Reliability-based Design Method Research Articles

Reliability-based design approach for high-rise buildings subject to earthquakes and strong winds

Current design specifications often deal with seismic and wind events in isolation, which may underestimate the failure probability. In this paper, a reliability-based approach is presented to compute the load modification factor for designing high-rise buildings in regions prone to earthquake and strong wind events. The paper illustrates the proposed procedure from the construction of hazard models to load modification calculations, which is implemented in a 42-story steel frame-reinforced concrete (RC) core tube building located in the Dali region, southwest of China. The uncertainties associated with hazard models, material properties, input loads, demand models and structural capacity are considered to improve the accuracy of failure probability estimations. The effects of individual and concurrent earthquakes and strong winds are accounted for in the reliability-based design method. Then, the load modification factor is determined by comparing the calculated failure probability with the rational target value. Finally, a suggested combined factor will be used to modify the value of the design wind load in the limit state function. More work is needed before load modification can be applied in practice. However, this study offers a practical and extensible approach to improve the future calibration of load combination criteria for designing high-performance structures against various hazards.

The Reliability-Based Design Optimization of considering Rock-Support Interaction for Rock Tunnels

Uncertainty is critical to the tunnel design. In this study, a novel reliability-based design (RBD) method was developed by integrating the rock-support interaction and its uncertainties for rock tunnels. In this method, the rock-support interactions were analyzed based on a convergence-confinement method. Uncertainties were estimated by reliability analysis using Excel Solver. Chaotic particle swarm optimization (CPSO) was adopted to search the optimal tunnel design parameters based on the rock-support interaction analysis. The proposed method for estimating the reliability index and determining the tunnel support parameters was introduced in detail. To illustrate the proposed method, it was applied to two tunnels with rock-bolt and combined support systems. The results indicated that the method could obtain accurate solutions with a dramatically improved computing efficiency, guaranteeing the tunnel stability at the same time. The developed method provides an excellent way to deal with the uncertainty in tunnel design. It was proved to be an efficient and effective method for the support designs of rock tunnels.

A Safety Factor Method for Reliability-Based Component Design

Abstract Reliability-based design (RBD) employs optimization to identify design variables that satisfy the reliability requirement. For many routine component design jobs that do not need optimization, however, RBD may not be applicable, especially for those design jobs which are performed manually or with a spreadsheet. This work develops a modified RBD approach to component design so that the reliability target can be achieved by conducting traditional component design repeatedly using a deterministic safety factor. The new component design is based on the first-order reliability method (FORM), which iteratively assigns the safety factor during the design process until the reliability requirement is satisfied. In addition to several iterations of deterministic component design, the other additional work is the calculation of the derivatives of the design margin with respect to the random input variables. The proposed method can be used for a wide range of component design applications. For example, if a deterministic component design is performed manually or with a spreadsheet, so is the reliability-based component design. Three examples are used to demonstrate the practicality of the new design method.

Comparison of Reliability Based Design (RBD) With Eurocode 2 for A Singly Reinforced Concrete Beam

This research compares the Reliability-Based Design (RBD) method with the Eurocode 2 (EC2) for a singly reinforced concrete beam. Advanced First Order Second Moment (AFOSM) was used and the equation for the ultimate limit state design consideration for Moment of resistance and Applied moment was applied. The parameters which were all functions of the Ultimate load, G were replaced respectively with variables and their derivatives G(x) obtained with being the characteristic strengths of concrete and the yield stress of steel respectively. Given the original vector space and the transformed reduced vector space, the Taylor series was used to expand the reduced vector space and thus reliability index ßx expressed. The procedure was then coded using JAVA to produce the Reliability Index and Probability of failure for respective steel ratio. The required probability index of 3.9 corresponds to 0.048% of the steel ratio. Typical analysis of a singly reinforced beam according to EC2 for b=300mm, h=500mm, d=447mm, cover of 40 mm, gave a steel ratio of 1.31 %. Comparing this to the reliability-based design of 0.048%, the code provision exceeded the RBD output by 2000 times and 63 times the minimum reinforcement requirement by the code.

