Efficient Reliability Evaluation Using Spreadsheet

Low, Bak Kong; Tang, Wilson H.

doi:10.1061/(asce)0733-9399(1997)123:7(749)

Cited by 222 publications

(78 citation statements)

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“…This margin of safety can be expressed through the concept of the reliability index (β) , Hasofer and Lind 1974, Low and Tang 1997. The reliability index is dependent on the mean and variance of each of the variables and also on the limit state under consideration.…”

Section: Design Mean and Limit State Values And The Reliability Indexmentioning

confidence: 99%

“…The reliability index for this initial trial is computed by finding x in (3.3.4) with the requirement that x be on the limit state surface and minimize β. These computations can be efficiently executed using the spreadsheet formulation of Low and Tang (1997). In this formulation, non-normal PDFs are substituted by normal distributions such that the cumulative probability at the limit state value is equal to that for the non-normal PDF.…”

Section: Design Mean and Limit State Values And The Reliability Indexmentioning

confidence: 99%

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Limit States Design (LSD) for Shallow and Deep Foundations

Foye¹,

Abou-Jaoude²,

Salgado³

2004

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IntroductionFoundation design consists of selecting and proportioning foundations in such a way that limit states are prevented. Limit states are of two types: Ultimate Limit States (ULS) and Serviceability Limit States (SLS). ULSs are associated with danger, involving such outcomes as structural collapse.SLSs are associated with impaired functionality, and in foundation design are often caused by excessive settlement. Reliability-based design (RBD) is a design philosophy that aims at keeping the probability of reaching limit states lower than some limiting value. Thus, a direct assessment of risk is possible with RBD. This evaluation is not possible with traditional working stress design. The use of RBD directly in projects is not straightforward and is cumbersome to designers, except in large-budget projects. Load and Resistance Factor Design (LRFD) shares most of the benefits of RBD while being much simpler to apply. LRFD has traditionally been used for ULS checks, but SLS's have been brought into the LRFD framework recently (AASHTO 1998).Load and Resistance Factor Design (LRFD) is a design method in which design loads are increased and design resistances are reduced through multiplication by factors that are greater than one and less than one, respectively. In this method, foundations are proportioned so that the factored loads are not greater than the factored resistances.In order for foundation design to be consistent with current structural design practice, the use of the same loads, load factors and load combinations would be required. In this study, we review the load factors presented in various LRFD Codes from the US, Canada and Europe. A simple first-order second moment (FOSM) reliability analysis is presented to determine appropriate ranges for the values of the load factors. These values are compared with those proposed in the Codes.For LRFD to gain acceptance in geotechnical engineering, a framework for the objective assessment of resistance factors is needed. Such a framework, based on reliability analysis is proposed in this study. Probability Density Functions (PDFs), representing design variable uncertainties, are required for analysis. A systematic approach to the selection of PDFs is presented.Such a procedure is a critical prerequisite to a rational probabilistic analysis in the development of LRFD methods in geotechnical engineering. Additionally, in order for LRFD to fulfill its promise for designs with more consistent reliability, the methods used to execute a design must be consistent with the methods assumed in the development of the LRFD factors. In this study, a methodology for the estimation of soil parameters for use in design equations is proposed that should allow for more statistical consistency in design inputs than is possible in traditional methods.The primary objective of this study is to propose a Limit States Design method for shallow and deep foundations that is based on a rational, probability-based investigation of design methods. FindingsThis research was able to deve...

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Section: Design Mean and Limit State Values And The Reliability Indexmentioning

confidence: 99%

Section: Design Mean and Limit State Values And The Reliability Indexmentioning

confidence: 99%

Limit States Design (LSD) for Shallow and Deep Foundations

Foye¹,

Abou-Jaoude²,

Salgado³

2004

View full text Add to dashboard Cite

show abstract

“…Although most traditional limit equilibrium methods do not consider spatial variability, some investigators have combined LEM with random eld theory (e.g., [28][29][30][31][32][33][34][35][36][37]). However, the inherent nature of LEM is that it leads to a critical failure surface which in 2-D analysis appears as a straight line or curvilinear shape that could be noncircular.…”

