Search results for: shallow water equations

Authors: Arcady Ponosov., Ramazan Kadiev

Abstract:

The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

Procedia PDF Downloads 184

Authors: Ahmad Fahim Nasiry, Shigeo Honma

Abstract:

We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: numerical simulation, immiscible, finite difference, IADI, IDE, waterflooding

Procedia PDF Downloads 295

Authors: Hossain Samani, Mohammad Ehteram

Abstract:

In this paper, we consider finite volume method (FVM) in water hammer. We will simulate these techniques on a looped network with complex boundary conditions. After comparing methods, we see the FVM method as the best method. We compare the results of FVM with experimental data. Finite volume using staggered grid is applied for solving water hammer equations.

Keywords: hydraulic transient, water hammer, interpolation, non-liner interpolation

Procedia PDF Downloads 317

Authors: Kamel Al-Khaled

Abstract:

Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

Procedia PDF Downloads 336

Authors: Qassun S. Mohammed Shafiqu, Murtadha A. Abdulrasool

Abstract:

The design of shallow foundations to withstand different dynamic loads has given considerable attention in recent years. Dynamic loads may be due to the earthquakes, pile driving, blasting, water waves, and machine vibrations. But, predicting the behavior of shallow foundations during earthquakes remains a difficult task for geotechnical engineers. A database for dynamic and static parameters for different soils in seismic active zones in Iraq is prepared which has been collected from geophysical and geotechnical investigation works. Then, analysis of a typical 3-D soil-raft foundation system under earthquake loading is carried out using the database. And a parametric study has been carried out taking into consideration the influence of some parameters on the dynamic behavior of the raft foundation, such as raft stiffness, damping ratio as well as the influence of the earthquake acceleration-time records. The results of the parametric study show that the settlement caused by the earthquake can be decreased by about 72% with increasing the thickness from 0.5 m to 1.5 m. But, it has been noticed that reduction in the maximum bending moment by about 82% was predicted by decreasing the raft thickness from 1.5 m to 0.5 m in all sites model. Also, it has been observed that the maximum lateral displacement, the maximum vertical settlement and the maximum bending moment for damping ratio 0% is about 14%, 20%, and 18% higher than that for damping ratio 7.5%, respectively for all sites model.

Keywords: shallow foundation, seismic behavior, raft thickness, damping ratio

Procedia PDF Downloads 118

Authors: Zaheer Ahmed Almani, Agha Faisal Habib Pathan, Aneel Kumar Hindu

Abstract:

In this study, the effects of ground reinforcement with stiff soil-cement columns on liquefiable ground and on the shallow foundation of structure were investigated. The modelling and analysis of shallow foundation of the structure founded on the composite reinforced ground were carried out with finite difference FLAC commercial software. The results showed that stiff columns were not effective to the redistribute the shear stresses in the composite ground, thus, were not effective to reduce shear stress and shear strain on the soil between the columns. The excessive pore pressure increase which is dependent on volumetric strain (contractive) tendency of loose sand upon shearing, was not reduced to a significant level that liquefaction potential could be remediated. Thus, mechanism of performance with reduction of pore pressure and consequent liquefaction was not predicted in numerical analysis. Nonetheless, the columns were effective to resist the load of structure in compression and reduced the liquefaction-induced large settlements of structure to tolerable limits when provided adjacent and beneath the pad of shallow foundation.

Keywords: earthquake, liquefaction, mechanism, soil-cement columns

Procedia PDF Downloads 125

Authors: Chih-Hua Wu, Bang-Fuh Chen, Keryea Soong

Abstract:

