Reliability analysis of three-dimensional dynamic slope stability and earthquake-induced permanent displacement

Different models were developed for evaluating the probabilistic three-dimensional (3D) stability analysis of earth slopes and embankments under earthquake loading using both the safety factor and the displacement criteria of slope failure. In the 3D analysis, the critical and total slope widths become two new and important parameters.The probabilistic models evaluate the probability of failure under seismic loading considering the different sources of uncertainties involved in the problem, i.e. uncertainties stemming from the discrepancies between laboratory-measured and in-situ values of shear strength parameters, randomness of earthquake occurrence, and earthquake-induced acceleration. The models also takes into consideration the spatial variabilities and correlations of soil properties.Five probabilistic models of earthquake-induced displacement were developed based on the non-exceedance of a limited value criterion. Moreover, a probabilistic model for dynamic slope stability analysis was developed based on 3D dynamic safety factor.These models are formulated and incorporated within a computer program (PTDDSSA).A sensitivity analysis was conducted on the different parameters involved in the developed models by applying those models to a well-known landslides (Selset landslide) under different levels of seismic hazard.The parametric study was conducted to evaluate the effect of different input parameters on the resulting critical failure width, 3D dynamic safety factor, earthquake-induced displacement and the probability of failure. Input parameters include: average values and coefficients of variations of water table, cohesion and angle of friction for effective stress analysis, scales of fluctuations in both distance and time, hypocentral distance, earthquake magnitude, earthquake strong shaking period, etc.The hypocentral distance and earthquake magnitude were found to have major influence on the earthquake-induced displacement, probability of failure (i.e. probability of allowable displacement exceedance), and dynamic 2D and 3D safety factors.     

Improved seismic hazard model with application to probabilistic seismic demand analysis

An improved seismic hazard model for use in performance‐based earthquake engineering is presented. The model is an improved approximation from the so‐called ‘power law’ model, which is linear in log–log space. The mathematics of the model and uncertainty incorporation is briefly discussed. Various means of fitting the approximation to hazard data derived from probabilistic seismic hazard analysis are discussed, including the limitations of the model. Based on these ‘exact’ hazard data for major centres in New Zealand, the parameters for the proposed model are calibrated. To illustrate the significance of the proposed model, a performance‐based assessment is conducted on a typical bridge, via probabilistic seismic demand analysis. The new hazard model is compared to the current power law relationship to illustrate its effects on the risk assessment. The propagation of epistemic uncertainty in the seismic hazard is also considered. To allow further use of the model in conceptual calculations, a semi‐analytical method is proposed to calculate the demand hazard in closed form. For the case study shown, the resulting semi‐analytical closed form solution is shown to be significantly more accurate than the analytical closed‐form solution using the power law hazard model, capturing the ‘exact’ numerical integration solution to within 7% accuracy over the entire range of exceedance rate. Copyright © 2007 John Wiley & Sons, Ltd.     

A simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures

A versatile, simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures is discussed in this work. A probabilistic foundation is used to address the various sources of uncertainties, either excitation or structural, and to characterize seismic risk. This risk is given, in this stochastic setting, by some statistics of the system response over the adopted probability models and stochastic simulation is implemented for its evaluation. An efficient, sampling‐based approach is also introduced for establishing a probabilistic sensitivity analysis to identify the importance of each of the uncertain model parameters in affecting the overall risk. This framework facilitates use of complex models for the structural system and the excitation. The adopted structural model explicitly addresses nonlinear characteristics of the isolators and of any supplemental dampers, and the effect of seismic pounding of the base to the surrounding retaining walls. An efficient stochastic ground motion model is also discussed for characterizing future near‐fault ground motions and relating them to the seismic hazard for the structural site. An illustrative example is presented that emphasizes the results from the novel probabilistic sensitivity analysis and their dependence on seismic pounding occurrences and on addition of supplemental dampers. Copyright © 2011 John Wiley & Sons, Ltd.     

