Annual Rate Of Exceedance Research Articles

Sensitivity of seismic fragility curves to multiple parameters using CyberShake simulated ground motions

AbstractSeveral alternatives exist to compute seismic fragility curves. This study takes advantage of the large pool of site‐specific CyberShake simulated ground motions (GMs) to investigate the sensitivity of fragility curves to multiple analysis parameters: the analysis method (Multiple Stripe Analysis (MSA), Cloud Analysis (CA), or Incremental Dynamic Analysis), the number and intensity measure distribution of the GMs used, the GM selection method, and the amount of scaling. To this end, the fragility curve of a two‐dimensional steel frame is calculated for every analysis variation at the life safety limit state. By varying one parameter at a time, we can separate the effects of the various parameters from one another. We also assess the effect of the analysis parameters on the mean annual rate of exceedance of life safety. We find that if GMs are selected adequately for each method, different analysis methods can lead to consistent mean annual rates of exceedance despite some differences in their fragility curves. Generally, MSA and the proposed CA that models the increase of response variability with ground motion intensity best match empirical fragility points. The number of GMs affects the results for all analysis methods, while the intensity distribution of GMs affects results differently in different methods. When GMs are required to match earthquake scenario parameters in addition to intensity, more conservative fragility curves are obtained. Finally, fragility curves are sensitive to excessive scaling. This study provides important insights for performance‐based earthquake engineering.

Space and time distribution of seismic source energy at Campi Flegrei, Italy through the last unrest phase (1.1.2000–31.12.2023)

We describe the space-time pattern of seismicity occurring on Campi Flegrei Caldera (CFC), Italy, where ground deformations and seismicity represent the drivers of its current bradyseismic crisis, well known and extensively studied at an international level. In detail we consider the seismicity in the time interval starting on 1.1.2000 and ending on 31.12.2023. We revise the statistics of the earthquake occurrence, focusing at possible precursory time changes of the b-parameter of the Gutenberg and Richter (G&R b−value) distribution and at the time distribution of the total seismic moment inside any swarm. To estimate the G&R b−value we use a Monte Carlo method instead of the ordinary Least Squares or Maximum likelihood methods, to easily measure the uncertainty on the b−value taking into account uncertainties on the magnitude estimates. Results show that G&R a−value and b−value calculated for cumulative and discrete distributions of Mw, the moment-magnitude, and Md, the so-called duration-magnitude, are the same inside the uncertainties; a−value and b−value for Md are significantly different from the same parameters estimated for Mw, being b−value for Mw close to the value of 1.0 and b−value for Md close to 0.8. The “bounded” G&R distribution fits the data yielding a−value and b−value close to those for the unbounded distribution. The mean annual rate of exceedance, calculated for the entire catalogue, results to be 0.033±0.015 (years−1) corresponding to a return period of 30±14 years for Mw=4.5. The time dependence of G&R b-parameter show a b−value time pattern characterized by variations slightly outside 1-σ uncertainty bar, tending to the value of 1 approaching present. As evidenced by several past studies, earthquakes in CFC occur in space-time clusters, with a mean time duration of 1 day. We selected the swarms with a selection algorithm, based on the joint estimation of inter-arrival times and inter-event distance for the consecutive event couples. The plot of the event number in each cluster vs the time of occurrence, clearly show that in CFC the number of cluster occurrences and the event number in each cluster accelerates during time starting from 2010. The time-pattern of the total seismic moment in each cluster shows that, contrarily to the event number, there is no evident striking increase of the total swarm moment as a function of time.We also consider distribution of the Energy Space Density of the CFC earthquakes, ESD. This quantity shows a clearly visible enlargement of the fractured rock volumes in the last 15 months, toward West, at a depth around 3000 m below sea level. The most fractured zone coincides with the greatest contrasts in seismic attenuation.The present study confirms that the current unrest phase is still ongoing, with an enlargement of the rock fracturing zone which extends southward and westward as compared with that measured 22 months before.

