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This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method (QFOSM). The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids. Based on this geometric interpretation, the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system. The proposed method has the advantage of computational simplicity, akin to the conventional first-order second-moment method (FOSM), while providing estimation accuracy close to that of the first-order reliability method (FORM). Its performance is demonstrated with a numerical example and three slope examples. The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters. The proposed method does not involve complex optimization or iteration required by the FORM. It can provide a valuable complement to the existing approximate reliability analysis methods, offering rapid sensitivity evaluation and slope reliability analysis.

The susceptibility mapping of rainfall-induced landslides is an effective tool for predicting and locating disaster-prone zones at the regional scale. One of the most important parts of landslide susceptibility models is the hydrological model. In this context, the present study considers three pore water pressure (PWP) profiles with surface runoff to estimate the spatiotemporal variation of wetting front depth (WFD) during rainfall episodes. To reasonably simulate the inherent uncertainty and variability involved in the hydrogeomechanical properties of the surficial soil layers at the regional scale, probabilistic analysis based on the recursive first-order reliability method (FORM) is employed to calculate the probability of slope failure. The regional time-dependent landslide susceptibility mapping is realised using a newly developed model called Physically-based probabilistic modelling of Rainfall Landslides using Simplified Transient Infiltration Model (PRL-STIM). The proposed model is applied in a representative area that suffered extensive rainfall-induced landslides in July 2013 (Niangniangba Town, Gansu Province, China). The results indicate that the PRL-STIM model achieved a satisfactory prediction accuracy of 75% AUC compared to existing models like transient rainfall infiltration and grid-based regional slope-stability model (72%) and the probabilistic analysis results based on the first-order second moment method (74%). It also performed well in predicting the spatial distribution of shallow landslides, with a success rate of 81.6%. Regarding the model efficiency, the completion of a raster file for calculating the landslide probabilities of the study area (including 711,051 cells) requires only 17.1 s. It is thus hoped that the proposed calculation framework of PRL-STIM that considers various uncertainties (e.g., nonlinearity of the physical model, non-normal probability distributions, random variable cross correlations, etc.) in geotechnical parameters is better suited for landslide susceptibility mapping at the regional scale, where only limited historical event data is available. [ABSTRACT FROM AUTHOR]

In the random field model's consideration of the spatial variability of soil, soil properties at different locations play different roles in the reliability analysis of the foundation. Investigating the importance distribution of the random field through reliability sensitivity analysis (RSA) is beneficial for understanding how the random field affects the reliability of the foundation. However, many existing RSA methods for the random field model are deficient in terms of efficiency, accuracy, and applicability under complex engineering conditions. Consequently, this study proposes an efficient RSA method for the random field model based on the Karhunen–Loève (KL) expansion method and the first-order reliability method (FORM) to identify the important random field domain in foundation engineering. In the proposed method, the mean reliability sensitivity index (MRSI) is extended to a random field model of continuous form to characterize the importance distribution of the random field. The MRSI is analytically derived based on the results of the KL expansion method and the FORM without additional limit state function (LSF) calculations. Subsequently, the important random field domain, in which the variation of the mean of the soil property contributes significantly to the reliability index, is identified based on the MRSI. Last, two foundation engineering examples that consider the cross-correlated random fields of cohesion and friction angle, including strip footing on single-layer soil and pile in multiple-layer soil, were used to verify the proposed method. The results showed that an important random field domain with a small area dominates the variation of the reliability index of a foundation, and important random field domain area increases with autocorrelation distance (ACD). This innovative identification method holds great engineering significance, because it allows geotechnical practitioners to gain a comprehensive understanding of the failure modes and foundation treatment areas of foundations in spatially varying soil. In the random field model's consideration of the spatial variability of soil, soil properties at different locations play different roles in the reliability analysis of the foundation. Investigating the importance distribution of the random field through RSA is beneficial for understanding how the random field affects the reliability of the foundation. However, many existing RSA methods for the random field model are deficient in terms of efficiency, accuracy, and applicability under complex engineering conditions. Consequently, this study proposes an efficient RSA method for the random field model to identify the important random field domain, in which the variation of the mean of the soil property contributes significantly to the reliability index. Two foundation engineering examples that consider the cross-correlated random fields of cohesion and friction angle, including strip footing on single-layer soil and pile in multiple-layer soil, were used to verify the proposed method. The results showed that the innovative identification will allow geotechnical practitioners to gain a comprehensive understanding of the failure modes and foundation treatment areas of foundations in spatially varying soil. [ABSTRACT FROM AUTHOR]

