A simplified approach to reliability evaluation of deep rock tunnel deformation using First-Order Reliability Method and Monte Carlo simulations

abstract: The Monte Carlo simulation (MCS) and First-Order Reliability Method (FORM) provide a reliability analysis in axisymmetric deep tunnels driven in elastoplastic rocks. The Convergence-Confinement method (CV-CF) and Mohr-Coulomb (M-C) criterion are used to model the mechanical interaction between the shotcrete lining and ground through deterministic parameters and random variables. Numerical models synchronize tunnel analytical models and reliability methods, whereas the limit state functions control the failure probability in both ground plastic zone and shotcrete lining. The results showed that a low dispersion of random variables affects the plastic zone's reliability analysis in unsupported tunnels. Moreover, the support pressure generates a significant reduction in the plastic zone's failure, whereas the increase of shotcrete thickness results in great reduction of the lining collapse probability.

Hybrid Approach to the First Order Reliability Method in the Reliability Analysis of a Spatial Structure

The objective of the article involves presenting two approaches to the structure reliability analysis. The primary research method was the First Order Reliability Method (FORM). The Hasofer–Lind reliability index β in conjunction with transformation method in the FORM was adopted as the measure of reliability. The first proposal was combining NUMPRESS software with the non-commercial KRATA program. In this case, the implicit form of the random variables function was created. Limit state function was symbolically given in the standard math notation as a function of the basic random and external variables. The second analysis proposed a hybrid approach enabling the introduction of explicit forms of limit state functions to the reliability program. To create the descriptions of this formula, the neural networks were used and our own original FEM module. The combination of conventional and neural computing can be seen as a hybrid system. The explicit functions were implemented into NUMPRESS software. The values of the reliability index for different descriptions of the mathematical model of the structure were determined. The proposed hybrid approach allowed us to obtain similar results to the results from the reference method.

COMPORTAMENTO DO ÍNDICE DE CONFIABILIDADE DE PILARES DE CONCRETO ARMADO EM FUNÇÃO DO TEMPO DE CARREGAMENTO

Este estudo tem como objetivo principal avaliar o comportamento do índice de confiabilidade de pilares de concreto armado em função do tempo em que permanecem carregados. Com isso busca-se inferir se parâmetros como índice de esbeltez, resistência à compressão do concreto e taxa de armadura afetam a variação da confiabilidade destas estruturas ao longo do tempo de carregamento, bem como estabelecer uma idade onde ocorra uma estabilização aceitável dos valores dos índices de confiabilidade. As simulações foram realizadas no software ANSYS, tendo sido os modelos constitutivos do concreto inseridos através da ferramenta USERMAT e baseados no CEB-FIP Model Code 2010, CEB-FIP Model Code 90 e em Bazant e Prasannan (1988). Os valores de β foram determinados através do Método da Superfície de Resposta em conjunto com o método FORM (First Order Reliability Method). Os resultados mostraram que as quedas mais significativas dos valores de β acontecem nos primeiros 900 dias de carregamento, principalmente em casos onde ocorrem valores de índices de confiabilidade mais baixos. Estabeleceu-se 1800 dias como tempo final de carregamento para um estudo de confiabilidade de pilares de concreto armado sob cargas de longa duração, com a segurança de que este valor representa de forma satisfatória os valores de β aos 50 anos de idade, bem como diminui o custo computacional na análise destas estruturas.

Dynamic Reliability Evaluation by First-Order Reliability Method Integrated with Stochastic Pseudo Excitation Method

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.

An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme

Hasofer-Lind and Rackwtiz-Fiessler (HLRF) method is an efficient iterative algorithm for locating the most probable failure point and calculating the first order reliability index in structural reliability analysis. However, this method may encounter numerical instability problems for high nonlinear limit state function (LSF). In this paper, an improved HLRF-based first order reliability method is developed based on a modified Armijo line search rule and an interpolation-based step size backtracking scheme to improve the robustness and efficiency of the original HLRF method. Compared with other improved HLRF-based methods, the proposed method can not only guarantee the global convergence but also adaptively estimate some sensitive algorithm parameters, such as initial step size, step-size reduction coefficient, using the current known iterative information. Ten selected examples with high nonlinear LSFs are used to compare the robustness and efficiency of the proposed method with the original HLRF method and the improved HLRF (iHLRF) method. Results indicate that the proposed method is not only more computationally efficient but also less sensitive to the remaining user-defined algorithm parameters than the iHLRF method.