Application of fuzzy set theory to evaluate the probability of failure in rock slopes

Park, Hyuck‐Jin; Um, J.; Woo, Ik; Kim, Jeong Woo

doi:10.1016/j.enggeo.2011.11.008

Cited by 100 publications

(26 citation statements)

References 37 publications

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“…Therefore, this study utilized Monte Carlo simulations to obtain the probability of failure by considering the strength parameters (cohesion and effective friction angle) as random variables. The random input parameters used in Monte Carlo simulation were considered as normally distributed variable, as in much previous research [72,83,97,127,129,139]. The same values of mean and standard deviation as used in the fuzzy analysis were applied to the random input parameters.…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, uncertainty in soil parameters is best dealt with using fuzzy set theory. Fuzzy set theory has been shown to be effective and suitable for modeling uncertainty in soil parameters when the data are insufficient to define a probability distribution fully [93,97,[101][102][103]. Therefore, a fuzzy number-a subset of a fuzzy set-was used to represent an uncertain soil parameters using fuzzy set theory.…”

Section: Uncertainty Modeling With Fuzzy Numbersmentioning

confidence: 99%

“…Fuzzy set theory has been found to be effective and suitable for modeling uncertainty in geotechnical parameters when data are insufficient to define a probability distribution fully [93]. Consequently, fuzzy set theory has been used in several site-specific slope stability analyses at hillslope scale [89,92,[94][95][96][97][98][99].…”

Section: Introductionmentioning

confidence: 99%

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Physically Based Susceptibility Assessment of Rainfall-Induced Shallow Landslides Using a Fuzzy Point Estimate Method

2017

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Abstract:The physically based model has been widely used in rainfall-induced shallow landslide susceptibility analysis because of its capacity to reproduce the physical processes governing landslide occurrence and a higher predictive capability. However, one of the difficulties in applying the physically based model is that uncertainties arising from spatial variability, measurement errors, and incomplete information apply to the input parameters and analysis procedure. Uncertainties have been recognized as an important cause of mismatch between predicted and observed distributions of landslide occurrence. Therefore, probabilistic analysis has been used to quantify the uncertainties. However, some uncertainties, because of incomplete information, cannot be managed satisfactorily using a probabilistic approach. Fuzzy set theory is applicable in this case. In this study, in order to handle uncertainty propagation through a physical model, fuzzy set theory, coupled with the vertex method and the point estimate method, was adopted for regional landslide susceptibility assessment. The proposed approach was used to evaluate susceptibility to rainfall-induced shallow landslides for a regional study area, and the analysis results were compared with landslide inventory to evaluate the performance of the proposed approach. The AUC values arising from the landslide susceptibility analyses using the proposed approach and probabilistic analysis were 0.734 and 0.736, respectively. However, when the COV values of the input parameters were reduced, the AUC values of the proposed approach and the probabilistic analysis were reduced to 0.722 and 0.688, respectively. It means that the performance of the fuzzy approach is similar to that of probabilistic analysis but is more robust against variation of input parameters. Thus, at catchment scale, the fuzzy approach can respond appropriately to the uncertainties inherent in physically based landslide susceptibility analysis, and is especially advantageous when the amount of quality data is very limited.

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Section: Resultsmentioning

confidence: 99%

Section: Uncertainty Modeling With Fuzzy Numbersmentioning

confidence: 99%

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Physically Based Susceptibility Assessment of Rainfall-Induced Shallow Landslides Using a Fuzzy Point Estimate Method

2017

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“…Thus the uncertain geotechnical parameters are more reasonably represented as fuzzy sets (Zadeh 1965;Juang et al 1992;Park et al 2012) when the data availability is limited. Within the context of fuzzy sets theory, the uncertainty is successfully propagated through the vertex method (Dong and Wong 1987), yielding a fuzzy output, generally in terms of factor of safety (Fs).…”

Section: Introductionmentioning

confidence: 99%

Robust Geotechnical Design of Shield-Driven Tunnels Using Fuzzy Sets

Huang

Gong

Juang³

et al. 2014

Tunneling and Underground Construction

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This paper presents a new geotechnical design concept, called robust geotechnical design (RGD), seeking to minimize the variation of the tunnel circumferential performance to the uncertainty of geotechnical parameters, which is a measure of design robustness, in addition to meeting the requirements of safety and cost efficiency. To this end, uncertain geotechnical parameters are represented as fuzzy sets (or more specifically fuzzy numbers) to copy with the scarcity of data, which provides an adequate measure of the uncertainties when the knowledge is incomplete or data is limited. Given fuzzy input parameters, the circumferential performance of a shield-driven tunnel is uncertain and logically expressed as a fuzzy factor of safety. Based upon which, the failure probabilities and robustness of the tunnel circumferential performance can be computed in the RGD framework. Finally, to aid in the selection of the optimal design that maximizes robustness and minimizes cost simultaneously while the safety is brought to the target level, non-dominated optimization is performed and a Pareto front is obtained, and the knee point located on the Pareto front is further identified and recommended as the optimal design, showing a the best compromise between robustness and cost. The proposed RGD methodology of shield-driven tunnels is deterministic in nature. Through an illustrative design example presented, the effectiveness and significance of the proposed RGD methodology in the design of shield-driven tunnels for the circumferential performance is demonstrated. Tunneling and Underground Construction GSP 242 © ASCE 2014Tunneling and Underground Construction Downloaded from ascelibrary.org by University Of British Columbia on 06/26/16.

