Reliability Analysis of a Deep Excavation Problem

The reliability of a simple turbomachinery model was calculated to demonstrate the application of a newly developing system integration tool, Probabilistic Design and Analysis Framework(PRODAF), along with efficient probabilistic methods using a response surface method. The model represents a system consisting of hypothetical turbine components. The parts include a blade, disk, and shaft with an applied angular velocity. All the components were modeled with the properties of the nickel alloy, Inconel 718. A response surface was calculated for the system of components to improve probabilistic computational efficiency. In addition, a fast probability integration method, Advanced First Order Reliability Method (AFORM), was used for the probabilistic analysis in order to provide an efficient analysis as possible. Geometric dimensions, the applied load, and material yield strength were varied for this study. The probability of failure was determined using the maximum first principal stress response and the material yield strength. A simple G function using the difference between strength and loading stress was used to determine failure limits. The probabilistic sensitivity of the failure response relative to the individual variables was determined also with material yield strength having the greatest influence. The model was recreated with every iteration of the probabilistic analysis in order to vary the geometry. As a result, the response surface method has a significant impact on improving computational efficiency and enabling reliability analysis with rapid turnaround.

Reliability has been incorporated in many pavement design procedures to account for the effects of inputs variabilities and uncertainties on predicted performance. The American Association of State Highway and Transportation Officials (AASHTO) mechanistic empirical pavement design guide (MEPDG) computes the reliability of pavement sections with the assumption that the variability of predicted distresses follows normal distribution. This approach does not account for the systematic contribution of each design input variability on the overall output variance. This paper evaluates a two-component reliability analysis methodology for pavement application. The two-component reliability analysis methodology uses a response surface method (RSM) for a surrogate model generation and the first order reliability method (FORM) for reliability computation. Three different response surface methods (central composite, Box–Behnken and Doehlert designs) were implemented and statistically verified for their suitability for surrogate model generation. The two-component reliability analysis methodology was further utilized for the generation of partial safety factors for the development of a load and resistance factor design (LRFD) procedure for pavement applications. Field pavement sections with a wide range in design inputs and target reliabilities were used to evaluate the proposed reliability analysis methodology. The results have shown that the three RSM can be used effectively for pavement reliability problems.

In this paper tunnel probabilistic structural analysis (TuPSA) was performed using the first order reliability method (FORM). In TuPSA, a tunnel performance function is defined according to the boundary between the structural stability and instability. Then the performance function is transformed from original space into the standard normal variable space to obtain the design point, reliability index, and also the probability of tunnel failure. In this method, it is possible to consider the design factors as the dependent or independent random parameters with arbitrary probability distributions. A software code is developed to perform the tunnel probabilistic structural analysis (TuPSA) using the FORM. For validation and verification of TuPSA, a typical tunnel example with random joints orientations as well as mechanical properties has been studied. The results of TuPSA were compared with those obtained from Monte-Carlo simulation. The results show, in spite of deterministic analysis which indicates that the rock blocks are stable, that TuPSA resulted in key-blocks failure with certain probabilities. Comparison between probabilistic and deterministic analyses results indicates that probabilistic results, including the design point and probability of failure, are more rational than deterministic factor of safety.

Mapping probability of liquefaction using geostatistics and first order reliability method based on CPTU measurements

Since the commencement of regulations and standards, the sustainability of civil engineering structures has been a recurrent issue for the construction industry and society at large. The practical design process of engineering structures, in accordance with national guidelines, addresses uncertainties related to the stochastic nature of parameters such as climate loads, structural materials, or model limits. These uncertainties are taken into consideration through initial probabilistic assumptions and safety factors. However, safety factors derived mathematically based on code‐driven presumptions often fail to accurately represent the unique conditions of an individual structure. Although the development of structural health monitoring (SHM) techniques allows for a significant reduction in the uncertainty of the action and resistance, the ability to transform monitoring information to reevaluate the design capacity of existing structures is limited at the practical level. This paper provides an example of how design can be enhanced by incorporating sensor data and using the Bayesian inference and First Order Reliability Method (FORM), tailored to accurately reflect the current structural condition.

Probabilistic resilience assessment framework of structures considering the combined functionality-recovery-duration uncertainty

Moderate (3H : 1V) to steep (2.5H : 1V) slopes and embankments underlain by expansive clayey soils are susceptible to shallow land sliding during intense and prolonged rainfall events. These failures are predominant in the North Texas area and cause significant maintenance problems for the Texas Department of Transportation (TxDOT). The recycled plastic pin (RPP) has potential to be utilized in slope stabilization as a remedial measure of shallow slope failure. A parametric study was conducted to evaluate the effect of different spacings of RPP on the factor of safety and deformation of the slope. The objective of the current study was to investigate the effect of spacing and length of RPP over the factor of safety using the finite element method (FEM). The analysis was conducted using 2D FEM software package PLAXIS 2D, and factor of safety of the slope was determined using the strength reduction technique. A highway slope constructed using high plastic clayey soil, located over US 287 near St. Paul overpass in Midlothian, Texas, was selected as the reference slope. The strength of the slope was back analyzed using PLAXIS 2D at factor of safety equals to unity. As a remediation technique, RPP was selected for slope stabilization, and the slope was analyzed with different lengths (2.44 m to 3.65 m, 8 ft to 12 ft) and spacings (0.61 m c/c to 2.44 m c/c, 3 ft c/c to 8 ft c/c) of RPP. The FEM results indicated that RPP provided resistance against the shallow failure and resulted increment in factor of safety by shifting the failure plane to a deeper depth toward deep-seated failure. In addition, the factor of safety increased with the increment in RPP length as higher resistance was observed from the foundation soil. The factor of safety of the reinforced slope remained almost constant up to RPP spacing of 1.5 m (5 ft) c/c and then decreased with further increments in spacing. The horizontal deformation of the slope was greater with the increments in spacing of RPP.