Stochastic reliability analysis is performed in the present work for variable fiber spacing composite (VFSC) laminates. The finite element model here is developed with third-order shear deformation theory (TSDT) to estimate buckling performance under thermal loading. The reliability analysis is performed with the first-order reliability method (FORM) and with the radial basis function network (RBFN) model as well. Further RBFN-based surrogate model is utilized for stochastic analysis, which is highly efficient and possesses a close match with traditionally used Monte Carlo simulation (MCS). The sensitivity of each input parameter is investigated, out of which the thermal expansion coefficient of the matrix ( α m ) is found to be the most sensitive one. [ABSTRACT FROM AUTHOR]

Changes in a structure's use can have a significant impact on distribution of live loads, both in the plan and elevation of a building. Unevenly distributed live loads can introduce variations in mass, causing irregularities in the structure and making it more susceptible to damage during earthquakes. Previous studies have extensively investigated the seismic vulnerability of structurally irregular buildings. However, due to computational challenges, simplified two-dimensional models are commonly employed, which fail to accurately capture the nonlinear interaction between torsional and lateral responses, thereby limiting their ability to reflect the actual structural behavior. This research focuses on examining the seismic fragility of reinforced concrete frames that exhibit mass irregularities in the elevation or plan caused by the change in structural usage. For accurate vulnerability evaluation, this research employs comprehensive three-dimensional models of reinforced concrete irregular structures. A total of 21 frame models encompassing various degrees of vertical and in-plan irregularities resulting from different scenarios of live-load distribution were studied. Nonlinear dynamic response history analysis was conducted with 10 earthquake input ground motions. To assess the vulnerability of the studied structures against the given earthquakes comprehensively, the concept of a fragility surface was introduced. The fragility surface is derived from fragility curves corresponding to various damage limit states, providing a complete overview of the seismic vulnerability of the structure in terms of peak ground accelerations and allowable drift ratios. In this study, eight allowable drift ratios were defined to establish failure limit-state conditions. The seismic vulnerability of all assumed building usage scenarios ware quantified, and this study highlights that uneven structure use in the regular structure can significantly affect its seismic performance. The findings of this study can contribute to a better understanding of the novel aspects related to the seismic behavior of irregular structures, enhancing our knowledge in this field. [ABSTRACT FROM AUTHOR]

The concept of reliability‐based design (RBD) of geotechnical works has seen great success in recent years, nevertheless, its application in real‐world engineering practice is still limited. This phenomenon could be mainly attributed to two aspects: the engineer's unfamiliarity of reliability algorithms even in their simplest forms, and the lack of direct connection between reliability algorithms and deterministic design tools. To promote the geotechnical RBD application, this study proposes an inverse first‐order reliability method (FORM) integrating adaptive conjugate direction search technique (RBD via conjugate FORM) to solve classical RBD problems where the number of (multiple) limit state functions is usually equal to the number of unknown design parameters. Notably, the RBD via conjugate FORM can readily back‐calculate those unknown design parameters subject to prescribed reliability index or probability of failure, by means of iterative evaluation of the parametric sensitivities. The proposed algorithm is first verified by several well‐documented examples. Comparative studies show that when the reliability problem to solve is highly nonlinear, the RBD results based on steepest descent search direction may fall in oscillation and non‐convergence, while the proposed RBD via conjugate FORM algorithm performs robustly and efficiently. It is then illustrated in combination with standalone numerical codes to conduct risk‐based optimization of unknown design parameters for two soil slope stability models. The first slope RBD model achieves designing the slope angle under specified reliability index, and the second slope RBD model is to optimize multiple design parameters of the stabilization pile, which can meet different slope reliability requirements under static and seismic loading conditions simultaneously. [ABSTRACT FROM AUTHOR]

It has been proved that external bonding of fiber-reinforced polymer (FRP) composite materials with epoxy interlocking (EB-FRP-EI) enhancement could significantly improve the strength of FRP-to-concrete joints from experimental studies. However, there still exists a barrier to comprehensively implementing the EB-FRP-EI method in practical applications, owing to the lack of full reliability-based design guidelines with consideration of the uncertainty raised from materials, model errors, and loading. In this study, a numerical function of bond strength for EB-FRP-EI was derived by taking both the adhesion effect and mechanism doweling enhancement into account. The reliability analysis of the EB-FRP-EI method was conducted by utilizing the first-order reliability method (FORM). Corresponding to the required reliability index, two-parameter (groove depth and number) reliability-based design was performed for 35 (7 × 5) FRP-to-concrete joints in total. The effects of design and modeling parameters, including depth of grooves, number of grooves, thickness of FRP, width of FRP, and strength of concrete, on reliability performance of the bond strength of FRP-to-concrete joints with epoxy interlocking enhancement are presented and discussed. As a result, this study provides suggestions for the proper design of FRP-to-concrete joints with epoxy enhancement based on these parameters. [ABSTRACT FROM AUTHOR]