Midges can move on the surface of the water at speeds of approximately 340 body-lengths/s and can move continuously for >90 min. Their wings periodically scull the sea surface to push water backward and thus generate thrust; their other body parts, including their three pairs of legs, touch the water only occasionally. The aim of this study was to investigate the locomotion mechanism of marine midges with a size of 2 mm and living in shallow reefs in Wanliton, southern Taiwan. We assumed that midges generate lift through two mechanisms: by sculling the surface of seawater to leverage the generated tension for thrust and by retracting their wings to generate aerodynamic lift at a suitable angle of attack. We performed computational fluid dynamic simulations to determine the mechanism of midge locomotion above the surface of the water. The simulations indicated that ground effects are essential and that both the midge trunk and wing tips must be very close to the water surface to produce sufficient lift to keep the midge airborne. Furthermore, a high wing-beat frequency is crucial for the midge to produce sufficient lift during wing retraction. Accordingly, ground effects, forward speed, and high wing-beat frequency are major factors influencing the ability of midges to generate sufficient lift and remain airborne above the water surface.

Keywords: ground effect, water locomotion, CFD, aerodynamic lift

Procedia PDF Downloads 41

Authors: Tugbanur Ozen Balaban, Gultekin Tarcan, Unsal Gemici, Mumtaz Colak, I. Hakki Karamanderesi

Abstract:

Buyuk Menderes Graben is located in the Western Anatolia (Turkey). The graben has become the largest industrial and agricultural area with a total population exceeding 3.000.000. There are two big cities within the study areas from west to east as Aydın and Denizli. The study area is very rich with regard to cold ground waters and thermal waters. Electrical production using geothermal potential has become very popular in the last decades in this area. Buyuk Menderes Graben is a tectonically active extensional region and is undergoing a north–south extensional tectonic regime which commenced at the latest during Early Middle Miocene period. The basement of the study area consists of Menderes massif rocks that are made up of high-to low-grade metamorphics and they are aquifer for both cold ground waters and thermal waters depending on the location. Neogene terrestrial sediments, which are mainly composed by alluvium fan deposits unconformably cover the basement rocks in different facies have very low permeability and locally may act as cap rocks for the geothermal systems. The youngest unit is Quaternary alluvium which is the shallow regional aquifer consists of Holocene alluvial deposits in the study area. All the waters are of meteoric origin and reflect shallow or deep circulation according to the 8O, 2H and 3H contents. Meteoric waters move to deep zones by fractured system and rise to the surface along the faults. Water samples (drilling well, spring and surface waters) and local seawater were collected between 2010 and 2012 years. Geochemical modeling was calculated distribution of the aqueous species and exchange processes by using PHREEQCi speciation code. Geochemical analyses show that cold ground water types are evolving from Ca–Mg–HCO3 to Na–Cl–SO4 and geothermal aquifer waters reflect the water types of Na-Cl-HCO3 in Aydın. Water types of Denizli are Ca-Mg-HCO3 and Ca-Mg-HCO3-SO4. Thermal water types reflect generally Na-HCO3-SO4. The B versus Cl rates increase from east to west with the proportion of seawater introduced into the fresh water aquifers and geothermal reservoirs. Concentrations of some elements (As, B, Fe and Ni) are higher than the tolerance limit of the drinking water standard of Turkey (TS 266) and international drinking water standards (WHO, FAO etc).

Keywords: Buyuk Menderes, isotope chemistry, geochemical modelling, water quality

Procedia PDF Downloads 504

Authors: Ahmed Alghurabi, Mysara Mohyaldinn, Shiferaw Jufar, Obai Younis, Abdullah Abduljabbar

Abstract:

