Target Reliability Index Research Articles

Reliability Design Method of Ground Wires in Transmission Lines

To satisfy the uniformity of design within the international standards, reliability design method is used to design ground wires in transmission lines. Based on the reliability calibration due to the Chinese national standard, it is found that the reliability indexes of ground wires meet safety levels. Then the load and resistance partial coefficients of ground wires in the ultimate state are calculated by the target reliability index. When the design method based on reliability theory is adopted, the suggested partial coefficients of ground wires can be obtained by analysing and optimizing. This method provides a popularization of reliability theory in the designing ground wires of transmission lines.

Fatigue Assessment on Suspenders under Stochastic Wind and Traffic Loads Based on In-Situ Monitoring Data

As a critical component of a suspension bridge, the integrity of the suspenders plays a critical role in the serviceability and reliability of the bridge during its life time. Despite the wide recognition of the importance of the suspenders, very few studies have been devoted to the condition evaluation of suspenders in operation. The present study performs the fatigue assessment on the suspenders accounting for the stochastic wind and traffic loads using the in-situ monitoring data. To this end, a probabilistic numerical framework is proposed to predict the time-dependent fatigue reliability of the suspenders under stochastic wind and traffic loads during the bridge’s life time, based on the linear fatigue damage rule. As a demonstration, the proposed numerical framework is applied to a long-span suspension bridge located in a mountainous canyon. The results indicate that it is of paramount importance to consider both the wind and traffic load effects in the fatigue reliability evaluation of the suspenders. In addition, it was also found that among the suspenders under investigation, the short suspender at the bridge mid-span (S36) is more prone to the fatigue damage, while the long suspender at the end of the bridge girder (S2) is less prone to the fatigue damage. Finally, provided with a target reliability index of 3.0, the fatigue life of the suspenders S36 and S2, considering the life time wind and traffic load, is estimated as 53 years and 167 years, respectively. The present research could provide essential guidelines for the optimization of inspection and replacement in maintenance practices for suspenders.

Time-dependent reliability assessment of existing concrete bridges including non-stationary vehicle load and resistance processes

It is well known that existing concrete bridges are time-varying working systems, and the corresponding maintenance strategy should be planned according to the time-varying service performance. In this work, a time-dependent reliability assessment procedure is proposed while including the non-stationarities of the vehicle load process and resistance deterioration process simultaneously, which are the two factors that significantly influence the time-varying service performance of a bridge structure. To achieve this goal, the following key tasks are conducted in sequence: (a) extreme value modelling of non-stationary vehicle load process; (b) model establishment and updating of non-stationary resistance deterioration process; (c) determination of target reliability index of a concrete bridge component in the operation stage; (d) performing time-dependent reliability analysis while considering the non-stationary properties. In addition, a case study is conducted to illustrate the application of the proposed procedure by considering an existing concrete bridge as an example. It is found that the proposed time-dependent reliability assessment procedure is feasible, and some critical information on the time-varying service performance of the existing concrete bridge component can be obtained, which can be further referenced in the planning of the structural inspection, management and maintenance, etc.

Determination of Optimal Load-Resistance Factors for Gravitational Loads-Governed Limit State of Korean Bridge Design Code

This paper presents an optimization scheme to determine the optimal load-resistance factors for a gravitational loads-governed limit state in the Korean Highway Bridge Design Code. The random variables in the limit state function are normalized to the total nominal load effect, and the optimization is formulated using the normalized variables. The objective function is defined as an L2-norm of errors between the design strength obtained by the load-resistance factors and the target strength evaluated by the inverse reliability analysis for the target reliability index. Two different types of optimization, reference and sequential optimizations, are proposed. The former is to determine absolute optimal load-resistance factors, while the latter is proposed to obtain the factors suitable for actual design codes. The reference optimization results in load-resistance factors that yield a more uniform reliability index than the sequential optimization. The reliability levels provided by the proposed load-resistance factors are presented in detail and compared with those obtained by the factors in the Korean Highway Bridge Design Code. It is shown that the factors in the code lead to a much higher reliability index than the target while the optimal load-resistance factors yield a reliability index within ± 5% error bounds to the target reliability index.

