Search results for: discontinuities

Authors: Nassim Ourabia, Malika Ourabia

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A new and efficient method is presented for the analysis of arbitrarily shaped discontinuities. The technique obtains closed form expressions for the equivalent circuits which are used to model these discontinuities. Then it would be easy to handle and to characterize complicated structures like T and Y junctions, truncated junctions, arbitrarily shaped junctions, cascading junctions, and more generally planar multiport junctions. Another advantage of this method is that the edge line concept for arbitrary shape junctions operates with real parameters circuits. The validity of the method was further confirmed by comparing our results for various discontinuities (bend, filters) with those from HFSS as well as from other published sources.

Keywords: CAD analysis, contour integral approach, microwave circuits, s-parameters

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Authors: N. Ourabia, M. Boubaker Ourabia

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An approach for modeling and numerical simulation of passive planar structures using the edge line concept is developed. With this method, we develop an efficient modeling technique for microstrip discontinuities. The technique obtains closed form expressions for the equivalent circuits which are used to model these discontinuities. Then, it would be easy to handle and to characterize complicated structures like T and Y junctions, truncated junctions, arbitrarily shaped junctions, cascading junctions and more generally planar multiport junctions. Another advantage of this method is that the edge line concept for arbitrary shape junctions operates with real parameters circuits. The validity of the method was further confirmed by comparing our results for various discontinuities (bend, filters) with those from HFSS as well as from other published sources.

Keywords: optimization, CAD analysis, microwave circuits, S-parameters

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Authors: A. Jameel, G. A. Harmain, Y. Anand, J. H. Masoodi, F. A. Najar

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The present study investigates the effect of inclusions on the shape and size of crack tip plastic zones in engineering materials subjected to static loads by employing the element free Galerkin method (EFGM). The modeling of the discontinuities produced by cracks and inclusions becomes independent of the grid chosen for analysis. The standard displacement approximation is modified by adding additional enrichment functions, which introduce the effects of different discontinuities into the formulation. The level set method has been used to represent different discontinuities present in the domain. The effect of inclusions on the extent of crack tip plastic zones is investigated by solving some numerical problems by the EFGM.

Keywords: EFGM, stress intensity factors, crack tip plastic zones, inclusions

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Authors: Malika Ourabia

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A new and efficient method is presented for the analysis of arbitrarily shaped discontinuities. The discontinuities is characterized using a hybrid spectral/numerical technique. This structure presents an arbitrary number of ports, each one with different orientation and dimensions. This article presents a hybrid method based on multimode contour integral and mode matching techniques. The process is based on segmentation and dividing the structure into key building blocks. We use the multimode contour integral method to analyze the blocks including irregular shape discontinuities. Finally, the multimode scattering matrix of the whole structure can be found by cascading the blocks. Therefore, the new method is suitable for analysis of a wide range of waveguide problems. Therefore, the present approach can be applied easily to the analysis of any multiport junctions and cascade blocks. The accuracy of the method is validated comparing with results for several complex problems found in the literature. CPU times are also included to show the efficiency of the new method proposed.

Keywords: segmentation, s parameters, simulation, optimization

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Authors: Mohamed Fredj, Abdallah Hafsaoui, Radouane Nakache

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The study of the stability of the mining works in rock masses fractured is the major concern of the operating engineer. For geotechnical works in mines and quarries, it there is not today's general methodology for analysis and the quantification of the risks relating to the dangers inherent in these concrete types (falling boulders, landslides, etc.). The reasons for this are uncertainty, which weighs on available data or lack of knowledge of the values of the parameters required for this analysis type. Stability calculations must be based on reliable knowledge of the distribution of discontinuities that dissect the Rocky massif and the resistance to shear of the intact rock and discontinuities. This study is aimed to study the stability of slope of mine (Kef Sennoun - Tebessa, Algeria). The problem is analyzed using a numerical model based on the finite elements (software Plaxis 3D).

Keywords: stability, discontinuities, finite elements, rock mass, open-pit mine

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Authors: Gelacio Juárez-Luna, Gustavo Ayala, Jaime Retama-Velasco

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This paper shows the advantages of the material failure process simulation by improve finite elements with embedded discontinuities, using a new definition of traction vector, dependent on the discontinuity length and the angle. Particularly, two families of this kind of elements are compared: kinematically optimal symmetric and statically and kinematically optimal non-symmetric. The constitutive model to describe the behavior of the material in the symmetric formulation is a traction-displacement jump relationship equipped with softening after reaching the failure surface. To show the validity of this symmetric formulation, representative numerical examples illustrating the performance of the proposed formulation are presented. It is shown that the non-symmetric family may over or underestimate the energy required to create a discontinuity, as this effect is related with the total length of the discontinuity, fact that is not noticed when the discontinuity path is a straight line.

