Reliability-based Design Approach Research Articles

MCS-based quantile value approach for reliability-based design of tunnel face support pressure

This paper develops a new approach for reliability-based design (RBD) of tunnel face support pressure from a quantile value perspective. A surrogate model is constructed to calculate the collapse pressures of the random samples generated by a single run of Monte Carlo simulation (MCS). The cumulative distribution function (CDF) of the collapse pressure is then obtained and the support pressure aiming at a target failure probability is chosen as the upper quantile value of the collapse pressures. The proposed approach does not require repetitive reliability analyses compared to the existing methods. Moreover, a direct relationship between the target failure probability and the required support pressure is established. An illustrative example is used to demonstrate the implementation procedure. The accuracy of the reliability-based support pressures is verified by direct MCS incorporating with three-dimensional numerical simulations. Finally, the influencing factors, including the sample size of MCS, the correlation coefficient between random variables, the choice of experimental points, and the surrogate model, are investigated. This method can play a complementary role to available approaches due to its advantages of simplicity and efficiency.

An efficient approach for safety factor-based and reliability-based design of tunnel face support pressure using BP Neural Network

ABSTRACT This paper develops an efficient approach for safety factor-based design and reliability-based design of tunnel face support pressure by constructing a surrogate model to predict limit support pressures. The Back Propagation Neural Network is utilised to fit a surrogate model based on a set of training samples with limit support pressures computed by a proposed numerical method. Several scenarios are used to demonstrate the applications after the prediction performance of the model has been evaluated. A safety factor-based design is implemented by predicting the limit support pressure of a scenario with strength parameters divided by the target safety factor from those of the original scenario, whereas a reliability-based design is performed by predicting the limit support pressures of a certain number of Monte Carlo simulation samples and then choosing a quantile value from the sorted limit support pressures. The design results are checked by direct numerical simulations, demonstrating that the model is valid for conventional scenarios within the specified design domain. The approach is convenient and efficient for applicable scenarios because the most complex and time-consuming process of constructing a surrogate model is no longer needed.

Solving Redundancy Allocation Problems using Jaya Algorithm

Reliability-based design is related to the performance analysis of engineering systems. The redundancy allocation problem is one of the most common problems in the reliability-based design approach. The redundancy allocation problem determines the redundancy level of components in a system to maximize system reliability, subject to several constraints. In recent years, obtaining solutions to reliability-related redundancy allocation problems by means of evolving meta-heuristic algorithms has appealed to researchers due to the several drawbacks of classical mathematical methods. Meta-heuristics have shown the potential of obtaining precise solution in optimization problems and many techniques have been applied in the literature for optimal redundancy allocation. In this paper, a recently developed Jaya optimization algorithm is proposed to be applied for redundancy allocation to maximize system reliability. The Jaya algorithm is a simple, population-based intelligent meta-heuristic algorithm consisting of a single phase and an algorithm-specific parameter-less algorithm. This paper aims to present an application of the Jaya algorithm for searching the optimal solution of two redundancy allocation problems from the literature with nonlinear constraints so that system reliability is maximized. The first problem is the over speed protection system for a gas turbine, whose control system is modelled as a four-stage series system. The objective is to determine the optimal level of redundancy of the valves of the protection system under cost and weight constraints. The second one is the redundancy allocation problem of a five-stage series system with volume, weight, and cost constraints. The results are validated by comparing them with two other meta-heuristics.

A simple Monte Carlo simulation method for geotechnical reliability-based design

ABSTRACT This paper proposes a simple reliability-based design approach from a quantile value perspective. The proposed approach allows the design variable to be efficiently determined without implementing repetitive “trial and error” procedures for a given target reliability index. Only a single run of Monte Carlo simulation is needed to calculate the threshold values of the design variable after the design variable function (DVF) is derived from the limit state function. The threshold values are then sorted in ascending order, and a quantile value is chosen as the desired design variable such that MCS samples with threshold values larger, or smaller than this value are undesired samples. Three illustrative examples are presented following the development of the proposed method and its implementation procedure. Results are validated by calculating the failure probabilities of desired designs using direct MCS, and they are also favorably comparable with those reported in literature. This method can play a complementary role to existing RBD methods due to its advantages of simplicity, efficiency, and robustness.