A framework for optimization of target reliability index for a building class based on aggregated cost

To effectively manage the seismic risk of the built-environment, the target safety levels that design standards are based on should be properly managed by considering the total risk to the built-environment and to the community. This paper introduces a framework for optimizing the target safety levels based on the total life-cycle cost of a portfolio of buildings. Building inventory is categorized to obtain a clear relationship between target safety level and its realizations to design, which is reflected in the proposed framework. To address the issue of unrealistic computation cost in implementing optimization process in target safety level determination, the framework utilizes a neural network for structural response estimation. A procedure to develop a neural network for dynamic response estimation of a group of buildings is also introduced in the paper. The proposed framework is illustrated to obtain the optimal target reliability index for mid-rise office buildings.

Investigation of the Adequacy of Bridge Design Loads in Pakistan

Weight, configuration, and volume of traffic vary from country to country. But, in developing countries like Pakistan, bridges are designed based on codes of developed countries. Hence, these bridges may not have desired safety level. In this study, safety levels of three sample bridges has been investigated in terms of structural reliability index. Live load effects (shear and moments) in girders were determined using weigh-in-motion data (WIM) and were extrapolated to 75 years using non-parametric fit. Two live load models and two strengths, required by 1967 Pakistan Code of Practice for Highway Bridges (PHB Design-Case) and that required by the 2012 AASHTO LRFD Bridge Design Specifications (AASHTO Design-Case) were used in reliability analysis. It is found that actual trucks produce moment and shear in girders 11 to 45 percent higher than live load models of PHB and AASHTO design cases. Values of structural reliability indices vary from 1.25 to 2.50 and from 2.45 to 3.15 for PHB and AASHTO design cases, respectively, and are less than the target reliability index value of 3.50 used in the design codes as benchmark. It is revealed after the research that bridges in Pakistan may not have desired safety level, and current live load models may not be the true representation of service-level truck traffic.

Research on reasonable value of target reliability index for steel main girder of cable-stayed bridge considering durability

This article studies the relationship between the target reliability index and the design life of the main girder of a long-span cable-stayed bridge to provide a theoretical basis for the design of steel girders for such an application. The changes of the bending section modulus under atmospheric corrosion and the residual ultimate stress of the section of a steel box girder under alternating loads are discussed. A resistance attenuation function for a steel girder of a cable-stayed bridge to predict the resistance change of a steel box girder over the service period is proposed, and the change characteristics of the time-varying reliability index of a steel box girder of a cable-stayed bridge are studied. By analysing the relationship between the time-varying reliability index and the evaluating benchmark value of the reliability index, the time point of maintenance and reinforcement is predicted. Based on the change over time of the difference between the time-varying reliability index and the evaluating benchmark value of the reliability index, the relation function between the target reliability index and the service lifetime of a bridge considering resistance attenuation are provided.

Reliability based assessment of axial pile bearing capacity: static analysis, SPT and CPT-based methods

ABSTRACT Since piles are one of the major geotechnical foundation systems, estimation of their axial bearing capacity is of great importance. Employing different design methods, resulting in a wide range of bearing capacity estimations, complicates the selection of an appropriate design scheme and confirms the existence of model error along with the inherent soil variability in bearing capacity prediction. This paper tends to evaluate different predictive methods in Reliability-Based Design (RBD) framework. In this regard, different static analyses, SPT and CPT-based methods are considered to evaluate which approaches collectively and which method individually, have more reliable predictions for compiled data bank. In order to assess reliability indices and resistance factors, two approaches have been considered, i.e. First Order Second Moment method (FOSM) and First Order Reliability Method (FORM). To investigate the reliability indices for different methods in both RBD approaches, various safety factors and loading ratios have been considered. Also, the Load and Resistance Factor Design (LRFD) resistance factors are calibrated for different target reliability indices and loading ratios. Results show that CPT-based methods are more reliable among other methods. Furthermore, the estimated efficiency ratio, i.e. the ratio of resistance factor to resistance bias factor, confirms this agreement.