The spatial variability is an inherent uncertainty of soils. The random field theory is used to represent the spatial variability of soils, and the random field discretization is performed by the Karhunen-Loève (KL) expansion method. Using the slope upper bound analysis based on the discrete mechanism, the discretization results of the internal friction angle random field at each point in the space are considered when generating the velocity discontinuity surface. And the strength reduction technique, bisection searching, and sequential quadratic programming method are combined to solve the safety factor of slopes. The first-order reliability method (FORM) and subset simulation (SS) are employed for slope reliability analysis. Given the characteristics of SS and the shear strength reduction technique, an optimization algorithm coupling the two is proposed to improve computational efficiency. By calculating and analyzing an earth slope, the similarities and differences between FORM and SS based on the KL expansion method in solving the slope reliability index and failure consequence are clarified. The influence of the coefficient of variation of soil strength parameters on the slope reliability index and failure consequence is investigated, providing a theoretical basis for risk analysis and prevention of slopes.

Geotechnical engineering analysis and design involves considerable uncertainties. Reliability-based design optimisation (RBDO) intends to minimise an objective function such as material quantity or cost subject to design requirements specified by probabilistic constraints. In this work, the RBDO of geotechnical systems is studied using a decoupled approach based on adaptive metamodels. To improve the traditional double-loop structure of RBDO, the proposed approach decouples the numerical reliability analysis loop from the design optimisation loop. A metamodeling method based on augmented radial basis function (ARBF) is adopted to create approximate functions of the reliability indices, so that the design optimisation is performed based on the metamodels of the probabilistic constraints. To improve the accuracy of predicting the reliability indices, an adaptive technique of the ARBF metamodels is applied. The optimal point in one design iteration is treated as an additional sample point for updating the metamodels of the reliability indices. The accuracy of the metamodels is progressively enhanced through this dynamic process, especially in the neighbourhood of the optimal point. Mathematical and geotechnical engineering examples are solved and numerical results are presented. The proposed design optimisation framework works well and is a useful alternative for solving RBDO of geotechnical engineering problems. [ABSTRACT FROM AUTHOR]

Reliability-based design (RBD) can overcome some limitations and ambiguities in the partial factor design approach found in Eurocode 7 (EC7) and the load and resistance factor design (LRFD) method used in North America. The aim of this study is to show how RBD via the first-order reliability method (FORM) can complement LRFD and EC7 codes. Three geotechnical engineering examples are used to demonstrate that RBD-via-FORM can provide guidance to the partial factor design approach in situations with load-resistance duality, shear strength parameters with context-dependent sensitivities, parameters not covered in design codes, cross-correlated parameters, and designs aimed at a target reliability or failure probability. Insights from RBD-via-FORM are presented. The differences and similarities between the design points in RBD, partial factor, and LRFD methods are explained. Comparisons are made with Monte Carlo simulations, the mean-value first-order second-moment method, and the Bathurst–Javankhoshdel closed-form reliability index solution which is restricted to simple linear limit state performance functions with lognormally distributed load and resistance terms and bias factors. It is suggested that RBD-via-FORM can be conducted in tandem with EC7 and LRFD methods in order to overcome limitations and ambiguities which sometimes arise using these methods. [ABSTRACT FROM AUTHOR]

This paper presents a method using small data to enhance maintenance efficiency, addressing the limitations of solely qualitative maintenance records. It involves the use of a model based on the Bayesian–Weibull first-order reliability method (BW-FORM) for component analysis and a stochastic analytic hierarchy process for system-level assessment, including fault-tree analysis and reliability-centered maintenance for prioritizing tasks. Key components such as "gate body" and "wire rope" significantly affect system reliability, whereas "rusted crane base" and "bolt on base falling" are the top maintenance priorities. The Mudan Reservoir case study validates this approach, with the life expectation estimated using the BW-FORM aligning well with expert predictions. • A generic maintenance strategy is developed based on limit information. • Component and system safety status are revealed and implemented in the proposed maintenance strategy. • Bayesian-Weibull-First-Order-Reliability model is established for current and future component reliability assessment. • A stochastic Analytic-Hierarchy-Process is integrated with Fault-Tree-Analysis (FTA) for system reliability. • The proposed reliability-based maintenance strategy is demonstrated for Mudan reservoir with digital visualization platform. [ABSTRACT FROM AUTHOR]