A novel reliability-based design method based on quantile-based first-order second-moment

Quantile-based first-order second-moment method is a novel reliability analysis method proposed by the authors that is with simplicity and efficiency close to the first-order second-moment method, yet with accuracy and robustness close to the first-order reliability method. However, the quantile-based first-order second-moment method is inefficient if directly applied to reliability-based design. The novelty of the current short communication is to re-formulate the quantile-based first-order second-moment method into inverse-reliability methods to enhance computational efficiency. Two inverse-reliability methods are proposed based on this re-formulation. One is more practical, whereas the other is often more efficient. The effectiveness of the proposed methods is illustrated by a friction pile design example and a spread footing design example for the National Geotechnical Experimentation Sites at Texas A&M University.

Reliability-Based Design for Passing Maneuvers Based on Observational Data

Two-lane roadways constitute the largest proportion of road networks. Their operational characteristics are significantly different from other road classifications. Allowing passing maneuvers is considered as one of the effective measures to improve mobility levels along two-lane highways, while crash records show that head-on collisions, which usually are attributed to passing maneuvers, are among the most common and most severe types of crashes on two-lane roadways. Therefore, rational and realistic estimation of the needed passing sight distance (PSD) considering driver behavior is essential for the safe design of passing zones along two-lane highways. Several random variables help to determine the minimum length required for safe passing maneuvers. Current PSD models are based on single deterministic values of the input variables to determine PSD values. This paper presents a reliability model PSD that accounts for the variability of the input random variables to offer a better representation of real-life conditions. The objectives of this paper are: (1) to design driving simulator and field experiments for data collection, (2) to develop a PSD model using the mechanics of passing maneuvers, (3) to develop a reliability model based on the first-order second-moment (FOSM) method, and (4) to validate the model using Monte Carlo simulation. In this study, driving simulator experiments were conducted to determine the passing behavior of drivers, and field data were used to validate the proposed PSD model. The proposed model accounts for the variability in the parameters by using the mean and standard deviation in a closed form estimation method. The analysis was performed for a design speed of 80 km/h, and the corresponding PSD distribution was established. A comparison of the results of the proposed model, which reflects driver behavior, and those of existing models was presented. Using the reliability-based design method, transportation engineers can adjust the PSD to fulfill a desired probability of non-compliance.

Discussion and application of a risk assessment method for spalling damage in a deep hard-rock tunnel

Abstract Quantitative risk assessment of spalling damage needs to address three key tasks: risk probability estimation, loss estimation and risk level determination. Here, based on uncertainty analysis of the damage initiation and spalling limit method, a general risk assessment method for spalling damage in hard-rock tunnels is proposed. First, with a reliability-based design method, a probability reliability estimation model for spalling damage depth was established to determine the probability of roof and wall spalling damage based on the stochastic response surface of the Hermite polynomial chaos expansion. Second, the direct economic loss due to damage was calculated by using the spalling damage depth of a unit length tunnel section and the average loss cost; thus, the risk estimation of spalling damage was carried out. Last, a theoretical analytical formula for the spalling damage expected cost ratio was derived to determine probability level thresholds, and the risk grading criteria were calculated. The method was applied to the case of the Canadian deep geologic repository project for low- and intermediate-level nuclear waste. The risk levels of roof spalling damage, wall spalling damage and both types of spalling damage were obtained, and the influences of the commonly used empirical formula for depth estimation, the coefficient of variation and the correlation coefficients of random variables on the estimated probability of spalling damage depth were analysed. The method was shown to be feasible for accurate risk assessment of spalling damage, and the results can be used to guide dynamic risk prevention and control and to support design optimization for hard-rock tunnel construction.