Monte Carlo Based Sampling Distribution of Annual Rate of Exceedance for Earthquake Insurance

ABSTRACT Seismic hazard expressed in terms of annual rate of exceedance and is used to calculate the earthquake insurance premium. Annual rate of exceedance is a complicated function of magnitudes, distances from site to earthquake sources and attenuation. Due to its complexity, determination of exact sampling distribution of earthquake insurance premium is not an easy task. This research proposes Monte Carlo simulation approach to determine the sampling distribution of earthquake insurance premium. Annual rate of exceedance was simulated first and then the insurance premium calculated based on simulation of annual rate of exceedance. The simulation involves quantifying synthetic catalogue similar to historical catalogue. Its simulation is conducted in order to construct annual rate of exceedance as an indicator of earthquake risk used in earthquake insurance. The simulation of 25 iteration and sample size of 100 shows that the sampling distribution of insurance premium is skewed to the right. The idea of using Monte Carlo simulation to study the sampling distribution of annual rate of exceedance is the originality of the study and the study contributes to the methodology of earthquake insurance.

An Efficient Method for Probability Prediction of Peak Ground Acceleration Using Fourier Amplitude Spectral Model

ABSTRACT The probabilistic prediction of peak ground acceleration (PGA) using the Fourier amplitude spectral (FAS) model has many advantages in regions lacking strong ground-motion records. Currently, the implementation of this approach for the calculation of annual exceedance rate of PGA relies on Monte Carlo simulations (MCSs). However, adopting MCS requires many times calculations of PGA from FAS, and each time of calculation includes complicated integrals, the computational cost is too high to be acceptable for practical applications. Therefore, this study proposes an efficient method for the probabilistic prediction of PGA using the FAS model. For this purpose, a probabilistic analysis method, referred to as the moment method, was introduced to improve computational efficiency. The probability distribution of PGA was approximated using a three-parameter distribution defined according to the first three moments. The first three moments of the PGA were obtained based on the point-estimate and dimension-reduction integration method. Numerical examples were conducted to verify the proposed method. It was found that the proposed method not only performed much more efficiently than using MCS in calculating the annual exceedance rate of PGA to obtain the hazard curve but also provides nearly the same accuracy as MCS.

SMA-braced steel frames influenced by temperature: Practical modelling strategy and probabilistic performance assessment

This study presents a practical and efficient modelling approach for shape memory alloy (SMA)-braced steel frames under various temperatures, and examines their probabilistic performance affected by temperature. A one-dimensional constitutive model is developed in OpenSees to capture the superelasticity (SE), partial SE, shape memory effect (SME), and permanent yielding behaviors of SMA elements subjected to varying temperatures. The proposed modelling approach is partly validated against an experimental study newly conducted in the present work. The material-level investigation is followed by a comprehensive probabilistic performance assessment of a typical steel frame employing SMA-based self-centering braces (SMA-SCBs), where a practical and realistic modelling strategy for the SMA-SCB is developed to capture the degradation behavior, especially at low temperatures. Seismic risk assessment is conducted to evaluate the collapse resistance and resilience performance of the considered structures, with the influence of temperature highlighted. Among other important findings, it is shown that the decrease in environment temperature significantly increases the peak inter-story drift (PID) and residual inter-story drift (RID) responses. Under the maximum considered earthquake (MCE), the probability of collapse increases from 2.7% to 19.7% when the temperature decreases from 30 °C to −15 °C. From a self-centering capability point of view, the probabilistic of exceedance of 0.5% RID threshold soars from negligible to nearly 100%, considering the same temperature variation. The study highlights the fact that temperature plays a significant role in the annual rate of exceedance of all damage states, and warns that the idealized flag-shaped modelling approach for SMA components is extremely unsafe at low temperatures.