Erosion modeling equations were typically acquired from regulated experimental trials for solid particles entrained in single-phase or multi-phase flows. Evidently, those equations were later employed to predict the erosion damage caused by the continuous impacts of solid particles entrained in streamflow. It is also well-known that the particle impact angle and velocity do not change drastically in gas-sand flow erosion prediction; hence an accurate prediction of erosion can be projected. On the contrary, high-density fluid flows, such as water flow, through complex geometries, such as sand screens, greatly affect the sand particles’ trajectories/tracks and consequently impact the erosion rate predictions. Particle tracking models and erosion equations are frequently applied simultaneously as a method to improve erosion visualization and estimation. In the present work, computational fluid dynamic (CFD)-based erosion modeling was performed using a commercially available software; ANSYS Fluent. The continuous phase (water flow) behavior was simulated using the realizable K-epsilon model, and the secondary phase (solid particles), having a 5% flow concentration, was tracked with the help of the discrete phase model (DPM). To accomplish a successful erosion modeling, three erosion equations from the literature were utilized and introduced to the ANSYS Fluent software to predict the screen wire-slot velocity surge and estimate the maximum erosion rates on the screen surface. Results of turbulent kinetic energy, turbulence intensity, dissipation rate, the total pressure on the screen, screen wall shear stress, and flow velocity vectors were presented and discussed. Moreover, the particle tracks and path-lines were also demonstrated based on their residence time, velocity magnitude, and flow turbulence. On one hand, results from the utilized erosion equations have shown similarities in screen erosion patterns, locations, and DPM concentrations. On the other hand, the model equations estimated slightly different values of maximum erosion rates of the wire-wrapped screen. This is solely based on the fact that the utilized erosion equations were developed with some assumptions that are controlled by the experimental lab conditions.

Keywords: CFD simulation, erosion rate prediction, material loss due to erosion, water-sand flow

Procedia PDF Downloads 127

Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop

Abstract:

In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: heat transfer, nanofluid, shrinking surface, stability analysis, three-dimensional flow

Procedia PDF Downloads 251

Authors: Christian H. Girsang, M. Razi B. Mansoor, Noorizal N. Huang

Abstract:

An offshore platform was installed in 1977 at about 260km offshore West Malaysia at the water depth of 73.6m. Twelve (12) piles were installed with four (4) are skirt piles. The piles have 1.219m outside diameter and wall thickness of 31mm and were driven to 109m below seabed. Deterministic analyses of the pile capacity under axial loading were conducted using the current API (American Petroleum Institute) method and the four (4) CPT-based methods: the ICP (Imperial College Pile)-method, the NGI (Norwegian Geotechnical Institute)-Method, the UWA (University of Western Australia)-method and the Fugro-method. A statistical analysis of the model uncertainty associated with each pile capacity method was performed. There were two (2) piles analysed: Pile 1 and piles other than Pile 1, where Pile 1 is the pile that was most affected by shallow gas problems. Using the mean estimate of soil properties, the five (5) methods used for deterministic estimation of axial pile capacity in compression predict an axial capacity from 28 to 42MN for Pile 1 and 32 to 49MN for piles other than Pile 1. These values refer to the static capacity shortly after pile installation. They do not include the effects of cyclic loading during the design storm or time after installation on the axial pile capacity. On average, the axial pile capacity is expected to have increased by about 40% because of ageing since the installation of the platform in 1977. On the other hand, the cyclic loading effects during the design storm may reduce the axial capacity of the piles by around 25%. The study concluded that all piles have sufficient safety factor when the pile aging and cyclic loading effect are considered, as all safety factors are above 2.0 for maximum operating and storm loads.

Keywords: axial capacity, cyclic loading, pile ageing, shallow gas

Procedia PDF Downloads 301

Authors: Khosrow Maleknejad, Yaser Rostami

Abstract:

In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

Procedia PDF Downloads 422

Authors: P. G. Siddheshwar, B. N. Veena

Abstract:

Rayleigh-B´enard convection of a nanoliquid in shallow, square and tall enclosures is studied using the Khanafer-Vafai-Lightstone single-phase model. The thermophysical properties of water, copper, copper-oxide, alumina, silver and titania at 3000 K under stagnant conditions that are collected from literature are used in calculating thermophysical properties of water-based nanoliquids. Phenomenological laws and mixture theory are used for calculating thermophysical properties. Free-free, rigid-rigid and rigid-free boundary conditions are considered in the study. Intractable Lorenz model for each boundary combination is derived and then reduced to the tractable Ginzburg-Landau model. The amplitude thus obtained is used to quantify the heat transport in terms of Nusselt number. Addition of nanoparticles is shown not to alter the influence of the nature of boundaries on the onset of convection as well as on heat transport. Amongst the three enclosures considered, it is found that tall and shallow enclosures transport maximum and minimum energy respectively. Enhancement of heat transport due to nanoparticles in the three enclosures is found to be in the range 3% - 11%. Comparison of results in the case of rigid-rigid boundaries is made with those of an earlier work and good agreement is found. The study has limitations in the sense that thermophysical properties are calculated by using various quantities modelled for static condition.

