Reliability-based Design Framework Research Articles

Improving the estimation of soil spatial variability by considering transformation uncertainty based on LDRFE analysis

Transformation uncertainty is an imperative consideration in the process of transforming measurement data to desired design parameters in geotechnical engineering. In the reliability-based design framework, an improved understanding of transformation uncertainty is expected to produce more appropriate design of geotechnical structures. This paper quantifies the site-specific and aleatory transformation uncertainty and investigates how to consider it in estimation of random field parameters through numerically simulated cone penetration tests in spatially variable clay by means of large deformation random finite element analysis. The transformation uncertainty of a transformation model is modelled as a random field. Random field parameters of transformation uncertainty, including the standard deviation, scale of fluctuation and sample path smoothness, are estimated using maximum likelihood estimation along with Whittle-Matérn autocorrelation function model. Random field parameters of predicted shear strength with and without considering transformation uncertainty are thereafter compared with those random field parameters of actual shear strength. Results show that the consideration of transformation uncertainty in the transformation model can considerably improve the prediction accuracy of random field parameters. It is important to consider the spatial correlation structure of transformation uncertainty. This study offers a simple-to-use framework to estimate random field parameters considering the site-specific and aleatory transformation uncertainty.

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.

System Reliability Analysis of Soil Nail Walls against Facing Failures

Abstract The facing design of soil nail walls against flexure, punching shear, and headed-stud tensile limit states has been rarely studied within the reliability-based design framework. This study...

Reliability-based Design Optimization of Laminated Composite Structures under Delamination and Material Property Uncertainties

Delamination is a major type of defects from manufacturing process in laminated composite structures, exhibiting uncertain characteristics which are represented by mixed random variables of continuous in-plane position and delamination size, as well as discrete through-the-thickness position, which should be considered in the design phase of composite structures. Thus, this paper presents a reliability-based design framework for optimal design of composite stacking sequence, for the first time to consider both delamination and material property uncertainties from manufacturing process. Mixed continuous-discrete random variables are involved, and a reliability analysis method is newly proposed to tackle this mixed-variable problem, maintaining high levels of both accuracy and efficiency. The formula of total probability is first employed to formulate the reliability constraint so that discrete and continuous random variables are decoupled; Monte Carlo simulation is then used for reliability analysis with respect to continuous random variables, and a surrogate modelling approach based on Gaussian process regression model is adopted to reduce computation costs. As design variables of ply angles are limited to a discrete set, a genetic algorithm with some proposed improvements is used to handle discrete design variables. Consequently, an optimization framework is devised for composite laminate design under uncertainties from manufacturing process, which is verified via case studies of a cantilever composite plate and can also be extended as a general solution for other composite laminates. With integrated consideration of manufacturing limitations and imperfections as well as structural performances, the presented framework provides a valuable tool in composite structure design.

Assessment and calibration of two models for estimation of soil nail loads and system reliability analysis of soil nails against internal failures

This study first presents accuracy assessments of two default models proposed in two popular soil nail wall design specifications and their calibrated versions for estimation of maximum soil nail loads under operational conditions. The assessments are based on a general nail load database reported in the literature. Evaluation results showed that predictions using the default and calibrated models are unsatisfactory as the dispersions are high to extremely high. Simple calibration terms are introduced to the calibrated models for performance enhancement. The recalibrated models are shown to be accurate on average, and the prediction dispersions are significantly reduced. The model biases for the above six models are demonstrated to be lognormal random variables. Individual reliability-based designs for the nail pullout and nail-in-tension limit states using the six models are carried out. System reliability of nails against internal failures is also explored. The correlation between the two limit states is investigated, and its influences on system reliability evaluation are discussed. The practical value of model calibration is demonstrated as using the recalibrated models for nail designs leads to the most cost-effective design outcomes. This study represents a solid step toward development of reliability-based design framework for soil nail walls.

A scenario optimization approach to reliability-based design

This article introduces a scenario optimization framework for reliability-based design given a set of observations of uncertain parameters. In contrast to traditional methods, scenario optimization makes direct use of the available data thereby eliminating the need for creating a probabilistic model of the uncertainty in the parameters. This feature makes the resulting design exempt from the subjectivity caused by prescribing an uncertainty model from insufficient data. Furthermore, scenario theory enables rigorously bounding the probability of the resulting design satisfying the reliability requirements imposed upon it with respect to additional, unseen observations drawn from the same data-generating-mechanism. This bound, which is non-asymptotic and distribution-free, requires calculating the set of support constraints corresponding to the optimal design. In this paper we propose a framework for seeking such a design and a computationally tractable algorithm for calculating such a set. This information allows determining the degree of stringency that each individual requirement imposes on the optimal design. Furthermore, we propose a chance-constrained optimization technique to eliminate the effect of outliers in the resulting optimal design. The ideas proposed are illustrated by a set of easily reproducible case studies having algebraic limit state functions.