An Integrated Uncertainty Quantification Framework for Probabilistic Seismic Hazard Analysis

Probabilistic seismic hazard analysis (PSHA) is a tool to quantify the annual rate of exceedance of seismic intensity measure at a location of interest. The present study investigates the uncertainty embedded in three PSHA parameters: magnitude of earthquake, source-to-site distance, and corresponding ground shaking. Although previous researchers have worked to quantify the uncertainty in these hazard parameters, the source-to-site distance uncertainty in PSHA has not been explicitly addressed to acquire more accurate and reliable seismic hazard estimates. This study develops an uncertainty quantification framework for PSHA considering source-to-site distance uncertainty, including interdependency between hazard parameters. To capture this uncertainty, an approach of considering grids in the area seismic source zone is adopted using a geographic information system (GIS) and implementing Latin hypercube sampling (LHS) to quantify the uncertainty of the occurrence of an earthquake at any distance from the site. The interaction of magnitude and source-to-site distance has been investigated using copula theory. As a part of practical implementation, PSHA of Silchar city in Northeast India is taken into consideration due to its tectonic features and high seismicity. This work applies two processes to quantify uncertainty: (1) considering the center point of a grid, and (2) stratified sampling of points within a grid by LHS. The results reveal that on applying LHS (with uncorrelated random events), the hazard increases due to discretization of the area sources, and robust consideration of uncertainty. While, in case of correlated random events, the hazard levels are relatively low. The results are being subjected to verification and are compared with the previous studies to ensure fulfilling specifications and its intended purpose. Structural designers and decision makers can utilize the developed PSHA framework to plan and build new projects and to evaluate the seismic risk of existing infrastructure in a city.

A Practical Approach of Probabilistic Seismic Hazard Analysis for Vector IMs Regarding Mainshock with Potentially Largest Aftershock

ABSTRACT Seismic hazard and risk may be underestimated if aftershocks are ignored within the traditional probabilistic seismic hazard analysis (PSHA). In this study, a practical approach is proposed to calculate the mean annual rate of the joint exceedance of different ground motion vector intensity measures (IMs) for mainshocks and their potentially largest aftershock. The proposed approach is built based on an indirect vector-valued PSHA framework, which was originally used to compute the joint hazard of multiple IMs for mainshocks. Within the proposed approach, the overall hazard caused by mainshock-aftershock scenarios is calculated by including two key components, namely: 1) the occurrence rate of a given hazard level of mainshock as calculated by the standard PSHA; and 2) the occurrence probability of a given hazard level of aftershock conditioned on the mainshock, which is calculated by establishing the joint distribution of the IMs for both mainshocks and aftershocks using the Copula theory. Based on 662 groups of mainshock-aftershock ground motions from 13 earthquake events in the NGA-West2 database, the empirical joint probability distribution model between the peak ground accelerations of mainshocks and aftershocks (i.e. PGA MS and PGA AS) is developed. The Clayton Copula function is calibrated as the optimal choice and the marginal distributions of PGA MS or PGA AS could be properly modelled using the generalized extreme value distributions. The proposed approach is implemented to construct the joint hazard surface regarding both PGA MS and PGA AS for a hypothetical site. The results indicate that using different types of copula functions and marginal distributions of PGA MS and PGA AS has a noticeable impact on the final joint hazard level. Moreover, a coarse assumption that PGA MS and PGA AS follow a joint Gaussian distribution in the logarithm scale would lead to considerable bias in the mainshock-aftershock joint hazard especially at low mean annual rates of exceedance.

Probabilistic Assessment of the Seismic Peak Ground Acceleration (PGA) at seven Colombian Cities

This paper presents a probabilistic assessment of peak ground acceleration (PGA) observations at seven Colombian cities located in regions with intermediate and high seismic activity. Frequency histograms of the annual exceedance rates were determined using historical data of the annual rate of exceedance for pre-established values of PGA. After determining distribution parameters by means of the method of moments, several probability density functions were examined in order to evaluate the performance of each function. In most sites, the maximum annual PGA appears to be best modeled by a lognormal distribution, which led to its adoption as parent distribution for the entire group of cities. Once the lognormal function is selected as parent distribution, series of PGA values for arbitrary periods of time may be generated through random simulation. Next, series of maximum values in fifty years of observation were simulated for the seven cities, assuming a Lognormal parent distribution. Analytical solutions for extreme values of different sample sizes of lognormal random variables are not known to the authors. However, since extreme values for large samples of lognormal random variables tend asymptotically to a Type I (Gumbel) probability distribution, the latter was adopted as a possible model for the 50 years PGA distributions suggested in the paper for several Colombian cities, as a useful tool for engineering design, whenever the PGA is regarded as an appropriate seismic intensity measure.

