Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet

Wang, Yu; Cao, Zhengguo; Au, Siu‐Kui

doi:10.1139/t10-044

Cited by 281 publications

(119 citation statements)

References 28 publications

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“…As the λ value decreases, the number of representative slip surfaces identified increases, and the p f is attributed to more than one slip surface. This is consistent with findings of previous studies (e.g., Wang et al 2011) that when the spatial variability is considered (i.e., a small λ value), the critical slip surface varies spatially (i.e., have more than one failure modes). The risk aggregation approach presented in this paper provides a 1st 2nd…”

Section: Identification Of Representative Slip Surfacessupporting

confidence: 93%

“…It is well-recognized in slope stability analysis that a slope may fail along an unlimited number of potential slip surfaces, although evaluating failure probability, p f , along all potential slip surfaces is considered a mathematically formidable task (e.g., El-Ramly et al 2002, Wang et al 2011. The p f is, therefore, frequently assessed only along one or a few pre-selected slip surfaces without proper consideration of the slip surface variation (e.g., Tang et al 1976; Low et al 1998; Hassan and Wolff 1999; Xue and Gavin 2007).…”

Section: Introductionmentioning

confidence: 99%

“…There are a few exceptions. For example, Wang et al (2011) used MCS to study the effect of the slip surface variation on p f and explicitly searching a large number of potential slip surfaces for the critical slip surface in each MCS sample. When the spatial variability of soil properties is considered, the critical slip surface was found to vary spatially, and such variation was shown to affect substantially the p f .…”

Section: Introductionmentioning

confidence: 99%

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Aggregation of landslide occurrence probability in spatially variable soil

Wang

Cao

2016

JGS Special Publication

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This paper presents a probabilistic slope stability analysis approach that formulates the slope failure event as a series of mutually exclusive and collectively exhaustive events using conditional probability and utilizes Monte Carlo simulation (MCS) to determine the occurrence probability for each of the mutually exclusive and collectively exhaustive events in a progressive manner. The probabilities of each event are aggregated to represent the overall slope failure probability p f . The p f values obtained from the proposed approach are shown to agree well with those p f values that have been obtained by searching a large number of potential slip surfaces for the minimum factor of safety in each MCS sample. The computational efficiency, however, is shown to improve by, at least, an order of magnitude. In addition, the approach identifies the key failure modes (i.e., those slip surfaces that have significant effects on p f ) which can be readily used in the mitigation of landslide risk.

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Section: Identification Of Representative Slip Surfacessupporting

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Aggregation of landslide occurrence probability in spatially variable soil

Wang

Cao

2016

JGS Special Publication

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“…Over recent years with advances in computing power there has been renewed interest in simulation methods, with numerous authors proposing quasi Monte Carlo methods (Malkawi et al, 2001;Wang et al, 2011;Cheng et al, 2015) as a means of finding the critical probabilistic slip surface. Simulation techniques can be used to find both the system reliability (Griffiths & Fenton, 2004;Huang et al, 2010) and the reliability index for a given slip surface.…”

Section: Introductionmentioning

confidence: 99%

System reliability of slopes using multimodal optimisation

2016

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Many engineered and natural slopes have complex geometries and are multi-layered. For these slopes traditional stability analyses will tend to predict critical failure surfaces in layers with the lowest mean strength. A move toward probabilistic analyses allows a designer to account for uncertainties with respect to input parameters that allow for a more complete understanding of risk. Railway slopes, which in some cases were built more than 150 years ago, form important assets on the European rail network. Many of these structures were built at slope angles significantly higher than those allowed in modern design codes. Depending on the local geotechnical conditions these slopes may be susceptible to deepseated failure; however, a significant number of failures each year occur as shallow translational slips that develop during periods of high rainfall. Thus, for a given slope, two potential failure mechanisms might exist with very similar probabilities of failure. In this paper a novel multimodal optimisation algorithm ('Slips') that is capable of detecting all feasible probabilistic slip surfaces simultaneously is presented. The system reliability analysis is applied using polar co-ordinates, as this approach has been shown to be less sensitive to local numerical instabilities, which can develop due to discontinuities on the limit state surface. The approach is applied to two example slopes where the complexity in terms of stratification and slope geometry is varied. In addition the methodology is validated using a real-life case study involving failure of a complex slope.

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“…It is a powerful technique that is applicable to both linear and non-linear problems, but requires a large number of simulations to provide a reliable distribution of the responses. Many attempts have been made to analyze the stability of slopes using Monte-Carlo simulation [10][11][12][13][14][15].…”

Section: Introductionmentioning

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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Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet

Cited by 281 publications

References 28 publications

Aggregation of landslide occurrence probability in spatially variable soil

Aggregation of landslide occurrence probability in spatially variable soil

System reliability of slopes using multimodal optimisation

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

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