Potential rupture surface model and its application on probabilistic seismic hazard analysis

Potential sources are simplified as point sources or linear sources in current probabilistic seismic hazard analysis (PSHA) methods. Focus size of large earthquakes is considerable, and fault rupture attitudes may have great influ-ence upon the seismic hazard of a site which is near the source. Under this circumstance, it is unreasonable to use the simplified potential source models in the PSHA, so a potential rupture surface model is proposed in this paper. Adopting this model, we analyze the seismic hazard near the Chelungpu fault that generated the Chi-Chi (Jiji) earthquake with magnitude 7.6 and the following conclusions are reached. 1 This model is reasonable on the base of focal mechanism, especially for sites near potential earthquakes with large magnitude; 2 The attitudes of poten-tial rupture surfaces have great influence on the results of probabilistic seismic hazard analysis and seismic zoning.     

Probabilistic performance‐based optimum design of seismic isolation for a California high‐speed rail prototype bridge

Previous comparison studies on seismic isolation have demonstrated its beneficial and detrimental effects on the structural performance of high‐speed rail bridges during earthquakes. Striking a balance between these 2 competing effects requires proper tuning of the controlling design parameters in the design of the seismic isolation system. This results in a challenging problem for practical design in performance‐based engineering, particularly when the uncertainty in seismic loading needs to be explicitly accounted for. This problem can be tackled using a novel probabilistic performance‐based optimum seismic design (PPBOSD) framework, which has been previously proposed as an extension of the performance‐based earthquake engineering methodology. For this purpose, a parametric probabilistic demand hazard analysis is performed over a grid in the seismic isolator parameter space, using high‐throughput cloud‐computing resources, for a California high‐speed rail (CHSR) prototype bridge. The derived probabilistic structural demand hazard results conditional on a seismic hazard level and unconditional, i.e., accounting for all seismic hazard levels, are used to define 2 families of risk features, respectively. Various risk features are explored as functions of the key isolator parameters and are used to construct probabilistic objective and constraint functions in defining well‐posed optimization problems. These optimization problems are solved using a grid‐based, brute‐force approach as an application of the PPBOSD framework, seeking optimum seismic isolator parameters for the CHSR prototype bridge. This research shows the promising use of seismic isolation for CHSR bridges, as well as the potential of the versatile PPBOSD framework in solving probabilistic performance‐based real‐world design problems.     

Generation of hazard-consistent ground motion

This paper presents an integrated approach for evaluating seismic hazard and establishing ground motion at a site. In this approach, we combine the advantage of probabilistic and deterministic seismic hazard analyses and generate synthetic ground motion by considering the characteristics of seismic source, path attenuation, and local soil condition. Furthermore, uncertainties in seismic and soil parameters are taken into account. The proposed approach can be used to establish site-specific ground motion for engineering applications.     

Loss estimation for non‐ductile reinforced concrete building in Victoria,British Columbia,Canada: effects of mega‐thrust Mw9‐class subduction earthquakes and aftershocks

This paper presents, within the performance‐based earthquake engineering framework, a comprehensive probabilistic seismic loss estimation method that accounts for main sources of uncertainty related to hazard, vulnerability, and loss. The loss assessment rigorously integrates multiple engineering demand parameters (maximum and residual inter‐story drift ratio and peak floor acceleration) with consideration of mainshock–aftershock sequences. A 4‐story non‐ductile reinforced concrete building located in Victoria, British Colombia, Canada, is considered as a case study. For 100 mainshock and mainshock–aftershock earthquake records, incremental dynamic analysis is performed, and the three engineering demand parameters are fitted with a probability distribution and corresponding dependence computed. Finally, with consideration of different demolition limit states, loss assessment is performed. From the results, it can be shown that when seismic vulnerability models are integrated with seismic hazard, the aftershock effects are relatively minor in terms of overall seismic loss (1–4% increase). Moreover, demolition limit state parameters, uncertainties of collapse fragility, and non‐collapse seismic demand prediction models have showed significant contribution to the loss assessment. The seismic loss curves for the reference case and for cases with the varied parameters can differ by as large as about 150%. Copyright © 2015 John Wiley & Sons, Ltd.     