Decoupled reliability-based geotechnical design of deep excavations of soil with spatial variability

This paper presents a general decoupled method for reliability-based geotechnical design that takes into account the spatial variability of soil properties. In this method, reliability analyses that require a lot of computational resources are decoupled from the optimization procedure by approximating the failure probability function globally. Failure samples are iteratively generated over the entire design space so that their global distribution information can be extracted to construct the failure probability function. The method is computationally efficient, is flexible to implement, and is well suited for geotechnical problems that may involve sophisticated models. A design example of two-dimensional deep excavation against basal heave is discussed for Singapore marine clay where the density and normalized undrained shear strength of soil mass are modeled as random fields. Results demonstrate that the proposed method works well in practice and is advantageous over the coupled or locally decoupled reliability-based geotechnical design methods.

Reliability-based shear design of corrugated web steel beams for AISC 360 specification and CSA-S16 standard

The available literature on the shear strength of corrugated web steel beams (CWSBs) includes a wealth of methods that specify the nominal buckling capacity, but with no consideration of reliability-based design. In the framework of Load and Resistance Factor Design (LRFD) codes, the design of steel members requires load factors to amplify the load effect and a resistance factor to scale-down the resistance based on a target reliability index. Therefore, for full integration of the shear design of CWSBs into the current design codes, resistance factors must be developed and calibrated for use within the LRFD context. This is crucial since the use of existing resistance factors that were specifically developed for welded plate girders for the design of CWSBs may lead to a level of safety that is not consistent with the philosophy of the code. Using a curated database of test results, the present paper attempts to address the lack of a reliability-based design method specific to CWSBs. Two North American design standards were selected in this study, namely, AISC 360 and CSA-S16. A series of reliability analyses are performed first to verify the consistency of reliability indices for welded plate girders designed following the two standards. Then, a probabilistic-based approach is used to calibrate the resistance factors for the shear limit state of CWSBs in accordance with the AISC 360 and CSA-S16 considering dead, live, wind, and snow loads. Finally, an iterative step-by-step procedure is then developed within the LRFD framework to aid in the design of corrugated webs to resist shear loads at ultimate. Findings of the study showed that the current AISC 360 resistance factor for welded plate girders when used for the shear design for CWSB, does not yield a safety level that is consistent with the target reliability; thus, a new factor equal to 0.85 is proposed. For CSA-S16, the current resistance factor of 0.90 for welded plate girders is found to be appropriate for corrugated web steel beams.

Reliability Analysis of Bearing Capacity of Shallow Foundation on c- φ Soil

Bearing capacity of shallow foundation is a challenging problem for geotechnical engineers. The difficulty comes from multiple sources of uncertainty. Only the uncertainties in Soil properties; unit weight (γ), cohesion(c), and angle of friction (φ) are taken in this study. The Reliability Based Design method is used for the assessment of bearing capacity of shallow foundation by First-and second-order approximation using Taylor’s series expansion and Mathcad Computer program which provide systematic analysis of uncertainties and allow the designer how reliable are their designs. The Terzaghi Bearing capacity equation is used for the analysis along with the certain range of variability (CV %) associated with the variables. For the reliability analysis, to become more realistic two real cases of shallow foundation on c-φ soil has been taken as a sample case.

Reliability based design method for buckling of steel columns in fire

Purpose This paper aims to reliability analysis of axially loaded steel columns at elevated temperatures considering the probabilistic features of fire. Design/methodology/approach The response function used in the reliability analysis is based on the non-linear FEM calculations. The stochastic variability of temperature is integrated with the procedure similar to the parameters of loading and material properties. Direct Monte Carlo simulations (MCSs) are implemented for probabilistic analysis. Computational costs are reduced by polynomial approximation of the response function of the column. Findings A design method for practical applications in the common Eurocode format is proposed. The proposed method can be used to estimate the failure probability of a steel column in fire conditions. If standard reliability criteria are applied, the results of the steel column buckling capacity in the fire according to the proposed procedure deviate from the Eurocode results in certain parameter ranges. Originality/value The proposed method for design calculations makes use of the advantages of MCS results, while the need for the tedious amount of calculations for the end user are avoided as the predefined factors are implemented in the procedure of Eurocode format. The proposed method allows better differentiation of the fire probability in the capacity assessment compared to the existing design methods.

