Mean Annual Rate Of Exceedance Research Articles

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.

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 Seismic Hazard Assessment for Amaravathi Region, Andhra Pradesh

This article explains an analytical attempt that estimates seismic hazard for Amaravathi city. The present study has been carried out contemplating the available faults and epicentral data within a radius of 300km of the Amaravathi region. The homogenous earthquake catalogue has been prepared for Amaravathi region by Steep’s method. The seismic hazard parameters ―a‖ and ―b‖ for Amaravathi city were evaluated by Gutenberg-Ritcher method. The ―a‖ and ―b‖ values obtained as 4.69, 0.6468 respectively. The total 353 epicenters and 31 faults were considered in this seismic analysis for the estimate of PSHA for Amaravathi. The ground motion produced by the faults at this site has been estimated by using the regionspecific Ground Motion Prediction Equation (GMPE) developed by the raghukanth and lyenger (2007). The probability of occurrence of different magnitude classes was estimated. The hazard curves and mean annual rate of exceedance for Peak Ground Acceleration were calculated by using ground motion estimated in this area. The Uniform Hazard Response Spectrum (UHRS) for the ranging time periods between 0.1 – 4 seconds was prepared. PGA values for Amaravati region was found to be in between 0.001g to 0.3g from seismic hazard map that was prepared in this study

Severity Measures and Stripe Analysis for Probabilistic Structural Fire Engineering

This paper presents modifications to the adoption of a Performance-Based Earthquake Engineering (PBEE) framework in Probabilistic Structural Fire Engineering. Potential Fire Severity Measures, which capture significant characteristics of fire scenarios, are investigated. A suitable Fire Severity Measure (FSM), which best relates fire hazard intensity with structural response, is identified by satisfying efficiency and sufficiency criteria as described by the PBEE framework. The study also implements a new analysis method called Fire Stripe Analysis (FSA) to obtain the relationship between FSM and the structural response. In order to obtain the annual rate of exceedance of damage and repair cost/time for an office building, an occurrence model and an attenuation model for office structure fires are generated for both Christchurch city and New Zealand. The process is demonstrated with the help of a case study performed for a steel–concrete composite beam. Structural response is recorded for the beam exposed to several fire profiles which are generated by varying fuel loads from 200 MJ/m2 to 1000 MJ/m2 and ventilation factors from 0.02 m1/2 to 0.08 m1/2. FSA and dispersion curves of structural response are plotted for every fire severity measure. Cumulative incident radiation is found to be the most efficient and sufficient FSM. The mean annual rate of exceedance of given levels of fire severity and structural response are evaluated for both New Zealand and Christchurch city. It is found that Christchurch city has a 15% less probability of exceedance of the given fire severity level in comparison to the whole of New Zealand. The extension of this work would facilitate designers/insurers to evaluate the probability of damage or failure of a structure due to a probable fire hazard.

PROBABILISTIC SEISMIC HAZARD ANALYSIS OF SOUTHWESTERN NIGERIA

For about ten decades, the seismic record of Nigeria has shown the occurrence of several magnitudes of earthquakes. This is contrary to the belief of some people in time past that Nigeria is aseismic. In number and in size, most of the witnessed earthquakes in Nigeria are found to occur in her South-Western region. Researchers have also begun to warn recently that some regions of Nigeria should prepare for devastating earthquakes in years to come. Hence this paper aimed at the probabilistic seismic hazard analysis of the South-Western region of Nigeria using the available historical and instrumentally recorded data. The Gutenberg-Richter (G-R) recurrence law was used to assess the seismicity parameters and to generate a modelfor calculating the mean annual rate of exceedance and to forecast probable future earthquake occurrence in the South-West. The findings of this assessment established that the South-West region of Nigeria is likely to experience earthquake magnitude as high as 7.2 in the year 2028 with a probability of 36.79%. Hence, this work enlightens on the extent of probable future earthquake magnitude in South-Western Nigeria and it is recommended that the government of Nigeria and inclined agencies begin to look into earthquake in this region.

Probabilistic seismic risk assessment of concrete bridge piers reinforced with different types of shape memory alloys

Shape memory alloy (SMA) has emerged as an alternative to conventional steel reinforcement for improving the seismic performance of bridges during an extreme earthquake. This paper presents the probabilistic seismic risk assessment of concrete bridge piers reinforced with different types of SMA (e.g. Ni-Ti, Cu-Al-Mn, and Fe-based) rebars. To achieve this objective, the bridge piers are designed following a performance-based approach. Ground motions with different probable earthquake hazard scenarios at the site of the bridge piers are considered. Probabilistic seismic demand models are generated using the response parameters obtained from incremental dynamic analysis. Considering maximum drift and residual drift as demand parameters, fragility curves are developed for five different SMA-RC bridge piers. Finally, seismic hazard curves are generated in order to compare the mean annual rate of exceedance of different damage states of different bridge piers. It is observed that all the bridge piers perform according to the design objective, and the performance of SMA-RC piers is significantly affected by the type of SMA used. The results show that all the SMA-RC piers have very low probability of collapse at maximum considered earthquake level. It is found that the bridge pier reinforced with FeNCATB-SMA (SMA-3) performed better as compared to the other SMA-RC piers.

