Probabilistic Stability Analysis of an Open-pit Dolomite Quarry in Hungary

The northern part of INDIA is most vulnerable in failure of slopes due to hill region with complex geology, high-intensity rainfall and frequently occurrence of earthquakes. The stability of slopes has traditionally analyzed using deterministic methods. But uncertainty plays major role in geotechnical engineering. the probabilistic characterization of uncertainties in input variables for the assessment of slope stability is very helpful. In this paper, the safety of slope using deterministic and probabilistic methods under static and pseudo-static loads is carried for Lungchok landslide which is in south district of Sikkim state, India. The Factor of safety calculated by deterministic cannot represent the stability of slope exactly as it is limited to the single value of parameters. The stability of slope is independent of single soil parameter but dependent on random process with distribution of soil parameters. Rather than the conventional factor of safety against the sliding failure the probability of sliding failure is most useful. The stability of slope is analyzed using two approaches deterministic and probabilistic analysis under the effects of static and pseudo static forces. The deterministic approach with Morgenstern Price limit equilibrium method and the probabilistic approach with Monte Carlo simulation have been performed for the stability analysis of Lungchok landslide using Geo-Studio Software. The dependence and efficiency of the probabilistic strategies in the investigation of slope stability was highlighted in this paper.

The stability of slopes directly affects human lives, the environment, and the economy. Inaccurate geological profiles within numerical slope stability models can lead to potentially catastrophic consequences when model conditions do not appropriately reflect real-life stratigraphy. In cases where localised deposits are prevalent, probabilistic methods are often necessary to accommodate for unknown or poorly defined stratigraphies. Currently, there are no commercial geotechnical software packages that simulate probabilistic constitutive behaviour of materials within finite element methods for large-scale stratigraphic analysis. Instead, commercially available probabilistic methods such as the random limit equilibrium method are incapable of incorporating non-linear constitutive soil behaviour. For this reason, advanced constitutive models are seldom coupled with probabilistically varying soil layers or spatially variable soil parameters. The objective of this research is the implementation of a simplified method for probabilistic stratigraphic analysis within a commercially available FE environment, providing a technique to assess the effects of stratigraphic uncertainty on slope stability. The proposed method is presented, highlighting the impact of localised thin layers of soft material as well as their frequency and location on the slope of an operational open-pit mine. The significance of these stratigraphic effects is presented through a case study of Australia’s second-largest open-pit mine, at which the stability of a collapsed coal slope is analysed. To improve the reliability of the finite element method for slope stability assessment, the Monte Carlo approach has been incorporated to consider varying shear strength distributions for models incorporating advanced constitutive behaviour. Thicker probabilistically generated deposits of silty material resulted in increased slope Factors of Safety. Similarly, greater proportions of silty deposits within a predominantly clayey interseam produced larger safety factors than slopes without localised thin silty layers. Stratigraphic analysis indicated that the Factor of Safety was most sensitive to localised silt layers at depths greater than 83 m below ground level.

5). For better understanding of the formation and turbulent breakdown of laminar separation bubbles (LSB), both local and two-dimensional global linear stability analysis are applied to investigate the stability of a CFD time-averaged non-parallel flowfield over a SD7003 airfoil at Reynolds number 6×10 4 . The flow is found to be unstable at all wavenumbers examined. The most unstable modes from local and global stability analysis are close to each other, and the frequency of this mode is in agreement with CFD results. Spatial structures of the disturbances at most unstable modes are discussed. By applying the stability analysis, the temporal flow structures of the LSB can be examined with the most unstable modes of global stability results.

The rock slope stability analysis can be performed using deterministic and probabilistic approaches. The deterministic analysis based on the safety concept factor uses fixed representative values for each input parameter involved without considering the variability and uncertainty of the rock mass properties. Probabilistic analysis with the calculation of probability of failure instead of the factor of safety against failure is emerging in practice. Such analyses offer a more rational approach to quantify risk by incorporating uncertainty in the input variables and evaluating the probability of the failure of a system. In rock slope engineering, uncertainty and variability involve a large scatter of geo-structural data and varied geomechanical test results. There has been extensive reliability analysis of rock slope stability in the literature, and different methods of reliability are being employed for assessment of the probability of failure and the reliability of a slope. Probabilistic approaches include Monte Carlo simulation (MCS), the point estimate method (PEM), the response surface method (RSM), first- and second-order reliability methods (FORMs and SORMs), and the first-order second-moment method (FOSM). Although these methods may be complicated, they provide a more complete definition of risk. Probabilistic slope stability analysis is an option in most commercial software; however, the use of this method is not common in practice. This paper provides an overview of the literature on some of the main probabilistic reliability-based methods available for the design of the rock slope in open pit mining. To demonstrate its applicability, the paper investigates the stability of a rock slope in an open pit mine in the Goldfields region, Western Australia. Two different approaches were adopted: deterministic stability analysis using two-dimensional limit equilibrium and finite element shear strength reduction methods using SLIDE and RS2 software, respectively, and probabilistic analysis by applying the MCS and RSM methods in the limit equilibrium method. In this example, the slope stability analysis was performed using the Spencer method with Cuckoo search optimization to locate the critical slip surface. The results obtained were compared and commented on.

