The use of the possibility theory to investigate the epistemic uncertainties within scenario-based earthquake risk assessments

This paper presents a methodology to represent and propagate epistemic uncertainties within a scenario-based earthquake risk model. Unlike randomness, epistemic uncertainty stems from incomplete, vague or imprecise information. This source of uncertainties still requires the development of adequate tools in seismic risk analysis. We propose to use the possibility theory to represent three types of epistemic uncertainties, namely imprecision, model uncertainty and vagueness due to qualitative information. For illustration, an earthquake risk assessment for the city of Lourdes (Southern France) using this approach is presented. Once adequately represented, uncertainties are propagated and they result in a family of probabilistic damage curves. The latter is synthesized, using the concept of fuzzy random variables, by means of indicators bounding the true probability to exceed a given damage grade. The gap between the pair of probabilistic indicators reflects the imprecise character of uncertainty related to the model, thus picturing the extent of what is ignored and can be used in risk management.     

Probabilistic disaggregation of a spatial portfolio of exposure for natural hazard risk assessment

In natural hazard risk assessment situations are encountered where information on the portfolio of exposure is only available in a spatially aggregated form, hindering a precise risk assessment. Recourse might be found in the spatial disaggregation of the portfolio of exposure to the resolution of the hazard model. Given the uncertainty inherent to any disaggregation, it is argued that the disaggregation should be performed probabilistically. In this paper, a methodology for probabilistic disaggregation of spatially aggregated values is presented. The methodology is exemplified with the disaggregation of a portfolio of buildings in two communes in Switzerland and the results are compared to sample observations. The relevance of probabilistic disaggregation uncertainty in natural hazard risk assessment is illustrated with the example of a simple flood risk assessment.     

Framework for probabilistic assessment of landslide: a case study of El Berrinche

Slope failure or landslide is a complex geological/geotechnical problem that involves much uncertainty. In this work, a framework for probabilistic assessment of landslide is presented with a focus on the El Berrinche landslide, Honduras. One unique feature of this case study involving the El Berrinche landslide is that the stability analysis has to be carried out with limited data. Another challenge in this study is to assess possible remedial measures in a way that can easily be communicated to the government and the public. A reliability-based framework for a probabilistic assessment is proposed. With this approach, different levels of risk for landslide are assessed and the associated costs are estimated; and all information is integrated into the decision-making process for choosing a remedial action.     

Non-Circular Rock-Fall Motion Behavior Modeling by the Eccentric Circle Model

The geometry of a block is a major factor affecting its rock-fall motion. A two-dimensional disc or three-dimensional sphere is often used to numerically simulate rock-fall motion, though circular or spherical blocks poorly represent the real geometry of rock falls. An eccentric circle model is specifically proposed to simulate the behavior of non-circular blocks in rock-fall motion using the distinct element method. In the eccentric circle model, the moment originates from the eccentricity. Three types of block shape, circle, ellipse, and eccentric circle, were used to simulate the fall of a single block through four different slope shapes to impact on a defense wall. The results of the simulation revealed that when the eccentricity falls below 0.5, the rock-fall motion is close to that of the ellipse model. As eccentricity grows, the rock-fall motion is closer to that of a flat piece, more stable, and tending to slide. When the block impacts the defensive wall using the circle model, a higher force and energy head in the wall is obtained. This case tends to be conservative, with the exception of the high slope angle case. The bouncing height using the circle model falls just between those of the ellipse and the eccentric circle models and tends to be unconservative. In conclusion, the rock-fall motion simulation using the proposed eccentric circle model appears to approach the non-circular block trajectory and energy loss, making it useful for rock-fall risk prevention and mitigation.     

Probabilistic assessment of soil liquefaction considering spatial variability of CPT measurements

The conventional liquefaction potential assessment methods (also known as simplified methods) profoundly rely on empirical correlations based on observations from case histories. A probabilistic framework is developed to incorporate uncertainties in the earthquake ground motion prediction, the cyclic resistance prediction, and the cyclic demand prediction. The results of a probabilistic seismic hazard assessment, site response analyses, and liquefaction potential analyses are convolved to derive a relationship for the annual probability and return period of liquefaction. The random field spatial model is employed to quantify the spatial uncertainty associated with the in-situ measurements of geotechnical material.     

