Target Reliability Index Research Articles

Composite overwrap repair of pipelines-reliability based design framework

Considering the ages and need for repairment of the gas and oil transmission pipes in the world, in the past years, lab and field experiments were performed on fiber reinforced polymer (FRP) wrapping to steel pipes. Although this technology has widely been employed for decades, further improvement on the design guidelines is still needed. In this context, this study proposes a reliability structural design framework for the repairment of corroded pipelines using FRP composite wrapping. To be consistent with international structural design standards, reliability-based design framework is to be proposed within a semi-probabilistic approach by calibrating safety factors to account for the associated uncertainties in capacity and load effects to best meet the cost-safety balance in design. Currently, the repair design practice for corroded pipelines is based on a deterministic approach, and it cannot ensure the proper consideration of uncertainties and meeting a consistent level of target reliability in design. This study involves comprehensive experiments of FRP materials under two different environmental conditions for onshore and offshore pipes, which were used to propose the best-fit statistical models to the design parameters to realistically represent the random variables in the proposed safety factor based structural design framework. Through extensive reliability analyses, the values for the safety factors for composite and steel have been proposed according to the target reliability indices and the corrosion rate. The proposed design framework for corroded steel pipes with FRP overwrap repairment is expected to improve the current design practice and optimize the cost and safety by meeting the target reliability level.

Sensitivity and Reliability Analyses in to Actively Controlled Structures Under Earthquake

This study aims for a probabilistic assessment of active seismic control of structures in the presence of uncertainties of the structural model and the stochastic model of the ground acceleration. First, sensitivity analyses based on the Borgonovo sensitivity index are conducted to measure the effect of uncertainty sources on the maximum and root mean square (RMS) of the main structural responses in different seismic hazard regions. Then, the reliability analyses are conducted using Monte Carlo simulation (MCS) and importance sampling (IS) methods to the estimation of failure probabilities and reliability indices of the structures in different seismic hazard regions, force capacity of actuators, and seismic performance levels. Numerical studies carried out on a 10-story structure show that the uncertainties in peak ground acceleration (PGA) and story stiffness have the most effects on the seismic responses of the structure. The effect of the considered uncertainties is negligible on the maximum demand control force. The results also show that equipping the structure with an active control system results in a significant reduction in the failure probabilities of the structure. The target reliability index for the uncontrolled structure in life safety seismic performance level may not be satisfied in high and very high seismic hazard regions, it can however be easily dealt with, using the proposed technique, in the corresponding controlled structures. By increasing the control force capacity, an increment is observed in the reliability index. A high and suitable reliability index is given for both controlled and uncontrolled in the collapse prevention seismic performance level.

Analysis Method of Design Strengths of P. edulis Bamboo

In order to determine the design strengths of P. edulis bamboo material, this research carried out a series of material tests on the full-culm P. edulis bamboo specimens, including compression tests parallel to the grain, bending tests, tension tests parallel to the grain, shear tests parallel to the grain and compression tests perpendicular to the grain. The standard values of different strengths for bamboo material were obtained by the Bootstrap method. The influence of the load combination and load effect ratio on the relationship between reliability index β and resistance factor γR was analyzed. A method for calculating the target reliability index of bending strength was proposed. The design strengths of the P. edulis bamboo material were determined and the adjustment method considering different design situations was also put forward. The research results show that the target reliability of the bending strength of bamboo material is suggested to be 3.57. With the same β value, γR is the maximum under the combination of constant load + snow load, and γR is the minimum under the combination of constant load + live load on the office building floor. Under the same load combination and load ratio, the shear strength along the grain has the maximum γR and the compression strength along the grain has the minimum γR. The design strengths of the P. edulis bamboo material were determined by the larger γR of two cases (one is that the load ratio of constant load over live load on the residential building floor is 1.0 and another is that the constant load over live load on the office building floor is 1.0). The design strengths can provide reference for the design and application of bamboo structure.

