Target Reliability Index Research Articles

Safety Factors for the Resistance of Steel Sections

The performance of the design equations given in the Australian Bridge and Steel Standards AS 5100.6 and AS 4100 have been evaluated when structural steel is used that conforms with the tolerances within the following overseas manufacturing standards: EN 10034, KS D 3502, JIS F 3192, JIS A 5526, ASTM A6/A6M-07 and AS/NZS 5100.6. From a consideration of the experimental results from full-scale bending tests, reliability analyses according to AS 5104:2005/IS0 2394:1998 and EN 1990 were conducted. From these analyses, a capacity factor of between 0.93 and 0.95 was determined for beams that have compact, not-compact and non-compact cross-sections when a target reliability index of 3.04 was used, based on the standardised FORM (first order reliability method) sensitivity factor for resistance given in AS 5104:2005/IS0 2394:1998. This finding demonstrates that the capacity factor of 0.90 given in AS 4100 and AS 5100.6 for beams in bending is on the conservative side for steel sections complying with overseas manufacturing standards, and supports the design practice that has been adopted in NZS 3404.1 for the last 35 years.

Safety factors for the resistance of steel sections

AbstractThe performance of the design equations given in the Australian Bridge and Steel Standards AS 5100.6 and AS 4100 have been evaluated when structural steel is used that conforms with the tolerances within the following overseas manufacturing standards: EN 10034, KS D 3502, JIS F 3192, JIS A 5526, ASTM A6/A6M-07 and AS/NZS 5100.6. From a consideration of the experimental results from full-scale bending tests, reliability analyses according to AS 5104:2005/IS0 2394:1998 and EN 1990 were conducted. From these analyses, a capacity factor of between 0.93 and 0.95 was determined for beams that have compact, not-compact and non-compact cross-sections when a target reliability index of 3.04 was used, based on the standardised FORM (first order reliability method) sensitivity factor for resistance given in AS 5104:2005/IS0 2394:1998. This finding demonstrates that the capacity factor of 0.90 given in AS 4100 and AS 5100.6 for beams in bending is on the conservative side for steel sections complying with ove...

Reliability analysis of intermediate crack-induced debonding failure in FRP-strengthened concrete members

This paper presents a study on the reliability analysis of intermediate crack-induced (IC) debonding failure, which is a dominant failure mode in concrete members strengthened with externally bonded fibre-reinforced polymer composites. First, the probabilistic characteristics of the model uncertainties for several typical IC debonding models are evaluated and presented, based on a comprehensive test database that contained 217 specimens that experienced IC debonding failure. Second, a Monte Carlo simulation analysis is performed to examine the variability in the IC debonding resistance considering the scatterness of different design variables. Subsequently, the reliability index is estimated by utilising the reliability analysis method, first-order reliability method, for each design case. The effect of each design variable on the average reliability index is examined. Finally, reduction factors for the investigated IC debonding models are calibrated based on the reliability analysis with the aim of meeting a target reliability index of 3.5.

Simplified Reliability-Based Design of Wall Displacements for Excavations in Soft Clay Considering Cross Walls

AbstractThis study proposes a simplified reliability-based design (RBD) method for the serviceability limit state (SLS) of excavations considering cross walls. Although the effects of cross walls are highlighted, the proposed method is applicable to cases without cross walls. In the proposed RBD method, partial factors are calibrated using rigorous reliability theory to meet the target reliability index. A design example is used to illustrate the use of calibrated partial factors and to demonstrate the effectiveness of cross walls.

Evaluation of Reliability Index of Governing Load Combination for Design of Cable Supported Bridge Members

Abstract In this paper the reliability analyses of the cable-supported bridge design code which is recently issued in Korea are performed and the results are presented. Governing load combinations for the member design and the statistical properties of the main members are introduced and the analysis is performed using an example cable-stayed bridge for which the design is performed following the load and resistance factors defined in the design code. The reliability analysis shows the target reliability index can be achieved by applying load and resistance factors and the application of the resistance modification factor can enhance the reliability level if the importance of the bridge needs to be increased. The sensitivity analysis reveals that decreasing uncertainty of the cable strength is critical for obtaining the target reliability index. The study results show that the design using the load and resistance factors of the code can achieve the target reliability indexes for the design of cable supported bridge.