Evaluating the Use of Multisite Probabilistic Seismic Hazard Analysis: A Case of Sarpol-e Zahab City, Iran.

This paper evaluates the use of multisite (MS) probabilistic seismic hazard analysis (PSHA), which estimates the annual exceedance rate of a given level of ground motion in at least one of several sites as one of several possible results. For this purpose, (1) MS-PSHA is implemented through the Monte Carlo approach, taking into account various area sizes and correlation distances (CDs), and then (2) two proposals are represented as applications of MS-PSHA outcomes, both with reference to Sarpol-e Zahab City, a seismically active region located in the west of Iran. The first proposal attempts to determine the current code design probability of exceedance in at least one site, and the second one defines collapse prevention levels based on different probabilities of exceedance in at least one site. The efficiency of the results is discussed mainly by comparing them to recorded peak ground accelerations (PGAs) of three earthquakes, including the 2017 Sarpol-e Zahab 7.3 Mw event that largely exceeded the code design spectrum. MS-PSHA results demonstrate reasonable performance both in determining design ground motions and evaluating current design code when the exact seismic parameters of the study area are used in the analysis. Moreover, developed code-type design spectra based on MS-PSHA provided safety against collapse compared to a recently occurring low-probability event. MS estimates for various CDs and probabilities of exceedance in at least one site can also provide flexible design strategies regarding the importance of a structure and expected damage on a regional scale.

A heuristic features selection approach for scenario analysis in a regional seismic probabilistic tsunami hazard assessment

Seismic Probabilistic Tsunami Hazard Analysis (SPTHA) is aimed at estimating the annual rate of exceedance of an earthquake-induced tsunami wave of a certain location with reference to a predefined height threshold. The analysis relies on computationally demanding numerical simulations of seismic-induced tsunami wave generation and propagation. A large number of scenarios needs to be simulated to account for uncertainties. However, the exceedance of tsunami wave threshold height is a rare event so that most of the simulated scenarios bring little statistical contribution to the estimation of the annual rate yet increasing the computational burden. To efficiently address this issue, we propose a wrapper-based heuristic approach to select the set of most relevant features of the seismic model, for deciding a priori the seismic scenarios to be simulated. The proposed approach is based on a Multi-Objective Differential Evolution Algorithm (MODEA) and is developed with reference to a case study whose objective is calculating the annual rate of threshold exceedance of the height of tsunami waves caused by subduction earthquakes that might be generated on a section of the Hellenic Arc, and propagated to a set of target sites: Siracusa, on the eastern coast of Sicily, Crotone, on the southern coast of Calabria, and Santa Maria di Leuca, on the southern coast of Puglia. The results show that, in all cases, the proposed approach allows a reduction of 95% of the number of scenarios with half of the features to be considered, and with no appreciable loss of accuracy.

Reliability-based optimum design of multiple tuned mass dampers for minimization of the probability of failure of buildings under earthquakes

This work proposes a methodology for reliability-based optimum design of multiple tuned mass dampers (MTMD) for installation in buildings situated in seismic regions. Unlike works that disregard uncertainties and perform deterministic optimizations, the approach proposed in this work aims to minimize the probability of failure of buildings under earthquakes taking the uncertainties into account. For this purpose, a modern optimization technique, the Whale Optimization Algorithm (WOA), is employed. Actual records of seismic accelerograms that occurred in the site of interest are used to characterize the seismic risk, determining the expected value of the peak ground acceleration (PGA) annual exceedance rate. Thus, the seismic risk is estimated by fitting probability distribution functions of the PGA for periods of one and fifty years, to assess, via numerical simulation, the building’s reliability. The proposed methodology is illustrated considering two buildings located in the city of Cúcuta, Colombia, where earthquake data are available. Robust estimators of the system reliability are calculated using a database of seismic records with notably different features. The results confirm that the proposed methodology for optimization of MTMD considerably increases the reliability of both buildings, highlighting the effectiveness of MTMD in minimizing the probability of failure of buildings situated in regions with significant seismic activity.

