Limit State Probabilities Research Articles

Assessment of remedial measures to reduce exceedance probability of performance limit states in embankment dams

Results of a series of numerical analyses, simulating three remedial measures applied to an embankment dam, are used to investigate the extent of lessening the severity of the distress level under flood loading. Conceptually, the three remedial measures are increasing the mean effective stress, adding a low permeability curtain to limit seepage, and improving drainage to lower pore water pressure magnitudes at key locations. The results are presented in the context of exceeding predefined limit states in terms of toe deformation and hydraulic gradient. Constructing a downstream berm has a significant impact on the exceedance probabilities of the deformation limit states at the toe, but a small impact on the toe gradient values. Adding a low permeability curtain below the dam crest considerably reduces both deformation and gradient magnitudes in relation to the predefined limit states. This occurs due to an increased seepage path leading to a higher drop of pressure head and lower phreatic surface level; these two effects result in lower shear strains and less deformations at the toe. Improvement was observed by adding the toe drainage system with a hydraulic conductivity that is 4–20 times higher than the hydraulic conductivity of the embankment material. In this case, the exceedance probabilities of deformation limit states decrease and the impact is higher for a higher hydraulic conductivity of the drainage system compared to the embankment soil. Given the analyses configurations and parameters, constructing a berm at the toe leads to the lowest exceedance probabilities, in terms of deformation limit state, and thus seems to be the most effective approach among the three analyzed remedial measures.

Application of Latin Hypercube Sampling Based Kriging Surrogate Models in Reliability Assessment

Reliability assessment is one of the necessary and critical parts in structural design under uncertainties. The methods for structural reliability assessment aim at evaluating the probability of limit state by considering the fluctuation of acting loads, variation of structural component or system, and complexity of operating environment. Latin Hypercube sampling (LHS) method as advanced Monte Carlo simulation (MCS) has higher efficiency in sampling. It will be chosen and applied in this paper in order to obtain an effective database for building Kriging surrogate models. In this paper, we propose an effective method to have reliability assessment by Latin Hypercube sampling based Kriging surrogate models. This method keeps the certain level of accuracy in prediction of the response of a structural finite element model or other explicit mathematical functions.

A systemic approach to moisture problems in buildings for mould safety modelling

Mould growth in buildings can have negative consequences on health, comfort, and durability of construction and can cause a significant problem for inhabitants. Confronted with significant uncertainty, deterministic tools supporting design have proved insufficient for decision making. A tool that addresses the probabilistic risk/reliability analysis of building performance is needed. A systemic approach provides a proper theoretical base for the analysis. Based on a qualitative fault tree analysis, structure related vulnerabilities to moisture problems have been classified at different levels of the building construction: whole structure, component or material. A general model for evaluating the reliability of structures with respect to mould safety and based on the concept of systemic analysis is applied to moisture problems in buildings using a probabilistic limit state approach.An example of a risk analysis of mould germination on the inner surface of a wooden roof panel in a cold attic is calculated using the proposed methodology. The surface's relative humidity (given certain surface temperature interval) is chosen as a performance aspect. The performance criteria for mould germination on wood are also treated as a random variables. The probability of mould germination is evaluated for different attic floor constructions in which changes to the construction were introduced on the material or component level. The application of the probabilistic model of mould germination makes comparisons of alternative cold attic constructions possible. Uncertainties coupled to the proposed methodology are discussed.

PROBABILISTIC SEISMIC ASSESSMENT OF BASE-ISOLATED NPPS SUBJECTED TO STRONG GROUND MOTIONS OF TOHOKU EARTHQUAKE

The probabilistic seismic performance of a standard Korean nuclear power plant (NPP) with an idealized isolation is investigated in the present work. A probabilistic seismic hazard analysis (PSHA) of the Wolsong site on the Korean peninsula is performed by considering peak ground acceleration (PGA) as an earthquake intensity measure. A procedure is reported on the categorization and selection of two sets of ground motions of the Tohoku earthquake, i.e. long-period and common as Set A and Set B respectively, for the nonlinear time history response analysis of the base-isolated NPP. Limit state values as multiples of the displacement responses of the NPP base isolation are considered for the fragility estimation. The seismic risk of the NPP is further assessed by incorporation of the rate of frequency exceedance and conditional failure probability curves. Furthermore, this framework attempts to show the unacceptable performance of the isolated NPP in terms of the probabilistic distribution and annual probability of limit states. The comparative results for long and common ground motions are discussed to contribute to the future safety of nuclear facilities against drastic events like Tohoku.