Slope stability analysis is a highly challenging task in geotechnical engineering as the influence of uncertainty involved in geotechnical properties on failure behavior of slopes is inevitable. Traditional deterministic slope stability approach, based on a single factor of safety (FoS) parameter, cannot explicitly encounter the uncertainties involved in geotechnical properties and failure mechanism, leading to erroneous results of slope stability. Hence, slope stability practice is highly persuadable to probabilistic treatment, which allows quantification of the uncertainty and rationally integrating the same into the analysis. The present study investigates the influence of inherent spatial variation of soil domain in probabilistic slope stability analysis. To accomplish this, a hypothetical slope is analyzed, considering 1D spatial variation, with the aid of GeoStudio 2007, using Morgenstern-Price limit equilibrium method (LEM) coupled with Monte Carlo simulation (MCS). The results are compared with those of Griffiths et al. (2007), wherein 2D random field for soil shear strength was considered and the analysis was carried out with the help of random finite element method (RFEM). The influence of correlation lengths on the probabilities of failure is compared. The results reveal that the probability of failure highly depends on spatial variation of soil property in both the methods. When correlation length is small, the failure probability is essentially zero; failure probability increases rapidly for intermediate correlation lengths, and for large correlation lengths, the failure probability becomes constant. It is also found that combining LEM with one-dimensional random field gives lower probabilities of failure than RFEM, as RFEM is more efficient in simulating the field uncertainty. Moreover, RFEM can search and identify the weakest path through the soil domain for the failure to occur, whereas LEM presumes a predefined failure plane.

Development of a probabilistic block theory analysis procedure and its application to a rock slope at a hydropower station in China

The geotechnical properties of municipal solid waste (MSW) in landfills vary considerably depending on the composition, time, and the rate of waste density. This variability in geotechnical properties leads to many uncertainties in the analysis of landfill slope stability. This study, using probabilistic methods investigates the slope stability and the probability of failure of a Kahrizak landfill under the conditions of spatial variability of physical and geotechnical properties of MSW. To achieve this goal, the random field theory has been used with a finite difference numerical method in the framework of the Monte Carlo simulation. MSW’s shear strength parameters such as cohesion and friction angle as well as the unit weight of layers are considered as random variables. An extensive literature review was conducted to address the probable variation of above-mentioned parameters in Kahrizak landfill. The results of several different laboratory researches on MSW samples collected from Kahrizak landfill were also employed in the modelings. Output results are presented in the form of probability distributions of the factor of safety as well as the probability of failure corresponding to these distributions. Moreover, the effect of various parameters such as coefficient of variation and correlation distance of input parameters on these output results has been investigated. The results show that considering the spatial variability in probabilistic methods would help to determine the various mechanisms affecting the performance and the probability of failure of the landfill slope. In addition, the output of such probabilistic analyses can be used as guidance for engineers to design safe and reliable landfill.

Probabilistic Risk Assessment (PRA) techniques are an increasingly-accepted alternative to standard hazard assessments based on Maximum Permissible Exposure (MPE) limits, where the use of high-output military lasers in outdoor environments is concerned. The adoption of a probabilistic approach is motivated by the relative inflexibility of a deterministic evaluation, in which a laser exposure is simply characterised as either “safe” or “unsafe” in comparison with the applicable MPE. The probabilistic method is alternately predicated on the socio-economic acceptability of a low risk of very minor levels of laser-induced injuries.The United Kingdom Ministry of Defence initiated the development of probabilistic laser hazard assessment models in the mid-1970s, while the United States Air Force has had the goal of developing probabilistic hazard assessment methods for High Energy Laser (HEL) Range testing purposes since the late 1990s. HEL Range clearances evaluated using an MPE-based approach would be virtually impracticable, due to the extraordinarily-large hazard areas involved. The purpose of this paper is to show that a probabilistic hazard analysis is underpinned by the same risk assessment process as the deterministic approach, with the method of choice dependent on the nature of the laser hazard and the risk management context.Probabilistic Risk Assessment (PRA) techniques are an increasingly-accepted alternative to standard hazard assessments based on Maximum Permissible Exposure (MPE) limits, where the use of high-output military lasers in outdoor environments is concerned. The adoption of a probabilistic approach is motivated by the relative inflexibility of a deterministic evaluation, in which a laser exposure is simply characterised as either “safe” or “unsafe” in comparison with the applicable MPE. The probabilistic method is alternately predicated on the socio-economic acceptability of a low risk of very minor levels of laser-induced injuries.The United Kingdom Ministry of Defence initiated the development of probabilistic laser hazard assessment models in the mid-1970s, while the United States Air Force has had the goal of developing probabilistic hazard assessment methods for High Energy Laser (HEL) Range testing purposes since the late 1990s. HEL Range clearances evaluated using an MPE-based approach would be virtuall...