System-based reliability analysis of stainless steel frames subjected to gravity and wind loads

In the process of developing the next generation of design standards for steel structures, most relevant international structural codes including AISC360, AISC370, AS/NZS4100 and Eurocode3 already incorporate preliminary versions of system-based design-by-analysis approaches that allow a direct evaluation of the strength of steel and stainless steel structures from advanced numerical simulations. As a result, recent research works have focused on building rigorous structural reliability frameworks to investigate acceptable target reliability indices for structural systems and to develop new design methods in conjunction with adequate system safety factors and system resistance factors. Although design recommendations exist for the direct design of hot-rolled and cold-formed steel structures based on advanced finite element analysis, the extension of the method to other materials such as stainless steel is under development. This paper is part of a research effort to build a reliability framework for stainless steel structures subject to different load combinations and presents the results of system reliability calibrations carried out on six stainless steel portal frames subjected to combined gravity and wind loads. The study covers the most common stainless steel families and three international design frameworks (i.e., Eurocode, US and Australian frameworks). From the reliability calibrations derived, suitable system safety factors γM,s and system resistance factors ϕs are proposed for the direct design of stainless steel frames under combined gravity and wind loads using advanced numerical simulations.

Machine learning-based shear capacity prediction and reliability analysis of shear-critical RC beams strengthened with inorganic composites

The application of inorganic composites has proven to be an effective strengthening technique for shear-critical reinforced concrete (RC) beams. However, accurate prediction of the shear capacity of RC beams strengthened with inorganic composites has been a challenging problem due to its complex failure mechanism and the interaction between the internal and external shear reinforcements. Besides, the predictive capabilities of the existing models are not satisfactory. Thus, this research proposed machine learning (ML) based models for predicting the shear capacity of RC beams strengthened in shear with inorganic composites, for the first time, considering all important variables. The results of the analyses evidenced that the proposed ML models can be successfully used to predict the shear capacity of shear-critical RC beams strengthened with inorganic composites. Among the ML models examined herein, the extreme gradient boosting (xgBoost) model showed the highest prediction capability. The comparison among the predictions of the proposed xgBoost and existing models evidenced that the efficacy of the xgBoost model is superior to the existing models in terms of accuracy, safety, and economic aspects. Finally, reliability analysis is performed to calibrate the resistance reduction factors in order to attain target reliability indices of 3.5 and 4.0 for the proposed model.

Reliability-based design of fiber reinforced concrete slabs-on-ground in flexure as per ACI 360

Modern design codes apply the Load and Resistance Factor Design (LRFD) format to account for all uncertainties involved, primarily manufacturing, fabrication, and modeling errors. In this format, load effects are scaled-up by load factors while a resistance factor scales down the resistance. In this way, the LRFD design format ensures that all designs meet, consistently, a certain safety level. To determine the most appropriate factors, a reliability-based procedure is required, in which a target reliability index is selected, which corresponds to an acceptable probability of failure. Unlike most of the American Concrete Institute (ACI) design codes, which adopted the LRFD design format, the current ACI 360R for slabs-on-ground design is based on the concept of safety factors. The present work aims at calibrating the resistance factor,ϕ, for the flexural design of fiber reinforced concrete slabs-on-ground. A total of 56 laboratory tests gathered from previous studies were analyzed to determine the statistical parameters of the resistance model. Then a series of reliability analyses were conducted to calibrate the resistance factor. In the calibration process, dead and live loads with and without impact were considered in the load combinations. This study suggests that for a flexural design of fiber reinforced concrete slabs-on-ground subjected to dead and live (with or without impact) loads, to meet the target reliability index, a resistance factor ϕ = 0.8 is recommended. An example is presented to showcase the application of LRFD for the design of FRC slabs-on-ground.

