of the measuring systems from which the data were obtained. The problem of estimating the parameter of a Poisson process is shown to be feasible by the use of Bayesian techniques and imprecise data. This background technique can be applied to a general problem of seismic hazard estimation. Initially, data in a regional earthquake catalog are assumed imprecise both in size and location (i.e errors in the epicenter or spreading over a given source). By means of scattered attenuation laws, the regional catalog can be translated into a so-called site catalog of imprecise events. The site catalog is then used to estimate return periods or occurrence probabilities, taking into account all sources of uncertainty. Special attention is paid to priors in the Bayesian estimation. They can be used to introduce additional information as well as scattered frequency-size laws for local events. A simple example is presented to illustrate the capabilities of this methodology.