Target Reliability Values Research Articles

Target reliabilities for heritage structures derived from cost optimization

AbstractIn the last decade, structural reliability and safety efforts have been oriented toward the assessment of existing structures and the development of related target reliability levels. However, up‐to‐date there is no consensus on the reliability philosophy that should be followed when considering the assessment of heritage structures, and the level of reliability which is appropriate to them. In this study, a framework is proposed which derives new values for the economically optimal target reliability for the upgrade of a structure, , and the reliability threshold for upgrade, , considering the cultural heritage value of the structure. The total expected life cycle cost is minimized, assuming that the structure is given up after collapse, as heritage value is typically lost after failure. The target reliability values are based on three main parameters: the relative annual benefit of using the structure (affected by its heritage value), the relative cost of failure and the relative cost of increasing the reliability. Target reliability values are proposed specifically for heritage structures, considering a range of the main input parameters.

On the ergodicity assumption in Performance-Based engineering

In the Performance-Based Engineering (PBE) framework, uncertainties in system parameters, or modelling uncertainties, have been shown to have significant effects on capacity fragilities and annual collapse rates of buildings. Yet, since modelling uncertainties are non-ergodic variables, their consideration in failure rate calculations offends the Poisson assumption of independent crossings. This problem has been addressed in the literature, and errors found negligible for small annual collapse failure rates. However, the errors could be significant for serviceability limit states, and when failure rates are integrated in time, to provide lifetime failure probabilities. Herein, we present a novel formulation to fully avoid the error in integration of non-ergodic variables. The proposed product-of-lognormals formulation is fully compatible with popular fragility modelling approaches in PBE context. Moreover, we address collapse limit states of realistic reinforced concrete buildings, and find errors of the order of 5 to 8% for 50-year lifetimes, up to 14% for 100 years. Computation of accurate lifetime failure probabilities in a PBE context is clearly important, as it allows comparison with lifetime target reliability values for other structural analysis formulations.

Consequence classes and associated models for predicting loss of life in collapse of building structures

Most building design codes distinguish structural reliability levels in terms of failure consequences, for which they normally define consequence classes based on building type and use. Although readily applicable in everyday practice, that approach may entail adopting inconsistent safety requirements. Such a significant drawback could be minimised by establishing separate reliability levels for key members on the grounds of the potential consequences of their collapse.Further to those concerns, this paper proposes a series of consequence classes determined in keeping with the number of persons at risk in a given collapse scenario and the extent of the respective damage. Consequence class-related models for predicting loss of life are derived from statistical assessments of data on over 150 collapsed buildings. The models developed estimate the number of fatalities and conditional probability of death of building users under given collapse circumstances. In addition to their utility in establishing target reliability values, these models can be applied in risk analysis of specific building structures, especially where the potential consequences of failure are high.

Structural reliability analysis of superstructure of highway bridges on China-Pakistan Economic Corridor (CPEC): a case study

ABSTRACTLive load models representing truck traffic are the governing factors for the design of bridges. In Pakistan, American Association of State Highway and Transportation Officials-Load Resistance and Factor Design (AASHTO-LRFD) and Pakistan Code of Practice for Highway Bridges (PCPHB) codes are used for the design of bridges. This article presents the reliability analysis of existing bridges of Pakistan for Chinese design trucks which are completely different from Pakistani design truck. Single span and multi-spans bridges are selected on western route of CPEC. Average Daily Truck Traffic data (ADTT) for these bridges was taken from National Highway Authority (NHA). Analysis of bridges is carried out using CSI-Bridge and AASHTO-LRFD, PCPHB and Chinese Codes are used to analyse the bridges. The resultant load effects are extrapolated using non-parametric and linear fit for 75 years return period to carry out the reliability analysis. It is concluded that the reliability index of various bridges is lesser than the target reliability value which is 3.5 in AASHTO-LRFD Code, so the existing bridges are less safe. The probability of failure in single span bridge is maximum using HL-93 truck while in case of multi-span bridges Class-A truck has maximum failure probability.LIST OF ABBREVIATIONSADTT Average Daily Truck TrafficAASHTO-LRFD American Association of State Highway and Transportation Officials - Load Resistance and Factor DesignCDF Cumulative Distribution FunctionCOV Coefficient of VariationCPEC China Pakistan Economic CorridorGVW Gross Vehicle WeightIM Impact loadMDOT Michigan Department of TransportationNCHRP National Cooperative Highway Research ProgramNHA National Highway AuthorityTB-3 Taxila Bridge having three SpansWCB-1 Wah Cantt Bridge having single SpanWGB-6 Wah Garden Bridge having six SpansWIM Weight-In- Motion data