On the Seismic Design of Structures with Tilting Located within a Seismic Region

A reliability-based criterion to estimate strength amplification factors for buildings with asymmetric yielding located within a seismic region presenting different soil conditions is proposed and applied. The approach involves the calculation of the mean annual rate of exceedance of structural demands of systems with different levels of asymmetric yielding. Two simplified mathematical expressions are developed considering different soil conditions of the valley of Mexico. The mathematical expressions depend on the ductility of the structural systems, their level of asymmetric yielding, their fundamental vibration period and the dominant period of the soil. In addition, the proposed expressions are compared with that recommended by the current Mexico City Building Code (MCBC). Since the expressions are developed with the help of simplified structural systems, the validity of such expressions is corroborated by comparing the expected ductility demand of multi-degree of freedom (MDOF) structural systems with respect to that of their equivalent simplified systems. Both structural representations are associated with a given annual rate of exceedance value of an engineering demand parameter. The expressions proposed in this study will be incorporated in the new version of the MCBC.

The seismic reliability of two connected SMRF structures

This article aims to investigate the possible retrofitting of a deficient building with soft story failure mode by connecting it to an adjacent building which is designed based on current code with friction dampers at all floors. Low cost and high performance reliability along with significant energy dissipation pertaining to stable hysteretic loops may be considered in order to choose the proper damper for connecting adjacent buildings. After connecting two neighbouring floors by friction dampers, the sliding forces of dampers at various stories are set in two arrangements: uniform sliding force and then variable sliding force. In order to account for the stochastic nature of the seismic events, incremental dynamic analyses are employed prior and after the installation of the friction dampers at the various floors. Based on these results, fragility curves and mean annual rate of exceedance of serviceability and ultimate limit states are obtained. The results of this study show that the collapse mode of the deficient building can affect the optimum arrangement of sliding forces of friction dampers at Collapse Prevention (CP) performance level. In particular, the Immediate Occupancy (IO) performance level is not tangible to the sliding force arrangement and it depends solely on sliding force value. Generally it can be claimed that this rehabilitation scheme can turn the challenge of pounding two adjacent buildings into the opportunity of dissipating a large amount of the seismic input energy by the friction dampers, thus improving significantly the poor seismic performance of the deficient structure.

Probabilistic Seismic and Tsunami Hazard Analysis Conditioned on a Megathrust Rupture of the Cascadia Subduction Zone

This paper presents a framework for a probabilistic hazard assessment for the multi-hazard seismic and tsunami phenomena (PSTHA). For this work, we consider a full-rupture event along the Cascadia Subduction Zone and apply the methodology to the study area of Seaside, Oregon, along the US Pacific Northwest coast. In this work, we show that the annual exceedance probabilities (AEP) of the tsunami intensity measures (IM) are qualitatively dissimilar to the IMs of the seismic ground motion in the study area. Specifically, the spatial gradients for the tsunami IM are much stronger across the length scale of the city owing to the physical differences of energy dissipation of the two mechanisms. Example results of probabilistic seismic hazard analysis (PSHA) and probabilistic tsunami hazard analysis (PTHA) are shown for three observation points in the study area of Seaside. For the seismic hazard, the joint mean annual rate of exceedance shows similar trends for the three observation points, even though there is a large scatter between and . For the tsunami hazard, the joint AEP of hmax and (MF)max shows a high correlation between the two IMs in the study area. The joint AEP at each of the three observation points follows a particular Froude number (Fr) due to the local site-specific conditions locally rather than the distributions of fault slips. The joint probability distribution of hmax and (MF)max throughout the study region falls between 0.1 ≤ Fr < 1.0 (i.e., the flow is subcritical) regardless of return interval (500-, 1,000-, and 2,500-yr). However, the peak of the joint probability distribution with respect to hmax and (MF)max varies with the return interval, and the largest values of hmax and (MF)max were observed with the highest return intervals (2,500 yr) as would be expected. The results of the PSTHA can be the basis for a probabilistic multi-hazard damage assessment and help to understand the uncertainties of the multi-hazard assessments.