A New Approach to Symmetry Reliability: Combination of Forward and Inverse Reliability Principle and Its Application to Frame Structures and Bamboo Bridges

Reliability theory is the core basis of engineering design, mainly including forward reliability theory and inverse reliability theory. Forward reliability theory is used to obtain the reliability index using the known design parameters, that is, it is a mapping function that translates the design parameters to the reliability index. Inverse reliability theory is used to obtain the design parameters using the known reliability index, that is, it is a mapping function that translates the reliability index to the design parameters. In other words, forward reliability theory and inverse reliability theory together constitute a method of dual mapping, which is the specific application of symmetry theory in the reliability field. In this paper, a new inverse reliability analysis method is proposed, which can satisfy the requirements of the target reliability index while obtaining the design parameters, without additional calculation and verification of reliability. The method simplifies the reliability inverse problem to the problem of the nonlinear equation, which is solved by identifying the design parameters, and finally obtains the design parameters by iterating the reliability index for each design parameter to gradually approach the target reliability index. For high-dimension and complex problems, the Levenberg–Marquardt method is introduced to avoid the problem of sensitivity to initial values and iterative divergence when identifying the design parameters. The implicit limit state function problem is solved by the interactive operation between ANSYS software and MATLAB software using finite element theory. The accuracy of the proposed method in this paper is verified by several numerical examples, the applicability of the implicit limit state function is verified by a single-story frame structure, and the engineering applicability of the proposed method is demonstrated with a bamboo bridge.

Explainable machine learning model and reliability analysis for flexural capacity prediction of RC beams strengthened in flexure with FRCM

This paper presents a data-driven approach to determine the load and flexural capacities of reinforced concrete (RC) beams strengthened with fabric reinforced cementitious matrix (FRCM) composites in flexure. A total of seven machine learning (ML) models such as kernel ridge regression, K-nearest neighbors, support vector regression, classification and regression trees, random forest, gradient boosted trees, and extreme gradient boosting (xgBoost) are evaluated to propose the best predictive model for FRCM-strengthened beams. Beam geometry, internal steel reinforcement area, FRCM reinforcement area, and mechanical characteristics of concrete, steel, and FRCM are the main input parameters included in the database. Among the studied ML models, the xgBoost model is the most accurate model with the highest coefficient of determination (R2=99.3%) and least root mean square (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). A comparative study of the performance of the proposed and existing analytical models revealed the superior predictive capability and robustness of the proposed model. The predicted flexural and load capacities of the beams based on the existing analytical models are highly scattered and either over-conservative or unsafe. A unified SHapley Additive exPlanations approach is employed to explain the output of the best ML model and identify the most significant input features and interactions that influence the capacity of FRCM-strengthened RC beams in flexure. Furthermore, a reliability analysis is performed to calibrate the resistance reduction factor (ϕ) to achieve a specified target reliability index (βT=3.5).

Reliability analysis of concrete beams reinforced with FRP bars

The strength reduction factors (ϕ) adopted by ACI-440.1R-15 standard code for the flexure design of Fiber Reinforced Polymers Reinforced Concrete (FRP-RC) beams are calibrated in this study. The code calibration process aims to achieve a particular target reliability index (βT) for the selected FRP-RC rectangular beams. An extensive experimental database is collected and used in the calibration process of the resistance factors. It was found that the calibrated ϕ led to a more economical and less conservative design while satisfying the safety requirements imposed by the design code. To meet the βT, a recommended value of ϕ, is found to be 0.70 for cast-in-situ beams failing in compression and 0.65 for tension-controlled cast-in-situ beams. Thus, the proposed values are slightly greater than comparable factors adopted by the ACI code of 0.65 for compressioncontrolled and 0.55 for tension-controlled cast-in-situ beams.

Reliability Calibration of Tower Members in Transmission Line System Crossing High‐Speed Railway

Due to the rapid development of high‐speed railway in China, transmission line systems across the high‐speed railway system have become more prevalent in recent years, which highlights the importance of reliable design for systems. The design is generally based on the structural reliability theory, in which the determination of target reliability level is the key. To determine the reliability level of a transmission line across high‐speed railway, the statistical parameters of load effects and resistances of tower members are derived and reliability calibration of tower elements satisfying the minimum design requirement in Chinese codes is performed by JC method. Furthermore, the reliability level of a transmission line across high‐speed railway is divided into three classes, in which Class 1 is the strongest. According to the calibration results, the minimum target reliability indices are recommended. The results show that the reliability level is similar to the reliability of tower elements in the U.S. but higher than that in Canada. The target reliability indices with values of 3.7, 3.2, and 2.7 are recommended for Class 1, Class 2, and Class 3, respectively.