Reliability-based robust geotechnical design of spread foundations considering multiple failure modes

This paper presents an update for the reliability-based robust geotechnical design (RGD) method in the design of a soil-foundation system by systematically considering four different potential failure modes including: bearing resistance failure of subsoil, excessive foundation settlement, punching and bending failure of the spread foundation. Given the uncertainties in the critical geotechnical and structural parameters, a comprehensive investigation of the reliability and robustness of the soil-foundation system considering both single failure mode and multiple failure modes were conducted in this study. Moreover, the optimal designs of the soil-foundation system with respect to robustness and cost efficiency are found on the premise of satisfying the safety requirements. The results from this study indicate that both the uncertainties of the geotechnical and structural parameters should be taken into account in the RGD of soil-foundation system considering multiple failure modes. Without properly accounting for the width-to-height ratio of the foundation, increase of the footing geometries and the construction cost will not always lead to a safer and robust design. Besides, bearing resistance failure of subsoil has most significant influence on the reliability and robustness of the soil-foundation system and is identified as the control failure mode.

Oparta na niezawodności systemu optymalizacja konstrukcji łańcucha przenośnikowego zgrzebłowego o zależnych przyczynach uszkodzeń

With the incomplete probability information, the joint probability distribution modelling and system reliability-based optimization design of structural systems with failure interactions are challenging problems in the domain of reliability. This article is designed to propose a system reliability-based optimization design method for optimizing the scraper chain with multiple failure modes. Firstly, the common failure modes of the scraper chain are analysed. For each failure mode, a reliability model for the failure of scraper chains is obtained. Secondly, aiming at the joint failure probability modelling problem, a method for estimating the failure probability of the scraper chain based on system reliability is proposed. The reliability of scraper chains is calculated by the stochastic perturbation technique and the four-moment method. And then, the optimization design problem is discussed based on system reliability. And the optimal model is established. Finally, the effectiveness of the method is verified by the illustrative example of scraper chains. The proposed joint failure probability estimation method and design optimization are shown in the example. The results obtained can provide a reference for the optimal design of the scraper chain.

A direct reliability-based design method for tunnel support using the performance measure approach with line search

The performance measure approach (PMA) is used to address reliability constraints, and line search is employed since the reliability-based design (RBD) problem is translated into the solution to nonlinear equations. This RBD method is proposed for geotechnical engineering such as tunnelling, which is able to find design parameters automatically and directly with no trial-and-error process. Parametric analysis of RBD of support pressure suggests a conservative combination for tunnel support in weak rock. Furthermore, investigation of in situ stress reveals a drawback in the application of RBD, and the proposed RBD method can be helpful to detect the extreme value.

Adaptive conjugate single-loop method for efficient reliability-based design and topology optimization

The single-loop approach (SLA) for reliability-based design optimization (RBDO) is one of the most efficient schemes for optimization problems with linear and weak nonlinear probabilistic constraints. However, it may produce unstable results or increase computational efforts when using the ordinary search direction to determine the optimum design in RBDO problems with highly nonlinear probabilistic constraints. The conjugate gradient (CG) is a promising sensitivity vector for locating the most probable point (MPP) of highly nonlinear concave performance functions. However, the MPP computation using the CG may require a high computational burden for convex constraints To overcome the drawbacks of the SLA the adaptive conjugate single-loop approach (AC-SLA) is proposed for RBDO problems with a large variety of nonlinear constraints. The sensitivity vector of the probabilistic constraints is adaptively computed using the CG vector with a dynamical conjugate scalar factor (DCF). The DCF is adjusted within the range from 0 to 2 using two adaptive coefficients, which are adapted based on the new and previous points. Moreover, the Lyapunov exponents are developed as a general tool for detecting the robustness of different MPP approximation algorithms. The method is also applied to solve a reliability-based topology optimization (RBTO) problem. The ability of the AC-SLA in six RBDO benchmark problems, one applicable to an RBDO aircraft engineering problem and one for RBTO problem, is compared in terms of both robustness and efficiency using the SLA, performance measure approach (PMA), reliability index approach (RIA), and sequential optimization and reliability assessment (SORA). The numerical experiments demonstrate that the convergence capability of the proposed AC-SLA is significantly superior to the PMA, RIA, and SORA. The computational effort of the AC-SLA is significantly reduced, with stable results.