Keywords: variational formulation, strong discontinuity, embedded discontinuities, strain localization

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Authors: Kiwon Yeom

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Change points are abrupt variations in a data sequence. Detection of change points is useful in modeling, analyzing, and predicting time series in application areas such as robotics and teleoperation. In this paper, a change point is defined to be a discontinuity in one of its derivatives. This paper presents a reliable method for detecting discontinuities within a three-dimensional trajectory data. The problem of determining one or more discontinuities is considered in regular and irregular trajectory data from teleoperation. We examine the geometric detection algorithm and illustrate the use of the method on real data examples.

Keywords: change point, discontinuity, teleoperation, abrupt variation

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Authors: Mohammad Moridzadeh, Aaron Gallant

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The paper will present the design and construction of the underground excavations of a pump station forebay and its related components including connector tunnels, access shaft, riser shaft and well shafts. The underground openings include an 8 m-diameter riser shaft, an 8-m-diameter access shaft, 34 2.4-m-diameter well shafts, a 107-m-long forebay with a cross section having a height of 11 m and width of 10 m, and a 6 m by 6 m stub connector tunnel between the access shaft and a future forebay extension. The riser shaft extends down from the existing forebay connector tunnel at elevation 247 m to the crown of the forebay at elevation 770.0 feet. The access shaft will extend from the platform at the surface down to El. 223.5 m. The pump station will have the capacity to deliver 600 million gallons per day. The project is located on an uplifted horst consisting of a mass of Precambrian metamorphic rock trending in a north-south direction. The eastern slope of the area is very steep and pronounced and is likely the result of high-angle normal faulting. Toward the west, the area is bordered by a high angle normal fault and recent alluvial, lacustrine, and colluvial deposits. An evaluation of rock mass properties, fault and discontinuities, foliation and joints, and in situ stresses was performed. The response of the rock mass was evaluated in 3DEC using Discrete Element Method (DEM) by explicitly accounting for both major and minor discontinuities within the rock mass (i.e. joints, shear zones, faults). Moreover, the stability of the entire subsurface structure including the forebay, access and riser shafts, future forebay, well shafts, and connecting tunnels and their interactions with each other were evaluated using a 3D coupled hydromechanical Finite Element Analysis (FEA).

Keywords: coupled hydromechanical analysis, discontinuities, discrete element, finite element, pump station

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Authors: Shervin Khazaeli, Shahab Haj-zamani

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Recently, advanced geotechnical engineering problems related to soil movement, particle loss, and modeling of local failure (i.e. discontinua) as well as modeling the in-contact structures (i.e. continua) are of the great interest among researchers. The aim of this research is to meet the requirements with respect to the modeling of the above-mentioned two different domains simultaneously. To this end, a coupled numerical method is introduced based on Discrete Element Method (DEM) and eXtended-Finite Element Method (X-FEM). In the coupled procedure, DEM is employed to capture the interactions and relative movements of soil particles as discontinua, while X-FEM is utilized to model in-contact structures as continua, which may consist of different types of discontinuities. For verification purposes, the new coupled approach is utilized to examine benchmark problems including different contacts between/within continua and discontinua. Results are validated by comparison with those of existing analytical and numerical solutions. This study proves that extended-finite-discrete element method can be used to robustly analyze not only contact problems, but also other types of discontinuities in continua such as (i) crack formations and propagations, (ii) voids and bimaterial interfaces, and (iii) combination of previous cases. In essence, the proposed method can be used vastly in advanced soil-structure interaction problems to investigate the micro and macro behaviour of the surrounding soil and the response of the embedded structure that contains discontinuities.