Calibration of model uncertainties in base heave stability for wide excavations in clay

In this study, the statistical properties for the model factor [the ratio of actual factor of safety (FS) to the calculated FS] of three popular base heave calculation methods are calibrated based on real case histories with wide excavation. The statistical properties of concern include the mean value and coefficient of variation (COV) of the model factor. It is found that the mean values of the model factors for the modified Terzaghi׳s and Bjerrum-Eide׳s methods are close to 1, whereas that for the slip circle method is significantly greater than 1. The COVs associated with the modified Terzaghi׳s and Bjerrum-Eide׳s methods are relatively low, while that associated with the slip circle method is relatively high. Based on the calibration results, reliability-based design charts are provided. It is concluded that the required factor of safety (FS) depends on two factors: (a) the target reliability index and (b) the COV of the calculated FS. For the case where this COV=10%, the required FS in codes for the modified Terzaghi׳s and slip circle methods (FS=1.5 and 1.2, respectively) seems reasonable. In contrast, the required FS for Bjerrum-Eide׳s method (FS=1.2) seems insufficient.

Assessment of the structural reliability of loadbearing concrete masonry designed to the Canadian Standard S304.1

A structural reliability analysis was performed on concrete masonry under axial compression using the First Order Reliability Method (FORM) to assess the reliability levels under the current (2004) and preceding (1994) editions of the Canadian masonry design standard S304.1. The Hasofer–Lind reliability index was evaluated at different live-to-dead load and snow-to-dead load ratios using the Rackwitz–Fiessler procedure. The reliability analysis revealed that neither the masonry material resistance factor of 0.6 adopted in the current Canadian masonry design standard (S304.1-04) nor the previous value of 0.55 in its predecessor (S304.1-94) achieve acceptable reliability levels for masonry in compression under combined dead and live or snow loads. Reliability levels close to the target reliability index recommended by the Canadian standard S408-11 and the levels evaluated for concrete in compression designed to the Canadian standard A23.3-04 were achieved when a masonry material resistance factor of 0.5 was used.

Target Reliability Levels in Present Standards

Abstract The target reliability levels recommended in national and international documents vary within a broad range, while the reference to relevant costs and failure consequences is mentioned only very vaguely. In some documents the target reliability index is indicated for one or two reference periods (1 year, 50 years or life-time) without providing appropriate links to the design working life. This contribution attempts to clarify the relationship between the target reliability levels, costs of safety measures, failure consequences, reference periods and the design working life