Keywords: enclosures, free-free, rigid-rigid, rigid-free boundaries, Ginzburg-Landau model, Lorenz model

Procedia PDF Downloads 210

Authors: Naila Nasreen, Dianchen Lu

Abstract:

This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

Procedia PDF Downloads 46

Authors: Ghazal Horiat, Alireza Hajiani Bushehrian

Abstract:

leakage of contamination from fuel or oil reservoirs can alter the geotechnical properties of the soil under their foundation and finally affect their performance in their service life. This article investigates the behavior of shallow foundations on the soil contaminated with diesel and kerosene using the Plaxis Tunnel3D V1.2 software. The information required for the numerical modeling in the paper was obtained from a similar experimental study. The present study seeks to compare the behavior of square foundations on sandy soil without contamination and the soil contaminated with different percentages of diesel and crude oil. The study was conducted on a small square foundation. The depth of the contamination was assumed constant, and the soil was evaluated with four different percentages of both contaminants. The results of analyses were plotted and assessed in the form of load-displacement curves for the foundation. The results indicate reduced bearing capacity of the foundation with the rise in the contamination percentage.

Keywords: bearing capacity, contaminated soils, shallow foundations, 3D numerical analysis

Procedia PDF Downloads 105

Authors: Kamel Al-Khaled

Abstract:

In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

Procedia PDF Downloads 490

Authors: Mauricio Terceros, Jann-Eike Saathoff, Martin Achmus

Abstract:

In non-cohesive soil, onshore wind turbines are often found on shallow foundations with a circular or octagonal shape. For the current generation of wind turbines, shallow foundations with very large breadths are required. The foundation support costs thus represent a considerable portion of the total construction costs. Therefore, an economic optimization of the type of foundation is highly desirable. A conceivable alternative foundation type would be a pier foundation, which combines the load transfer over the foundation area at the pier base with the transfer of horizontal loads over the shaft surface of the pier. The present study aims to evaluate the load-bearing behavior of a pier foundation based on comprehensive parametric studies. Thereby, three-dimensional numerical simulations of both pier and shallow foundations are developed. The evaluation of the results focuses on the rotational stiffnesses of the proposed soil-foundation systems. In the design, the initial rotational stiffness is decisive for consideration of natural frequencies, whereas the rotational secant stiffness for a maximum load is decisive for serviceability considerations. A systematic analysis of the results at different load levels shows that the application of the typical pier foundation is presumably limited to relatively small onshore wind turbines.

Keywords: onshore wind foundation, pier foundation, rotational stiffness of soil-foundation system, shallow foundation

Procedia PDF Downloads 119

Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

Abstract:

An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

Procedia PDF Downloads 571

Authors: Divij Gupta

Abstract:

Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

Procedia PDF Downloads 170

Authors: Jae-Yeong Choi, Gyu-Mok Jeon, Jong-Chun Park, Yong-Jin Cho, Seok-Tae Yoon

Abstract:

When air flow is injected into water, bubbles are formed in various types inside the water pool along with the air flow rate. The bubbles are floated in equilibrium with forces such as buoyancy, surface tension and shear force. Single bubble generated at low flow rate maintains shape, but bubbles with high flow rate break up to make mixing and turbulence. In addition to this phenomenon, as the hot air bubbles are injected into the water, heat affects the interface of phases. Therefore, the main scope of the present work reveals how to proceed heat transfer between water and hot air bubbles injected into water. In the present study, a series of CFD simulation for the heat transfer of hot bubbles injected through a nozzle near the bottom in a cylindrical water column are performed using a commercial CFD software, STAR-CCM+. The governing equations for incompressible and viscous flow are the continuous and the RaNS (Reynolds- averaged Navier-Stokes) equations and discretized by the FVM (Finite Volume Method) manner. For solving multi-phase flow, the Eulerian multiphase model is employed and the interface is defined by VOF (Volume-of-Fluid) technique. As a turbulence model, the SST k-w model considering the buoyancy effects is introduced. For spatial differencing the 3th-order MUSCL scheme is adopted and the 2nd-order implicit scheme for time integration. As the results, the dynamic behavior of the rising hot bubbles with the flow rate injected and regarding heat transfer mechanism are discussed based on the simulation results.