Keywords: contact problems, discrete element method, extended-finite element method, soil-structure interaction

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Authors: Josephine Shamash, Stuart Smith

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We examine reasons for introducing definitions in teaching mathematics in a number of different cases. We try to determine if, where, and when to provide a definition, and which definition to choose. We characterize different types of definitions and the different purposes we may have for formulating them, and detail examples of each type. Giving a definition at a certain stage can sometimes be detrimental to the development of the concept image. In such a case, it is advisable to delay the precise definition to a later stage. We describe two models, the 'successive approximation model', and the 'model of the extending definition' that fit such situations. Detailed examples that fit the different models are given based on material taken from a number of textbooks, and analysis of the way the concept is introduced, and where and how its definition is given. Our conclusions, based on this analysis, is that some of the definitions given may cause discontinuities in the learning sequence and constitute obstacles and unnecessary cognitive conflicts in the formation of the concept definition. However, in other cases, the discontinuity in passing from definition to definition actually serves a didactic purpose, is unavoidable for the mathematical evolution of the concept image, and is essential for students to deepen their understanding.

Keywords: concept image, mathematical definitions, mathematics education, mathematics teaching

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Authors: Teng Li, Kamran Mohseni

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This paper presents an inviscid regularization technique for the incompressible two-phase flow simulations. This technique is known as observable method due to the understanding of observability that any feature smaller than the actual resolution (physical or numerical), i.e., the size of wire in hotwire anemometry or the grid size in numerical simulations, is not able to be captured or observed. Differ from most regularization techniques that applies on the numerical discretization, the observable method is employed at PDE level during the derivation of equations. Difficulties in the simulation and analysis of realistic fluid flow often result from discontinuities (or near-discontinuities) in the calculated fluid properties or state. Accurately capturing these discontinuities is especially crucial when simulating flows involving shocks, turbulence or sharp interfaces. Over the past several years, the properties of this new regularization technique have been investigated that show the capability of simultaneously regularizing shocks and turbulence. The observable method has been performed on the direct numerical simulations of shocks and turbulence where the discontinuities are successfully regularized and flow features are well captured. In the current paper, the observable method will be extended to two-phase interfacial flows. Multiphase flows share the similar features with shocks and turbulence that is the nonlinear irregularity caused by the nonlinear terms in the governing equations, namely, Euler equations. In the direct numerical simulation of two-phase flows, the interfaces are usually treated as the smooth transition of the properties from one fluid phase to the other. However, in high Reynolds number or low viscosity flows, the nonlinear terms will generate smaller scales which will sharpen the interface, causing discontinuities. Many numerical methods for two-phase flows fail at high Reynolds number case while some others depend on the numerical diffusion from spatial discretization. The observable method regularizes this nonlinear mechanism by filtering the convective terms and this process is inviscid. The filtering effect is controlled by an observable scale which is usually about a grid length. Single rising bubble and Rayleigh-Taylor instability are studied, in particular, to examine the performance of the observable method. A pseudo-spectral method is used for spatial discretization which will not introduce numerical diffusion, and a Total Variation Diminishing (TVD) Runge Kutta method is applied for time integration. The observable incompressible Euler equations are solved for these two problems. In rising bubble problem, the terminal velocity and shape of the bubble are particularly examined and compared with experiments and other numerical results. In the Rayleigh-Taylor instability, the shape of the interface are studied for different observable scale and the spike and bubble velocities, as well as positions (under a proper observable scale), are compared with other simulation results. The results indicate that this regularization technique can potentially regularize the sharp interface in the two-phase flow simulations

Keywords: Euler equations, incompressible flow simulation, inviscid regularization technique, two-phase flow

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Authors: G. Judakova, M. Bause

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The ability to model and simulate numerically natural gas flow in pipelines has become of high importance for the design of pipeline systems. The understanding of the formation of hydrate particles and their dynamical behavior is of particular interest, since these processes govern the operation properties of the systems and are responsible for system failures by clogging of the pipelines under certain conditions. Mathematically, natural gas flow can be described by multiphase flow models. Using the two-fluid modeling approach, the gas phase is modeled by the compressible Euler equations and the particle phase is modeled by the pressureless Euler equations. The numerical simulation of compressible multiphase flows is an important research topic. It is well known that for nonlinear fluxes, even for smooth initial data, discontinuities in the solution are likely to occur in finite time. They are called shock waves or contact discontinuities. For hyperbolic and singularly perturbed parabolic equations the standard application of the Galerkin finite element method (FEM) leads to spurious oscillations (e.g. Gibb's phenomenon). In our approach, we use stabilized FEM, the streamline upwind Petrov-Galerkin (SUPG) method, where artificial diffusion acting only in the direction of the streamlines and using a special treatment of the boundary conditions in inviscid convective terms, is added. Numerical experiments show that the numerical solution obtained and stabilized by SUPG captures discontinuities or steep gradients of the exact solution in layers. However, within this layer the approximate solution may still exhibit overshoots or undershoots. To suitably reduce these artifacts we add a discontinuity capturing or shock capturing term. The performance properties of our numerical scheme are illustrated for two-phase flow problem.