Reliability-based design optimization of a concrete dam

abstract: Performance and safety of geotechnical structures are affected by uncertainties. Yet, the design of dams is nowadays still made using deterministic methods and design codes. Dam optimization in a deterministic setting may lead to compromised safety margins. In this setting, Reliability-Based Design Optimization (RBDO) appears as an alternative, allowing one to optimize dam performance, but respecting specified reliability constraints. In this paper, we employ an efficient and accurate Single-Loop Approach (SLA) in the RBDO of a concrete dam. Considering dam equilibrium reliability constraints, we find the optimal dam base and optimal placement of drainage galleries, for different dam heights and different target reliability index ( β T). We show how the governing failure mode changes for each optimal solution: for large β T, sliding limit state is the active constraint; for smaller β T values, the eccentricity limit state function is found to be the active constraint for the optimum dam. We also investigate how the importance of random parameters change for each optimum solution: for large β T and failure controlled by sliding, the cohesion and friction angle along dam base interface with foundation rock are the most relevant uncertain parameters for dam equilibrium. For smaller β T with failure controlled by eccentricity, the more relevant uncertain geotechnical parameters are the base length of the dam, the specific weight of concrete, and the coefficient of drainage gallery inefficiency.

Determination of structural reliability of a reinforced concrete slab under fire Load

Four reinforced concrete rooms are used in this study, with varying floor areas, openings, and fuel loads. These rooms are office, Classroom, computer, and chemical laboratories of institutional buildings. The time versus Eurocode (EC) parametric fire relationship is determined and compared with ISO 834 and ASTM 119. The performance of the slab is evaluated based on the EC target reliability index of 3.8 for 50 years design period using the First Order Reliability Method (FORM). The probability of failure and structural reliability of each fire compartment at different fire duration is determined. Variables used were concrete compressive strength, a reduction factor of concrete compressive strength, steel yield strength, concrete cover, slab depth, unit width, and area of steel reinforcement provided. The reliability is determined at each 30 minutes fire duration for all fire compartments. The starting point is ambient temperature, then after every thirty minutes until the time when the maximum gas temperature is reached. The fire compartments were able to show fire resistance for two hours and then started to drop over time. Yield strength reduction factor, concrete cover, and area of reinforcement respectively were the most significant variables to determine the reliability index. The structure was able to withhold fire until two hours with a reliability of more than 3.8after that, the slab reliability was less than the target reliability and will need a repair.

Lateral-Torsional Buckling Research Needs and Validation of an Experimental Setup in the Elastic Range

The AISC Specification Chapter F I-section member flexural resistance equations are a central part of structural steel design in the United States. The provisions of Sections F4 and F5 address general singly and doubly symmetric I-section members. Analytical studies and experimental tests subsequent to the implementation of these provisions within the 2005 AISC Specification suggest that the corresponding inelastic lateral-torsional buckling (LTB) and tension flange yielding (TFY) resistance equations can be improved, resulting in significantly larger predicted strengths in certain cases and somewhat smaller predicted strengths in other cases. Additional large-scale experimental tests, specifically pushing into the inelastic LTB range, need to be conducted to further investigate these predictions. The broad objective of the additional tests is to achieve a target reliability index of b = 2.6 for building design at a live-to-dead load ratio of 3.0 throughout the design space involving all types of statically determinate I-section flexural members. This paper discusses the need for these tests, specifically focusing on the details of how the test fixtures and bracing systems were configured to minimize incidental restraint, which is a critical consideration when conducting flexural experimental testing. The paper discusses the validation of the testing system by comparison of elastic buckling experimental results to analytical and numerical solutions.

