Discontinuity In Slope Research Articles

3D key‐group method for slope stability analysis

SUMMARYBecause of the simplicity and the speed of execution, methods used in static stability analyses have yet remained relevant. The key‐block method, which is the most famous of them, is used for the stability analysis of fractured rock masses. The KBM method is just based on finding key blocks, and if no such blocks are found to be unstable, it is concluded that the whole of the rock mass is stable. Literally, though groups of ‘stable’ blocks are taken together into account, in some cases, it may prove to be unstable. An iterative and progressive stability analysis of the discontinuous rock slopes can be performed using the key‐group method, in which groups of collapsible blocks are combined. This method is literally a two‐dimensional (2D) limit equilibrium approach. Because of the normally conservational results of 2D analysis, a three‐dimensional (3D) analysis seems to be necessary.In this paper, the 2D key‐group method is developed into three dimensions so that a more literal analysis of a fractured rock mass can be performed. Using Mathematica software, a computer program was prepared to implement the proposed methodology on a real case. Then, in order to assess the proposed 3D procedure, its implementation results are compared with the outcomes of the 2D key‐group method. Finally, tectonic block No.2 of Choghart open pit mine was investigated as a case study using the proposed 3D methodology. Results of the comparison revealed that the outcomes of the 3D analysis of this block conform to the reality and the results of 2D analysis. Copyright © 2011 John Wiley & Sons, Ltd.

Generalized Poisson Integral Formula applied to potential flow solutions for free and confined jets with secondary flow

A generalized form of the Poisson Integral Formula is presented and applied to obtain a new class of two-dimensional, incompressible, potential flowfield solutions for free and confined jets. Two basic configurations are considered that demonstrate the procedure, a jet issuing from a straight wall or flowing from a semi-infinite, constant area duct. In either case the jet can be free or confined, with or without uniform external flow. A discretized form of the Poisson Integral Formula is also presented so that arbitrary boundary value distributions (i.e., boundary conditions) can be handled, including those with functional and/or slope discontinuities. The procedure makes use of conformal mapping and complex variable theory so that jet flowfield determination is reduced to solution of a boundary value problem on a simple domain (i.e., upper half-plane). The entire velocity field is described analytically; stream function and velocity potential contour maps are readily constructed. These solutions can serve as the zero-order inviscid outer solution (replacing the usual assumption of uniform or quiescent outer flow) in a matched asymptotic expansion process whereby viscous effects are introduced near the jet axis by means of a boundary-layer-type analysis. A number of example solutions are presented, most without any form of singularity in the flowfield as a result of having the freedom to arbitrarily select boundary conditions. Solutions are also presented having separation and recirculation regions adjacent to sharp jet exit corners. Several additional examples of the generalized Poisson Integral Formula applied to other types of problems are also described, including periodic boundary distributions and distributions having discontinuities.

Vibration analysis of composite laminated plates using higher-order shear deformation theory with zig-zag function

The ever increasing use of composite materials in advanced technology areas like aerospace, automotive, and sports equipments, have prompted to play a prominent role. A theory which can predict accurately the behavior of the composite structure and the failure mechanism is very much essential. In this work an analytical procedure is developed, to investigate the free vibration characteristics of different laminated composite plates based on higher order shear displacement model with zig-zag function. This function improves slope discontinuities at the interfaces of laminated composite plates. The related functions are obtained using the dynamic version of principle of virtual work or Hamilton’s principle. The solutions are obtained using Navier’s and numerical methods for anti-symmetric cross-ply and angle-ply laminates with a specific type of simply supported boundary conditions SS-1 and SS-2 respectively. In this paper the Numerical results are presented for free vibration of anti-symmetric cross-ply and angle-ply laminated plates. All the solutions presented are close agreement with the theory of elasticity and closed form solutions available in the literature. Keywords: Vibrational analysis, composite material, zig-zag function

Generating mechanism and formation criteria of kinked surface in peripheral end milling

A kinked surface is commonly generated in a peripheral end milling process. In this paper, the generating mechanism of a kinked surface in end milling is systematically analyzed and revealed under the convolution framework through the establishment of a surface generation and form error model. It is found that the shape and kink positions of a form error profile can be determined by the three angular parameters: the axial and radial immersion angles and the flute spacing angle. From these angular parameters, four types of flute/work engagement conditions are defined to serve as the kink formation criteria with each type generating its own distinctive surface error profile in both down and up milling configurations. These form error profiles are characterized by either a kink-free form or by a single or a combination of three types of kink forms, which are defined based on changes in the flute/work engagement conditions and the resulting slope discontinuity in the force profile. Based on the kink formation criteria, kink charts scaled in normalized axial and radial depths of cut are devised to identify the types of kinked surface generated at any given depths of cut. An algebraic closed-form expression for the positions of kink points is also derived. The proposed kink formation criteria, the kink chart and the kink height prediction are validated through experiments and by comparison with data extracted from previously published results.