Keywords: heat transfer, hot bubble injection, eulerian multiphase model, flow rate, CFD (Computational Fluid Dynamics)

Procedia PDF Downloads 125

Authors: H. Aissa, L. Mouzai, M. Bouhadef

Abstract:

The effects of down slope steepness on soil splash distribution under a water drop impact have been investigated in this study. The equipment used are the burette to simulate a water drop, a splash cup filled with sandy soil which forms the source area and a splash board to collect the ejected particles. The results found in this study have shown that the apparent mass increased with increasing downslope angle following a linear regression equation with high coefficient of determination. In the same way, the radial soil splash distribution over the distance has been analyzed statistically, and an exponential function was the best fit of the relationship for the different slope angles. The curves and the regressions equations validate the well known FSDF and extend the theory of Van Dijk.

Keywords: splash distribution, water drop, slope steepness, soil detachment

Procedia PDF Downloads 301

Authors: Kausar Alam, Mohammad Yazdi, Peiman Zogh, Ramin Motamed

Abstract:

An earthquake is an unpredictable natural disaster. It induces liquefaction, which causes considerable damage to the structure, life support, and piping systems because of ground settlement. As a result, people are incredibly concerned about how to resolve the situation. Previous researchers adopted different ground improvement techniques to reduce the settlement of the structure during earthquakes. This study evaluates the effectiveness of lowering the water table as a technique to mitigate foundation settlement in liquefiable soil. The performance will be evaluated based on foundation settlement and the reduction of excessive pore water pressure. In this study, a scaled model was prepared based on a full-scale shale table experiment conducted at the University of California, San Diego (UCSD). The model ground consists of three soil layers having a relative density of 55%, 45%, and 90%, respectively. A shallow foundation is seated over an unsaturated crust layer. After preparation of the model ground, the water table was measured to be at 45, 40, and 35 cm (from the bottom). Then, the input motions were applied for 10 seconds, with a peak acceleration of 0.25g and a constant frequency of 2.73 Hz. Based on the experimental results, the effectiveness of the lowering water table in reducing the foundation settlement and excess pore water pressure was evident. The foundation settlement was reduced from 50 mm to 5 mm. In addition, lowering the water table as a mitigation measure is a cost-effective way to decrease liquefaction-induced building settlement.

Keywords: foundation settlement, ground water table, liquefaction, hake table test

Procedia PDF Downloads 76

Authors: I. Kruashvili, I. Inashvili, K. Bziava, M. Lomishvili

Abstract:

Seepage capillary anomalies in the active layer of soil, related to the soil water movement, often cause variation of soil hydrophysical properties and become one of the main objectives of the hydroecology. It is necessary to mention that all existing equations for computing the seepage flow particularly from soil channels, through dams, bulkheads, and foundations of hydraulic engineering structures are preferable based on the linear seepage law. Regarding the existing beliefs, anomalous seepage is based on postulates according to which the fluid in free volume is characterized by resistance against shear deformation and is presented in the form of initial gradient. According to the above-mentioned information, we have determined: Equation to calculate seepage coefficient when the velocity of transition flow is equal to seepage flow velocity; by means of power function, equations for the calculation of average and maximum velocities of seepage flow have been derived; taking into consideration the fluid continuity condition, average velocity for calculation of average velocity in capillary tube has been received.