Default risk-based probabilistic decision model for risk management and control

This study describes how risk-based risk control allocation models work. We begin by discussing the economic rationale for allocating risk control in a diversified organization such as an enterprise. For a probability model for risk control decision making under uncertainty and risk, we propose a model involving stochastic total loss amount constraints with respect to various tolerable default levels. Our main objective is to develop a method that will allow shaping of the risk associated with risk control outcomes. The direct and indirect losses caused by simulated disasters can be estimated using an engineering and financial analysis model. Based on this model, we can generate an exceeding probability curve and then calculate how much of the loss can be eliminated or transferred to other entities should funds be allocated to risk control. The optimal natural disaster risk control arrangement with a probabilistic formulation is explained in this paper. Results from the proposed formulations are compared in case studies. The model attempts to apply risk-based budget guidelines to risk reduction measurement within a portfolio-based risk framework.     

A Probabilistic Modelling System for Assessing Flood Risks

In order to be economically viable, flood disaster mitigation should be based on a comprehensive assessment of the flood risk. This requires the estimation of the flood hazard (i.e. runoff and associated probability) and the consequences of flooding (i.e. property damage, damage to persons, etc.). Within the “German Research Network Natural Disasters” project, the working group on “Flood Risk Analysis” investigated the complete flood disaster chain from the triggering event down to its various consequences. The working group developed complex, spatially distributed models representing the relevant meteorological, hydrological, hydraulic, geo-technical, and socio-economic processes. In order to assess flood risk these complex deterministic models were complemented by a simple probabilistic model. The latter model consists of modules each representing one process of the flood disaster chain. Each module is a simple parameterisation of the corresponding more complex model. This ensures that the two approaches (simple probabilistic and complex deterministic) are compatible at all steps of the flood disaster chain. The simple stochastic approach allows a large number of simulation runs in a Monte Carlo framework thus providing the basis for a probabilistic risk assessment. Using the proposed model, the flood risk including an estimation of the flood damage was quantified for an example area at the river Rhine. Additionally, the important influence of upstream levee breaches on the flood risk at the lower reaches was assessed. The proposed model concept is useful for the integrated assessment of flood risks in flood prone areas, for cost-benefit assessment and risk-based design of flood protection measures and as a decision support tool for flood management.     

A GIS-based logistic regression model in rock-fall susceptibility mapping along a mountainous road: Salavat Abad case study, Kurdistan, Iran

This study describes the application of logistic regression to rock-fall susceptibility mapping along 11?km of a mountainous road on the Salavat Abad saddle, in southwest Kurdistan, Iran. To determine the factors influencing rock-falls, data layers of slope degree, slope aspect, slope curvature, elevation, distance to road, distance to fault, lithology, and land use were analyzed by logistic regression analysis. The results are shown as rock-fall susceptibility maps. A spatial database, which included 68 sites (34 rock-fall point cells with value of 1 and 34 no rock-fall point cells with value of 0) was developed and analyzed using a Geographic Information System, GIS. The results are shown as four classes of rock-fall susceptibility. In this study, distance to fault, lithology, slope curvature, slope degree, and distance to road were found to be the most important factors affecting rock-fall. It was concluded that about 76?% of the study area can be classified as having moderate and high susceptibility classes. Rock-fall point cells were used to verify results of the rock-fall susceptibility map using success curve rate and the area under the curve. The verification results showed that the area under the curve for rock-fall susceptibility map is 77.57?%. The results from this study demonstrated that the use of a logistic regression model within a GIS framework is useful and suitable for rock-fall susceptibility mapping. The rock-fall susceptibility map can be used to reduce susceptibility associated with rock-fall.     

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.     

A Hazard Assessment Method for Potential Earthquake-Induced Landslides – A Case Study in Huaxian County, Shaanxi Province

The hazard assessment of potential earthquake-induced landslides is an important aspect of the study of earthquake-induced landslides. In this study, we assessed the hazard of potential earthquake-induced landslides in Huaxian County with a new hazard assessment method. This method is based on probabilistic seismic hazard analysis and the Newmark cumulative displacement assessment model. The model considers a comprehensive suite of information, including the seismic activities and engineering geological conditions in the study area, and simulates the uncertainty of the intensity parameters of the engineering geological rock groups using the Monte Carlo method. Unlike previous assessment studies on ground motions with a given exceedance probability level, the hazard of earthquake-induced landslides obtained by the method presented in this study allows for the possibility of earthquake-induced landslides in different parts of the study area in the future. The assessment of the hazard of earthquake-induced landslides in this study showed good agreement with the historical distribution of earthquake-induced landslides. This indicates that the assessment properly reflects the macroscopic rules for the development of earthquake-induced landslides in the study area, and can provide a reference framework for the management of the risk of earthquake-induced landslides and land planning.     