Slope stability analysis and discontinuous slope failure simulation by elasto-plastic smoothed particle hydrodynamics (SPH)

Most slope stability analyses have employed limit equilibrium methods (LEMs) or the finite-element method (FEM) as the standard approach. However, slope instability is often accompanied by discontinuous failure of the soil, which cannot be modelled by either LEMs or FEM. To overcome this limitation, this paper presents an extension of the smoothed particle hydrodynamics (SPH) method to evaluate the stability of a slope, and to simulate the post-failure behaviour of soil. For the slope stability analysis, the shear strength reduction technique with a modified failure criterion for distinguishing convergent from non-convergent solutions is applied to estimate the safety factor of a slope, and the critical slip surface is determined from a contour plot of accumulated plastic strain. To take the pore water pressure into account, a new SPH formulation for soil motion is developed. It is suggested that this equation can be applied to further developments of SPH for saturated soil. As an application of the proposed method, several smoothed particle slope stability analyses and corresponding slope failure simulations are presented, and compared with other solutions. The results show good agreements with other methods in terms of the safety factor and the critical slip surface. As compared with such traditional methods, however, an advantage of SPH is that it can simulate large deformation and post-failure of soil, and can thereby treat a wide range of applications in computational geomechanics, especially those that include large deformation and failure of geomaterials.

Monitoring Cu nodule formation using Ni marker layers

We have used Ni marker layers to study the evolution of the characteristic spheroidal nodule morphology in electrodeposited Cu films. Ultrathin Ni layers were electrodeposited in-between Cu layers, and cross sections prepared by electrochemical polishing. During growth of a typical spheroidal feature, the edge (i.e. where there is a discontinuity in the surface slope) traces out a straight line in the cross-sectional image. At high overpotential, the cross-sections show nodule-on-nodule growth, giving rise to the well known cauliflower morphology. Rotating disk electrode studies reveal that, surprisingly, the absolute diffusion layer thickness does not appear to play a major role in the development of spheres.

A hybrid approach for the modal analysis of continuous systems with discrete piecewise-linear constraints

The analysis of continuous systems with piecewise-linear constraints in their domains have previously been limited to either numerical approaches, or analytical methods that are constrained in the parameter space, boundary conditions, or order of the system. The present analysis develops a robust method for studying continuous systems with arbitrary boundary conditions and discrete piecewise-linear constraints. A superposition method is used to generate homogeneous boundary conditions, and modal analysis is used to find the displacement of the system in each state of the piecewise-linear constraint. In order to develop a mapping across each slope discontinuity in the piecewise-linear force-deflection profile, a variational calculus approach is taken that minimizes the L 2 energy norm between the previous and current states. An approach for calculating the finite-time Lyapunov exponents is presented in order to determine chaotic regimes. To illustrate this method, two examples are presented: a pinned–pinned beam with a deadband constraint, and a leaf spring coupled with a connector pin immersed in a viscous fluid. The pinned–pinned beam example illustrates the method for a non-operator based analysis. Results are used to show that the present method does not necessitate the need of a large number of basis functions to adequately map the displacement and velocity of the system across states. In the second example, the leaf spring is modeled as a clamped-free beam. The interaction between the beam and the connector pin is modeled with a preload and a penalty stiffness. Several experiments are conducted in order to validate aspects of the leaf spring model. From the results of the convergence and parameter studies, a high correlation between the finite-time Lyapunov exponents and the contact time per period of the excitation is observed. The parameter studies also indicate that when the system's parameters are changed in order to reduce the magnitude of the impact velocity between the leaf spring and the connector pin, the extent of the regions over which a chaotic response is observed increases.