A reliability assessment formulation for stiffened panels using the Model Correction Factor Method (MCFM) is derived from semi-empirical design equations of the IACS Common Structural Rules (CSR) for double-hull oil tankers. The approach consists of using the IACS-CSR buckling strength requirements of stiffened panels as a simplified response model that is calibrated iteratively at the design points calculated by the first-order reliability method using the results of non-linear finite element analysis of the stiffened panel. The approach is applied to a deck stiffened panel of a Suezmax oil tanker, designed according to the CSR for Double Hull Oil Tankers that has been used in the development of codes for the structural design of ships. The stiffened panels are subjected to uniaxial compressive loads induced by the hull girder vertical bending moment in a typical seagoing operational condition of the oil tanker in full load. It is shown that the application of the MCFM leads to a fast convergence towards the design point since the IACS-CSR formulation can capture the correct failure mode of the stiffened panels and the important mechanical features related to the prediction of their ultimate strength providing a convenient response surface model for reliability assessment. • This paper presents a reliability assessment for stiffened panels using the Model Correction Factor Method. • The IACS-CSR buckling strength requirements of stiffened panels as a simplified response model that is calibrated. • The approach is applied to a deck stiffened panel of a Suezmax tanker, designed according to the Common Structural Rules. • The stiffened panels are subjected to uniaxial compressive loads induced by the hull girder vertical bending moment. • The application of MCFM leads to a fast convergence since the IACS-CSR formulation can capture the correct failure mode. [ABSTRACT FROM AUTHOR]

This work presents a novel methodology for fatigue life reliability analysis using a newly developed Dual Boundary Element Method-based Implicit Differentiation Method (DBEM-IDM) in shallow shell structures. The proposed DBEM formulations evaluate stress intensity factors and fatigue life sensitivities in shallow shells considering geometrical variables and curvature. The IDM formulations, obtained through direct differentiation of the shallow shell DBEM formulations, uses the First-Order Reliability Method (FORM) to assess the reliability index and probability of failure of shallow shell structures with multiple cracks. Two numerical examples were simulated to illustrate the effectiveness of the proposed methodology. The first example examines a shallow shell with a centre hole and cracks subjected to various loads. The critical crack length required to ensure structural reliability and inspectability is determined. Fatigue reliability assessment is performed for the same example, employing limit state functions expressed in terms of fatigue life. FORM results are compared with the results of Monte Carlo Simulations (MCS), and provided a maximum difference of 3.67%. Parametric analyses are conducted to identify significant variables that affect reliability, and it was found that precise determination of design parameters is necessary to reduce the probability of failure, particularly for the Paris law constants. The second example, featuring more complex geometry, involved assessing fatigue reliability in a cylindrical shallow shell structure with multiple cracks. The results of this example indicate a 3.49% maximum difference between FORM and MCS. The results exhibit a low error compared to the MCS, and the inherent efficiency of the IDM-based FORM underscores its suitability for addressing uncertainty in reliability analysis. [ABSTRACT FROM AUTHOR]

The screw anchor design model was recently adopted in ACI 318-19, and similar strength reduction factors for post-installed anchors were applied to screw anchors despite its reliable performance, which has been proven in experimental studies. Accordingly, this study presents a comprehensive reliability assessment of the safety level for the design of screw anchors governed by concrete breakout. A worldwide database that includes single anchors embedded in cracked and uncracked concrete, anchors with edge effects, and a group of anchors is used in the reliability analysis. Anchor design inherently has different uncertainties related to multiple variables like concrete strength and variability in load. These variables have been modeled using multiple distributions. Furthermore, in this paper, anchors are grouped into three classes based on the installation effort sensitivity classes 1 to 3, where this sensitivity is described in a beta distribution. Based on a 3.5 selected reliability index threshold, the ACI 318-19 strength reduction factors result in conservative reliability indexes that exceed the selected threshold. Thus, revised strength reduction factors (ϕ) are proposed. For anchors embedded in uncracked concrete, the proposed ϕ factors are 0.80 for anchor classes 1 and 2 and 0.75 for anchor class 3. For anchors embedded in cracked concrete, ϕ factors are 0.75, 0.7, and 0.65 for classes 1, 2, and 3, respectively. The study also presents a sensitivity analysis to quantify the effect of each model error parameter on the results. [ABSTRACT FROM AUTHOR]

This paper addresses the first passage problem of linear systems subjected to non-Gaussian excitations by means of simulation. A non-Gaussian simulation technique based on the unified Hermite polynomial model (UHPM) is adopted to model input excitations, and then the output responses are further obtained through time-domain analysis. The novel contribution of this paper is to construct an efficient importance sampling (IS) density function based on UHPM and the first-order reliability method (FORM) to release the computational burden. A simple and efficient sampling procedure is also provided for convenient implementation. Such an approach allows the failure probabilities in the order of 10−3 or lower to be estimated reliably with a reduced computational cost. The accuracy and efficiency of the proposed method are demonstrated by three examples, including a single-degree-of-freedom oscillator, a 3-story linear shear frame, and a relatively large-scale finite-element model. [ABSTRACT FROM AUTHOR]