Regional minimum 1-D P-wave velocity model for a new seismicity catalogue with precise and consistent earthquake locations in southern Iran

For faster and more robust ray tracing in 1-D velocity models and also due to the lack of reliable 3-D models, most seismological centers use 1-D models for routine earthquake locations. In this study, as solution to the coupled hypocenter-velocity problem, we compute a regional P-wave velocity model for southern Iran that can be used for routine earthquake location and also a reference initial model for 3-D seismic tomography. The inversion process was based on travel time data from local earthquakes paired reports obtained by merging the catalogues of Iranian Seismic Center (IRSC, 6422 events) and by the Broadband Iranian National Seismic Network (BIN, 4333 events) for southern Iran in the period 2006 through July 2017. After cleaning the data set from large individual reading errors and by identifying event reports from both networks belonging to same earthquake (a process called event pairing), we obtained a data set of 1115 well-locatable events with a total number of 24,606 P-wave observations. This data set was used to calculate a regional minimum 1-D model for southern Iran as result of an extensive model search by trial-and-error process including several dozens of inversions. Significantly different from previous models, we find a smoothly increasing P-velocity by depth with velocities of 5.8 km/s at shallow and velocities of 6.4 km/s at deepest crustal levels. For well-locatable events, location uncertainties are estimated in the order of ±?3 km for epicenter and double this uncertainty for hypocentral depth. The use of the minimum 1-D model with appropriate station delays in routine hypocenter location processing will yield a high-quality seismic catalogue with consistent uncertainty estimates across the region and it will also allow detection of outlier observations. Based on the two catalogues by IRSC and BIN and using the minimum 1-D model and station delays for all stations in the region, we established a new combined earthquake catalogue for southern Iran. While the general distribution of the seismicity corresponds well with that of the two individual catalogues by IRSC and BIN, the new catalogue significantly enhances the correlation of seismicity with the regional fault systems within and between the major crustal blocks that as an assembly build this continental region. Furthermore, the unified seismic catalogue and the minimum 1-D model resulting from this study provide important ingredients for seismic hazard studies.     

Interrelation among several important links in seismic risk analysis

Introduction In the probability analysis method of seismic risk considering time-space inhomogeneity of seismic activity and adopted commonly in China (State Seismological Bureau, 1996) (called in-homogeneous distribution model for short), the division of seismic statistical regions, delimitation of potential seismic sources and estimation of seismicity parameters are the main links that affect significantly the estimation of ground motion parameters of a site. HUANG and WU (2005) studied …     

Probabilistic permanent fault displacement hazard via Monte Carlo simulation and its consideration for the probabilistic risk assessment of buried continuous steel pipelines

Permanent fault displacements (PFDs) because of fault ruptures emerging at the surface are critical for seismic design and risk assessment of continuous pipelines. They impose significant compressive and tensile strains to the pipe cross‐section at pipe‐fault crossings. The complexity of fault rupture, inaccurate mapping of fault location and uncertainties in fault‐pipe crossing geometries require probabilistic approaches for assessing the PFD hazard and mitigating pipeline failure risk against PFD. However, the probabilistic approaches are currently waived in seismic design of pipelines. Bearing on these facts, this paper first assesses the probabilistic PFD hazard by using Monte Carlo‐based stochastic simulations whose theory and implementation are given in detail. The computed hazard is then used in the probabilistic risk assessment approach to calculate the failure probability of continuous pipelines under different PFD levels as well as pipe cross‐section properties. Our probabilistic pipeline risk computations consider uncertainties arising from complex fault rupture and geomorphology that result in inaccurate mapping of fault location and fault‐pipe crossings. The results presented in this paper suggest the re‐evaluation of design provisions in current pipeline design guidelines to reduce the seismic risk of these geographically distributed structural systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Distant‐earthquake simulations considering source rupture propagation: refining the seismic hazard of Hong Kong

