Probabilistic Slope Analysis Research Articles

Seismic failure probability analysis of slopes via stochastic material point method

Earthquakes, an important factor in inducing landslides, usually have great randomness. Moreover, landslides are investigated as large deformations, and traditional grid-based methods encounter mesh distortions when dealing with such problems. In this context, the spectral expression method and random functions are introduced to generate stochastic ground motions, and the material point method is adopted to perform probabilistic slope analysis. First, the dry aluminum bar collapse test and the Chiu-fen-erh-shan landslide were simulated to verify the effectiveness of this improved procedure. Then, three typical stochastic ground motions were selected to investigate the effects of material parameters (internal friction angle and cohesion) and slope geometry (slope inclination and height) on the sliding distance of the slope. Finally, the uncertainty of ground motions was taken into account when conducting the probabilistic analysis of earthquake-induced landslides. The results demonstrate that the sliding distance of slopes varies with earthquake action, exhibiting certain randomness, particularly in strong earthquakes. In addition, slope geometry influences sliding distances more than material parameters, and slope geometry should be the prior consideration for slope prevention and mitigation.

Stability Analysis of Slopes with Spatially Variable Strength Properties

Natural variability of rock properties can significantly affect the strength of rock masses and factor of safety of slopes. The results of a comprehensive point load testing program showed that coefficient of variation of intact rock strength can reach unity in highly heterogeneous formations. Probabilistic numerical analysis was carried out to explore the effect of strength variability on uniaxial compressive strength of large heterogeneous samples. It was shown that mean large-scale strength decreases with increasing small-scale variability. The effect of spatial variability of strength properties on slope stability was examined using limit equilibrium and shear strength reduction methods. Both approaches gave similar results indicating that for stable slopes, increasing strength variability leads to a reduction in mean factor of safety and increase in the probability of failure. In addition, ignoring spatial variability in probabilistic slope analysis can lead to erroneous estimates of the probability of failure. Based on the results of probabilistic analyses on large heterogeneous samples and slopes, an equivalent uniaxial compressive strength can be obtained by reducing the mean strength by one-third of its standard deviation. This relationship was validated using a dataset of back-analyzed strength values in heterogeneous open pit slopes.

New pole-searching algorithm with applications to probabilistic circular slope stability assessment

Conventional deterministic analysis for evaluating slope stability, although computationally efficient, is gradually shadowed by probabilistic analysis in two aspects. First deterministic analysis does not account for inevitable soil variability, and secondly its assessment would be deficient especially under a critical condition. However, probabilistic analysis that is computationally expensive sometime deters itself from being used when efficient algorithms are absent. For optimizing the calculation during probabilistic slope analysis, this study introduces a new algorithm in searching for the center of a circular slip surface, referred to as the pole. Not only can this algorithm effectively locate the pole, but its accuracy is improved compared to that of the conventional method. This study further demonstrates the algorithm by performing a probabilistic analysis for a benchmark slope through Monte Carlo Simulation. Such a probabilistic analysis saves 106h from the use of the conventional pole-searching algorithm in an equivalent analysis. The results show that circular slope stability is indeed affected by soil variability, which should not be overlooked since it is inevitable owing to natural randomness.

Impact of reservoir impoundment-caused groundwater level changes on regional slope stability: a case study in the Loess Plateau of Western China

Due to its impact on regional groundwater levels, the impoundment of a reservoir is an important consideration for assessing the stability of surrounding slopes. This study presents a method for risk assessment and control of landslides in regions where groundwater levels can be affected by reservoir water levels. The method is illustrated with a case study of the Hongzhuang reservoir in Yanan city, northern Shaanxi province, China. A groundwater numerical model was developed using MODFLOW and the groundwater flow fields were calculated for different reservoir water levels. Safety factors were then obtained and the slope stability was analyzed. Moreover, a probabilistic slope analysis was performed by Monte-Carlo simulation to evaluate the reliability of slope stability and the probability of slope failure. Finally, a reasonable reservoir water level was determined according to the acceptable risk level, and a comprehensive risk mitigation method was proposed considering water level control, relocation, and drainage measures.

Stratified Response Surfaces for System Probabilistic Evaluation of Slopes

AbstractThe need for probabilistic slope analysis that takes into account the uncertainty of soil properties has been acknowledged by the geotechnical profession. Traditionally, probabilistic slope analysis involves only single-mode failure that is considered based on the critical slip surface. This may result in underestimating the failure probability. In contrast, system reliability analysis for slopes is deemed more rational. This study aims at improving the existing methods of slope reliability analysis by considering system reliability. A stratified response surface method (stratified RSM) is proposed to describe the performance functions of possible failure modes. The proposed method differs from conventional response-surface–based slope reliability analysis (which constructs a single approximate performance function) by generating a group of (stratified) response surfaces. Based on these stratified response surfaces, system reliability analysis can be efficiently carried out by means of either a fi...

Lodalen slide: a probabilistic assessment

Conventional slope practice, based on the deterministic factor of safety, cannot address the uncertainty in the input parameters of slope analyses in any explicit way. It relies entirely on the subjective judgment of the designer, which varies substantially among geotechnical engineers. Probabilistic techniques are powerful tools that can be used to quantify and incorporate uncertainty into slope analysis and design. A probabilistic slope analysis methodology based on Monte Carlo simulation using Microsoft® Excel and @Risk software is applied to investigate the Lodalen slide that occurred in Norway in 1954. Starting with field and laboratory data, the study demonstrates the techniques used in quantifying the uncertainties in soil properties and pore-water pressure, conducting a probabilistic assessment, and estimating the probability of unsatisfactory performance. The probability of unsatisfactory performance of the Lodalen slope is estimated to be 0.70, indicating that failure was imminent. The inclination of the Lodalen slope is then flattened, hypothetically, to different angles and the relationships between the slope angle, the factor of safety, and the probability of unsatisfactory performance are investigated.Key words: probabilistic analysis, slope stability, Monte Carlo simulation, spatial variability, Lodalen slide.

