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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]

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]

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]