A Reliability-Based Robust Design Method for the Sealing of Slipper-Swash Plate Friction Pair in Hydraulic Piston Pump

In mechanical engineering field, sealing technology is of vital importance for the success of a product. A poor sealing design of a slipper-swash plate friction pair (SSPFP) could lower the reliability of a hydraulic piston pump and lead to the failure of the pump. In this paper, a reliability-based robust design method for the sealing of the SSPFP in hydraulic piston pumps is first established. The matrix expression of the relation between the numerical characteristics of the state function of the SSPFP and the random variables is derived. Methods for calculating the sealing reliability and analyzing the reliability sensitivity of the SSPFP in the hydraulic piston pump are provided. Then, the reliability-based robust design is formulated as a multiobjective design optimization problem to meet the reliability requirements. A numerical example is presented to demonstrate performance of the proposed sealing reliability-based robust design method.

System reliability-based Direct Design Method for space frames with cold–formed steel hollow sections

Design-by-analysis methods for steel structures are receiving considerable attention from professional engineers, researchers and standard-writing groups. Designing by analysis, termed as the Direct Design Method (DDM), is premised on the use of geometric nonlinear inelastic finite element analysis to determine the ultimate strength of steel structural frames and subsequently incorporating a system resistance factor (ϕs) to account for the effects of uncertainties in geometric parameters, stiffness and strength. This paper outlines the DDM in the context of cold-formed compact Hollow Steel Sections (HSS), including the reliability analysis framework at system level underpinning the Method. The system resistance factors for a series of representative 3D frames with hollow locally stable cross-sections are derived.

A novel reliability-based two-level optimization method for composite laminated structures

Due to the existence of large number of design variables for large-scale composite laminated structures, such as ply thicknesses and stacking sequence, etc., it has become one of most important concerns to build an efficient optimization design method for composites. In this paper, the purpose is to propose a novel reliability-based two-level optimization design method including thickness and stacking sequence optimizations, where uncertain parameters of composites are taken into account for reliability evaluation. Firstly, by characterizing existing uncertain parameters of composites as random or interval variables, one can carry out uncertainty analysis for structural responses. Then the evaluation models of probabilistic and non-probabilistic reliabilities are separately introduced when treating uncertainties as random and interval variables. Furthermore, by combining the reliabilities with the two-level optimization model, a novel reliability-based two-level optimization model is advanced and the detailed optimization procedures are listed for convenience of understanding. Lastly, two numerical examples including a simple-supported composite plate and a composite wingtip of aerospace plane are given out to demonstrate the validity and availability of the proposed method. The results show that the proposed method can be successfully and efficiently applied in the optimization design of composite structures.

Probabilistic investigations on the watertightness of jet-grouted ground considering geometric imperfections in diameter and position

The effect of geometric imperfections in both diameter and position of jet-grouted columns on the watertightness of an underground cement-treated slab is investigated in this study. A three-dimensional discretized algorithm is proposed to facilitate the detection and measurement of untreated zones that penetrate the treated slab. The normalized flow rate of a cement-treated slab is then evaluated by calculating the harmonic average area of the penetrated defect. Statistical evaluation of the gross flow rate through the penetrated defects is carried out via Monte Carlo simulations. The results show that a more economic design is obtainable if intracolumn variation of diameter is considered or multi-shaft jet-grouting is used. Based on the statistical results, a reliability-based design method is proposed for designers to strike a balance among various design parameters, including slab thickness, depth, column diameter, and column spacing.

Concept of reliability based design method and its significance

Concept of reliability based design method and its significance