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“…FOS is defined as a ratio of resisting force to unresisting force. FOS is a function of physical and mechanical properties of surrounding rock mass (and soil) of slope as well as geometrical characteristic of slope (Park et al, 2012). The quantitative process of obtaining data from ground (including soil and rock mass properties) is always uncertain in nature.…”

Section: Introductionmentioning

confidence: 99%

Investigating the Slope Stability Based on Uncertainty by Using Fuzzy Possibility Theory

Hosseini¹,

Gholinejad²

2014

Archives of Mining Sciences

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The main purpose of this paper is to investigate the slope stability condition by using fuzzy estimation method based on fuzzy possibility theory. Due to use of this theory, the inaccuracy, ambiguity and uncertainty in input parameters are considered and therefore, the calculated factor of safety (FOS) is highly reliable. In this research, first, the input parameters of slope stability analysis, based on statistical characteristics and grade of membership concept, as a fuzzy numbers are defined. Then the performance function of slope behavior is defined and by using the fuzzy parameters, the FOS is calculated. In next step, by using the several α -cut, the calculated FOS is defined as a fuzzy form and subsequently, the slope stability condition based on fuzzy presentation of FOS is evaluated. The results show that, although based on deterministic analysis the studied slope is stable but based on fuzzy interpretation of FOS, the slope stability condition is scare. The fuzzy analysis of slope stability condition, by applying the uncertainty in calculating the FOS and defining the grade of membership for each unknown input parameters in model, a more realistic interpretation of slope stability condition is provided. In addition, the fuzzy presentation of the FOS, allowing more accurate judgments about slope stability condition.Keywords: fuzzy possibility theory, uncertainty, factor of safety, slope stability Celem pracy jest zbadanie warunku stabilności skarpy w oparciu o metody szacunkowe wykorzystujące elementy logiki rozmytej i teorii prawdopodobieństwa. Z uwagi na zastosowanie tych teorii w parametrach wejściowych uwzględniono niedokładność, niepewność i niejednoznaczność, dlatego też obliczone współczynniki bezpieczeństwa uznać można za wysoce wiarygodne. W pierwszym etapie pracy zdefiniowano parametry wejściowe do analizy stabilności skarpy w oparciu o charakterystyki statystyczne i przyjęte funkcje przynależności, i określone parametry rozmyte. Następnie zdefiniowano zachowanie zbocza skarpy w oparciu o parametry rozmyte i obliczono współczynnik bezpieczeństwa. W kolejnym kroku przy założeniu wielokrotnego wybierania przy założonym kącie α (α -cut), obliczono współczyn-nik bezpieczeństwa w formie rozmytej i zbadano warunek stabilności skarpy oparty na współczynniku bezpieczeństwa w formie rozmytej. Wyniki wskazują, że pomimo iż zbocze badane w oparciu o analizy deterministyczne wydaje się stabilne, to współczynnik bezpieczeństwa w ujęciu rozmytym sugeruje, że warunek stabilności zbocza będzie spełniony w niewielkim stopniu. Analiza warunku stabilności zbocza wykorzystujące elementy logiki rozmytej uwzględniająca zagadnienie niepewności przy obliczaniu współczynnika bezpieczeństwa i przy określaniu stopnia funkcji przynależności dla poszczególnych parametrów wejściowych modelu pozwala bardziej realistycznie określić warunek bezpieczeństwa. Ponadto, przedstawienie warunku bezpieczeństwa w postaci rozmytej pozwala na bardziej dokładną ocenę warunków stabilności.

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Application of fuzzy set theory to evaluate the probability of failure in rock slopes

Cited by 100 publications

References 37 publications

Physically Based Susceptibility Assessment of Rainfall-Induced Shallow Landslides Using a Fuzzy Point Estimate Method

Physically Based Susceptibility Assessment of Rainfall-Induced Shallow Landslides Using a Fuzzy Point Estimate Method

Robust Geotechnical Design of Shield-Driven Tunnels Using Fuzzy Sets

Investigating the Slope Stability Based on Uncertainty by Using Fuzzy Possibility Theory

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