Practical reliability analysis and design by Monte Carlo Simulation in spreadsheet - Risk and Reliability in Geotechnical Engineering - page 296

Practical reliability analysis
and design by Monte Carlo
Simulation in spreadsheet
Yu Wang and Zijun Cao
7.1 IntroDuCtIon
Uncertainties are unavoidable in geotechnical engineering, and they arise from loads, geo-
technical properties, calculation models, and so on (e.g., Baecher and Christian, 2003;
Ang and Tang, 2007). To deal rationally with these uncertainties in geotechnical analysis
and design, several reliability (probability)-based analysis and design approaches have
been developed for geotechnical structures (e.g., Tang et al., 1976; Christian et al., 1994;
Phoon et al., 1995; Low and Tang, 1997; El-Ramly et al., 2005; Wang, 2011; Wang et al.,
2011a,b). Although these efforts significantly facilitate the understanding and application
of geotechnical reliability-based approaches, practicing engineers are reluctant to adopt
them in geotechnical practice, at least, due to two reasons: (1) the training of geotechni-
cal practitioners in probability and statistics is often limited and, hence, they feel less
comfortable dealing with probabilistic modeling than working with deterministic model-
ing (El-Ramly et al., 2002); and (2) the reliability algorithms are often mathematically
and computationally sophisticated and become a major hurdle for geotechnical practi-
tioners when using geotechnical reliability-based approaches. It is, therefore, worthwhile
for geotechnical practitioners to have a practical and conceptually simple framework that
is directly extended from conventional deterministic modeling and removes the hurdle of
reliability algorithms.
This chapter presents a Monte Carlo Simulation (MCS)-based practical framework for
reliability analysis and design of geotechnical structures in a commonly available spread-
sheet platform, such as Microsoft Excel (Microsoft Corporation, 2012). The MCS-based
practical framework deliberately decouples the conventional deterministic modeling from
the probabilistic modeling and effectively removes the computational hurdle of reliability
algorithms. MCS is a numerical process of repeatedly calculating a mathematical or empir-
ical operator, in which the variables within the operator are random or contain uncertainty
with prescribed probability distributions (e.g., Ang and Tang, 2007). The repeated calcu-
lations lead to a large number of sets of operator outputs that can be used in statistical
analysis for directly estimating the failure probability P ( F ) and probabilistic properties
(e.g., mean, standard deviation, probability density function (PDF), cumulative distribu-
tion function (CDF)) of the operator outputs. MCS is conceptually simple and it can be
treated by geotechnical practitioners as repetitive computer executions of the conventional
deterministic modeling in a systematic manner. When compared with analytical reliability
methods (e.g., first- or second-order reliability method, FORM, or SORM), MCS has wide
applicability to complex engineering problems and systems that defy analytical solutions of
the probabilities associated with their responses to random inputs (Baecher and Christian,
2003; Fenton and Griffiths, 2008). It has been widely used in probabilistic analysis of
geotechnical engineering problems, such as slope stability analysis (e.g., El-Ramly et al.,
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