Probabilistic seismic response transformation factors between SDOF and MDOF systems using artificial neural networks

An approach to obtain with acceptable accuracy probabilistic response transformation factors by training an artificial neural network (ANN) model is presented. The transformation factors are defined as the ratio of the seismic response of multi-degree-of-freedom structures and their equivalent single-degree-of-freedom systems, associated with a given annual exceedance rate. The approach is used for predicting the seismic response of steel framed buildings. Equations useful to obtain probabilistic response transformation factors for maximum ductility and inter-story drift, as functions of their mean annual rate of exceedance, and of the fundamental vibration period of the structure, are proposed. It is shown that artificial neural networks are a useful tool for reliability-based seismic design procedures of framed buildings and for the improvement toward the next generation of earthquake design methodologies based on structural reliability.

Residual drift demands in moment‐resisting steel frames subjected to narrow‐band earthquake ground motions

SUMMARYThis paper presents the main results of the evaluation of residual inter‐story drift demands in typical moment‐resisting steel buildings designed accordingly to the Mexican design practice when subjected to narrow‐band earthquake ground motions. Analytical 2D‐framed models representative of the study‐case buildings were subjected to a set of 30 narrow‐band earthquake ground motions recorded on stations placed in soft‐soil sites of Mexico City, where most significant structural damage was found in buildings as a consequence of the 1985 Michoacan earthquake, and scaled to reach several levels of intensity to perform incremental dynamic analyses. Thus, results were statistically processed to obtain hazard curves of peak (maximum) and residual drift demands for each frame model. It is shown that the study‐case frames might exhibit maximum residual inter‐story drift demands in excess of 0.5%, which is perceptible for building's occupants and could cause human discomfort, for a mean annual rate of exceedance associated to peak inter‐story drift demands of about 3%, which is the limiting drift to avoid collapse prescribed in the 2004 Mexico City Seismic Design Provisions. The influence of a member's post‐yield stiffness ratio and material overstrength in the evaluation of maximum residual inter‐story drift demands is also discussed. Finally, this study introduces response transformation factors, Tp, that allow establishing residual drift limits compatible with the same mean annual rate of exceedance of peak inter‐story drift limits for future seismic design/evaluation criteria that take into account both drift demands for assessing a building's seismic performance. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Method for Probabilistic Displacement-Based Design of RC Structures

An approximate method is proposed for seismic design of reinforced concrete (RC) structures to meet multiple structural performance requirements expressed in terms of exceedance probabilities. The method is approximate in nature and rests on two main results: (1) the closed-form solution for the mean annual rate of exceedance of a limit state and (2) the empirical equal-displacement rule. Compliance with design objectives is obtained through a gradient-based search algorithm in the space of the design variables with reference to a linear elastic proxy of the structure. To this purpose, analytical gradients for Cornell’s formula are derived. An application illustrates the method and its validation through inelastic time-history analysis. From the limited investigation carried out, the method appears to offer satisfactory accuracy.

Disaggregation of Probabilistic Ground-Motion Hazard in Italy

Abstract Probabilistic seismic hazard analysis is a process that integrates over aleatory uncertainties (e.g., future earthquake locations and magnitudes) to calculate the mean annual rate of exceedance (MRE) of given ground-motion parameter values at a site. These rates reflect the contributions of all the sources whose seismic activity is deemed to affect the hazard at that site. Seismic hazard disaggregation provides insights into the earthquake scenarios driving the hazard at a given ground-motion level. This work presents the disaggregation at each grid point of the Italian rock ground-motion hazard maps developed by Gruppo di Lavoro MPS (2004), Meletti and Montaldo (2007), and Montaldo and Meletti (2007). Disaggregation is used here to compute the contributions to the MRE of peak ground horizontal acceleration (PGA) and 5%-damped 0.2, 1.0, and 2.0 sec spectral acceleration values corresponding to different mean return periods (MRPs of 475 and 2475 yr) from different scenarios. These scenarios are characterized by bins of magnitude, M , source-to-site distance, R , and number, e , of standard deviations that the ground-motion parameter is away from its median value for that M - R pair as estimated by a prediction equation. Maps showing the geographical distribution of the mean and modal values of M , R , and e are presented for the first time for all of Italy. Complete joint M – R – e distributions are also presented for selected cities. Except for sites where the earthquake activity is characterized by sporadic low-magnitude events, the hazard is generally dominated by local seismicity. Moreover, as expected, the MRE of long-period spectral accelerations is generally controlled by large magnitude earthquakes at long distances while smaller events at shorter distances dominate the PGA and short-period spectral acceleration hazard. Finally, for a given site, as the MRP increases the dominant earthquakes tend to become larger and to occur closer to the site investigated.

