Slope stability charts for two-layered purely cohesive soils based on finite-element limit analysis methods

Stability charts for soil slopes, first produced in the first half of the twentieth century, continue to be used extensively as design tools, and draw the attention of many investigators. This paper uses finite-element upper and lower bound limit analysis to assess the short-term stability of slopes in which the slopematerial and subgrade foundation material have two distinctly different undrained strengths. The stability charts are proposed, and the exact theoretical solutions are bracketed to within 4.2% or better. In addition, results from the limit-equilibrium method (LEM) have been used for comparison. Differences of up to 20% were found between the numerical limit analysis and LEM solutions. It also shown that the LEM sometimes leads to errors, although it is widely used in practice for slope stability assessments.

Three-dimensional slope stability charts for frictional fill materials placed on purely cohesive clay

This paper investigates slope stability and produces a set of stability charts for three-dimensional (3D) slopes for a specific case in which frictional fill materials are placed on purely cohesive clay. As slopes are not usually plane strain in nature and are influenced by physical boundaries, this study uses a 3D analysis using the finite-element LB limit analysis method. Stability charts are convenient tools for geotechnical engineers during design in practice. For comparison purposes, the results from two-dimensional (2D) analyses are also discussed. The results from this study quantify the increase in the factors of safety obtained when 3D conditions are analyzed as opposed to the more traditional 2D.

The Kuhse-Singer euthanasia survey: why it fails to undermine the slippery slope argument - comparing apples and apples

A survey published in the Medical Journal of Australia in 1997 showed that the incidence of non-voluntary euthanasia in Australia was higher than in the Netherlands. Euthanasia is illegal in Australia, while it is openly practiced in the Netherlands. It has been suggested that the results of the survey undermine the slippery slope argument against legalising euthanasia. This is wrong. Although at the time of the survey, euthanasia was formally prohibited by the law in Australia, the medical and legal culture was such that doctors could practice euthanasia with impunity — in certain circumstances euthanasia by doctors was effectively condoned. This is in fact supported by the findings of the survey. The survey suggests that there were approximately 6,700 cases of euthanasia in Australia in the year from July 1994 to June 1995 — not one of which was prosecuted, let alone resulted in a conviction. Ultimately the survey merely shows that in a climate where voluntary euthanasia is tolerated, wide scale abuses (in the form of nonvoluntary euthanasia) occur. Paradoxically the results of the survey give further support to the slippery slope argument.

Hyperstereopsis in helmet-mounted NVDs : slope perception

Modern helmet-mounted night vision devices, such as the Thales TopOwl helmet, project imagery from intensifiers mounted on the sides of the helmet onto the helmet faceplate. This produces a situation of hyperstereopsis in which binocular disparities are magnified. This has the potential to distort the perception of slope in depth (an important cue to landing), because the slope cue provided by binocular disparity conflicts with veridical cues to slope, such as texture gradients and motion parallax. In the experiments, eight observers viewed sparse and dense textured surfaces tilted in depth under three viewing conditions: normal stereo hyper-stereo (4 times magnification), and hypostereo (1 / 4 magnification). The surfaces were either stationary, or rotated slowly around a central vertical axis. Stimuli were projected at 6 metres to minimise conflict between accommodation and convergence, and stereo viewing was provided by a Z-screen and passive polarised glasses. Observers matched perceived visual slope using a small tilt table set by hand. We found that slope estimates were distorted by hyperstereopsis, but to a much lesser degree than predicted by disparity magnification. The distortion was almost completely eliminated when motion parallax was present.

Tackling trigonometry - up the slippery slope?

This paper challenges mathematics teachers to go back and re-examine ideas as far as possible from the genuine beginner's point of view rather than in terms of being experts on the subject. It suggests tasks that teachers can do to achieve this. Topics covered are the shock of the new, the best single short lesson on trigonometry, the difficulty of remembering not knowing, first student trigonometric steps (scouts and flagpoles), first human steps in trigonometry (examining the stars), rotation becomes number, showing relations and learning ideas, plus a lengthy discussion on trigonometry.

Determination of plastic yield stress from spherical indentation slope curve

The indentation slope curve from a spherical indentation on elastic-plastic materials is examined. By comparing it with that of an linear elastic material of the same elastic properties, we found that the start point of plastic yielding for an elastic-plastic material can be easily located from the indentation slope curve. Based on this analysis, a simple but effective method is proposed to measure the plastic yield stress of very small samples from a spherical nano-indentation slope curve.

