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Engineered Cementitious Composite (ECC) material, as a hybrid material, also has uncertainties. In addition, the shear failure mechanism of reinforced ECC (R-ECC) member is different from that of ordinary reinforced concrete (RC) member, and a new material partial factor of ECC is needed. This paper conducted experiments for the statistical mechanics of ECC strength. The shear failure test data of 36 R-ECC members were collected, and four representative bearing capacity calculation models were also collected and assessed. Then, the limit state function of the shear capacity of R-ECC beams was derived, and the reliability indexes were calculated. To evaluate the ECC material partial factor reasonably, it was calibrated. The results indicate that ECC strength obeys a normal distribution, and the coefficient of variation can be taken as 6.0%. The calculated reliability index will increase with the increase of the material partial factor and the increase of the ratio k between dead load and live load. Considering the different k values comprehensively, for the guidelines GB 50068-2018, CSA S806, ACI 440.2R, CIDAR, fIB TG 9.3 and UK TR 55, the recommended values for the material partial factor are 1.20, 1.10., 1.15, 1.55, 1.05, and 1.05, respectively. [ABSTRACT FROM AUTHOR]

Earthquake resistance of bridge structures is an important part of ensuring the functionality of transportation network systems. The structural system of a bridge is composed of multiple components, and the damage of different components may affect the function of the bridge, while the system seismic fragility analysis provides an effective way to evaluate the overall seismic performance of the bridge. In the past, the failure probability of a system is often estimated by the correlation between components, but the complex correlation between components brings certain difficulties to the actual calculation. In this paper, an efficient, accurate and universal method of system fragility analysis is proposed. This method decouples the correlation between components from the perspective of relative damage, adopts the critical demand-to-capacity ratio as the response variable of the system, realizing the dimensionality reduction of the response variables and simplifying the system fragility analysis from high-dimensional fragility analysis to one-dimensional fragility analysis. This methodology offers a viable solution to the challenges posed by the wide estimation of fragility boundaries in the boundaries estimation method and the complexities involved in analyzing correlation of components in the joint probability method. Comparison with traditional methods indicates that the proposed method exhibits high efficiency and convenience, making it suitable for practical engineering applications in system fragility computation. The proposed method holds great potential for future applications in the field of complex bridge structure fragility analysis, large-scale regional seismic damage prediction, rapid assessment, and beyond. [ABSTRACT FROM AUTHOR]

Engineered Cementitious Composite (ECC) material, as a hybrid material, also has uncertainties. In addition, the shear failure mechanism of reinforced ECC (R-ECC) member is different from that of ordinary reinforced concrete (RC) member, and a new material partial factor of ECC is needed. This paper conducted experiments for the statistical mechanics of ECC strength. The shear failure test data of 36 R-ECC members were collected, and four representative bearing capacity calculation models were also collected and assessed. Then, the limit state function of the shear capacity of R-ECC beams was derived, and the reliability indexes were calculated. To evaluate the ECC material partial factor reasonably, it was calibrated. The results indicate that ECC strength obeys a normal distribution, and the coefficient of variation can be taken as 6.0%. The calculated reliability index will increase with the increase of the material partial factor and the increase of the ratio k between dead load and live load. Considering the different k values comprehensively, for the guidelines GB 50068-2018, CSA S806, ACI 440.2R, CIDAR, fIB TG 9.3 and UK TR 55, the recommended values for the material partial factor are 1.20, 1.10., 1.15, 1.55, 1.05, and 1.05, respectively.