A performance‐based framework for adaptive seismic aftershock risk assessment

SUMMARYOperative seismic aftershock risk forecasting can be particularly useful for rapid decision‐making in the presence of an ongoing sequence. In such a context, limit state first‐excursion probabilities (risk) for the forecasting interval (a day) can represent the potential for progressive state of damage in a structure. This work lays out a performance‐based framework for adaptive aftershock risk assessment in the immediate post‐mainshock environment. A time‐dependent structural performance variable is adopted in order to measure the cumulative damage in a structure. A set of event‐dependent fragility curves as a function of the first‐mode spectral acceleration for a prescribed limit state is calculated by employing back‐to‐back nonlinear dynamic analyses. An epidemic‐type aftershock sequence model is employed for estimating the spatio‐temporal evolution of aftershocks. The event‐dependent fragility curves for a given limit state are then integrated together with the probability distribution of aftershock spectral acceleration based on the epidemic‐type aftershock sequence aftershock hazard. The daily probability of limit state first‐excursion is finally calculated as a weighted combination of the sequence of limit state probabilities conditioned on the number of aftershocks. As a numerical example, daily aftershock risk is calculated for the L'Aquila 2009 aftershock sequence (central Italy). A representative three‐story reinforced concrete frame with infill panels, which has cyclic strength and stiffness degradation, is used in order to evaluate the progressive damage. It is observed that the proposed framework leads to a sound forecasting of limit state first‐excursion in the structure for two limit states of significant damage and near collapse. Copyright © 2014 John Wiley & Sons, Ltd.

A Model for Service Life Control of Selected Device Systems

Abstract This paper presents a way of determining distribution of limit state exceedence time by a diagnostic parameter which determines accuracy of maintaining zero state. For calculations it was assumed that the diagnostic parameter is deviation from nominal value (zero state). Change of deviation value occurs as a result of destructive processes which occur during service. For estimation of deviation increasing rate in probabilistic sense, was used a difference equation from which, after transformation, Fokker-Planck differential equation was obtained [4, 11]. A particular solution of the equation is deviation increasing rate density function which was used for determining exceedance probability of limit state. The so-determined probability was then used to determine density function of limit state exceedance time, by increasing deviation. Having at disposal the density function of limit state exceedance time one determined service life of a system of maladjustment. In the end, a numerical example based on operational data of selected aircraft [weapon] sights was presented. The elaborated method can be also applied to determining residual life of shipboard devices whose technical state is determined on the basis of analysis of values of diagnostic parameters.

Checking and Strengthening Scaffolding of the Home Block for Hanging Cradle Construction of Qinhe Bridge

In order to ensure the safety of the scaffolding of the home block for hanging cradle construction, this paper makes use of probabilistic limit state method, and carries out the checking computation. According to the actual drawings of the Qinhe bridge and the actual load case, the analytical model is established through the finite element analysis software MIDAS/CIVIL. The results show that the slant tube may be flexural buckling, and the stress of side standing tube is over the design strength of material, so that there is potential danger of the scaffolding. After the horizontal tubes were installed along the boundary of scaffolding, the stresses of all tubes are less than the design strength of corresponding material.

Risk-based seismic performance assessment of Yielding Shear Panel Device

Yielding Shear Panel Devices (YSPDs) have recently been proposed to facilitate passive energy dissipation of building frames during seismic activity and hence protect major structural components from excessive stress. A YSPD is composed of a thin steel diaphragm plate encapsulated within a square hollow steel tube, which is bolted to the structure to utilize the inelastic shear deformation capability of the steel diaphragm plate for energy dissipation and for consequent modification to the structural response. This paper conducts probabilistic performance evaluation to assess the appropriateness of YSPDs given uncertainty in the occurrence and intensity of earthquakes, material strength, stiffness, structural response, etc., and evaluate performance based on size, number and configuration of YSPDs. A fragility analysis is conducted, which identifies the probability of exceeding a structural damage level depending on ground motion intensity, along with a limit state probability analysis to quantify the annual exceedance probability of a specified damage level. A mathematical model to represent YSPDs in a finite element code is developed and the model is used for analyzing a case study steel moment frame with alternative YSPD designs. The study reveals the potential for considerable reduction in the median fragility and annual limit state exceedance probability due to the inclusion of YSPDs through a V-brace system. However, the effectiveness of different YSPD orientations is varied and their relative performance levels are discussed in detail. Overall, the study shows the suitability of YSPD as a passive energy dissipation device and the potential to utilize this device to help achieve performance-based objectives for buildings in seismic zones.