A new unit root test with two structural breaks in level and slope at unknown time

In this paper, we propose a new augmented Dickey–Fuller-type test for unit roots which accounts for
two structural breaks. We consider two different specifications: (a) two breaks in the level of a trending data series and (b) two breaks in the level and slope of a trending data series. The breaks whose time of occurrence is assumed to be unknown are modeled as innovational outliers and thus take effect gradually. Using Monte Carlo simulations, we showthat our proposed test has correct size, stable power, and identifies the structural breaks accurately.

Rock slope risk analysis based on non-linear failure criterion

The probability of failure of a rock slope is generally estimated by using the Limit Equilibrium Method (LEM) in conjunction with a reliability analysis. Although the LEM is relatively simple and time efficient, recent studies have indicated that using the LEM may overestimate the factor of safety by 21%, when based on a non-linear failure criterion. Fortunately, the solutions presented by Li et al. (2008, 2009) can provide more accurate evaluations for rock slope stability as the numerical upper and lower bound limit analysis methods (2002a, 2002b, 2005) were employed. The advantages of these methods are used in this study to assess the rock slope probability of failure. The motivation is that with more accurate methods to evaluate the factor of safety, more economic designs can be performed.

Limit analysis solutions for very gentle undrained slopes

In view of the demand for energy resources, offshore engineering has drawn the attention of many investigators over the past decade. Recent studies have revealed that seabed landslides can have a sig-nificant influence on the performance of offshore infrastructure, such as pipelines. The vulnerability triggered by seabed landslides can even lead to loss of life. In this context, the importance of offshore slope stability evaluation is obvious. Slope stability is generally assessed by the limit equilibrium method (LEM). However, the accuracy of the method is often questioned due to the underlying assumptions that it makes. This study utilises numerical finite element upper and lower bound limit analysis to produce solutions for very gentle undrained slopes. Using these techniques, the stability can be bracketed from above and below. In this paper, a range of slope geometries and the inhomogeneity of the natural soil have been taken into account. The solu-tions presented are useful tools for preliminary design.

Comparisons of seismic rock slope stability assessments between the Hoek-Brown and Mohr-Coulomb failure criteria

Current investigations have shown that earthquakes can trigger significant damages of equipment, property infrastructure and environment. This is a persistent cause of economic loss for any country, especially for the loss of life. The conventional method for slope stability design is to utilize limit equilibrium method (LEM) in conjunction with the pseudo-static (PS) approach. However, the LEM has a significant drawback which is to determine the slip surface before factor of safety calculation. The numerical upper and lower bound limit analysis method employed in this paper can avoid this limitation. In this study, the presented slope stability evaluations considering earthquake effects based on the finite difference method will be discussed and compared with the results from the numerical limit analysis methods.

Quantifying heteroskedasticity using slope of local variances index

In econometrics, heteroskedasticity refers to the case when the variances of the error terms of the data in hand are not equal. Heteroskedastic time series are challenging to different forecasting models. However, all available solutions adopt the strategy of accommodating heteroskedasticity in the time series and consider it as a type of noise. Some statistical tests were developed over the past three decades to determine whether a time series features heteroskedastic behaviour. This paper presents a novel strategy to handle this problem by deriving a quantifying measure for heteroskedasticity. The proposed measure relies on the definition of heteroskedasticity as a time-variant variance in the time series. In this work, heteroskedasticity is measured by calculating local variances using linear filters, estimating variance trends, calculating changes in variance slopes, and finally obtaining the average slope angle. The results confirm that the proposed index complies with the widely popular heteroskedasticity tests.

Slope stability analysis for cohesive materials filled on purely cohesive undrained clay

Stability charts for soil slopes were first produced by Taylor in 1937 and they continue to be used extensively as design tools and draw the attention of many investigators. From a review of literature, it was found that there is no convenient solution has been provided for cohesive materials filled on purely cohesive undrained clay. A recent study revealed that the embankment slope which has two-layered clays failed in an undrained state which shows the importance of this study. In order to obtain the solutions for this type of fill slope. A number of numerical method are employed, namely the finite element upper and lower bound limit analysis methods and limit equilibrium method. The numerical upper and lower bound limit analysis method can bracket true solutions within a small range (6%). The solutions of limit equilibrium analysis are used for comparison purpose.