Keywords: two-phase flow, gas-particle mixture, inviscid two-fluid model, euler equation, finite element method, streamline upwind petrov-galerkin, shock capturing

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Authors: Eugene Stepanov, Arkadi Ponossov

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Ordinary differential equations with switching nonlinearities constitute a very useful tool in many applications. The solutions of such equations can usually be calculated analytically if they cross the discontinuities transversally. Otherwise, one has trajectories that slides along the discontinuity, and the calculations become less straightforward in this case. For instance, one of the problems one faces is non-uniqueness of the sliding modes. In the presentation, it is proposed to apply the theory of hybrid dynamical systems to calculate the solutions that are ‘hidden’ in the discontinuities. Roughly, one equips the underlying switched system with an explicitly designed discrete dynamical system (‘automaton’), which governs the dynamics of the switched system. This construction ‘splits’ the dynamics, which, as it is shown in the presentation, gives uniqueness of the resulting hybrid trajectories and at the same time provides explicit formulae for them. Projecting the hybrid trajectories back onto the original continuous system explains non-uniqueness of its trajectories. The automaton is designed with the help of the attractors of the specially constructed adjoint dynamical system. Several examples are provided in the presentation, which supports the efficiency of the suggested scheme. The method can be of interest in control theory, gene regulatory networks, neural field models and other fields, where switched dynamics is a part of the analysis.

Keywords: hybrid dynamical systems, singular perturbation analysis, sliding modes, switched dynamics

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Authors: Eda Gök

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Peridynamics is a new modeling concept of non-local interactions for solid structures. The formulations of Peridynamic (PD) theory are based on integral equations rather than differential equations. Through, undefined equations of associated problems are avoided. PD theory might be defined as continuum version of molecular dynamics. The medium is usually modeled with mass particles bonded together. Particles interact with each other directly across finite distances through central forces named as bonds. The main assumption of this theory is that the body is composed of material points which interact with other material points within a finite distance. Although, PD theory developed for discontinuities, it gives good results for structures which have no discontinuities. In this paper, displacement control of the isotropic plate under the effect of tensile and bending loading has been investigated by means of PD theory. A MATLAB code is generated to create PD bonds and corresponding surface correction factors. Using generated MATLAB code the geometry of the specimen is generated, and the code is implemented in Finite Element Software. The results obtained from non-local continuum theory are compared with the Finite Element Analysis results and analytical solution. The results show good agreement.

Keywords: non-local continuum mechanics, peridynamic theory, solid structures, tensile loading, flexural loading

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Authors: Abbas Kamalibandpey, Alain Beland, Joseph Mukendi Kabuya

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Since a rock mass is a discontinuum medium, its behaviour is governed by discontinuities such as faults, joint sets, lithologic contact, and bedding planes. Thus, rock slope stability analysis in jointed rock masses is largely dependent upon discontinuities constitutive equations. This paper studies the difference between the Mohr-Coulomb (MC) and the Barton-Bandis (BB) joint constitutive numerical models for lithological contacts and joint sets. For the rock in these models, generalized Hoek-Brown criteria have been considered. The joint roughness coefficient (JRC) and the joint wall compressive strength (JCS) are vital parameters in the BB model. The numerical models are applied to the rock slope stability analysis in the Mont-Wright (MW) mine. The Mont-Wright mine is owned and operated by ArcelorMittal Mining Canada (AMMC), one of the largest iron-ore open pit operations in Canada. In this regard, one of the high walls of the mine has been selected to undergo slope stability analysis with RS2D software, finite element method. Three piezometers have been installed in this zone to record pore water pressure and it is monitored by radar. In this zone, the AMP-IF and QRMS-IF contacts and very persistent and altered joint sets in IF control the rock slope behaviour. The height of the slope is more than 250 m and consists of different lithologies such as AMP, IF, GN, QRMS, and QR. To apply the B-B model, the joint sets and geological contacts have been scanned by Maptek, and their JRC has been calculated by different methods. The numerical studies reveal that the JRC of geological contacts, AMP-IF and QRMS-IF, and joint sets in IF had a significant influence on the safety factor. After evaluating the results of rock slope stability analysis and the radar data, the B-B constitutive equation for discontinuities has shown acceptable results to the real condition in the mine. It should be noted that the difference in safety factors in MC and BB joint constitutive models in some cases is more than 30%.