Physical modelling of in-ground waste repository capping systems

This paper describes a series of geotechnical centrifuge tests carried out to investigate aspects of landfill capping system performance, in the context of a low-level radioactive waste disposal site. The effects of the basic cap geometry (sloping or flat) and the subsidence pattern imposed as the underlying waste degrades (ramp or step, i.e. slope or displacement discontinuity) are shown to influence cap performance. The effect of moving the toe of a sloping cap outside the landfill subsidence zone, thereby increasing the depth of inert fill below the cap, is also shown to be effective in limiting the displacements transmitted to the resistive layer. Analysis of the runoff from sloping capping systems shows that if the resistive layer fails, there is the potential for the infiltration rate through the cap to increase from near zero to almost 100% of the incident rainfall.

Potassium-doped FePc thin-film on metal surfaces: observation of different empty state occupation

Iron-Phthalocyanine molecules deposited on the Cu(119) vicinal surface form molecular chains along the vicinal surface steps, as deduced by the low-energy electron diffraction (LEED) reconstruction pattern. The work-function lowers at the FePc single-layer completion, due to the formation of an interface dipole. Further FePc deposition induces a different growth morphology, as suggested by the slope discontinuity in the work function variation. Upon depositing potassium onto the FePc thin-film prepared on Cu(119), the K-injected electrons fill up the Fe-d-associated and ligand-π-related orbitals, as observed by means of high-resolution ultraviolet photoelectron spectroscopy.

Failure Mode and Ultimate Strength of Precast Concrete Barrier

This study examines the validity of design formulas adopted from the yield line theory of American Association of State Highway and Transportation Officials load and resistance factor design (AATSHTO LRFD) specifications for precast concrete barriers with a potential longitudinal discontinuity and for barrier sections with a slope discontinuity. A full-scale static test was performed on newly-developed type of precast concrete barrier system. Protruded reinforcements and a mortar filling were used to combine the barrier and deck. Five specimens were fabricated with different test variables that simulate the cantilevered part of the deck and a series of precast barriers. Test levels and the corresponding loading patterns simulating a vehicle crash were adopted from AASHTO LRFD specifications. Findings show that the new precast concrete barrier system had an ultimate capacity equivalent to that of a conventional barrier. The longitudinal continuity of a series of precast barrier segments significantly affected the ultimate strength of the whole barrier system. The shapes of the yield liens obtained in the static test were different than those presented in the AASHTO specifications. An alternative failure mode and corresponding predictive equations of the strength based on actual yield lines were proposed. The proposed theories may be applicable to barriers with a tapered section with some points of slope discontinuity.

Free transverse vibrations of cracked nanobeams with surface effects

The flexural vibrations of cracked micro- and nanobeams in the presence of surface effects are studied. The cracked-beam model is set up by dividing the classical cracked beam element into two segments connected by a rotational spring located at the cracked section. This model promotes a discontinuity in bending slope, which is proportional to the second derivative of the displacements. Numerical examples demonstrate the effects of beam length, and crack position and severity on the calculated values of natural frequencies of an anodic alumina nanowire in the presence of surface effects. Limiting cases are considered and good agreements with the data available in the literature are obtained.

General Method for Modeling Slope Discontinuities and T-Sections Using ANCF Gradient Deficient Finite Elements

Abstract Slope discontinuities and T-sections can be modeled in a straight forward manner using fully parameterized absolute nodal coordinate formulation (ANCF) finite elements that have a complete set of gradient vectors. Linear transformations that define the element connectivity can always be obtained and used to preserve ANCF desirable features that include constant mass matrix and zero Coriolis and centrifugal forces in the case of spinning structures. The objective of this paper is to develop a general method that allows for modeling slope discontinuities and T-sections using gradient deficient ANCF finite elements that do not have a complete set of coordinate lines and gradient vectors. Linear connectivity conditions that preserve all the ANCF desirable features including the constant mass matrix are developed at the nodes of slope discontinuities. At these nodes of discontinuity, one can always define a complete set of independent coordinate lines that lie on the structure. These coordinate lines can be used to define a complete set of independent gradient vectors at these nodes. Since the proposed method is based on linear coordinate transformations, the method can be implemented in a preprocessor computer program. The application of the proposed general method is demonstrated using ANCF gradient deficient beam element example.