하한지지력이 현장타설말뚝의 저항계수에 미치는 영향

한계상태설계법의 하나인 하중저항계수설계법의 이용이 북미를 중심으로 점차 확산되고 있는 가운데, 국내에서도 이에 대한 연구가 활발하게 진행되고 있다. 하지만, 국내에서는 자료가 충분히 확보되지 못하여 기초구조물의 설계에 AASHTO에서 제안한 저항계수를 설계에 이용하고 있다. AASHTO에서 제안하고 있는 저항계수는 북미에 보편적으로 존재하는 암반조건을 이용하여 결정된 저항계수로서, 국내지반에 적합한 저항계수를 독자적으로 개발할 필요가 있다. 또한, 기존의 신뢰성 분석 기법에서는 하중저항계수를 결정할 때, 저항의 최소값을 0으로 가정하는 일반적인 대수정규 분포를 이용하기 때문에, 이로부터 산정한 파괴확률은 비현실적이라고 알려져 있다. 따라서, 이를 개선하기 위하여 저항계수를 산정할 때 저항의 하한값이 0이 아닌, 현실적으로 의미가 있는 하한지지력을 이용하는 방법이 최근에 고안되었다. 따라서, 본 연구에서는 국내에서 수행된 현장타설말뚝 13본에 대한 재하시험자료를 면밀히 분석하여 저항계수를 산정한 다음, 현실성 있는 하한지지력을 산정하여 저항계수 값을 보정하였다. 그 결과, 목표신뢰도지수가 3.0일때, 기존의 신뢰성 분석 기법으로부터 산정된 주면저항계수와 선단저항계수는 각각 0.13-0.32, 0.19-0.29 이었으며, 하한지지력을 보정하여 구한 주면저항계수와 선단저항계수는 Carter & Kulhawy 공식의 경우 각각 8%와 13% 증가하였다. Load and Resistance Factor Design (LRFD) is one of the limit state design methods, and has been used worldwide, especially in North America. Also, the study for LRFD has been actively conducted in Korea. However, the data for LRFD in Korea were not sufficient, so resistance factors suggested by AASTTO have been used for the design in Korea. But the resistance factors suggested by AASHTO represent the characteristics of bedrocks defined in the US, therefore, it is necessary to determine the resistance factors for designs in Korea, which can reflect the characteristics of bedrocks in Korea. Also, the calculated probabilities of failure from conventional reliability analyses which commonly use log-normal distribution are not realistic because of the lower tail that can be extended to zero. Therefore, it is necessary to calibrate the resistance factors considering the lower-bound resistance. Thus, this study calculates the resistance factors using thirteen sets of drilled shaft load test results, and then calibrates the resistance factors considering the lower-bound resistance corresponding to a target reliability index of 3.0. As a result, resistance factors from conventional reliability analyses were determined in the range of 0.13-0.32 for the shaft resistance, and 0.19-0.29 for the base resistance, respectively. Also, the lower bounds of resistance were determined based on the Hoek-Brown failure criteria (2002) and GSI downgrading. Considering the lower-bound resistances, resistance factors increased by 0~8% for the shaft, and 0~13% for the base, respectively.

Gradient-based design robustness measure for robust geotechnical design

This paper presents a gradient-based robustness measure for robust geotechnical design (RGD) that considers safety, design robustness, and cost efficiency simultaneously. In the context of robust design, a design is deemed robust if the system response of concern is insensitive, to a certain degree, to the variation of noise factors (i.e., uncertain geotechnical parameters, loading parameters, construction variation, and model biases or errors). The key to a robust design is a quantifiable robustness measure with which the robust design optimization can be effectively and efficiently implemented. Based on the developed gradient-based robustness measure, a robust design optimization framework is proposed. In this framework, the design (safety) constraint is analyzed using advanced first-order second-moment (AFOSM) method, considering the variation in the noise factors. The design robustness, in terms of sensitivity index (SI), is evaluated using the normalized gradient of the system response to the noise factors, which can be efficiently computed from the by-product of AFOSM analysis. Within the proposed framework, robust design optimization is performed with two objectives, design robustness and cost efficiency, while the design (safety) constraint is satisfied by meeting a target reliability index. Generally, cost efficiency and design robustness are conflicting objectives and the robust design optimization yields a Pareto front, which reveals a tradeoff between the two objectives. Through an illustrative example of a shallow foundation design, the effectiveness and significance of this new robust design approach is demonstrated.

Serviceability limit state design of deep foundations

Although the settlement of deep foundations (piles) is not generally a concern if the piles are driven to refusal, settlement can become a design issue if no stiff substratum is encountered. This paper investigates the reliability-based design factors required for the serviceability limit state design of deep foundations. The goals of the paper are first to develop a probabilistic deep foundation model, which includes the effects of spatial variability and which is validated by simulation, and second to recommend the geotechnical resistance factors required to achieve specified target reliability indices against excessive settlement of deep foundations.

Reliability of corroded thin walled pipes repaired with composite overwrap

Current design codes provide two design methods: allowable stress/strain design and limit state design. Design in the current pipework composite repair codes is based on the allowable design method and only two safety factors are applied to the ultimate strain of the composite layer and to the yield stress of steel. On the other hand, safety factors are applied to each of the load and resistance parameters in the limit state design method. The limit state design method is probabilistic based in which the safety factors are calibrated based on a target reliability index. In this study, an investigation into the reliability of rehabilitated pipelines is conducted. The limit state function is defined based on ASME PCC-2, and reliability analysis is conducted using the AFOSM method. Results show that ASME PCC-2 generally provides adequate safety although the level of safety is not uniform for different percentages of corrosion. Comparing the achieved results and the ISO 2394 target reliability indices, some resistance factors are proposed.