The accuracy and efficiency of an approach using surrogate models are investigated, in comparison with traditional structural reliability methods, in the analysis of two steel structures subjected to natural fire. For this purpose, an algorithm is used, coupled to a finite-element computational package, which includes the first-order reliability method (FORM), the approximate method most used in this type of problem, and Monte Carlo simulation (MCS), which is usually taken as a reference. On the other hand, the literature indicates surrogate models as a promising alternative to maintain, at acceptable levels, the computational cost in similar analyses. Therefore, two approaches using surrogate models are also applied to the algorithm, more specifically adaptive and nonadaptive artificial neural networks. The analyses led to differences of up to 21.83% between the failure probabilities obtained via FORM and via MCS. Furthermore, while the nonadaptive approach fails to achieve sufficient accuracy, the adaptive approach is confirmed to be a viable alternative, with differences, on average, close to 1.00% and computational times less than 1.60% of the time required by MCS. [ABSTRACT FROM AUTHOR]

In this study, the resistance factors (RF) in the load and resistance factor design (LRFD) for the drilled-shaft foundation of transmission line structures subjected to lateral loads were investigated. Various load test results were collected to establish a database and used in the reliability analysis. The first-order reliability method (FORM) was implemented to calibrate RF for the Broms, Brinch-Hansen, and Prasad and Chari methods. Loads for transmission line structures were categorized and characterized statistically for calibrating RF. Uncertainties of the transverse tension load (TTL), wind-on-structure load (WLs), and wind-on-ice-coated conductor load (WLc), all dominant in transmission line structures, were evaluated. RF varied largely with nominal load ratios of WLs/TTL and WLc/TTL , which should be considered for the selection of RF in the design to maintain a consistent safety margin. Increases in nominal WLs and WLc induced higher RF while increasing nominal TTL yielded lower RF. The higher RF values obtained in this study were due to the low bias factors of wind-induced loads and the large load factors of the tension and wind loads. The equivalent factor of safety (FSeq) was evaluated and analyzed for the proposed RF s. [ABSTRACT FROM AUTHOR]

The stochastic pseudo excitation method (SPEM), which is based on the principle of pseudo excitation method (PEM), is introduced to represent the randomness of dynamic input in which the amplitude of excitation is adopted as a random variable. Based on the mathematic definition of power spectral density, a physical interpolation of the SPEM is discussed. Even if one random variable is involved in calculation, the effects of the uncertainties are required to be investigated. The SPEM offers a simple but quite effective way to solve the dynamic reliability problem. Through integrating the new algorithm into first-order reliability method (FORM), the dynamic reliability of uncertain structure subjected to random excitation is studied. A linear oscillator with three types of white noise is adopted to verify the SPEM for dynamic reliability of linear random vibration analysis. Also, the accuracy and efficiency of SPEM to handle the multi-degree-of-freedom structure is investigated in this paper. [ABSTRACT FROM AUTHOR]

Summary: In this study, a new reliability analysis method was developed based on the adaptive high‐dimensional model representation (HDMR) and applied to geotechnical engineering problems. For practical problems requiring finite element (FE) analysis or other numerical methods to evaluate system responses such as stresses and deformations, an efficient and accurate metamodeling technique is needed because it is not efficient or straightforward to directly adopt the conventional sampling‐based or gradient‐based reliability analysis approaches. In this work, an adaptive metamodeling approach was created and studied based on the HDMR framework and augmented radial basis functions (ARBFs). In this adaptive ARBF‐HDMR technique, a simple and inexpensive first‐order ARBF‐HDMR metamodel was first constructed to explicitly express a performance function, and an alternate first‐order reliability method (FORM) was applied to locate the design point and compute the reliability index. A local window was then defined such that additional sample points were generated and a higher‐order HDMR component function was created using ARBF and added to the existing ARBF‐HDMR metamodel. The accuracy of the ARBF‐HDMR metamodel was improved through this adaptive process, especially in the region surrounding the design point. One mathematical and four geotechnical engineering problems were studied and solved using the proposed adaptive ARBF‐HDMR approach. The proposed method was found to be capable of obtaining accurate reliability indices within a few iterations in all test problems. [ABSTRACT FROM AUTHOR]

