New Approximations for SORM: Part 1

Zhao, Yan‐Gang; Ono, Tetsuro

doi:10.1061/(asce)0733-9399(1999)125:1(79)

Cited by 82 publications

(26 citation statements)

References 15 publications

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“…A more accurate three‐term formula was proposed by Tvedt , who also derived exact results for a paraboloid as well as all the quadratic forms of Gaussian variables . These and later formulations require the principal curvatures of the limit state surface at the design point to be solved. The conventional approach involves the computation of the second‐order derivative matrix.…”

Section: Brief Review Of the Second‐order Reliability Methodsmentioning

confidence: 99%

“…Under certain conditions, some of the SORM formulas may breakdown (e.g., Tvedt and Breitung formulas require κ ⩾ − 1/ β ; Hohenbichler–Rackwitz and Hong formulas require κ ⩾ [Φ( β ) − 1]/ϕ( β )). Zhao and Ono investigated four of the formulas, namely Tvedt, Breitung, Koyluoglu, and Cai, and concluded that they worked well for cases involving small curvatures or a small number of random variables. Significant errors may arise if otherwise, or for limit state surface having curvatures of different signs.…”

Section: Example 2: Bearing Capacity Of Shallow Footingmentioning

confidence: 99%

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Practical second‐order reliability analysis applied to foundation engineering

Chan

Low

2011

Num Anal Meth Geomechanics

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SUMMARYA practical and efficient approach of implementing second-order reliability method (SORM) is presented and illustrated for cases related to foundation engineering involving explicit and implicit limit state functions. The proposed SORM procedure is based on an approximating paraboloid fitted to the limit state surface in the neighborhood of the design point and can be easily carried out in a spreadsheet. Complex mathematical operations are relegated to relatively simple user-created functions. The failure probability is calculated automatically based on the reliability index and principal curvatures of the limit state surface using established closed-form SORM formulas. Four common foundation engineering examples are analyzed using the proposed method and discussed: immediate settlement of a flexible rectangular foundation, bearing capacity of a shallow footing, axial capacity of a vertical single pile, and deflection of a pile under lateral load. Comparisons with Monte Carlo simulations are made. In the case of the laterally loaded pile, the friction angle of the soil is represented as a one-dimensional random field, and pile deflections are computed based on finite element analysis on a stand-alone computer package. The implicit limit state function is approximated via the response surface method using two quadratic models.

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Section: Brief Review Of the Second‐order Reliability Methodsmentioning

confidence: 99%

Section: Example 2: Bearing Capacity Of Shallow Footingmentioning

confidence: 99%

Practical second‐order reliability analysis applied to foundation engineering

Chan

Low

2011

Num Anal Meth Geomechanics

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“…Posteriormente, outros autores realizaram aproximações com base na mesma ideia de equações quadráticas (TVEDT, 1983;CAI;ELISHAKOFF, 1994;KÖYLÜOǦLU;NIELSEN, 1994;ZHAO;ONO, 1999).…”

Section: Sorm -Second Order Reliability Methodsunclassified

Análise probabilística da contaminação da água subterrânea usando métodos de confiabilidade de primeira e segunda ordem

Godoy

Napa-García

2017

R. Águas Subter.

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Resumo: Este artigo mostra um exemplo de aplicação da estimativa da probabilidade de um contaminante exceder uma máxima concentração especificada (probabilidade de excedência, Pf), usando métodos de confiabilidade de primeira (FORM) e segunda ordem (SORM) para diversas concentrações iniciais de um soluto hipotético, sem biodegradação e tempos de análise de 5 e 10 anos, considerando-se um fluxo unidimensional em solo arenoso. A validade dos resultados foi avaliada comparando os resultados obtidos de FORM e SORM com aqueles da Simulação de Monte Carlo (SMC). Para uma mesma concentração inicial, a Pf aumentou com o aumento do tempo de análise. Para ambos os tempos de análise (5 e 10 anos) e métodos aplicados, a Pf tende a aumentar com o aumento da concentração inicial. A comparação entre os valores de Pf obtidos com FORM e SORM e com a SMC mostra que a partir de 50 μg/L de concentração inicial a SMC e o FORM apresentam valores de Pf muito próximos. Os valores obtidos com o SORM apresentaram proximidade com aqueles resultantes da SMC apenas para as concentrações iniciais de 50 e 100 μg/L. A proximidade dos valores de Pf obtidos com SMC e FORM indicam que o uso deste método de confiabilidade é útil na obtenção da Pf, além de ser uma maneira mais rápida do que a SMC. Palavras-chave: Transporte de contaminante. Probabilidade de excedência. FORM. SORM. SMC.Abstract: This paper shows an example of the application of the estimation of the probability of a contaminant exceeding a specified maximum concentration (probability of exceedance, Pf) using first order (FORM) and second order (SORM) reliability methods for several initial concentrations and analysis times of 5 and 10 years. INTRODUÇÃOApesar da importância estratégica da preservação da qualidade das águas subterrâneas, esse recurso vem sofrendo várias pressões em decorrência do aumento da quantidade de áreas contaminadas por atividades industriais, urbanas e agrícolas, o que pode aumentar o risco relacionado às contaminações. Neste artigo, será utilizada a definição de risco proposta por Freeze et al. (1990), em que o mesmo é definido como a probabilidade de excedência, ou seja, probabilidade de ser identificada uma concentração superior a uma concentração objetivo, ou aceitável, determinada por algum órgão ambiental, multiplicada pelos custos esperados de falha (consequências), dessa

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“…This is for instance the case in certain problems dealing with reliability-based design and response surface methodology, see e.g. Reference [1].…”

Section: Introductionmentioning

confidence: 98%

Refined second order semi‐analytical design sensitivities

Boer

Keulen

Vervenne

2002

Numerical Meth Engineering

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SUMMARYAccurate and e cient calculation of second order design sensitivities in a ÿnite element context is often di cult. The semi-analytical (SA) method is e cient and easy to implement but has accuracy problems even for ÿrst order shape design sensitivities. To overcome accuracy problems a reÿned semianalytical (RSA) method has been developed for ÿrst order sensitivities. The present paper investigates the application of the RSA method to second order design sensitivities. It is found that second order RSA sensitivities are signiÿcantly more accurate than their SA counterparts.

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New Approximations for SORM: Part 1

Cited by 82 publications

References 15 publications

Practical second‐order reliability analysis applied to foundation engineering

Practical second‐order reliability analysis applied to foundation engineering

Análise probabilística da contaminação da água subterrânea usando métodos de confiabilidade de primeira e segunda ordem

Refined second order semi‐analytical design sensitivities

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