Effect of dampers on the seismic performance of masonry walls assessed through fragility and demand hazard curves

In a damage avoidance design perspective, seismic rocking of rigid-like blocks, such as masonry walls, precast r.c./timber panels, art objects, etc., can be controlled through viscous elastic dampers. This paper discusses how to perform a seismic risk assessment of masonry walls undamped and damped by viscous-elastic dampers installed at the top of them. Firstly, a preliminary fragility analysis allows understanding the role of the damper, whose coupling with a recentering component attenuates the motion, increases the rotation frequency and, in some cases, impedes overturning as compared to to the undamped case. Secondly, the risk assessment is made by developing a multiple stripe analysis to compute univariate fragility curves combining uplift, overturning probability and probability of exceedance. Thirdly, seismic demand hazard curves are obtained for two walls representative of buildings and monumental structures in an Italian site of high seismicity. The PSHA results show the remarkable risk reduction of the ultimate limit states, for which the annual exceedance rate is respectively one and two orders of magnitude lower than the undamped case.

Seismic reliability evaluation of steel gabled frames consisting of web-tapered members using joint analysis of hazard and fragility

Despite the wide application of steel gabled frame (SGF) systems in large industrial projects, the current literature lacks accurate information on their seismic performance to ensure satisfactory performance at different levels of earthquake intensity. Also, given the scant information on the structural performance and their seismic design parameters in most of the available guidelines, the use of joint analysis of hazard and fragility can be very important, since both the reference hazard on site and the structural performance are considered. To address this issue, in the present paper, incremental dynamic analysis (IDA) was performed using 20 ground motions on four SGFs and their results were collected in the form of fragility curves. Then to obtain the annual rate of exceedance, hazard curves of the study region were generated and combined with the fragility curves, and finally, the seismic reliability of SGFs was evaluated at design basis earthquake (DBE) and maximum considered earthquake (MCE) hazard levels. Seismic reliability results indicated that the available seismic design guidelines lead to a too conservative design for SGFs, especially when they have long periods, where at the MCE hazard level, long-period SGFs with about 58% safety margin do not even experience LS performance level. The results of this study can prove useful for a more efficient design of SGFs in seismic regions.

Probabilistic assessment of seismic-induced slope displacements: an application in Italy

Earthquake-induced slope instability is one of the most important hazards related to ground shaking, causing damages to the environment and, often, casualties. Therefore, it is important to assess the seismic performance of slopes, especially in the near fault regions, evaluating the permanent displacements induced by seismic loading. This paper applies a probabilistic approach to evaluate the seismic performance of slopes using an updated database of ground motions recorded during the earthquakes occurred in Italy. The main advantage of this approach is that of accounting for the aleatory variability of both ground motions and prediction of seismic-induced displacements of slopes. The results are presented in terms of hazard curves, showing the annual rate of exceedance of permanent slope displacement evaluated using ground motion data provided by a standard probabilistic hazard analysis and a series of semi-empirical relationships linking the permanent displacements of slopes to one or more ground motion parameters. The procedure has been implemented on a regional scale to produce seismic landslide hazard maps for the Irpinia district, in Southern Italy, characterised by a severe seismic hazard. Seismic landslide hazard maps represent a useful tool for practitioners and government agencies for a regional planning to identify and monitor zones that are potentially susceptible to earthquake-induced slope instability, thus requiring further detailed, site-specific studies.