In the European Union since 2010, the design of any type of structures must comply with EN-1997 Geotechnical Design (CEN 2004) (EC7) referring to engineering projects in the rock mechanics field. However, the design of debris flow countermeasures in compliance with EC7 requirements is not feasible: EC7 uses partial safety factors for design calculations, but safety factors are not provided for phenomena such as debris flows and rock falls. Consequently, how EC7 can be applied to the design of debris flow barriers is not clear, although the basic philosophy of reliability-based design (RBD), as defined in EN1990 (CEN 2002) and applicable to geotechnical applications, may be a suitable approach. However, there is insufficient understanding of interactions between debris flows and structures to support RBD application to debris flow barrier design, as full-scale experimental data are very limited and difficult to obtain. Laboratory data are available but they are governed by scale effects that limit their usefulness for full-scale problems. The article describes an analysis, using the first-order reliability method (FORM), of two different datasets, one obtained through laboratory experiments and the other reflecting historical debris flow events in the Jiangjia Ravine (China). Statistical analysis of laboratory data enabled a definition of the statistical distributions of the parameters that primarily influence debris flow and barrier interactions. These statistical distributions were then compared to the field data to explore the links between flume experiments and full-scale problems. This paper reports a first attempt to apply RBD to debris flow countermeasures, showing how the choice of the target probability of failure influences the barrier design resistance value. An analysis of the factors governing debris flows highlights the applicability and limitations of EN1990 and EN1997 in the design of these rock engineering structures. [ABSTRACT FROM AUTHOR]

Abstract The dynamic response and reliability analysis of a 13.2 MW offshore wind turbine supported by a moored semi-submersible platform is the subject of this study. Loads data for the extreme response analysis involve time-domain simulations for a range of sea states representative of expected site-specific metocean conditions. To gain deeper insight into the dynamic behavior of this system and to obtain long-term loads efficiently and accurately, two studies are carried out sequentially. First, the short-term response of the integrated system is studied based on 1-h simulations for sea states identified using the Environmental Contour method for a 50-year return period. Response extremes for the integrated wind turbine system as well as system sensitivity to metocean conditions are studied. Next, the long-term response associated with the 50-year return period is estimated using statistical extrapolation based on loads derived from the 1-h simulations. Inverse First-Order Reliability Method procedures are employed to seek appropriate response quantile levels, e.g., the median response for 2D Inverse FORM. A more comprehensive 3D approach, which accounts for system response uncertainties, improves long-term response estimates. A proposed adaptive procedure in the 3D approach helps determine the number of simulations needed to guarantee accuracy in the long-term response estimation. Highlights • An integrated system for a large offshore wind turbine on a moored semi-submersible floating platform is briefly described. • From short-term extreme loads based on one-hour long stochastic simulations, critical sea states are identified. • A study of the system response variability identifies which sea states lead to largest loads on the integrated system. • Platform motions and loads are found to be most sensitive to the inflow wind turbulence. • Response variability is significant relative to metocean conditions variability in comparing 3-D Inverse FORM with EC method. [ABSTRACT FROM AUTHOR]

Rock explosion has always been a complex problem because neither rock characteristics nor explosion waves could be accurately estimated. As such, this imposes a high uncertainty on deterministic methodologies available for damage prediction. In this paper, by defining two damage zones around the blast hole, including crushed and cracked zones, a first-order reliability analysis (FORM) was adopted to address this issue. For this purpose, FORM was used in a double-loop algorithm, where the inner loop was responsible for converging the FORM, and the outer loop was assigned to feed the inner loop with new cases. Using such nested-loop algorithm, the probability of exceedance was calculated for any desired damage zone radius. The maximum effect of the involved parameters on the failure probability induced around the blast hole was additionally studied using a parametric reliability analysis. The results showed that the radii for crushed and cracked zones are limited to 0.5 and 4.2 m, respectively, so that the probability of going beyond these limits is less than 1%. Moreover, the analyses of decoupled explosions showed that increasing the gap between the explosion charge and wall of the borehole could severely reduce the failure probability; however, the maximum effect of decoupling ratio occurs in the small range of radii between 0.3 mm and 2.35 m. [ABSTRACT FROM AUTHOR]

Abstract To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF (Hasofer–Lind–Rackwitz–Fiessler) iterative algorithm for first-order reliability method (FORM). It is simply formulated in x -space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone (deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability. Graphical abstract Image 1 Highlights • An improved HLRF algorithm reformulated in the original space. • Case study of slope reliability analysis. • Spatial variability modelling based on in-situ shear strength. [ABSTRACT FROM AUTHOR]

The management of disaster waste is one of the most critical tasks associated with recovery after a disaster. Having a general idea of the required capacity, cost and target clean-up time while considering the uncertainties involved in the system before the detailed plan of a disaster waste clean-up system is significant. Reliability analysis is a method to judge the performance of a system and deal with uncertainties in the system. Evaluating the reliability of the system, which can indicate the possibility to complete the clean-up within the target time and cost, and optimising the system to maximise the reliability to provide information to decision-makers regarding the capacity, cost and time required to finish the clean-up is the purpose of this paper. A mathematical model is developed applying the First Order Reliability Method (FORM) to address the problem. Additionally, a non-linear optimisation model is developed to improve the reliability of the disaster waste clean-up system with consideration of the total cost and clean-up time constraints, and solved using a Genetic Algorithm. The proposed models are implemented to solve a case study in Queensland, Australia. It is shown that the models have the capability of maximising the reliability and minimising the total clean-up costs by optimising the arrangement of vehicles during the clean-up process. [ABSTRACT FROM AUTHOR]