Reliability-based design in rock engineering: Application of Bayesian regression methods to rock strength data

Reliability-based design (RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown (HB) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated HB parameters m and σc, and corresponding predicted axial strength. The results suggest that within- and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile (both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and σc suitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an HB criterion. The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion. These criteria are presented in terms of characteristic parameters mk and σck, the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the HB criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of uncertainty in nonlinear strength criteria is identified.

Variability of overconsolidated soils from Poland in geotechnical practice

AbstractThe advantages of establishing databases of soil parameters are recognized within the geotechnical community. Especially, statistical description of soils is necessary tool for establishing probability distribution functions used in reliability based design framework and in standard deterministic approach of limit state design; previous knowledge, comparable experience, and engineering judgement, all play a major role in the selection process of characteristic values of most essential parameters. This is often done in face of limited amount of data from site investigation. The paper presents preliminary database compilation attempt for some parameters of overconsolidated glacial tills and clays from Poland. Due to a rapid growth of infrastructure and cities, analysis of already gathered data is essential for providing engineers with guidance on the variability of soil conditions, which is most noticeable in the case of fine‐grained overconsolidated strata. Focus is given to parameters obtained from triaxial laboratory tests, including small‐strain shear stiffness obtained from Bender Element Test.

A reliability-based design framework for early stages of design process

The traditional decision-making process during early design stages deals with deterministically evaluating the design candidates in accordance with concrete objectives by assuming optimal or nominal design performance values for the candidates. However, this may increase subjectivity in the decision process since the design knowledge during early design is usually imprecise and incomplete, and mostly needs to be iteratively updated throughout product design development. To diminish the subjectivity, the knowledge of the design requirements can be precisely and accurately represented by means of probabilistic constraints that describe the uncertainties in the design requirements; therefore, in this work, a systematic design framework supported by reliability analysis is developed in such a way that it is able to provide an effective connection among the early design steps especially both at system level and component level. Thus, the probability of failures of the design candidates and their sub-solutions are investigated, based on design constraints with Gaussian distributions, or lower and upper bounds, by utilizing Monte Carlo method. To illustrate the potential applicability and efficacy of the proposed framework, a two-finger gripper design problem is considered. The results clearly demonstrate that the proposed framework is effective to achieve reliable design solutions that have uncertain quantitative characteristics to be used further in probabilistic structural analysis during the next design stages such as embodiment and detail design stages.

Reliability-Based Design of Representative Wing and Tail System Together with Structural Tests

Mostreliability-basedoptimizationstudiesfocusonvariablesthatareavailableinthedesignstage.However,ithas been shown that inclusion of postdesign measures, such as structural tests and health monitoring, can lead to better design choices. More recently, a new reliability-based design framework that can include both predesign and postdesign uncertainty-reduction variables has been proposed in an earlier work. The present study elaborates on that study by including the system reliability considerations. A representative wing and tail system is considered in this study, and the wing and the tail are designed together with their corresponding structural tests. The number of coupon tests, the number of structural element tests, and the additional company knockdown factors for each component are selected as design variables to perform system reliability-based optimization for minimum direct operating cost. It is found that the optimum company knockdown factor for the wing is larger than that of the tail, becauseasmallfractionofthewingmaterialismovedtotailforoptimalreliabilityallocation.Itisalsofoundthatthe optimum number of structural element tests for the wing is larger than or equal to that of the tail. Finally, the optimum number of coupon tests for the wing is found to be smaller than that of the tail.

Development of a Reliability-Based Design Framework for Transmission Line Structure Foundations

This paper presents the reliability-based design (RBD) initiative sponsored by the Electric Power Research Institute for transmission line structure foundations. The role of RBD is presented within the context of geotechnical limit state design. Design parameters that are amenable to statistical description can be propagated systematically to a consistent measure of design risk using reliability techniques such as the first-order reliability method (FORM). Less quantifiable factors are incorporated approximately into RBD by judicious selection of the target reliability level. A simplified RBD approach based on the load and resistance factor design (LRFD) and multiple resistance factor design (MRFD) formats is proposed for practical implementation. The resistance factors for the LRFD and MRFD formats are calibrated rigorously using FORM to produce designs that can achieve a known level of reliability consistently.