We propose a reliability-based anti-disturbance control (RADC) method for systems with parametric stochastic uncertainty based on the linear matrix inequality (LMI) and the limit state function. Differing from the existing anti-disturbance control, the parametric stochastic uncertainty is considered in both the concerned system and the exogenous disturbance system. With this consideration, the condition for system stability and performance robustness is described by a stochastic LMI which holds with a certain probability (reliability). Through the limit state function method, the stochastic LMI is subtly transformed into two probabilistic LMIs for two different cases. The proposed probabilistic LMIs contain two probabilistic parameters of reliability indexes that quantify the effect of parametric stochastic uncertainty. At different prescribed reliability indexes, controllers with different reliability can be flexibly and reliably designed. Two illustrative examples with Monte-Carlo verification are presented to demonstrate the feasibility and effectiveness of the proposed RADC method. • A reliability model for uncertain systems is established by stochastic LMI. • A novel concept/method of probabilistic LMI for RADC is proposed. • The proposed RADC greatly extends the application of traditional LMI. [ABSTRACT FROM AUTHOR]

Reliability is defined as the probability that an item or structure will perform a required function for a specified period under defined conditions. The objective of reliability analysis methods is to determine the probability of failure and/or the reliability index of structures, by taking into account the uncertainties related to resistances and stresses (loads). With the very powerful tools of probabilistic theory and ever-increasing calculation methods, reliability analysis methods have shown their effectiveness in considering uncertainties. Many probabilistic methods that efficiently calculate the probability of failure and/or the reliability index are frequently used in engineering: the first order approximation methods FORM / FOSM (First Order Reliability Method / First Order Second Moment), the second-order approximation methods SORM / SOSM (Second Order Reliability Method / Second Order Second Moment), the Rosenbleuth method (Point Estimates Method) and the Monte Carlo (MC) simulation method, which notably makes it possible to obtain the probability sampling failure of the input distributions. In this work, an application of Monte Carlo simulation will be presented to evaluate the reliability of a retaining wall. The triangular distribution is used to simulate random variables. The calculations and the simulations have been carried out in Matlab. [ABSTRACT FROM AUTHOR]

Fatigue crack propagation tests are carried out on arc-shaped specimens prepared from MDPE gas pipes. Damage zone characterization is achieved using the diamond wafer sectioning technique from partially propagated and prematurely arrested cracks. Damage ahead of the crack-tip is used to assess a damage parameter and reliability based on statistical laws and subsequent use the PHIMECA Software. It is shown that a length and a width associated with a corresponding change in thickness at the fracture surface satisfactorily describe the damage zone size. The 3-parameter Weibull model gives the best reliability behavior and a critical lifetime of 82%. When considering separately both the Dugdale model and experimental damage zone measurements, it is possible to establish the evolution of the reliability index as a function of crack length. It is concluded that the reliability index approach based on damage provides a more consistent representation compared to analytical models.

Sampling of training data is the most important step in active learning slope reliability analysis, which controls the analysis accuracy. In this study, a novel surrogate-assisted normal search particle swarm optimization (SANSPSO) was proposed to enhance the accuracy and robustness of existing methodologies. In SANSPSO, the sampling process was considered a minimum problem with an objective function defined as the absolute value of the performance function. Initiated with a normal search paradigm and supplemented by three algorithm strategies, this approach seeks to preserve the continuity of the solution while refining the algorithm's efficacy and efficiency. To reduce computation cost, surrogate-assistance was used, in which a surrogate model substitutes the objective function in most iterations. This surrogate model evolves during the iteration process and ultimately replaces the actual performance function within Monte Carlo simulation. Finally, this study presents a comparative study with five state-of-the-art methods across four explicit problems and three engineering cases, where test data suggest that the SANSPSO methodology yields a 20% improvement in accuracy and a 30% rise in stability under different dimensional problems relative to the most efficacious of the alternate methods assessed because of the improved and more consistent prediction of limit state function. These findings substantiate the validity and robustness of the SANSPSO approach. [ABSTRACT FROM AUTHOR]