Interval reliability sensitivity analysis using Monte Carlo simulation and mouth brooding fish algorithm (MBF)

In reliability analysis and reliability-based design approach, sensitivity analysis establishes a relation between the variation in random variable parameters and that in reliability. The analysis of sensitivity is also employed to determine key random variables with the greatest contribution to reliability. The sensitivity analysis of a non-linear limit state function is relatively complicated and time-consuming. Therefore, a novel approach is proposed in this study to calculate the reliability sensitivity parameter in terms of an interval. In the proposed algorithm, the non-linear limit state function is initially converted to a linear limit state function by the Monte Carlo simulation method. Then, the interval random variables are introduced to include both epistemic and aleatory uncertainties so as to obtain a realistic result. In the second step of the proposed methodology, the mouth-brooding fish algorithm (MBF) is applied to capture the upper and lower bounds of the reliability sensitivity parameters. Several illustrative examples were then presented, showing the capability of the proposed approach in obtaining results accurately and efficiently. According to the results, the percentage of improvement in the sensitivity analysis of random variables in the proposed method, compared to the classical method, by using the MBF optimization algorithm to the parameters of random variables due to the variation Coefficient is more than 40 percents. This means that the length of the response interval has increased.

Sustainable Binary Blending for Low-Volume Roads—Reliability-Based Design Approach and Carbon Footprint Analysis

The utilization of industrial by-products as stabilizers is gaining attention from the sustainability perspective. Along these lines, granite sand (GS) and calcium lignosulfonate (CLS) are used as alternatives to traditional stabilizers for cohesive soil (clay). The unsoaked California Bearing Ratio (CBR) was taken as a performance indicator (as a subgrade material for low-volume roads). A series of tests were performed by varying the dosages of GS (30%, 40%, and 50%) and CLS (0.5%, 1%, 1.5%, and 2%) for different curing periods (0, 7, and 28 days). This study revealed that the optimal dosages of granite sand (GS) are 35%, 34%, 33%, and 32% for dosages of calcium lignosulfonate (CLS) of 0.5%, 1.0%, 1.5%, and 2.0%, respectively. These values are needed to maintain a reliability index greater than or equal to 3.0 when the coefficient of variation (COV) of the minimum specified value of the CBR is 20% for a 28-day curing period. The proposed RBDO (reliability-based design optimization) presents an optimal design methodology for designing low-volume roads when GS and CLS are blended for clay soils. The optimal mix, i.e., 70% clay blended with 30% GS and 0.5% CLS (exhibiting the highest CBR value) is considered an appropriate dosage for the pavement subgrade material. Carbon footprint analysis (CFA) was performed on a typical pavement section according to Indian Road Congress recommendations. It is observed that the use of GS and CLS as stabilizers of clay reduces the carbon energy by 97.52% and 98.53% over the traditional stabilizers lime and cement at 6% and 4% dosages, respectively.

Study Investigates Casing Wear in the Culzean Field

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 206221, “Casing Wear: Prediction, Monitoring, Analysis, and Management in the Culzean Field,” by Florian Aichinger, SPE, Loic Brillaud, SPE, and Ben Nobbs, SPE, H&P Technologies, et al. The paper has not been peer reviewed. _ This paper presents predicted vs. measured wear for six wells in the Culzean field, a high-pressure/high-temperature (HP/HT) gas condensate field in the central North Sea. The focus of the complete paper is on the monitoring and analyzing process, particularly how to use offset data to improve accuracy of casing-wear prediction. Field and Well Background Wells in the Culzean field are quite deep, with a measured depth (MD) of 15,000–16,500 ft, and are J-shaped with a slight sail angle (inclination 30–40°). These features result in significant tension loads at the buildup and, potentially, at unplanned curvatures in the vertical section. Combined with possibly high rotating hours, these factors create a considerable risk of high casing wear. Additionally, a challenging pressure regime is present. The steep pressure-transition zone (PTZ) overlying the target reservoir, and the expected predrilled narrow mud-weight window between the pore pressure and formation at the top of the Pentland reservoir of 0.060 ppg, called for a new well-design approach. To address this challenge, the production casing was designed as a 10-in. production liner and a 10¾×10-in. tieback production string. The well design and operations plan required drilling both 12¼- and 8½-in. sections without the 10¾×10-in. tieback production string installed. Consequently, the 14×13⅝-in. intermediate casing could be exposed to higher pressures than usual. Extensive work was performed to enhance casing-wear prediction and to determine the likelihood of failure if a well-control risk materialized. The 12¼-in. section and 10-in. production liner shoe were placed as deeply as possible into the PTZ in the Upper Valhall/Tuxen formation. An appreciable risk was the possibility of a kick while drilling the 12¼-in. section from the Pentland reservoir. The most extreme well-control event the 14×13⅝-in. intermediate casing could experience, however, would have been a well-full-of-gas event while drilling the 8½-in. section. The assessment of the risk associated with such an event was addressed by careful attention to an assessment of casing wear and remaining casing wall thickness and the probability of failure of the 14×13⅝-in. casing, assuming that the casing was worn. The failure-probability assessment of the 14×13⅝-in. intermediate casing was performed using a reliability-based design approach using survival design principles and probability-of-failure estimation. Methodology: Wear Computation and Measurement Analysis of casing wear between a drillstring and the inner surface of casing requires application of an appropriate casing-wear model. A stiff-string model, as used in this work, is advantageous because it can consider pipe clearance, pipe stiffness, and axial and radial casing contact-point location. The simulation uses an adaptable 3D mesh, allowing the calculation of wear in all radial orientations for every chosen MD. The multifinger-caliper-log (MFCL) interpretation methodology uses inner-diameter measurements to calculate an ellipse that best fits the casing shape. The methodology does not require a base log and increases accuracy compared with the traditional method of comparing the maximum inner diameter of MFCL logs taken before and after drilling. The methodology also can be applied to sonic logs as a second information source apart from the direct wall-thickness measurement if the latter is not available. A detailed overview of this process is included in the complete paper.

