Probabilistic stability analysis of excavations in jointed rock

1995 ◽  
Vol 32 (3) ◽  
pp. 397-407 ◽  
Author(s):  
C.F. Leung ◽  
S.T. Quek
Keyword(s):  
Stability Analysis ◽  
Site Investigation ◽  
Jointed Rock ◽  
Rock Block ◽  
Dispersion Data ◽  
Discontinuity Orientation ◽  
The Mean ◽  
The Stability ◽  
Selection Of ◽  
Block Volume

Excavations in jointed rock may liberate rock blocks that may fall by gravity or slide along the discontinuity. The orientation of discontinuities is one of the major input parameters in the conventional deterministic stability analysis of rock blocks. As the mean orientation of a discontinuity is often derived from a large number of joint-set data obtained from site investigation, Fisher's constant is commonly employed to represent the degree of dispersion of individual discontinuity orientation. However, such dispersion factors are rarely used in the conventional analysis. A probabilistic-based approach is proposed in this paper to incorporate Fisher's constant in the stability analysis of rock blocks. To account for the uncertainty reflected by the sample dispersion, data are generated systematically around each mean discontinuity normal, based on its Fisher's constant. The probability of rock block failure at a certain location and the largest possible block volume are determined in a logical manner. A microcomputer program has been developed to automate the analysis, and illustrative examples are shown to demonstrate the importance of incorporating the Fisher's constant of individual discontinuity in the stability analysis. In addition, risk mapping plots are presented to enable visual selection of an optimal route for excavation from one location to another. Key words : discontinuity, factor of safety, probability of failure, rock block, rock excavation, stability analysis.

The instability of the thin vortex ring of constant vorticity

1977 ◽  
Vol 287 (1344) ◽  
pp. 273-305 ◽  
Keyword(s):  
Stability Analysis ◽  
Vortex Ring ◽  
Mean Flow ◽  
Bending Waves ◽  
Constant Vorticity ◽  
Ring Radius ◽  
Amplification Rate ◽  
The Mean ◽  
The Stability ◽  
Good Agreement

A theoretical investigation of the instability of a vortex ring to short azimuthal bending waves is presented. The theory considers only the stability of a thin vortex ring with a core of constant vorticity (constant /r) in an ideal fluid. Both the mean flow and the disturbance flow are found as an asymptotic solution in e = a /R, the ratio of core radius to ring radius. Only terms linear in wave amplitude are retained in the stability analysis. The solution to 0 (e 2 ) is presented, although the details of the stability analysis are carried through completely only for a special class of bending waves that are known to be unstable on a line filament in the presence of strain (Tsai & Widnall 1976) and have been identified in the simple model of Widnall, Bliss & Tsai (1974) as a likely mode of instability for the vortex ring: these occur at certain critical wavenumbers for which waves on a line filament of the same vorticity distribution would not rotate (w 0 = 0). The ring is found to be always unstable for at least the lowest two critical wavenumbers ( ka = 2.5 and 4.35). The amplification rate and wavenumber predicted by the theory are found to be in good agreement with available experimental results.

scholarly journals Application of the Multiple Exp-Function, Cross-Kink, Periodic-Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Haifa Bin Jebreen ◽  
Yurilev Chalco-Cano
Keyword(s):  
Stability Analysis ◽  
Exponential Function ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Kink Solution ◽  
Engineering Sciences ◽  
Hirota Bilinear Form ◽  
The Stability ◽  
Wave Methods ◽  
Selection Of

In this article, the exact wave structures are discussed to the Caudrey-Dodd-Gibbon equation with the assistance of Maple based on the Hirota bilinear form. It is investigated that the equation exhibits the trigonometric, hyperbolic, and exponential function solutions. We first construct a combination of the general exponential function, periodic function, and hyperbolic function in order to derive the general periodic-kink solution for this equation. Then, the more periodic wave solutions are presented with more arbitrary autocephalous parameters, in which the periodic-kink solution localized in all directions in space. Furthermore, the modulation instability is employed to discuss the stability of the available solutions, and the special theorem is also introduced. Moreover, the constraint conditions are also reported which validate the existence of solutions. Furthermore, 2-dimensional graphs are presented for the physical movement of the earned solutions under the appropriate selection of the parameters for stability analysis. The concluded results are helpful for the understanding of the investigation of nonlinear waves and are also vital for numerical and experimental verification in engineering sciences and nonlinear physics.

scholarly journals Stability analysis of the Kosciuszko Mound using terrestrial laser scanner and numerical modelling