Performance-based optimum design of structures with vulnerability objectives

A methodology is proposed for the Performance-Based optimum seismic Design (PBD) of structures implementing vulnerability objectives. Vulnerability objectives are introduced through target limit-state probabilities of exceedance. This is achieved by performing additional probabilistic design checks. The PBD framework implementing vulnerability objectives allows designers to explicitly determine acceptable probabilities of exceedance of selected performance indices that must be satisfied simultaneously for all limit-states. The proposed methodology is formulated as a structural optimisation problem. The numerical results demonstrate that PBD framework implementing vulnerability objectives can be easily integrated into a design procedure and is generally applicable.

Rhombus Cradle System Checking Computation of Jinqinggang Bridge

In order to be sure the safety of rhombus cradle system during the concretes cantilever cast-in-place construction, the paper makes use of probabilistic limit state method, and carries out the checking computation. According to the rhombus cradle design drawings of the Jinqinggang bridge and the actual load case, the analytical model is founded through the finite element analysis software MIDAS/CIVIL. The results show that stress of all parts of the rhombus cradle system and the concrete local pressure stress is less than the corresponding material design value, and the safety factor of anchor rod tensile stress is less than 2.0 which should be strengthened, and the deformation of the steel moulding plate is less than 20mm.

Performance Evaluation of an Optical Burst Switched Core Node With Generalized Arrivals and Partial Wavelength Conversion Capability

Many of the burst assembly algorithms employed in optical burst switching (OBS) networks preserve the IP traffic self-similarity property in the burst traffic. We introduce a mathematical model for performance evaluation of an OBS core node employing either no, a partial or a full wavelength conversion strategy. The model assumes long-range dependent (LRD) traffic arrivals to the OBS intermediate node whose inter-arrival times are accurately modeled by a Pareto distribution, whereas exponential holding times are assumed. In our proposed model, each output port in the node is modeled as a GI/M/w/w queue with partial server accessibility. An imbedded Markov chain approach is used to derive the limiting state probability distribution for the number of bursts currently served by an output port as seen by arriving bursts. Next, the average burst loss probability is evaluated from steady-state occupancy probabilities. In addition, the results of our mathematical model are validated via simulation. Furthermore, the results of the model are compared with those when assuming short-range dependent Poisson arrivals. Comparison shows that traditional Poisson traffic models yield over-optimistic performance measures compared to the LRD Pareto traffic models, especially for light traffic scenarios. Furthermore, we study the impact of varying different traffic parameters, such as the average arrival rate and the Hurst parameter, on the burst loss probability. Finally, the impact of varying the wavelength conversion capability on the burst loss probability is studied, where we compare two strategies for contention resolution: adding new channels (wavelengths) or adding wavelength converters, while taking the cost into consideration.

Checking Computation for Bracket Structure of Jinqinggang Bridge

In order to ensure the safety of bracket structure during the cast-in-place construction of No.0 and No.1 piece concretes, this paper makes use of probabilistic limit state method to do the checking computation. According to the design drawings of bracket structure of the Jinqinggang bridge and the actual load case, the analytical model is founded by the finite element analysis software MIDAS/CIVIL. The results show that the stresses of all parts of the bracket structure including the concrete local compressive stress and the tensile stress of embedded steel bar are less than the allowed value of corresponding materials, but the deformation of the steel moulding plate is larger than standard allowance value. The weld joint between upper chord and slanting pole with embedded steel plate satisfies the design requirement.

Interval importance sampling method for finite element-based structural reliability assessment under parameter uncertainties

Parameters of a probabilistic model often cannot be determined precisely on the basis of limited data. In this case the unknown parameters can be introduced as intervals, and the imprecise probability can be modeled using a probability bounding approach. Common methods for bounding imprecise probability involve interval analysis to compute bounds of the limit state probability. A large number of interval finite element (FE) analyses have to be performed if the structural response defined as the limit state is determined implicitly through FE analysis. A new interval importance sampling method is developed in this paper which applies importance sampling technique to the imprecise probability. The proposed methodology has a desirable feature that expensive interval analyses are not required. Point samples are generated according to the importance sampling function. The limit states are computed using deterministic FE analyses. The bounds of the imprecise probability density function are introduced in the formulation at a later stage to incorporate the effects of the imprecision in the probability functions on the reliability results. Examples are given to illustrate the accuracy and efficiency of the interval importance sampling method. The second example also compares the proposed method with the conventional Bayesian approach.