Probabilistic parameter estimation and predictive uncertainty based on field measurements for unsaturated soil slope

A key issue in assessment of rainfall-induced slope failure is a reliable evaluation of pore water pressure distribution and its variations during rainstorm, which in turn requires accurate estimation of soil hydraulic parameters. In this study, the uncertainties of soil hydraulic parameters and their effects on slope stability prediction are evaluated, within the Bayesian framework, using the field measured temporal pore-water pressure data. The probabilistic back analysis and parameter uncertainty estimation is conducted using the Markov Chain Monte Carlo simulation. A case study of a natural terrain site is presented to illustrate the proposed method. The 95% total uncertainty bounds for the calibration period are relatively narrow, indicating an overall good performance of the infiltration model for the calibration period. The posterior uncertainty bounds of slope safety factors are much narrower than the prior ones, implying that the reduction of uncertainty in soil hydraulic parameters significantly reduces the uncertainty of slope stability.     

Probabilistic geotechnical analyses for offshore facilities

Society requires increasingly that the hazard and risk associated with engineered constructions be quantified. The current paper presents geotechnical hazard assessment in the context of a risk framework. Concepts of uncertainties, reliability, safety and risk are briefly reviewed. The use of the approach is exemplified for offshore facilities, including piled foundations, jack-up structures, gravity foundations and underwater slopes. The applications demonstrate that probabilistic analyses complement the conventional deterministic safety factor and deformation-based analyses, and contribute to achieving a safe and optimum design. The probabilistic approach adds value to the results with a modest additional effort. The conclusions emphasize the usefulness of a risk assessment, the importance of engineering judgement in the assessment and the need for involving multi-disciplinary competences to achieve reliable estimates of hazard and risk. The profession can only gain by implementing probabilistic-based thinking and risk-based approaches more systematically than before.     

Risk and uncertainty analysis in the planning stages of a risk decision-making process

Natural disaster risk, a long-time concern in the insurance industry, is increasingly recognized as a present danger in the business strategies of risk control and enterprise management agencies. Floods and earthquakes can cause massive loss of life and infrastructure, resulting in business interruption and heavy casualties. Many of the short-term developmental strategies employed throughout the world have only served to exacerbate the impact of natural disasters. Therefore, this study presents a review of formal methods that are commonly used in risk and uncertainty analysis in planning and concludes with a critical assessment of the advantages and disadvantages of the different priority setting methods. Our focus is a preliminary proposal for developing an efficient probabilistic approach to facilitate design optimization that involves probabilistic constraints.     

Effect of spatial variability of cross‐correlated soil properties on bearing capacity of strip footing

Geotechnical engineering problems are characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for a probabilistic analysis that considers the spatial variability of cross‐correlated soil properties is presented and applied to study the bearing capacity of spatially random soil with different autocorrelation distances in the vertical and horizontal directions. The approach integrates a commercial finite difference method and random field theory into the framework of a probabilistic analysis. Two‐dimensional cross‐correlated non‐Gaussian random fields are generated based on a Karhunen–Loève expansion in a manner consistent with a specified marginal distribution function, an autocorrelation function, and cross‐correlation coefficients. A Monte Carlo simulation is then used to determine the statistical response based on the random fields. A series of analyses was performed to study the effects of uncertainty due to the spatial heterogeneity on the bearing capacity of a rough strip footing. The simulations provide insight into the application of uncertainty treatment to geotechnical problems and show the importance of the spatial variability of soil properties with regard to the outcome of a probabilistic assessment. Copyright © 2009 John Wiley & Sons, Ltd.     