Keywords: barton-Bandis criterion, Hoek-brown and Mohr-Coulomb criteria, open pit, slope stability

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Authors: Azariah Sosa, Carlos Renedo Sanchez

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The development of a new motorway north of Auckland (New Zealand) includes steep rock cuts, from 63 up to 85 degrees, in an interbedded sandstone and siltstone rock mass of the geological unit Waitemata Group (Pakiri Formation), which shows sub-horizontal bedding planes, various sub-vertical joint sets, and a diverse weathering profile. In this kind of rock mass -that can be classified as a weak rock- the definition of the stable maximum geometry is not only governed by discontinuities and defects evident in the rock but is important to also consider the global stability of the rock slope, including (in the analysis) the rock mass characterisation, influence of the groundwater, the geological evolution, and the weathering processes. Depending on the weakness of the rock and the processes suffered, the global stability could, in fact, be a more restricting element than the potential instability of individual blocks through discontinuities. This paper discusses those elements that govern the stability of the rock slopes constructed in a rock formation with favourable bedding and distribution of discontinuities (horizontal and vertical) but with a weak behaviour in terms of global rock mass characterisation. In this context, classifications as Q-Slope and slope stability assessment methodology (SSAM) have been demonstrated as important tools which complement the assessment of the global stability together with the analytical tools related to the wedge-type failures and limit equilibrium methods. The paper focuses on the applicability of these two new empirical classifications to evaluate the slope stability in 18 already excavated rock slopes in the Pakiri formation through comparison between the predicted and observed stability issues and by reviewing the outcome of analytical methods (Rocscience slope stability software suite) compared against the expected stability determined from these rock classifications. This exercise will help validate such findings and correlations arising from the two empirical methods in order to adjust the methods to the nature of this specific kind of rock mass and provide a better understanding of the long-term stability of the slopes studied.

Keywords: Pakiri formation, Q-slope, rock slope stability, SSAM, weak rock

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Authors: Hui Luo, Zhenhong Li, Zhen Dong

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The analysis of multi-temporal InSAR (MTInSAR) such as persistent scatterer (PS) and small baseline subset (SBAS) techniques usually relies on temporal/spatial phase unwrapping (PU). Unfortunately, it always fails to unwrap the phase for two reasons: 1) spatial phase jump between adjacent pixels larger than π, such as layover and high discontinuous terrain; 2) temporal phase discontinuities such as time varied atmospheric delay. To overcome these limitations, a least-square based PU method is introduced in this paper, which incorporates baseline-combination interferograms and adjacent phase gradient network. Firstly, permanent scatterers (PS) are selected for study. Starting with the linear baseline-combination method, we obtain equivalent 'small baseline inteferograms' to limit the spatial phase difference. Then, phase different has been conducted between connected PSs (connected by a specific networking rule) to suppress the spatial correlated phase errors such as atmospheric artifact. After that, interval phase difference along arcs can be computed by least square method and followed by an outlier detector to remove the arcs with phase ambiguities. Then, the unwrapped phase can be obtained by spatial integration. The proposed method is tested on real data of TerraSAR-X, and the results are also compared with the ones obtained by StaMPS(a software package with 3D PU capabilities). By comparison, it shows that the proposed method can successfully unwrap the interferograms in urban areas even when high discontinuities exist, while StaMPS fails. At last, precise DEM errors can be got according to the unwrapped interferograms.

Keywords: phase unwrapping, time series, InSAR, urban areas

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Authors: S. Mehrab Amiri, Nasser Talebbeydokhti

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Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme.  In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.