Probabilistic seismic performance assessment of code-compliant multi-story RC buildings

Fragility analyses are conducted in this study to evaluate the relative seismic safety margins of seismic code-designed multi-story reinforced concrete (RC) buildings with varying input motion intensity, ductility level and configuration. Structural variations are accounted for by using twelve buildings [13] with diverse structural systems, heights and ductile detailing. The design peak ground acceleration (PGA) is also varied. The reference structures also include regular and irregular buildings in order to cover a wide spectrum of contemporary mid-rise buildings. Incremental dynamic analyses (IDAs) are deployed using the twelve inelastic fiber-based simulation models of the reference structures and sixty natural ground motions recorded on different soil conditions with a wide range of spectral amplifications. The regression analyses of the selected response quantities show that the soil condition has a marginal effect on the demand-ground motion intensity relationships when adopting spectral acceleration to characterize the ground shaking intensity. The damage state probabilities of wall-frame structures designed to high PGA and ductility levels do not satisfactorily achieve the most favorable safety objectives. Fragilities are reduced by decreasing the design PGA due to the higher contribution of gravity loads to the details of the building design. Using extensive results from twelve buildings subjected to sixty ground motions, a relationship is proposed to enable the quantifying of the Life Safety limit state probabilities of code-compliant mid-rise RC buildings.

지진 취약성 등고선을 이용한 내진성능 평가 방법

기존의 확률적 지진 취약성 분석은 그 중요성에도 불구하고 시간과 노력의 과도한 소요로 인하여 내진 성능 평가에 사용되기에 많은 제약이 따라왔다. 본 연구에서는 이를 극복하기 위해 획기적 수준의 신속성과 확장성을 갖춘 지진 취약성 분석 체계와 이를 실용화 하기위한 취약성 등고선을 개발하였다. 응답 데이터베이스를 활용하여 광범위한 구조물의 최대 응답을 즉각적으로 구하고 이를 바탕으로 구조물의 주기와 강성에 따른 한계상태확률의 변화를 한눈에 파악할 수 있는 취약성 등고선을 도출하였다. 최대응답 등고선의 도출과 비교를 통해서 최대응답의 분포는 연성도 요구치로 나타내는 것이 변위의 절대값으로 표현하는 것보다 안정적인 예측곡선을 보여 주며, 구조물의 응답특성변수인 주기와 강도비가 최대응답에 미치는 영향을 분석하는데도 유리함을 확인하였다. 연성도를 내진성능 평가의 기준으로 사용하기 위해서 내진설계기준에서 한계상태변위로서 제시되는 층간변위비와 연성도 요구치 사이의 상호 변환 관계를 정의하였다. 예제 구조물의 내진보강 전략 수립에 대한 논의를 통해서 신뢰성 이론에 기반 한 내진 보강과 설계에 취약성 등고선이 매우 유용하게 활용될 수 있음을 보여주었다. Extensive computer simulations to account for the randomness in the process of seismic demand estimation have been a serious obstacle to the adoption of probabilistic performance assessments for the decision of applying seismic intervention schemes. In this study, a method for rapid fragility assessments based on a response database and the fragility contour method are presented. By the comparison of response contours in different formats, it is shown that representing maximum responses in ductility demand is better for the investigation of the effect of structural parameter changes on seismic demands than representations in absolute values. The presented fragility contour enables designers to practically investigate the probabilistic performance level of every possible retrofit option in a convenient manner using visualized data sets. This example demonstrates the extreme efficiency of the proposed approach in performing fragility assessments and successful application to the seismic retrofit strategies based on limit state probabilities.