A time-independent reliability based design approach for debris flow flexible barriers

The design of debris flow protective structures has represented a challenge since the last decades. The design process might consider several variables related to actions and resistances, mainly linked to impact pressure and dynamic pressure resistance. Debris flow events do not have always the same magnitude, and small events can occur with a high probability. Therefore, an events frequency-magnitude relationship might be considered in the design of protective structures. In the Eurocodes framework, the fixed partial safety factors design approach not considering the intrinsic site variability of these phenomena, does not allow obtaining a specific probability of failure. Reliability-based approaches reveal to be compelling solutions. Focusing on flexible barriers, the paper presents a novel time-independent reliability approach, which considers all the possible debris flow events and provides the failure probability of a barrier in a given temporal interval.

Reliability-based optimal control design for seismic-excited structures: A hybrid IS-MTLBO pseudo-double loop method

This study addressed a reliability-based optimal control design (RBOCD) approach for seismic-excited structures. For this aim, a hybrid importance sampling-modified teaching-learning based optimization (IS-MTLBO) pseudo-double loop method is developed. Uncertainty sources such as structural model, stochastic model of the ground acceleration, structural response measurements in sensors, and designed/applied forces in actuators are considered in this study. Numerical studies are carried out on a 10-story building subjected to earthquake excited. A deterministic optimal control design (DOCD) approach based on the MTLBO algorithm is firstly conducted for the structure. Then, a sensitivity analysis using the Borgonovo sensitivity method is carried out to identify and measure the effectiveness of the mentioned uncertainty sources on the seismic responses. Finally, the IS-MTLBO pseudo-double loop approach as an RBOCD approach is implemented for the studied structure. The average reductions of the seismic responses in terms of maximum displacement, acceleration, and drift of floors are obtained as 18.95%, 27.7%, and 24.65% for the RBOCD approach, while, the corresponding reduction are 7.30%, 19.45%, and 14.05% for the DOCD approach. It is shown that although the designed controller based on the DOCD approach satisfies the limitation considered for the maximum floor drift in the nominal model, it is not able to satisfy it in the presence of uncertainties. In other words, the RBOCD approach represents a robust control design against uncertainties, while the DOCD approach gives an uncertainty-sensitive control scheme. Considering four well-known earthquakes, the failure probabilities of the structure controlled by both DOCD and RBOCD approaches are compared. The results indicate the failure probability of the structure controlled by the RBOCD approach is much less than those given using the DOCD approach.

Chronology of Service Limit State Development for Geotechnical Elements Designed Using AASHTO Load and Resistance Factor Design

The purpose of this paper is to provide a chronology of the development of the Service Limit State design process for geotechnical elements that are designed using the reliability-based Load and Resistance Factor Design (LRFD) approach in the Bridge Design Specifications of AASHTO. This chronology will help future researchers to better understand the basis of decisions made by AASHTO, with input from the FHWA, and thus will serve as an important benchmark for future work.

Explicit Approach for Reliability-Based Design of Lining Structures Subjected to Water Seepage Considering Spatial Correlation and Uncertainty

AbstractWith the rapid urbanization in this era, it has become an economic imperative to make use of underground space in many countries. Achieving long-term durability goals of lining structures i...