The stability of underground parallelepiped coal pillars formed during trunk road development in inclined coal seams is very important for safe access to the mine workings. These protective coal pillars developed around the trunk roads have the longest life span in coal mines. Although these pillars are designed with high safety factors, their failures continue to occur especially in inclined coal mines. The acute corners of parallelepiped coal pillars are highly stressed and prone to failure. These failures may be attributed to the deterministic safety factor which does not consider field geotechnical uncertainties in their design parameters. This research work identified the geotechnical uncertainties in pillar designs and incorporated them in designing stable pillars in inclined coal seams. A probabilistic approach based on limit state function has been proposed for designing stable parallelepiped coal pillars and validated in an inclined coal mine. In this study, the working stresses of the inclined coal pillars are varied for evaluating their influence on pillar reliability using the three cases of the limit state functions namely, empirical, numerical average, and numerical maximum. The pillar reliabilities were estimated by Monte Carlo Simulation. The results indicate that the empirical and numerical average cases yielded stable pillars, whereas the numerical maximum case provided an unstable design. The correlation between safety factor and reliability has been established which can predict the reliability for a given safety factor of pillars with a similar range of design inputs. Further, the threshold values of pillar sizes, acute corner angles, and seam gradients for the reliable pillar design have been determined by sensitivity analysis. These findings can help in designing stable parallelopiped pillars, especially in inclined coal seams to reduce pillar failures and enhance mine safety. Highlights: Key geotechnical uncertainties in coal pillar stability parameters are identified A limit state function-based probabilistic design approach is proposed to include geotechnical uncertainties. The reliabilities of parallelepiped pillars in inclined coal seams are estimated using the Monte Carlo Simulation method. The correlation between pillar reliability and the safety factor of parallelepiped coal pillars is established. Threshold values of design parameters are determined for stable parallelepiped pillars using sensitivity analysis. [ABSTRACT FROM AUTHOR]

Traditional 3D slope reliability analysis methods have high computational costs and are difficult to popularize in engineering practice. Under the framework of the limit equilibrium method with 3D slip surface normal stress correction, the critical horizontal acceleration coefficient K c , which is equivalent to the safety factor F s , is selected to characterize the slope stability. The limit state function uses the difference between K c and the known critical value K c 0 . A simplified method for calculating the reliability of 3D slope is proposed. Through two typical slope examples, the 3D reliability calculation results of six methods after coupling two limit state functions and three reliability algorithms are compared. The results show that this method is reliable and effective, and the method coupled with subset simulation (SS) is the one with good calculation accuracy and efficiency. In the case of long slopes, 2D analysis results may underestimate the probability of slope instability, and 3D reliability of the slope must be analyzed. [ABSTRACT FROM AUTHOR]

Traditional rigorous limit equilibrium methods satisfy all equilibrium conditions and usually have high accuracy, however, which are less efficient for slope reliability analysis. The main reason is that the limit state functions are highly nonlinear implicit functions of safety factor. Complex numerical iterations are required, which may sometimes lead to computational convergence problems. A new method for computing slope reliability calculation with high efficiency and accuracy was proposed. This method was based on the rigorous limit equilibrium method by modifying normal stresses over the slip surface. The critical horizontal acceleration factor Kc{K}_{c}, which can be expressed explicitly, was used to replace the implicit safety factor as a representation of slope stability. The difference between Kc{K}_{c} and the known value Kc0{K}_{c0} was used as the limit state function. Two slope examples were analyzed. The results showed that the calculation results of this method were in good agreement with those of the traditional Morgenstern–Price limit equilibrium method, but the computational efficiency was significantly improved. When this method was combined with the subset simulation method, the calculation time was only a few seconds. Therefore, this method can be used for rapid calculation of slope reliability.

Fatigue crack propagation tests are carried out on arc-shaped specimens prepared from MDPE gas pipes. Damage zone characterization is achieved using the diamond wafer sectioning technique from partially propagated and prematurely arrested cracks. Damage ahead of the crack-tip is used to assess a damage parameter and reliability based on statistical laws and subsequent use the PHIMECA Software. It is shown that a length and a width associated with a corresponding change in thickness at the fracture surface satisfactorily describe the damage zone size. The 3-parameter Weibull model gives the best reliability behavior and a critical lifetime of 82%. When considering separately both the Dugdale model and experimental damage zone measurements, it is possible to establish the evolution of the reliability index as a function of crack length. It is concluded that the reliability index approach based on damage provides a more consistent representation compared to analytical models. [ABSTRACT FROM AUTHOR]

