Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields

Abstract

The paper investigates the probability of failure of slopes using both traditional and more advanced probabilistic analysis tools. The advanced method, called the random finite-element method, uses elastoplasticity in a finite-element model combined with random field theory in a Monte-Carlo framework. The traditional method, called the first-order reliability method, computes a reliability index which is the shortest distance ͑in units of directional equivalent standard deviations͒ from the equivalent mean-value point to the limit state surface and estimates the probability of failure from the reliability index. Numerical results show that simplified probabilistic analyses in which spatial variability of soil properties is not properly accounted for, can lead to unconservative estimates of the probability of failure if the coefficient of variation of the shear strength parameters exceeds a critical value. The influences of slope inclination, factor of safety ͑based on mean strength values͒, and cross correlation between strength parameters on this critical value have been investigated by parametric studies in this paper. The results indicate when probabilistic approaches, which do not model spatial variation, may lead to unconservative estimates of slope failure probability and when more advanced probabilistic methods are warranted.

The role of uncertainty in bedrock depth and hydraulic properties on the stability of a variably-saturated slope

“…We conveniently assumed constant values of the strength parameters in all of our numerical simulations. This approach ignores spatial variabilities in c 0 and / 0 [11], and may lead to inadequate characterization of the stability of hillslopes during rainfall events [8,14]. Nevertheless, the use of constant strength parameters simplifies investigations into the impact of bedrock depth uncertainty and/or soil hydraulic uncertainty in slope stability studies.…”

“…As hillslope interiors are costly, labor-intensive, and difficult to access, most slope stability studies use a relatively simple description of the bedrock surface [3,6,7,11]. Resulting topographic maps often do not do justice to complex field measurements of the bedrock depth, which often demonstrate significant spatial variability [3,33] with a geometry that is difficult to characterize adequately with some closed-form mathematical expression, while hydraulic and strength parameters can vary abruptly at the soil-bedrock interface.…”

“…Numerous contributions to the geotechnical literature have investigated the triggering mechanisms and probability of occurrence of rainfall-induced landslides. This body of work has shown that the stability of hillslopes is controlled by many different factors including surface topography [2], depth to unweathered bedrock [3][4][5][6], the hydraulic properties [7,8] and shear strength [9][10][11] including their spatial variability [12,13].…”

“…Such methods allow us to calculate confidence intervals of the SF due to uncertainty in soil properties and stratigraphic conditions, data errors, and model structural inadequacies [15,17]. The impact of uncertainty in the soil properties on the SF is relatively easily quantified using statistical methods [15], and has been explored by different authors [7,9,11,18,19]. This includes treatment of uncertainty in the porosity [20], specific weight [11,17], cohesion [11,17], and friction angle [11,17] of the soil mantle, and the spatial variability of the hydraulic conductivity [7,20].…”

Reliability updating in geotechnical engineering including spatial variability of soil

“…In addition, the uncertain material properties tend to vary in space, even within homogeneous layers. Several studies have shown that the spatial variability of the soil has an important influence on the computed reliability [5][6][7]. An accurate representation of the spatial variability of the uncertain soil material properties requires a random field modelling.…”