Keywords: artificial neural network, morphodynamic model, sediment continuity equation, shallow water equations

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Authors: Deane Roehl, Roberto Quevedo

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Gas migration from pressurized formations is a problem reported in the oil and gas industry. This means increased risks for drilling, production, well integrity, and hydrocarbon escape. Different processes can contribute to the development of pressurized formations, particularly in High-Pressure–High-Temperature (HPHT) gas fields. Over geological time-scales, the different formations of those fields have maintained and/or developed abnormal pressures owing to low permeability and the presence of an impermeable seal. However, if this seal is broken, large volumes of gas could migrate into other less pressurized formations. Three main mechanisms for gas migration have been identified in the literature –molecular diffusion, continuous-phase flow, and continuous-phase flow coupled with mechanical effects. In relation to the latter, gas migration can occur as a consequence of the mechanical effects triggered by reservoir depletion. The compaction of the reservoir can redistribute the in-situ stresses sufficiently to induce deformations that may increase the permeability of rocks and lead to fracture processes or reactivate nearby faults. The understanding of gas flow through discontinuities is still under development. However, some models based on porosity changes and fracture aperture have been developed in order to obtain enhanced permeabilities in numerical simulations. In this work, a simple relationship to integrate fluid flow through rock matrix and discontinuities has been implemented in a fully thermo-hydro-mechanical simulator developed in-house. Numerical simulations of hydrocarbon production in an HPHT field were carried out. Results suggest that rock permeability can be considerably affected by the deformation of the field, creating preferential flow paths for the transport of large volumes of gas.

Keywords: gas migration, pressurized formations, fractured rocks, numerical modeling

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Authors: Philippe Bich, Yu Lu

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We provide n-dimensional fixed-point theorems for possibly discontinuous functions which extend Brouwer’s fixed-point theorem and encompass interesting cases of Tarski’s fixed-point theorem. The main idea is to require that at any discontinuity point where the graph of the function “crosses the diagonal”, the function satisfies a specific assumption (similar to upward jumps). For this purpose, we classify some types of discontinuities, and use them to prove our new fixed-point theorems, with some applications in game theory.

Keywords: fixed-point, Brouwer's fixed-point theorem, Tarski's fixed-point theorem, discontinuity, Nash equilibrium, supermodular game

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Authors: Sunjay

Abstract:

Plate tectonics is of very great significance as it represents the spatial relationships of volcanic rock suites at plate margins, the distribution in space and time of the conditions of different metamorphic facies, the scheme of deformation in mountain belts, or orogens, and the association of different types of economic deposit. Orogenic belts are characterized by extensive thrust faulting, movements along large strike-slip fault zones, and extensional deformation that occur deep within continental interiors. Within oceanic areas there also are regions of crustal extension and accretion in the backarc basins that are located on the landward sides of many destructive plate margins.Collisional orogens develop where a continent or island arc collides with a continental margin as a result of subduction. collisional and noncollisional orogens can be explained by differences in the strength and rheology of the continental lithosphere and by processes that influence these properties during orogenesis.Seismic Imaging Difficulties-In triangle zones, several factors reduce the effectiveness of seismic methods. The topography in the central part of the triangle zone is usually rugged and is associated with near-surface velocity inversions which degrade the quality of the seismic image. These characteristics lead to low signal-to-noise ratio, inadequate penetration of energy through overburden, poor geophone coupling with the surface and wave scattering. Depth Seismic Imaging Techniques-Seismic processing relates to the process of altering the seismic data to suppress noise, enhancing the desired signal (higher signal-to-noise ratio) and migrating seismic events to their appropriate location in space and depth. Processing steps generally include analysis of velocities, static corrections, moveout corrections, stacking and migration. Exploration seismology Bow-tie effect -Shadow Zones-areas with no reflections (dead areas). These are called shadow zones and are common in the vicinity of faults and other discontinuous areas in the subsurface. Shadow zones result when energy from a reflector is focused on receivers that produce other traces. As a result, reflectors are not shown in their true positions. Subsurface Discontinuities-Diffractions occur at discontinuities in the subsurface such as faults and velocity discontinuities (as at “bright spot” terminations). Bow-tie effect caused by the two deep-seated synclines. Seismic imaging of thrust faults and structural damage-deepwater thrust belts, Imaging deformation in submarine thrust belts using seismic attributes,Imaging thrust and fault zones using 3D seismic image processing techniques, Balanced structural cross sections seismic interpretation pitfalls checking, The seismic pitfalls can originate due to any or all of the limitations of data acquisition, processing, interpretation of the subsurface geology,Pitfalls and limitations in seismic attribute interpretation of tectonic features, Seismic attributes are routinely used to accelerate and quantify the interpretation of tectonic features in 3D seismic data. Coherence (or variance) cubes delineate the edges of megablocks and faulted strata, curvature delineates folds and flexures, while spectral components delineate lateral changes in thickness and lithology. Carbon capture and geological storage leakage surveillance because fault behave as a seal or a conduit for hydrocarbon transportation to a trap,etc.

