Slope stability analysis using Phase 2

Analysing the rock slope stability is a classical problem for geotechnicalengineers. Recently, Hoek-Brown failure criterion has drawn more and more attentionfor rock slope stability assessments. It would be due to the fact that the nonlinearity ismore pronounced at the low confining stresses that are operational in slope stabilityproblems. However, it is still not popular yet. Therefore, in this study, slope stabilityanalyses will be performed based on the generalised Hoek-Brown failure criterionusing a commercial software, Phase 2. The Hoek-Brown strength parameters will beused as direct inputs in numerical simulations. In addition, two rock slope cases willbe investigated. It is expected that better understandings of rock slope mechanisms canbe obtained.

Mixing layer oscillations for a submerged horizontal wall-jet

Measurements of the horizontal velocity component were made for a horizontal wall-jet emanating from a submerged sluice gate forming one side of a large flow compartment. The existence of large-scale vortex structures was quantified by spectral analysis of the velocity measurements taken at various distances from the floor of the flow compartment, for different measurement stations from the jet exit. Close to the jet exit, the spectra of the velocity measurements within the potential core exhibit multiple peaks. Further downstream, the spectra are more defined and peak at the same frequency, irrespective of whether the measurements were made within the potential core or the mixing layer. The spectral peak corresponds to the passage frequency of large-scale vortex structures. Downstream of the potential core, the peak frequencies of the velocity spectra increase as the measurement location was moved towards the floor of the flow compartment. The increase in peak frequencies is attributed to fluctuations associated with the wall boundary layer. Predictions of the mixing layer instabilities were made using linear stability analysis. The predictions are in good agreement with the observed vortex shedding frequencies in the mixing layer

Strain localisation patterns under equal-channel angular pressing

Instabilities of plastic flow in the form of localised shear bands were experimentally observed to result from equal-channel angular pressing (ECAP) of magnesium alloy AZ31. The appearance of shear bands and their spacing were dependent on velocity of the pressing and applied back-pressure. A generic gradient plasticity theory involving second-order strain gradient terms in a constitutive model was applied to the case of AZ31 deformed by ECAP. Linear stability analysis was applied to the set of equations describing the deformation behaviour in the process zone idealised as a planar shear zone. A full analytical solution providing a dispersion relation between the rate of growth of a perturbation and the wave number was obtained. It was shown that the pattern of incipient localised shear bands exhibits a spectrum of characteristic lengths corresponding to admissible wave numbers. The interval of the spectrum of wave numbers of viable, i.e. growing, perturbations predicted by linear stability analysis was shown to be in good agreement with the experimentally observed spectrum. The effect of back-pressure applied during ECAP was also considered. The predicted displacement of the shear band spectrum towards lower wave numbers, shown to be a result of the decreased shear strain rate in the shear zone, was consistent with the experimentally observed increase of the band spacing with increased back-pressure. A good predictive capability of the general modelling frame used in conjunction with linear stability analysis was thus demonstrated in the instance of the particular alloy system and the specific processing conditions considered.

Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control

Abstract
In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode-dependent probabilistic time-varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is considered and transformed into one with deterministic time-varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov-Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple-integral term is introduced for deriving the delay-dependent stability conditions. Furthermore, mode-dependent mean square exponential stability criteria are derived by constructing a new Lyapunov-Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results.

Dynamical analysis of neural networks with time-varying delays using the LMI approach

This study is concerned with the delay-range-dependent stability analysis for neural networks with time-varying delay and Markovian jumping parameters. The time-varying delay is assumed to lie in an interval of lower and upper bounds. The Markovian jumping parameters are introduced in delayed neural networks, which are modeled in a continuous-time along with finite-state Markov chain. Moreover, the sufficient condition is derived in terms of linear matrix inequalities based on appropriate Lyapunov-Krasovskii functionals and stochastic stability theory, which guarantees the globally asymptotic stable condition in the mean square. Finally, a numerical example is provided to validate the effectiveness of the proposed conditions.

Exponential stability of time-delay systems via new weighted integral inequalities

In this paper, new weighted integral inequalities (WIIs) are first derived based on Jensen's integral inequalities in single and double forms. It is theoretically shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvement based on Wirtinger's integral inequality. The potential capability of WIIs is demonstrated through applications to exponential stability analysis of some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

New finite-sum inequalities with applications to stability of discrete time-delay systems

This paper is concerned with the problem of stability analysis of discrete time-delay systems. New finite-sum inequalities, which encompass the ones based on Abel lemma or Wirtinger type inequality, are first proposed. The potential capability of the newly derived inequalities is then demonstrated by establishing less conservative stability conditions for some classes of linear discrete-time systems with delay. The derived stability criteria are theoretically and numerically proved to be less conservative than existing results.

Stability of two-dimensional Roesser systems with time-varying delays via novel 2D finitesum inequalities

This study considers the problem of stability analysis of discrete-time two-dimensional (2D) Roesser systems with interval time-varying delays. New 2D finite-sum inequalities, which provide a tighter lower bound than the existing ones based on 2D Jensen-type inequalities, are first developed. Based on an improved Lyapunov-Krasovskii functional, the newly derived inequalities are then utilised to establish delay-range-dependent linear matrix inequality-based stability conditions for a class of discrete time-delay 2D systems. The effectiveness of the obtained results is demonstrated by numerical examples.

A novel approach to exponential stability of continuous-time Roesser systems with directional time-varying delays

This paper addresses the problem of exponential stability analysis of two-dimensional (2D) linearcontinuous-time systems with directional time-varying delays. An abstract Lyapunov-like theorem whichensures that a 2D linear system with delays is exponentially stable for a prescribed decay rate is exploitedfor the first time. In light of the abstract theorem, and by utilizing new 2D weighted integral inequalitiesproposed in this paper, new delay-dependent exponential stability conditions are derived in terms oftractable matrix inequalities which can be solved by various computational tools to obtain maximumallowable bound of delays and exponential decay rate. Two numerical examples are given to illustrate theeffectiveness of the obtained results.