Deterministic and probabilistic seismic hazard analyses should be complementary, in the sense that probabilistic analysis may be used to identify the controlling deterministic design‐level earthquake events, and more sophisticated models of these events may then be developed to account for uncertainties that could not have been included directly in the probabilistic analysis. De‐aggregation of the tentative uniform hazard spectra (UHS) in Hong Kong resulting from a probabilistic seismic hazard assessment (PSHA) indicates that strong and major distant earthquakes, rather than moderate local earthquakes, make the largest contribution to the seismic hazard level within the natural‐period range longer than 0.3 s. Ground‐motion simulations of controlling events located 90 and 340 km from Hong Kong, taking into account uncertainties in the rupture process, reveal that the tentative UHS resulting from the PSHA may have significantly underestimated the mid‐to‐long period components. This is attributed mainly to the adoption of double‐corner source‐spectrum models in the attenuation relationships employed in the PSHA. The results of the simulations indicate clearly that rupture directivity and rupture velocity can significantly affect the characteristics of ground motions, even from such distant earthquakes. The rupture‐directivity effects have profound implications in elongating the second corner period where the constant velocity intersects the constant displacement, thus increasing the associated displacement demand. However, demands for acceleration and velocity are found to be not sensitive to the presence of the directivity pulses. Ground pulses resulting from forward rupture directivity of distant earthquakes have longer predominant periods than the usual near‐fault directivity pulses. These long‐period pulses may have profound implications for metropolises, such as Hong Kong and others in Southeast Asia, having large concentration of high‐rise buildings. Copyright © 2005 John Wiley & Sons, Ltd.     

Probabilistic seismic hazard model for Cairo,Egypt: estimates and uncertainties

A new seismic hazard model for Cairo, the capital city of Egypt is developed herein based on comprehensive consideration of uncertainties in various components of the probabilistic seismic hazard analysis. The proposed seismic hazard model is developed from an updated catalogue of historical and instrumental seismicity, geodetic strain rates derived from GPS-based velocity-field of the crust, and the geologic slip rates of active faults. The seismic source model consists of area sources and active faults characterised to forecast the seismic productivity in the region. Ground motion prediction models are selected to describe the expected ground motion at the sites of interest. The model accounts for inherent epistemic uncertainties of statistical earthquake recurrence; maximum magnitude; ground motion prediction models, and their propagation toward the obtained results. The proposed model is applied to a site-specific hazard analysis for Kottamiya, Rehab City and Zahraa-Madinat-Nasr (hereinafter referred to as Zahraa) to the East of Cairo (Egypt). The site-specific analysis accounts for the site response, through the parameterization of the sites in terms of average 30-m shear-wave velocity (Vs30). The present seismic hazard model can be considered as a reference model for earthquake risk mitigation and proper resilience planning.     

Accurate Location of Synthetic Acoustic Emissions and Location Sensitivity to Relocation Methods, Velocity Perturbations, and Seismic Anisotropy

Acoustic emission (AE) monitoring is a non-invasive method of monitoring fracturing both in situ, and in experimental rock deformation studies. Until recently, the major impediment for imaging brittle failure within a rock mass is the accuracy at which the hypocenters may be located. However, recent advances in the location of regional scale earthquakes have successfully reduced hypocentral uncertainties by an order of magnitude. The least-squares Geiger, master event relocation, and double difference methods have been considered in a series of synthetic experiments which investigate their ability to resolve AE hypocentral locations. The effect of AE hypocenter location accuracy due to seismic velocity perturbations, uncertainty in the first arrival pick, array geometry and the inversion of a seismically anisotropic structure with an isotropic velocity model were tested. Hypocenters determined using the Geiger procedure for a homogeneous, isotropic sample with a known velocity model gave a RMS error for the hypocenter locations of 2.6 mm; in contrast the double difference method is capable of reducing the location error of these hypocenters by an order of magnitude. We test uncertainties in velocity model of up to ±10% and show that the double difference method can attain the same RMS error as using the standard Geiger procedure with a known velocity model. The double difference method is also capable of precise locations even in a 40% anisotropic velocity structure using an isotropic model for location and attains a RMS mislocation error of 2.6 mm that is comparable to a RMS mislocation error produced with an isotropic known velocity model using the Geiger approach. We test the effect of sensor geometry on location accuracy and find that, even when sensors are missing, the double difference method is capable of a 1.43 mm total RMS mislocation compared to 4.58 mm for the Geiger method. The accuracy of automatic picking algorithms used for AE studies is ±0.5 μs (1 time sample when the sampling rate is 0.2 μs). We investigate how AE locations are effected by the accuracy of first arrival picking by randomly delaying the actual first arrival by up to 5 time samples. We find that even when noise levels are set to 5 time samples the double difference method successfully relocates the synthetic AE.     