Introduction:Reliability analysis is a good tool to deal with the uncertainty and has been widely used in the engineering system. The first order reliability method (FORM) is generally used to calculate the reliability index but FORM is time-consuming and requires derivative computing.Methods:Artificial Bee Colony (ABC) algorithm is a very simple, robust and population-based stochastic optimization algorithm. In this study, an ABC-based reliability analysis was proposed to calculate the reliability index of engineering system through combining Artificial Bee Colony (ABC) algorithm with FORM. FORM was adopted to calculate the reliability index and design point. ABC is used to solve the constrained optimization about FORM. The procedure of ABC-based reliability analysis was presented in detail.Results and Conclusion:The proposed method was verified by two classic examples and then applied to geotechnical engineering. The results show that the ABC algorithm can effectively solve the global optimization problem in FORM. Results demonstrate that ABC-based reliability analysis is a good approach to obtain the reliability index and design point with a good accuracy so that it can be applied to analyze the reliability of a complex engineering system.

This paper presents a reliability-based analysis of a shallow foundation subjected to a central vertical load, using the limit equilibrium theory. The reliability index is calculated by applying the first order reliability method (FORM). A deterministic model based on the Meyerhof equations is employed to compute the ultimate bearing capacity of the foundation. The concept of response surface method (RSM) is used for the assessment of the Hasofer–Lind reliability indexes by generating an approximate polynomial function for the performance function. In this study, unit weight and the soil shear strength parameters are considered as random variables. The optimization of the Hasofer-Lind reliability index is performed using a combination of response surface model and the multi-objective genetic algorithm.KeywordsReliability analysisShallow foundationRSMOptimizationGenetic algorithm

This paper presents an integrated approach to robust product design using a probability of conformance metric. By integrated we imply that parameter design and tolerance design are performed simultaneously. The probability metric measures conformance of quality characteristics (responses) with respect to their specified limits, or tolerances. Probability is calculated from joint probability distributions of the design variables using first order reliability methods (FORM). When multiple quality characteristics arise, it is convenient to determine the probability of the union of the non-conformance regions. This probability combined with unit scrap costs is used to directly evaluate the so-called loss of quality costs. Any appropriate model of the production costs may be invoked. The methods used in this paper are model-based and the models can be mechanistic or derived using response surface methodology or any other method. An algorithm is presented that minimises the sum of production costs and loss of quality costs. The method herein is quite different from the expected loss approach. In this paper, the method is discussed and compared with expected loss approaches using two supporting examples.

This paper presents a methodology to perform global reliability based design optimization (RBDO) of the size and shape of truss structures. This methodology is comprised by the use of a global constraint and the response surface method to deal with the reliability analysis together with the firefly algorithm (FA) to carry out the structural optimization. The former is responsible for the reduction of the computational cost required in the evaluation of the probabilistic constraints. The latter overcomes the issues related to the non-convexity and mixed-variables of the optimization problem. Two examples are analysed in order to show the effectiveness of the methodology. In these examples, the FA is compared to other two well-known algorithms, the harmony search (HS) and genetic algorithm (GA). As a result, the FA reached the best performance in the examples analysed. All the optima found were checked using a classical first order reliability method (FORM) approach, validating the results provided by the response surface method.

In this work, a novel framework is proposed for the risk based design optimization of engineering systems by minimizing the demand on the system components’ accuracy (which directly relates to their cost). The fundamental development of this work is an analytical upper bound for calculating the probability of failure. This is in contrast with First Order Reliability Method (FORM), where a lower bound is used in calculating the probability of failure. FORM is one of the most popular methods for reliability analysis of engineering systems. In this paper, we show that FORM results in an optimistic measure of risk, hence potentially catastrophic in engineering design. A more accurate measure of failure is proposed by utilizing an analytical upper bound for the distribution of reliability index (the length of the most probable point vector to origin). This distribution is a function of the eigenvalues of the linearized limit state function in the normal space which results in a better understanding of failure phenomenon. The proposed formulation is computationally efficient and straightforward to solve, since it only involves finding eigenvalues in each iteration. This algorithm is applicable to any linearizable continuous limit state function with any type of distribution for the design variables. The method is applied to two examples and its accuracy is compared with the Monte Carlo simulation and FORM, demonstrating its effectiveness and value.

A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis

Improved response surface method and its application to stiffened plate reliability analysis

Reliability analysis of corroded pipelines: Novel adaptive conjugate first order reliability method