Reliability analysis of bridges is essential for the design of civil engineering structures. The classical methods, such as Monte Carlo Simulation (MCS) and subset simulation techniques, may provide accurate results. However, since the finite element model of the large‐scale civil engineering structures usually consists of a large number of degrees of freedom, structural reliability analysis of such structures is time‐consuming and computational intensive, which may restrict the use of these methods. This paper proposes a novel method for the reliability analysis of bridge under different types of loads by combining Polynomial Chaos (PC) and subset simulation techniques. The surrogate model of the limit state function is approximated by using the PC expansion, in which the PC coefficients are obtained from the least‐squares method. The subset simulation with a PC‐based surrogate model is then used to estimate the rare failure probability. Reliability analyses of bridge structures under different loading types, that is, static load, dynamic moving load, and seismic load are performed. Studies by using the MCS method and the classical subset simulation are also conducted, and the results from the proposed approach are compared with those from MCS and subset simulation to demonstrate the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Featured Application: The present study can provide an efficient sampling method for candidate points in the iteration process of active learning reliability analysis. In active learning reliability methods, an approximation of limit state function (LSF) with high precision is the key to accurately calculating the failure probability (Pf). However, existing sampling methods cannot guarantee that candidate samples can approach the LSF actively, which lowers the accuracy and stability of the results and causes excess computational effort. In this paper, a novel candidate samples-generating algorithm was proposed, by which a group of evenly distributed candidate points on the predicted LSF of performance function (either the real one or the surrogate model) could be obtained. In the proposed method, determination of LSF is considered as an optimization problem in which the absolute value of performance function was considered as objective function. After this, a normal search particle swarm optimization (NSPSO) was designed to deal with such problems, which consists of a normal search pattern and a multi-strategy framework that ensures the uniform distribution and diversity of the solution that intends to cover the optimal region. Four explicit performance functions and two engineering cases were employed to verify the effectiveness and accuracy of NSPSO sampling method. Four state-of-the-art multi-modal optimization algorithms were used as competitive methods. Analysis results show that the proposed method outperformed all competitive methods and can provide candidate samples that evenly distributed on the LSF. [ABSTRACT FROM AUTHOR]

In structural reliability analysis, Hasofer-Lind and Rackwitz-Fiessler (HL-RF) method is a widely used approximation method for evaluating the reliability index. However, by increasing the nonlinearity or complexity in the limit state function of a structure, HL-RF may get in trouble for convergence. This paper represents an iterative algorithm that tries to minimize the Lagrange function, associated with the reliability problem. In each iteration of this method, two steps are followed, to satisfy the minimization condition and the existing constraint. In the first step, a movement for minimization in a descent direction is followed. In the second step, another search direction contributes to approach limit state surface, and therefore the next iteration can start from the vicinity of the surface. Employing Lagrange reliability function and limit state function simultaneously in the proposed two-step Lagrangian-based method (TSLB) can help to control the numerical instability in highly nonlinear problems. The accuracy and robustness of the proposed algorithm are shown in illustrative examples of the literature. Keywords two-step Lagrangian-based method (TSLB), reliability index, limit state function, HL-RF method [ABSTRACT FROM AUTHOR]

• Limit state surface is approximated by piecewise hyperplanes at multiple points. • Joint focal elements are divided into three sets to reduce computation cost. • A new rule for reliability analysis based on evidence theory is presented. • Accuracy and efficiency of the methodology are verified by numerical examples. Evidence theory has been applied in structural reliability assessment to address epistemic uncertainties, given its capability to deal with imprecise, incomplete and even contradictory information. An important challenge in structural reliability assessment based on the framework of evidence theory is its expensive computational cost in multidimensional problems. In this work, a modified multiple linearization method is proposed to identify a set of hyperplane approximations to the limit state function. It provides a clear guidance for the hyperplanes by evaluating curvature magnitude of the original limit state at the most probable point along each axis in the rotated standard normal space, and shows good stability and satisfactory accuracy in nonlinear reliability analysis based on evidence theory. The belief measure and plausibility measure of the structure are assessed by the hyperplanes through the intersection or union of the failure domains. In the meantime, the classification and division of focal elements in failure set, safety set and uncertain set will be made through the segment edge of the failure and safety domain to reduce the computation burden. Finally, four mathematical examples and engineering cases are explored to illustrate the methodology and show its benefits. [ABSTRACT FROM AUTHOR]