Probabilistic assessment of stability of a cut slope in residual soil

A probabilistic slope analysis methodology based on Monte Carlo simulation using Microsoft Excel and @Risk software is applied to investigate the failure of the Shek Kip Mei cut in Hong Kong. The study demonstrates the techniques used in quantifying uncertainties in shear strength of granitic soils based on a large database of triaxial tests. Probabilistic back-analyses of the failure are applied to estimate the probability distribution of the pore water pressure. Using the back-calculated pore pressure, the inclination of the Shek Kip Mei slope is redesigned to a flatter inclination, and the probability of unsatisfactory performance and reliability index are estimated.

Probabilistic stability analysis of a tailings dyke on presheared clay–shale

Probabilistic slope stability analysis offers an efficient framework for logical, systematic incorporation of uncertainty into slope design. The slow integration of probabilistic slope analyses into practice is attributed, among other factors, to the lack of published studies illustrating the implementation and benefits of such techniques. A spreadsheet-based, probabilistic slope analysis methodology is applied to evaluate the stability of a section of the Syncrude Tailings Dyke in Fort McMurray, Canada. The dyke is approximately 44 m high and is founded on presheared clay–shale. The performance of the dyke is governed by uncertainties about material properties and pore-water pressures. Starting with field and laboratory data, this study demonstrates the techniques used in quantifying the various components of parameter uncertainty, conducting a probabilistic assessment, and estimating the probability of unsatisfactory performance. The probability of unsatisfactory performance of the dyke is estimated to be 1.6 × 10–3. Field monitoring data indicate that the dyke performance is adequate. The study thus provides a first link between probability figures and performance. The analysis also quantifies the relative contributions of the various sources of uncertainty to the overall uncertainty in the factor of safety.Key words: probabilistic analysis, slope stability, Monte Carlo simulation, spatial variability, tailings dyke, clay–shale.

The Time-Dependent Reduction of Sliding Cohesion due to Rock Bridges Along Discontinuities: A Fracture Mechanics Approach

In this paper, a fracture mechanics model is developed to illustrate the importance of time-dependence for brittle fractured rock. In particular a model is developed for the time-dependent degradation of rock joint cohesion. Degradation of joint cohesion is modeled as the time-dependent breaking of intact patches or rock bridges along the joint surface. A fracture mechanics model is developed utilizing subcritical crack growth, which results in a closed-form solution for joint cohesion as a function of time. As an example, a rock block containing rock bridges subjected to plane sliding is analyzed. The cohesion is found to continually decrease, at first slowly and then more rapidly. At a particular value of time the cohesion reduces to value that results in slope instability. A second example is given where variations in some of the material parameters are assumed. A probabilistic slope analysis is conducted, and the probability of failure as a function of time is predicted. The probability of failure is found to increase with time, from an initial value of 5% to a value at 100 years of over 40%. These examples show the importance of being able to predict the time-dependent behavior of a rock mass containing discontinuities, even for relatively short-term rock structures.

Probabilistic slope stability analysis for practice

The impact of uncertainty on the reliability of slope design and performance assessment is often significant. Conventional slope practice based on the factor of safety cannot explicitly address uncertainty, thus compromising the adequacy of projections. Probabilistic techniques are rational means to quantify and incorporate uncertainty into slope analysis and design. A spreadsheet approach for probabilistic slope stability analysis is developed. The methodology is based on Monte Carlo simulation using the familiar and readily available software, Microsoft® Excel 97 and @Risk. The analysis accounts for the spatial variability of the input variables, the statistical uncertainty due to limited data, and biases in the empirical factors and correlations used. The approach is simple and can be applied in practice with little effort beyond that needed in a conventional analysis. The methodology is illustrated by a probabilistic slope analysis of the dykes of the James Bay hydroelectric project. The results are compared with those obtained using the first-order second-moment method, and the practical insights gained through the analysis are highlighted. The deficiencies of a simpler probabilistic analysis are illustrated. Key words: probabilistic analysis, slope stability, Monte Carlo simulation, spatial variability.

Probabilistic slope analysis using Janbu's generalized procedure of slices

Abstract Practical spreadsheet techniques are proposed for the deterministic slope stability analysis based on Janbu's generalized procedure of slices (GPS) and a probabilistic analysis that obtains the same reliability index as the first order reliability method (FORM). The equilibrium equations of slices are solved automatically. An intuitive ellipsoid perspective greatly simplifies the reliability analysis. A search for the deterministic critical slip surface and the reliability-based critical slip surface is automatic, despite the fact that the factor-of-safety expressions and the performance function are non-explicit. The conceptual simplicity, ease of implementation, and practical versatility of the proposed perspectives and methods are emphasized.

Probabilistic slope analysis for structural failure

A method to estimate the localized probability of slope failure was developed for open pit slopes in fractured rock masses by combining geostatistical modeling techniques with key block analysis. Indicator kriging was employed to create a localized probabilistic cell-block model of joint systems observed in the pit. Key block kinematic analysis of wedge failure was applied to the joint system model and a full probability of slope failure in each cell-block or local area was obtained. Compared to the stochastic simulation of slope failure based on the global sample statistics and the deterministic failure analysis by its mean data, the localized stochastic approach provided much greater resolution in slope stability analysis.