Using random forest for the risk assessment of coal-floor water inrush in Panjiayao Coal Mine,northern China

Coal-floor water-inrush incidents account for a large proportion of coal mine disasters in northern China, and accurate risk assessment is crucial for safe coal production. A novel and promising assessment model for water inrush is proposed based on random forest (RF), which is a powerful intelligent machine-learning algorithm. RF has considerable advantages, including high classification accuracy and the capability to evaluate the importance of variables; in particularly, it is robust in dealing with the complicated and non-linear problems inherent in risk assessment. In this study, the proposed model is applied to Panjiayao Coal Mine, northern China. Eight factors were selected as evaluation indices according to systematic analysis of the geological conditions and a field survey of the study area. Risk assessment maps were generated based on RF, and the probabilistic neural network (PNN) model was also used for risk assessment as a comparison. The results demonstrate that the two methods are consistent in the risk assessment of water inrush at the mine, and RF shows a better performance compared to PNN with an overall accuracy higher by 6.67%. It is concluded that RF is more practicable to assess the water-inrush risk than PNN. The presented method will be helpful in avoiding water inrush and also can be extended to various engineering applications.     

An Environmental Risk Assessment/Management Framework for Climate Change Impact Assessments

This paper presents an environmental risk assessment/risk management framework to assess the impacts of climate change on individual exposure units identified as potentially vulnerable to climate change. This framework is designed specifically to manage the systematic uncertainties that accompany the propagation of climate change scenarios through a sequence of biophysical and socio-economic climate impacts. Risk analysis methods consistent with the IPCC Technical Guidelines for Assessing Climate Change Impacts and Adaptations are set within a larger framework that involves stakeholders in the identification, assessment and implementation of adaptation measures. Extensive consultation between parties occurs in a flexible structure that embeds scientific methods of risk analysis within a broad setting of social decision-making. This format is consistent with recent forms of environmental risk assessment/management frameworks. The risk analysis links key climatic variables expressed as projected ranges of climate change with an upper and lower limit, with impact thresholds identified collaboratively by researchers and stakeholders. The conditional probabilities of exceeding these thresholds are then assessed (probabilities using this method are conditional as the full range of uncertainty for the various drivers of climate change, and their probability distributions, remains unknown). An example based on exceeding irrigation demand limited by an annual farm cap is used to show how conditional probabilities for the exceedance of a critical threshold can be used to assess the need for adaptation. The time between the identification of an acceptable level of risk and its exceedance is identified as a window of adaptation.The treatment of risk consists of two complementary actions, adaptation to anticipated changes in climate and the mitigation of climate change through reductions in greenhouse gas emissions. Both of these actions will reduce the risk of critical thresholds being exceeded. The potential of this framework for addressing specific requirements of the United Nations Framework Convention for Climate Change is discussed.     

A workflow for decision making under uncertainty

We propose a workflow for decision making under uncertainty aiming at comparing different field development plan scenarios. The approach applies to mature fields where the residual uncertainty is estimated using a probabilistic inversion approach. Moreover, a robust optimization method is presented to optimize controllable parameters in the presence of uncertainty. The key element of this approach is the use of response surface model to reduce the very high number of simulator model evaluations that are classically needed to perform such workflows. The major issue is to be able to build an efficient and reliable response surface. This is achieved using a Gaussian process (kriging) statistical model and using a particular training set (experimental design) developed to take into account the variable correlation induced by the probabilistic inversion process. For the problem of optimization under uncertainty, an iterative training set is proposed, aiming at refining the response surface iteratively such as to effectively reduce approximation errors and converging faster to the true solution. The workflow is illustrated on a realistic test case of a mature field where the approach is used to compare two new development plan scenarios both in terms of expectation and of risk mitigation and to optimize well position parameters in the presence of uncertainty.     

节理岩体关键块体稳定的概率分析

基于地下岩体受节理面的控制,节理面的几何和力学参数随机分布,从而导致岩体系统具有高度不确定性,提出以关键块体理论为基础,考虑节理几何和力学参数随机性的岩体开挖可靠度分析方法,并给出了块体稳定的总失效概率评价模型。以澳大利亚阿德莱德地区一铜矿地质条件为例,以节理面倾角、倾向、摩擦系数和黏聚力为随机变量,通过Monte Carlo模拟和概率图方法,进行了岩体可靠度和失效概率的计算。最后,采用条件概率的分析方法,计算了单面滑动块体的总失效概率。计算结果表明,块体沿单面滑动并且出现的概率为11.0%,总的失效概率为3.85%,超过一般岩体工程可允许的风险水平,认为该方法可以作为评价块体可靠性的依据。