Keywords: seepage, soil, velocity, water

Procedia PDF Downloads 429

Authors: Ahmed I. Raheem

Abstract:

In this thesis, stratified and stratified wavy flow regimes have been investigated numerically for the oil (1.57 mPa s viscosity and 780 kg/m3 density) and water twophase flow in small and large horizontal steel pipes with a diameter between 0.0254 to 0.508 m by ANSYS Fluent software. Volume of fluid (VOF) with two phases flows using two equations family models (Realizable k-

Keywords: CFD, two-phase flow, pressure gradient, volume of fluid, large diameter, horizontal pipe, oil-water stratified and stratified wavy flow

Procedia PDF Downloads 401

Authors: A. M. Sagir

Abstract:

Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

Procedia PDF Downloads 452

Authors: Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

Procedia PDF Downloads 452

Authors: Siti Khadijah Che Osmi, Syed Mohd Ahmad

Abstract:

This paper presents a methodology to develop fragility curves for shallow tunnels so as to describe a relationship between seismic hazard and tunnel vulnerability. Emphasis is given to the influence of surrounding soil material properties because the dynamic behaviour of the tunnel mostly depends on it. Four ground properties of soils ranging from stiff to soft soils are selected. A 3D nonlinear time history analysis is used to evaluate the seismic response of the tunnel when subjected to five real earthquake ground intensities. The derived curves show the future probabilistic performance of the tunnels based on the predicted level of damage states corresponding to the peak ground acceleration. A comparison of the obtained results with the previous literature is provided to validate the reliability of the proposed fragility curves. Results show the significant role of soil properties and input motions in evaluating the seismic performance and response of shallow tunnels.

Keywords: fragility analysis, seismic performance, tunnel lining, vulnerability

Procedia PDF Downloads 280

Authors: F. Maass, P. Martin, J. Olivares

Abstract:

The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

Procedia PDF Downloads 212

Authors: E. Arcos, E. Bautista, F. Méndez

Abstract:

In this work, a scaling analysis of the liquefaction phenomena is presented. The characteristic scales are obtained by balancing term by term of the well-known partial dynamics governing equations, (U − P). From the above, the order of magnitude of the horizontal displacement is very smaller compared with the vertical displacement and therefore the governing equation is only a function of the dependent vertical variables. The U − P approximation is reduced and presented in its dimensionless version. This scaling analysis can be used to obtain analytical solutions of the liquefaction phenomena under the action of the water waves.

Keywords: approximation U-P, porous seabed, scaling analysis, water waves

Procedia PDF Downloads 318

Authors: Zhiqiang Yan, Chen Fan, Beicheng Xia

Abstract:

Urban lakes play an invaluable role in urban water systems such as flood control, landscape, entertainment, and energy utilization, and have suffered from severe eutrophication over the past few years. To investigate the ecological response of main aquatic species and system stability to chlorine interference in shallow urban lakes, a mini system dynamic model, based on the competition and predation of main aquatic species and TP circulation, was developed. The main species of submerged macrophyte, phytoplankton, zooplankton, benthos and TP in water and sediment were simulated as variables in the model with the interference of chlorine which effect function was attenuation equation. The model was validated by the data which was investigated in the Lotus Lake in Guangzhou from October 1, 2015 to January 31, 2016. Furthermore, the eco-exergy was used to analyze the change in complexity of the shallow urban lake. The results showed the correlation coefficient between observed and simulated values of all components presented significant. Chlorine showed a significant inhibitory effect on Microcystis aeruginosa，Rachionus plicatilis, Diaphanosoma brachyurum Liévin and Mesocyclops leuckarti (Claus).The outbreak of Spiroggra spp. inhibited the growth of Vallisneria natans (Lour.) Hara, caused a gradual decrease of eco-exergy, reflecting the breakdown of ecosystem internal equilibria. It was concluded that the study gives important insight into using chlorine to achieve eutrophication control and understand mechanism process.

Keywords: system dynamic model, urban lake, chlorine, eco-exergy

Procedia PDF Downloads 177