A new reliability analysis method for tunnels was developed by integrating an adaptive Radial Basis Function (RBF) metamodeling technique with a First-Order Reliability Method (FORM). In each iteration of the adaptive RBF (A-RBF) technique, an explicit metamodel of the performance function was constructed using an augmented RBF, before an alternate FORM was applied. Additional sample points were then added in the neighborhood of the design point in order to improve the accuracy of the metamodel. Three examples were solved and the proposed approach worked well. This work provides an efficient and effective reliability analysis method for practical tunnel engineering problems. [ABSTRACT FROM AUTHOR]

Accidents such as those caused by rollovers and sideslips in complex driving environments involving heavy-duty vehicles (HDVs) often have serious consequences. Such accidents can be due to many factors. In this paper, a probabilistic method for predicting and preventing these accidents is presented. First, a specific vehicle dynamics model based on various random parameters that consider the wind velocity and road curvature is developed. Second, a safety margin function is defined to divide the safe and dangerous domains in the parameter space. Then, the first-order reliability method and second-order reliability method approximations are developed to evaluate the probability of such an accident by using the vehicle dynamics model. Finally, the probability model is applied to explore the interrelations and sensitivities of those parameters with regard to their effects on the accident probability in different scenarios. The study suggests that the presented probabilistic methodology can effectively estimate rollovers and sideslips of HDVs in complex environments, which represent a challenge for the prediction of accidents based on sensors alone. [ABSTRACT FROM PUBLISHER]

This paper presents a comparative study of long-time irregular waves and equivalent design waves (EDW) in terms of geometric similarity and probability of exceedance (POE) distribution of the wave crest. For a proper comparison between the two wave types, the same nonlinear model was applied in the wave generation by application of the Higher-Order Spectral-Numerical Wave Tank (HOS-NWT), a fully nonlinear propagation solver. Numerical and experimental Monte-Carlo results were obtained through a number of realizations of a given sea state, and results were used as a reference for the EDW results. The experimental measurements and numerical simulations for a given sea state were analyzed and compared in terms of the wave spectrum estimation and the POE distribution of wave crests. The agreement between experimental and numerical results in wave quality seemed sufficient for it to be used as a reference for EDW cases. The First-Order Reliability Method (FORM) approach was applied in the calculation of EDW. The geometrical similarity between the measured EDW wave signal and the corresponding irregular wave signals measured in a given sea state was reviewed. It confirmed that the FORM-based EDW generates a comparable wave profile. In the statistical analysis, however, the results showed that for some EDW cases in relatively severe sea states, the POE estimates by the FORM method appeared to have conservative values compared to the Monte-Carlo reference POE distribution, whereas for the EDW cases in moderate sea states, the estimated POEs were in very good agreement with the empirical wave crest POE distribution of a given sea state. • Validation of HOW-NWT ability to reproduce crest statistics in breaking sea state through the cross-validation with experimental results. • Development and validation of the FORM optimization algorithm coupled with the fully nonlinear wave solver HOS-NWT. • Evaluation of geometrical characteristics and estimated crest statistics of the FORM-based EDW to the long-time irregular wave results. [ABSTRACT FROM AUTHOR]

The first-order reliability method (FORM) is a powerful tool for structural reliability analysis, providing a good trade-off between computational accuracy and efficiency. Nevertheless, it has two main drawbacks: (1) its approximation is not necessarily adequate for limit state surfaces which depart significantly from linearity, and (2) it does not give information about the degree of accuracy achieved. In this paper, the secant hyperplane method (SHM) is proposed, which is a new linear approximation of the limit state surface based on the support vector method (SVM). The key idea is to treat structural reliability as a classification problem and to seek a suitable secant hyperplane to the limit state that gives improved approximation over the use of a tangent hyperplane. The two drawbacks of FORM are thereby resolved, while keeping the geometrical simplicity and ease of implementation of FORM. The implication of very high-dimensional geometry is examined, demonstrating that FORM can give good approximations if reinterpreted as a linear classifier, and SHM has the potential of scalability to spaces of high dimensionality. Two numerical examples, including stochastic dynamic analysis, show the accuracy and effectiveness of SHM. [ABSTRACT FROM AUTHOR]

Reliability and optimization are two key elements for structural design. The reliability-based topology optimization (RBTO) is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topology optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach (the performance measure approach, PMA) and the decoupled approaches (the so-called Hybrid method and the sequential optimization and reliability assessment, SORA). For reliability analysis, the stochastic response surface method (SRSM) was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the deterministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn. [ABSTRACT FROM AUTHOR]