RELSPEC: a framework for reliability aware design of component based embedded systems

With the increase in the complexity of safety-critical embedded applications, the reliability analysis of such systems have also become increasingly difficult. For such complex system specifications, if the reliability provisions are declared upfront in the design flow then the overall system level reliability can be easily inferred given that the system components satisfy their individual reliability requirements. Moreover, such an early-stage specification and analysis paves newer and scalable ways for synthesis of reliable systems. This paper develops a reliability specification and analysis framework, RELSPEC, which enables system level reliability analysis at an early-stage of design by leveraging automatically constructed intermediate probabilistic models of the system. In addition to this, we provide a mechanized method of system synthesis with the objective of satisfying a target reliability value for the overall system. To this end, we explore the application of existing optimization methods and also provide domain specific techniques which outperform such existing methods. Experiments over a few automotive case-studies show the efficacy of this methodology.

Granite plates as structural slabs in Brazilian buildings: application of reliability concepts

Polished finishing granites are greatly accepted for claddings because of the plates’ shape, design and color variety. The features depend on the geological conditions that occur during the formation process, which include the mineralogy of the stone, the fluids formed during the process, the grain size of the minerals and the way in which the minerals interact with each other. One of the noblest uses of stone plates is in non-adherent covering systems (without mortar), such as ventilated facades and pedestrian paving systems. Currently, the methodology for non-adherent systems uses the allowable stress design criteria. In recent years, the number of papers indicating reliability analysis as an important design tool for natural stones has increased. However, a lack of information concerning the design methodology still happens. Therefore, the structural properties assessed as complementing these studies were: compressive strength, three-point flexural tensile strength, Young’s modulus and Poisson’s ratio. A granite slab design example was also presented. First, the thickness of the plates was determined based on the formulation proposed by Timoshenko [Strength of materials (original language, Portuguese), Volume II. Editora Ao Livro Tecnico S. A., Rio de Janeiro, 1977], using the allowable stress design criteria. Next, the reliability analysis was performed by Monte Carlo simulation. Results showed that the Desiree White granitic plate presented a higher reliability index than the Capao Bonito Red granitic plate. This result seems to be paradoxical, owing that the Capao Bonito Red presented a higher value of mean flexural strength than the Desiree White. The minimal safety factors to satisfy the target reliability value of 3.8 as recommended by the standard EN 1990:2002 (Eurocode) were found to be 2.61, 1.98 and 2.72, respectively, for the three stone types.

An efficient approach to obtain optimal load factors for structural design.

An efficient optimization approach is described to calibrate load factors used for designing of structures. The load factors are calibrated so that the structural reliability index is as close as possible to a target reliability value. The optimization procedure is applied to find optimal load factors for designing of structures in accordance with the new version of the Mexico City Building Code (RCDF). For this aim, the combination of factors corresponding to dead load plus live load is considered. The optimal combination is based on a parametric numerical analysis of several reinforced concrete elements, which are designed using different load factor values. The Monte Carlo simulation technique is used. The formulation is applied to different failure modes: flexure, shear, torsion, and compression plus bending of short and slender reinforced concrete elements. Finally, the structural reliability corresponding to the optimal load combination proposed here is compared with that corresponding to the load combination recommended by the current Mexico City Building Code.