Preliminary Study on Probabilistic Prediction of Seismic Hazard in a Period of 10 Years

Many uncertainty factors need be dealt with in the prediction of seismic hazard for a 10-year period.Restricted by these uncertainties,the result of prediction is also uncertain to a certain extent,so the probabilistic analysis method of seismic hazard should be adopted.In consideration of the inhomogeneity of the time,location,and magnitude of future earthquakes and the probabilistic combination of the background of long-term seismic hazard(geology,geophysical field,etc.)and the precursors of earthquake occurrence,a model of probabilistic prediction of seismic hazard in a period of 10 years s proposed.Considering the inhomogeneity of data and earthquake precursors for different regions in China,a simplified model is also proposed in order to satisfy the needs of different regions around the country.A trial in North China is used to discuss the application of the model.The method proposed in this paper can be used in the probabilistic prediction of seismic hazard in a period of 10 years.According to the     

Probabilistic seismic hazard assessment for Romania and sensitivity analysis: A case of joint consideration of intermediate-depth (Vrancea) and shallow (crustal) seismicity

The earthquake risk on Romania is one of the highest in Europe, and seismic hazard for almost half of the territory of Romania is determined by the Vrancea seismic region, which is situated beneath the southern Carpathian Arc. The region is characterized by a high rate of occurrence of large earthquakes in a narrow focal volume at depth from 70 to 160 km. Besides the Vrancea area, several zones of shallow seismicity located within and outside the Romanian territory are considered as seismically dangerous. We present the results of probabilistic seismic hazard analysis, which implemented the “logic tree” approach, and which considered both the intermediate-depth and the shallow seismicity. Various available models of seismicity and ground-motion attenuation were used as the alternative variants. Seismic hazard in terms of macroseismic intensities, peak ground acceleration, and response spectra was evaluated for various return periods. Sensitivity study was performed to analyze the impact of variation of input parameters on the hazard results. The uncertainty on hazard estimates may be reduced by better understanding of parameters of the Vrancea source zone and the zones of crustal seismicity. Reduction of uncertainty associated with the ground-motion models is also very important issue for Romania.     

十年尺度地震危险性概率预测方法的初步研究

在十年尺度（５—１０年）地震危险性预测中，需要处理众多的不确定因素。受这些不确定因素的约束，地震预测的结果必然带有相当的不确定性，因此应该用概率分析的方法进行预测。考虑地震发生的时间、空间和强度的非均匀性及相关特征和地震危险性长期背景（地质、地球物理场等因素）与地震发生前兆的概率结合，提出了十年尺度地震危险性预测的概率模型。考虑资料的不均匀性和适宜不同地区的地震前兆方法的差异，本文还提出了概率预测模型简化形式，以满足全国不同地区的需要。本文以华北北部地区为例讨论了该模型的实际应用。文中提出的方法可以用于全国十年尺度地震危险性的概率预测。根据本项研究提供的结果和计算程序，可以满足地震对策和地震损失估计对地震中长期概率预测的需要。     