Identification of a multi-crack in a shaft system using transverse frequency response functions

The identification of multiple cracks in a shaft is still a real challenge. In the present work, a two-stage identification methodology has been developed, which identifies a number of cracks, their locations on a cracked shaft and its sizes. The methodology uses transverse forced responses of the shaft system at different frequencies of a harmonic excitation. In the first stage, a multi-crack detection and its localization algorithm are developed. Transverse forced vibrations of a non-rotating cracked shaft in two orthogonal planes are analyzed with the help of the finite element method by using the Timoshenko beam theory. The presence of a crack in a shaft introduces a slope discontinuity in the elastic line of the shaft. This causes a jump in the value of the curvature of the shaft elastic line, and it is difficult to measure in the presence of measurement noise. In the present work, the shaft curvature is obtained by approximating forced responses of the shaft at consecutive axial measurement locations by a polynomial. The effect of noise is reduced by utilizing forced responses of the shaft at several frequencies. This stage of the algorithm gives the number of cracks and their approximate locations over the shaft. In the second stage of the algorithm, the size and the accurate location of cracks are obtained by using multi-objective genetic algorithms. Responses of the shaft at several frequencies are used to define objective functions in GA. The proposed two-stage methodology is tested with numerically simulated noisy forced responses from the finite element modeling of a simply supported shaft having two cracks. The methodology identifies very well the presence of cracks and also estimates quite accurately the location and the size of cracks on the shaft.

Ground Filtering Algorithms for Airborne LiDAR Data: A Review of Critical Issues

This paper reviews LiDAR ground filtering algorithms used in the process of creating Digital Elevation Models. We discuss critical issues for the development and application of LiDAR ground filtering algorithms, including filtering procedures for different feature types, and criteria for study site selection, accuracy assessment, and algorithm classification. This review highlights three feature types for which current ground filtering algorithms are suboptimal, and which can be improved upon in future studies: surfaces with rough terrain or discontinuous slope, dense forest areas that laser beams cannot penetrate, and regions with low vegetation that is often ignored by ground filters.

Second-gradient plane deformations of ideal fibre-reinforced materials II: forming flows of fibre–resin systems when fibres resist bending

The continuum theory of ideal fibre-reinforced fluids, namely incompressible viscous fluids exhibiting some direction of inextensibility is extended to account for the fibre bending stiffness; namely a property that prevents discontinuity of the fibre slope under normal loading conditions. The principal kinematics of this new theoretical development is consistent with three-dimensional forming flows of fibre–resin systems though, for simplicity, formulation of relevant constitutive equations is confined within the framework of relevant plane flows. The theory adopts the macroscopic view that the resin matrix behaves as a viscous fluid but the resin and fibres form a homogeneous composite material. Consideration of the fibre bending resistance requires the inclusion of couple-stress and, hence, non-symmetric stress. The outlined theoretical developments are therefore relevant to polar-media behaviour; in this context, the anisotropic viscous fluids of interest become part of the material class of the so-called polar fluids. For plane flows of this type of fluids, a manner is also outlined in which the non-symmetric stress distributions sought can be determined by solving two simultaneous, first-order linear differential equations. Moreover, a relevant stress-resultants technique is adopted and extended appropriately to make possible complete determination of the kinematics dictating the creeping forming plane flow of the composite fluids of interest. Details of the mechanisms that capture fibre bending resistance are revealed and illustrated through a relatively simple example application. This considers and resolves the forming flow process of an ideal fibre-reinforced composite, moulded into a sharp corner under the action of an external line force.

Generation of spline approximations to parametric tessellations

In geometrical modeling, one is often provided a description of a surface that is defined in terms of a triangulation, which is supported by a discrete number of nodes in space. These faceted surface representations are defined to be C-0 continuous, and therefore in general have slope and curvature discontinuities at the triangle sides, unless the tessellation is planar. Unfortunately, analytical and computational methods often require a surface description that has well-defined and smoothly varying gradients and curvatures; in general spline surfaces possess such properties. Described herein is a process for generating a cubic spline surface that approximates, to within a user-specified tolerance, a given tessellated surface that may be non-convex or multiply connected. The method combines a local least-squares technique for specifying knot properties as well as an adaptation technique for selecting the necessary knot spacings. This new technique is first described along a curve for illustrative purposes. It is then expanded to the case of the general surface. A reparameterization technique that is required for surfaces with non-smooth parameterizations is described next. Computed results for two configurations are then shown.