2018 ◽  
Vol 66 ◽  
pp. 01018
Author(s):  
Elżbieta Pilecka ◽  
Karolina Tomaszkiewicz
Keyword(s):  
Stability Analysis ◽  
Laser Scanner ◽  
Technical Condition ◽  
Point Of View ◽  
Terrestrial Laser Scanner ◽  
The Finite Element Method ◽  
Anthropogenic Soils ◽  
Differential Model ◽  
The Stability ◽  
Selection Of

Landslides which form in anthropogenic soils are complicated from a geological engineering and geotechnical point of view. Each case requires a detailed investigation and the selection of effective reinforcements is a difficult project issue. The study presents the problem of the stability analysis of landslides occurring in the anthropogenic soils of the Kosciuszko Mound in Cracow. The previously performed protections are discussed to highlight their ineffectiveness and the current technical condition of the mound is also presented. By overlapping the results of displacement measurements made with a terrestrial laser scanner, a differential model of the terrain was created which made it possible to determine the size and direction of the deformation of the slopes of the mound and the tendencies for the development of landslide movements in this area. A cross-section, selected on the basis of the model, was numerically analysed using the finite element method (FEM) in the Midas GTS NX program. As a result of the analysis, the values of the displacements and strains occurring in the Mound were calculated. On the basis of the value of the safety factor obtained, it was also possible to assess the risk of landslide movements.

scholarly journals Stability Analysis for Yield and Its Component Characters in Blackgram [Vigna mungo (L.) Hepper]

2021 ◽  
Author(s):  
C. Shobanadevi ◽  
R. Elangaimannan ◽  
K. Vadivel
Keyword(s):  
Stability Analysis ◽  
Seed Yield ◽  
Climatic Conditions ◽  
Vigna Mungo ◽  
Indian Agriculture ◽  
Stable Performance ◽  
High Yielding Varieties ◽  
The Stability ◽  
High Seed Yield ◽  
Selection Of

Background: Blackgram [Vigna mungo (L.) Hepper] is an important pulse crop occupying a unique position in Indian agriculture. Blackgram provides a major share of the protein requirement of the vegetarian population of the country. The crop is resistant to adverse climatic conditions and improves the soil fertility by fixing atmospheric nitrogen in the soil. Phenotypically stable genotypes are of great importance because the environmental conditions vary from season to season and year to year. Stable performance of blackgram genotypes across contrasting environments is essential for the successful selection of stable and high yielding varieties. Methods: A total of seven genotypes of blackgram were evaluated one season (Rabi - 2019) in three environments to study the G x E interaction for three traits.Result: Based on the stability analysis of Eberhart and Russell model, two genotypes viz., MDU 1 and NRIB 002 were found to be stable across the environments for seed yield. These genotypes had high seed yield with a unity regression coefficient and deviation from regression equal to zero.

scholarly journals ANALISIS STABILITAS MENGGUNAKAN MODEL MATERIAL PERALIHAN TANAH-BATUAN

2019 ◽  
Vol 1 (3) ◽  
pp. 225-230
Author(s):  
Putera Agung ◽  
Ardianto A
Keyword(s):  
Stability Analysis ◽  
Friction Stress ◽  
Model Material ◽  
Dam Construction ◽  
Stress Strain ◽  
Angle Of Internal Friction ◽  
Analysis Of Stability ◽  
The Stability ◽  
Selection Of

AbstractAn analysis of stability needs to predict stress-strain values of soil, rock, and/or intermediate material (soil-rock) layers around the gate shaft during excavation works. Selection of stress-strain of intermediate material foccused on this paper will affect to the analysis result. This analysis concerned on some consideration to the selection the stress-strain parameters in determination of c’ and f’ parameters. In excavation works,the parameters were applied to the stability analysis of gate shaft construction of dam construction. The stability analysis used a 2 D software of PLAXIS. Each condition of gate shaft was reinforcement and un-reinforcement wall types. From several analyses, the parameters of c’ and f’ from stress-strain of soil was smaller than intermediate material.Keywords: Cohesion; angle of internal friction, stress, strain, gate shaft.Abstrak Suatu analisis stabilitas perlu untuk memperkirakan besarnya tegangan-regangan tanah, batuan, dan atau lapisan material peralihan tanah-batuan (intermediate material) di sekitar lubang galian vertikal. Pemilihan tegangan-regangan dari material peralihan tanah-batuan yang difokuskan pada paper ini akan berpengaruh terhadap hasil analisis. Analisis ini memusatkan perhatian pada beberapa pertimbangan pemilihan parameter tegangan-regangan dalam analisis stabilitas saluran pengalihn vertikal pada konstruksi dam. Analisis stabilitas ini menggunakan software Plaxis 2 D (dimensi). Masing-masing tipe dinding saluran vertikal ini adalah dengan dan tanpa perkuatan tulangan. Dari beberapa analisis, parameter c’ dan f’ dari tanah adalah lebih kecil dari material peralihan.  Katakunci: Kohesi, sudut geser dalam, tegangan, regangan, saluran pengalihan vertikal.