Calibration of Load and Resistance Factors for Breakwater Foundation Design. Application on Different Types of Superstructures

Load and resistance factor design is an efficient design approach that provides a system of consistent design solutions. This study aims to determine the load and resistance factors needed for the design of breakwater foundations within a probabilistic framework. In the study, four typical types of Korean breakwaters, namely, rubble mound breakwaters, vertical composite caisson breakwaters, perforated caisson breakwaters, and horizontal composite breakwaters, are investigated. The bearing capacity of breakwater foundations under wave loading conditions is thoroughly examined. Two levels of the target reliability index (RI) of 2.5 and 3.0 are selected to implement the load and resistance factors calibration using Monte Carlo simulations with 100,000 cycles. The normalized resistance factors are found to be lower for the higher target RI as expected. Their ranges are from 0.668 to 0.687 for the target RI of 2.5 and from 0.576 to 0.634 for the target RI of 3.0.

Load & Resistance Factors Calibration for Front Covered Caisson Breakwater

Calibration of load-resistance factors for the limit state design of front covered caisson breakwaters were presented. Reliability analysis of the breakwaters which are constructed in Korean coast was conducted. Then, partial safety factors and load-resistance factors were sequentially calculated according to target reliability index. Load resistance factors were optimized to give one set of factor for limit state design of breakwater. The breakwaters were redesigned by using the optimal load resistance factor and verified whether reliability indices larger than the target value. Finally, load-resistance factors were compared with foreign country’s code for verification.

Effect of randomly dispersed short fibers on the flexural resistance factor of concrete beams reinforced with GFRP bars

Purpose The purpose of this paper is to investigate the potential design advantage in terms of resistance factors for normal weight concrete beams containing moderate-dose randomly dispersed short fibers and reinforced with glass fiber reinforced polymer (GFRP) bars.Design/methodology/approach An analytical model based on the current code specifications is used to calculate the moment capacity of over-reinforced sections. The vast majority of the considered beams are over-reinforced, compression-controlled. The data of the fiber-reinforced concrete (FRC) reinforced with GFRP bars are collected from three published research studies which are based on experimentally tested results. Three different types of short fibers with four volume fractions are considered. Probabilistic model is established to conduct reliability-based calibration using Monte-Carlo Simulation. Limit state function, relevant load and resistance random variables are identified, and adequate statistical parameters are selected. Target reliability index consistent with the one used to develop current design code specifications is used.Findings Reliability analysis and calibration process are carried out with the intention of estimating the flexural resistance factors for FRC beams reinforced with GFRP bars.Originality/value The predicted flexural resistance factors ranged from 0.72 to 0.95, giving the resistance factors the potential to be increased above the currently specified value of 0.65 for compression-controlled members reinforced with FRP bars.

Tropical-cyclone-wind-induced flutter failure analysis of long-span bridges

Continuously growing number and span length of long-span bridges in coastal region of China require a robust aeroelastic design to against the tropical-cyclone (TC) -induced flutter instability. Instead of using the deterministic approach, this study presents a Monte-Carlo-technique-based framework to analyze the flutter reliability of a long-span suspension bridge subjected to TC winds. A limit state function formulated as the difference between the flutter capacity and the extreme gust wind, termed as the product of a random gust factor and the TC mean wind hazard is employed. The flutter fragility curve in terms of the critical wind speed is derived using 2D and 3D flutter analysis models accounting for the structural modal and damping randomness as well as experiment-induced errors of aeroelastic flutter derivatives. The TC wind hazard curves at the height of the bridge deck described as the probability of exceedance at any given years of interest versus the extreme 10-min mean wind speed are estimated through generating a large quantity of synthetic tracks around the bridge site. The probabilistic solutions of the gust factor associated with any gust duration of interest are determined utilizing the statistics of observed TCs coupled with a theoretical model. The TC-induced flutter failure probabilities of present bridge are then predicted in different combinations of gust duration, surface roughness length and flutter analysis models, which enables the assessment of flutter risk subjected to TC winds as compared to code-suggested target reliability indices. The present reliability analysis provides some basic information to assist and enhance the flutter-resistant design of long-span bridges due to TC winds during the preliminary stage.