Reliability Analysis of CPT Measurements for Calculating Undrained Shear Strength

Abstract The cone penetration test (CPT) has been widely used in Louisiana to classify soils, measure undrained shear strength (Su), and identify bearing stratum for driven piles. This paper compares the values of Su based on CPT measurement with Su of the unconfined compression test. A total of 752 CPT soundings were collected and archived using ArcGIS software in which 503 were matched with adjacent boreholes and 249 did not have adjacent borehole data available. The dataset was analyzed for general as well as specific trends in order to identify appropriate parameters to be included in the investigation. The calibration of the CPT expression for Su was conducted using the first order reliability method (FORM) and accounting for all sources of uncertainty. Optimum CPT coefficient (Nkt) values to calculate Su were computed for various target reliability values. It was determined that the soil classification is the only parameter showing clear trends that affect CPT estimates of the undrained shear strength. Values of Nkt for each soil type based on the Robertson (1990) classification and the Zhang and Tumay (1999) classification were determined for three target reliability levels. It is obvious that the Nkt coefficient for soils with higher clay content is lower than those with less clay content. A single Nkt value that is valid for all soil types is unwarranted as will lead to acceptable results for some soil conditions and unacceptable results for others, which can be unconservative.

Reliability of shallow foundations designed to Eurocode 7

Eurocode 7, the new European standard for geotechnical design, is based on the limit state design method, with partial factors and characteristic parameter values. An objective of the Eurocodes is that the chosen partial factors should achieve reliability levels for a structure close to a prescribed target value. The target ultimate limit state reliability index for a medium risk structure for 50 years is 3.8. This paper examines the reliability of an inclined-eccentrically and vertically loaded square foundation designed using all three Design Approaches in Eurocode 7 with the recommended partial factor values given in EN1997-1. The reliabilities obtained using the three Design Approaches are compared with the target reliability value and the reliabilities of traditional designs using overall factors of safety. The paper provides evidence that Eurocode 7 gives more consistent reliabilities for a greater range of parameter values than the traditional allowable stress method and demonstrates the importance of selecting appropriate characteristic values.

Reliability-based design criterion for TLP tendons

This paper presents a methodology to perform a Load and Resistance Factor Design (LRFD) criterion for the design of Tension Leg Platform (TLP) tendons in their intact condition. The proposed design criterion considers the Ultimate Limit State (ULS) for the tendon sections, expressed in terms of the expected value of the extreme Interaction Ratio (IR), considering long-term storm sea states, and takes into account the dynamic load effects interaction and the statistics of its associated extreme response. The partial safety factors are calibrated through a long-term reliability-based methodology for the storm environmental conditions in deep waters of the Campeche Bay, Mexico. Different target reliability values are considered in order to evaluate the effect of this key parameter on safety factors. The results show that the partial safety factors reflect both the uncertainty content and the importance of the random variables in structural reliability analysis. When tendons are designed according to the developed LRFD criterion, a less scattered variation of reliability indexes is obtained for different tendon sections across a single or a variety of TLP designs. Finally, it is observed that the target reliability value has a strong influence over the safety factor values and thus over the final size of the structural elements.

Comparing target spectral design acceleration values by using different acceptability criteria

A central issue in earthquake engineering design is the treatment of ground motion uncertainty and the non-linear structural response for defining the design acceleration. This paper first proposes a probabilistic design spectrum which includes as input, in addition to common design parameters, the probability that the design acceleration is exceeded. Furthermore, it presents several alternatives for defining the bounds of the ALARP region to define target reliability values. In order to define acceptable probabilities of exceedence several alternatives have been considered and compared. Finally, the importance and the impact of selecting target reliabilities is demonstrated for the case of low income housing developments in Colombia.