In active learning reliability methods, an approximation of limit state function (LSF) with high precision is the key to accurately calculating the failure probability (Pf). However, existing sampling methods cannot guarantee that candidate samples can approach the LSF actively, which lowers the accuracy and stability of the results and causes excess computational effort. In this paper, a novel candidate samples-generating algorithm was proposed, by which a group of evenly distributed candidate points on the predicted LSF of performance function (either the real one or the surrogate model) could be obtained. In the proposed method, determination of LSF is considered as an optimization problem in which the absolute value of performance function was considered as objective function. After this, a normal search particle swarm optimization (NSPSO) was designed to deal with such problems, which consists of a normal search pattern and a multi-strategy framework that ensures the uniform distribution and diversity of the solution that intends to cover the optimal region. Four explicit performance functions and two engineering cases were employed to verify the effectiveness and accuracy of NSPSO sampling method. Four state-of-the-art multi-modal optimization algorithms were used as competitive methods. Analysis results show that the proposed method outperformed all competitive methods and can provide candidate samples that evenly distributed on the LSF.

Reconstructing the probability density function (PDF) of the limit state function (LSF) is regarded as a non-intrusive method for forward uncertainty propagation and reliability analysis. In this paper, a novel non-parametric density estimation method is proposed to derive the unknown distribution of the LSF for this purpose, where the efficiency and accuracy are ensured. The main innovation of the paper is to derive the PDF of the LSF via a novel concept, i.e., the harmonic transform, regardless of the complexity of the problem. First, the non-parametric method for PDF estimation based on complex fractional moments/Mellin transform is briefly revisited, where the limitations are also pointed out. Inspired from Mellin transform, the concept of harmonic transform is put forward, which overcomes the disadvantages of Mellin transform. Then, the unknown PDF is recovered via the inverse harmonic transform, where the analytical formula is derived accordingly. Numerical estimation method is also given for practical implementations, where some critical issues are also pointed out. Detailed step-by-step procedures of the proposed method are also outlined. The proposed method is a non-parametric one since it does not require a distribution model in advance. Some commonly-used distributions are first applied to validate the efficacy of the proposed method. Then, four numerical examples involving different types of problems are extensively investigated to validate the proposed method for forward uncertainty propagation and reliability analysis. The results demonstrate that the proposed method is effective for deriving the PDFs for both static and dynamic reliability analyses with nonlinear explicit or implicit LSFs. • A novel concept, named as harmonic transform, is proposed. • A non-parametric density estimation method is established. • The proposed method can recover the unknown distribution with irregular shape. • The proposed method outperforms Mellin transform and other reliability analysis methods. [ABSTRACT FROM AUTHOR]

• Three heuristic algorithms for reliability estimation. • Reducing redundant samplings using breadth-first search of a grid tree. • Securing a prescribed accuracy of reliability. • Detecting large curvatures on the limit state surface. • Fast computation of the reliability index via a deleting process. A complete search of the input space is crucial for securing the accuracy of reliability estimation, but conventional search algorithm-based methods require a large number of samples to visit the entire input space. To this end, this paper presents three heuristic algorithms for reliability estimation based on breadth-first search (BFS) of a grid tree (GT), namely the reliability accuracy supervised search algorithm (RASSA), the limit state surface resolution supervised search algorithm (LSSRSSA), and the reliability index precision supervised search algorithm (RIPSSA). All the proposed algorithms are characterized by traversing the entire input space through a GT while simultaneously reducing redundant samplings through BFS, and each one has its own special advantage as follows: RASSA can guarantee a prescribed accuracy of reliability estimation; LSSRSSA is able to probe large curvatures on limit-state surfaces; and RIPSSA quickly computes the reliability index. The computational costs and limitations of the proposed algorithms are analyzed. In addition, the accuracy, efficiency, and practicality of the proposed algorithm are validated through comparisons with other methods and an engineering application. [ABSTRACT FROM AUTHOR]