青藏高原东北缘地震活动性广义帕累托模型的全域敏感性分析

基于广义帕累托分布构建地震活动性模型,因其输入参数取值难以避免不确定性,导致依据该模型所得的地震危险性估计结果具有不确定性。鉴于此,本文选取青藏高原东北缘为研究区,提出了基于全域敏感性分析的地震危险性估计的不确定性分析流程和方法。首先,利用地震活动性广义帕累托模型,进行研究区地震危险性估计;然后,选取地震记录的起始时间和震级阈值作为地震活动性模型的输入参数,采用具有全域敏感性分析功能的E-FAST方法,对上述两个参数的不确定性以及两参数之间的相互作用对地震危险性估计不确定性的影响进行定量分析。结果表明：地震危险性估计结果（不同重现期的震级重现水平、震级上限及相应的置信区间）对两个输入参数中的震级阈值更为敏感;不同重现期的地震危险性估计结果对震级阈值的敏感程度不同;对不同的重现期而言,在影响地震危险性估计结果的不确定性上,两个输入参数之间存在非线性效应,且非线性效应程度不同。本文提出的不确定性分析流程和方法,可以推广应用于基于其它类型地震活动性模型的地震危险性估计不确定性分析。     

Improving seismic hazard approaches for critical infrastructures: a pilot study in the Po Plain

Paper describes the extensive work done in the SIGMA project, aimed at improving knowledge on data, methods and tools to better quantify uncertainties in seismic hazard assessment (SHA). The authors cooperated in the study of potential faults and geological structures, earthquake catalogues, selection of ground motion prediction equations, and methods for site effect evaluation suitable for SHA. All the contributions merged into a probabilistic seismic hazard study conducted for three representative sites of the Po Plain in Northern Italy. Po Plain is a low-to-moderate seismicity region, characterized by some critical features, such as blind faulting and deep alluvium sediments, and by scarcity of strong motion data; these sources of uncertainties in seismic hazard estimation are common to other low seismicity areas around the world. Within SIGMA, special care was devoted to: (a) the use of the single station sigma approach inside the probabilistic SHA, (b) the comparative use of generalized attenuation functions to evaluate the hazard contribution of composite fault systems, and (c) the study of the epistemic uncertainties at play when different modelling approaches to site effects are used.     

Uncertainty Analysis and Expert Judgment in Seismic Hazard Analysis

The large uncertainty associated with the prediction of future earthquakes is usually regarded as the main reason for increased hazard estimates which have resulted from some recent large scale probabilistic seismic hazard analysis studies (e.g. the PEGASOS study in Switzerland and the Yucca Mountain study in the USA). It is frequently overlooked that such increased hazard estimates are characteristic for a single specific method of probabilistic seismic hazard analysis (PSHA): the traditional (Cornell?CMcGuire) PSHA method which has found its highest level of sophistication in the SSHAC probability method. Based on a review of the SSHAC probability model and its application in the PEGASOS project, it is shown that the surprising results of recent PSHA studies can be explained to a large extent by the uncertainty model used in traditional PSHA, which deviates from the state of the art in mathematics and risk analysis. This uncertainty model, the Ang?CTang uncertainty model, mixes concepts of decision theory with probabilistic hazard assessment methods leading to an overestimation of uncertainty in comparison to empirical evidence. Although expert knowledge can be a valuable source of scientific information, its incorporation into the SSHAC probability method does not resolve the issue of inflating uncertainties in PSHA results. Other, more data driven, PSHA approaches in use in some European countries are less vulnerable to this effect. The most valuable alternative to traditional PSHA is the direct probabilistic scenario-based approach, which is closely linked with emerging neo-deterministic methods based on waveform modelling.     

Seismic hazard and uncertainty analysis of the Taiwan area

The objectives of this paper are (1) to obtain estimates on the effect of uncertainties of the hazard model, and (2) to evaluate the seismic hazard in Taiwan for structural analysis and design purposes. The seismic hazard in the Taiwan area is presented in terms of an iso-acceleration map. Such a map is developed for return periods of peak ground acceleration of 225 years and 475 years. The contour map of b-values and mean occurence rates for this region is also presented. Uncertainty analyses of model parameters in hazard analysis are concentrated on the analysis of dispersion of PGA values and the probabilistic modeling of stationary and nonstationary Poisson models of occurrences. Th e overall results are considered to be conservative since for most uncertainty analyses the more conservative values are used.