To Confirm Structural Coefficient for Design of Penstocks in Hydropower Stations by Partial Factors-Based Method

When confirming the partial factors in design formulas by the probability-based limit states design method (PLSDM), the structural coefficient can determined by two methods. On one hand, the structural coefficient is determined by the engineering experience calibration method, which is calculated by decomposition of the safety coefficient in the former specifications SD144-85. On the other hand, it can be determined by the probability analysis method and optimization calculation based on the target reliability index resulted from reliability calibration analysis. The appropriate value is finally determined by synthesizing results of the two methods.

Reliability based topology optimization for continuum structures with local failure constraints

This paper presents an effective method for stress constrained topology optimization problems under load and material uncertainties. Based on the Performance Measure Approach (PMA), the optimization problem is formulated as to minimize the objective function under a large number of (stress-related) target performance constraints. In order to overcome the stress singularity phenomenon caused by the combined stress and reliability constraints, a reduction strategy on target reliability index is proposed and utilized together with the ε-relaxation approach. Meanwhile, an enhanced aggregation method is employed to aggregate the selected active constraints using a general K–S function, which avoids expensive computational cost from the large-scale nature of local failure constraints. Several numerical examples are given to demonstrate the validity of the present method.

Analysis of the Implied Reliability Index and Load and Resistance Coefficients for China’s Current Highway Bridge Load-Carrying Capacity Evaluation Code

China’s current load-carrying capacity evaluation code for highway bridges is a semi reliability-based code. The reliability level of the code is analyzed through a comparative study, and methods used to update the reliability level of this code are specified in this paper. A formula to calculate the implied reliability index is proposed and verified by comparison with calibrated reliability indexes in design codes. Then the formula is used to calculate the implied reliability index with statistical parameters derived from the load and resistance coefficients in the current code. It is proposed that the implied reliability index should be adjusted by considering historical failure rates. Different criteria used to define historical failure rates of highway bridges are discussed. In addition, the paper compares the reliability level, applicability, evaluation frequency, target reliability indexes, and resistance and load coefficients between AASHTO and China’s current code. The paper would serve as a reference for the upcoming research on the updating of current highway bridge Load-carrying capacity evaluation code.

Optimization design of piles subjected to horizontal loads based on reliability theory

Based on reliability theory, a general method for the optimization design of piles subjected to horizontal loads is presented. This method takes into consideration various uncertainties caused by pile installation, variability of geotechnical materials from one location to another, and so on. It also deals with behavior and side constraints specified by standard specifications for piles. To more accurately solve the optimization design model, the first order reliability method is employed. The results from the numerical example indicate that the target reliability index has significant influence on design parameters. In addition, the optimization weight increases with the target reliability index. Especially when the target reliability index is relatively large, the target reliability index has significant influence on design weight of piles.

Development of serviceability limit state design criteria for stresses in prestressed concrete girders

The objective of this paper is to perform the reliability analysis of stresses in prestressed concrete girders and development of design criteria for serviceability limit state design. Limit state functions for Serviceability Limit State (SLS) for compressive and tensile stresses at initial and service load stages are formulated based on fundamental design principles in the code. To establish statistical characteristics of concrete tension strength, two kinds of cylinder test, splitting tension tests and bending tension tests are performed for various specified strength of concrete. Other statistical characteristics for other variables such as live load, prestress forces, girder dimensions, and etc. are collected from related studies and references. Reliability indices are calculated for actually designed section and minimum section conformed with design requirement of typical prestressed concrete I-shaped girder and box type girder using first-order reliability method. Results are compared with reliability level of Ultimate Limit States (ULS) and target reliability indices of international standards. Finally, the live load factors in load combination for tensile stresses in prestressed concrete girder are proposed.

Determination of New Load and Resistance Factors for Reinforced Concrete Structural Members

In this study, a procedure for the determination of new load and resistance factors for reinforced concrete structural members is proposed in view of the fact that the design practice in Turkey has changed after the occurrence of major earthquakes. The implementation of the procedure is carried out for the shear failure mode of reinforced concrete beams subjected to dead and live load combination. First, the statistical parameters for the quantification of uncertainty involved in the design variables, modeling and loads are assessed based on the available data and knowledge. Then, the level of risk related with the current design practice is quantified in terms of the reliability index, β. Target reliability index βT, is selected in view of the β values computed for the current design practice. By using the resulting target reliability index βT, the load and resistance factors are computed based on the Advanced First Order Second Moment Method.