Keywords: tectonics, seismic imaging, fold and thrust belts, seismic interpretation

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Authors: Enqing Chen, Jianbo Wang

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It is well known that the wavelet transform provides a very effective framework for multiscale edges analysis. However, wavelets are not very effective in representing images containing distributed discontinuities such as edges. In this paper, we propose a novel multiscale edge detection method in nonsubsampled contourlet transform (NSCT) domain, which is based on the dominant multiscale, multidirection edge expression and outstanding edge location of NSCT. Through real images experiments, simulation results demonstrate that the proposed method is better than other edge detection methods based on Canny operator, wavelet and contourlet. Additionally, the proposed method also works well for noisy images.

Keywords: edge detection, NSCT, shift invariant, modulus maxima

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Authors: Frederic Henry-Couannier

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Dark Gravity is a natural extension of general relativity in presence of a flat non dynamical background. Matter and radiation fields from its dark sector, as soon as their gravity dominates over our side fields gravity, produce a constant acceleration law of the scale factor. After a brief reminder of the Dark Gravity theory foundations, the confrontation with the main cosmological probes is carried out. We show that, amazingly, the sudden transition between the usual matter dominated decelerated expansion law a(t) ∝ t²/³ and this accelerated expansion law a(t) ∝ t² predicted by the theory should be able to fit the main cosmological probes (SN, BAO, CMB and age of the oldest stars data) but also direct H₀ measurements with two free parameters only: H₀ and the transition redshift.

Keywords: anti-gravity, negative energies, time reversal, field discontinuities, dark energy theory

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Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna

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Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: Atefeh Saljooghi Khoshkar, Jafar Hassanpour

Abstract:

One of the main problems of the design stage relating to many tunneling projects is the lack of an appropriate standard for the provision of engineering geological data in a predefined format. In particular, this is more reflected in highway and railroad tunnel projects in which there is a number of tunnels and different professional teams involved. In this regard, comprehensive software needs to be designed using the accepted methods in order to help engineering geologists to prepare standard reports, which contain sufficient input data for the design stage. Regarding this necessity, applied software has been designed using macro capabilities and Visual Basic programming language (VBA) through Microsoft Excel. In this software, all of the engineering geological input data, which are required for designing different parts of tunnels, such as discontinuities properties, rock mass strength parameters, rock mass classification systems, boreability classification, the penetration rate, and so forth, can be calculated and reported in a standard format.

Keywords: engineering geology, rock mass classification, rock mechanic, tunnel

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Authors: Maria Konstadinou, Etienne Alderlieste, Anderson Peccin da Silva, Ben Arntz, Leonard van der Bijl, Wouter Verschueren

Abstract:

The shear strength and compression properties of stiff Boom clay from Belgium at the depth of about 30 m has been investigated by means of cone penetration and laboratory testing. The latter consisted of index classification, constant rate of strain, direct, simple shear, and unconfined compression tests. The Boom clay samples exhibited strong swelling tendencies. The suction pressure was measured via different procedures and has been compared to the expected in-situ stress. The undrained shear strength and OCR profile determined from CPTs is not compatible with the experimental measurements, which gave significantly lower values. The observed response can be attributed to the presence of pre-existing discontinuities, as shown in microscale CT scans of the samples. The results of this study demonstrate that the microstructure of the clay prior to testing has an impact on the mechanical behaviour and can cause inconsistencies in the comparison of the laboratory test results with in-situ data.

Keywords: boom clay, laboratory testing, overconsolidation ratio, stress-strain response, swelling, undrained shear strength

Procedia PDF Downloads 116

Authors: Ugo Galvanetto, Pirto G. Pavan, Mirco Zaccariotto

Abstract:

