Development of fragility functions for slope instability analysis

Abstract

This paper presents a methodology for constructing fragility functions to characterise slope stability under a range of catastrophic earthquakes and rainfalls. The procedures for creating fragility functions, including the first-order reliability method (FORM) and the copula-based sampling method (CBSM), are demonstrated using a selection of typical slopes. The most common failure modes are included, such as the shallow sliding of an infinite slope, circular slip surface of a homogeneous slope, and tetrahedral wedge failure in a rock slope. Owing to the proposed approach, the fragility function can be applied to quantify the failure probabilities over a range of loading conditions with ease, as these are attributed to a function, rather than a design point. The advantage of these definitions is that the uncertainties of correlated soil shear strengths can be incorporated into the reliability models. The established procedure can provide a basis for describing vulnerable behaviour of a slope under various loading conditions and geometries.

Implementing statistical fitting and reliability analysis for geotechnical engineering problems in R

“…Shallow landslide failure is a common seasonal occurrence on natural slopes, especially subjected to potential earthquake and/or rainfall (Wu 2015b). When the slope fails at or near the contact between the soil colluvium and impervious bedrock and the slope gradient is constant throughout the length, such a slope may be analysed as an infinite one, as given in Figure 6.…”

“…The soil saturation index m represents the relative position of the water table in the soil layer, which is a function of the groundwater flow and rainfall intensity. In this study, K h is set to 0.1 and m is set to 0.2 (Wu 2015b). To simplify the calculation, only four dependent random variables of soil properties (c, w, g, and g sat ) are considered.…”

“…When the slope fails at or near the contact between the soil colluvium and impervious bedrock and the slope gradient is constant throughout the length, such a slope may be analysed as an infinite one, as given in Figure 6. The performance function of the stability is defined as the ratio of the available resisting force R to the driving force S (Phoon 2008;Wu 2015b): where R = cL + N tan f, S = (1 + K v )(W n + W sat ) sin u + F w + K h (W n + W sat ) cos u, and N = (1 + K v ) (W n + W sat ) cos u − K h (W n + W sat ) sin u. Herein, u is slope inclination, the weight of a slice (as depicted in Figure 6) associated with saturated zone is given by W sat = g sat V sat = g sat Lh cos u, the weight of a slice associated with natural zone is W n = gV n = gL(H − h) cos u, the seepage force is denoted as F w = i s g w V sat = g w Lh sin u cos u, the seepage gradient is set to i s = sin u, L is the width of the slice, and H is the depth of soil above bedrock. Moreover, the depth of groundwater table above bedrock is given by h = mH.…”

“…In the practice of geotechnical engineering or geosciences, several researchers have demonstrated the abilities of the R programming language (Grunsky 2002;Wu 2013aWu , 2013bWu , 2015aWu , 2015bKaklamanos and Elmy 2016), and their studies cover specific aspects of both the deterministic and probabilistic applications. These applications are still in their nascent stages, and the full potential of R for analysing geotechnical problems has yet to be realised.…”

Fragilidad estructural de componentes ante incertidumbres no gaussianas correlacionadas

“…El análisis estocástico de la falla de componentes se ha utilizado extensamente en la evaluación probabilista del riesgo estructural desde finales de la década de los setentas, en aplicaciones relacionadas con el diseño de plantas de energía nuclear (Kennedy et al 1980(Kennedy et al , 1984. Este tipo de análisis también se ha utilizado ampliamente en ingeniería sísmica para analizar la fragilidad -llamada en ocasiones vulnerabilidad sísmica- (Mayoral et al, 2016), y en geotecnia para determinar la probabilidad de falla de elementos de cimentación y otras obras (Popescu et al, 2005;Wu, 2015). En ingeniería hidráulica, este tipo de análisis se utiliza para evaluar el riesgo de inundación de las poblaciones (Vorogushyng et al, 2010;Apel et al, 2004).…”