Development of partial factor design method on bearing capacity of pile foundations for Japanese Specifications for Highway Bridges

ABSTRACTThis paper shows the development of a partial factor design method on the bearing capacity of pile foundations for Japanese Specifications for Highway Bridges. Firstly, estimation design equations on the bearing capacities of pile foundations are improved by analysis of pile load test results and uncertainties in the bearing capacities are evaluated. Secondly, the reliabilities of pile foundations designed by the former specifications are evaluated based on reliability analysis considering the uncertainties in the bearing capacities and coefficients of subgrade reaction. Finally, a partial factor design method is developed based on the target reliability index obtained based on the conventional pile installation method by the pile installation methods. The factors are different for each pile installation method.

Risk-Informed Requirements for Design and Assessment of Structures Under Temporary Use.

The relatively high failure rates, with important consequences in many cases, suggest that the implicitly acceptable risk levels corresponding to temporary civil engineering structures and activities might exceed the bounds of normally acceptable levels associated with different societal activities. Among other reasons, this may be attributed to the lack of a rational approach for the assessment of risks associated with the different technologies supporting these activities in general, and for structures in particular. There is a need for establishing appropriate target reliability levels for structures under temporary use taking into account specific circumstances such as reduced risk exposure times. This issue is being addressed in this article. Acceptance criteria for building-structure-related risks to persons obtained in prior studies are adapted to the special circumstances of nonpermanent risk exposure. Thereby, the general principle followed is to maintain the same risk levels per time unit as for permanently occupied buildings. The adaptation is based on the statistical annual fatality rate, a life safety risk metric that allows for a consistent comparison of risks across different societal activities and technologies. It is shown that the target reliability indices taking account of the temporary use of buildings might be significantly higher than the values suggested for permanently used structures.

An augmented step size adjustment method for the performance measure approach: Toward general structural reliability-based design optimization

Heavy computational burden has been one of the largest barriers to the application of reliability-based design optimization (RBDO) in real-world structures. The key difficulty of RBDO lies in how to perform reliability analysis efficiently and robustly. In performance measure approach (PMA)-based RBDO, the reliability analysis process searches for the minimum performance target point (MPTP) with the target reliability index in standard normal space. Many methods have been proposed to improve the efficiency and robustness of the PMA. However, these methods may face the convergence problem for highly nonlinear constraint functions; or high computational cost for weakly nonlinear ones. More importantly, most existing methods are very sensitive to the selection of algorithm parameters. In this paper, an augmented step size adjustment (ASSA) method is proposed to boost the iterative process in terms of both efficiency and robustness. According to the relative positions of the direction vector and negative gradient direction and the angle between them at each iterative point, a fire-new strategy is established to identify the oscillation during the iterative process and define the iterative step size. Seven inverse reliability analysis problems and three RBDO benchmarks are used to validate the performance of the ASSA method. The results indicate that the ASSA method has wide applicability for nonlinear constraint functions and achieves efficient and robust performance. Furthermore, the results demonstrate that the ASSA method can be regarded as a reliable and effective method for addressing PMA-based RBDO problems.

A performance measure approach for risk optimization

In recent years, several approaches have been proposed for solving reliability-based design optimization (RBDO), where the probability of failure is a design constraint. The same cannot be said about risk optimization (RO), where probabilities of failure are part of the objective function. In this work, we propose a performance measure approach (PMA) for RO problems. We first demonstrate that RO problems can be solved as a sequence of RBDO sub-problems. The main idea is to take target reliability indexes (i.e., probabilities of failure) as design variables. This allows the use of existing RBDO algorithms to solve RO problems. The idea also extends the literature concerning RBDO to the context of RO. Here, we solve the resulting RBDO sub-problems using the PMA. Sensitivity expressions required by the proposed approach are also presented. The proposed approach is compared to an algorithm that employs the first-order reliability method (FORM) for evaluation of the probabilities of failure. The numerical examples show that the proposed approach is efficient and more stable than direct employment of FORM. This behavior has also been observed in the context of RBDO, and was the main reason for the development of PMA. Consequently, the proposed approach can be seen as an extension of PMA approaches to RO, which result in more stable optimization algorithms.