Reliability-based load and resistance factor design for piping: an exploratory case study

This paper presents an exploratory case study on the application of Load and Resistance Factor Design (LRFD) approach to the Section III of ASME Boiler and Pressure Vessel code for piping design. The failure criterion for defining the performance function is considered as plastic instability. Presently used design equation is calibrated by evaluating the minimum reliability levels associated with it. If the target reliability in the LRFD approach is same as that evaluated for the presently used design equation, it is shown that the total safety factors for the two design equations are identical. It is observed that the load and resistance factors are not dependent upon the diameter to thickness ratio. A sensitivity analysis is also conducted to study the variations in the load and resistance factors due to changes in (a) coefficients of variation for pressure, moment, and ultimate stress, (b) ratio of mean design pressure to mean design moment, (c) distribution types used for characterizing the random variables, and (d) statistical correlation between random variables. It is observed that characterization of random variables by log-normal distribution is reasonable. Consideration of statistical correlation between the ultimate stress and section modulus gives higher values of the load factor for pressure but lower value for the moment than the corresponding values obtained by considering the variables to be uncorrelated. Since the effect of statistical correlation on the load and resistance factors is relatively insignificant for target reliability values of practical interest, the effect of correlated variables may be neglected.

WHEN SHOULD SEISMIC RETROFITTING OF EXISTING STRUCTURES BE IMPLEMENTED IN ORDER TO MINIMIZE EXPECTED LOSSES

The usual outcomes of the seismic safety analysis for an existing civil engineering structure axe the probability of exceedance of specified limit states and the increase in safety due to retrofitting interventions. This information can be used in several ways. For a single structure, one can compare it with desired target reliability values; for structures belonging to a network, e.g. highway bridges [Donferri et al., 1998], electric networks [Vanzi 1996, 2000) or strategic buildings [Nuti and Vanzi, 1998] they can also be used to assess the priority of interventions. In this study, an alternative use of the reliability values for existing structures is proposed, which answers the following question: when, i.e. in which year from the date of construction, should seismic retrofitting be implemented so as to minimize the expected total cost? In the expected total cost, here, both the costs of retrofitting and possible disruption, due to delayed retrofitting, are accounted for. The method proposed computes the expected costs by analysing the branches of the event tree for the problem built after strong but reasonable and highly simplifying assumptions on the problem. Although these assumptions limit the general applicability of the solutions obtained, they allow the building up of an extremely agile and effective solution scheme. The results obtained from the study, i.e. the year in which it is economically best to implement retrofitting and what the expected annual equivalent cost is, are presented in diagrams and in analytical form, as a function of the most important variables. Finally, an example application on a real structure is presented, which shows all the steps to undertake with the proposed method.

RELIABILITY-BASED FATIGUE INSPECTION PLANNINGOF FIXED OFFSHORE STRUCTURES

This paper proposes the practical application of a reliability-based procedure for fatigue inspection planning of fixed offshore structures. This procedure is based on a simplified probabilistic crack growth model for welded tubular joints available in the literature, which encompasses fracture mechanics and S-N curves and uses the results of the original fatigue design. Current techniques for reliability updating are implemented to re-evaluate the fatigue failure probability after inspection campaigns. Target reliability values are defined to be compatible with the simplicity of the procedure. Actual applications illustrate the inspection costs reduction that can be obtained.

Fatigue Reliability Reassessment Applications: State-of-the-Art Paper

The problem of assessing the damage to and remaining life of structures subjected to fatigue is explored, with particular emphasis on railroad bridges, highway bridges, and offshore structures. In railroad structures, the fatigue reliability estimates are typically calculated based on fatigue life predictions. The resulting predictions are used for budgeting purposes rather than for scheduling repairs. Examples are given of economic decision based on fatigue life calculations. Fatigue reliability estimates for highway bridges are also typically based on fatigue life calculations. Target reliability values have been suggested and are used in both the design of new bridges and the evaluation of existing bridges. Given the economics of offshore structures, it is feasible to develop more elaborate fracture mechanics models. These models have the advantage of explicitly allowing updated estimates of fatigue reliability based on inspection results. The economics of inspection of offshore structures also dictates that inspection scheduling be based on fatigue realiability estimates.