Seismic reliability of spherical containers retrofitted by means of energy dissipation devices

For the purpose of enhancing the seismic reliability of structures, external energy dissipation systems may be advantageously used. In this paper, the reliabilities of a spherical storage tank in original and updated states are assessed by means of simulation. The effect of the energy dissipation system is numerically evaluated by performing a set of nonlinear dynamic analyses on a spherical tank based on a detailed model that takes the fluid–structure interaction into account. To obtain robust estimators of the reliability, an ensemble including acceleration records with markedly different characteristics is used in the simulation study. The full reliability analysis shows that, for a typical spherical container widely used in the petrochemical industries, a reduction of the limit state probability in the order of 85% may be expected by introducing additional energy dissipation systems.

Interval Monte Carlo methods for structural reliability

This paper considers structural reliability assessment when statistical parameters of distribution functions can not be determined precisely due to epistemic uncertainty. Uncertainties in parameter estimates are modeled by interval bounds constructed from confidence intervals. Reliability analysis needs to consider families of distributions whose parameters are within the intervals. Consequently, the probability of failure will vary in an interval itself. To estimate the interval failure probability, an interval Monte Carlo method has been developed which combines simulation process with the interval analysis. In this method, epistemic uncertainty and aleatory uncertainty are propagated separately through finite element-based reliability analysis. Interval finite element method is utilized to model the ranges of structural responses accurately. Examples are presented to compare the interval estimates of limit state probability obtained from the proposed method and the Bayesian approach.

Role of accidental torsion in seismic reliability assessment for steel buildings

This study investigates the role of accidental torsion in seismic reliability assessment. The analyzed structures are regular 6-story and 20-story steel office buildings. The eccentricity in a floor plan was simulated by shifting the mass from the centroid by 5% of the dimension normal to earthquake shaking. The eccentricity along building heights was replicated by Latin hypercube sampling. The fragilities for immediate occupancy and life safety were evaluated using 0.7% and 2.5% inter-story drift limits. Two limit-state probabilities and the corresponding earthquake intensities were compared. The effect of ignoring accidental torsion and the use of code accidental eccentricity were also assessed. The results show that accidental torsion may influence differently the structural reliability and limit-state PGAs. In terms of structural reliability, significant differences in the probability of failure are obtained depending on whether accidental torsion is considered or not. In terms of limit-state PGAs, accidental torsion does not have a significant effect. In detail, ignoring accidental torsion leads to underestimates in low-rise buildings and at small drift limits. On the other hand, the use of code accidental eccentricity gives conservative estimates, especially in high-rise buildings at small drift limits.

Seismic Fragility Analysis and Retrofit of Conventional Residential Wood-Frame Structures in the Central United States

Site-built wood-frame (light-frame) construction is the most common form of construction for residential structures in the United States. Such structures have suffered significant damage in recent earthquakes, and wood-frame construction practices in the western United States (WUS) have improved considerably in the last 2decades. On the other hand, little is understood about the expected performance of wood-frame structures located in the central and eastern United States (CEUS), where the seismicity is moderate compared to the WUS and construction practices seldom provide earthquake resistance. This paper examines the seismic performance of typical one- and two-story wood-frame structures in the CEUS. Six structures with two foundation types were considered, for which conditional limit state probabilities (fragilities) were evaluated considering three possible failure mechanisms: excessive interstory drift, wall uplift, and sill plate splitting. This examination shows that seismic damage to wood-frame structures in the CEUS under earthquakes of moderate intensity is unlikely to lead to loss of life, but may result in significant financial losses. An evaluation of two possible retrofit strategies illustrates how the expected seismic performance of the CEUS structures can be improved by adding more anchor bolts and perimeter sheathing nails to the shear walls.

Reliability-Based Analysis of Strip Footings Using Response Surface Methodology

A reliability-based analysis of a strip foundation subjected to a central vertical load is presented. Both the ultimate and the serviceability limit states are considered. Two deterministic models based on numerical simulations are used. The first one computes the ultimate bearing capacity of the foundation and the second one calculates the footing displacement due to an applied load. The response surface methodology is utilized for the assessment of the Hasofer-Lind reliability indexes. Only the soil shear strength parameters are considered as random variables while studying the ultimate limit state. Also, the randomness of only the soil elastic properties is taken into account in the serviceability limit state. The assumption of uncorrelated variables was found to be conservative in comparison to the one of negatively correlated variables. The failure probability of the ultimate limit state was highly influenced by the variability of the angle of internal friction. However, for the serviceability limit state, the accurate determination of the uncertainties of the Young's modulus was found to be very important in obtaining reliable probabilistic results. Finally, the computation of the system failure probability involving both ultimate and serviceability limit states was presented and discussed.