Wind Pressure Statistics and Target Reliability Index for Wind Load-governed Limit State of Reliability-based Bridge Design Codes

This paper presents a general procedure for evaluating a proper target reliability index and corresponding wind load factor for a wind load-governed limit state in reliability-based design codes. The Monte-Carlo simulation is conducted to reveal relationships between statistical parameters of wind velocity and pressure. The normalized wind pressure is defined and used in the simulations. The analytical form of the wind load factor is presented in terms of the statistical parameters of wind velocity and the target reliability index. The return period of a nominal wind velocity is expressed for the target reliability index and the wind load factor. An approach determining the target reliability index based on the return period of wind velocity at the limit state is proposed. The return period of wind velocity at the limit state is set to that of the design earthquake in a design code. The proposed approach is applied to calculate the target reliability index for the Korean Highway Bridge Design Code-Cable supported Bridge. The target reliability index is found as 2.25, and the corresponding wind load factor ranges from 1.60 to 1.82 depending on the Coefficient of Variation (COV) of wind velocity. Detailed discussions on the return period of wind velocity, target reliability index and wind load factor are made. A simplified expression of the wind load factor corresponding to the target reliability of 2.25 is proposed. The basic wind velocities for five regions in the Korean Highway Bridge Design Code (Limit State Design) are estimated through the proposed procedure.

Characterization of model uncertainty of adhesively bonded CFRP-to-steel joints

This paper presents a critical characterization of the uncertainty of bond strength models of adhesively bonded carbon fiber-reinforced polymer (CFRP)-to-steel joints. A model factor ε was defined as the ratio of a tested ultimate load to the corresponding predicted value. A database consisted of 414 CFRP-to-steel single/double-lap shear tests was collected and two frequently used bond strength models were used in the evaluation. The statistics of ε indicated a high level of both the mean value and coefficient of variation (COV). The model factor was found to be highly dependent on input parameters rather than purely random. A systematic part (f) was consequently introduced by a multiple regression analysis to remove this kind of correlation, leaving a residual lognormally distributed random variable (ε*). After the critical characterization, performance of the model factor was significantly improved. Afterwards, a reliability analysis was performed to compare the model performance given the condition whether the model factor was properly considered or not. The merit of the critical calibration of the model factor is highlighted in the reliability analysis. The resistance factor for the two bond strength models was calibrated given a target reliability index βT of 3.5. The sensitivity analysis indicated that the adhesive tensile strength is the most influential parameter to the reliability index among all the input parameters.

Fatigue reliability analysis of butt welded joints with misalignments based on hotspot stress approach

Fatigue reliability of butt welded joints with misalignments is assessed, based on the structural hotspot stress approach. The unsymmetrical weld profile induced stress concentration is evaluated using the finite element and Monte Carlo methods based on a series of simulated weld profiles from published statistical data. The Monte Carlo method is also used to assess the uncertainty on the critical stress magnification factor proposed to represent the margin left for the misalignment effect to trigger fatigue failure. A limit state function is formulated based on the critical and actual stress magnification factors. The first order reliability method is applied to evaluate the reliability levels of different welding processes, reliability levels of standards and the lateral distortion limits for a target reliability index. The results show the advantage of the laser welding over the conventional arc welding regarding fatigue reliability. The tolerance limits of misalignments specified by standards lead to different reliability levels for different welded joint plate thicknesses. The thin-plate joints show a low reliability level and the reliability index increases with the plate thickness.

Unified system reliability approach for single and group pile foundations – Theory and resistance factor calibration

Load and Resistance Factor Design (LRFD) optimization is concerned with calibrating load and resistance factors against a pre-defined target safety level. The uncertainty in soil properties, the incomplete understanding of soil-structure interaction and the lack of statistical information slowed the development in the field of foundation optimization. A unified target reliability index is proposed for the design of a single pile, a non-redundant pile group, and a redundant pile group foundation. Resistance factors for axially loaded drilled and driven piles based on the statistical results of over 4000 pile load tests were calibrated using the proposed approach.

Characteristic values of geotechnical parameters in Eurocode 7

Lack of harmonisation between reliability-based design and the partial factor method in Eurocode 7 (EN 1997-1:2004) is preventing the widespread introduction of a risk-based concept in geotechnical design. This paper discusses how uncertainties are managed according to EN 1997-1:2004 and possible implications of not harmonising the current safety format with reliability-based design. One of several challenges highlighted is how EN 1997-1:2004 defines the characteristic value and design value. The characteristic value is therein defined based on a classical frequentist approach through a confidence interval. From a Bayesian point of view, the current definition does not treat the characteristic value as an uncertain variable. Consequently, the definitions of the characteristic value and design value in EN 1997-1:2004 feature weak connections between uncertainties in the geotechnical properties and the consequences of failure, as regulated by the target reliability index.