Time-dependent robustness-based condition assessment of RC bridges subjected to corrosion

At present, the main methods of bridge condition assessment are reliability analysis and analytic hierarchy process method. Robustness, as a measure of the structural ability to maintain the performance after the occurrence of variations, can provide a different perspective based more on the structural property itself. Although robustness has been mainly used in structural design optimization against progressive collapse and extreme events, it can also be used in assessing the condition of bridges with material deterioration. In this paper, a time-varying robustness index model is proposed to quantify the condition of the reinforced concrete bridge girder under corrosion. In this model, the robustness index represents the average performance of the concrete girder in the remaining life. The method is exemplified through a case study of an existing reinforced concrete bridge girder. Combining with the current specification, the robustness index is compared with the reliability analysis results of the girder in the case study. The result shows that when the reliability index drops below the target reliability index, the robustness index descends to Grade 5 specified in the Code for Maintenance of Highway Bridge and Culvers (JTG H11-2004). Both results indicate that the safety of the girder cannot satisfy demand.

Improved design provisions for reinforced concrete block masonry walls under axial compression

The provisions pertaining to design of reinforced masonry (RM) walls under axial compression in the Australian masonry standard AS 3700 (2018 version) have been revised based on the recent findings that the lateral restraining ties do not significantly affect the performance under axial compression. The other design codes such as Canadian (CSA S304.1-14), American (MJSC) and previous version of Australian (AS 3700-2011) standards consider the RM walls as unreinforced masonry (URM) under axial compression, if they are not restrained with lateral ties in both directions. However, it is widely believed that these provisions are stringent and over-conservative, as proven by the experimental studies that the compression bars in RM are effectively restrained by the surrounding well compacted grout. Hitherto, no systematic studies have been carried out to determine the applicability of these provisions to the reliability of the compression design approaches of RM walls. Therefore, in this research an attempt has been made to evaluate the accuracy and reliability of the design provisions outlined in the selected design standards (AS 3700, CSA S304.1-14 and MSJC). The experimental database generated in the authors’ previous study was used to verify the reliability of the design provisions. The reliabilities of the design expressions were verified using the first-order reliability method (FORM). The reliability analyses revealed that the provisions specified in the standards are quite conservative as they have exceeded the target reliability index of 3.6 for the analysed RM walls. The current provisions of AS 3700 (2018 version) have shown to predict the axial capacities of the walls better than other standards, while satisfying the target reliability limit. Thus, it can be stated that revisions made in AS 3700 (2018 version) are effective and economical for designing the RM walls as they have eased the requirement of lateral restrainers and account for a realistic contribution of grout and compression steel strengths in determining the axial capacity.

Reliability-Based Design of Driven Piles Considering Setup Effects

The total ultimate resistance (or bearing capacity) of driven piles considering setup effects is composed of initial ultimate resistance and setup resistance, and the setup effects of driven piles are mainly reflected by the setup resistance. In literature, a logarithmic empirical formula is generally used to quantify the setup effects of driven piles. This paper proposes an increase factor (Msetup) to modify the resistance factor and factor of safety calculation formula in accordance with the load and resistance factor design (LFRD) principle; here, the increase factor is defined as the ratio of the setup resistance (Rsetup) to the initial ultimate resistance (R0) of driven piles. Meanwhile, the correlation between R0 and Rsetup is fully considered in the resistance factor and factor of safety calculation. Finally, the influence of four key parameters (ratio of dead load to live load ρ = QD/QL, target reliability index βT, Msetup, correlation coefficient between R0 and Rsetup, ρR0,Rsetup) on the resistance factor and factor of safety are analyzed. Parametric research shows that ρ has basically no effect on the resistance factor, which can be taken as a constant in further research, and ρ has a significant influence on the factor of safety. The value of Msetup has almost no effect on the resistance factor and factor of safety. However, βT and ρR0,Rsetup have a significant influence on the resistance factor and factor of safety, so the value selection of βT and ρR0,Rsetup are crucial for reliability-based design of driven piles. Through this study, it is concluded that considering setup effects in reliability-based design of driven piles will greatly improve the prediction for design capacity.