Enhanced Seismic Structural Reliability on Reinforced Concrete Buildings by Using Buckling Restrained Braces

The control of vibrations and damage in traditional reinforced concrete (RC) buildings under earthquakes is a difficult task. It requires the use of innovative devices to enhance the seismic behavior of concrete buildings. In this paper, we design RC buildings with buckling restrained braces (BRBs) to achieve this objective. For this aim, three traditional RC framed structures with 3, 6, and 9 story levels are designed by using the well‐known technique nondominated sorting genetic algorithm (NSGA‐II) in order to reduce the cost and maximize the seismic performance. Then, equivalent RC buildings are designed but including buckling restrained braces. Both structural systems are subjected to several narrow‐band ground motions recorded at soft soil sites of Mexico City scaled at different levels of intensities in terms of the spectral acceleration at first mode of vibration of the structure Sa(T1). Then, incremental dynamic analysis, seismic fragility, and structural reliability in terms of the maximum interstory drift are computed for all the buildings. For the three selected structures and the equivalent models with BRBs, it is concluded that the annual rate of exceedance is considerably reduced when BRBs are incorporated. For this reason, the structural reliability of the RC buildings with BRBs has a better behavior in comparison with the traditional reinforced concrete buildings. The use of BRBs is a good option to improve strength and seismic behavior and hence the structural reliability of RC buildings subjected to strong earthquake ground motions.

Life-cycle cost-based risk assessment of aging bridge networks

Road infrastructures and bridge networks are becoming increasingly complex systems due to the development of technology in transportation engineering and the continual growth of urban communities. Infrastructure disservice due to seismic events may lead to unacceptable discomfort for commuters. Moreover, network downtime results into economic losses for the affected community, to be quantified in monetary terms by user costs. Seismically vulnerable bridges are also affected by aging and deterioration processes that can reduce the bridge structural performance over time. This paper presents a comprehensive life-cycle cost-based probabilistic framework for seismic risk assessment of spatially distributed aging bridge networks. The seismic risk measure is formulated in terms of annual exceedance rate of a target threshold of user costs. The methodology is applied to a road system in Lombardy region, Italy, reproducing network connectivity and daily travel demands among four major cities and smaller neighbouring municipalities. Despite the area of interest is characterized by low seismicity, the results allow to quantify the impact of aging and deterioration in exacerbating the network seismic risk, highlighting the need for a life-cycle-informed approach to optimal management of infrastructure systems.

Reliability analysis of steel buildings considering the flexibility of the connections of the GFs

A numerical study to evaluate the reliability of 3D steel buildings with moment-resisting frames (MRFs) at the perimeter and gravity frames (GFs) at the interior under the action of seismic loading, is carried out. To this aim, the median values (MV) of the maximum drifts (MD) and fragility curves are obtained. The reliability, expressed as the mean annual rate of exceeding (υ) particular values of MD, is calculated by using the probabilistic seismic hazard analysis format. Three models, representing steel buildings of low-, mid- and high-rise are considered. The interior connections are assumed to be, first perfectly pinned (PP) as considered in practical design, and then as semi-rigid (SR). The Beam-Line Theory together with The Model of Richard are used to represent the SR connections. Results indicate that the MV demands and the seismic fragility can be significantly reduced when the stiffness and dissipation of energy at interior connections are considered; reductions larger than 40% and 60%, respectively, are observed in many of the cases. The structural reliability is also significantly improved; reductions close to 20% in the expected maximum drift are observed in many cases. It is concluded that the effects of the stiffness and energy dissipation of the connections of GFs on the seismic response (in terms of MV), on the fragility curves, and on the mean annual rate of exceedance (υ), are significant so they should not be ignored. Even for shear connections whose contribution in practical design is totally ignored, the effect is considerable.

Probabilistic estimation of seismic parameters for Bangladesh

This paper estimates the following seismic parameters: the maximum recorded magnitude (Mmax), the Gutenberg-Richter b-value, the annual rate of exceedance of particular magnitude, and return period of that magnitude are examined. The catalog is extracted from the Advanced National Seismic System (ANSS) catalog. The working catalog, originated from longitude 87 to 93 and latitude 20 to 27 that covers the whole Bangladesh and some parts of India and Myanmar, contains 406 events from 1918 to 2017. To define the working catalog, magnitudes were converted into moment magnitude. All parameters had been calculated from the time-independent catalog. Since no formula available in the literature to calculate the confidence interval for annual rate and return period, the confidence interval of the estimates were calculated using simulation technique. For this case, 100,000 simulations were considered and calculated 0.025th and 0.975th quantiles of the simulated values as 95% confidence interval.