The discipline of Computer-integrated surgery (CIS) will provide equipment able to improve the efficiency of healthcare systems and, which is more important, clinical results. Surgeons and machines will cooperate in new ways that will extend surgeons’ ability to train, plan and carry out surgery. Patient specific CIS of the brain requires several steps: 1 - Fast generation of brain models. Based on image recognition of MR images and equipped with artificial intelligence, image recognition techniques should differentiate among all brain tissues and segment them. After that, automatic mesh generation should create the mathematical model of the brain in which the various tissues (white matter, grey matter, cerebrospinal fluid …) are clearly located in the correct positions. 2 – Reliable and fast simulation of the surgical process. Computational mechanics will be the crucial aspect of the entire procedure. New algorithms will be used to simulate the mechanical behaviour of cutting through cerebral tissues. 3 – Real time provision of visual and haptic feedback A sophisticated human-machine interface based on ergonomics and psychology will provide the feedback to the surgeon. The present work will address in particular point 2. Modelling the cutting of soft tissue in a structure as complex as the human brain is an extremely challenging problem in computational mechanics. The finite element method (FEM), that accurately represents complex geometries and accounts for material and geometrical nonlinearities, is the most used computational tool to simulate the mechanical response of soft tissues. However, the main drawback of FEM lies in the mechanics theory on which it is based, classical continuum Mechanics, which assumes matter is a continuum with no discontinuity. FEM must resort to complex tools such as pre-defined cohesive zones, external phase-field variables, and demanding remeshing techniques to include discontinuities. However, all approaches to equip FEM computational methods with the capability to describe material separation, such as interface elements with cohesive zone models, X-FEM, element erosion, phase-field, have some drawbacks that make them unsuitable for surgery simulation. Interface elements require a-priori knowledge of crack paths. The use of XFEM in 3D is cumbersome. Element erosion does not conserve mass. The Phase Field approach adopts a diffusive crack model instead of describing true tissue separation typical of surgical procedures. Modelling discontinuities, so difficult when using computational approaches based on classical continuum Mechanics, is instead easy for novel computational methods based on Peridynamics (PD). PD is a non-local theory of mechanics formulated with no use of spatial derivatives. Its governing equations are valid at points or surfaces of discontinuity, and it is, therefore especially suited to describe crack propagation and fragmentation problems. Moreover, PD does not require any criterium to decide the direction of crack propagation or the conditions for crack branching or coalescence; in the PD-based computational methods, cracks develop spontaneously in the way which is the most convenient from an energy point of view. Therefore, in PD computational methods, crack propagation in 3D is as easy as it is in 2D, with a remarkable advantage with respect to all other computational techniques.

Keywords: computational mechanics, peridynamics, finite element, biomechanics

Procedia PDF Downloads 50

Authors: M. Mazraehli, F. Mehrabani, S. Zare

Abstract:

In general, mechanical and hydraulic processes are not independent of each other in jointed rock masses. Therefore, the study on hydro-mechanical coupling of geomaterials should be a center of attention in rock mechanics. Rocks in their nature contain discontinuities whose presence extremely influences mechanical and hydraulic characteristics of the medium. Assuming this effect, experimental investigations on intact rock cannot help to identify jointed rock mass behavior. Hence, numerical methods are being used for this purpose. In this paper, water inflow into a tunnel under significant water table has been estimated using hydro-mechanical discrete element method (HM-DEM). Besides, effects of geomechanical and geometrical parameters including constitutive model, friction angle, joint spacing, dip of joint sets, and stress factor on the estimated inflow rate have been studied. Results demonstrate that inflow rates are not identical for different constitutive models. Also, inflow rate reduces with increased spacing and stress factor.

Keywords: distinct element method, fluid flow, hydro-mechanical coupling, jointed rock mass, underground excavations

Procedia PDF Downloads 140

Authors: Hesam Sedaghat Nejad, Navid Hosseini, Arash Nikvar Hassani

Abstract:

Determination of the optimum block size with high profitability is one of the significant parameters in designation of the building stone mines. The aim of this study was to determine the optimum dimensions of building stone blocks in Delichai travertine mine of Damavand in Tehran province through combining the effective parameters proven in determination of the optimum dimensions in building stones such as the spacing of joints and gaps, extraction tools constraints with the help of modeling by Gemcom software. To this end, following simulation of the topography of the mine, the block model was prepared and then in order to use spacing joints and discontinuities as a limiting factor, the existing joints set was added to the model. Since only one almost horizontal joint set with a slope of 5 degrees was available, this factor was effective only in determining the optimum height of the block, and thus to determine the longitudinal and transverse optimum dimensions of the extracted block, the power of available loader in the mine was considered as the secondary limiting factor. According to the aforementioned factors, the optimal block size in this mine was measured as 3.4×4×7 meter.

Keywords: building stone, optimum block size, Delichay travertine mine, loader power

Procedia PDF Downloads 331