Site classification and estimation of surface level seismic hazard using geophysical data and probabilistic approach

This paper presents the site classification of Bangalore Mahanagar Palike (BMP) area using geophysical data and the evaluation of spectral acceleration at ground level using probabilistic approach. Site classification has been carried out using experimental data from the shallow geophysical method of Multichannel Analysis of Surface wave (MASW). One-dimensional (1-D) MASW survey has been carried out at 58 locations and respective velocity profiles are obtained. The average shear wave velocity for 30 m depth (Vs 30) has been calculated and is used for the site classification of the BMP area as per NEHRP (National Earthquake Hazards Reduction Program). Based on the Vs 30 values major part of the BMP area can be classified as “site class D”, and “site class C”. A smaller portion of the study area, in and around Lalbagh Park, is classified as “site class B”. Further, probabilistic seismic hazard analysis has been carried out to map the seismic hazard in terms spectral acceleration (S a) at rock and the ground level considering the site classes and six seismogenic sources identified. The mean annual rate of exceedance and cumulative probability hazard curve for S a have been generated. The quantified hazard values in terms of spectral acceleration for short period and long period are mapped for rock, site class C and D with 10% probability of exceedance in 50 years on a grid size of 0.5 km. In addition to this, the Uniform Hazard Response Spectrum (UHRS) at surface level has been developed for the 5% damping and 10% probability of exceedance in 50 years for rock, site class C and D. These spectral acceleration and uniform hazard spectrums can be used to assess the design force for important structures and also to develop the design spectrum.

Probabilistic seismic hazard analysis for Bangalore

This article presents the results of probabilistic seismic hazard analysis (PSHA) for Bangalore, South India. Analyses have been carried out considering the seismotectonic parameters of the region covering a radius of 350 km keeping Bangalore as the center. Seismic hazard parameter ‘b’ has been evaluated considering the available earthquake data using (1) Gutenberg–Richter (G–R) relationship and (2) Kijko and Sellevoll (1989, 1992) method utilizing extreme and complete catalogs. The ‘b’ parameter was estimated to be 0.62 to 0.98 from G–R relation and 0.87 ± 0.03 from Kijko and Sellevoll method. The results obtained are a little higher than the ‘b’ values published earlier for southern India. Further, probabilistic seismic hazard analysis for Bangalore region has been carried out considering six seismogenic sources. From the analysis, mean annual rate of exceedance and cumulative probability hazard curve for peak ground acceleration (PGA) and spectral acceleration (Sa) have been generated. The quantified hazard values in terms of the rock level peak ground acceleration (PGA) are mapped for 10% probability of exceedance in 50 years on a grid size of 0.5 km × 0.5 km. In addition, Uniform Hazard Response Spectrum (UHRS) at rock level is also developed for the 5% damping corresponding to 10% probability of exceedance in 50 years. The peak ground acceleration (PGA) value of 0.121 g obtained from the present investigation is slightly lower (but comparable) than the PGA values obtained from the deterministic seismic hazard analysis (DSHA) for the same area. However, the PGA value obtained in the current investigation is higher than PGA values reported in the global seismic hazard assessment program (GSHAP) maps of Bhatia et al. (1999) for the shield area.

Mean and Modal in the Deaggregation of Probabilistic Ground Motion

An important element of probabilistic seismic-hazard analysis (PSHA) is the incorporation of ground-motion uncertainty from the earthquake sources. The standard normal variate ϵ measures the difference between any specified spectral-acceleration level, or SA, and the estimated median spectral acceleration from each probabilistic source. In this article, mean and modal values of ϵ for a specified SA are defined and computed from all sources considered in the USGS 1996 PSHA maps. Contour maps of ϵ are presented for the conterminous United States for 1-, 0.3-, and 0.2-sec SA and for peak horizontal acceleration, PGA corresponding to a 2% probability of exceedance (PE) in 50 yr, or mean annual rate of exceedance, r , of 0.000404. Mean and modal ϵ exhibit a wide variation geographically for any specified PE. Modal ϵ for the 2% in 50 yr PE exceeds 2 near the most active western California faults, is less than –1 near some less active faults of the western United States (principally in the Basin and Range), and may be less than 0 in areal fault zones of the central and eastern United States (CEUS). This geographic variation is useful for comparing probabilistic ground motions with ground motions from scenario earthquakes on dominating faults, often used in seismic-resistant provisions of building codes. An interactive seismic-hazard deaggregation menu item has been added to the USGS probabilistic seismic-hazard analysis Web site, , allowing visitors to compute mean and modal distance, magnitude, and ϵ corresponding to ground motions having mean return times from 250 to 5000 yr for any site in the United States.