Partial safety factors for retaining walls and slopes: A reliability based approach

Uncertainties in design variables and design equations have a significant impact on the safety of geotechnical structures like retaining walls and slopes. This paper presents a possible framework for obtaining the partial safety factors based on reliability approach for different random variables affecting the stability of a reinforced concrete cantilever retaining wall and a slope under static loading conditions. Reliability analysis is carried out by Mean First Order Second Moment Method, Point Estimate Method, Monte Carlo Simulation and Response Surface Methodology. A target reliability index <TEX>${\beta}$</TEX> = 3 is set and partial safety factors for each random variable are calculated based on different coefficient of variations of the random variables. The study shows that although deterministic analysis reveals a safety factor greater than 1.5 which is considered to be safe in conventional approach, reliability analysis indicates quite high failure probability due to variation of soil properties. The results also reveal that a higher factor of safety is required for internal friction angle <TEX>${\varphi}$</TEX>, while almost negligible values of safety factors are required for soil unit weight <TEX>${\gamma}$</TEX> in case of cantilever retaining wall and soil unit weight <TEX>${\gamma}$</TEX> and cohesion c in case of slope. Importance of partial safety factors is shown by analyzing two simple geotechnical structures. However, it can be applied for any complex system to achieve economization.

한계상태설계를 위한 단일 쇄석다짐말뚝의 목표신뢰도지수

목표신뢰도지수는 한계상태설계법에서 안전여유의 지표가 되며, 부분계수를 결정하는데 있어 매우 중요한 역할을 한다. 본 연구에서는 한계상태설계법에서 필요로 하는 목표신뢰도지수의 결정을 위하여 쇄석다짐말뚝이 적용된 6개소의 설계-시공사례를 조사하였다. 쇄석다짐말뚝의 주요 파괴모드인 팽창파괴에 대한 한계상태함수를 정의하고, 일계신뢰성해석법(FORM)을 이용하여 극한지지력, 이론식별, 신뢰도수준을 평가하였다. 현행 쇄석다짐말뚝의 신뢰도지수는 허용응력설계법에 의해 산정된 안전율과 비례하는 경향을 보였으며, 평균 신뢰도지수는<TEX>${\beta}$</TEX>=2.30으로 평가되었다. 신뢰성해석에 의해 평가된 신뢰도 수준과 기존 구조물 기초에 대한 목표신뢰도지수를 비교 분석한바, 쇄석다짐말뚝 기초는 말뚝기초 및 얕은기초에 비하여 비교적 낮은 안정성 수준이 요구되며, 쇄석다짐말뚝의 현재 신뢰도수준은 보강토옹벽, 쏘일네일링에서 제안된 목표신뢰도지수와 유사한 범위를 보이므로 쇄석다짐말뚝의 목표신뢰도지수를 <TEX>${\beta}_T$</TEX>= 2.33으로 제안하였다. Target reliability index in the limit state design indicated the safety margin and it is important to determine the partial factor. To determine the target reliability index which is needed in the limit state design, the six design and construction case histories of gravel compaction piles (GCP) were investigated. The limit state functions were defined by bulging failure for the major failure mode of GCP. The reliability analysis were performed using the first order reliability method (FORM) and the reliability index was calculated for each ultimate bearing capacity formulation. The reliability index of GCP tended to be penportional to the safety factor of allowable stress design and average value was <TEX>${\beta}$</TEX>=2.30. Reliability level that was assessed by reliability analysis and target reliability index for existing structure foundations were compared and analyzed. As a result, The GCP was required a relatively low level of safety compared with deep and shallow foundations and the currd t reliability level were similar to the target reliability in the reinforced earth retaining-wall and soil-nailing. Therefore the target reliability index of GCP suggested as <TEX>${\beta}_T$</TEX>=2.33 by various literatures together with the computed reliability level in this study.