Rock slopes with soft interlayer are common in nature and engineering projects. They are usually the characteristic of poor stability and low safety level. Landslides that induced by the instability and destruction of rock slopes with soft interlayer have caused a large number of casualties and heavy economic losses around the world. Therefore,the stability of rock slopes containing soft interlayer is one of important research topic in engineering geology and geotechnical engineering. This paper is based on the collection and review of the domestic and foreign literatures related to the stability of rock slopes with soft interlayer. It summarizes the advances of some important aspects on the research current situations and progress of rock slope stability in the aspect of gravity load conditions,excavation conditions,heavy rain and reservoir storage conditions,and earthquake conditions. The findings are as follows. (1)The presence of a soft interlayer usually plays an adverse role in slope stability. The stability is poorer for rock slopes with soft interlayer than for homogeneous rock slopes and layered rock slopes without soft interlayer. (2)The stability and deformation failure mechanism of rock slopes containing soft interlayer are linked to the water content,shear strength,dip angles,thickness,the number of layers,intervals of soft interlayer and the slope angles. (3)Slope failure can easily occur along soft interlayer after the completion of slope excavation without support. When excavation with supporting in time,the stability of slopes can be effectively controlled. (4)Lamination effect caused by blasting changes the contact state between soft interlayer and surrounding rock and decreases the cohesion and friction of contact interfaces,thus decreases the stability of rock slopes. (5)Heavy rainfall and reservoir impoundment are both against the stability of rock slopes with soft interlayer. (6)The dynamic responses,deformation and failure process of rock slopes with soft interlayer under earthquakes are related to the property of soft interlayer(thickness,dip angle and water content),the characteristics of seismic wave(wave types,vibration intensity and frequency of earthquake waves,loading direction) and slope structure(bedding and counter-tilt rock slopes with soft interlayer). (7)The amplification or weakening effect of soft interlayer on the horizontal dynamic responses of rock slopes under earthquake and the role of thick soft interlayer in energy dissipation and shock absorption during shakings are not unified. Subsequently,on this basis,the advantages and disadvantages of research methods are analyzed in detail. Furthermore,the main problems existing in current research are also discussed. Finally,on account of research status in this field,some important research emphases and directions in the future are proposed. The contents are listed as follows: the progressive failure process and stability of rock slopes with multi-soft interlayer; the effect mechanism of individual factors(including excavation unloading,blasting,earthquake,heavy rain,the change of reservoir water levels,underground water) on the stability of rock slopes with soft interlayer; the stability of rock slopes with multi-soft interlayer under multi-factor coupling participation; and the reinforcement mechanism of retaining structural system for rock slopes with multi-soft interlayer.

A large gold reserve was recently discovered at Haveri district of Karnataka state of India where open-pit mining was planned to extract these deposits. Stability analysis for open-pit mine slope at this site is presented in the article. Extensive geological investigations and laboratory testing suggested high variability in geological features of discontinuities, rock mass quality and intact rock properties. Hence, it was decided to perform stability analysis of the rock slope using probabilistic approach along with deterministic approach. Deterministic analysis was carried out with average properties of rock, and reliability analysis of the rock slope was carried out using both traditional and advanced probabilistic methods. In traditional probabilistic method, rock mass strength properties were treated as random variables without considering spatial variation of rock properties and reliability index was evaluated by Monte Carlo (MC) simulation on augmented radial basis function-based response surface. In advanced probabilistic analysis, spatial variability of rock mass strength properties was considered by generating anisotropic random field using Fourier series method with spatial averaging over finite difference zones. Reliability index was then estimated by performing MC simulation using random finite difference method. A comparison was provided between the results of stability analysis of slope from all these approaches. Rock slope was found to be stable in both deterministic and probabilistic approaches; however, the degree of stability predicted was different for both methods. Deterministic approach was found to be inappropriate to analyse the stability of slope having rock mass with variable properties. Further, reliability index and expected performance level of slope were highly underestimated by traditional probabilistic method as compared to advanced probabilistic method.