Simplified seismic assessment of infilled RC frame structures

Earthquake-induced structural damage, characterised by the exceedance of different damage states during ground shaking, is typically quantified using fragility curves generated through non-linear dynamic analyses often requiring a large computational effort. This level of effort has led to the necessity of simplified methods and approximate analysis tools. In this regard, SPO2IDA has emerged as a convenient tool for the assessment of structures. It relates a structure’s backbone characteristics to a set of incremental dynamic analysis (IDA) curves using static pushover analysis (SPO) results and a library of empirical fitting coefficients for the different branches of the idealised SPO backbone. It permits the quantification of structural performance up to structural collapse as a function of seismic intensity in a simple and efficient manner. It has been developed mainly for ductile structures that can be sufficiently represented via a SPO backbone with a certain ductile post-yield hardening followed by a post-peak degradation. This behaviour is quite representative of ductile RC and steel moment-resisting frames and has resulted in the tool being widely adopted. However, the same may not be observed when dealing with reinforced concrete (RC) frames with masonry infill, a structural typology that still requires significant addressing in the earthquake engineering field. The present study describes an extension to this methodology for structural typologies with a more particular backbone behaviour, typical of RC frames with masonry infill panels, since differences in backbone behaviour compared to typical structures render the extension of the original tool inappropriate and at times unconservative. Extensive analyses were conducted to investigate the behaviour and trends when pushing infilled RC frames up to complete structural collapse. A new library of empirical coefficients was then fitted and proposed by considering a large database of representative backbones to result in an extended SPO2IDA proposal for infilled RC frames. It is then shown how these coefficients provide a much-improved matching, when compared to the original tool for this specific case, both in terms of the produced IDA traces and also the drift-based mean annual rates of exceedance.

Probabilistic Evaluation of Off-Fault Displacements of the 2016 Kumamoto Earthquake

The 2016 Kumamoto earthquake occurred on April 16, 2016, and induced the complex distribution of surface ruptures and fault displacements, which revealed the difficulty of evaluating off-fault displacement hazards. The evaluation of off-fault displacements is necessary for the site investigation of an important facility, such as nuclear installations, but is difficult because off-fault displacements are thought to occur on unmapped or small-scale structures. A probabilistic fault displacement hazard analysis (PFDHA) assesses an off-fault displacement hazard as well as an on-fault one. Several PFDHA models have been developed from fault displacement datasets parsed by global-specific and Japanese-various faulting types. We developed a procedure to assess off-fault displacement hazards based on probabilistic and numerical simulation approaches. In the probabilistic approach, we constructed strike-slip and reverse-slip PFDHA models from a dataset of Japanese fault displacements. The off-fault components in PFDHA had a probability of non-zero off-fault displacement and an attenuation relationship. In the case of evaluating the site of an important facility, detailed field surveys were performed to collect numerous site-specific information. There is little site-specific data of off-fault displacements in Japan. The trench surveys were performed at off-fault displacement sites from the 2016 Kumamoto earthquake. The two trench sites were selected based on a linear low-coherence zone derived from the InSAR analysis, which emphasizes small-scale displacements. The excavation survey result at one site suggests a shorter recurrence interval than that of the active fault long-term evaluation. We also performed a probabilistic fault hazard analysis (PFDHA) of the trench sites by using the global strike-slip model and Japanese PFDHA models with and without the site-specific data. For the PFDHA results without site-specific data, the difference in the annual rates of exceedance between the global strike-slip and Japanese models increased with increasing fault displacements. This is because of the reduced decrease in the attenuation relationship of Japanese models. The differences in the annual rates of exceedance constrained with the site-specific data are independent of fault displacements due to variation in the probability of non-zero off-fault displacement between the global strike-slip and Japanese PFDHA models. These results suggest that the off-fault PFDHA models have high variability. In the case of PFDHA evaluation with several models, the individual PFDHA components are carefully selected by considering the individual effects. The site-specific short recurrence interval revealed by the trench survey leads to higher annual rates of exceedance.