Zonal approach to centrifugal, elliptic and hyperbolic instabilities in Stuart vortices with external rotation

2001 ◽  
Vol 449 ◽  
pp. 1-37 ◽  
Author(s):  
FABIEN S. GODEFERD ◽  
CLAUDE CAMBON ◽  
S. LEBLANC
Keyword(s):  
Stability Analysis ◽  
External Rotation ◽  
Short Wave ◽  
Rotating Flows ◽  
Mean Flow ◽  
Mode Decomposition ◽  
Centrifugal Instability ◽  
The Mean ◽  
The Stability ◽  
Stuart Vortices

The stability analysis of a street of Stuart vortices in a rotating frame is performed by integrating the Kelvin–Townsend equations along the mean flow trajectories, using the geometrical optics technique (Lifschitz & Hameiri 1991) for short-wave perturbations. A parallel is drawn between the formulations of this zonal approach and that of rapid distortion theory, better known to the turbulence community. The results presented confirm those obtained by the standard stability analysis based on normal-mode decomposition: depending on the rotation parameter and the oblique mode considered, three unstable zones are identified, related to the centrifugal, elliptic and hyperbolic instabilities, as observed for Taylor–Green cells (Sipp et al. 1999). Anticyclonic rotation is shown to destabilize Stuart vortices through a combination of the elliptical and centrifugal instability mechanisms, depending on the ratio of its rate to the structure core vorticity. Available stability criteria are discussed in the general case of two-dimensional rotating flows, in relation to their streamline topology and the values of the local Rossby number or vorticity.

scholarly journals Mean flow stability analysis of oscillating jet experiments

2014 ◽  
Vol 757 ◽  
pp. 1-32 ◽  
Author(s):  
Kilian Oberleithner ◽  
Lothar Rukes ◽  
Julio Soria
Keyword(s):  
Stability Analysis ◽  
Wave Model ◽  
Flow Stability ◽  
Mean Flow ◽  
Axisymmetric Mode ◽  
Wide Range ◽  
Flow Oscillations ◽  
The Mean ◽  
Wave Models ◽  
The Stability

AbstractLinear stability analysis (LSA) is applied to the mean flow of an oscillating round jet with the aim of investigating the robustness and accuracy of mean flow stability wave models. The jet’s axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry (PIV) and decomposed into a mean and periodic part utilizing proper orthogonal decomposition (POD). Local LSA is applied to the measured mean flow adopting a weakly non-parallel flow approach. The resulting global perturbation field is carefully compared with the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{>}40\, \%$), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows. The high accuracy of mean flow stability wave models as demonstrated here is of great importance for the analysis of coherent structures in turbulent shear flows.

scholarly journals Convergent Properties of Riccati Equation with Application to Stability Analysis of State Estimation

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
X. Cai ◽  
Y. S. Ding ◽  
S. Y. Li
Keyword(s):  
Stability Analysis ◽  
State Estimation ◽  
Kalman Filters ◽  
Sufficient Conditions ◽  
Time Instant ◽  
Novel Method ◽  
Finite Memory ◽  
The Stability ◽  
Time Invariant ◽  
Selection Of

Since the recursive nature of Kalman filtering always results in a growing size of the optimization problem, state estimation is usually realized by use of finite-memory, receding horizon, sliding window, or “frozen” techniques, which causes difficulties on stability analysis. This paper proposes a novel method on selection of an initial covariance matrix and a horizon for the Kalman filter to make sure that a sequence of the closed-loop Kalman filters are stable as time-invariant filters at subsequent time instant. Convergent properties of Riccati Difference Equation (RDE) are first exploited. Based on these properties, sufficient conditions for stability of a sequence of Kalman filters are obtained. Compared with the existent literature, the convergent properties and the stability conditions are less conservative since they provide analytic results and are applicable to more common cases where the RDEs are not monotonic.

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