Dynamic yielding in lithium fluoride and aluminum

At a time immediately after shock loading, a kink (a weak discontinuity or a discontinuity in slope) occurs at a position in an unsteady portion in a smooth plane wave front in a lithium fluoride single crystal (material IIIb) or in 1060-0 aluminum due to the instability of the wave front. After the occurrence of the kink, a zone is produced and broadened with time between a near steady precursor ahead of the kink and a plastic wave behind it in a weak-discontinuity plane wave by the difference in the propagation velocity between them. Stress relaxes in the zone, which is called a follower, and the precursor decay takes place due to the stress relaxation. During the decay process, the large increase in plastic flow occurs in the vicinity of the leading edge of the follower, causes yielding at the leading edge, and stabilizes the weak-discontinuity wave. The stress-strain (σ-ε) history caused by the follower rotates clockwise with time around the yield point. The rotation yields different σ-ε histories behind the point and therefore different types of the dynamic σ-ε relation. Dynamic yield phenomena are illustrated by showing the schematic diagrams of three different types of the dynamic σ-ε relation, which are caused by weak-discontinuity plane waves composed of a precursor C, a follower (i) C, (ii) I or II, or (iii) R′ or Rb, and a plastic wave C behind the follower. Here C is the contraction (compression) wave, I and II are the degenerate contraction waves I and II, R′ is the subrarefaction wave, and Rb is the rarefaction wave.

An equation of state of a carbon-fibre epoxy composite under shock loading

An anisotropic equation of state (EOS) is proposed for the accurate extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic) states to other thermodynamic (anisotropic and isotropic) states for a shocked carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a generalised decomposition of a stress tensor [A.A. Lukyanov, Int. J. Plasticity 24, 140 (2008)], represents a mathematical and physical generalisation of the Mie-Grüneisen EOS for isotropic material and reduces to this equation in the limit of isotropy. Although a linear relation between the generalised anisotropic bulk shock velocity Us A and particle velocity up was adequate in the through-thickness orientation, damage softening process produces discontinuities both in value and slope in the Us A-up relation. Therefore, the two-wave structure (non-linear anisotropic and isotropic elastic waves) that accompanies damage softening process was proposed for describing CFC behaviour under shock loading. The linear relationship Us A-up over the range of measurements corresponding to non-linear anisotropic elastic wave shows a value of c0 A (the intercept of the Us A-up curve) that is in the range between first and second generalised anisotropic bulk speed of sound [A.A. Lukyanov, Eur. Phys. J. B 64, 159 (2008)]. An analytical calculation showed that Hugoniot Stress Levels (HSLs) in different directions for a CFC composite subject to the two-wave structure (non-linear anisotropic elastic and isotropic elastic waves) agree with experimental measurements at low and at high shock intensities. The results are presented, discussed and future studies are outlined.

Curvature continuous path generation for autonomous vehicle using B-spline curves

In this paper we introduce a roadmap algorithm for generating collision-free paths in terms of cubic B-spline curves for unmanned vehicles used in mining operations. The algorithm automatically generates collision-free paths that are curvature continuous with an upper bounded curvature and a small slope discontinuity of curvature at knots, when we are given the locations of the obstacles, the boundary geometry of the working area, positions and directions of the vehicle at the start, loading, and the goal points. Our algorithm also allows us to find a switch back point where the vehicle reverses its direction to enter the loading area. Examples are provided to demonstrate the effectiveness of the proposed algorithms.

A Linear Time Algorithm for Near Minimax Continuous Piecewise Linear Representations of Discrete Data

An algorithm that constructs a continuous piecewise linear representation, subject to a certain slope/segment length constraint, of a given set of data is described. The algorithm yields an optimal or near optimal representation, subject to this constraint, in the $L_{\infty}$ norm and does so in at worst $O(nK)$ time, where n is the number of data points and K the number of segments. The constraint is determined by a user-specified parameter, $t_{\min}$, which dictates a lower bound for the distance between opposite-sign slope discontinuities. For reasonable $t_{\min}$ values, the resulting representation of the data captures the signal and both smooths the noise and provides a measure of it. This representation is useful for applications that require a specified interval for the data values and also allows easy and continuous interpolation of ranges between recorded time points. The algorithm is described, some of its properties are proven, and its capabilities demonstrated with several examples. Comparisons are made with alternative techniques.