A time-independent reliability based design approach for rockfall net fences: a comparative analysis within the Eurocode framework

The design of net fences as passive mitigation measures against rockfall events has represented a challenge since the last decades. The choice of the proper effect of the actions to consider in the design is still under debate. Recently, the Authors have proposed a novel time-independent reliability approach encompassing the large variability of the size and the kinematics of the possible impacting blocks. The entire statistics of all these quantities (size, velocity, and height) enters into the calculations, differently from other approaches that consider specific values of the parameters. In addition, the variability in time of the inputs is tackled, with particular reference to the size of the falling block. The recent approach is herein merged and compared with the current semi-probabilistic ultimate limit state design approach, suggested in the Eurocodes and implemented in the Italian recommendations UNI 11211-4:2018, with the purpose of finding the equivalent partial safety factors of kinetic energy and trajectory height of the impacting block. A sensitivity analysis with different synthetic profiles, representing possible real situations, is performed highlighting that if a set of partial safety factors is assigned to different sites, an intrinsic variability in the failure probability has to be accepted.

Additional insights to EC7 from the application of reliability-based design methods: the case of debris flow protection structures

Debris flows are dangerous natural processes that cause extensive damages to infrastructures and urbanized areas and can lead to loss of human lives. Their unpredictability, their extremely high motion and their magnitude are the main causes of these harms. Mitigation measures are fundamental for reducing the associated risk and protecting infrastructures in mountainous areas. Their design is still an open issue: there are many formulations to evaluating impact pressure. Moreover, the uncertainties in the determination of flow characteristics (velocity and thickness) are significantly high and difficult to quantify. In the European Union, the design of any type of structures involved in rock mechanics field must comply with EN-1997 Geotechnical Design (CEN 2004) (EC7). For debris flow countermeasures, EC7 requirements are very difficult to apply in practice since partial safety factors are not provided for these phenomena. However, the basic philosophy of reliability-based design (RBD), as defined in EN1990 (CEN 2002) may be a suitable and complementary approach to provide geotechnical structures with a uniform probability of failure. Reliability Based Design (RBD) can provide additional insights to EC7 design and can be applied when partial factors have still to be proposed (by EC7) to cover uncertainties of less common parameters, as in case of debris flow countermeasures. This paper presents an analysis of the advantages and limitations on the applicability of RBD approach to debris flow countermeasures, by using the first-order reliability method (FORM). In particular, data availability, the possibilities for analysing data in a statistical framework and the choice of performance function are the main limitation of the method, which force to make assumptions regarding statistical distribution of the considered parameters. A sensitivity analyses, comparing different equations, commonly used for debris flow impact pressure estimation, were performed for quantifying the effect of the selected performance function on the RBD results.

A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds

Reliability-based design approaches via scenario optimization are driven by data thereby eliminating the need for creating a probabilistic model of the uncertain parameters. A scenario approach not only yields a reliability-based design that is optimal for the existing data, but also a probabilistic certificate of its correctness against future data drawn from the same source. In this article, we seek designs that minimize not only the failure probability but also the risk measured by the expected severity of requirement violations. The resulting risk-based solution is equipped with a probabilistic certificate of correctness that depends on both the amount of data available and the complexity of the design architecture. This certificate is comprised of an upper and lower bound on the probability of exceeding a value-at-risk (quantile) level. A reliability interval can be easily derived by selecting a specific quantile value and it is mathematically guaranteed for any reliability constraints having a convex dependency on the decision variable, and an arbitrary dependency on the uncertain parameters. Furthermore, the proposed approach enables the analyst to mitigate the effect of outliers in the data set and to trade-off the reliability of competing requirements.

Reliability-Based Design of an Aircraft Wing Using a Fuzzy-Based Metaheuristic

The purpose of this paper is to design aircraft wing using reliability-based design optimization concerned to fuzzy uncertainty variables. A possibilistic safety index-based design optimization (PSIBDO) with fuzzy uncertainties is proposed to overcome difficult tasks from the original probabilistic problem. The design problem is to minimize mass of a composite aircraft wing subject to aeroelastic and structural constraints through consideration of the material properties are the uncertainties. The design variables include aircraft wing structure dimensions. The reliability-based design approach is needed to alleviate such a problem. Due to the complexity of the aircraft wing structures design and aeroelastic analysis, nonprobability-based design is an alternative choice to increase computational efficiency in the design process. The optimum results show the efficiency of our proposed approach.