Convergence analysis of multi-stage PIC detectors

This paper analyses the convergence behaviour of the parallel interference cancellation (PIC) detector in code division multiple access (CDMA) systems. Using the results from previous stability analysis of an iterated-map neural network, the paper derives a general condition from which the sufficient condition for convergence of the PIC detector with tentative decision functions that are monotonically increasing at a sublinear rate can be calculated. As examples, the paper derives the sufficient conditions for convergence of the PIC detector with the clip decision and the hyperbolic tangent decision functions. The paper also examines the convergence behaviour of the PIC detector with hyperbolic tangent decision function via computer simulation and compares it with the analytical results.

Comparisons between two empirical yield criteria for rock masses

In general, rock masses are inhomogeneous, discontinuous media composed of rock material and naturally occurring discontinuities such as joints, fractures and bedding planes. Because of these features, the strength of rock masses is notoriously difficult to assess. Nonetheless, many criteria have been proposed for estimating rock mass strength. Based on the finite element upper and lower bound limit analysis methods, this study examined two empirical yield criteria for rock masses, the Hoek-Brown failure criterion (2002) and the Douglas criterion (2002). The comparisons showed that very different results may be obtained using the same input parameters. Therefore, it is interesting to discuss the source of these differences.

A novel aggregate gene selection method for microarray data classification

This paper introduces a novel method for gene selection based on a modification of analytic hierarchy process (AHP). The modified AHP (MAHP) is able to deal with quantitative factors that are statistics of five individual gene ranking methods: two-sample t-test, entropy test, receiver operating characteristic curve, Wilcoxon test, and signal to noise ratio. The most prominent discriminant genes serve as inputs to a range of classifiers including linear discriminant analysis, k-nearest neighbors, probabilistic neural network, support vector machine, and multilayer perceptron. Gene subsets selected by MAHP are compared with those of four competing approaches: information gain, symmetrical uncertainty, Bhattacharyya distance and ReliefF. Four benchmark microarray datasets: diffuse large B-cell lymphoma, leukemia cancer, prostate and colon are utilized for experiments. As the number of samples in microarray data datasets are limited, the leave one out cross validation strategy is applied rather than the traditional cross validation. Experimental results demonstrate the significant dominance of the proposed MAHP against the competing methods in terms of both accuracy and stability. With a benefit of inexpensive computational cost, MAHP is useful for cancer diagnosis using DNA gene expression profiles in the real clinical practice.

Pore pressure effect on slope stability assessment

Slope stability assessment has been an integral problem for geotechnical engineering all these years. While stability of slopes is affected by various factors, pore pressure is one of the common naturalelements that influence slope stability analysis. This paper studies the effect of pore pressure on slope stability assessment by using Limit Equilibrium Method (LEM). The results will be compared to the solutions of Hoek and Bray charts. In this study, slopes with different levels of water table corresponding to those of Hoek and Bray charts are investigated. It’s interesting to observe that the results obtained from the Hoek and Bray charts yielded different factor of safety compare to those in the study here-in. In fact, the different between the factors of safety could be up to 30%. Hence this issue should be taken into consideration during slope design.

Investigation of seismic effects on disturbed rock slope stability assessments

For general stability analysis of rock slopes, rock mass strength and rock mass disturbance are definitely should be considered. In addition, the impact of earthquakes must be taken into account. In fact, the rock mass strength is very difficult to be assessed which causes the difficulty of analysing rock slope stability. Therefore, an empirical failure criterion, the Hoek-Brown failure criterion, has been proposed. It is one of the most widely accepted approaches to estimate rock mass strength. The rock mass disturbance is important and was found having significant influence on evaluating rock slope stability, especially for rock slope with poor quality rock mass. In the Hoek-Brown failure criterion, the disturbance factor can represent the level of the rock mass disturbance which would provide a reasonable basis for estimating rock mass strength. This research will not only discuss the slope factor of safety, but also consider the influence of the seismic force on rock slope stability assessment using pseudo-static method. In practice, only horizontal seismic coefficient is used. Various magnitudes of the disturbance factor and recommended blasting damage zone thickness are also taken into account. The blasting damage zone thickness considered ranges from 0.5 to 2.5 times of slope height. The research results have potential to be extended and then sets of comprehensive stability charts can be provided for the rock slope stability evaluations. They will be convenient tools for practising engineers. In this study, finite element upper bound and lower bound limit analysis methods are employed. Their applicability has been investigated in some previous studies. The differences between upper bound and lower bound solutions are less than ±10% which would provide reasonable and acceptable range for rock slope stability safety factor estimation.

Analysis of texture and R value variations in asymmetric rolling of if steel

Asymmetric rolling (ASR) is a potential process to reach better grain refinement than in conventional rolling, thus, can lead to better mechanical properties. It is not known, however, how the introduction of a shear component will change the ideal orientations of the textures, and consequently, the evolution of plastic anisotropy. To understand the effect of the added shear on texture evolution in ASR, a stability analysis is carried out in orientation space and the variations in the position and strength of the ideal orientations are analysed as a function of the shear component. Then, modelling of R values is presented for various cases. On that basis, it is shown that there is an upper limit for the shear component in asymmetric rolling that still retains the 〈1 1 1〉 ND fibre (ND: direction normal to the sheet) which is good for formability. It is also found that better persistence of the ND fibre can be obtained by cyclically alternating the shear component. The theoretical results are well supported by comparison to experimental evidences. © 2011 Elsevier B.V. All rights reserved.