Although deterministic analysis can provide initial insights into slope stability, there is no way to reflect the true distribution of soil properties within a slope. To further investigate the effects of the spatial variability of soil properties on the stability and failure mechanism of slope under different foundation types, this study develops a framework combining simple limit equilibrium method (LEM), Monte Carlo Simulation (MCS), and random field to incorporate these factors into slope probabilistic stability analysis. The slope models of two typical foundations (e.g., soft soil and silty clay foundations) are used to illustrate the proposed methodology. The results show that the shape of critical failure slip surface in slope with a soft foundation is deep and passes through the soft soil layer, indicating that the slope with a soft foundation has a variable failure mechanism. Due to the presence of soft soil foundation, the correlation between different critical failure slip surfaces is low and deterministic analysis may significantly overestimate slope stability. When performing a probabilistic stability analysis of the slope under the silty clay foundation, it is noted that the shape of critical failure slip surface is relatively shallow and the correlation between different critical failure slip surfaces is high. The degree of slope stability overestimation caused by deterministic analysis is significantly reduced. Note that when the factor of safety is used to evaluate slope stability, deterministic analysis can only evaluate slope stability more reasonably when the correlation of failure slip surface is high, while probabilistic method can evaluate slope stability more comprehensively and reasonably. The sensitivity analysis results show that the sensitivity of internal friction angle to slope stability is much higher than that of cohesive under different scales of fluctuation, coefficients of variation, and cross correlation coefficients.

Cut slopes are prone to fail due to the disturbance on original geometry and strength. In addition, because of these disturbances and stress relief, natural apertures which increase the weathering effects widen in engineering time. Owing to these reasons, slope stability assessment has a prominent role on these road cuts. Generally, slope stabilities are assessed by deterministic approaches with a significant engineering judgment. Because of this reason the reputation of probabilistic approaches is increasing. In this study, 20 road cuts located in North West Black Sea region of Turkey were evaluated using slope stability probability classification (SSPC). Considering this probabilistic approach, rock strength parameters and failure mechanisms were determined. Furthermore, slope mass rating (SMR) classification was applied for each road cut in order to compare with the results obtained from SSPC. These overall results were then evaluated with the field observations considering rockslope deterioration assessment (RDA) and Falling Rock Hazard Index (FRHI) for the disturbed/weathered zones, and failure mechanisms. According to these, SSPC is found to be more accurate for surficial degradations (raveling and fall) using samples taken from the disturbed/weathered zones rather than using relatively fresh samples beyond the disturbed zone. Moreover, despite strength differences between weathered and relatively fresh zones, SMR classification is identified to reveal the same stable probabilities. It is found that SSPC shows more detailed probabilistic results than SMR. Lastly, rockfall and raveling mechanisms determined by RDA and rockfall risk by FRHI were found to be coherent with SSPC and field observations.

Probabilistic slope stability analysis based on conditional random field

The linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height $h$ and diameter $d$ immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each of its sides. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar–turbulent transition process. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes is related to a different physical mechanism. While the varicose mode has its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and has its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability: whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake region, for larger roughness elements the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio ${\it\eta}=1$ (with ${\it\eta}=d/h$) roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff–Braslow transition diagram provides qualitatively good agreement.

An ASME Plant Systems Design (PSD-1) standard is being developed for design of facilities with potential for significant hazards to the health and safety of the public, the worker, and the environment. The standard includes requirements and guidance for design organizations to incorporate risk informed probabilistic design methodologies with traditional deterministic design methods, using reliability and availability targets. Previous papers have described the overall approach of PSD-1, where the plant systems and structures overall design is developed using appropriate probabilistic methods and then followed by component level design. This paper describes the component level design approach and the structure of the PSD-1 requirements and guidance. The steps include defining the component boundaries, assessing where a probabilistic method is appropriate, defining failure modes and mechanisms, defining mechanistic models, selecting appropriate probabilistic analysis methods, and performing the probabilistic analysis. The selected probabilistic models can depend on the availability of input data, the resolution of the model, and the computational cost for the analysis. The outcome of the probabilistic analysis for the component is fed back into the system and structures level analysis to verify that the system and structure level reliability and availability targets are met. If not met, the analysis may be repeated with changes to the system and structure design so the targets can be met. The process is demonstrated using an example of a steam generator with reliability and availability targets based on the system and structure design assessment.