The model correction factor method (MCFM) is adopted to assess the reliability of a Suezmax oil tanker considering the ultimate vertical bending moment capacity of the hull girder as a limit state. The approach uses the incremental iterative method proposed by the International Association of Classification Societies (IACS) Common Structural Rules (CSR) to evaluate the hull girder ultimate strength as a response model that is calibrated iteratively at the design points calculated by the First Order Reliability method (FORM) by means of advanced non-linear Finite Element Analyses (FEA). The considered loads are the still water and the wave-induced bending moments in a typical seagoing operational condition of the oil tanker in the full load and ballast load conditions. First, the predictions of the hull girder bending capacities calculated by the IACS-CSR method and by non-linear FEA are compared and then the efficiency of the MCFM for hull girder reliability problems is illustrated. It is shown that using semi-empirical response models, which include the important mechanical features with respect to the bending capacity of the ship hull girder, the reliability evaluation can be performed with a limited number of non-linear FEAs (less than 10) promoting the application of advanced response and reliability methods to complex structures. [ABSTRACT FROM AUTHOR]

Bridge scour is the loss of soil by erosion because of water flowing around bridge supports. Scour has been the number one cause of bridge failure in the United States with an average annual rate of 22 bridges collapsing or being closed owing to severe deformation. This paper addresses three topics related to bridge scour. First, a set of databases was used to quantify the statistical parameters associated with the scatter between the predicted and measured pier scour depth, as well as the probability that a deterministically predicted pier scour depth will be exceeded. These databases also were used to provide the bias factors in current predictions. Secondly, these statistical parameters were used to develop a reliability-based load and resistance factor design for shallow and deep foundations subjected to scour. The goal was to provide a design procedure where the reliability of the foundation is the same with or without scour. Reliability only addresses the probability of success and, therefore, of failure. Finally, the discussion was broadened by using the concept of risk defined as the probability of failure times the value of the consequences. In this third part, the risk associated with bridge scour was quantified and compared to risks associated with other engineering structures. Target values of acceptable risk were recommended as part of the conclusions. [ABSTRACT FROM AUTHOR]

The uncertainty in material properties and traffic characterization in the design of flexible pavements has led to significant efforts in recent years to incorporate reliability methods and probabilistic design procedures for the design, rehabilitation, and maintenance of pavements. In the mechanistic-empirical (ME) design of pavements, despite the fact that there are multiple failure modes, the design criteria applied in the majority of analytical pavement design methods guard only against fatigue cracking and subgrade rutting, which are usually considered as independent failure events. This study carries out the reliability analysis for a flexible pavement section for these failure criteria based on the first-order reliability method (FORM) and the second-order reliability method (SORM) techniques and the crude Monte Carlo simulation. Through a sensitivity analysis, the most critical parameter affecting the design reliability for both fatigue and rutting failure criteria was identified as the surface layer thickness. However, reliability analysis in pavement design is most useful if it can be efficiently and accurately applied to components of pavement design and the combination of these components in an overall system analysis. The study shows that for the pavement section considered, there is a high degree of dependence between the two failure modes, and demonstrates that the probability of simultaneous occurrence of failures can be almost as high as the probability of component failures. Thus, the need to consider the system reliability in the pavement analysis is highlighted, and the study indicates that the improvement of pavement performance should be tackled in the light of reducing this undesirable event of simultaneous failure and not merely the consideration of the more critical failure mode. Furthermore, this probability of simultaneous occurrence of failures is seen to increase considerably with small increments in the mean traffic loads, which also results in wider system reliability bounds. The study also advocates the use of narrow bounds to the probability of failure, which provides a better estimate of the probability of failure, as validated from the results obtained from Monte Carlo simulation (MCS). [ABSTRACT FROM AUTHOR]

The response surface method (RSM) is a powerful approach for carrying out reliability analysis for complicate engineering with implicit limit state functions. The quality of a response surface mainly depends on the choice of response surface function and the selection of sample points. To investigate the influence of the types of response surface functions and to reduce the computation efforts, two new sampling methods and a hybrid RSM are proposed. In the hybrid RSM, four types of response surface functions and three sampling methods are involved, and each Response surface function can be connected to each sampling method. The four response surface functions are quadratic polynomial without cross terms (PN1), quadratic polynomial with cross terms, radial basic function network (RBFN) and support vector machine (SVM). The three RSMs using the traditional sampling method, the new iterative sampling method and the new experiment design method are RSM1, RSM2 and RSM3, respectively. The accuracy and efficiency of different RSMs are illustrated through three examples. When an iterative method is used for locating sample points, the PN1-based RSM2 is proposed for its accuracy and efficiency. And when an experiment design method is used for locating sample points, the RBFN- or SVM-based RSM3 is suggested because the RBFN or SVM is suitable for global fitting. [ABSTRACT FROM AUTHOR]