Section: Random Limit Equilibrium Methods (Rlem)mentioning

confidence: 99%

Uncertainty assessment of critical excavation depth of vertical unsupported cuts in undrained clay using random eld theorem

Chenari

2016

Scientia Iranica

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KEYWORDSCritical excavation depth; Probability of failure; Spatial variability; Random nite di erence method; Random limit equilibrium method.Abstract. Classical methods such as limit equilibrium or limit analysis, dealing with the stability analysis of open cuts and trenches and calculation of critical excavation depth for them, do not fully satisfy the theoretical requirements for stability problems leading to di erent solutions depending on the adopted method. It is now appreciated that geomaterials exhibit considerable heterogeneity, caused by the lithological and inherent variation, which cannot be fully covered by simple methods. This paper highlights the uncertainty embedded in critical excavation depth calculation, arising from spatial variability of shear strength parameters, using Random Finite Di erence Method (RFDM) and Random Limit Equilibrium Method (RLEM). In the present study, the lognormally distributed undrained shear strength is considered spatially correlated throughout the domain. Surface cohesion value and the shear strength density were introduced as the deterministic parameters along with the coe cient of variation of undrained shear strength and its scale of uctuation as stochastic parameters; these parameters were studied to see their e ect on uncertainty in critical excavation depth estimation. The results clearly demonstrated the uncertainty in critical excavation depth arising from the inherent variability of shear strength parameters using the RFDM results; however, RLEM did not prove to re ect such uncertainty e ciently due to local averaging in prescribed failure surfaces.

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“…Independent standard normal variables are chosen by them as basic random variables and transformed into correlated non-normal variables in the original space of random variables for constructing the response surface. Also a practical method for calculation of second moment reliability index using spreadsheets was previously reported by the members of this research group (Low and Tang 1997). Then the reliability analyses involving non-normal distributions are investigated by them.…”

Section: Application Of Reliability In Tunnel Engineeringmentioning

confidence: 99%

Reliability analysis of idealized tunnel support system using probability-based methods with case studies

Gharouni-Nik

Naeimi

Ahadi

et al. 2014

Int J Adv Struct Eng

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In order to determine the overall safety of a tunnel support lining, a reliability-based approach is presented in this paper. Support elements in jointed rock tunnels are provided to control the ground movement caused by stress redistribution during the tunnel drive. Main support elements contribute to stability of the tunnel structure are recognized owing to identify various aspects of reliability and sustainability in the system. The selection of efficient support methods for rock tunneling is a key factor in order to reduce the number of problems during construction and maintain the project cost and time within the limited budget and planned schedule. This paper introduces a smart approach by which decision-makers will be able to find the overall reliability of tunnel support system before selecting the final scheme of the lining system. Due to this research focus, engineering reliability which is a branch of statistics and probability is being appropriately applied to the field and much effort has been made to use it in tunneling while investigating the reliability of the lining support system for the tunnel structure. Therefore, reliability analysis for evaluating the tunnel support performance is the main idea used in this research. Decomposition approaches are used for producing system block diagram and determining the failure probability of the whole system. Effectiveness of the proposed reliability model of tunnel lining together with the recommended approaches is examined using several case studies and the final value of reliability obtained for different designing scenarios. Considering the idea of linear correlation between safety factors and reliability parameters, the values of isolated reliabilities determined for different structural components of tunnel support system. In order to determine individual safety factors, finite element modeling is employed for different structural subsystems and the results of numerical analyses are obtained in different design scenarios. Finally, the reliability index values are obtained for the entire support structure in different design scenarios. The results of the work demonstrates that proposed reliability evaluation method of tunnel support system is effective not only for investigating the reliability of individual elements in the structure, but also for building an overall estimation about reliability performance of the entire tunnel structure.

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Efficient Reliability Evaluation Using Spreadsheet

Cited by 222 publications

References 4 publications

Limit States Design (LSD) for Shallow and Deep Foundations

Limit States Design (LSD) for Shallow and Deep Foundations

Uncertainty assessment of critical excavation depth of vertical unsupported cuts in undrained clay using random eld theorem

Reliability analysis of idealized tunnel support system using probability-based methods with case studies

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