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.

Numerical approach to study the effect of shape defect in multi-fastened joints during the assembly process

When designing joined structures, deterministic approaches are commonly considered insufficient to ensure a good compromise between mechanical performances and manufacturing tolerances due to the many sources of variability. Reliability-based design approaches are promising, but they require structural models that take into account the different sources of variability and the complex physical phenomena that govern their effects on mechanical behaviour.This paper proposes a method to analyse the fastening process of parts that include geometric form defects. The structural behaviour of the joint is simulated using a finite element model combining connectors and rigid surfaces to represent fasteners. With this approach, the calculation time can be drastically reduced while frictional contact is maintained between fasteners and parts. Shape defects are generated by translating parts mesh nodes. The method is applied to a case study and its efficiency is evaluated by analysing the evolution of axial bolt preloads and transverse bolt forces during the assembly process. Results demonstrate the ability of the method to simulate different clamping sequences and to capture the interaction between shape defects, bolt-hole clearance and target axial preload.

Reliability Assessment for Time-Dependent Behaviour of Soft Soils Considering Cross Correlation between Visco-Plastic Model Parameters

An elastic visco-plastic creep model was combined with the Monte-Carlo probabilistic method incorporating multivariate copula and nonlinear analysis to investigate the effects of uncertainties in the elastic visco-plastic model parameters on time-dependent settlement and the distribution of excess pore water pressure in soft soils under applied loads. The elastic-plastic model parameter (λ/V) and creep coefficient (ψ0/V) were considered as random variables with lognormal distribution while considering the cross correlation between these two random variables. When λ/V and ψ0/V were used as random variables, the coefficient of variation of time-dependent deformation gradually decreased approximately 25% over time until reaching an asymptote. By adopting over 50 years of monitoring data from the case study of Väsby test fill and results from the settlement ratio, the most appropriate cross correlation coefficient between selected random variables was introduced. The results revealed that increasing the cross correlation coefficient between λ/V and ψ0/V increased the standard deviation and the coefficient of variation of settlement up to 40%. Meanwhile, the corresponding statistical features for the predicted excess pore water pressure decreased as the cross correlation coefficient increased. This study also provides a practical insight into selecting the most suitable cross correlation coefficient between elastic visco-plastic model parameters, while adopting reliability-based design approach that captures the time-dependent deformation of embankments and structures built on soft soils.

Multidisciplinary Design of Bipropellant Propulsion System in Three Methods, Optimal Design, Reliability Based Design and Optimal Reliability Based Design

The need to improve the reliability and safety requirements, has led to increasingly utilization of reliability based design approaches. In this study, reliability based multidisciplinary design optimization for a bipropellant propulsion system has been investigated. The objective function is minimizing the total system mass and design constraints are the total impulse and the temperature of the wall of the combustion chamber. Monte Carlo simulation methodology is used to apply uncertainties in the problem and to show the reliability of the system under these uncertainties. The mass, functional and geometric results of the bipropellant propulsion system are differentiated for optimal design, reliability based design and optimal reliability based design. Then, considering the results, the concepts and definitions of design methods are compared and discussed and it is shown that the reliability based multidisciplinary optimization while having the desired mass, has high reliability.

Probabilistic Studies on the Shear Strength of Slender Steel Fiber Reinforced Concrete Structures

Shear failure is a brittle and undesirable mode of failure in reinforced concrete structures. Many of the existing shear design equations for steel fiber reinforced concrete (SFRC) beams include significant uncertainty due to the failure in accurately predicting the true shear capacity. Given these, adequate quantification and description of model uncertainties considering the systematic variation in the model prediction and measured shear capacity is crucial for reliability-based investigation. Reliability analysis must account for model uncertainties in order to predict the probability of failure under prescribed limit states. This study focuses on the quantification and description of model uncertainty related to the current shear resistance predictive models for SFRC beams without shear reinforcement. The German (DAfStB) model displayed the lowest bias and dispersion, whereas the fib Model 2010 and the Bernat et al., model displayed the highest bias and dispersion. The inconsistencies observed in the resistance model uncertainties at the variation of shear span to effective depth ratio are a major cause for concern, and differentiation with respect to this parameter is advised. Finally, in line with the EN 1990 semi-probabilistic approach for reliability-based design, the global partial safety factors related to model uncertainties in the shear resistance prediction of SFRC beams are proposed.