Probabilistic analysis of Improved Austin-Moore stem used in cementless total hip arthroplasty considering loading uncertainty

Austin-Moore hemiarthroplasty had been critically utilized for aged patients with femoral neck fractures. However, this implant became no longer favorable when increasing life activity. A multiobjective shape optimization has been integrated to improve its performance. The resulting configuration is called Improved Austin-Moore (IAM) model. Probabilistic analysis is very important when the input data are random, that leads to stochastic results. In this paper, a probabilistic analysis is applied to solid and IAM stems implanted in a proximal femur in order to show their advantages. This way it is possible to control the biomechanical effects of the implanted femur to determine its performance. The applied loads are generated randomly using Monte Carlo Simulations (MCS). MSC sampling technique is applied and the different von-Mises stresses of the layers (bone and metal) are selected as performance indicators. Two simple 2D implant-bone models of the solid and IAM designs are studied with a target reliability index equals to  3 t , which corresponds to a high level of confidence (reliability) 99.87%. The major finding of this article is that the skewness values of all output parameters of the IAM stem are positive which means that the majority of the maximum von-Mises stress values are closer to their minimum values than those associated with the solid stem. In addition, the sensitivity analysis shows that the input parameters for the IAM stem are more effective on the output parameters relative to those associated with the solid stem. The IAM stem shows a high interdependence (correlation) between the input and output parameters when comparing with the solid stem. Since this study is carried out considering loading uncertainty, the geometry can affect the load transfer. Therefore, a correlation study between the input parameters is carried out and showed significant coefficient values for the IAM stem relative to the solid one. The results show that the IAM stem is much more advantageous than the solid stem.

Fillet welds around circular hollow sections

An experimental and numerical research program was conducted to evaluate the safety of North American design rules for fillet welds around the perimeter of steel circular hollow sections (CHS). This assessment was performed in the context of the current American Institute of Steel Construction (AISC) steel building specification, AISC 360. Specifically, the appropriateness of the fillet weld directional strength-enhancement factor in AISC 360-16 Clause J2.4b was investigated for fillet welds to CHS branches, and the effect of non-uniform connection flexibility on the strength of welds in CHS-to-CHS connections was studied. A total of 24 large-scale, weld-critical experiments were tested, and a further 290 non-linear finite element models were used to parametrically expand the database. It was found that if the directional-strength factor is used, the target reliability (or safety) index prescribed by AISC for connectors, even when the welds are fully effective, is not achieved; hence, a recommendation to prohibit this factor for all fillet welds around the perimeter of CHS is made. With this restriction, it is then shown that AISC 360-16 Clause J2.4a fillet weld design provisions meet AISC’s target safety index for welds in CHS-to-CHS X-connections, where a weld effective length phenomenon exists. It is therefore recommended that AISC advocate 100% weld effective lengths for fillet welds in CHS-to-CHS X-connections, provided that the directional strength-enhancement factor (1.0 + 0.5sin1.5θ) is not used.

Calibration of foundation movements for AASHTO LRFD bridge design specifications

ABSTRACTIn the bridge design specifications of the American Association of State Highway and Transportation Officials using the Load and Resistance Factor Design method, the loads and resulting force effects are given two-letter designations, e.g. “SE” for “force effects due to settlement”. The same two-letter designation is used as a subscript to distinguish load factors, γ, to be applied to loads and other actions acting on the bridge. Thus, the load factor γSE is used to develop factored values of the additional induced force effects such as moments and shears in a bridge structure due to foundation movements. This paper presents the process to calibrate the SE load factor as a function of the target reliability index based on structural service limit states such as cracking in a bridge superstructure. In this process, the target reliability index, uncertainty in predicted movements, and user-specified deterministic tolerable movements are considered in a unified manner. The calibration process can be used for any analytical method and any pattern of movement. The calibration process is demonstrated by an example of immediate settlement for five analytical methods using a dataset based on 20 instrumented spread footings from 10 bridges in the northeast USA.